%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM268_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:58:15 AM UTC 2026
% Result : Theorem 185.82s 94.35s
% Output : Refutation 177.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 456
% Syntax : Number of formulae : 1780 ( 963 unt; 0 typ; 207 def)
% Number of atoms : 5774 (3659 equ; 0 cnn)
% Maximal formula atoms : 431 ( 3 avg)
% Number of connectives : 22086 (2364 ~;2133 |;1343 &;16017 @)
% ( 0 <=>; 229 =>; 0 <=; 0 <~>)
% Maximal formula depth : 75 ( 6 avg)
% Number of types : 27 ( 26 usr)
% Number of type conns : 214 ( 214 >; 0 *; 0 +; 0 <<)
% Number of symbols : 323 ( 320 usr; 26 con; 0-4 aty)
% Number of variables : 5891 ( 276 ^;4308 !;1100 ?;5891 :)
% ( 0 !>; 0 ?*; 0 @-; 207 @+)
% Comments :
%------------------------------------------------------------------------------
thf(vEntry_type,type,
vEntry: $tType ).
thf(vYN_type,type,
vYN: $tType ).
thf(vMapConf_type,type,
vMapConf: $tType ).
thf(vOptAType_type,type,
vOptAType: $tType ).
thf(vATMap_type,type,
vATMap: $tType ).
thf(vQuestionnaire_type,type,
vQuestionnaire: $tType ).
thf(vOptMapConf_type,type,
vOptMapConf: $tType ).
thf(vQConf_type,type,
vQConf: $tType ).
thf(vstring_type,type,
vstring: $tType ).
thf(vchar_type,type,
vchar: $tType ).
thf(vAval_type,type,
vAval: $tType ).
thf(vOptQConf_type,type,
vOptQConf: $tType ).
thf(vOptQuestion_type,type,
vOptQuestion: $tType ).
thf(vAnsMap_type,type,
vAnsMap: $tType ).
thf(vExp_type,type,
vExp: $tType ).
thf(vQMap_type,type,
vQMap: $tType ).
thf(vQID_type,type,
vQID: $tType ).
thf(vLabel_type,type,
vLabel: $tType ).
thf(vOptAval_type,type,
vOptAval: $tType ).
thf(vnat_type,type,
vnat: $tType ).
thf(vOptExp_type,type,
vOptExp: $tType ).
thf(vGID_type,type,
vGID: $tType ).
thf(vATList_type,type,
vATList: $tType ).
thf(vBinOpT_type,type,
vBinOpT: $tType ).
thf(vUnOpT_type,type,
vUnOpT: $tType ).
thf(vAType_type,type,
vAType: $tType ).
thf(vconstant_decl,type,
vconstant: vAval > vExp ).
thf(vqmempty_decl,type,
vqmempty: vQMap ).
thf(vquestion_decl,type,
vquestion: vQID > vLabel > vAType > vEntry ).
thf(vsomeExp_decl,type,
vsomeExp: vExp > vOptExp ).
thf(vqcond_decl,type,
vqcond: vExp > vQuestionnaire > vQuestionnaire > vQuestionnaire ).
thf(vandop_decl,type,
vandop: vBinOpT ).
thf(vnotop_decl,type,
vnotop: vUnOpT ).
thf(vNum_decl,type,
vNum: vnat > vAval ).
thf(vnoAType_decl,type,
vnoAType: vOptAType ).
thf(vyes_decl,type,
vyes: vYN ).
thf(vT_decl,type,
vT: vstring > vAval ).
thf(vNumber_decl,type,
vNumber: vAType ).
thf(vabind_decl,type,
vabind: vQID > vAval > vAnsMap > vAnsMap ).
thf(vYesNo_decl,type,
vYesNo: vAType ).
thf(vdefquestion_decl,type,
vdefquestion: vQID > vLabel > vAType > vEntry ).
thf(vunop_decl,type,
vunop: vUnOpT > vExp > vExp ).
thf(vaempty_decl,type,
vaempty: vAnsMap ).
thf(vqseq_decl,type,
vqseq: vQuestionnaire > vQuestionnaire > vQuestionnaire ).
thf(vqempty_decl,type,
vqempty: vQuestionnaire ).
thf(vsomeQConf_decl,type,
vsomeQConf: vQConf > vOptQConf ).
thf(vnoQConf_decl,type,
vnoQConf: vOptQConf ).
thf(vnoExp_decl,type,
vnoExp: vOptExp ).
thf(vbinop_decl,type,
vbinop: vExp > vBinOpT > vExp > vExp ).
thf(vB_decl,type,
vB: vYN > vAval ).
thf(vQC_decl,type,
vQC: vAnsMap > vQMap > vQuestionnaire > vQConf ).
thf(vorop_decl,type,
vorop: vBinOpT ).
thf(veqop_decl,type,
veqop: vBinOpT ).
thf(vText_decl,type,
vText: vAType ).
thf(vqsingle_decl,type,
vqsingle: vEntry > vQuestionnaire ).
thf(vMC_decl,type,
vMC: vATMap > vATMap > vMapConf ).
thf(vsomeQuestion_decl,type,
vsomeQuestion: vQID > vLabel > vAType > vOptQuestion ).
thf(vqvar_decl,type,
vqvar: vQID > vExp ).
thf(vatmbind_decl,type,
vatmbind: vQID > vAType > vATMap > vATMap ).
thf(vqmbind_decl,type,
vqmbind: vQID > vLabel > vAType > vQMap > vQMap ).
thf(vask_decl,type,
vask: vQID > vEntry ).
thf(vsomeAType_decl,type,
vsomeAType: vAType > vOptAType ).
thf(vnoQuestion_decl,type,
vnoQuestion: vOptQuestion ).
thf(vqgroup_decl,type,
vqgroup: vGID > vQuestionnaire > vQuestionnaire ).
thf(vatmempty_decl,type,
vatmempty: vATMap ).
thf(vno_decl,type,
vno: vYN ).
thf(vvalue_decl,type,
vvalue: vQID > vAType > vExp > vEntry ).
thf(vgetAnswer_decl,type,
vgetAnswer: vLabel > vAType > vAval ).
thf(vecheck_decl,type,
vecheck: vATMap > vExp > vOptAType ).
thf(vgetAM_decl,type,
vgetAM: vQConf > vAnsMap ).
thf(vaskText_decl,type,
vaskText: vLabel > vstring ).
thf(vtypeOf_decl,type,
vtypeOf: vAval > vAType ).
thf(vevalBinOp_decl,type,
vevalBinOp: vBinOpT > vAval > vAval > vOptExp ).
thf(vgetQM_decl,type,
vgetQM: vQConf > vQMap ).
thf(vexpIsValue_decl,type,
vexpIsValue: vExp > $o ).
thf(vaskYesNo_decl,type,
vaskYesNo: vLabel > vYN ).
thf(visValue_decl,type,
visValue: vQuestionnaire > $o ).
thf(vtypeAM_decl,type,
vtypeAM: vAnsMap > vATMap ).
thf(vlookupQMap_decl,type,
vlookupQMap: vQID > vQMap > vOptQuestion ).
thf(vaskNumber_decl,type,
vaskNumber: vLabel > vnat ).
thf(vappendATMap_decl,type,
vappendATMap: vATMap > vATMap > vATMap ).
thf(vor_decl,type,
vor: vYN > vYN > vYN ).
thf(visSomeAType_decl,type,
visSomeAType: vOptAType > $o ).
thf(vlookupATMap_decl,type,
vlookupATMap: vQID > vATMap > vOptAType ).
thf(vqcappend_decl,type,
vqcappend: vQConf > vQuestionnaire > vQConf ).
thf(visSomeQC_decl,type,
visSomeQC: vOptQConf > $o ).
thf(visSomeAval_decl,type,
visSomeAval: vOptAval > $o ).
thf(vgetQuest_decl,type,
vgetQuest: vQConf > vQuestionnaire ).
thf(vevalUnOp_decl,type,
vevalUnOp: vUnOpT > vAval > vOptExp ).
thf(vcheckBinOp_decl,type,
vcheckBinOp: vBinOpT > vAType > vAType > vOptAType ).
thf(vnot_decl,type,
vnot: vYN > vYN ).
thf(vreduce_decl,type,
vreduce: vQuestionnaire > vAnsMap > vQMap > vOptQConf ).
thf(vappendAnsMap_decl,type,
vappendAnsMap: vAnsMap > vAnsMap > vAnsMap ).
thf(vcheckUnOp_decl,type,
vcheckUnOp: vUnOpT > vAType > vOptAType ).
thf(vtypeQM_decl,type,
vtypeQM: vQMap > vATMap ).
thf(visSomeExp_decl,type,
visSomeExp: vOptExp > $o ).
thf(vintersectATM_decl,type,
vintersectATM: vATMap > vATMap > vATMap ).
thf(vlookupAnsMap_decl,type,
vlookupAnsMap: vQID > vAnsMap > vOptAval ).
thf(vreduceExp_decl,type,
vreduceExp: vExp > vAnsMap > vOptExp ).
thf(vand_decl,type,
vand: vYN > vYN > vYN ).
thf(visSomeQuestion_decl,type,
visSomeQuestion: vOptQuestion > $o ).
thf(vptcheck_decl,type,
vptcheck: vMapConf > vQuestionnaire > vMapConf > $o ).
thf(vgetQuestionLabel_decl,type,
vgetQuestionLabel: vOptQuestion > vLabel ).
thf(vgetAType_decl,type,
vgetAType: vOptAType > vAType ).
thf(vgetQuestionAType_decl,type,
vgetQuestionAType: vOptQuestion > vAType ).
thf(vgetQC_decl,type,
vgetQC: vOptQConf > vQConf ).
thf(vgetExpValue_decl,type,
vgetExpValue: vExp > vAval ).
thf(vgetAval_decl,type,
vgetAval: vOptAval > vAval ).
thf(vgetExp_decl,type,
vgetExp: vOptExp > vExp ).
thf(sk1_decl,type,
sk1: vQMap ).
thf(sk2_decl,type,
sk2: vAType ).
thf(sk3_decl,type,
sk3: vATMap ).
thf(sk4_decl,type,
sk4: vATMap ).
thf(sk5_decl,type,
sk5: vAnsMap ).
thf(sk6_decl,type,
sk6: vQID ).
thf(sk7_decl,type,
sk7: vExp ).
thf(sk8_decl,type,
sk8: vOptAType > vAType ).
thf(sk9_decl,type,
sk9: vOptExp > vExp ).
thf(sk10_decl,type,
sk10: vAval > vnat ).
thf(sk11_decl,type,
sk11: vOptQuestion > vQID ).
thf(sk12_decl,type,
sk12: vOptQuestion > vLabel ).
thf(sk13_decl,type,
sk13: vOptQuestion > vAType ).
thf(sk14_decl,type,
sk14: vAval > $o ).
thf(sk15_decl,type,
sk15: vAval > vYN ).
thf(sk16_decl,type,
sk16: vAval > vnat ).
thf(sk17_decl,type,
sk17: vAval > vstring ).
thf(sk18_decl,type,
sk18: vExp > vAval ).
thf(sk19_decl,type,
sk19: vExp > vQID ).
thf(sk20_decl,type,
sk20: vExp > vExp ).
thf(sk21_decl,type,
sk21: vExp > vBinOpT ).
thf(sk22_decl,type,
sk22: vExp > vExp ).
thf(sk23_decl,type,
sk23: vExp > vUnOpT ).
thf(sk24_decl,type,
sk24: vExp > vExp ).
thf(sk25_decl,type,
sk25: vAval > vUnOpT > vYN ).
thf(sk26_decl,type,
sk26: vOptExp > vExp ).
thf(sk27_decl,type,
sk27: vOptExp > vExp ).
thf(sk28_decl,type,
sk28: vAval > vYN ).
thf(sk29_decl,type,
sk29: vAval > vnat ).
thf(sk30_decl,type,
sk30: vAval > vstring ).
thf(sk31_decl,type,
sk31: vUnOpT > vAval > $o ).
thf(sk32_decl,type,
sk32: vAval > vUnOpT > vYN ).
thf(sk33_decl,type,
sk33: vAval > vUnOpT > vUnOpT ).
thf(sk34_decl,type,
sk34: vAval > vUnOpT > vAval ).
thf(sk35_decl,type,
sk35: vATMap > vExp > $o ).
thf(sk36_decl,type,
sk36: vExp > vATMap > vATMap ).
thf(sk37_decl,type,
sk37: vExp > vATMap > vYN ).
thf(sk38_decl,type,
sk38: vATMap > vExp > $o ).
thf(sk39_decl,type,
sk39: vExp > vATMap > vATMap ).
thf(sk40_decl,type,
sk40: vExp > vATMap > vnat ).
thf(sk41_decl,type,
sk41: vATMap > vExp > $o ).
thf(sk42_decl,type,
sk42: vExp > vATMap > vATMap ).
thf(sk43_decl,type,
sk43: vExp > vATMap > vstring ).
thf(sk44_decl,type,
sk44: vExp > vATMap > $o ).
thf(sk45_decl,type,
sk45: vExp > vATMap > vQID ).
thf(sk46_decl,type,
sk46: vExp > vATMap > vATMap ).
thf(sk47_decl,type,
sk47: vExp > vATMap > $o ).
thf(sk48_decl,type,
sk48: vExp > vATMap > vATMap ).
thf(sk49_decl,type,
sk49: vExp > vATMap > vOptAType ).
thf(sk50_decl,type,
sk50: vExp > vATMap > vExp ).
thf(sk51_decl,type,
sk51: vExp > vATMap > vOptAType ).
thf(sk52_decl,type,
sk52: vExp > vATMap > vExp ).
thf(sk53_decl,type,
sk53: vExp > vATMap > vBinOpT ).
thf(sk54_decl,type,
sk54: vExp > vATMap > $o ).
thf(sk55_decl,type,
sk55: vExp > vATMap > vATMap ).
thf(sk56_decl,type,
sk56: vExp > vATMap > vOptAType ).
thf(sk57_decl,type,
sk57: vExp > vATMap > vExp ).
thf(sk58_decl,type,
sk58: vExp > vATMap > vOptAType ).
thf(sk59_decl,type,
sk59: vExp > vATMap > vExp ).
thf(sk60_decl,type,
sk60: vExp > vATMap > vBinOpT ).
thf(sk61_decl,type,
sk61: vExp > vATMap > $o ).
thf(sk62_decl,type,
sk62: vExp > vATMap > vUnOpT ).
thf(sk63_decl,type,
sk63: vExp > vATMap > vExp ).
thf(sk64_decl,type,
sk64: vExp > vATMap > vOptAType ).
thf(sk65_decl,type,
sk65: vExp > vATMap > vATMap ).
thf(sk66_decl,type,
sk66: vExp > vATMap > vUnOpT ).
thf(sk67_decl,type,
sk67: vExp > vATMap > vExp ).
thf(sk68_decl,type,
sk68: vExp > vATMap > vOptAType ).
thf(sk69_decl,type,
sk69: vExp > vATMap > vATMap ).
thf(sk70_decl,type,
sk70: vAval > vstring ).
thf(sk71_decl,type,
sk71: vExp > vAnsMap > $o ).
thf(sk72_decl,type,
sk72: vAnsMap > vExp > vAval ).
thf(sk73_decl,type,
sk73: vAnsMap > vExp > vAnsMap ).
thf(sk74_decl,type,
sk74: vExp > vAnsMap > $o ).
thf(sk75_decl,type,
sk75: vAnsMap > vExp > vQID ).
thf(sk76_decl,type,
sk76: vAnsMap > vExp > vOptAval ).
thf(sk77_decl,type,
sk77: vAnsMap > vExp > vAnsMap ).
thf(sk78_decl,type,
sk78: vExp > vAnsMap > $o ).
thf(sk79_decl,type,
sk79: vAnsMap > vExp > vQID ).
thf(sk80_decl,type,
sk80: vAnsMap > vExp > vOptAval ).
thf(sk81_decl,type,
sk81: vAnsMap > vExp > vAnsMap ).
thf(sk82_decl,type,
sk82: vExp > vAnsMap > $o ).
thf(sk83_decl,type,
sk83: vAnsMap > vExp > vExp ).
thf(sk84_decl,type,
sk84: vAnsMap > vExp > vBinOpT ).
thf(sk85_decl,type,
sk85: vAnsMap > vExp > vExp ).
thf(sk86_decl,type,
sk86: vAnsMap > vExp > vAnsMap ).
thf(sk87_decl,type,
sk87: vExp > vAnsMap > $o ).
thf(sk88_decl,type,
sk88: vAnsMap > vExp > vExp ).
thf(sk89_decl,type,
sk89: vAnsMap > vExp > vOptExp ).
thf(sk90_decl,type,
sk90: vAnsMap > vExp > vAnsMap ).
thf(sk91_decl,type,
sk91: vAnsMap > vExp > vExp ).
thf(sk92_decl,type,
sk92: vAnsMap > vExp > vBinOpT ).
thf(sk93_decl,type,
sk93: vExp > vAnsMap > $o ).
thf(sk94_decl,type,
sk94: vAnsMap > vExp > vExp ).
thf(sk95_decl,type,
sk95: vAnsMap > vExp > vOptExp ).
thf(sk96_decl,type,
sk96: vAnsMap > vExp > vAnsMap ).
thf(sk97_decl,type,
sk97: vAnsMap > vExp > vExp ).
thf(sk98_decl,type,
sk98: vAnsMap > vExp > vBinOpT ).
thf(sk99_decl,type,
sk99: vExp > vAnsMap > $o ).
thf(sk100_decl,type,
sk100: vAnsMap > vExp > vExp ).
thf(sk101_decl,type,
sk101: vAnsMap > vExp > vOptExp ).
thf(sk102_decl,type,
sk102: vAnsMap > vExp > vAnsMap ).
thf(sk103_decl,type,
sk103: vAnsMap > vExp > vExp ).
thf(sk104_decl,type,
sk104: vAnsMap > vExp > vBinOpT ).
thf(sk105_decl,type,
sk105: vExp > vAnsMap > $o ).
thf(sk106_decl,type,
sk106: vAnsMap > vExp > vExp ).
thf(sk107_decl,type,
sk107: vAnsMap > vExp > vOptExp ).
thf(sk108_decl,type,
sk108: vAnsMap > vExp > vAnsMap ).
thf(sk109_decl,type,
sk109: vAnsMap > vExp > vExp ).
thf(sk110_decl,type,
sk110: vAnsMap > vExp > vBinOpT ).
thf(sk111_decl,type,
sk111: vExp > vAnsMap > $o ).
thf(sk112_decl,type,
sk112: vAnsMap > vExp > vUnOpT ).
thf(sk113_decl,type,
sk113: vAnsMap > vExp > vExp ).
thf(sk114_decl,type,
sk114: vAnsMap > vExp > vAnsMap ).
thf(sk115_decl,type,
sk115: vExp > vAnsMap > $o ).
thf(sk116_decl,type,
sk116: vAnsMap > vExp > vUnOpT ).
thf(sk117_decl,type,
sk117: vAnsMap > vExp > vExp ).
thf(sk118_decl,type,
sk118: vAnsMap > vExp > vOptExp ).
thf(sk119_decl,type,
sk119: vAnsMap > vExp > vAnsMap ).
thf(sk120_decl,type,
sk120: vAnsMap > vExp > vUnOpT ).
thf(sk121_decl,type,
sk121: vAnsMap > vExp > vExp ).
thf(sk122_decl,type,
sk122: vAnsMap > vExp > vOptExp ).
thf(sk123_decl,type,
sk123: vAnsMap > vExp > vAnsMap ).
thf(sk124_decl,type,
sk124: vLabel > vAType > $o ).
thf(sk125_decl,type,
sk125: vAType > vLabel > vLabel ).
thf(sk126_decl,type,
sk126: vLabel > vAType > $o ).
thf(sk127_decl,type,
sk127: vAType > vLabel > vLabel ).
thf(sk128_decl,type,
sk128: vAType > vLabel > vLabel ).
thf(sk129_decl,type,
sk129: vLabel > vAType > vOptQuestion > vQID ).
thf(sk130_decl,type,
sk130: vQID > vAType > vOptQuestion > vLabel ).
thf(sk131_decl,type,
sk131: vQID > vLabel > vOptQuestion > vAType ).
thf(sk132_decl,type,
sk132: vBinOpT > vExp > vExp > vExp ).
thf(sk133_decl,type,
sk133: vExp > vExp > vExp > vBinOpT ).
thf(sk134_decl,type,
sk134: vExp > vBinOpT > vExp > vExp ).
thf(sk135_decl,type,
sk135: vExp > vQID ).
thf(sk136_decl,type,
sk136: vExp > vExp > vUnOpT ).
thf(sk137_decl,type,
sk137: vUnOpT > vExp > vExp ).
thf(sk138_decl,type,
sk138: vAval > vYN ).
thf(sk139_decl,type,
sk139: vYN > vYN > $o ).
thf(sk140_decl,type,
sk140: vYN > vYN > vYN ).
thf(sk141_decl,type,
sk141: vYN > vYN > vYN ).
thf(sk142_decl,type,
sk142: vQuestionnaire > vQuestionnaire > vQuestionnaire ).
thf(sk143_decl,type,
sk143: vQuestionnaire > vQuestionnaire > vQuestionnaire ).
thf(sk150_decl,type,
sk150: vEntry > vQID ).
thf(sk151_decl,type,
sk151: vYN > vYN > $o ).
thf(sk152_decl,type,
sk152: vYN > vYN > vYN ).
thf(sk153_decl,type,
sk153: vYN > vYN > vYN ).
thf(sk154_decl,type,
sk154: vLabel > vAType > vEntry > vQID ).
thf(sk155_decl,type,
sk155: vQID > vAType > vEntry > vLabel ).
thf(sk156_decl,type,
sk156: vQID > vLabel > vEntry > vAType ).
thf(sk157_decl,type,
sk157: vATMap > vQID > $o ).
thf(sk158_decl,type,
sk158: vATMap > vQID > vQID ).
thf(sk159_decl,type,
sk159: vATMap > vQID > $o ).
thf(sk160_decl,type,
sk160: vATMap > vQID > vQID ).
thf(sk161_decl,type,
sk161: vATMap > vQID > vAType ).
thf(sk162_decl,type,
sk162: vATMap > vQID > vATMap ).
thf(sk163_decl,type,
sk163: vATMap > vQID > vQID ).
thf(sk164_decl,type,
sk164: vATMap > vQID > vQID ).
thf(sk165_decl,type,
sk165: vATMap > vQID > vAType ).
thf(sk166_decl,type,
sk166: vATMap > vQID > vATMap ).
thf(sk167_decl,type,
sk167: vATMap > vQID > vQID ).
thf(sk169_decl,type,
sk169: vQID > vQMap > $o ).
thf(sk170_decl,type,
sk170: vQMap > vQID > vQID ).
thf(sk171_decl,type,
sk171: vQID > vQMap > $o ).
thf(sk172_decl,type,
sk172: vQMap > vQID > vQMap ).
thf(sk173_decl,type,
sk173: vQMap > vQID > vQID ).
thf(sk174_decl,type,
sk174: vQMap > vQID > vAType ).
thf(sk175_decl,type,
sk175: vQMap > vQID > vLabel ).
thf(sk176_decl,type,
sk176: vQMap > vQID > vQID ).
thf(sk177_decl,type,
sk177: vQMap > vQID > vQMap ).
thf(sk178_decl,type,
sk178: vQMap > vQID > vQID ).
thf(sk179_decl,type,
sk179: vQMap > vQID > vAType ).
thf(sk180_decl,type,
sk180: vQMap > vQID > vLabel ).
thf(sk181_decl,type,
sk181: vQMap > vQID > vQID ).
thf(sk182_decl,type,
sk182: vOptAType > vAType ).
thf(sk187_decl,type,
sk187: vATMap > vATMap > $o ).
thf(sk188_decl,type,
sk188: vATMap > vATMap > vATMap ).
thf(sk189_decl,type,
sk189: vATMap > vATMap > $o ).
thf(sk190_decl,type,
sk190: vATMap > vATMap > vATMap ).
thf(sk191_decl,type,
sk191: vATMap > vATMap > vATMap ).
thf(sk192_decl,type,
sk192: vATMap > vATMap > vOptAType ).
thf(sk193_decl,type,
sk193: vATMap > vATMap > vAType ).
thf(sk194_decl,type,
sk194: vATMap > vATMap > vATMap ).
thf(sk195_decl,type,
sk195: vATMap > vATMap > vQID ).
thf(sk196_decl,type,
sk196: vATMap > vATMap > vATMap ).
thf(sk197_decl,type,
sk197: vATMap > vATMap > vATMap ).
thf(sk198_decl,type,
sk198: vATMap > vATMap > vOptAType ).
thf(sk199_decl,type,
sk199: vATMap > vATMap > vAType ).
thf(sk200_decl,type,
sk200: vATMap > vATMap > vATMap ).
thf(sk201_decl,type,
sk201: vATMap > vATMap > vQID ).
thf(sk203_decl,type,
sk203: vLabel > vAType > vEntry > vQID ).
thf(sk204_decl,type,
sk204: vQID > vAType > vEntry > vLabel ).
thf(sk205_decl,type,
sk205: vQID > vLabel > vEntry > vAType ).
thf(sk207_decl,type,
sk207: vExp > vAval ).
thf(sk215_decl,type,
sk215: vUnOpT > vAType > $o ).
thf(sk216_decl,type,
sk216: vAType > vUnOpT > vUnOpT ).
thf(sk217_decl,type,
sk217: vAType > vUnOpT > vAType ).
thf(sk222_decl,type,
sk222: vAType > vATMap > vATMap > vQID ).
thf(sk223_decl,type,
sk223: vQID > vATMap > vATMap > vAType ).
thf(sk224_decl,type,
sk224: vQID > vAType > vATMap > vATMap ).
thf(sk225_decl,type,
sk225: vAval > vAnsMap > vAnsMap > vQID ).
thf(sk226_decl,type,
sk226: vQID > vAnsMap > vAnsMap > vAval ).
thf(sk227_decl,type,
sk227: vQID > vAval > vAnsMap > vAnsMap ).
thf(sk228_decl,type,
sk228: vQuestionnaire > vQuestionnaire > vGID ).
thf(sk229_decl,type,
sk229: vGID > vQuestionnaire > vQuestionnaire ).
thf(sk230_decl,type,
sk230: vQuestionnaire > vQuestionnaire > vQuestionnaire > vExp ).
thf(sk231_decl,type,
sk231: vExp > vQuestionnaire > vQuestionnaire > vQuestionnaire ).
thf(sk232_decl,type,
sk232: vExp > vQuestionnaire > vQuestionnaire > vQuestionnaire ).
thf(sk242_decl,type,
sk242: vQMap > vQuestionnaire > vQConf > vAnsMap ).
thf(sk243_decl,type,
sk243: vAnsMap > vQuestionnaire > vQConf > vQMap ).
thf(sk244_decl,type,
sk244: vAnsMap > vQMap > vQConf > vQuestionnaire ).
thf(sk245_decl,type,
sk245: vAType > vExp > vEntry > vQID ).
thf(sk246_decl,type,
sk246: vQID > vExp > vEntry > vAType ).
thf(sk247_decl,type,
sk247: vQID > vAType > vEntry > vExp ).
thf(sk253_decl,type,
sk253: vMapConf > vATMap ).
thf(sk254_decl,type,
sk254: vMapConf > vATMap ).
thf(sk255_decl,type,
sk255: vQuestionnaire > vQConf > vAnsMap ).
thf(sk256_decl,type,
sk256: vQuestionnaire > vQConf > vQMap ).
thf(sk257_decl,type,
sk257: vQuestionnaire > vQConf > vQuestionnaire ).
thf(sk258_decl,type,
sk258: vQuestionnaire > vQConf > vQuestionnaire ).
thf(sk261_decl,type,
sk261: vQConf > vAnsMap ).
thf(sk262_decl,type,
sk262: vQConf > vQMap ).
thf(sk263_decl,type,
sk263: vQConf > vQuestionnaire ).
thf(sk264_decl,type,
sk264: vOptQConf > vQConf ).
thf(sk354_decl,type,
sk354: vQuestionnaire > vQuestionnaire ).
thf(sk363_decl,type,
sk363: vQuestionnaire > vEntry ).
thf(sk367_decl,type,
sk367: vQConf > vAnsMap ).
thf(sk368_decl,type,
sk368: vQConf > vQMap ).
thf(sk369_decl,type,
sk369: vQConf > vQuestionnaire ).
thf(sk386_decl,type,
sk386: vQConf > vAnsMap ).
thf(sk387_decl,type,
sk387: vQConf > vQMap ).
thf(sk388_decl,type,
sk388: vQConf > vQuestionnaire ).
thf(sk399_decl,type,
sk399: vQConf > vAnsMap ).
thf(sk400_decl,type,
sk400: vQConf > vQMap ).
thf(sk401_decl,type,
sk401: vQConf > vQuestionnaire ).
thf(sk411_decl,type,
sk411: vATMap > vMapConf > vATMap ).
thf(sk412_decl,type,
sk412: vATMap > vMapConf > vATMap ).
thf(sk1_def,definition,
( sk1
= ( @+[A: vQMap] :
~ ! [B: vAType,C: vATMap,D: vATMap,E: vAnsMap,F: vQID,G: vExp] :
( ( ( D @ ( C @ vMC ) @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ ( A @ vtypeQM @ ( E @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ visValue ) )
=> ? [H: vAnsMap,I: vQMap,J: vQuestionnaire] :
( ( A @ ( E @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( J @ ( I @ ( H @ vQC ) ) @ vsomeQConf ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: vAType] :
~ ! [B: vATMap,C: vATMap,D: vAnsMap,E: vQID,F: vExp] :
( ( ( C @ ( B @ vMC ) @ ( F @ ( A @ ( E @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( D @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( F @ ( A @ ( E @ vvalue ) ) @ vqsingle @ visValue ) )
=> ? [G: vAnsMap,H: vQMap,I: vQuestionnaire] :
( ( sk1 @ ( D @ ( F @ ( A @ ( E @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( I @ ( H @ ( G @ vQC ) ) @ vsomeQConf ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: vATMap] :
~ ! [B: vATMap,C: vAnsMap,D: vQID,E: vExp] :
( ( ( B @ ( A @ vMC ) @ ( E @ ( sk2 @ ( D @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( C @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( E @ ( sk2 @ ( D @ vvalue ) ) @ vqsingle @ visValue ) )
=> ? [F: vAnsMap,G: vQMap,H: vQuestionnaire] :
( ( sk1 @ ( C @ ( E @ ( sk2 @ ( D @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( H @ ( G @ ( F @ vQC ) ) @ vsomeQConf ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: vATMap] :
~ ! [B: vAnsMap,C: vQID,D: vExp] :
( ( ( A @ ( sk3 @ vMC ) @ ( D @ ( sk2 @ ( C @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( B @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( D @ ( sk2 @ ( C @ vvalue ) ) @ vqsingle @ visValue ) )
=> ? [E: vAnsMap,F: vQMap,G: vQuestionnaire] :
( ( sk1 @ ( B @ ( D @ ( sk2 @ ( C @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( G @ ( F @ ( E @ vQC ) ) @ vsomeQConf ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: vAnsMap] :
~ ! [B: vQID,C: vExp] :
( ( ( sk4 @ ( sk3 @ vMC ) @ ( C @ ( sk2 @ ( B @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( A @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( C @ ( sk2 @ ( B @ vvalue ) ) @ vqsingle @ visValue ) )
=> ? [D: vAnsMap,E: vQMap,F: vQuestionnaire] :
( ( sk1 @ ( A @ ( C @ ( sk2 @ ( B @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( F @ ( E @ ( D @ vQC ) ) @ vsomeQConf ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: vQID] :
~ ! [B: vExp] :
( ( ( sk4 @ ( sk3 @ vMC ) @ ( B @ ( sk2 @ ( A @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( B @ ( sk2 @ ( A @ vvalue ) ) @ vqsingle @ visValue ) )
=> ? [C: vAnsMap,D: vQMap,E: vQuestionnaire] :
( ( sk1 @ ( sk5 @ ( B @ ( sk2 @ ( A @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( E @ ( D @ ( C @ vQC ) ) @ vsomeQConf ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: vExp] :
~ ( ( ( sk4 @ ( sk3 @ vMC ) @ ( A @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( A @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ visValue ) )
=> ? [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( sk1 @ ( sk5 @ ( A @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( D @ ( C @ ( B @ vQC ) ) @ vsomeQConf ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: vOptAType] :
@+[B: vAType] :
( A
= ( B @ vsomeAType ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: vOptExp > vExp] :
! [B: vExp] :
( ( B @ vsomeExp @ A )
= B ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: vAval > vnat] :
! [B: vnat] :
( ( B @ vNum @ A )
= B ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: vOptQuestion] :
@+[B: vQID] :
? [C: vLabel,D: vAType] :
( A
= ( D @ ( C @ ( B @ vsomeQuestion ) ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: vOptQuestion] :
@+[B: vLabel] :
? [C: vAType] :
( A
= ( C @ ( B @ ( A @ sk11 @ vsomeQuestion ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: vOptQuestion] :
@+[B: vAType] :
( A
= ( B @ ( A @ sk12 @ ( A @ sk11 @ vsomeQuestion ) ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: vAval] :
@+[B: vYN] :
( A
= ( B @ vB ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: vAval] :
@+[B: vnat] :
( A
= ( B @ vNum ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: vAval] :
@+[B: vstring] :
( A
= ( B @ vT ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: vExp] :
@+[B: vAval] :
( A
= ( B @ vconstant ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [A: vExp] :
@+[B: vQID] :
( A
= ( B @ vqvar ) ) ) ) ).
thf(sk20_def,definition,
( sk20
= ( ^ [A: vExp] :
@+[B: vExp] :
? [C: vBinOpT,D: vExp] :
( A
= ( D @ ( C @ ( B @ vbinop ) ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: vExp] :
@+[B: vBinOpT] :
? [C: vExp] :
( A
= ( C @ ( B @ ( A @ sk20 @ vbinop ) ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: vExp] :
@+[B: vExp] :
( A
= ( B @ ( A @ sk21 @ ( A @ sk20 @ vbinop ) ) ) ) ) ) ).
thf(sk23_def,definition,
( sk23
= ( ^ [A: vExp] :
@+[B: vUnOpT] :
? [C: vExp] :
( A
= ( C @ ( B @ vunop ) ) ) ) ) ).
thf(sk24_def,definition,
( sk24
= ( ^ [A: vExp] :
@+[B: vExp] :
( A
= ( B @ ( A @ sk23 @ vunop ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: vAval,B: vUnOpT] :
@+[C: vYN] :
( A
= ( C @ vB ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: vOptExp] :
@+[B: vExp] :
( A
= ( B @ vsomeExp ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: vOptExp] :
@+[B: vExp] :
( A
= ( B @ vsomeExp ) ) ) ) ).
thf(sk28_def,definition,
( sk28
= ( ^ [A: vAval] :
@+[B: vYN] :
( A
= ( B @ vB ) ) ) ) ).
thf(sk29_def,definition,
( sk29
= ( ^ [A: vAval] :
@+[B: vnat] :
( A
= ( B @ vNum ) ) ) ) ).
thf(sk30_def,definition,
( sk30
= ( ^ [A: vAval] :
@+[B: vstring] :
( A
= ( B @ vT ) ) ) ) ).
thf(sk32_def,definition,
( sk32
= ( ^ [A: vAval,B: vUnOpT] :
@+[C: vYN] :
( ( ( A @ ( B @ vevalUnOp ) )
= ( C @ vnot @ vB @ vconstant @ vsomeExp ) )
& ( A
= ( C @ vB ) ) ) ) ) ).
thf(sk33_def,definition,
( sk33
= ( ^ [A: vAval,B: vUnOpT] :
@+[C: vUnOpT] :
? [D: vAval] :
( ( ( A @ ( B @ vevalUnOp ) )
= vnoExp )
& ( A = D )
& ( B = C )
& ( ~ ? [E: vYN] :
( D
= ( E @ vB ) )
| ( C != vnotop ) ) ) ) ) ).
thf(sk34_def,definition,
( sk34
= ( ^ [A: vAval,B: vUnOpT] :
@+[C: vAval] :
( ( ( A @ ( B @ vevalUnOp ) )
= vnoExp )
& ( A = C )
& ( B
= ( B @ ( A @ sk33 ) ) )
& ( ~ ? [D: vYN] :
( C
= ( D @ vB ) )
| ( ( B @ ( A @ sk33 ) )
!= vnotop ) ) ) ) ) ).
thf(sk36_def,definition,
( sk36
= ( ^ [A: vExp,B: vATMap] :
@+[C: vATMap] : ( B = C ) ) ) ).
thf(sk37_def,definition,
( sk37
= ( ^ [A: vExp,B: vATMap] :
@+[C: vYN] :
( A
= ( C @ vB @ vconstant ) ) ) ) ).
thf(sk39_def,definition,
( sk39
= ( ^ [A: vExp,B: vATMap] :
@+[C: vATMap] : ( B = C ) ) ) ).
thf(sk40_def,definition,
( sk40
= ( ^ [A: vExp,B: vATMap] :
@+[C: vnat] :
( A
= ( C @ vNum @ vconstant ) ) ) ) ).
thf(sk42_def,definition,
( sk42
= ( ^ [A: vExp,B: vATMap] :
@+[C: vATMap] : ( B = C ) ) ) ).
thf(sk43_def,definition,
( sk43
= ( ^ [A: vExp,B: vATMap] :
@+[C: vstring] :
( A
= ( C @ vT @ vconstant ) ) ) ) ).
thf(sk45_def,definition,
( sk45
= ( ^ [A: vExp,B: vATMap] :
@+[C: vQID] :
? [D: vATMap] :
( ( ( A @ ( B @ vecheck ) )
= ( D @ ( C @ vlookupATMap ) ) )
& ( A
= ( C @ vqvar ) )
& ( B = D ) ) ) ) ).
thf(sk46_def,definition,
( sk46
= ( ^ [A: vExp,B: vATMap] :
@+[C: vATMap] :
( ( ( A @ ( B @ vecheck ) )
= ( C @ ( B @ ( A @ sk45 ) @ vlookupATMap ) ) )
& ( A
= ( B @ ( A @ sk45 ) @ vqvar ) )
& ( B = C ) ) ) ) ).
thf(sk48_def,definition,
( sk48
= ( ^ [A: vExp,B: vATMap] :
@+[C: vATMap] :
? [D: vOptAType,E: vExp] :
( ? [F: vOptAType,G: vExp] :
( ? [H: vBinOpT] :
( ( ( A @ ( B @ vecheck ) )
= ( F @ vgetAType @ ( D @ vgetAType @ ( H @ vcheckBinOp ) ) ) )
& ( A
= ( G @ ( H @ ( E @ vbinop ) ) ) ) )
& ( B = C )
& ( F @ visSomeAType )
& ( D @ visSomeAType )
& ( F
= ( G @ ( C @ vecheck ) ) ) )
& ( D
= ( E @ ( C @ vecheck ) ) ) ) ) ) ).
thf(sk49_def,definition,
( sk49
= ( ^ [A: vExp,B: vATMap] :
@+[C: vOptAType] :
? [D: vExp] :
( ? [E: vOptAType,F: vExp] :
( ? [G: vBinOpT] :
( ( ( A @ ( B @ vecheck ) )
= ( E @ vgetAType @ ( C @ vgetAType @ ( G @ vcheckBinOp ) ) ) )
& ( A
= ( F @ ( G @ ( D @ vbinop ) ) ) ) )
& ( B
= ( B @ ( A @ sk48 ) ) )
& ( E @ visSomeAType )
& ( C @ visSomeAType )
& ( E
= ( F @ ( B @ ( A @ sk48 ) @ vecheck ) ) ) )
& ( C
= ( D @ ( B @ ( A @ sk48 ) @ vecheck ) ) ) ) ) ) ).
thf(sk50_def,definition,
( sk50
= ( ^ [A: vExp,B: vATMap] :
@+[C: vExp] :
( ? [D: vOptAType,E: vExp] :
( ? [F: vBinOpT] :
( ( ( A @ ( B @ vecheck ) )
= ( D @ vgetAType @ ( B @ ( A @ sk49 ) @ vgetAType @ ( F @ vcheckBinOp ) ) ) )
& ( A
= ( E @ ( F @ ( C @ vbinop ) ) ) ) )
& ( B
= ( B @ ( A @ sk48 ) ) )
& ( D @ visSomeAType )
& ( B @ ( A @ sk49 ) @ visSomeAType )
& ( D
= ( E @ ( B @ ( A @ sk48 ) @ vecheck ) ) ) )
& ( ( B @ ( A @ sk49 ) )
= ( C @ ( B @ ( A @ sk48 ) @ vecheck ) ) ) ) ) ) ).
thf(sk51_def,definition,
( sk51
= ( ^ [A: vExp,B: vATMap] :
@+[C: vOptAType] :
? [D: vExp] :
( ? [E: vBinOpT] :
( ( ( A @ ( B @ vecheck ) )
= ( C @ vgetAType @ ( B @ ( A @ sk49 ) @ vgetAType @ ( E @ vcheckBinOp ) ) ) )
& ( A
= ( D @ ( E @ ( B @ ( A @ sk50 ) @ vbinop ) ) ) ) )
& ( B
= ( B @ ( A @ sk48 ) ) )
& ( C @ visSomeAType )
& ( B @ ( A @ sk49 ) @ visSomeAType )
& ( C
= ( D @ ( B @ ( A @ sk48 ) @ vecheck ) ) ) ) ) ) ).
thf(sk52_def,definition,
( sk52
= ( ^ [A: vExp,B: vATMap] :
@+[C: vExp] :
( ? [D: vBinOpT] :
( ( ( A @ ( B @ vecheck ) )
= ( B @ ( A @ sk51 ) @ vgetAType @ ( B @ ( A @ sk49 ) @ vgetAType @ ( D @ vcheckBinOp ) ) ) )
& ( A
= ( C @ ( D @ ( B @ ( A @ sk50 ) @ vbinop ) ) ) ) )
& ( B
= ( B @ ( A @ sk48 ) ) )
& ( B @ ( A @ sk51 ) @ visSomeAType )
& ( B @ ( A @ sk49 ) @ visSomeAType )
& ( ( B @ ( A @ sk51 ) )
= ( C @ ( B @ ( A @ sk48 ) @ vecheck ) ) ) ) ) ) ).
thf(sk53_def,definition,
( sk53
= ( ^ [A: vExp,B: vATMap] :
@+[C: vBinOpT] :
( ( ( A @ ( B @ vecheck ) )
= ( B @ ( A @ sk51 ) @ vgetAType @ ( B @ ( A @ sk49 ) @ vgetAType @ ( C @ vcheckBinOp ) ) ) )
& ( A
= ( B @ ( A @ sk52 ) @ ( C @ ( B @ ( A @ sk50 ) @ vbinop ) ) ) ) ) ) ) ).
thf(sk55_def,definition,
( sk55
= ( ^ [A: vExp,B: vATMap] :
@+[C: vATMap] :
? [D: vOptAType,E: vExp] :
( ? [F: vOptAType,G: vExp] :
( ( ( A @ ( B @ vecheck ) )
= vnoAType )
& ? [H: vBinOpT] :
( A
= ( G @ ( H @ ( E @ vbinop ) ) ) )
& ( B = C )
& ~ ( ( F @ visSomeAType )
& ( D @ visSomeAType ) )
& ( F
= ( G @ ( C @ vecheck ) ) ) )
& ( D
= ( E @ ( C @ vecheck ) ) ) ) ) ) ).
thf(sk56_def,definition,
( sk56
= ( ^ [A: vExp,B: vATMap] :
@+[C: vOptAType] :
? [D: vExp] :
( ? [E: vOptAType,F: vExp] :
( ( ( A @ ( B @ vecheck ) )
= vnoAType )
& ? [G: vBinOpT] :
( A
= ( F @ ( G @ ( D @ vbinop ) ) ) )
& ( B
= ( B @ ( A @ sk55 ) ) )
& ~ ( ( E @ visSomeAType )
& ( C @ visSomeAType ) )
& ( E
= ( F @ ( B @ ( A @ sk55 ) @ vecheck ) ) ) )
& ( C
= ( D @ ( B @ ( A @ sk55 ) @ vecheck ) ) ) ) ) ) ).
thf(sk57_def,definition,
( sk57
= ( ^ [A: vExp,B: vATMap] :
@+[C: vExp] :
( ? [D: vOptAType,E: vExp] :
( ( ( A @ ( B @ vecheck ) )
= vnoAType )
& ? [F: vBinOpT] :
( A
= ( E @ ( F @ ( C @ vbinop ) ) ) )
& ( B
= ( B @ ( A @ sk55 ) ) )
& ~ ( ( D @ visSomeAType )
& ( B @ ( A @ sk56 ) @ visSomeAType ) )
& ( D
= ( E @ ( B @ ( A @ sk55 ) @ vecheck ) ) ) )
& ( ( B @ ( A @ sk56 ) )
= ( C @ ( B @ ( A @ sk55 ) @ vecheck ) ) ) ) ) ) ).
thf(sk58_def,definition,
( sk58
= ( ^ [A: vExp,B: vATMap] :
@+[C: vOptAType] :
? [D: vExp] :
( ( ( A @ ( B @ vecheck ) )
= vnoAType )
& ? [E: vBinOpT] :
( A
= ( D @ ( E @ ( B @ ( A @ sk57 ) @ vbinop ) ) ) )
& ( B
= ( B @ ( A @ sk55 ) ) )
& ~ ( ( C @ visSomeAType )
& ( B @ ( A @ sk56 ) @ visSomeAType ) )
& ( C
= ( D @ ( B @ ( A @ sk55 ) @ vecheck ) ) ) ) ) ) ).
thf(sk59_def,definition,
( sk59
= ( ^ [A: vExp,B: vATMap] :
@+[C: vExp] :
( ( ( A @ ( B @ vecheck ) )
= vnoAType )
& ? [D: vBinOpT] :
( A
= ( C @ ( D @ ( B @ ( A @ sk57 ) @ vbinop ) ) ) )
& ( B
= ( B @ ( A @ sk55 ) ) )
& ~ ( ( B @ ( A @ sk58 ) @ visSomeAType )
& ( B @ ( A @ sk56 ) @ visSomeAType ) )
& ( ( B @ ( A @ sk58 ) )
= ( C @ ( B @ ( A @ sk55 ) @ vecheck ) ) ) ) ) ) ).
thf(sk60_def,definition,
( sk60
= ( ^ [A: vExp,B: vATMap] :
@+[C: vBinOpT] :
( A
= ( B @ ( A @ sk59 ) @ ( C @ ( B @ ( A @ sk57 ) @ vbinop ) ) ) ) ) ) ).
thf(sk62_def,definition,
( sk62
= ( ^ [A: vExp,B: vATMap] :
@+[C: vUnOpT] :
? [D: vExp,E: vOptAType,F: vATMap] :
( ( ( A @ ( B @ vecheck ) )
= ( E @ vgetAType @ ( C @ vcheckUnOp ) ) )
& ( A
= ( D @ ( C @ vunop ) ) )
& ( B = F )
& ( E @ visSomeAType )
& ( E
= ( D @ ( F @ vecheck ) ) ) ) ) ) ).
thf(sk63_def,definition,
( sk63
= ( ^ [A: vExp,B: vATMap] :
@+[C: vExp] :
? [D: vOptAType,E: vATMap] :
( ( ( A @ ( B @ vecheck ) )
= ( D @ vgetAType @ ( B @ ( A @ sk62 ) @ vcheckUnOp ) ) )
& ( A
= ( C @ ( B @ ( A @ sk62 ) @ vunop ) ) )
& ( B = E )
& ( D @ visSomeAType )
& ( D
= ( C @ ( E @ vecheck ) ) ) ) ) ) ).
thf(sk64_def,definition,
( sk64
= ( ^ [A: vExp,B: vATMap] :
@+[C: vOptAType] :
? [D: vATMap] :
( ( ( A @ ( B @ vecheck ) )
= ( C @ vgetAType @ ( B @ ( A @ sk62 ) @ vcheckUnOp ) ) )
& ( A
= ( B @ ( A @ sk63 ) @ ( B @ ( A @ sk62 ) @ vunop ) ) )
& ( B = D )
& ( C @ visSomeAType )
& ( C
= ( B @ ( A @ sk63 ) @ ( D @ vecheck ) ) ) ) ) ) ).
thf(sk65_def,definition,
( sk65
= ( ^ [A: vExp,B: vATMap] :
@+[C: vATMap] :
( ( ( A @ ( B @ vecheck ) )
= ( B @ ( A @ sk64 ) @ vgetAType @ ( B @ ( A @ sk62 ) @ vcheckUnOp ) ) )
& ( A
= ( B @ ( A @ sk63 ) @ ( B @ ( A @ sk62 ) @ vunop ) ) )
& ( B = C )
& ( B @ ( A @ sk64 ) @ visSomeAType )
& ( ( B @ ( A @ sk64 ) )
= ( B @ ( A @ sk63 ) @ ( C @ vecheck ) ) ) ) ) ) ).
thf(sk66_def,definition,
( sk66
= ( ^ [A: vExp,B: vATMap] :
@+[C: vUnOpT] :
? [D: vExp,E: vOptAType,F: vATMap] :
( ( ( A @ ( B @ vecheck ) )
= vnoAType )
& ( A
= ( D @ ( C @ vunop ) ) )
& ( B = F )
& ~ ( E @ visSomeAType )
& ( E
= ( D @ ( F @ vecheck ) ) ) ) ) ) ).
thf(sk67_def,definition,
( sk67
= ( ^ [A: vExp,B: vATMap] :
@+[C: vExp] :
? [D: vOptAType,E: vATMap] :
( ( ( A @ ( B @ vecheck ) )
= vnoAType )
& ( A
= ( C @ ( B @ ( A @ sk66 ) @ vunop ) ) )
& ( B = E )
& ~ ( D @ visSomeAType )
& ( D
= ( C @ ( E @ vecheck ) ) ) ) ) ) ).
thf(sk68_def,definition,
( sk68
= ( ^ [A: vExp,B: vATMap] :
@+[C: vOptAType] :
? [D: vATMap] :
( ( ( A @ ( B @ vecheck ) )
= vnoAType )
& ( A
= ( B @ ( A @ sk67 ) @ ( B @ ( A @ sk66 ) @ vunop ) ) )
& ( B = D )
& ~ ( C @ visSomeAType )
& ( C
= ( B @ ( A @ sk67 ) @ ( D @ vecheck ) ) ) ) ) ) ).
thf(sk69_def,definition,
( sk69
= ( ^ [A: vExp,B: vATMap] :
@+[C: vATMap] :
( ( ( A @ ( B @ vecheck ) )
= vnoAType )
& ( A
= ( B @ ( A @ sk67 ) @ ( B @ ( A @ sk66 ) @ vunop ) ) )
& ( B = C )
& ~ ( B @ ( A @ sk68 ) @ visSomeAType )
& ( ( B @ ( A @ sk68 ) )
= ( B @ ( A @ sk67 ) @ ( C @ vecheck ) ) ) ) ) ) ).
thf(sk70_def,definition,
( sk70
= ( @+[A: vAval > vstring] :
! [B: vstring] :
( ( B @ vT @ A )
= B ) ) ) ).
thf(sk72_def,definition,
( sk72
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAval] :
( B
= ( C @ vconstant ) ) ) ) ).
thf(sk73_def,definition,
( sk73
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAnsMap] : ( A = C ) ) ) ).
thf(sk75_def,definition,
( sk75
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vQID] :
? [D: vOptAval,E: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= ( D @ vgetAval @ vconstant @ vsomeExp ) )
& ( A = E )
& ( B
= ( C @ vqvar ) )
& ( D @ visSomeAval )
& ( D
= ( E @ ( C @ vlookupAnsMap ) ) ) ) ) ) ).
thf(sk76_def,definition,
( sk76
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vOptAval] :
? [D: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= ( C @ vgetAval @ vconstant @ vsomeExp ) )
& ( A = D )
& ( B
= ( B @ ( A @ sk75 ) @ vqvar ) )
& ( C @ visSomeAval )
& ( C
= ( D @ ( B @ ( A @ sk75 ) @ vlookupAnsMap ) ) ) ) ) ) ).
thf(sk77_def,definition,
( sk77
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= ( B @ ( A @ sk76 ) @ vgetAval @ vconstant @ vsomeExp ) )
& ( A = C )
& ( B
= ( B @ ( A @ sk75 ) @ vqvar ) )
& ( B @ ( A @ sk76 ) @ visSomeAval )
& ( ( B @ ( A @ sk76 ) )
= ( C @ ( B @ ( A @ sk75 ) @ vlookupAnsMap ) ) ) ) ) ) ).
thf(sk79_def,definition,
( sk79
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vQID] :
? [D: vOptAval,E: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = E )
& ( B
= ( C @ vqvar ) )
& ~ ( D @ visSomeAval )
& ( D
= ( E @ ( C @ vlookupAnsMap ) ) ) ) ) ) ).
thf(sk80_def,definition,
( sk80
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vOptAval] :
? [D: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = D )
& ( B
= ( B @ ( A @ sk79 ) @ vqvar ) )
& ~ ( C @ visSomeAval )
& ( C
= ( D @ ( B @ ( A @ sk79 ) @ vlookupAnsMap ) ) ) ) ) ) ).
thf(sk81_def,definition,
( sk81
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = C )
& ( B
= ( B @ ( A @ sk79 ) @ vqvar ) )
& ~ ( B @ ( A @ sk80 ) @ visSomeAval )
& ( ( B @ ( A @ sk80 ) )
= ( C @ ( B @ ( A @ sk79 ) @ vlookupAnsMap ) ) ) ) ) ) ).
thf(sk83_def,definition,
( sk83
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
( ? [D: vBinOpT,E: vExp] :
( ( ( A @ ( B @ vreduceExp ) )
= ( E @ vgetExpValue @ ( C @ vgetExpValue @ ( D @ vevalBinOp ) ) ) )
& ? [F: vAnsMap] : ( A = F )
& ( B
= ( E @ ( D @ ( C @ vbinop ) ) ) )
& ( E @ vexpIsValue ) )
& ( C @ vexpIsValue ) ) ) ) ).
thf(sk84_def,definition,
( sk84
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vBinOpT] :
? [D: vExp] :
( ( ( A @ ( B @ vreduceExp ) )
= ( D @ vgetExpValue @ ( B @ ( A @ sk83 ) @ vgetExpValue @ ( C @ vevalBinOp ) ) ) )
& ? [E: vAnsMap] : ( A = E )
& ( B
= ( D @ ( C @ ( B @ ( A @ sk83 ) @ vbinop ) ) ) )
& ( D @ vexpIsValue ) ) ) ) ).
thf(sk85_def,definition,
( sk85
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
( ( ( A @ ( B @ vreduceExp ) )
= ( C @ vgetExpValue @ ( B @ ( A @ sk83 ) @ vgetExpValue @ ( B @ ( A @ sk84 ) @ vevalBinOp ) ) ) )
& ? [D: vAnsMap] : ( A = D )
& ( B
= ( C @ ( B @ ( A @ sk84 ) @ ( B @ ( A @ sk83 ) @ vbinop ) ) ) )
& ( C @ vexpIsValue ) ) ) ) ).
thf(sk86_def,definition,
( sk86
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAnsMap] : ( A = C ) ) ) ).
thf(sk88_def,definition,
( sk88
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
( ? [D: vOptExp,E: vAnsMap,F: vExp] :
( ? [G: vBinOpT] :
( ( ( A @ ( B @ vreduceExp ) )
= ( D @ vgetExp @ ( G @ ( C @ vbinop ) ) @ vsomeExp ) )
& ( A = E )
& ( B
= ( F @ ( G @ ( C @ vbinop ) ) ) ) )
& ( D @ visSomeExp )
& ( D
= ( E @ ( F @ vreduceExp ) ) )
& ~ ( F @ vexpIsValue ) )
& ( C @ vexpIsValue ) ) ) ) ).
thf(sk89_def,definition,
( sk89
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vOptExp] :
? [D: vAnsMap,E: vExp] :
( ? [F: vBinOpT] :
( ( ( A @ ( B @ vreduceExp ) )
= ( C @ vgetExp @ ( F @ ( B @ ( A @ sk88 ) @ vbinop ) ) @ vsomeExp ) )
& ( A = D )
& ( B
= ( E @ ( F @ ( B @ ( A @ sk88 ) @ vbinop ) ) ) ) )
& ( C @ visSomeExp )
& ( C
= ( D @ ( E @ vreduceExp ) ) )
& ~ ( E @ vexpIsValue ) ) ) ) ).
thf(sk90_def,definition,
( sk90
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAnsMap] :
? [D: vExp] :
( ? [E: vBinOpT] :
( ( ( A @ ( B @ vreduceExp ) )
= ( B @ ( A @ sk89 ) @ vgetExp @ ( E @ ( B @ ( A @ sk88 ) @ vbinop ) ) @ vsomeExp ) )
& ( A = C )
& ( B
= ( D @ ( E @ ( B @ ( A @ sk88 ) @ vbinop ) ) ) ) )
& ( B @ ( A @ sk89 ) @ visSomeExp )
& ( ( B @ ( A @ sk89 ) )
= ( C @ ( D @ vreduceExp ) ) )
& ~ ( D @ vexpIsValue ) ) ) ) ).
thf(sk91_def,definition,
( sk91
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
( ? [D: vBinOpT] :
( ( ( A @ ( B @ vreduceExp ) )
= ( B @ ( A @ sk89 ) @ vgetExp @ ( D @ ( B @ ( A @ sk88 ) @ vbinop ) ) @ vsomeExp ) )
& ( A
= ( B @ ( A @ sk90 ) ) )
& ( B
= ( C @ ( D @ ( B @ ( A @ sk88 ) @ vbinop ) ) ) ) )
& ( B @ ( A @ sk89 ) @ visSomeExp )
& ( ( B @ ( A @ sk89 ) )
= ( B @ ( A @ sk90 ) @ ( C @ vreduceExp ) ) )
& ~ ( C @ vexpIsValue ) ) ) ) ).
thf(sk92_def,definition,
( sk92
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vBinOpT] :
( ( ( A @ ( B @ vreduceExp ) )
= ( B @ ( A @ sk89 ) @ vgetExp @ ( C @ ( B @ ( A @ sk88 ) @ vbinop ) ) @ vsomeExp ) )
& ( A
= ( B @ ( A @ sk90 ) ) )
& ( B
= ( B @ ( A @ sk91 ) @ ( C @ ( B @ ( A @ sk88 ) @ vbinop ) ) ) ) ) ) ) ).
thf(sk94_def,definition,
( sk94
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
( ? [D: vOptExp,E: vAnsMap,F: vExp] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = E )
& ? [G: vBinOpT] :
( B
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ~ ( D @ visSomeExp )
& ( D
= ( E @ ( F @ vreduceExp ) ) )
& ~ ( F @ vexpIsValue ) )
& ( C @ vexpIsValue ) ) ) ) ).
thf(sk95_def,definition,
( sk95
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vOptExp] :
? [D: vAnsMap,E: vExp] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = D )
& ? [F: vBinOpT] :
( B
= ( E @ ( F @ ( B @ ( A @ sk94 ) @ vbinop ) ) ) )
& ~ ( C @ visSomeExp )
& ( C
= ( D @ ( E @ vreduceExp ) ) )
& ~ ( E @ vexpIsValue ) ) ) ) ).
thf(sk96_def,definition,
( sk96
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAnsMap] :
? [D: vExp] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = C )
& ? [E: vBinOpT] :
( B
= ( D @ ( E @ ( B @ ( A @ sk94 ) @ vbinop ) ) ) )
& ~ ( B @ ( A @ sk95 ) @ visSomeExp )
& ( ( B @ ( A @ sk95 ) )
= ( C @ ( D @ vreduceExp ) ) )
& ~ ( D @ vexpIsValue ) ) ) ) ).
thf(sk97_def,definition,
( sk97
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A
= ( B @ ( A @ sk96 ) ) )
& ? [D: vBinOpT] :
( B
= ( C @ ( D @ ( B @ ( A @ sk94 ) @ vbinop ) ) ) )
& ~ ( B @ ( A @ sk95 ) @ visSomeExp )
& ( ( B @ ( A @ sk95 ) )
= ( B @ ( A @ sk96 ) @ ( C @ vreduceExp ) ) )
& ~ ( C @ vexpIsValue ) ) ) ) ).
thf(sk98_def,definition,
( sk98
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vBinOpT] :
( B
= ( B @ ( A @ sk97 ) @ ( C @ ( B @ ( A @ sk94 ) @ vbinop ) ) ) ) ) ) ).
thf(sk100_def,definition,
( sk100
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
( ? [D: vOptExp,E: vAnsMap] :
( ? [F: vExp,G: vBinOpT] :
( ( ( A @ ( B @ vreduceExp ) )
= ( F @ ( G @ ( D @ vgetExp @ vbinop ) ) @ vsomeExp ) )
& ( A = E )
& ( B
= ( F @ ( G @ ( C @ vbinop ) ) ) ) )
& ( D @ visSomeExp )
& ( D
= ( E @ ( C @ vreduceExp ) ) ) )
& ~ ( C @ vexpIsValue ) ) ) ) ).
thf(sk101_def,definition,
( sk101
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vOptExp] :
? [D: vAnsMap] :
( ? [E: vExp,F: vBinOpT] :
( ( ( A @ ( B @ vreduceExp ) )
= ( E @ ( F @ ( C @ vgetExp @ vbinop ) ) @ vsomeExp ) )
& ( A = D )
& ( B
= ( E @ ( F @ ( B @ ( A @ sk100 ) @ vbinop ) ) ) ) )
& ( C @ visSomeExp )
& ( C
= ( D @ ( B @ ( A @ sk100 ) @ vreduceExp ) ) ) ) ) ) ).
thf(sk102_def,definition,
( sk102
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAnsMap] :
( ? [D: vExp,E: vBinOpT] :
( ( ( A @ ( B @ vreduceExp ) )
= ( D @ ( E @ ( B @ ( A @ sk101 ) @ vgetExp @ vbinop ) ) @ vsomeExp ) )
& ( A = C )
& ( B
= ( D @ ( E @ ( B @ ( A @ sk100 ) @ vbinop ) ) ) ) )
& ( B @ ( A @ sk101 ) @ visSomeExp )
& ( ( B @ ( A @ sk101 ) )
= ( C @ ( B @ ( A @ sk100 ) @ vreduceExp ) ) ) ) ) ) ).
thf(sk103_def,definition,
( sk103
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
? [D: vBinOpT] :
( ( ( A @ ( B @ vreduceExp ) )
= ( C @ ( D @ ( B @ ( A @ sk101 ) @ vgetExp @ vbinop ) ) @ vsomeExp ) )
& ( A
= ( B @ ( A @ sk102 ) ) )
& ( B
= ( C @ ( D @ ( B @ ( A @ sk100 ) @ vbinop ) ) ) ) ) ) ) ).
thf(sk104_def,definition,
( sk104
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vBinOpT] :
( ( ( A @ ( B @ vreduceExp ) )
= ( B @ ( A @ sk103 ) @ ( C @ ( B @ ( A @ sk101 ) @ vgetExp @ vbinop ) ) @ vsomeExp ) )
& ( A
= ( B @ ( A @ sk102 ) ) )
& ( B
= ( B @ ( A @ sk103 ) @ ( C @ ( B @ ( A @ sk100 ) @ vbinop ) ) ) ) ) ) ) ).
thf(sk106_def,definition,
( sk106
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
( ? [D: vOptExp,E: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = E )
& ? [F: vExp,G: vBinOpT] :
( B
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ~ ( D @ visSomeExp )
& ( D
= ( E @ ( C @ vreduceExp ) ) ) )
& ~ ( C @ vexpIsValue ) ) ) ) ).
thf(sk107_def,definition,
( sk107
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vOptExp] :
? [D: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = D )
& ? [E: vExp,F: vBinOpT] :
( B
= ( E @ ( F @ ( B @ ( A @ sk106 ) @ vbinop ) ) ) )
& ~ ( C @ visSomeExp )
& ( C
= ( D @ ( B @ ( A @ sk106 ) @ vreduceExp ) ) ) ) ) ) ).
thf(sk108_def,definition,
( sk108
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = C )
& ? [D: vExp,E: vBinOpT] :
( B
= ( D @ ( E @ ( B @ ( A @ sk106 ) @ vbinop ) ) ) )
& ~ ( B @ ( A @ sk107 ) @ visSomeExp )
& ( ( B @ ( A @ sk107 ) )
= ( C @ ( B @ ( A @ sk106 ) @ vreduceExp ) ) ) ) ) ) ).
thf(sk109_def,definition,
( sk109
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
? [D: vBinOpT] :
( B
= ( C @ ( D @ ( B @ ( A @ sk106 ) @ vbinop ) ) ) ) ) ) ).
thf(sk110_def,definition,
( sk110
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vBinOpT] :
( B
= ( B @ ( A @ sk109 ) @ ( C @ ( B @ ( A @ sk106 ) @ vbinop ) ) ) ) ) ) ).
thf(sk112_def,definition,
( sk112
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vUnOpT] :
? [D: vExp] :
( ( ( A @ ( B @ vreduceExp ) )
= ( D @ vgetExpValue @ ( C @ vevalUnOp ) ) )
& ? [E: vAnsMap] : ( A = E )
& ( B
= ( D @ ( C @ vunop ) ) )
& ( D @ vexpIsValue ) ) ) ) ).
thf(sk113_def,definition,
( sk113
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
( ( ( A @ ( B @ vreduceExp ) )
= ( C @ vgetExpValue @ ( B @ ( A @ sk112 ) @ vevalUnOp ) ) )
& ? [D: vAnsMap] : ( A = D )
& ( B
= ( C @ ( B @ ( A @ sk112 ) @ vunop ) ) )
& ( C @ vexpIsValue ) ) ) ) ).
thf(sk114_def,definition,
( sk114
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAnsMap] : ( A = C ) ) ) ).
thf(sk116_def,definition,
( sk116
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vUnOpT] :
? [D: vExp] :
( ? [E: vOptExp,F: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= ( E @ vgetExp @ ( C @ vunop ) @ vsomeExp ) )
& ( A = F )
& ( B
= ( D @ ( C @ vunop ) ) )
& ( E @ visSomeExp )
& ( E
= ( F @ ( D @ vreduceExp ) ) ) )
& ~ ( D @ vexpIsValue ) ) ) ) ).
thf(sk117_def,definition,
( sk117
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
( ? [D: vOptExp,E: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= ( D @ vgetExp @ ( B @ ( A @ sk116 ) @ vunop ) @ vsomeExp ) )
& ( A = E )
& ( B
= ( C @ ( B @ ( A @ sk116 ) @ vunop ) ) )
& ( D @ visSomeExp )
& ( D
= ( E @ ( C @ vreduceExp ) ) ) )
& ~ ( C @ vexpIsValue ) ) ) ) ).
thf(sk118_def,definition,
( sk118
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vOptExp] :
? [D: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= ( C @ vgetExp @ ( B @ ( A @ sk116 ) @ vunop ) @ vsomeExp ) )
& ( A = D )
& ( B
= ( B @ ( A @ sk117 ) @ ( B @ ( A @ sk116 ) @ vunop ) ) )
& ( C @ visSomeExp )
& ( C
= ( D @ ( B @ ( A @ sk117 ) @ vreduceExp ) ) ) ) ) ) ).
thf(sk119_def,definition,
( sk119
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= ( B @ ( A @ sk118 ) @ vgetExp @ ( B @ ( A @ sk116 ) @ vunop ) @ vsomeExp ) )
& ( A = C )
& ( B
= ( B @ ( A @ sk117 ) @ ( B @ ( A @ sk116 ) @ vunop ) ) )
& ( B @ ( A @ sk118 ) @ visSomeExp )
& ( ( B @ ( A @ sk118 ) )
= ( C @ ( B @ ( A @ sk117 ) @ vreduceExp ) ) ) ) ) ) ).
thf(sk120_def,definition,
( sk120
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vUnOpT] :
? [D: vExp] :
( ? [E: vOptExp,F: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = F )
& ( B
= ( D @ ( C @ vunop ) ) )
& ~ ( E @ visSomeExp )
& ( E
= ( F @ ( D @ vreduceExp ) ) ) )
& ~ ( D @ vexpIsValue ) ) ) ) ).
thf(sk121_def,definition,
( sk121
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vExp] :
( ? [D: vOptExp,E: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = E )
& ( B
= ( C @ ( B @ ( A @ sk120 ) @ vunop ) ) )
& ~ ( D @ visSomeExp )
& ( D
= ( E @ ( C @ vreduceExp ) ) ) )
& ~ ( C @ vexpIsValue ) ) ) ) ).
thf(sk122_def,definition,
( sk122
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vOptExp] :
? [D: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = D )
& ( B
= ( B @ ( A @ sk121 ) @ ( B @ ( A @ sk120 ) @ vunop ) ) )
& ~ ( C @ visSomeExp )
& ( C
= ( D @ ( B @ ( A @ sk121 ) @ vreduceExp ) ) ) ) ) ) ).
thf(sk123_def,definition,
( sk123
= ( ^ [A: vAnsMap,B: vExp] :
@+[C: vAnsMap] :
( ( ( A @ ( B @ vreduceExp ) )
= vnoExp )
& ( A = C )
& ( B
= ( B @ ( A @ sk121 ) @ ( B @ ( A @ sk120 ) @ vunop ) ) )
& ~ ( B @ ( A @ sk122 ) @ visSomeExp )
& ( ( B @ ( A @ sk122 ) )
= ( C @ ( B @ ( A @ sk121 ) @ vreduceExp ) ) ) ) ) ) ).
thf(sk125_def,definition,
( sk125
= ( ^ [A: vAType,B: vLabel] :
@+[C: vLabel] :
( ( ( A @ ( B @ vgetAnswer ) )
= ( C @ vaskYesNo @ vB ) )
& ( A = vYesNo )
& ( B = C ) ) ) ) ).
thf(sk127_def,definition,
( sk127
= ( ^ [A: vAType,B: vLabel] :
@+[C: vLabel] :
( ( ( A @ ( B @ vgetAnswer ) )
= ( C @ vaskNumber @ vNum ) )
& ( A = vNumber )
& ( B = C ) ) ) ) ).
thf(sk128_def,definition,
( sk128
= ( ^ [A: vAType,B: vLabel] :
@+[C: vLabel] :
( ( ( A @ ( B @ vgetAnswer ) )
= ( C @ vaskText @ vT ) )
& ( A = vText )
& ( B = C ) ) ) ) ).
thf(sk129_def,definition,
( sk129
= ( @+[A: vLabel > vAType > vOptQuestion > vQID] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vsomeQuestion ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk130_def,definition,
( sk130
= ( @+[A: vQID > vAType > vOptQuestion > vLabel] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vsomeQuestion ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk131_def,definition,
( sk131
= ( @+[A: vQID > vLabel > vOptQuestion > vAType] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vsomeQuestion ) ) @ ( C @ ( B @ A ) ) )
= D ) ) ) ).
thf(sk132_def,definition,
( sk132
= ( @+[A: vBinOpT > vExp > vExp > vExp] :
! [B: vExp,C: vBinOpT,D: vExp] :
( ( D @ ( C @ ( B @ vbinop ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk133_def,definition,
( sk133
= ( @+[A: vExp > vExp > vExp > vBinOpT] :
! [B: vExp,C: vBinOpT,D: vExp] :
( ( D @ ( C @ ( B @ vbinop ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk134_def,definition,
( sk134
= ( @+[A: vExp > vBinOpT > vExp > vExp] :
! [B: vExp,C: vBinOpT,D: vExp] :
( ( D @ ( C @ ( B @ vbinop ) ) @ ( C @ ( B @ A ) ) )
= D ) ) ) ).
thf(sk135_def,definition,
( sk135
= ( @+[A: vExp > vQID] :
! [B: vQID] :
( ( B @ vqvar @ A )
= B ) ) ) ).
thf(sk136_def,definition,
( sk136
= ( @+[A: vExp > vExp > vUnOpT] :
! [B: vUnOpT,C: vExp] :
( ( C @ ( B @ vunop ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk137_def,definition,
( sk137
= ( @+[A: vUnOpT > vExp > vExp] :
! [B: vUnOpT,C: vExp] :
( ( C @ ( B @ vunop ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk138_def,definition,
( sk138
= ( @+[A: vAval > vYN] :
! [B: vYN] :
( ( B @ vB @ A )
= B ) ) ) ).
thf(sk140_def,definition,
( sk140
= ( ^ [A: vYN,B: vYN] :
@+[C: vYN] :
? [D: vYN] :
( ( ( A @ ( B @ vand ) )
= vno )
& ( A = D )
& ( B = C )
& ( ( D != vyes )
| ( C != vyes ) ) ) ) ) ).
thf(sk141_def,definition,
( sk141
= ( ^ [A: vYN,B: vYN] :
@+[C: vYN] :
( ( ( A @ ( B @ vand ) )
= vno )
& ( A = C )
& ( B
= ( B @ ( A @ sk140 ) ) )
& ( ( C != vyes )
| ( ( B @ ( A @ sk140 ) )
!= vyes ) ) ) ) ) ).
thf(sk142_def,definition,
( sk142
= ( @+[A: vQuestionnaire > vQuestionnaire > vQuestionnaire] :
! [B: vQuestionnaire,C: vQuestionnaire] :
( ( C @ ( B @ vqseq ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk143_def,definition,
( sk143
= ( @+[A: vQuestionnaire > vQuestionnaire > vQuestionnaire] :
! [B: vQuestionnaire,C: vQuestionnaire] :
( ( C @ ( B @ vqseq ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk150_def,definition,
( sk150
= ( @+[A: vEntry > vQID] :
! [B: vQID] :
( ( B @ vask @ A )
= B ) ) ) ).
thf(sk152_def,definition,
( sk152
= ( ^ [A: vYN,B: vYN] :
@+[C: vYN] :
? [D: vYN] :
( ( ( A @ ( B @ vor ) )
= vyes )
& ( A = D )
& ( B = C )
& ( ( D != vno )
| ( C != vno ) ) ) ) ) ).
thf(sk153_def,definition,
( sk153
= ( ^ [A: vYN,B: vYN] :
@+[C: vYN] :
( ( ( A @ ( B @ vor ) )
= vyes )
& ( A = C )
& ( B
= ( B @ ( A @ sk152 ) ) )
& ( ( C != vno )
| ( ( B @ ( A @ sk152 ) )
!= vno ) ) ) ) ) ).
thf(sk154_def,definition,
( sk154
= ( @+[A: vLabel > vAType > vEntry > vQID] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vdefquestion ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk155_def,definition,
( sk155
= ( @+[A: vQID > vAType > vEntry > vLabel] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vdefquestion ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk156_def,definition,
( sk156
= ( @+[A: vQID > vLabel > vEntry > vAType] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vdefquestion ) ) @ ( C @ ( B @ A ) ) )
= D ) ) ) ).
thf(sk158_def,definition,
( sk158
= ( ^ [A: vATMap,B: vQID] :
@+[C: vQID] : ( B = C ) ) ) ).
thf(sk160_def,definition,
( sk160
= ( ^ [A: vATMap,B: vQID] :
@+[C: vQID] :
? [D: vAType,E: vATMap,F: vQID] :
( ( ( A @ ( B @ vlookupATMap ) )
= ( D @ vsomeAType ) )
& ( A
= ( E @ ( D @ ( C @ vatmbind ) ) ) )
& ( B = F )
& ( F = C ) ) ) ) ).
thf(sk161_def,definition,
( sk161
= ( ^ [A: vATMap,B: vQID] :
@+[C: vAType] :
? [D: vATMap,E: vQID] :
( ( ( A @ ( B @ vlookupATMap ) )
= ( C @ vsomeAType ) )
& ( A
= ( D @ ( C @ ( B @ ( A @ sk160 ) @ vatmbind ) ) ) )
& ( B = E )
& ( E
= ( B @ ( A @ sk160 ) ) ) ) ) ) ).
thf(sk162_def,definition,
( sk162
= ( ^ [A: vATMap,B: vQID] :
@+[C: vATMap] :
? [D: vQID] :
( ( ( A @ ( B @ vlookupATMap ) )
= ( B @ ( A @ sk161 ) @ vsomeAType ) )
& ( A
= ( C @ ( B @ ( A @ sk161 ) @ ( B @ ( A @ sk160 ) @ vatmbind ) ) ) )
& ( B = D )
& ( D
= ( B @ ( A @ sk160 ) ) ) ) ) ) ).
thf(sk163_def,definition,
( sk163
= ( ^ [A: vATMap,B: vQID] :
@+[C: vQID] :
( ( ( A @ ( B @ vlookupATMap ) )
= ( B @ ( A @ sk161 ) @ vsomeAType ) )
& ( A
= ( B @ ( A @ sk162 ) @ ( B @ ( A @ sk161 ) @ ( B @ ( A @ sk160 ) @ vatmbind ) ) ) )
& ( B = C )
& ( C
= ( B @ ( A @ sk160 ) ) ) ) ) ) ).
thf(sk164_def,definition,
( sk164
= ( ^ [A: vATMap,B: vQID] :
@+[C: vQID] :
? [D: vAType,E: vATMap,F: vQID] :
( ( ( A @ ( B @ vlookupATMap ) )
= ( E @ ( F @ vlookupATMap ) ) )
& ( A
= ( E @ ( D @ ( C @ vatmbind ) ) ) )
& ( B = F )
& ( F != C ) ) ) ) ).
thf(sk165_def,definition,
( sk165
= ( ^ [A: vATMap,B: vQID] :
@+[C: vAType] :
? [D: vATMap,E: vQID] :
( ( ( A @ ( B @ vlookupATMap ) )
= ( D @ ( E @ vlookupATMap ) ) )
& ( A
= ( D @ ( C @ ( B @ ( A @ sk164 ) @ vatmbind ) ) ) )
& ( B = E )
& ( E
!= ( B @ ( A @ sk164 ) ) ) ) ) ) ).
thf(sk166_def,definition,
( sk166
= ( ^ [A: vATMap,B: vQID] :
@+[C: vATMap] :
? [D: vQID] :
( ( ( A @ ( B @ vlookupATMap ) )
= ( C @ ( D @ vlookupATMap ) ) )
& ( A
= ( C @ ( B @ ( A @ sk165 ) @ ( B @ ( A @ sk164 ) @ vatmbind ) ) ) )
& ( B = D )
& ( D
!= ( B @ ( A @ sk164 ) ) ) ) ) ) ).
thf(sk167_def,definition,
( sk167
= ( ^ [A: vATMap,B: vQID] :
@+[C: vQID] :
( ( ( A @ ( B @ vlookupATMap ) )
= ( B @ ( A @ sk166 ) @ ( C @ vlookupATMap ) ) )
& ( A
= ( B @ ( A @ sk166 ) @ ( B @ ( A @ sk165 ) @ ( B @ ( A @ sk164 ) @ vatmbind ) ) ) )
& ( B = C )
& ( C
!= ( B @ ( A @ sk164 ) ) ) ) ) ) ).
thf(sk170_def,definition,
( sk170
= ( ^ [A: vQMap,B: vQID] :
@+[C: vQID] : ( B = C ) ) ) ).
thf(sk172_def,definition,
( sk172
= ( ^ [A: vQMap,B: vQID] :
@+[C: vQMap] :
? [D: vQID,E: vAType,F: vLabel,G: vQID] :
( ( ( A @ ( B @ vlookupQMap ) )
= ( E @ ( F @ ( G @ vsomeQuestion ) ) ) )
& ( A
= ( C @ ( E @ ( F @ ( D @ vqmbind ) ) ) ) )
& ( B = G )
& ( G = D ) ) ) ) ).
thf(sk173_def,definition,
( sk173
= ( ^ [A: vQMap,B: vQID] :
@+[C: vQID] :
? [D: vAType,E: vLabel,F: vQID] :
( ( ( A @ ( B @ vlookupQMap ) )
= ( D @ ( E @ ( F @ vsomeQuestion ) ) ) )
& ( A
= ( B @ ( A @ sk172 ) @ ( D @ ( E @ ( C @ vqmbind ) ) ) ) )
& ( B = F )
& ( F = C ) ) ) ) ).
thf(sk174_def,definition,
( sk174
= ( ^ [A: vQMap,B: vQID] :
@+[C: vAType] :
? [D: vLabel,E: vQID] :
( ( ( A @ ( B @ vlookupQMap ) )
= ( C @ ( D @ ( E @ vsomeQuestion ) ) ) )
& ( A
= ( B @ ( A @ sk172 ) @ ( C @ ( D @ ( B @ ( A @ sk173 ) @ vqmbind ) ) ) ) )
& ( B = E )
& ( E
= ( B @ ( A @ sk173 ) ) ) ) ) ) ).
thf(sk175_def,definition,
( sk175
= ( ^ [A: vQMap,B: vQID] :
@+[C: vLabel] :
? [D: vQID] :
( ( ( A @ ( B @ vlookupQMap ) )
= ( B @ ( A @ sk174 ) @ ( C @ ( D @ vsomeQuestion ) ) ) )
& ( A
= ( B @ ( A @ sk172 ) @ ( B @ ( A @ sk174 ) @ ( C @ ( B @ ( A @ sk173 ) @ vqmbind ) ) ) ) )
& ( B = D )
& ( D
= ( B @ ( A @ sk173 ) ) ) ) ) ) ).
thf(sk176_def,definition,
( sk176
= ( ^ [A: vQMap,B: vQID] :
@+[C: vQID] :
( ( ( A @ ( B @ vlookupQMap ) )
= ( B @ ( A @ sk174 ) @ ( B @ ( A @ sk175 ) @ ( C @ vsomeQuestion ) ) ) )
& ( A
= ( B @ ( A @ sk172 ) @ ( B @ ( A @ sk174 ) @ ( B @ ( A @ sk175 ) @ ( B @ ( A @ sk173 ) @ vqmbind ) ) ) ) )
& ( B = C )
& ( C
= ( B @ ( A @ sk173 ) ) ) ) ) ) ).
thf(sk177_def,definition,
( sk177
= ( ^ [A: vQMap,B: vQID] :
@+[C: vQMap] :
? [D: vQID,E: vAType,F: vLabel,G: vQID] :
( ( ( A @ ( B @ vlookupQMap ) )
= ( C @ ( G @ vlookupQMap ) ) )
& ( A
= ( C @ ( E @ ( F @ ( D @ vqmbind ) ) ) ) )
& ( B = G )
& ( G != D ) ) ) ) ).
thf(sk178_def,definition,
( sk178
= ( ^ [A: vQMap,B: vQID] :
@+[C: vQID] :
? [D: vAType,E: vLabel,F: vQID] :
( ( ( A @ ( B @ vlookupQMap ) )
= ( B @ ( A @ sk177 ) @ ( F @ vlookupQMap ) ) )
& ( A
= ( B @ ( A @ sk177 ) @ ( D @ ( E @ ( C @ vqmbind ) ) ) ) )
& ( B = F )
& ( F != C ) ) ) ) ).
thf(sk179_def,definition,
( sk179
= ( ^ [A: vQMap,B: vQID] :
@+[C: vAType] :
? [D: vLabel,E: vQID] :
( ( ( A @ ( B @ vlookupQMap ) )
= ( B @ ( A @ sk177 ) @ ( E @ vlookupQMap ) ) )
& ( A
= ( B @ ( A @ sk177 ) @ ( C @ ( D @ ( B @ ( A @ sk178 ) @ vqmbind ) ) ) ) )
& ( B = E )
& ( E
!= ( B @ ( A @ sk178 ) ) ) ) ) ) ).
thf(sk180_def,definition,
( sk180
= ( ^ [A: vQMap,B: vQID] :
@+[C: vLabel] :
? [D: vQID] :
( ( ( A @ ( B @ vlookupQMap ) )
= ( B @ ( A @ sk177 ) @ ( D @ vlookupQMap ) ) )
& ( A
= ( B @ ( A @ sk177 ) @ ( B @ ( A @ sk179 ) @ ( C @ ( B @ ( A @ sk178 ) @ vqmbind ) ) ) ) )
& ( B = D )
& ( D
!= ( B @ ( A @ sk178 ) ) ) ) ) ) ).
thf(sk181_def,definition,
( sk181
= ( ^ [A: vQMap,B: vQID] :
@+[C: vQID] :
( ( ( A @ ( B @ vlookupQMap ) )
= ( B @ ( A @ sk177 ) @ ( C @ vlookupQMap ) ) )
& ( A
= ( B @ ( A @ sk177 ) @ ( B @ ( A @ sk179 ) @ ( B @ ( A @ sk180 ) @ ( B @ ( A @ sk178 ) @ vqmbind ) ) ) ) )
& ( B = C )
& ( C
!= ( B @ ( A @ sk178 ) ) ) ) ) ) ).
thf(sk182_def,definition,
( sk182
= ( @+[A: vOptAType > vAType] :
! [B: vAType] :
( ( B @ vsomeAType @ A )
= B ) ) ) ).
thf(sk188_def,definition,
( sk188
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vATMap] : ( A = C ) ) ) ).
thf(sk190_def,definition,
( sk190
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vATMap] :
? [D: vATMap,E: vOptAType,F: vAType,G: vATMap] :
( ? [H: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= ( D @ ( F @ ( H @ vatmbind ) ) ) )
& ( A = C )
& ( B
= ( G @ ( F @ ( H @ vatmbind ) ) ) )
& ( ( E @ vgetAType )
= F )
& ( E @ visSomeAType )
& ( E
= ( C @ ( H @ vlookupATMap ) ) ) )
& ( D
= ( C @ ( G @ vintersectATM ) ) ) ) ) ) ).
thf(sk191_def,definition,
( sk191
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vATMap] :
? [D: vOptAType,E: vAType,F: vATMap] :
( ? [G: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= ( C @ ( E @ ( G @ vatmbind ) ) ) )
& ( A
= ( B @ ( A @ sk190 ) ) )
& ( B
= ( F @ ( E @ ( G @ vatmbind ) ) ) )
& ( ( D @ vgetAType )
= E )
& ( D @ visSomeAType )
& ( D
= ( B @ ( A @ sk190 ) @ ( G @ vlookupATMap ) ) ) )
& ( C
= ( B @ ( A @ sk190 ) @ ( F @ vintersectATM ) ) ) ) ) ) ).
thf(sk192_def,definition,
( sk192
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vOptAType] :
? [D: vAType,E: vATMap] :
( ? [F: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= ( B @ ( A @ sk191 ) @ ( D @ ( F @ vatmbind ) ) ) )
& ( A
= ( B @ ( A @ sk190 ) ) )
& ( B
= ( E @ ( D @ ( F @ vatmbind ) ) ) )
& ( ( C @ vgetAType )
= D )
& ( C @ visSomeAType )
& ( C
= ( B @ ( A @ sk190 ) @ ( F @ vlookupATMap ) ) ) )
& ( ( B @ ( A @ sk191 ) )
= ( B @ ( A @ sk190 ) @ ( E @ vintersectATM ) ) ) ) ) ) ).
thf(sk193_def,definition,
( sk193
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vAType] :
? [D: vATMap] :
( ? [E: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= ( B @ ( A @ sk191 ) @ ( C @ ( E @ vatmbind ) ) ) )
& ( A
= ( B @ ( A @ sk190 ) ) )
& ( B
= ( D @ ( C @ ( E @ vatmbind ) ) ) )
& ( ( B @ ( A @ sk192 ) @ vgetAType )
= C )
& ( B @ ( A @ sk192 ) @ visSomeAType )
& ( ( B @ ( A @ sk192 ) )
= ( B @ ( A @ sk190 ) @ ( E @ vlookupATMap ) ) ) )
& ( ( B @ ( A @ sk191 ) )
= ( B @ ( A @ sk190 ) @ ( D @ vintersectATM ) ) ) ) ) ) ).
thf(sk194_def,definition,
( sk194
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vATMap] :
( ? [D: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= ( B @ ( A @ sk191 ) @ ( B @ ( A @ sk193 ) @ ( D @ vatmbind ) ) ) )
& ( A
= ( B @ ( A @ sk190 ) ) )
& ( B
= ( C @ ( B @ ( A @ sk193 ) @ ( D @ vatmbind ) ) ) )
& ( ( B @ ( A @ sk192 ) @ vgetAType )
= ( B @ ( A @ sk193 ) ) )
& ( B @ ( A @ sk192 ) @ visSomeAType )
& ( ( B @ ( A @ sk192 ) )
= ( B @ ( A @ sk190 ) @ ( D @ vlookupATMap ) ) ) )
& ( ( B @ ( A @ sk191 ) )
= ( B @ ( A @ sk190 ) @ ( C @ vintersectATM ) ) ) ) ) ) ).
thf(sk195_def,definition,
( sk195
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= ( B @ ( A @ sk191 ) @ ( B @ ( A @ sk193 ) @ ( C @ vatmbind ) ) ) )
& ( A
= ( B @ ( A @ sk190 ) ) )
& ( B
= ( B @ ( A @ sk194 ) @ ( B @ ( A @ sk193 ) @ ( C @ vatmbind ) ) ) )
& ( ( B @ ( A @ sk192 ) @ vgetAType )
= ( B @ ( A @ sk193 ) ) )
& ( B @ ( A @ sk192 ) @ visSomeAType )
& ( ( B @ ( A @ sk192 ) )
= ( B @ ( A @ sk190 ) @ ( C @ vlookupATMap ) ) ) ) ) ) ).
thf(sk196_def,definition,
( sk196
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vATMap] :
? [D: vATMap,E: vOptAType,F: vAType,G: vATMap] :
( ? [H: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= D )
& ( A = C )
& ( B
= ( G @ ( F @ ( H @ vatmbind ) ) ) )
& ~ ( ( ( E @ vgetAType )
= F )
& ( E @ visSomeAType ) )
& ( E
= ( C @ ( H @ vlookupATMap ) ) ) )
& ( D
= ( C @ ( G @ vintersectATM ) ) ) ) ) ) ).
thf(sk197_def,definition,
( sk197
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vATMap] :
? [D: vOptAType,E: vAType,F: vATMap] :
( ? [G: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= C )
& ( A
= ( B @ ( A @ sk196 ) ) )
& ( B
= ( F @ ( E @ ( G @ vatmbind ) ) ) )
& ~ ( ( ( D @ vgetAType )
= E )
& ( D @ visSomeAType ) )
& ( D
= ( B @ ( A @ sk196 ) @ ( G @ vlookupATMap ) ) ) )
& ( C
= ( B @ ( A @ sk196 ) @ ( F @ vintersectATM ) ) ) ) ) ) ).
thf(sk198_def,definition,
( sk198
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vOptAType] :
? [D: vAType,E: vATMap] :
( ? [F: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= ( B @ ( A @ sk197 ) ) )
& ( A
= ( B @ ( A @ sk196 ) ) )
& ( B
= ( E @ ( D @ ( F @ vatmbind ) ) ) )
& ~ ( ( ( C @ vgetAType )
= D )
& ( C @ visSomeAType ) )
& ( C
= ( B @ ( A @ sk196 ) @ ( F @ vlookupATMap ) ) ) )
& ( ( B @ ( A @ sk197 ) )
= ( B @ ( A @ sk196 ) @ ( E @ vintersectATM ) ) ) ) ) ) ).
thf(sk199_def,definition,
( sk199
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vAType] :
? [D: vATMap] :
( ? [E: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= ( B @ ( A @ sk197 ) ) )
& ( A
= ( B @ ( A @ sk196 ) ) )
& ( B
= ( D @ ( C @ ( E @ vatmbind ) ) ) )
& ~ ( ( ( B @ ( A @ sk198 ) @ vgetAType )
= C )
& ( B @ ( A @ sk198 ) @ visSomeAType ) )
& ( ( B @ ( A @ sk198 ) )
= ( B @ ( A @ sk196 ) @ ( E @ vlookupATMap ) ) ) )
& ( ( B @ ( A @ sk197 ) )
= ( B @ ( A @ sk196 ) @ ( D @ vintersectATM ) ) ) ) ) ) ).
thf(sk200_def,definition,
( sk200
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vATMap] :
( ? [D: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= ( B @ ( A @ sk197 ) ) )
& ( A
= ( B @ ( A @ sk196 ) ) )
& ( B
= ( C @ ( B @ ( A @ sk199 ) @ ( D @ vatmbind ) ) ) )
& ~ ( ( ( B @ ( A @ sk198 ) @ vgetAType )
= ( B @ ( A @ sk199 ) ) )
& ( B @ ( A @ sk198 ) @ visSomeAType ) )
& ( ( B @ ( A @ sk198 ) )
= ( B @ ( A @ sk196 ) @ ( D @ vlookupATMap ) ) ) )
& ( ( B @ ( A @ sk197 ) )
= ( B @ ( A @ sk196 ) @ ( C @ vintersectATM ) ) ) ) ) ) ).
thf(sk201_def,definition,
( sk201
= ( ^ [A: vATMap,B: vATMap] :
@+[C: vQID] :
( ( ( A @ ( B @ vintersectATM ) )
= ( B @ ( A @ sk197 ) ) )
& ( A
= ( B @ ( A @ sk196 ) ) )
& ( B
= ( B @ ( A @ sk200 ) @ ( B @ ( A @ sk199 ) @ ( C @ vatmbind ) ) ) )
& ~ ( ( ( B @ ( A @ sk198 ) @ vgetAType )
= ( B @ ( A @ sk199 ) ) )
& ( B @ ( A @ sk198 ) @ visSomeAType ) )
& ( ( B @ ( A @ sk198 ) )
= ( B @ ( A @ sk196 ) @ ( C @ vlookupATMap ) ) ) ) ) ) ).
thf(sk203_def,definition,
( sk203
= ( @+[A: vLabel > vAType > vEntry > vQID] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vquestion ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk204_def,definition,
( sk204
= ( @+[A: vQID > vAType > vEntry > vLabel] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vquestion ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk205_def,definition,
( sk205
= ( @+[A: vQID > vLabel > vEntry > vAType] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vquestion ) ) @ ( C @ ( B @ A ) ) )
= D ) ) ) ).
thf(sk207_def,definition,
( sk207
= ( @+[A: vExp > vAval] :
! [B: vAval] :
( ( B @ vconstant @ A )
= B ) ) ) ).
thf(sk216_def,definition,
( sk216
= ( ^ [A: vAType,B: vUnOpT] :
@+[C: vUnOpT] :
? [D: vAType] :
( ( ( A @ ( B @ vcheckUnOp ) )
= vnoAType )
& ( A = D )
& ( B = C )
& ( ( D != vYesNo )
| ( C != vnotop ) ) ) ) ) ).
thf(sk217_def,definition,
( sk217
= ( ^ [A: vAType,B: vUnOpT] :
@+[C: vAType] :
( ( ( A @ ( B @ vcheckUnOp ) )
= vnoAType )
& ( A = C )
& ( B
= ( B @ ( A @ sk216 ) ) )
& ( ( C != vYesNo )
| ( ( B @ ( A @ sk216 ) )
!= vnotop ) ) ) ) ) ).
thf(sk222_def,definition,
( sk222
= ( @+[A: vAType > vATMap > vATMap > vQID] :
! [B: vQID,C: vAType,D: vATMap] :
( ( D @ ( C @ ( B @ vatmbind ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk223_def,definition,
( sk223
= ( @+[A: vQID > vATMap > vATMap > vAType] :
! [B: vQID,C: vAType,D: vATMap] :
( ( D @ ( C @ ( B @ vatmbind ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk224_def,definition,
( sk224
= ( @+[A: vQID > vAType > vATMap > vATMap] :
! [B: vQID,C: vAType,D: vATMap] :
( ( D @ ( C @ ( B @ vatmbind ) ) @ ( C @ ( B @ A ) ) )
= D ) ) ) ).
thf(sk225_def,definition,
( sk225
= ( @+[A: vAval > vAnsMap > vAnsMap > vQID] :
! [B: vQID,C: vAval,D: vAnsMap] :
( ( D @ ( C @ ( B @ vabind ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk226_def,definition,
( sk226
= ( @+[A: vQID > vAnsMap > vAnsMap > vAval] :
! [B: vQID,C: vAval,D: vAnsMap] :
( ( D @ ( C @ ( B @ vabind ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk227_def,definition,
( sk227
= ( @+[A: vQID > vAval > vAnsMap > vAnsMap] :
! [B: vQID,C: vAval,D: vAnsMap] :
( ( D @ ( C @ ( B @ vabind ) ) @ ( C @ ( B @ A ) ) )
= D ) ) ) ).
thf(sk228_def,definition,
( sk228
= ( @+[A: vQuestionnaire > vQuestionnaire > vGID] :
! [B: vGID,C: vQuestionnaire] :
( ( C @ ( B @ vqgroup ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk229_def,definition,
( sk229
= ( @+[A: vGID > vQuestionnaire > vQuestionnaire] :
! [B: vGID,C: vQuestionnaire] :
( ( C @ ( B @ vqgroup ) @ ( B @ A ) )
= C ) ) ) ).
thf(sk230_def,definition,
( sk230
= ( @+[A: vQuestionnaire > vQuestionnaire > vQuestionnaire > vExp] :
! [B: vExp,C: vQuestionnaire,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vqcond ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk231_def,definition,
( sk231
= ( @+[A: vExp > vQuestionnaire > vQuestionnaire > vQuestionnaire] :
! [B: vExp,C: vQuestionnaire,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vqcond ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk232_def,definition,
( sk232
= ( @+[A: vExp > vQuestionnaire > vQuestionnaire > vQuestionnaire] :
! [B: vExp,C: vQuestionnaire,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vqcond ) ) @ ( C @ ( B @ A ) ) )
= D ) ) ) ).
thf(sk242_def,definition,
( sk242
= ( @+[A: vQMap > vQuestionnaire > vQConf > vAnsMap] :
! [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vQC ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk243_def,definition,
( sk243
= ( @+[A: vAnsMap > vQuestionnaire > vQConf > vQMap] :
! [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vQC ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk244_def,definition,
( sk244
= ( @+[A: vAnsMap > vQMap > vQConf > vQuestionnaire] :
! [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vQC ) ) @ ( C @ ( B @ A ) ) )
= D ) ) ) ).
thf(sk245_def,definition,
( sk245
= ( @+[A: vAType > vExp > vEntry > vQID] :
! [B: vQID,C: vAType,D: vExp] :
( ( D @ ( C @ ( B @ vvalue ) ) @ ( D @ ( C @ A ) ) )
= B ) ) ) ).
thf(sk246_def,definition,
( sk246
= ( @+[A: vQID > vExp > vEntry > vAType] :
! [B: vQID,C: vAType,D: vExp] :
( ( D @ ( C @ ( B @ vvalue ) ) @ ( D @ ( B @ A ) ) )
= C ) ) ) ).
thf(sk247_def,definition,
( sk247
= ( @+[A: vQID > vAType > vEntry > vExp] :
! [B: vQID,C: vAType,D: vExp] :
( ( D @ ( C @ ( B @ vvalue ) ) @ ( C @ ( B @ A ) ) )
= D ) ) ) ).
thf(sk253_def,definition,
( sk253
= ( ^ [A: vMapConf] :
@+[B: vATMap] :
? [C: vATMap] :
( A
= ( C @ ( B @ vMC ) ) ) ) ) ).
thf(sk254_def,definition,
( sk254
= ( ^ [A: vMapConf] :
@+[B: vATMap] :
( A
= ( B @ ( A @ sk253 @ vMC ) ) ) ) ) ).
thf(sk255_def,definition,
( sk255
= ( ^ [A: vQuestionnaire,B: vQConf] :
@+[C: vAnsMap] :
? [D: vQMap,E: vQuestionnaire] :
( ? [F: vQuestionnaire] :
( ( ( A @ ( B @ vqcappend ) )
= ( F @ ( E @ vqseq ) @ ( D @ ( C @ vQC ) ) ) )
& ( A = F ) )
& ( B
= ( E @ ( D @ ( C @ vQC ) ) ) ) ) ) ) ).
thf(sk256_def,definition,
( sk256
= ( ^ [A: vQuestionnaire,B: vQConf] :
@+[C: vQMap] :
? [D: vQuestionnaire] :
( ? [E: vQuestionnaire] :
( ( ( A @ ( B @ vqcappend ) )
= ( E @ ( D @ vqseq ) @ ( C @ ( B @ ( A @ sk255 ) @ vQC ) ) ) )
& ( A = E ) )
& ( B
= ( D @ ( C @ ( B @ ( A @ sk255 ) @ vQC ) ) ) ) ) ) ) ).
thf(sk257_def,definition,
( sk257
= ( ^ [A: vQuestionnaire,B: vQConf] :
@+[C: vQuestionnaire] :
( ? [D: vQuestionnaire] :
( ( ( A @ ( B @ vqcappend ) )
= ( D @ ( C @ vqseq ) @ ( B @ ( A @ sk256 ) @ ( B @ ( A @ sk255 ) @ vQC ) ) ) )
& ( A = D ) )
& ( B
= ( C @ ( B @ ( A @ sk256 ) @ ( B @ ( A @ sk255 ) @ vQC ) ) ) ) ) ) ) ).
thf(sk258_def,definition,
( sk258
= ( ^ [A: vQuestionnaire,B: vQConf] :
@+[C: vQuestionnaire] :
( ( ( A @ ( B @ vqcappend ) )
= ( C @ ( B @ ( A @ sk257 ) @ vqseq ) @ ( B @ ( A @ sk256 ) @ ( B @ ( A @ sk255 ) @ vQC ) ) ) )
& ( A = C ) ) ) ) ).
thf(sk261_def,definition,
( sk261
= ( ^ [A: vQConf] :
@+[B: vAnsMap] :
? [C: vQMap,D: vQuestionnaire] :
( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ) ) ).
thf(sk262_def,definition,
( sk262
= ( ^ [A: vQConf] :
@+[B: vQMap] :
? [C: vQuestionnaire] :
( A
= ( C @ ( B @ ( A @ sk261 @ vQC ) ) ) ) ) ) ).
thf(sk263_def,definition,
( sk263
= ( ^ [A: vQConf] :
@+[B: vQuestionnaire] :
( A
= ( B @ ( A @ sk262 @ ( A @ sk261 @ vQC ) ) ) ) ) ) ).
thf(sk264_def,definition,
( sk264
= ( @+[A: vOptQConf > vQConf] :
! [B: vQConf] :
( ( B @ vsomeQConf @ A )
= B ) ) ) ).
thf(sk354_def,definition,
( sk354
= ( ^ [A: vQuestionnaire] :
@+[B: vQuestionnaire] :
( ( A = B )
& ( B != vqempty ) ) ) ) ).
thf(sk363_def,definition,
( sk363
= ( @+[A: vQuestionnaire > vEntry] :
! [B: vEntry] :
( ( B @ vqsingle @ A )
= B ) ) ) ).
thf(sk367_def,definition,
( sk367
= ( ^ [A: vQConf] :
@+[B: vAnsMap] :
? [C: vQMap,D: vQuestionnaire] :
( ( ( A @ vgetQuest )
= D )
& ( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ) ) ) ).
thf(sk368_def,definition,
( sk368
= ( ^ [A: vQConf] :
@+[B: vQMap] :
? [C: vQuestionnaire] :
( ( ( A @ vgetQuest )
= C )
& ( A
= ( C @ ( B @ ( A @ sk367 @ vQC ) ) ) ) ) ) ) ).
thf(sk369_def,definition,
( sk369
= ( ^ [A: vQConf] :
@+[B: vQuestionnaire] :
( ( ( A @ vgetQuest )
= B )
& ( A
= ( B @ ( A @ sk368 @ ( A @ sk367 @ vQC ) ) ) ) ) ) ) ).
thf(sk386_def,definition,
( sk386
= ( ^ [A: vQConf] :
@+[B: vAnsMap] :
( ( ( A @ vgetAM )
= B )
& ? [C: vQMap,D: vQuestionnaire] :
( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ) ) ) ).
thf(sk387_def,definition,
( sk387
= ( ^ [A: vQConf] :
@+[B: vQMap] :
? [C: vQuestionnaire] :
( A
= ( C @ ( B @ ( A @ sk386 @ vQC ) ) ) ) ) ) ).
thf(sk388_def,definition,
( sk388
= ( ^ [A: vQConf] :
@+[B: vQuestionnaire] :
( A
= ( B @ ( A @ sk387 @ ( A @ sk386 @ vQC ) ) ) ) ) ) ).
thf(sk399_def,definition,
( sk399
= ( ^ [A: vQConf] :
@+[B: vAnsMap] :
? [C: vQMap] :
( ( ( A @ vgetQM )
= C )
& ? [D: vQuestionnaire] :
( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ) ) ) ).
thf(sk400_def,definition,
( sk400
= ( ^ [A: vQConf] :
@+[B: vQMap] :
( ( ( A @ vgetQM )
= B )
& ? [C: vQuestionnaire] :
( A
= ( C @ ( B @ ( A @ sk399 @ vQC ) ) ) ) ) ) ) ).
thf(sk401_def,definition,
( sk401
= ( ^ [A: vQConf] :
@+[B: vQuestionnaire] :
( A
= ( B @ ( A @ sk400 @ ( A @ sk399 @ vQC ) ) ) ) ) ) ).
thf(sk411_def,definition,
( sk411
= ( @+[A: vATMap > vMapConf > vATMap] :
! [B: vATMap,C: vATMap] :
( ( C @ ( B @ vMC ) @ ( C @ A ) )
= B ) ) ) ).
thf(sk412_def,definition,
( sk412
= ( @+[A: vATMap > vMapConf > vATMap] :
! [B: vATMap,C: vATMap] :
( ( C @ ( B @ vMC ) @ ( B @ A ) )
= C ) ) ) ).
thf(85,axiom,
! [A: vATMap,B: vYN] :
( ( B @ vB @ vconstant @ ( A @ vecheck ) )
= ( vYesNo @ vsomeAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','echeck-0') ).
thf(823,plain,
! [A: vATMap,B: vYN] :
( ( B @ vB @ vconstant @ ( A @ vecheck ) )
= ( vYesNo @ vsomeAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(824,plain,
! [B: vYN,A: vATMap] :
( ( B @ vB @ vconstant @ ( A @ vecheck ) )
= ( vYesNo @ vsomeAType ) ),
inference(cnf,[status(esa)],[823]) ).
thf(825,plain,
! [B: vYN,A: vATMap] :
( ( B @ vB @ vconstant @ ( A @ vecheck ) )
= ( vYesNo @ vsomeAType ) ),
inference(lifteq,[status(thm)],[824]) ).
thf(41,axiom,
! [A: vATMap,B: vExp] :
( ? [C: vUnOpT,D: vExp,E: vOptAType,F: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= vnoAType )
& ( B
= ( D @ ( C @ vunop ) ) )
& ( A = F )
& ~ ( E @ visSomeAType )
& ( E
= ( D @ ( F @ vecheck ) ) ) )
| ? [C: vUnOpT,D: vExp,E: vOptAType,F: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= ( E @ vgetAType @ ( C @ vcheckUnOp ) ) )
& ( B
= ( D @ ( C @ vunop ) ) )
& ( A = F )
& ( E @ visSomeAType )
& ( E
= ( D @ ( F @ vecheck ) ) ) )
| ? [C: vATMap,D: vOptAType,E: vExp,F: vOptAType,G: vExp,H: vBinOpT] :
( ( ( B @ ( A @ vecheck ) )
= vnoAType )
& ( B
= ( G @ ( H @ ( E @ vbinop ) ) ) )
& ( A = C )
& ~ ( ( F @ visSomeAType )
& ( D @ visSomeAType ) )
& ( F
= ( G @ ( C @ vecheck ) ) )
& ( D
= ( E @ ( C @ vecheck ) ) ) )
| ? [C: vATMap,D: vOptAType,E: vExp,F: vOptAType,G: vExp,H: vBinOpT] :
( ( ( B @ ( A @ vecheck ) )
= ( F @ vgetAType @ ( D @ vgetAType @ ( H @ vcheckBinOp ) ) ) )
& ( B
= ( G @ ( H @ ( E @ vbinop ) ) ) )
& ( A = C )
& ( F @ visSomeAType )
& ( D @ visSomeAType )
& ( F
= ( G @ ( C @ vecheck ) ) )
& ( D
= ( E @ ( C @ vecheck ) ) ) )
| ? [C: vQID,D: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= ( D @ ( C @ vlookupATMap ) ) )
& ( B
= ( C @ vqvar ) )
& ( A = D ) )
| ? [C: vstring,D: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= ( vText @ vsomeAType ) )
& ( B
= ( C @ vT @ vconstant ) )
& ( A = D ) )
| ? [C: vnat,D: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= ( vNumber @ vsomeAType ) )
& ( B
= ( C @ vNum @ vconstant ) )
& ( A = D ) )
| ? [C: vATMap,D: vYN] :
( ( ( B @ ( A @ vecheck ) )
= ( vYesNo @ vsomeAType ) )
& ( B
= ( D @ vB @ vconstant ) )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','echeck-INV') ).
thf(417,plain,
! [A: vATMap,B: vExp] :
( ? [C: vUnOpT,D: vExp,E: vOptAType,F: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= vnoAType )
& ( B
= ( D @ ( C @ vunop ) ) )
& ( A = F )
& ~ ( E @ visSomeAType )
& ( E
= ( D @ ( F @ vecheck ) ) ) )
| ? [C: vUnOpT,D: vExp,E: vOptAType,F: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= ( E @ vgetAType @ ( C @ vcheckUnOp ) ) )
& ( B
= ( D @ ( C @ vunop ) ) )
& ( A = F )
& ( E @ visSomeAType )
& ( E
= ( D @ ( F @ vecheck ) ) ) )
| ? [C: vATMap,D: vOptAType,E: vExp,F: vOptAType,G: vExp,H: vBinOpT] :
( ( ( B @ ( A @ vecheck ) )
= vnoAType )
& ( B
= ( G @ ( H @ ( E @ vbinop ) ) ) )
& ( A = C )
& ~ ( ( F @ visSomeAType )
& ( D @ visSomeAType ) )
& ( F
= ( G @ ( C @ vecheck ) ) )
& ( D
= ( E @ ( C @ vecheck ) ) ) )
| ? [C: vATMap,D: vOptAType,E: vExp,F: vOptAType,G: vExp,H: vBinOpT] :
( ( ( B @ ( A @ vecheck ) )
= ( F @ vgetAType @ ( D @ vgetAType @ ( H @ vcheckBinOp ) ) ) )
& ( B
= ( G @ ( H @ ( E @ vbinop ) ) ) )
& ( A = C )
& ( F @ visSomeAType )
& ( D @ visSomeAType )
& ( F
= ( G @ ( C @ vecheck ) ) )
& ( D
= ( E @ ( C @ vecheck ) ) ) )
| ? [C: vQID,D: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= ( D @ ( C @ vlookupATMap ) ) )
& ( B
= ( C @ vqvar ) )
& ( A = D ) )
| ? [C: vstring,D: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= ( vText @ vsomeAType ) )
& ( B
= ( C @ vT @ vconstant ) )
& ( A = D ) )
| ? [C: vnat,D: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= ( vNumber @ vsomeAType ) )
& ( B
= ( C @ vNum @ vconstant ) )
& ( A = D ) )
| ? [C: vATMap,D: vYN] :
( ( ( B @ ( A @ vecheck ) )
= ( vYesNo @ vsomeAType ) )
& ( B
= ( D @ vB @ vconstant ) )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(418,plain,
! [A: vATMap,B: vExp] :
( ? [C: vUnOpT,D: vExp,E: vOptAType,F: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= vnoAType )
& ( B
= ( D @ ( C @ vunop ) ) )
& ( A = F )
& ~ ( E @ visSomeAType )
& ( E
= ( D @ ( F @ vecheck ) ) ) )
| ? [C: vUnOpT,D: vExp,E: vOptAType,F: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= ( E @ vgetAType @ ( C @ vcheckUnOp ) ) )
& ( B
= ( D @ ( C @ vunop ) ) )
& ( A = F )
& ( E @ visSomeAType )
& ( E
= ( D @ ( F @ vecheck ) ) ) )
| ? [C: vATMap,D: vOptAType,E: vExp] :
( ? [F: vOptAType,G: vExp] :
( ( ( B @ ( A @ vecheck ) )
= vnoAType )
& ? [H: vBinOpT] :
( B
= ( G @ ( H @ ( E @ vbinop ) ) ) )
& ( A = C )
& ~ ( ( F @ visSomeAType )
& ( D @ visSomeAType ) )
& ( F
= ( G @ ( C @ vecheck ) ) ) )
& ( D
= ( E @ ( C @ vecheck ) ) ) )
| ? [C: vATMap,D: vOptAType,E: vExp] :
( ? [F: vOptAType,G: vExp] :
( ? [H: vBinOpT] :
( ( ( B @ ( A @ vecheck ) )
= ( F @ vgetAType @ ( D @ vgetAType @ ( H @ vcheckBinOp ) ) ) )
& ( B
= ( G @ ( H @ ( E @ vbinop ) ) ) ) )
& ( A = C )
& ( F @ visSomeAType )
& ( D @ visSomeAType )
& ( F
= ( G @ ( C @ vecheck ) ) ) )
& ( D
= ( E @ ( C @ vecheck ) ) ) )
| ? [C: vQID,D: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= ( D @ ( C @ vlookupATMap ) ) )
& ( B
= ( C @ vqvar ) )
& ( A = D ) )
| ( ( ( B @ ( A @ vecheck ) )
= ( vText @ vsomeAType ) )
& ? [C: vstring] :
( B
= ( C @ vT @ vconstant ) )
& ? [C: vATMap] : ( A = C ) )
| ( ( ( B @ ( A @ vecheck ) )
= ( vNumber @ vsomeAType ) )
& ? [C: vnat] :
( B
= ( C @ vNum @ vconstant ) )
& ? [C: vATMap] : ( A = C ) )
| ( ( ( B @ ( A @ vecheck ) )
= ( vYesNo @ vsomeAType ) )
& ? [C: vYN] :
( B
= ( C @ vB @ vconstant ) )
& ? [C: vATMap] : ( A = C ) ) ),
inference(miniscope,[status(thm)],[417]) ).
thf(419,plain,
! [B: vExp,A: vATMap] :
( ( ( ( B @ ( A @ vecheck ) )
= vnoAType )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( B
= ( A @ ( B @ sk67 ) @ ( A @ ( B @ sk66 ) @ vunop ) ) )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A
= ( A @ ( B @ sk69 ) ) )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ~ ( A @ ( B @ sk68 ) @ visSomeAType )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( ( A @ ( B @ sk68 ) )
= ( A @ ( B @ sk67 ) @ ( A @ ( B @ sk69 ) @ vecheck ) ) )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk61 ) )
| ( ( B @ ( A @ vecheck ) )
= ( A @ ( B @ sk64 ) @ vgetAType @ ( A @ ( B @ sk62 ) @ vcheckUnOp ) ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk61 ) )
| ( B
= ( A @ ( B @ sk63 ) @ ( A @ ( B @ sk62 ) @ vunop ) ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk61 ) )
| ( A
= ( A @ ( B @ sk65 ) ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk61 ) )
| ( A @ ( B @ sk64 ) @ visSomeAType )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk61 ) )
| ( ( A @ ( B @ sk64 ) )
= ( A @ ( B @ sk63 ) @ ( A @ ( B @ sk65 ) @ vecheck ) ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk54 ) )
| ( ( B @ ( A @ vecheck ) )
= vnoAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk54 ) )
| ( B
= ( A @ ( B @ sk59 ) @ ( A @ ( B @ sk60 ) @ ( A @ ( B @ sk57 ) @ vbinop ) ) ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk54 ) )
| ( A
= ( A @ ( B @ sk55 ) ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk58 ) @ visSomeAType )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk54 ) )
| ( ( A @ ( B @ sk58 ) )
= ( A @ ( B @ sk59 ) @ ( A @ ( B @ sk55 ) @ vecheck ) ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk54 ) )
| ( ( A @ ( B @ sk56 ) )
= ( A @ ( B @ sk57 ) @ ( A @ ( B @ sk55 ) @ vecheck ) ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk47 ) )
| ( ( B @ ( A @ vecheck ) )
= ( A @ ( B @ sk51 ) @ vgetAType @ ( A @ ( B @ sk49 ) @ vgetAType @ ( A @ ( B @ sk53 ) @ vcheckBinOp ) ) ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk47 ) )
| ( B
= ( A @ ( B @ sk52 ) @ ( A @ ( B @ sk53 ) @ ( A @ ( B @ sk50 ) @ vbinop ) ) ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk47 ) )
| ( A
= ( A @ ( B @ sk48 ) ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk47 ) )
| ( A @ ( B @ sk51 ) @ visSomeAType )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk47 ) )
| ( A @ ( B @ sk49 ) @ visSomeAType )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk47 ) )
| ( ( A @ ( B @ sk51 ) )
= ( A @ ( B @ sk52 ) @ ( A @ ( B @ sk48 ) @ vecheck ) ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk47 ) )
| ( ( A @ ( B @ sk49 ) )
= ( A @ ( B @ sk50 ) @ ( A @ ( B @ sk48 ) @ vecheck ) ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk44 ) )
| ( ( B @ ( A @ vecheck ) )
= ( A @ ( B @ sk46 ) @ ( A @ ( B @ sk45 ) @ vlookupATMap ) ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk44 ) )
| ( B
= ( A @ ( B @ sk45 ) @ vqvar ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( A @ ( B @ sk44 ) )
| ( A
= ( A @ ( B @ sk46 ) ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( B @ ( A @ sk41 ) )
| ( ( B @ ( A @ vecheck ) )
= ( vText @ vsomeAType ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( B @ ( A @ sk41 ) )
| ( B
= ( A @ ( B @ sk43 ) @ vT @ vconstant ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( B @ ( A @ sk41 ) )
| ( A
= ( A @ ( B @ sk42 ) ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( B @ ( A @ sk38 ) )
| ( ( B @ ( A @ vecheck ) )
= ( vNumber @ vsomeAType ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( B @ ( A @ sk38 ) )
| ( B
= ( A @ ( B @ sk40 ) @ vNum @ vconstant ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( B @ ( A @ sk38 ) )
| ( A
= ( A @ ( B @ sk39 ) ) )
| ~ ( B @ ( A @ sk35 ) ) )
& ( ( B @ ( A @ sk35 ) )
| ( ( B @ ( A @ vecheck ) )
= ( vYesNo @ vsomeAType ) ) )
& ( ( B @ ( A @ sk35 ) )
| ( B
= ( A @ ( B @ sk37 ) @ vB @ vconstant ) ) )
& ( ( B @ ( A @ sk35 ) )
| ( A
= ( A @ ( B @ sk36 ) ) ) ) ),
inference(cnf,[status(esa)],[418]) ).
thf(436,plain,
! [B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk68 ) )
= ( A @ ( B @ sk67 ) @ ( A @ ( B @ sk69 ) @ vecheck ) ) )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(455,plain,
! [B: vExp,A: vATMap] :
( ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk68 ) )
= ( A @ ( B @ sk67 ) @ ( A @ ( B @ sk69 ) @ vecheck ) ) ) ),
inference(lifteq,[status(thm)],[436]) ).
thf(429,plain,
! [B: vExp,A: vATMap] :
( ~ ( A @ ( B @ sk68 ) @ visSomeAType )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(8449,plain,
! [D: vExp,C: vATMap,B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk68 ) )
!= ( C @ ( D @ sk68 ) ) )
| ~ ( A @ ( B @ sk67 ) @ ( A @ ( B @ sk69 ) @ vecheck ) @ visSomeAType )
| ~ ( C @ ( D @ sk61 ) )
| ~ ( C @ ( D @ sk54 ) )
| ~ ( C @ ( D @ sk47 ) )
| ~ ( C @ ( D @ sk44 ) )
| ~ ( D @ ( C @ sk41 ) )
| ~ ( D @ ( C @ sk38 ) )
| ~ ( D @ ( C @ sk35 ) )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[455,429]) ).
thf(8450,plain,
! [B: vExp,A: vATMap] :
( ~ ( A @ ( B @ sk67 ) @ ( A @ ( B @ sk69 ) @ vecheck ) @ visSomeAType )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(pattern_uni,[status(thm)],[8449:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(8488,plain,
! [B: vExp,A: vATMap] :
( ~ ( A @ ( B @ sk67 ) @ ( A @ ( B @ sk69 ) @ vecheck ) @ visSomeAType )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(simp,[status(thm)],[8450]) ).
thf(8558,plain,
! [D: vExp,C: vATMap,B: vYN,A: vATMap] :
( ( ( B @ vB @ vconstant @ ( A @ vecheck ) )
!= ( C @ ( D @ sk67 ) @ ( C @ ( D @ sk69 ) @ vecheck ) ) )
| ~ ( vYesNo @ vsomeAType @ visSomeAType )
| ~ ( C @ ( D @ sk61 ) )
| ~ ( C @ ( D @ sk54 ) )
| ~ ( C @ ( D @ sk47 ) )
| ~ ( C @ ( D @ sk44 ) )
| ~ ( D @ ( C @ sk41 ) )
| ~ ( D @ ( C @ sk38 ) )
| ~ ( D @ ( C @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[825,8488]) ).
thf(8583,plain,
! [D: vExp,C: vATMap,B: vYN,A: vATMap] :
( ( ( B @ vB @ vconstant )
!= ( C @ ( D @ sk67 ) ) )
| ( A
!= ( C @ ( D @ sk69 ) ) )
| ~ ( vYesNo @ vsomeAType @ visSomeAType )
| ~ ( C @ ( D @ sk61 ) )
| ~ ( C @ ( D @ sk54 ) )
| ~ ( C @ ( D @ sk47 ) )
| ~ ( C @ ( D @ sk44 ) )
| ~ ( D @ ( C @ sk41 ) )
| ~ ( D @ ( C @ sk38 ) )
| ~ ( D @ ( C @ sk35 ) ) ),
inference(simp,[status(thm)],[8558]) ).
thf(8596,plain,
! [C: vExp,B: vATMap,A: vYN] :
( ( ( A @ vB @ vconstant )
!= ( B @ ( C @ sk67 ) ) )
| ~ ( vYesNo @ vsomeAType @ visSomeAType )
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(simp,[status(thm)],[8583]) ).
thf(15,axiom,
! [A: vOptAType] :
( ~ ( A @ visSomeAType )
=> ( A = vnoAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeAType-false-INV') ).
thf(295,plain,
! [A: vOptAType] :
( ~ ( A @ visSomeAType )
=> ( A = vnoAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(296,plain,
! [A: vOptAType] :
( ( A = vnoAType )
| ( A @ visSomeAType ) ),
inference(cnf,[status(esa)],[295]) ).
thf(297,plain,
! [A: vOptAType] :
( ( A @ visSomeAType )
| ( A = vnoAType ) ),
inference(lifteq,[status(thm)],[296]) ).
thf(5,axiom,
( ( vYesNo @ ( vYesNo @ ( vandop @ vcheckBinOp ) ) )
= ( vYesNo @ vsomeAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','checkBinOp-6') ).
thf(262,plain,
( ( vYesNo @ ( vYesNo @ ( vandop @ vcheckBinOp ) ) )
= ( vYesNo @ vsomeAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(263,plain,
( ( vYesNo @ ( vYesNo @ ( vandop @ vcheckBinOp ) ) )
= ( vYesNo @ vsomeAType ) ),
inference(lifteq,[status(thm)],[262]) ).
thf(4956,plain,
! [A: vOptAType] :
( ( A
!= ( vYesNo @ ( vYesNo @ ( vandop @ vcheckBinOp ) ) ) )
| ( ( vYesNo @ vsomeAType )
= vnoAType )
| ( A @ visSomeAType ) ),
inference(paramod_ordered,[status(thm)],[297,263]) ).
thf(4957,plain,
( ( ( vYesNo @ vsomeAType )
= vnoAType )
| ( vYesNo @ ( vYesNo @ ( vandop @ vcheckBinOp ) ) @ visSomeAType ) ),
inference(pattern_uni,[status(thm)],[4956:[bind(A,$thf( vYesNo @ ( vYesNo @ ( vandop @ vcheckBinOp ) ) ))]]) ).
thf(4996,plain,
( ( ( vYesNo @ vsomeAType )
= vnoAType )
| ( vYesNo @ vsomeAType @ visSomeAType ) ),
inference(rewrite,[status(thm)],[4957,263]) ).
thf(132,axiom,
! [A: vAType] :
( vnoAType
!= ( A @ vsomeAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noAType-someAType') ).
thf(1106,plain,
! [A: vAType] :
( vnoAType
!= ( A @ vsomeAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1107,plain,
~ ? [A: vAType] :
( vnoAType
= ( A @ vsomeAType ) ),
inference(miniscope,[status(thm)],[1106]) ).
thf(1108,plain,
! [A: vAType] :
( vnoAType
!= ( A @ vsomeAType ) ),
inference(cnf,[status(esa)],[1107]) ).
thf(1109,plain,
! [A: vAType] :
( ( A @ vsomeAType )
!= vnoAType ),
inference(lifteq,[status(thm)],[1108]) ).
thf(4997,plain,
vYesNo @ vsomeAType @ visSomeAType,
inference(simplifyReflect,[status(thm)],[4996,1109]) ).
thf(8606,plain,
! [C: vExp,B: vATMap,A: vYN] :
( ( ( A @ vB @ vconstant )
!= ( B @ ( C @ sk67 ) ) )
| ~ $true
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(rewrite,[status(thm)],[8596,4997]) ).
thf(8607,plain,
! [C: vExp,B: vATMap,A: vYN] :
( ( ( A @ vB @ vconstant )
!= ( B @ ( C @ sk67 ) ) )
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(simp,[status(thm)],[8606]) ).
thf(248,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap] :
( ( ( B @ ( A @ vMC ) )
= ( D @ ( C @ vMC ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-MC') ).
thf(4851,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap] :
( ( ( B @ ( A @ vMC ) )
= ( D @ ( C @ vMC ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(4852,plain,
! [D: vATMap,C: vATMap,B: vATMap,A: vATMap] :
( ( ( B = D )
| ( ( B @ ( A @ vMC ) )
!= ( D @ ( C @ vMC ) ) ) )
& ( ( A = C )
| ( ( B @ ( A @ vMC ) )
!= ( D @ ( C @ vMC ) ) ) ) ),
inference(cnf,[status(esa)],[4851]) ).
thf(4854,plain,
! [D: vATMap,C: vATMap,B: vATMap,A: vATMap] :
( ( B = D )
| ( ( B @ ( A @ vMC ) )
!= ( D @ ( C @ vMC ) ) ) ),
inference(cnfConj,[status(thm)],[4852]) ).
thf(4858,plain,
! [D: vATMap,C: vATMap,B: vATMap,A: vATMap] :
( ( B = D )
| ( ( B @ ( A @ vMC ) )
!= ( D @ ( C @ vMC ) ) ) ),
inference(lifteq,[status(thm)],[4854]) ).
thf(4859,plain,
? [A: vATMap > vMapConf > vATMap] :
! [B: vATMap,C: vATMap] :
( ( C @ ( B @ vMC ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[4858]) ).
thf(4860,plain,
! [B: vATMap,A: vATMap] :
( ( B @ ( A @ vMC ) @ ( A @ sk412 ) )
= B ),
inference(cnf,[status(esa)],[4859]) ).
thf(6085,plain,
! [B: vATMap,A: vATMap] :
( ( B @ ( A @ vMC ) @ ( A @ sk412 ) )
= B ),
inference(lifteq,[status(thm)],[4860]) ).
thf(174,axiom,
! [A: vQConf] :
? [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( A
= ( D @ ( C @ ( B @ vQC ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-QConf') ).
thf(1337,plain,
! [A: vQConf] :
? [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( A
= ( D @ ( C @ ( B @ vQC ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(74,axiom,
! [A: vQuestionnaire,B: vQuestionnaire,C: vQuestionnaire,D: vQuestionnaire] :
( ( ( B @ ( A @ vqseq ) )
= ( D @ ( C @ vqseq ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-qseq') ).
thf(753,plain,
! [A: vQuestionnaire,B: vQuestionnaire,C: vQuestionnaire,D: vQuestionnaire] :
( ( ( B @ ( A @ vqseq ) )
= ( D @ ( C @ vqseq ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(754,plain,
! [D: vQuestionnaire,C: vQuestionnaire,B: vQuestionnaire,A: vQuestionnaire] :
( ( ( B = D )
| ( ( B @ ( A @ vqseq ) )
!= ( D @ ( C @ vqseq ) ) ) )
& ( ( A = C )
| ( ( B @ ( A @ vqseq ) )
!= ( D @ ( C @ vqseq ) ) ) ) ),
inference(cnf,[status(esa)],[753]) ).
thf(756,plain,
! [D: vQuestionnaire,C: vQuestionnaire,B: vQuestionnaire,A: vQuestionnaire] :
( ( B = D )
| ( ( B @ ( A @ vqseq ) )
!= ( D @ ( C @ vqseq ) ) ) ),
inference(cnfConj,[status(thm)],[754]) ).
thf(760,plain,
! [D: vQuestionnaire,C: vQuestionnaire,B: vQuestionnaire,A: vQuestionnaire] :
( ( B = D )
| ( ( B @ ( A @ vqseq ) )
!= ( D @ ( C @ vqseq ) ) ) ),
inference(lifteq,[status(thm)],[756]) ).
thf(761,plain,
? [A: vQuestionnaire > vQuestionnaire > vQuestionnaire] :
! [B: vQuestionnaire,C: vQuestionnaire] :
( ( C @ ( B @ vqseq ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[760]) ).
thf(762,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
( ( B @ ( A @ vqseq ) @ ( A @ sk143 ) )
= B ),
inference(cnf,[status(esa)],[761]) ).
thf(5918,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
( ( B @ ( A @ vqseq ) @ ( A @ sk143 ) )
= B ),
inference(lifteq,[status(thm)],[762]) ).
thf(143,axiom,
! [A: vAnsMap] :
( ( A @ ( vaempty @ vappendAnsMap ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','appendAnsMap-0') ).
thf(1168,plain,
! [A: vAnsMap] :
( ( A @ ( vaempty @ vappendAnsMap ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(239,axiom,
! [A: vQID,B: vAType,C: vQID,D: vAType,E: vExp,F: vLabel] :
( ( B @ ( F @ ( C @ vquestion ) ) )
!= ( E @ ( D @ ( A @ vvalue ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-question-value') ).
thf(4821,plain,
! [A: vQID,B: vAType,C: vQID,D: vAType,E: vExp,F: vLabel] :
( ( B @ ( F @ ( C @ vquestion ) ) )
!= ( E @ ( D @ ( A @ vvalue ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(4822,plain,
~ ? [A: vQID,B: vAType,C: vQID,D: vAType,E: vExp,F: vLabel] :
( ( B @ ( F @ ( C @ vquestion ) ) )
= ( E @ ( D @ ( A @ vvalue ) ) ) ),
inference(miniscope,[status(thm)],[4821]) ).
thf(4823,plain,
! [F: vLabel,E: vExp,D: vAType,C: vQID,B: vAType,A: vQID] :
( ( B @ ( F @ ( C @ vquestion ) ) )
!= ( E @ ( D @ ( A @ vvalue ) ) ) ),
inference(cnf,[status(esa)],[4822]) ).
thf(4824,plain,
! [F: vLabel,E: vExp,D: vAType,C: vQID,B: vAType,A: vQID] :
( ( B @ ( F @ ( C @ vquestion ) ) )
!= ( E @ ( D @ ( A @ vvalue ) ) ) ),
inference(lifteq,[status(thm)],[4823]) ).
thf(25,axiom,
! [A: vAval,B: vUnOpT,C: vExp] :
( ( A @ vconstant )
!= ( C @ ( B @ vunop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-constant-unop') ).
thf(347,plain,
! [A: vAval,B: vUnOpT,C: vExp] :
( ( A @ vconstant )
!= ( C @ ( B @ vunop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(88,axiom,
! [A: vQID] :
( ( vqmempty @ ( A @ vlookupQMap ) )
= vnoQuestion ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookupQMap-0') ).
thf(846,plain,
! [A: vQID] :
( ( vqmempty @ ( A @ vlookupQMap ) )
= vnoQuestion ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(22,axiom,
! [A: vUnOpT,B: vAval] :
( ( ! [C: vYN] :
( B
!= ( C @ vB ) )
| ( A != vnotop ) )
=> ( ( B @ ( A @ vevalUnOp ) )
= vnoExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','evalUnOp-1') ).
thf(333,plain,
! [A: vUnOpT,B: vAval] :
( ( ! [C: vYN] :
( B
!= ( C @ vB ) )
| ( A != vnotop ) )
=> ( ( B @ ( A @ vevalUnOp ) )
= vnoExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(219,axiom,
! [A: vQuestionnaire] :
( ( A @ visValue )
=> ( A = vqempty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isValue-true-INV') ).
thf(4728,plain,
! [A: vQuestionnaire] :
( ( A @ visValue )
=> ( A = vqempty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(163,axiom,
! [A: vQID,B: vAType,C: vExp,D: vQID] :
( ( C @ ( B @ ( A @ vvalue ) ) )
!= ( D @ vask ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-value-ask') ).
thf(1292,plain,
! [A: vQID,B: vAType,C: vExp,D: vQID] :
( ( C @ ( B @ ( A @ vvalue ) ) )
!= ( D @ vask ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(1293,plain,
~ ? [A: vQID,B: vAType,C: vExp,D: vQID] :
( ( C @ ( B @ ( A @ vvalue ) ) )
= ( D @ vask ) ),
inference(miniscope,[status(thm)],[1292]) ).
thf(1294,plain,
! [D: vQID,C: vExp,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vvalue ) ) )
!= ( D @ vask ) ),
inference(cnf,[status(esa)],[1293]) ).
thf(1295,plain,
! [D: vQID,C: vExp,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vvalue ) ) )
!= ( D @ vask ) ),
inference(lifteq,[status(thm)],[1294]) ).
thf(224,axiom,
! [A: vQConf] :
? [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( ( A @ vgetQuest )
= D )
& ( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getQuest-INV') ).
thf(4743,plain,
! [A: vQConf] :
? [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( ( A @ vgetQuest )
= D )
& ( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(4744,plain,
! [A: vQConf] :
( ( ( A @ vgetQuest )
= ( A @ sk369 ) )
& ( A
= ( A @ sk369 @ ( A @ sk368 @ ( A @ sk367 @ vQC ) ) ) ) ),
inference(cnf,[status(esa)],[4743]) ).
thf(4745,plain,
! [A: vQConf] :
( A
= ( A @ sk369 @ ( A @ sk368 @ ( A @ sk367 @ vQC ) ) ) ),
inference(cnfConj,[status(thm)],[4744]) ).
thf(4747,plain,
! [A: vQConf] :
( ( A @ sk369 @ ( A @ sk368 @ ( A @ sk367 @ vQC ) ) )
= A ),
inference(lifteq,[status(thm)],[4745]) ).
thf(4746,plain,
! [A: vQConf] :
( ( A @ vgetQuest )
= ( A @ sk369 ) ),
inference(cnfConj,[status(thm)],[4744]) ).
thf(4748,plain,
! [A: vQConf] :
( ( A @ sk369 )
= ( A @ vgetQuest ) ),
inference(lifteq,[status(thm)],[4746]) ).
thf(6359,plain,
! [A: vQConf] :
( ( A @ vgetQuest @ ( A @ sk368 @ ( A @ sk367 @ vQC ) ) )
= A ),
inference(rewrite,[status(thm)],[4747,4748]) ).
thf(176,axiom,
! [A: vAnsMap,B: vQMap,C: vQuestionnaire] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetAM )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getAM-0') ).
thf(1345,plain,
! [A: vAnsMap,B: vQMap,C: vQuestionnaire] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetAM )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(1346,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetAM )
= A ),
inference(cnf,[status(esa)],[1345]) ).
thf(1347,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetAM )
= A ),
inference(lifteq,[status(thm)],[1346]) ).
thf(6360,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ vgetQuest @ ( A @ sk368 @ ( A @ sk367 @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ vgetAM )
= B ) ),
inference(paramod_ordered,[status(thm)],[6359,1347]) ).
thf(6361,plain,
! [A: vQConf] :
( ( A @ sk367 )
= ( A @ vgetAM ) ),
inference(pattern_uni,[status(thm)],[6360:[bind(A,$thf( G )),bind(B,$thf( G @ sk367 )),bind(C,$thf( G @ sk368 )),bind(D,$thf( G @ vgetQuest ))]]) ).
thf(6374,plain,
! [A: vQConf] :
( ( A @ sk367 )
= ( A @ vgetAM ) ),
inference(simp,[status(thm)],[6361]) ).
thf(133,axiom,
! [A: vUnOpT,B: vAType] :
( ? [C: vUnOpT,D: vAType] :
( ( ( B @ ( A @ vcheckUnOp ) )
= vnoAType )
& ( B = D )
& ( A = C )
& ( ( D != vYesNo )
| ( C != vnotop ) ) )
| ( ( ( B @ ( A @ vcheckUnOp ) )
= ( vYesNo @ vsomeAType ) )
& ( B = vYesNo )
& ( A = vnotop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','checkUnOp-INV') ).
thf(1110,plain,
! [A: vUnOpT,B: vAType] :
( ? [C: vUnOpT,D: vAType] :
( ( ( B @ ( A @ vcheckUnOp ) )
= vnoAType )
& ( B = D )
& ( A = C )
& ( ( D != vYesNo )
| ( C != vnotop ) ) )
| ( ( ( B @ ( A @ vcheckUnOp ) )
= ( vYesNo @ vsomeAType ) )
& ( B = vYesNo )
& ( A = vnotop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(30,axiom,
! [A: vATMap,B: vExp,C: vExp,D: vBinOpT] :
( ( ( C @ ( A @ vecheck ) @ visSomeAType )
& ( B @ ( A @ vecheck ) @ visSomeAType ) )
=> ( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= ( C @ ( A @ vecheck ) @ vgetAType @ ( B @ ( A @ vecheck ) @ vgetAType @ ( D @ vcheckBinOp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','echeck-4') ).
thf(362,plain,
! [A: vATMap,B: vExp,C: vExp,D: vBinOpT] :
( ( ( C @ ( A @ vecheck ) @ visSomeAType )
& ( B @ ( A @ vecheck ) @ visSomeAType ) )
=> ( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= ( C @ ( A @ vecheck ) @ vgetAType @ ( B @ ( A @ vecheck ) @ vgetAType @ ( D @ vcheckBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(363,plain,
! [A: vATMap,B: vExp,C: vExp] :
( ( ( C @ ( A @ vecheck ) @ visSomeAType )
& ( B @ ( A @ vecheck ) @ visSomeAType ) )
=> ! [D: vBinOpT] :
( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= ( C @ ( A @ vecheck ) @ vgetAType @ ( B @ ( A @ vecheck ) @ vgetAType @ ( D @ vcheckBinOp ) ) ) ) ),
inference(miniscope,[status(thm)],[362]) ).
thf(364,plain,
! [D: vBinOpT,C: vExp,B: vExp,A: vATMap] :
( ( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= ( C @ ( A @ vecheck ) @ vgetAType @ ( B @ ( A @ vecheck ) @ vgetAType @ ( D @ vcheckBinOp ) ) ) )
| ~ ( C @ ( A @ vecheck ) @ visSomeAType )
| ~ ( B @ ( A @ vecheck ) @ visSomeAType ) ),
inference(cnf,[status(esa)],[363]) ).
thf(365,plain,
! [D: vBinOpT,C: vExp,B: vExp,A: vATMap] :
( ~ ( C @ ( A @ vecheck ) @ visSomeAType )
| ~ ( B @ ( A @ vecheck ) @ visSomeAType )
| ( ( C @ ( A @ vecheck ) @ vgetAType @ ( B @ ( A @ vecheck ) @ vgetAType @ ( D @ vcheckBinOp ) ) )
= ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) ) ) ),
inference(lifteq,[status(thm)],[364]) ).
thf(183,axiom,
! [A: vATMap,B: vATMap,C: vAType,D: vLabel,E: vQID] :
( ( ( B @ ( E @ vlookupATMap ) )
= vnoAType )
=> ( A @ ( B @ ( C @ ( E @ vatmbind ) ) @ vMC ) @ ( C @ ( D @ ( E @ vquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tquestion') ).
thf(1369,plain,
! [A: vATMap,B: vATMap,C: vAType,D: vLabel,E: vQID] :
( ( ( B @ ( E @ vlookupATMap ) )
= vnoAType )
=> ( A @ ( B @ ( C @ ( E @ vatmbind ) ) @ vMC ) @ ( C @ ( D @ ( E @ vquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(109,axiom,
~ ( vnoQuestion @ visSomeQuestion ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeQuestion-0') ).
thf(962,plain,
~ ( vnoQuestion @ visSomeQuestion ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(453,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk35 ) )
| ( ( B @ ( A @ vecheck ) )
= ( vYesNo @ vsomeAType ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(468,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk35 ) )
| ( ( B @ ( A @ vecheck ) )
= ( vYesNo @ vsomeAType ) ) ),
inference(lifteq,[status(thm)],[453]) ).
thf(38,axiom,
! [A: vLabel] :
( ( vText @ ( A @ vgetAnswer ) )
= ( A @ vaskText @ vT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getAnswer-2') ).
thf(406,plain,
! [A: vLabel] :
( ( vText @ ( A @ vgetAnswer ) )
= ( A @ vaskText @ vT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(407,plain,
! [A: vLabel] :
( ( vText @ ( A @ vgetAnswer ) )
= ( A @ vaskText @ vT ) ),
inference(cnf,[status(esa)],[406]) ).
thf(408,plain,
! [A: vLabel] :
( ( vText @ ( A @ vgetAnswer ) )
= ( A @ vaskText @ vT ) ),
inference(lifteq,[status(thm)],[407]) ).
thf(58,axiom,
! [A: vOptExp] :
( ~ ( A @ visSomeExp )
=> ( A = vnoExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeExp-false-INV') ).
thf(683,plain,
! [A: vOptExp] :
( ~ ( A @ visSomeExp )
=> ( A = vnoExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(10,axiom,
vYesNo != vText,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-YesNo-Text') ).
thf(276,plain,
vYesNo != vText,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(125,axiom,
! [A: vYN] :
( ( ( ( A @ vnot )
= vyes )
& ( A = vno ) )
| ( ( ( A @ vnot )
= vno )
& ( A = vyes ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','not-INV') ).
thf(1060,plain,
! [A: vYN] :
( ( ( ( A @ vnot )
= vyes )
& ( A = vno ) )
| ( ( ( A @ vnot )
= vno )
& ( A = vyes ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(1061,plain,
! [A: vYN] :
( ( ( ( A @ vnot )
= vyes )
| ( ( A @ vnot )
= vno ) )
& ( ( A = vno )
| ( ( A @ vnot )
= vno ) )
& ( ( ( A @ vnot )
= vyes )
| ( A = vyes ) )
& ( ( A = vno )
| ( A = vyes ) ) ),
inference(cnf,[status(esa)],[1060]) ).
thf(1064,plain,
! [A: vYN] :
( ( A = vno )
| ( ( A @ vnot )
= vno ) ),
inference(cnfConj,[status(thm)],[1061]) ).
thf(1068,plain,
! [A: vYN] :
( ( A = vno )
| ( ( A @ vnot )
= vno ) ),
inference(lifteq,[status(thm)],[1064]) ).
thf(168,axiom,
! [A: vMapConf] :
? [B: vATMap,C: vATMap] :
( A
= ( C @ ( B @ vMC ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-MapConf') ).
thf(1314,plain,
! [A: vMapConf] :
? [B: vATMap,C: vATMap] :
( A
= ( C @ ( B @ vMC ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(1315,plain,
! [A: vMapConf] :
( A
= ( A @ sk254 @ ( A @ sk253 @ vMC ) ) ),
inference(cnf,[status(esa)],[1314]) ).
thf(1316,plain,
! [A: vMapConf] :
( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
= A ),
inference(lifteq,[status(thm)],[1315]) ).
thf(249,axiom,
( ( vaempty @ vtypeAM )
= vatmempty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','typeAM-0') ).
thf(4861,plain,
( ( vaempty @ vtypeAM )
= vatmempty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(4862,plain,
( ( vaempty @ vtypeAM )
= vatmempty ),
inference(lifteq,[status(thm)],[4861]) ).
thf(177,axiom,
( ( vqmempty @ vtypeQM )
= vatmempty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','typeQM-0') ).
thf(1348,plain,
( ( vqmempty @ vtypeQM )
= vatmempty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(1349,plain,
( ( vqmempty @ vtypeQM )
= vatmempty ),
inference(lifteq,[status(thm)],[1348]) ).
thf(1,conjecture,
! [A: vQMap,B: vAType,C: vATMap,D: vATMap,E: vAnsMap,F: vQID,G: vExp] :
( ( ( D @ ( C @ vMC ) @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ ( A @ vtypeQM @ ( E @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ visValue ) )
=> ? [H: vAnsMap,I: vQMap,J: vQuestionnaire] :
( ( A @ ( E @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( J @ ( I @ ( H @ vQC ) ) @ vsomeQConf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Progress-qsingle-value') ).
thf(2,negated_conjecture,
~ ! [A: vQMap,B: vAType,C: vATMap,D: vATMap,E: vAnsMap,F: vQID,G: vExp] :
( ( ( D @ ( C @ vMC ) @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ ( A @ vtypeQM @ ( E @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ visValue ) )
=> ? [H: vAnsMap,I: vQMap,J: vQuestionnaire] :
( ( A @ ( E @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( J @ ( I @ ( H @ vQC ) ) @ vsomeQConf ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(251,plain,
~ ! [A: vQMap,B: vAType,C: vATMap,D: vATMap,E: vAnsMap,F: vQID,G: vExp] :
( ( ( D @ ( C @ vMC ) @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ ( A @ vtypeQM @ ( E @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ visValue ) )
=> ? [H: vAnsMap,I: vQMap,J: vQuestionnaire] :
( ( A @ ( E @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( J @ ( I @ ( H @ vQC ) ) @ vsomeQConf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(252,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( C @ ( B @ ( A @ vQC ) ) @ vsomeQConf ) )
& ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ visValue ) ),
inference(cnf,[status(esa)],[251]) ).
thf(254,plain,
sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ),
inference(cnfConj,[status(thm)],[252]) ).
thf(4873,plain,
( ( ( sk1 @ vtypeQM )
!= ( vqmempty @ vtypeQM ) )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1349,254]) ).
thf(4874,plain,
( ( sk1 != vqmempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[4873]) ).
thf(4877,plain,
( ( ( sk5 @ vtypeAM )
!= ( vaempty @ vtypeAM ) )
| ( sk1 != vqmempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( vatmempty @ vMC ) @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[4862,4874]) ).
thf(4878,plain,
( ( sk5 != vaempty )
| ( sk1 != vqmempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( vatmempty @ vMC ) @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[4877]) ).
thf(5681,plain,
! [A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk4 @ ( sk3 @ vMC ) ) )
| ( sk5 != vaempty )
| ( sk1 != vqmempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( vatmempty @ vMC ) @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,4878]) ).
thf(5696,plain,
! [A: vMapConf] :
( ( ( A @ sk254 )
!= sk4 )
| ( ( A @ sk253 )
!= sk3 )
| ( sk5 != vaempty )
| ( sk1 != vqmempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( vatmempty @ vMC ) @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5681]) ).
thf(91,axiom,
! [A: vOptQConf] :
( ~ ( A @ visSomeQC )
=> ( A = vnoQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeQC-false-INV') ).
thf(876,plain,
! [A: vOptQConf] :
( ~ ( A @ visSomeQC )
=> ( A = vnoQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(877,plain,
! [A: vOptQConf] :
( ( A = vnoQConf )
| ( A @ visSomeQC ) ),
inference(cnf,[status(esa)],[876]) ).
thf(878,plain,
! [A: vOptQConf] :
( ( A @ visSomeQC )
| ( A = vnoQConf ) ),
inference(lifteq,[status(thm)],[877]) ).
thf(5687,plain,
! [A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk4 @ ( sk3 @ vMC ) ) )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,254]) ).
thf(5691,plain,
! [A: vMapConf] :
( ( ( A @ sk254 )
!= sk4 )
| ( ( A @ sk253 )
!= sk3 )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5687]) ).
thf(7,axiom,
veqop != vorop,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-eqop-orop') ).
thf(267,plain,
veqop != vorop,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(268,plain,
veqop != vorop,
inference(polarity_switch,[status(thm)],[267]) ).
thf(269,plain,
veqop != vorop,
inference(lifteq,[status(thm)],[268]) ).
thf(45,axiom,
! [A: vLabel,B: vAType] :
( ? [C: vLabel] :
( ( ( B @ ( A @ vgetAnswer ) )
= ( C @ vaskText @ vT ) )
& ( B = vText )
& ( A = C ) )
| ? [C: vLabel] :
( ( ( B @ ( A @ vgetAnswer ) )
= ( C @ vaskNumber @ vNum ) )
& ( B = vNumber )
& ( A = C ) )
| ? [C: vLabel] :
( ( ( B @ ( A @ vgetAnswer ) )
= ( C @ vaskYesNo @ vB ) )
& ( B = vYesNo )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getAnswer-INV') ).
thf(597,plain,
! [A: vLabel,B: vAType] :
( ? [C: vLabel] :
( ( ( B @ ( A @ vgetAnswer ) )
= ( C @ vaskText @ vT ) )
& ( B = vText )
& ( A = C ) )
| ? [C: vLabel] :
( ( ( B @ ( A @ vgetAnswer ) )
= ( C @ vaskNumber @ vNum ) )
& ( B = vNumber )
& ( A = C ) )
| ? [C: vLabel] :
( ( ( B @ ( A @ vgetAnswer ) )
= ( C @ vaskYesNo @ vB ) )
& ( B = vYesNo )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(145,axiom,
! [A: vQID,B: vAnsMap,C: vAval,D: vAval,E: vQID,F: vAnsMap] :
( ( ( F @ ( C @ ( E @ vabind ) ) )
= ( B @ ( D @ ( A @ vabind ) ) ) )
=> ( ( F = B )
& ( C = D )
& ( E = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-abind') ).
thf(1173,plain,
! [A: vQID,B: vAnsMap,C: vAval,D: vAval,E: vQID,F: vAnsMap] :
( ( ( F @ ( C @ ( E @ vabind ) ) )
= ( B @ ( D @ ( A @ vabind ) ) ) )
=> ( ( F = B )
& ( C = D )
& ( E = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(4853,plain,
! [D: vATMap,C: vATMap,B: vATMap,A: vATMap] :
( ( A = C )
| ( ( B @ ( A @ vMC ) )
!= ( D @ ( C @ vMC ) ) ) ),
inference(cnfConj,[status(thm)],[4852]) ).
thf(4855,plain,
! [D: vATMap,C: vATMap,B: vATMap,A: vATMap] :
( ( A = C )
| ( ( B @ ( A @ vMC ) )
!= ( D @ ( C @ vMC ) ) ) ),
inference(lifteq,[status(thm)],[4853]) ).
thf(4856,plain,
? [A: vATMap > vMapConf > vATMap] :
! [B: vATMap,C: vATMap] :
( ( C @ ( B @ vMC ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[4855]) ).
thf(4857,plain,
! [B: vATMap,A: vATMap] :
( ( B @ ( A @ vMC ) @ ( B @ sk411 ) )
= A ),
inference(cnf,[status(esa)],[4856]) ).
thf(5979,plain,
! [B: vATMap,A: vATMap] :
( ( B @ ( A @ vMC ) @ ( B @ sk411 ) )
= A ),
inference(lifteq,[status(thm)],[4857]) ).
thf(5980,plain,
! [C: vATMap,B: vATMap,A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( C @ ( B @ vMC ) ) )
| ( ( A @ ( C @ sk411 ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[1316,5979]) ).
thf(5981,plain,
! [A: vMapConf] :
( ( A @ ( A @ sk254 @ sk411 ) )
= ( A @ sk253 ) ),
inference(pattern_uni,[status(thm)],[5980:[bind(A,$thf( E )),bind(B,$thf( E @ sk253 )),bind(C,$thf( E @ sk254 ))]]) ).
thf(5982,plain,
! [A: vMapConf] :
( ( A @ ( A @ sk254 @ sk411 ) )
= ( A @ sk253 ) ),
inference(simp,[status(thm)],[5981]) ).
thf(136,axiom,
! [A: vYN] :
( ( A @ vB @ vtypeOf )
= vYesNo ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','typeOf-0') ).
thf(1133,plain,
! [A: vYN] :
( ( A @ vB @ vtypeOf )
= vYesNo ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(1134,plain,
! [A: vYN] :
( ( A @ vB @ vtypeOf )
= vYesNo ),
inference(cnf,[status(esa)],[1133]) ).
thf(1135,plain,
! [A: vYN] :
( ( A @ vB @ vtypeOf )
= vYesNo ),
inference(lifteq,[status(thm)],[1134]) ).
thf(245,axiom,
! [A: vQID,B: vAval,C: vAnsMap] :
( ( C @ ( B @ ( A @ vabind ) ) @ vtypeAM )
= ( C @ vtypeAM @ ( B @ vtypeOf @ ( A @ vatmbind ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','typeAM-1') ).
thf(4843,plain,
! [A: vQID,B: vAval,C: vAnsMap] :
( ( C @ ( B @ ( A @ vabind ) ) @ vtypeAM )
= ( C @ vtypeAM @ ( B @ vtypeOf @ ( A @ vatmbind ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(4844,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( C @ ( B @ ( A @ vabind ) ) @ vtypeAM )
= ( C @ vtypeAM @ ( B @ vtypeOf @ ( A @ vatmbind ) ) ) ),
inference(cnf,[status(esa)],[4843]) ).
thf(4845,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( C @ vtypeAM @ ( B @ vtypeOf @ ( A @ vatmbind ) ) )
= ( C @ ( B @ ( A @ vabind ) ) @ vtypeAM ) ),
inference(lifteq,[status(thm)],[4844]) ).
thf(9402,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( ( vaempty @ vtypeAM )
!= ( C @ vtypeAM ) )
| ( ( vatmempty @ ( B @ vtypeOf @ ( A @ vatmbind ) ) )
= ( C @ ( B @ ( A @ vabind ) ) @ vtypeAM ) ) ),
inference(paramod_ordered,[status(thm)],[4862,4845]) ).
thf(9403,plain,
! [B: vAval,A: vQID] :
( ( vatmempty @ ( B @ vtypeOf @ ( A @ vatmbind ) ) )
= ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM ) ),
inference(pattern_uni,[status(thm)],[9402:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( vaempty ))]]) ).
thf(9458,plain,
! [C: vAval,B: vQID,A: vYN] :
( ( ( A @ vB @ vtypeOf )
!= ( C @ vtypeOf ) )
| ( ( vatmempty @ ( vYesNo @ ( B @ vatmbind ) ) )
= ( vaempty @ ( C @ ( B @ vabind ) ) @ vtypeAM ) ) ),
inference(paramod_ordered,[status(thm)],[1135,9403]) ).
thf(9459,plain,
! [B: vYN,A: vQID] :
( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) )
= ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM ) ),
inference(pattern_uni,[status(thm)],[9458:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ vB ))]]) ).
thf(9480,plain,
! [B: vYN,A: vQID] :
( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) )
= ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM ) ),
inference(simp,[status(thm)],[9459]) ).
thf(153,axiom,
! [A: vQID,B: vAType,C: vATMap] :
( vatmempty
!= ( C @ ( B @ ( A @ vatmbind ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-atmempty-atmbind') ).
thf(1226,plain,
! [A: vQID,B: vAType,C: vATMap] :
( vatmempty
!= ( C @ ( B @ ( A @ vatmbind ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(1227,plain,
~ ? [A: vQID,B: vAType,C: vATMap] :
( vatmempty
= ( C @ ( B @ ( A @ vatmbind ) ) ) ),
inference(miniscope,[status(thm)],[1226]) ).
thf(1228,plain,
! [C: vATMap,B: vAType,A: vQID] :
( vatmempty
!= ( C @ ( B @ ( A @ vatmbind ) ) ) ),
inference(cnf,[status(esa)],[1227]) ).
thf(1229,plain,
! [C: vATMap,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(lifteq,[status(thm)],[1228]) ).
thf(9424,plain,
! [F: vATMap,E: vAType,D: vQID,C: vAnsMap,B: vAval,A: vQID] :
( ( ( C @ vtypeAM @ ( B @ vtypeOf @ ( A @ vatmbind ) ) )
!= ( F @ ( E @ ( D @ vatmbind ) ) ) )
| ( ( C @ ( B @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[4845,1229]) ).
thf(9425,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( C @ ( B @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[9424:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( H )),bind(D,$thf( A )),bind(E,$thf( G @ vtypeOf )),bind(F,$thf( H @ vtypeAM ))]]) ).
thf(9436,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( C @ ( B @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ),
inference(simp,[status(thm)],[9425]) ).
thf(10016,plain,
! [E: vAnsMap,D: vAval,C: vQID,B: vYN,A: vQID] :
( ( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM )
!= ( E @ ( D @ ( C @ vabind ) ) @ vtypeAM ) )
| ( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9480,9436]) ).
thf(10017,plain,
! [A: vQID] :
( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[10016:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ vB )),bind(E,$thf( vaempty ))]]) ).
thf(449,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk61 ) )
| ( A @ ( B @ sk64 ) @ visSomeAType )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(34,axiom,
! [A: vAval] :
( ? [B: vstring] :
( A
= ( B @ vT ) )
| ? [B: vnat] :
( A
= ( B @ vNum ) )
| ? [B: vYN] :
( A
= ( B @ vB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-Aval') ).
thf(379,plain,
! [A: vAval] :
( ? [B: vstring] :
( A
= ( B @ vT ) )
| ? [B: vnat] :
( A
= ( B @ vNum ) )
| ? [B: vYN] :
( A
= ( B @ vB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(159,axiom,
! [A: vQID,B: vExp,C: vAType,D: vQID,E: vAType,F: vExp] :
( ( ( F @ ( C @ ( D @ vvalue ) ) )
= ( B @ ( E @ ( A @ vvalue ) ) ) )
=> ( ( F = B )
& ( C = E )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-value') ).
thf(1269,plain,
! [A: vQID,B: vExp,C: vAType,D: vQID,E: vAType,F: vExp] :
( ( ( F @ ( C @ ( D @ vvalue ) ) )
= ( B @ ( E @ ( A @ vvalue ) ) ) )
=> ( ( F = B )
& ( C = E )
& ( D = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(184,axiom,
! [A: vQuestionnaire] :
( ( A != vqempty )
=> ~ ( A @ visValue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isValue-1') ).
thf(1372,plain,
! [A: vQuestionnaire] :
( ( A != vqempty )
=> ~ ( A @ visValue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(1373,plain,
! [A: vQuestionnaire] :
( ~ ( A @ visValue )
| ( A = vqempty ) ),
inference(cnf,[status(esa)],[1372]) ).
thf(1374,plain,
! [A: vQuestionnaire] :
( ~ ( A @ visValue )
| ( A = vqempty ) ),
inference(lifteq,[status(thm)],[1373]) ).
thf(154,axiom,
! [A: vGID,B: vQuestionnaire] :
( vqempty
!= ( B @ ( A @ vqgroup ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qempty-qgroup') ).
thf(1230,plain,
! [A: vGID,B: vQuestionnaire] :
( vqempty
!= ( B @ ( A @ vqgroup ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(1231,plain,
~ ? [A: vGID,B: vQuestionnaire] :
( vqempty
= ( B @ ( A @ vqgroup ) ) ),
inference(miniscope,[status(thm)],[1230]) ).
thf(1232,plain,
! [B: vQuestionnaire,A: vGID] :
( vqempty
!= ( B @ ( A @ vqgroup ) ) ),
inference(cnf,[status(esa)],[1231]) ).
thf(1233,plain,
! [B: vQuestionnaire,A: vGID] :
( ( B @ ( A @ vqgroup ) )
!= vqempty ),
inference(lifteq,[status(thm)],[1232]) ).
thf(5293,plain,
! [C: vQuestionnaire,B: vGID,A: vQuestionnaire] :
( ( A
!= ( C @ ( B @ vqgroup ) ) )
| ( vqempty != vqempty )
| ~ ( A @ visValue ) ),
inference(paramod_ordered,[status(thm)],[1374,1233]) ).
thf(5294,plain,
! [C: vQuestionnaire,B: vGID,A: vQuestionnaire] :
( ( A
!= ( C @ ( B @ vqgroup ) ) )
| ~ ( A @ visValue ) ),
inference(simp,[status(thm)],[5293]) ).
thf(5295,plain,
! [B: vQuestionnaire,A: vGID] :
~ ( B @ ( A @ vqgroup ) @ visValue ),
inference(pattern_uni,[status(thm)],[5294:[bind(A,$thf( E @ ( D @ vqgroup ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(5348,plain,
! [B: vQuestionnaire,A: vGID] :
~ ( B @ ( A @ vqgroup ) @ visValue ),
inference(simp,[status(thm)],[5295]) ).
thf(26,axiom,
! [A: vstring] :
( ( A @ vT @ vtypeOf )
= vText ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','typeOf-2') ).
thf(351,plain,
! [A: vstring] :
( ( A @ vT @ vtypeOf )
= vText ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(352,plain,
! [A: vstring] :
( ( A @ vT @ vtypeOf )
= vText ),
inference(cnf,[status(esa)],[351]) ).
thf(353,plain,
! [A: vstring] :
( ( A @ vT @ vtypeOf )
= vText ),
inference(lifteq,[status(thm)],[352]) ).
thf(9446,plain,
! [C: vAval,B: vQID,A: vstring] :
( ( ( A @ vT @ vtypeOf )
!= ( C @ vtypeOf ) )
| ( ( vatmempty @ ( vText @ ( B @ vatmbind ) ) )
= ( vaempty @ ( C @ ( B @ vabind ) ) @ vtypeAM ) ) ),
inference(paramod_ordered,[status(thm)],[353,9403]) ).
thf(9447,plain,
! [B: vstring,A: vQID] :
( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) )
= ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM ) ),
inference(pattern_uni,[status(thm)],[9446:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ vT ))]]) ).
thf(9477,plain,
! [B: vstring,A: vQID] :
( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) )
= ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM ) ),
inference(simp,[status(thm)],[9447]) ).
thf(140,axiom,
! [A: vQID,B: vATMap,C: vATMap,D: vAType,E: vQID,F: vAType] :
( ( ( C @ ( D @ ( E @ vatmbind ) ) )
= ( B @ ( F @ ( A @ vatmbind ) ) ) )
=> ( ( C = B )
& ( D = F )
& ( E = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-atmbind') ).
thf(1146,plain,
! [A: vQID,B: vATMap,C: vATMap,D: vAType,E: vQID,F: vAType] :
( ( ( C @ ( D @ ( E @ vatmbind ) ) )
= ( B @ ( F @ ( A @ vatmbind ) ) ) )
=> ( ( C = B )
& ( D = F )
& ( E = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(1147,plain,
! [F: vAType,E: vQID,D: vAType,C: vATMap,B: vATMap,A: vQID] :
( ( ( C = B )
| ( ( C @ ( D @ ( E @ vatmbind ) ) )
!= ( B @ ( F @ ( A @ vatmbind ) ) ) ) )
& ( ( D = F )
| ( ( C @ ( D @ ( E @ vatmbind ) ) )
!= ( B @ ( F @ ( A @ vatmbind ) ) ) ) )
& ( ( E = A )
| ( ( C @ ( D @ ( E @ vatmbind ) ) )
!= ( B @ ( F @ ( A @ vatmbind ) ) ) ) ) ),
inference(cnf,[status(esa)],[1146]) ).
thf(1150,plain,
! [F: vAType,E: vQID,D: vAType,C: vATMap,B: vATMap,A: vQID] :
( ( C = B )
| ( ( C @ ( D @ ( E @ vatmbind ) ) )
!= ( B @ ( F @ ( A @ vatmbind ) ) ) ) ),
inference(cnfConj,[status(thm)],[1147]) ).
thf(1157,plain,
! [F: vAType,E: vQID,D: vAType,C: vATMap,B: vATMap,A: vQID] :
( ( C = B )
| ( ( C @ ( D @ ( E @ vatmbind ) ) )
!= ( B @ ( F @ ( A @ vatmbind ) ) ) ) ),
inference(lifteq,[status(thm)],[1150]) ).
thf(1158,plain,
? [A: vQID > vAType > vATMap > vATMap] :
! [B: vQID,C: vAType,D: vATMap] :
( ( D @ ( C @ ( B @ vatmbind ) ) @ ( C @ ( B @ A ) ) )
= D ),
inference(detectInverse,[status(thm)],[1157]) ).
thf(1159,plain,
! [C: vATMap,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vatmbind ) ) @ ( B @ ( A @ sk224 ) ) )
= C ),
inference(cnf,[status(esa)],[1158]) ).
thf(8152,plain,
! [C: vATMap,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vatmbind ) ) @ ( B @ ( A @ sk224 ) ) )
= C ),
inference(lifteq,[status(thm)],[1159]) ).
thf(9460,plain,
! [E: vATMap,D: vAType,C: vQID,B: vAval,A: vQID] :
( ( ( vatmempty @ ( B @ vtypeOf @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ ( D @ ( C @ sk224 ) ) )
= E ) ),
inference(paramod_ordered,[status(thm)],[9403,8152]) ).
thf(9461,plain,
! [B: vAval,A: vQID] :
( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ ( B @ vtypeOf @ ( A @ sk224 ) ) )
= vatmempty ),
inference(pattern_uni,[status(thm)],[9460:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ vtypeOf )),bind(E,$thf( vatmempty ))]]) ).
thf(9481,plain,
! [B: vAval,A: vQID] :
( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ ( B @ vtypeOf @ ( A @ sk224 ) ) )
= vatmempty ),
inference(simp,[status(thm)],[9461]) ).
thf(11608,plain,
! [D: vAval,C: vQID,B: vstring,A: vQID] :
( ( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ ( D @ ( C @ vabind ) ) @ vtypeAM ) )
| ( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) @ ( D @ vtypeOf @ ( C @ sk224 ) ) )
= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9477,9481]) ).
thf(11609,plain,
! [B: vstring,A: vQID] :
( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) @ ( B @ vT @ vtypeOf @ ( A @ sk224 ) ) )
= vatmempty ),
inference(pattern_uni,[status(thm)],[11608:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vT ))]]) ).
thf(11636,plain,
! [B: vstring,A: vQID] :
( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) @ ( B @ vT @ vtypeOf @ ( A @ sk224 ) ) )
= vatmempty ),
inference(simp,[status(thm)],[11609]) ).
thf(11724,plain,
! [A: vQID] :
( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) @ ( vText @ ( A @ sk224 ) ) )
= vatmempty ),
inference(rewrite,[status(thm)],[11636,353]) ).
thf(128,axiom,
! [A: vQID,B: vAType,C: vATMap] :
( ( C @ ( B @ ( A @ vatmbind ) ) @ ( A @ vlookupATMap ) )
= ( B @ vsomeAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookupATMap-1') ).
thf(1078,plain,
! [A: vQID,B: vAType,C: vATMap] :
( ( C @ ( B @ ( A @ vatmbind ) ) @ ( A @ vlookupATMap ) )
= ( B @ vsomeAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(37,axiom,
! [A: vUnOpT,B: vAval] :
( ? [C: vUnOpT,D: vAval] :
( ( ( B @ ( A @ vevalUnOp ) )
= vnoExp )
& ( B = D )
& ( A = C )
& ( ! [E: vYN] :
( D
!= ( E @ vB ) )
| ( C != vnotop ) ) )
| ? [C: vYN] :
( ( ( B @ ( A @ vevalUnOp ) )
= ( C @ vnot @ vB @ vconstant @ vsomeExp ) )
& ( B
= ( C @ vB ) )
& ( A = vnotop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','evalUnOp-INV') ).
thf(389,plain,
! [A: vUnOpT,B: vAval] :
( ? [C: vUnOpT,D: vAval] :
( ( ( B @ ( A @ vevalUnOp ) )
= vnoExp )
& ( B = D )
& ( A = C )
& ( ! [E: vYN] :
( D
!= ( E @ vB ) )
| ( C != vnotop ) ) )
| ? [C: vYN] :
( ( ( B @ ( A @ vevalUnOp ) )
= ( C @ vnot @ vB @ vconstant @ vsomeExp ) )
& ( B
= ( C @ vB ) )
& ( A = vnotop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(390,plain,
! [A: vUnOpT,B: vAval] :
( ? [C: vUnOpT,D: vAval] :
( ( ( B @ ( A @ vevalUnOp ) )
= vnoExp )
& ( B = D )
& ( A = C )
& ( ~ ? [E: vYN] :
( D
= ( E @ vB ) )
| ( C != vnotop ) ) )
| ( ? [C: vYN] :
( ( ( B @ ( A @ vevalUnOp ) )
= ( C @ vnot @ vB @ vconstant @ vsomeExp ) )
& ( B
= ( C @ vB ) ) )
& ( A = vnotop ) ) ),
inference(miniscope,[status(thm)],[389]) ).
thf(391,plain,
! [C: vYN,B: vAval,A: vUnOpT] :
( ( ( ( B @ ( A @ vevalUnOp ) )
= vnoExp )
| ~ ( B @ ( A @ sk31 ) ) )
& ( ( B
= ( A @ ( B @ sk34 ) ) )
| ~ ( B @ ( A @ sk31 ) ) )
& ( ( A
= ( A @ ( B @ sk33 ) ) )
| ~ ( B @ ( A @ sk31 ) ) )
& ( ( ( A @ ( B @ sk34 ) )
!= ( C @ vB ) )
| ( ( A @ ( B @ sk33 ) )
!= vnotop )
| ~ ( B @ ( A @ sk31 ) ) )
& ( ( B @ ( A @ sk31 ) )
| ( ( B @ ( A @ vevalUnOp ) )
= ( A @ ( B @ sk32 ) @ vnot @ vB @ vconstant @ vsomeExp ) ) )
& ( ( B @ ( A @ sk31 ) )
| ( B
= ( A @ ( B @ sk32 ) @ vB ) ) )
& ( ( B @ ( A @ sk31 ) )
| ( A = vnotop ) ) ),
inference(cnf,[status(esa)],[390]) ).
thf(398,plain,
! [B: vAval,A: vUnOpT] :
( ( B
= ( A @ ( B @ sk34 ) ) )
| ~ ( B @ ( A @ sk31 ) ) ),
inference(cnfConj,[status(thm)],[391]) ).
thf(401,plain,
! [B: vAval,A: vUnOpT] :
( ~ ( B @ ( A @ sk31 ) )
| ( ( A @ ( B @ sk34 ) )
= B ) ),
inference(lifteq,[status(thm)],[398]) ).
thf(394,plain,
! [C: vYN,B: vAval,A: vUnOpT] :
( ( ( A @ ( B @ sk34 ) )
!= ( C @ vB ) )
| ( ( A @ ( B @ sk33 ) )
!= vnotop )
| ~ ( B @ ( A @ sk31 ) ) ),
inference(cnfConj,[status(thm)],[391]) ).
thf(402,plain,
! [C: vYN,B: vAval,A: vUnOpT] :
( ~ ( B @ ( A @ sk31 ) )
| ( ( A @ ( B @ sk34 ) )
!= ( C @ vB ) )
| ( ( A @ ( B @ sk33 ) )
!= vnotop ) ),
inference(lifteq,[status(thm)],[394]) ).
thf(27,axiom,
! [A: vUnOpT] : ( A = vnotop ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-UnOpT') ).
thf(354,plain,
! [A: vUnOpT] : ( A = vnotop ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(355,plain,
! [A: vUnOpT] : ( A = vnotop ),
inference(cnf,[status(esa)],[354]) ).
thf(356,plain,
! [A: vUnOpT] : ( A = vnotop ),
inference(lifteq,[status(thm)],[355]) ).
thf(6784,plain,
! [C: vYN,B: vAval,A: vUnOpT] :
( ~ ( B @ ( A @ sk31 ) )
| ( ( A @ ( B @ sk34 ) )
!= ( C @ vB ) ) ),
inference(simplifyReflect,[status(thm)],[402,356]) ).
thf(6932,plain,
! [E: vYN,D: vAval,C: vUnOpT,B: vAval,A: vUnOpT] :
( ( ( A @ ( B @ sk34 ) )
!= ( C @ ( D @ sk34 ) ) )
| ~ ( D @ ( C @ sk31 ) )
| ( B
!= ( E @ vB ) )
| ~ ( B @ ( A @ sk31 ) ) ),
inference(paramod_ordered,[status(thm)],[401,6784]) ).
thf(6933,plain,
! [C: vYN,B: vAval,A: vUnOpT] :
( ~ ( B @ ( A @ sk31 ) )
| ( B
!= ( C @ vB ) )
| ~ ( B @ ( A @ sk31 ) ) ),
inference(pattern_uni,[status(thm)],[6932:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(6934,plain,
! [B: vYN,A: vUnOpT] :
( ~ ( B @ vB @ ( A @ sk31 ) )
| ~ ( B @ vB @ ( A @ sk31 ) ) ),
inference(simp,[status(thm)],[6933]) ).
thf(6939,plain,
! [B: vYN,A: vUnOpT] :
~ ( B @ vB @ ( A @ sk31 ) ),
inference(simp,[status(thm)],[6934]) ).
thf(1270,plain,
! [F: vExp,E: vAType,D: vQID,C: vAType,B: vExp,A: vQID] :
( ( ( F = B )
| ( ( F @ ( C @ ( D @ vvalue ) ) )
!= ( B @ ( E @ ( A @ vvalue ) ) ) ) )
& ( ( C = E )
| ( ( F @ ( C @ ( D @ vvalue ) ) )
!= ( B @ ( E @ ( A @ vvalue ) ) ) ) )
& ( ( D = A )
| ( ( F @ ( C @ ( D @ vvalue ) ) )
!= ( B @ ( E @ ( A @ vvalue ) ) ) ) ) ),
inference(cnf,[status(esa)],[1269]) ).
thf(1272,plain,
! [F: vExp,E: vAType,D: vQID,C: vAType,B: vExp,A: vQID] :
( ( C = E )
| ( ( F @ ( C @ ( D @ vvalue ) ) )
!= ( B @ ( E @ ( A @ vvalue ) ) ) ) ),
inference(cnfConj,[status(thm)],[1270]) ).
thf(1277,plain,
! [F: vExp,E: vAType,D: vQID,C: vAType,B: vExp,A: vQID] :
( ( C = E )
| ( ( F @ ( C @ ( D @ vvalue ) ) )
!= ( B @ ( E @ ( A @ vvalue ) ) ) ) ),
inference(lifteq,[status(thm)],[1272]) ).
thf(1278,plain,
? [A: vQID > vExp > vEntry > vAType] :
! [B: vQID,C: vAType,D: vExp] :
( ( D @ ( C @ ( B @ vvalue ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[1277]) ).
thf(1279,plain,
! [C: vExp,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vvalue ) ) @ ( C @ ( A @ sk246 ) ) )
= B ),
inference(cnf,[status(esa)],[1278]) ).
thf(8915,plain,
! [C: vExp,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vvalue ) ) @ ( C @ ( A @ sk246 ) ) )
= B ),
inference(lifteq,[status(thm)],[1279]) ).
thf(43,axiom,
! [A: vExp,B: vAnsMap] :
( ? [C: vUnOpT,D: vExp,E: vOptExp,F: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = F )
& ( A
= ( D @ ( C @ vunop ) ) )
& ~ ( E @ visSomeExp )
& ( E
= ( F @ ( D @ vreduceExp ) ) )
& ~ ( D @ vexpIsValue ) )
| ? [C: vUnOpT,D: vExp,E: vOptExp,F: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= ( E @ vgetExp @ ( C @ vunop ) @ vsomeExp ) )
& ( B = F )
& ( A
= ( D @ ( C @ vunop ) ) )
& ( E @ visSomeExp )
& ( E
= ( F @ ( D @ vreduceExp ) ) )
& ~ ( D @ vexpIsValue ) )
| ? [C: vUnOpT,D: vExp,E: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= ( D @ vgetExpValue @ ( C @ vevalUnOp ) ) )
& ( B = E )
& ( A
= ( D @ ( C @ vunop ) ) )
& ( D @ vexpIsValue ) )
| ? [C: vExp,D: vOptExp,E: vAnsMap,F: vExp,G: vBinOpT] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = E )
& ( A
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ~ ( D @ visSomeExp )
& ( D
= ( E @ ( C @ vreduceExp ) ) )
& ~ ( C @ vexpIsValue ) )
| ? [C: vExp,D: vOptExp,E: vAnsMap,F: vExp,G: vBinOpT] :
( ( ( B @ ( A @ vreduceExp ) )
= ( F @ ( G @ ( D @ vgetExp @ vbinop ) ) @ vsomeExp ) )
& ( B = E )
& ( A
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ( D @ visSomeExp )
& ( D
= ( E @ ( C @ vreduceExp ) ) )
& ~ ( C @ vexpIsValue ) )
| ? [C: vExp,D: vOptExp,E: vAnsMap,F: vExp,G: vBinOpT] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = E )
& ( A
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ~ ( D @ visSomeExp )
& ( D
= ( E @ ( F @ vreduceExp ) ) )
& ~ ( F @ vexpIsValue )
& ( C @ vexpIsValue ) )
| ? [C: vExp,D: vOptExp,E: vAnsMap,F: vExp,G: vBinOpT] :
( ( ( B @ ( A @ vreduceExp ) )
= ( D @ vgetExp @ ( G @ ( C @ vbinop ) ) @ vsomeExp ) )
& ( B = E )
& ( A
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ( D @ visSomeExp )
& ( D
= ( E @ ( F @ vreduceExp ) ) )
& ~ ( F @ vexpIsValue )
& ( C @ vexpIsValue ) )
| ? [C: vExp,D: vBinOpT,E: vExp,F: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= ( E @ vgetExpValue @ ( C @ vgetExpValue @ ( D @ vevalBinOp ) ) ) )
& ( B = F )
& ( A
= ( E @ ( D @ ( C @ vbinop ) ) ) )
& ( E @ vexpIsValue )
& ( C @ vexpIsValue ) )
| ? [C: vQID,D: vOptAval,E: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = E )
& ( A
= ( C @ vqvar ) )
& ~ ( D @ visSomeAval )
& ( D
= ( E @ ( C @ vlookupAnsMap ) ) ) )
| ? [C: vQID,D: vOptAval,E: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= ( D @ vgetAval @ vconstant @ vsomeExp ) )
& ( B = E )
& ( A
= ( C @ vqvar ) )
& ( D @ visSomeAval )
& ( D
= ( E @ ( C @ vlookupAnsMap ) ) ) )
| ? [C: vAval,D: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = D )
& ( A
= ( C @ vconstant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-INV') ).
thf(490,plain,
! [A: vExp,B: vAnsMap] :
( ? [C: vUnOpT,D: vExp,E: vOptExp,F: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = F )
& ( A
= ( D @ ( C @ vunop ) ) )
& ~ ( E @ visSomeExp )
& ( E
= ( F @ ( D @ vreduceExp ) ) )
& ~ ( D @ vexpIsValue ) )
| ? [C: vUnOpT,D: vExp,E: vOptExp,F: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= ( E @ vgetExp @ ( C @ vunop ) @ vsomeExp ) )
& ( B = F )
& ( A
= ( D @ ( C @ vunop ) ) )
& ( E @ visSomeExp )
& ( E
= ( F @ ( D @ vreduceExp ) ) )
& ~ ( D @ vexpIsValue ) )
| ? [C: vUnOpT,D: vExp,E: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= ( D @ vgetExpValue @ ( C @ vevalUnOp ) ) )
& ( B = E )
& ( A
= ( D @ ( C @ vunop ) ) )
& ( D @ vexpIsValue ) )
| ? [C: vExp,D: vOptExp,E: vAnsMap,F: vExp,G: vBinOpT] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = E )
& ( A
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ~ ( D @ visSomeExp )
& ( D
= ( E @ ( C @ vreduceExp ) ) )
& ~ ( C @ vexpIsValue ) )
| ? [C: vExp,D: vOptExp,E: vAnsMap,F: vExp,G: vBinOpT] :
( ( ( B @ ( A @ vreduceExp ) )
= ( F @ ( G @ ( D @ vgetExp @ vbinop ) ) @ vsomeExp ) )
& ( B = E )
& ( A
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ( D @ visSomeExp )
& ( D
= ( E @ ( C @ vreduceExp ) ) )
& ~ ( C @ vexpIsValue ) )
| ? [C: vExp,D: vOptExp,E: vAnsMap,F: vExp,G: vBinOpT] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = E )
& ( A
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ~ ( D @ visSomeExp )
& ( D
= ( E @ ( F @ vreduceExp ) ) )
& ~ ( F @ vexpIsValue )
& ( C @ vexpIsValue ) )
| ? [C: vExp,D: vOptExp,E: vAnsMap,F: vExp,G: vBinOpT] :
( ( ( B @ ( A @ vreduceExp ) )
= ( D @ vgetExp @ ( G @ ( C @ vbinop ) ) @ vsomeExp ) )
& ( B = E )
& ( A
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ( D @ visSomeExp )
& ( D
= ( E @ ( F @ vreduceExp ) ) )
& ~ ( F @ vexpIsValue )
& ( C @ vexpIsValue ) )
| ? [C: vExp,D: vBinOpT,E: vExp,F: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= ( E @ vgetExpValue @ ( C @ vgetExpValue @ ( D @ vevalBinOp ) ) ) )
& ( B = F )
& ( A
= ( E @ ( D @ ( C @ vbinop ) ) ) )
& ( E @ vexpIsValue )
& ( C @ vexpIsValue ) )
| ? [C: vQID,D: vOptAval,E: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = E )
& ( A
= ( C @ vqvar ) )
& ~ ( D @ visSomeAval )
& ( D
= ( E @ ( C @ vlookupAnsMap ) ) ) )
| ? [C: vQID,D: vOptAval,E: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= ( D @ vgetAval @ vconstant @ vsomeExp ) )
& ( B = E )
& ( A
= ( C @ vqvar ) )
& ( D @ visSomeAval )
& ( D
= ( E @ ( C @ vlookupAnsMap ) ) ) )
| ? [C: vAval,D: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = D )
& ( A
= ( C @ vconstant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(491,plain,
! [A: vExp,B: vAnsMap] :
( ? [C: vUnOpT,D: vExp] :
( ? [E: vOptExp,F: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = F )
& ( A
= ( D @ ( C @ vunop ) ) )
& ~ ( E @ visSomeExp )
& ( E
= ( F @ ( D @ vreduceExp ) ) ) )
& ~ ( D @ vexpIsValue ) )
| ? [C: vUnOpT,D: vExp] :
( ? [E: vOptExp,F: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= ( E @ vgetExp @ ( C @ vunop ) @ vsomeExp ) )
& ( B = F )
& ( A
= ( D @ ( C @ vunop ) ) )
& ( E @ visSomeExp )
& ( E
= ( F @ ( D @ vreduceExp ) ) ) )
& ~ ( D @ vexpIsValue ) )
| ? [C: vUnOpT,D: vExp] :
( ( ( B @ ( A @ vreduceExp ) )
= ( D @ vgetExpValue @ ( C @ vevalUnOp ) ) )
& ? [E: vAnsMap] : ( B = E )
& ( A
= ( D @ ( C @ vunop ) ) )
& ( D @ vexpIsValue ) )
| ? [C: vExp] :
( ? [D: vOptExp,E: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = E )
& ? [F: vExp,G: vBinOpT] :
( A
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ~ ( D @ visSomeExp )
& ( D
= ( E @ ( C @ vreduceExp ) ) ) )
& ~ ( C @ vexpIsValue ) )
| ? [C: vExp] :
( ? [D: vOptExp,E: vAnsMap] :
( ? [F: vExp,G: vBinOpT] :
( ( ( B @ ( A @ vreduceExp ) )
= ( F @ ( G @ ( D @ vgetExp @ vbinop ) ) @ vsomeExp ) )
& ( B = E )
& ( A
= ( F @ ( G @ ( C @ vbinop ) ) ) ) )
& ( D @ visSomeExp )
& ( D
= ( E @ ( C @ vreduceExp ) ) ) )
& ~ ( C @ vexpIsValue ) )
| ? [C: vExp] :
( ? [D: vOptExp,E: vAnsMap,F: vExp] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = E )
& ? [G: vBinOpT] :
( A
= ( F @ ( G @ ( C @ vbinop ) ) ) )
& ~ ( D @ visSomeExp )
& ( D
= ( E @ ( F @ vreduceExp ) ) )
& ~ ( F @ vexpIsValue ) )
& ( C @ vexpIsValue ) )
| ? [C: vExp] :
( ? [D: vOptExp,E: vAnsMap,F: vExp] :
( ? [G: vBinOpT] :
( ( ( B @ ( A @ vreduceExp ) )
= ( D @ vgetExp @ ( G @ ( C @ vbinop ) ) @ vsomeExp ) )
& ( B = E )
& ( A
= ( F @ ( G @ ( C @ vbinop ) ) ) ) )
& ( D @ visSomeExp )
& ( D
= ( E @ ( F @ vreduceExp ) ) )
& ~ ( F @ vexpIsValue ) )
& ( C @ vexpIsValue ) )
| ? [C: vExp] :
( ? [D: vBinOpT,E: vExp] :
( ( ( B @ ( A @ vreduceExp ) )
= ( E @ vgetExpValue @ ( C @ vgetExpValue @ ( D @ vevalBinOp ) ) ) )
& ? [F: vAnsMap] : ( B = F )
& ( A
= ( E @ ( D @ ( C @ vbinop ) ) ) )
& ( E @ vexpIsValue ) )
& ( C @ vexpIsValue ) )
| ? [C: vQID,D: vOptAval,E: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ( B = E )
& ( A
= ( C @ vqvar ) )
& ~ ( D @ visSomeAval )
& ( D
= ( E @ ( C @ vlookupAnsMap ) ) ) )
| ? [C: vQID,D: vOptAval,E: vAnsMap] :
( ( ( B @ ( A @ vreduceExp ) )
= ( D @ vgetAval @ vconstant @ vsomeExp ) )
& ( B = E )
& ( A
= ( C @ vqvar ) )
& ( D @ visSomeAval )
& ( D
= ( E @ ( C @ vlookupAnsMap ) ) ) )
| ( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
& ? [C: vAnsMap] : ( B = C )
& ? [C: vAval] :
( A
= ( C @ vconstant ) ) ) ),
inference(miniscope,[status(thm)],[490]) ).
thf(492,plain,
! [B: vAnsMap,A: vExp] :
( ( ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
| ~ ( B @ ( A @ sk115 ) )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B
= ( A @ ( B @ sk123 ) ) )
| ~ ( B @ ( A @ sk115 ) )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( A
= ( A @ ( B @ sk121 ) @ ( A @ ( B @ sk120 ) @ vunop ) ) )
| ~ ( B @ ( A @ sk115 ) )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ~ ( A @ ( B @ sk122 ) @ visSomeExp )
| ~ ( B @ ( A @ sk115 ) )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( ( A @ ( B @ sk122 ) )
= ( A @ ( B @ sk123 ) @ ( A @ ( B @ sk121 ) @ vreduceExp ) ) )
| ~ ( B @ ( A @ sk115 ) )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ~ ( A @ ( B @ sk121 ) @ vexpIsValue )
| ~ ( B @ ( A @ sk115 ) )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk115 ) )
| ( ( B @ ( A @ vreduceExp ) )
= ( A @ ( B @ sk118 ) @ vgetExp @ ( A @ ( B @ sk116 ) @ vunop ) @ vsomeExp ) )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk115 ) )
| ( B
= ( A @ ( B @ sk119 ) ) )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk115 ) )
| ( A
= ( A @ ( B @ sk117 ) @ ( A @ ( B @ sk116 ) @ vunop ) ) )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk115 ) )
| ( A @ ( B @ sk118 ) @ visSomeExp )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk115 ) )
| ( ( A @ ( B @ sk118 ) )
= ( A @ ( B @ sk119 ) @ ( A @ ( B @ sk117 ) @ vreduceExp ) ) )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk115 ) )
| ~ ( A @ ( B @ sk117 ) @ vexpIsValue )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk111 ) )
| ( ( B @ ( A @ vreduceExp ) )
= ( A @ ( B @ sk113 ) @ vgetExpValue @ ( A @ ( B @ sk112 ) @ vevalUnOp ) ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk111 ) )
| ( B
= ( A @ ( B @ sk114 ) ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk111 ) )
| ( A
= ( A @ ( B @ sk113 ) @ ( A @ ( B @ sk112 ) @ vunop ) ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk111 ) )
| ( A @ ( B @ sk113 ) @ vexpIsValue )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk105 ) )
| ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk105 ) )
| ( B
= ( A @ ( B @ sk108 ) ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk105 ) )
| ( A
= ( A @ ( B @ sk109 ) @ ( A @ ( B @ sk110 ) @ ( A @ ( B @ sk106 ) @ vbinop ) ) ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk105 ) )
| ~ ( A @ ( B @ sk107 ) @ visSomeExp )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk105 ) )
| ( ( A @ ( B @ sk107 ) )
= ( A @ ( B @ sk108 ) @ ( A @ ( B @ sk106 ) @ vreduceExp ) ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk105 ) )
| ~ ( A @ ( B @ sk106 ) @ vexpIsValue )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk99 ) )
| ( ( B @ ( A @ vreduceExp ) )
= ( A @ ( B @ sk103 ) @ ( A @ ( B @ sk104 ) @ ( A @ ( B @ sk101 ) @ vgetExp @ vbinop ) ) @ vsomeExp ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk99 ) )
| ( B
= ( A @ ( B @ sk102 ) ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk99 ) )
| ( A
= ( A @ ( B @ sk103 ) @ ( A @ ( B @ sk104 ) @ ( A @ ( B @ sk100 ) @ vbinop ) ) ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk99 ) )
| ( A @ ( B @ sk101 ) @ visSomeExp )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk99 ) )
| ( ( A @ ( B @ sk101 ) )
= ( A @ ( B @ sk102 ) @ ( A @ ( B @ sk100 ) @ vreduceExp ) ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk99 ) )
| ~ ( A @ ( B @ sk100 ) @ vexpIsValue )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk93 ) )
| ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk93 ) )
| ( B
= ( A @ ( B @ sk96 ) ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk93 ) )
| ( A
= ( A @ ( B @ sk97 ) @ ( A @ ( B @ sk98 ) @ ( A @ ( B @ sk94 ) @ vbinop ) ) ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk93 ) )
| ~ ( A @ ( B @ sk95 ) @ visSomeExp )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk93 ) )
| ( ( A @ ( B @ sk95 ) )
= ( A @ ( B @ sk96 ) @ ( A @ ( B @ sk97 ) @ vreduceExp ) ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk93 ) )
| ~ ( A @ ( B @ sk97 ) @ vexpIsValue )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk93 ) )
| ( A @ ( B @ sk94 ) @ vexpIsValue )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk87 ) )
| ( ( B @ ( A @ vreduceExp ) )
= ( A @ ( B @ sk89 ) @ vgetExp @ ( A @ ( B @ sk92 ) @ ( A @ ( B @ sk88 ) @ vbinop ) ) @ vsomeExp ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk87 ) )
| ( B
= ( A @ ( B @ sk90 ) ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk87 ) )
| ( A
= ( A @ ( B @ sk91 ) @ ( A @ ( B @ sk92 ) @ ( A @ ( B @ sk88 ) @ vbinop ) ) ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk87 ) )
| ( A @ ( B @ sk89 ) @ visSomeExp )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk87 ) )
| ( ( A @ ( B @ sk89 ) )
= ( A @ ( B @ sk90 ) @ ( A @ ( B @ sk91 ) @ vreduceExp ) ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk87 ) )
| ~ ( A @ ( B @ sk91 ) @ vexpIsValue )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk87 ) )
| ( A @ ( B @ sk88 ) @ vexpIsValue )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk82 ) )
| ( ( B @ ( A @ vreduceExp ) )
= ( A @ ( B @ sk85 ) @ vgetExpValue @ ( A @ ( B @ sk83 ) @ vgetExpValue @ ( A @ ( B @ sk84 ) @ vevalBinOp ) ) ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk82 ) )
| ( B
= ( A @ ( B @ sk86 ) ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk82 ) )
| ( A
= ( A @ ( B @ sk85 ) @ ( A @ ( B @ sk84 ) @ ( A @ ( B @ sk83 ) @ vbinop ) ) ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk82 ) )
| ( A @ ( B @ sk85 ) @ vexpIsValue )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk82 ) )
| ( A @ ( B @ sk83 ) @ vexpIsValue )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk78 ) )
| ( ( B @ ( A @ vreduceExp ) )
= vnoExp )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk78 ) )
| ( B
= ( A @ ( B @ sk81 ) ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk78 ) )
| ( A
= ( A @ ( B @ sk79 ) @ vqvar ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk78 ) )
| ~ ( A @ ( B @ sk80 ) @ visSomeAval )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk78 ) )
| ( ( A @ ( B @ sk80 ) )
= ( A @ ( B @ sk81 ) @ ( A @ ( B @ sk79 ) @ vlookupAnsMap ) ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk74 ) )
| ( ( B @ ( A @ vreduceExp ) )
= ( A @ ( B @ sk76 ) @ vgetAval @ vconstant @ vsomeExp ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk74 ) )
| ( B
= ( A @ ( B @ sk77 ) ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk74 ) )
| ( A
= ( A @ ( B @ sk75 ) @ vqvar ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk74 ) )
| ( A @ ( B @ sk76 ) @ visSomeAval )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk74 ) )
| ( ( A @ ( B @ sk76 ) )
= ( A @ ( B @ sk77 ) @ ( A @ ( B @ sk75 ) @ vlookupAnsMap ) ) )
| ~ ( B @ ( A @ sk71 ) ) )
& ( ( B @ ( A @ sk71 ) )
| ( ( B @ ( A @ vreduceExp ) )
= vnoExp ) )
& ( ( B @ ( A @ sk71 ) )
| ( B
= ( A @ ( B @ sk73 ) ) ) )
& ( ( B @ ( A @ sk71 ) )
| ( A
= ( A @ ( B @ sk72 ) @ vconstant ) ) ) ),
inference(cnf,[status(esa)],[491]) ).
thf(500,plain,
! [B: vAnsMap,A: vExp] :
( ~ ( A @ ( B @ sk122 ) @ visSomeExp )
| ~ ( B @ ( A @ sk115 ) )
| ~ ( B @ ( A @ sk111 ) )
| ~ ( B @ ( A @ sk105 ) )
| ~ ( B @ ( A @ sk99 ) )
| ~ ( B @ ( A @ sk93 ) )
| ~ ( B @ ( A @ sk87 ) )
| ~ ( B @ ( A @ sk82 ) )
| ~ ( B @ ( A @ sk78 ) )
| ~ ( B @ ( A @ sk74 ) )
| ~ ( B @ ( A @ sk71 ) ) ),
inference(cnfConj,[status(thm)],[492]) ).
thf(62,axiom,
vYesNo != vNumber,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-YesNo-Number') ).
thf(696,plain,
vYesNo != vNumber,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(697,plain,
vYesNo != vNumber,
inference(polarity_switch,[status(thm)],[696]) ).
thf(698,plain,
vYesNo != vNumber,
inference(lifteq,[status(thm)],[697]) ).
thf(72,axiom,
! [A: vQuestionnaire,B: vQuestionnaire,C: vGID,D: vQuestionnaire] :
( ( B @ ( A @ vqseq ) )
!= ( D @ ( C @ vqgroup ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qseq-qgroup') ).
thf(747,plain,
! [A: vQuestionnaire,B: vQuestionnaire,C: vGID,D: vQuestionnaire] :
( ( B @ ( A @ vqseq ) )
!= ( D @ ( C @ vqgroup ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(36,axiom,
! [A: vnat] :
( ( A @ vNum @ vtypeOf )
= vNumber ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','typeOf-1') ).
thf(386,plain,
! [A: vnat] :
( ( A @ vNum @ vtypeOf )
= vNumber ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(387,plain,
! [A: vnat] :
( ( A @ vNum @ vtypeOf )
= vNumber ),
inference(cnf,[status(esa)],[386]) ).
thf(388,plain,
! [A: vnat] :
( ( A @ vNum @ vtypeOf )
= vNumber ),
inference(lifteq,[status(thm)],[387]) ).
thf(9450,plain,
! [C: vAval,B: vQID,A: vnat] :
( ( ( A @ vNum @ vtypeOf )
!= ( C @ vtypeOf ) )
| ( ( vatmempty @ ( vNumber @ ( B @ vatmbind ) ) )
= ( vaempty @ ( C @ ( B @ vabind ) ) @ vtypeAM ) ) ),
inference(paramod_ordered,[status(thm)],[388,9403]) ).
thf(9451,plain,
! [B: vnat,A: vQID] :
( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) )
= ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM ) ),
inference(pattern_uni,[status(thm)],[9450:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ vNum ))]]) ).
thf(9478,plain,
! [B: vnat,A: vQID] :
( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) )
= ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM ) ),
inference(simp,[status(thm)],[9451]) ).
thf(9800,plain,
! [E: vATMap,D: vAType,C: vQID,B: vnat,A: vQID] :
( ( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9478,1229]) ).
thf(9801,plain,
! [B: vnat,A: vQID] :
( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[9800:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( vNumber )),bind(E,$thf( vatmempty ))]]) ).
thf(23,axiom,
! [A: vOptExp] :
( ( A @ visSomeExp )
=> ? [B: vExp] :
( A
= ( B @ vsomeExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeExp-true-INV') ).
thf(340,plain,
! [A: vOptExp] :
( ( A @ visSomeExp )
=> ? [B: vExp] :
( A
= ( B @ vsomeExp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(179,axiom,
! [A: vAnsMap,B: vQMap] :
( ( B @ ( A @ ( vqempty @ vreduce ) ) )
= vnoQConf ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-0') ).
thf(1354,plain,
! [A: vAnsMap,B: vQMap] :
( ( B @ ( A @ ( vqempty @ vreduce ) ) )
= vnoQConf ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(48,axiom,
! [A: vExp,B: vExp,C: vExp,D: vExp,E: vBinOpT,F: vBinOpT] :
( ( ( A @ ( E @ ( D @ vbinop ) ) )
= ( B @ ( F @ ( C @ vbinop ) ) ) )
=> ( ( A = B )
& ( E = F )
& ( D = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-binop') ).
thf(634,plain,
! [A: vExp,B: vExp,C: vExp,D: vExp,E: vBinOpT,F: vBinOpT] :
( ( ( A @ ( E @ ( D @ vbinop ) ) )
= ( B @ ( F @ ( C @ vbinop ) ) ) )
=> ( ( A = B )
& ( E = F )
& ( D = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(635,plain,
! [F: vBinOpT,E: vBinOpT,D: vExp,C: vExp,B: vExp,A: vExp] :
( ( ( A = B )
| ( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( B @ ( F @ ( C @ vbinop ) ) ) ) )
& ( ( E = F )
| ( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( B @ ( F @ ( C @ vbinop ) ) ) ) )
& ( ( D = C )
| ( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( B @ ( F @ ( C @ vbinop ) ) ) ) ) ),
inference(cnf,[status(esa)],[634]) ).
thf(637,plain,
! [F: vBinOpT,E: vBinOpT,D: vExp,C: vExp,B: vExp,A: vExp] :
( ( E = F )
| ( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( B @ ( F @ ( C @ vbinop ) ) ) ) ),
inference(cnfConj,[status(thm)],[635]) ).
thf(642,plain,
! [F: vBinOpT,E: vBinOpT,D: vExp,C: vExp,B: vExp,A: vExp] :
( ( E = F )
| ( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( B @ ( F @ ( C @ vbinop ) ) ) ) ),
inference(lifteq,[status(thm)],[637]) ).
thf(643,plain,
? [A: vExp > vExp > vExp > vBinOpT] :
! [B: vExp,C: vBinOpT,D: vExp] :
( ( D @ ( C @ ( B @ vbinop ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[642]) ).
thf(644,plain,
! [C: vExp,B: vBinOpT,A: vExp] :
( ( C @ ( B @ ( A @ vbinop ) ) @ ( C @ ( A @ sk133 ) ) )
= B ),
inference(cnf,[status(esa)],[643]) ).
thf(6877,plain,
! [C: vExp,B: vBinOpT,A: vExp] :
( ( C @ ( B @ ( A @ vbinop ) ) @ ( C @ ( A @ sk133 ) ) )
= B ),
inference(lifteq,[status(thm)],[644]) ).
thf(195,axiom,
! [A: vQuestionnaire] :
( ~ ( A @ visValue )
=> ? [B: vQuestionnaire] :
( ( A = B )
& ( B != vqempty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isValue-false-INV') ).
thf(4629,plain,
! [A: vQuestionnaire] :
( ~ ( A @ visValue )
=> ? [B: vQuestionnaire] :
( ( A = B )
& ( B != vqempty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(4630,plain,
! [A: vQuestionnaire] :
( ( ( A
= ( A @ sk354 ) )
| ( A @ visValue ) )
& ( ( ( A @ sk354 )
!= vqempty )
| ( A @ visValue ) ) ),
inference(cnf,[status(esa)],[4629]) ).
thf(4631,plain,
! [A: vQuestionnaire] :
( ( ( A @ sk354 )
!= vqempty )
| ( A @ visValue ) ),
inference(cnfConj,[status(thm)],[4630]) ).
thf(4633,plain,
! [A: vQuestionnaire] :
( ( A @ visValue )
| ( ( A @ sk354 )
!= vqempty ) ),
inference(lifteq,[status(thm)],[4631]) ).
thf(35,axiom,
! [A: vYN,B: vnat] :
( ( A @ vB )
!= ( B @ vNum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-B-Num') ).
thf(382,plain,
! [A: vYN,B: vnat] :
( ( A @ vB )
!= ( B @ vNum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(383,plain,
~ ? [A: vYN,B: vnat] :
( ( A @ vB )
= ( B @ vNum ) ),
inference(miniscope,[status(thm)],[382]) ).
thf(384,plain,
! [B: vnat,A: vYN] :
( ( A @ vB )
!= ( B @ vNum ) ),
inference(cnf,[status(esa)],[383]) ).
thf(385,plain,
! [B: vnat,A: vYN] :
( ( A @ vB )
!= ( B @ vNum ) ),
inference(lifteq,[status(thm)],[384]) ).
thf(244,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vQuestionnaire,E: vATMap,F: vATMap,G: vATMap,H: vATMap,I: vATMap,J: vQuestionnaire] :
( ( ( C @ ( B @ vMC ) @ ( J @ ( F @ ( H @ vMC ) @ vptcheck ) ) )
& ( F @ ( H @ vMC ) @ ( D @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( I @ ( G @ vMC ) @ ( J @ ( D @ vqseq ) @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) )
=> ( G = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqseq_inv3') ).
thf(4839,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vQuestionnaire,E: vATMap,F: vATMap,G: vATMap,H: vATMap,I: vATMap,J: vQuestionnaire] :
( ( ( C @ ( B @ vMC ) @ ( J @ ( F @ ( H @ vMC ) @ vptcheck ) ) )
& ( F @ ( H @ vMC ) @ ( D @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( I @ ( G @ vMC ) @ ( J @ ( D @ vqseq ) @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) )
=> ( G = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(1079,plain,
! [C: vATMap,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vatmbind ) ) @ ( A @ vlookupATMap ) )
= ( B @ vsomeAType ) ),
inference(cnf,[status(esa)],[1078]) ).
thf(1080,plain,
! [C: vATMap,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vatmbind ) ) @ ( A @ vlookupATMap ) )
= ( B @ vsomeAType ) ),
inference(lifteq,[status(thm)],[1079]) ).
thf(137,axiom,
! [A: vATMap,B: vQID] :
( ( B @ vqvar @ ( A @ vecheck ) )
= ( A @ ( B @ vlookupATMap ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','echeck-3') ).
thf(1136,plain,
! [A: vATMap,B: vQID] :
( ( B @ vqvar @ ( A @ vecheck ) )
= ( A @ ( B @ vlookupATMap ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(1137,plain,
! [B: vQID,A: vATMap] :
( ( B @ vqvar @ ( A @ vecheck ) )
= ( A @ ( B @ vlookupATMap ) ) ),
inference(cnf,[status(esa)],[1136]) ).
thf(1138,plain,
! [B: vQID,A: vATMap] :
( ( A @ ( B @ vlookupATMap ) )
= ( B @ vqvar @ ( A @ vecheck ) ) ),
inference(lifteq,[status(thm)],[1137]) ).
thf(6675,plain,
! [C: vATMap,B: vAType,A: vQID] :
( ( A @ vqvar @ ( C @ ( B @ ( A @ vatmbind ) ) @ vecheck ) )
= ( B @ vsomeAType ) ),
inference(rewrite,[status(thm)],[1080,1138]) ).
thf(81,axiom,
! [A: vYN,B: vYN] :
( ? [C: vYN,D: vYN] :
( ( ( B @ ( A @ vor ) )
= vyes )
& ( B = D )
& ( A = C )
& ( ( D != vno )
| ( C != vno ) ) )
| ( ( ( B @ ( A @ vor ) )
= vno )
& ( B = vno )
& ( A = vno ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','or-INV') ).
thf(797,plain,
! [A: vYN,B: vYN] :
( ? [C: vYN,D: vYN] :
( ( ( B @ ( A @ vor ) )
= vyes )
& ( B = D )
& ( A = C )
& ( ( D != vno )
| ( C != vno ) ) )
| ( ( ( B @ ( A @ vor ) )
= vno )
& ( B = vno )
& ( A = vno ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(149,axiom,
! [A: vQuestionnaire,B: vQuestionnaire,C: vExp,D: vQuestionnaire,E: vQuestionnaire,F: vExp] :
( ( ( D @ ( E @ ( F @ vqcond ) ) )
= ( B @ ( A @ ( C @ vqcond ) ) ) )
=> ( ( D = B )
& ( E = A )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-qcond') ).
thf(1202,plain,
! [A: vQuestionnaire,B: vQuestionnaire,C: vExp,D: vQuestionnaire,E: vQuestionnaire,F: vExp] :
( ( ( D @ ( E @ ( F @ vqcond ) ) )
= ( B @ ( A @ ( C @ vqcond ) ) ) )
=> ( ( D = B )
& ( E = A )
& ( F = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(1203,plain,
! [F: vExp,E: vQuestionnaire,D: vQuestionnaire,C: vExp,B: vQuestionnaire,A: vQuestionnaire] :
( ( ( D = B )
| ( ( D @ ( E @ ( F @ vqcond ) ) )
!= ( B @ ( A @ ( C @ vqcond ) ) ) ) )
& ( ( E = A )
| ( ( D @ ( E @ ( F @ vqcond ) ) )
!= ( B @ ( A @ ( C @ vqcond ) ) ) ) )
& ( ( F = C )
| ( ( D @ ( E @ ( F @ vqcond ) ) )
!= ( B @ ( A @ ( C @ vqcond ) ) ) ) ) ),
inference(cnf,[status(esa)],[1202]) ).
thf(1204,plain,
! [F: vExp,E: vQuestionnaire,D: vQuestionnaire,C: vExp,B: vQuestionnaire,A: vQuestionnaire] :
( ( F = C )
| ( ( D @ ( E @ ( F @ vqcond ) ) )
!= ( B @ ( A @ ( C @ vqcond ) ) ) ) ),
inference(cnfConj,[status(thm)],[1203]) ).
thf(1207,plain,
! [F: vExp,E: vQuestionnaire,D: vQuestionnaire,C: vExp,B: vQuestionnaire,A: vQuestionnaire] :
( ( F = C )
| ( ( D @ ( E @ ( F @ vqcond ) ) )
!= ( B @ ( A @ ( C @ vqcond ) ) ) ) ),
inference(lifteq,[status(thm)],[1204]) ).
thf(1208,plain,
? [A: vQuestionnaire > vQuestionnaire > vQuestionnaire > vExp] :
! [B: vExp,C: vQuestionnaire,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vqcond ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[1207]) ).
thf(1209,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vExp] :
( ( C @ ( B @ ( A @ vqcond ) ) @ ( C @ ( B @ sk230 ) ) )
= A ),
inference(cnf,[status(esa)],[1208]) ).
thf(8353,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vExp] :
( ( C @ ( B @ ( A @ vqcond ) ) @ ( C @ ( B @ sk230 ) ) )
= A ),
inference(lifteq,[status(thm)],[1209]) ).
thf(9408,plain,
! [D: vAnsMap,C: vAval,B: vQID,A: vnat] :
( ( ( A @ vNum @ vtypeOf )
!= ( C @ vtypeOf ) )
| ( ( D @ vtypeAM @ ( vNumber @ ( B @ vatmbind ) ) )
= ( D @ ( C @ ( B @ vabind ) ) @ vtypeAM ) ) ),
inference(paramod_ordered,[status(thm)],[388,4845]) ).
thf(9409,plain,
! [C: vnat,B: vAnsMap,A: vQID] :
( ( B @ vtypeAM @ ( vNumber @ ( A @ vatmbind ) ) )
= ( B @ ( C @ vNum @ ( A @ vabind ) ) @ vtypeAM ) ),
inference(pattern_uni,[status(thm)],[9408:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ vNum ))]]) ).
thf(9428,plain,
! [C: vnat,B: vAnsMap,A: vQID] :
( ( B @ vtypeAM @ ( vNumber @ ( A @ vatmbind ) ) )
= ( B @ ( C @ vNum @ ( A @ vabind ) ) @ vtypeAM ) ),
inference(simp,[status(thm)],[9409]) ).
thf(197,axiom,
! [A: vAnsMap,B: vQMap,C: vQuestionnaire] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetQuest )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getQuest-0') ).
thf(4638,plain,
! [A: vAnsMap,B: vQMap,C: vQuestionnaire] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetQuest )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(424,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk61 ) )
| ( A
= ( A @ ( B @ sk65 ) ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(472,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk65 ) )
= A ) ),
inference(lifteq,[status(thm)],[424]) ).
thf(54,axiom,
! [A: vAType] : ( A @ vsomeAType @ visSomeAType ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeAType-1') ).
thf(669,plain,
! [A: vAType] : ( A @ vsomeAType @ visSomeAType ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(670,plain,
! [A: vAType] : ( A @ vsomeAType @ visSomeAType ),
inference(cnf,[status(esa)],[669]) ).
thf(97,axiom,
! [A: vOptQuestion] :
( ~ ( A @ visSomeQuestion )
=> ( A = vnoQuestion ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeQuestion-false-INV') ).
thf(898,plain,
! [A: vOptQuestion] :
( ~ ( A @ visSomeQuestion )
=> ( A = vnoQuestion ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(9444,plain,
! [E: vATMap,D: vAType,C: vQID,B: vAval,A: vQID] :
( ( ( vatmempty @ ( B @ vtypeOf @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( C @ vqvar @ ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ vecheck ) )
= ( D @ vsomeAType ) ) ),
inference(paramod_ordered,[status(thm)],[9403,6675]) ).
thf(9445,plain,
! [B: vAval,A: vQID] :
( ( A @ vqvar @ ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ vecheck ) )
= ( B @ vtypeOf @ vsomeAType ) ),
inference(pattern_uni,[status(thm)],[9444:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ vtypeOf )),bind(E,$thf( vatmempty ))]]) ).
thf(9476,plain,
! [B: vAval,A: vQID] :
( ( A @ vqvar @ ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ vecheck ) )
= ( B @ vtypeOf @ vsomeAType ) ),
inference(simp,[status(thm)],[9445]) ).
thf(10021,plain,
! [E: vATMap,D: vAType,C: vQID,B: vYN,A: vQID] :
( ( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM @ ( D @ ( C @ sk224 ) ) )
= E ) ),
inference(paramod_ordered,[status(thm)],[9480,8152]) ).
thf(10022,plain,
! [B: vYN,A: vQID] :
( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM @ ( vYesNo @ ( A @ sk224 ) ) )
= vatmempty ),
inference(pattern_uni,[status(thm)],[10021:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( vYesNo )),bind(E,$thf( vatmempty ))]]) ).
thf(190,axiom,
vqempty @ visValue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isValue-0') ).
thf(1391,plain,
vqempty @ visValue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(77,axiom,
! [A: vQuestionnaire,B: vQuestionnaire,C: vGID,D: vQuestionnaire,E: vExp] :
( ( B @ ( D @ ( E @ vqcond ) ) )
!= ( A @ ( C @ vqgroup ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qcond-qgroup') ).
thf(782,plain,
! [A: vQuestionnaire,B: vQuestionnaire,C: vGID,D: vQuestionnaire,E: vExp] :
( ( B @ ( D @ ( E @ vqcond ) ) )
!= ( A @ ( C @ vqgroup ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(17,axiom,
! [A: vAval] :
( ? [B: vstring] :
( ( ( A @ vtypeOf )
= vText )
& ( A
= ( B @ vT ) ) )
| ? [B: vnat] :
( ( ( A @ vtypeOf )
= vNumber )
& ( A
= ( B @ vNum ) ) )
| ? [B: vYN] :
( ( ( A @ vtypeOf )
= vYesNo )
& ( A
= ( B @ vB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','typeOf-INV') ).
thf(301,plain,
! [A: vAval] :
( ? [B: vstring] :
( ( ( A @ vtypeOf )
= vText )
& ( A
= ( B @ vT ) ) )
| ? [B: vnat] :
( ( ( A @ vtypeOf )
= vNumber )
& ( A
= ( B @ vNum ) ) )
| ? [B: vYN] :
( ( ( A @ vtypeOf )
= vYesNo )
& ( A
= ( B @ vB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1338,plain,
! [A: vQConf] :
( A
= ( A @ sk263 @ ( A @ sk262 @ ( A @ sk261 @ vQC ) ) ) ),
inference(cnf,[status(esa)],[1337]) ).
thf(1339,plain,
! [A: vQConf] :
( ( A @ sk263 @ ( A @ sk262 @ ( A @ sk261 @ vQC ) ) )
= A ),
inference(lifteq,[status(thm)],[1338]) ).
thf(6224,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ sk263 @ ( A @ sk262 @ ( A @ sk261 @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ vgetAM )
= B ) ),
inference(paramod_ordered,[status(thm)],[1339,1347]) ).
thf(6225,plain,
! [A: vQConf] :
( ( A @ sk261 )
= ( A @ vgetAM ) ),
inference(pattern_uni,[status(thm)],[6224:[bind(A,$thf( G )),bind(B,$thf( G @ sk261 )),bind(C,$thf( G @ sk262 )),bind(D,$thf( G @ sk263 ))]]) ).
thf(6234,plain,
! [A: vQConf] :
( ( A @ sk261 )
= ( A @ vgetAM ) ),
inference(simp,[status(thm)],[6225]) ).
thf(6251,plain,
! [A: vQConf] :
( ( A @ sk263 @ ( A @ sk262 @ ( A @ vgetAM @ vQC ) ) )
= A ),
inference(rewrite,[status(thm)],[1339,6234]) ).
thf(4639,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetQuest )
= C ),
inference(cnf,[status(esa)],[4638]) ).
thf(4640,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetQuest )
= C ),
inference(lifteq,[status(thm)],[4639]) ).
thf(6230,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ sk263 @ ( A @ sk262 @ ( A @ sk261 @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ vgetQuest )
= D ) ),
inference(paramod_ordered,[status(thm)],[1339,4640]) ).
thf(6231,plain,
! [A: vQConf] :
( ( A @ sk263 )
= ( A @ vgetQuest ) ),
inference(pattern_uni,[status(thm)],[6230:[bind(A,$thf( G )),bind(B,$thf( G @ sk261 )),bind(C,$thf( G @ sk262 )),bind(D,$thf( G @ sk263 ))]]) ).
thf(6237,plain,
! [A: vQConf] :
( ( A @ sk263 )
= ( A @ vgetQuest ) ),
inference(simp,[status(thm)],[6231]) ).
thf(250,axiom,
! [A: vAnsMap,B: vQMap,C: vQuestionnaire] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetQM )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getQM-0') ).
thf(4863,plain,
! [A: vAnsMap,B: vQMap,C: vQuestionnaire] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetQM )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(4864,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetQM )
= B ),
inference(cnf,[status(esa)],[4863]) ).
thf(4865,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ vgetQM )
= B ),
inference(lifteq,[status(thm)],[4864]) ).
thf(6232,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ sk263 @ ( A @ sk262 @ ( A @ sk261 @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ vgetQM )
= C ) ),
inference(paramod_ordered,[status(thm)],[1339,4865]) ).
thf(6233,plain,
! [A: vQConf] :
( ( A @ sk262 )
= ( A @ vgetQM ) ),
inference(pattern_uni,[status(thm)],[6232:[bind(A,$thf( G )),bind(B,$thf( G @ sk261 )),bind(C,$thf( G @ sk262 )),bind(D,$thf( G @ sk263 ))]]) ).
thf(6238,plain,
! [A: vQConf] :
( ( A @ sk262 )
= ( A @ vgetQM ) ),
inference(simp,[status(thm)],[6233]) ).
thf(6513,plain,
! [A: vQConf] :
( ( A @ vgetQuest @ ( A @ vgetQM @ ( A @ vgetAM @ vQC ) ) )
= A ),
inference(rewrite,[status(thm)],[6251,6237,6238]) ).
thf(157,axiom,
! [A: vQMap,B: vAnsMap,C: vQuestionnaire,D: vAnsMap,E: vQuestionnaire,F: vQMap] :
( ( ( E @ ( A @ ( D @ vQC ) ) )
= ( C @ ( F @ ( B @ vQC ) ) ) )
=> ( ( E = C )
& ( A = F )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-QC') ).
thf(1252,plain,
! [A: vQMap,B: vAnsMap,C: vQuestionnaire,D: vAnsMap,E: vQuestionnaire,F: vQMap] :
( ( ( E @ ( A @ ( D @ vQC ) ) )
= ( C @ ( F @ ( B @ vQC ) ) ) )
=> ( ( E = C )
& ( A = F )
& ( D = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(1253,plain,
! [F: vQMap,E: vQuestionnaire,D: vAnsMap,C: vQuestionnaire,B: vAnsMap,A: vQMap] :
( ( ( E = C )
| ( ( E @ ( A @ ( D @ vQC ) ) )
!= ( C @ ( F @ ( B @ vQC ) ) ) ) )
& ( ( A = F )
| ( ( E @ ( A @ ( D @ vQC ) ) )
!= ( C @ ( F @ ( B @ vQC ) ) ) ) )
& ( ( D = B )
| ( ( E @ ( A @ ( D @ vQC ) ) )
!= ( C @ ( F @ ( B @ vQC ) ) ) ) ) ),
inference(cnf,[status(esa)],[1252]) ).
thf(1256,plain,
! [F: vQMap,E: vQuestionnaire,D: vAnsMap,C: vQuestionnaire,B: vAnsMap,A: vQMap] :
( ( E = C )
| ( ( E @ ( A @ ( D @ vQC ) ) )
!= ( C @ ( F @ ( B @ vQC ) ) ) ) ),
inference(cnfConj,[status(thm)],[1253]) ).
thf(1263,plain,
! [F: vQMap,E: vQuestionnaire,D: vAnsMap,C: vQuestionnaire,B: vAnsMap,A: vQMap] :
( ( E = C )
| ( ( E @ ( A @ ( D @ vQC ) ) )
!= ( C @ ( F @ ( B @ vQC ) ) ) ) ),
inference(lifteq,[status(thm)],[1256]) ).
thf(1264,plain,
? [A: vAnsMap > vQMap > vQConf > vQuestionnaire] :
! [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vQC ) ) @ ( C @ ( B @ A ) ) )
= D ),
inference(detectInverse,[status(thm)],[1263]) ).
thf(1265,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ ( B @ ( A @ sk244 ) ) )
= C ),
inference(cnf,[status(esa)],[1264]) ).
thf(8693,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ ( B @ ( A @ sk244 ) ) )
= C ),
inference(lifteq,[status(thm)],[1265]) ).
thf(8696,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ vgetQuest @ ( A @ vgetQM @ ( A @ vgetAM @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ ( C @ ( B @ sk244 ) ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[6513,8693]) ).
thf(8697,plain,
! [A: vQConf] :
( ( A @ ( A @ vgetQM @ ( A @ vgetAM @ sk244 ) ) )
= ( A @ vgetQuest ) ),
inference(pattern_uni,[status(thm)],[8696:[bind(A,$thf( G )),bind(B,$thf( G @ vgetAM )),bind(C,$thf( G @ vgetQM )),bind(D,$thf( G @ vgetQuest ))]]) ).
thf(8699,plain,
! [A: vQConf] :
( ( A @ ( A @ vgetQM @ ( A @ vgetAM @ sk244 ) ) )
= ( A @ vgetQuest ) ),
inference(simp,[status(thm)],[8697]) ).
thf(4875,plain,
( ( ( sk5 @ vtypeAM )
!= ( vaempty @ vtypeAM ) )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( vatmempty @ vMC ) @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[4862,254]) ).
thf(4876,plain,
( ( sk5 != vaempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( vatmempty @ vMC ) @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[4875]) ).
thf(5686,plain,
! [A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk1 @ vtypeQM @ ( vatmempty @ vMC ) ) )
| ( sk5 != vaempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,4876]) ).
thf(5689,plain,
! [A: vMapConf] :
( ( ( A @ sk254 )
!= ( sk1 @ vtypeQM ) )
| ( ( A @ sk253 )
!= vatmempty )
| ( sk5 != vaempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5686]) ).
thf(5749,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk4 @ ( sk3 @ vMC ) ) )
| ( ( B @ sk254 )
!= ( sk1 @ vtypeQM ) )
| ( ( B @ sk253 )
!= vatmempty )
| ( sk5 != vaempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( B @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,5689]) ).
thf(5750,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 )
!= sk4 )
| ( ( A @ sk253 )
!= sk3 )
| ( ( B @ sk254 )
!= ( sk1 @ vtypeQM ) )
| ( ( B @ sk253 )
!= vatmempty )
| ( sk5 != vaempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( B @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5749]) ).
thf(598,plain,
! [B: vAType,A: vLabel] :
( ( ( ( B @ ( A @ vgetAnswer ) )
= ( A @ ( B @ sk128 ) @ vaskText @ vT ) )
| ~ ( B @ ( A @ sk126 ) )
| ~ ( B @ ( A @ sk124 ) ) )
& ( ( B = vText )
| ~ ( B @ ( A @ sk126 ) )
| ~ ( B @ ( A @ sk124 ) ) )
& ( ( A
= ( A @ ( B @ sk128 ) ) )
| ~ ( B @ ( A @ sk126 ) )
| ~ ( B @ ( A @ sk124 ) ) )
& ( ( B @ ( A @ sk126 ) )
| ( ( B @ ( A @ vgetAnswer ) )
= ( A @ ( B @ sk127 ) @ vaskNumber @ vNum ) )
| ~ ( B @ ( A @ sk124 ) ) )
& ( ( B @ ( A @ sk126 ) )
| ( B = vNumber )
| ~ ( B @ ( A @ sk124 ) ) )
& ( ( B @ ( A @ sk126 ) )
| ( A
= ( A @ ( B @ sk127 ) ) )
| ~ ( B @ ( A @ sk124 ) ) )
& ( ( B @ ( A @ sk124 ) )
| ( ( B @ ( A @ vgetAnswer ) )
= ( A @ ( B @ sk125 ) @ vaskYesNo @ vB ) ) )
& ( ( B @ ( A @ sk124 ) )
| ( B = vYesNo ) )
& ( ( B @ ( A @ sk124 ) )
| ( A
= ( A @ ( B @ sk125 ) ) ) ) ),
inference(cnf,[status(esa)],[597]) ).
thf(605,plain,
! [B: vAType,A: vLabel] :
( ( B @ ( A @ sk124 ) )
| ( B = vYesNo ) ),
inference(cnfConj,[status(thm)],[598]) ).
thf(610,plain,
! [B: vAType,A: vLabel] :
( ( B @ ( A @ sk124 ) )
| ( B = vYesNo ) ),
inference(lifteq,[status(thm)],[605]) ).
thf(7857,plain,
! [B: vAType,A: vLabel] :
( ( B != sk2 )
| ( sk5 != vaempty )
| ( sk1 != vqmempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( vatmempty @ vMC ) @ vptcheck ) ) )
| ( B @ ( A @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[610,4878]) ).
thf(7858,plain,
! [A: vLabel] :
( ( sk5 != vaempty )
| ( sk1 != vqmempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( vatmempty @ vMC ) @ vptcheck ) ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(pattern_uni,[status(thm)],[7857:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(397,plain,
! [B: vAval,A: vUnOpT] :
( ( B @ ( A @ sk31 ) )
| ( ( B @ ( A @ vevalUnOp ) )
= ( A @ ( B @ sk32 ) @ vnot @ vB @ vconstant @ vsomeExp ) ) ),
inference(cnfConj,[status(thm)],[391]) ).
thf(404,plain,
! [B: vAval,A: vUnOpT] :
( ( B @ ( A @ sk31 ) )
| ( ( B @ ( A @ vevalUnOp ) )
= ( A @ ( B @ sk32 ) @ vnot @ vB @ vconstant @ vsomeExp ) ) ),
inference(lifteq,[status(thm)],[397]) ).
thf(66,axiom,
! [A: vAval] :
( ( A @ ( A @ ( veqop @ vevalBinOp ) ) )
= ( vyes @ vB @ vconstant @ vsomeExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','evalBinOp-8') ).
thf(707,plain,
! [A: vAval] :
( ( A @ ( A @ ( veqop @ vevalBinOp ) ) )
= ( vyes @ vB @ vconstant @ vsomeExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(708,plain,
! [A: vAval] :
( ( A @ ( A @ ( veqop @ vevalBinOp ) ) )
= ( vyes @ vB @ vconstant @ vsomeExp ) ),
inference(cnf,[status(esa)],[707]) ).
thf(709,plain,
! [A: vAval] :
( ( A @ ( A @ ( veqop @ vevalBinOp ) ) )
= ( vyes @ vB @ vconstant @ vsomeExp ) ),
inference(lifteq,[status(thm)],[708]) ).
thf(1148,plain,
! [F: vAType,E: vQID,D: vAType,C: vATMap,B: vATMap,A: vQID] :
( ( E = A )
| ( ( C @ ( D @ ( E @ vatmbind ) ) )
!= ( B @ ( F @ ( A @ vatmbind ) ) ) ) ),
inference(cnfConj,[status(thm)],[1147]) ).
thf(1151,plain,
! [F: vAType,E: vQID,D: vAType,C: vATMap,B: vATMap,A: vQID] :
( ( E = A )
| ( ( C @ ( D @ ( E @ vatmbind ) ) )
!= ( B @ ( F @ ( A @ vatmbind ) ) ) ) ),
inference(lifteq,[status(thm)],[1148]) ).
thf(1152,plain,
? [A: vAType > vATMap > vATMap > vQID] :
! [B: vQID,C: vAType,D: vATMap] :
( ( D @ ( C @ ( B @ vatmbind ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[1151]) ).
thf(1153,plain,
! [C: vATMap,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vatmbind ) ) @ ( C @ ( B @ sk222 ) ) )
= A ),
inference(cnf,[status(esa)],[1152]) ).
thf(8147,plain,
! [C: vATMap,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vatmbind ) ) @ ( C @ ( B @ sk222 ) ) )
= A ),
inference(lifteq,[status(thm)],[1153]) ).
thf(9470,plain,
! [E: vATMap,D: vAType,C: vQID,B: vAval,A: vQID] :
( ( ( vatmempty @ ( B @ vtypeOf @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ ( E @ ( D @ sk222 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[9403,8147]) ).
thf(9471,plain,
! [B: vAval,A: vQID] :
( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ ( vatmempty @ ( B @ vtypeOf @ sk222 ) ) )
= A ),
inference(pattern_uni,[status(thm)],[9470:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ vtypeOf )),bind(E,$thf( vatmempty ))]]) ).
thf(9484,plain,
! [B: vAval,A: vQID] :
( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ ( vatmempty @ ( B @ vtypeOf @ sk222 ) ) )
= A ),
inference(simp,[status(thm)],[9471]) ).
thf(12119,plain,
! [D: vAval,C: vQID,B: vstring,A: vQID] :
( ( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ ( D @ ( C @ vabind ) ) @ vtypeAM ) )
| ( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) @ ( vatmempty @ ( D @ vtypeOf @ sk222 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[9477,9484]) ).
thf(12120,plain,
! [B: vstring,A: vQID] :
( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) @ ( vatmempty @ ( B @ vT @ vtypeOf @ sk222 ) ) )
= A ),
inference(pattern_uni,[status(thm)],[12119:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vT ))]]) ).
thf(12156,plain,
! [B: vstring,A: vQID] :
( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) @ ( vatmempty @ ( B @ vT @ vtypeOf @ sk222 ) ) )
= A ),
inference(simp,[status(thm)],[12120]) ).
thf(12212,plain,
! [A: vQID] :
( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) @ ( vatmempty @ ( vText @ sk222 ) ) )
= A ),
inference(rewrite,[status(thm)],[12156,353]) ).
thf(49,axiom,
! [A: vnat,B: vstring] :
( ( A @ vNum )
!= ( B @ vT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-Num-T') ).
thf(648,plain,
! [A: vnat,B: vstring] :
( ( A @ vNum )
!= ( B @ vT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(649,plain,
~ ? [A: vnat,B: vstring] :
( ( A @ vNum )
= ( B @ vT ) ),
inference(miniscope,[status(thm)],[648]) ).
thf(650,plain,
! [B: vstring,A: vnat] :
( ( A @ vNum )
!= ( B @ vT ) ),
inference(cnf,[status(esa)],[649]) ).
thf(651,plain,
! [B: vstring,A: vnat] :
( ( A @ vNum )
!= ( B @ vT ) ),
inference(lifteq,[status(thm)],[650]) ).
thf(3,axiom,
( ( vYesNo @ ( vYesNo @ ( vorop @ vcheckBinOp ) ) )
= ( vYesNo @ vsomeAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','checkBinOp-7') ).
thf(257,plain,
( ( vYesNo @ ( vYesNo @ ( vorop @ vcheckBinOp ) ) )
= ( vYesNo @ vsomeAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(123,axiom,
! [A: vQMap,B: vQID,C: vAType,D: vLabel,E: vQID] :
( ( E != B )
=> ( ( A @ ( C @ ( D @ ( B @ vqmbind ) ) ) @ ( E @ vlookupQMap ) )
= ( A @ ( E @ vlookupQMap ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookupQMap-2') ).
thf(1055,plain,
! [A: vQMap,B: vQID,C: vAType,D: vLabel,E: vQID] :
( ( E != B )
=> ( ( A @ ( C @ ( D @ ( B @ vqmbind ) ) ) @ ( E @ vlookupQMap ) )
= ( A @ ( E @ vlookupQMap ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(12862,plain,
! [F: vAnsMap,E: vAval,D: vQID,C: vnat,B: vAnsMap,A: vQID] :
( ( ( B @ ( C @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( F @ ( E @ ( D @ vabind ) ) @ vtypeAM ) )
| ( ( B @ vtypeAM @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9428,9436]) ).
thf(12863,plain,
! [B: vAnsMap,A: vQID] :
( ( B @ vtypeAM @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[12862:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( A )),bind(E,$thf( G @ vNum )),bind(F,$thf( B ))]]) ).
thf(13138,plain,
! [D: vAnsMap,C: vQID,B: vYN,A: vQID] :
( ( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM )
!= ( D @ vtypeAM ) )
| ( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( vNumber @ ( C @ vatmbind ) ) )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9480,12863]) ).
thf(13139,plain,
! [B: vQID,A: vQID] :
( ( vatmempty @ ( vYesNo @ ( B @ vatmbind ) ) @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[13138:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( vaempty @ ( H @ vB @ ( E @ vabind ) ) ))]]) ).
thf(13156,plain,
! [B: vQID,A: vQID] :
( ( vatmempty @ ( vYesNo @ ( B @ vatmbind ) ) @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(simp,[status(thm)],[13139]) ).
thf(13165,plain,
! [D: vQID,C: vQID,B: vYN,A: vQID] :
( ( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) )
!= ( vatmempty @ ( vYesNo @ ( D @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM @ ( vNumber @ ( C @ vatmbind ) ) )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9480,13156]) ).
thf(13166,plain,
! [C: vQID,B: vYN,A: vQID] :
( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM @ ( vNumber @ ( C @ vatmbind ) ) )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[13165:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(13632,plain,
! [E: vQID,D: vYN,C: vQID,B: vYN,A: vQID] :
( ( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ ( D @ vB @ ( C @ vabind ) ) @ vtypeAM ) )
| ( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( vNumber @ ( E @ vatmbind ) ) )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9480,13166]) ).
thf(13633,plain,
! [B: vQID,A: vQID] :
( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( vNumber @ ( B @ vatmbind ) ) )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[13632:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(13658,plain,
! [B: vQID,A: vQID] :
( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( vNumber @ ( B @ vatmbind ) ) )
!= vatmempty ),
inference(simp,[status(thm)],[13633]) ).
thf(423,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk35 ) )
| ( B
= ( A @ ( B @ sk37 ) @ vB @ vconstant ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(458,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk37 ) @ vB @ vconstant )
= B ) ),
inference(lifteq,[status(thm)],[423]) ).
thf(348,plain,
~ ? [A: vAval,B: vUnOpT,C: vExp] :
( ( A @ vconstant )
= ( C @ ( B @ vunop ) ) ),
inference(miniscope,[status(thm)],[347]) ).
thf(349,plain,
! [C: vExp,B: vUnOpT,A: vAval] :
( ( A @ vconstant )
!= ( C @ ( B @ vunop ) ) ),
inference(cnf,[status(esa)],[348]) ).
thf(350,plain,
! [C: vExp,B: vUnOpT,A: vAval] :
( ( A @ vconstant )
!= ( C @ ( B @ vunop ) ) ),
inference(lifteq,[status(thm)],[349]) ).
thf(9025,plain,
! [E: vExp,D: vUnOpT,C: vAval,B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk37 ) @ vB @ vconstant )
!= ( C @ vconstant ) )
| ( B
!= ( E @ ( D @ vunop ) ) )
| ( B @ ( A @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[458,350]) ).
thf(9026,plain,
! [D: vATMap,C: vExp,B: vExp,A: vUnOpT] :
( ( C
!= ( B @ ( A @ vunop ) ) )
| ( C @ ( D @ sk35 ) ) ),
inference(pattern_uni,[status(thm)],[9025:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ sk37 ) @ vB )),bind(D,$thf( D )),bind(E,$thf( E ))]]) ).
thf(9067,plain,
! [C: vATMap,B: vExp,A: vUnOpT] : ( B @ ( A @ vunop ) @ ( C @ sk35 ) ),
inference(simp,[status(thm)],[9026]) ).
thf(165,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vATMap,F: vQID] :
( ( ( ( A @ ( F @ vlookupATMap ) )
= ( D @ vsomeAType ) )
& ( C @ ( E @ vMC ) @ ( F @ vask @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) ) )
=> ( E
= ( B @ ( D @ ( F @ vatmbind ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Task_inv3') ).
thf(1298,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vATMap,F: vQID] :
( ( ( ( A @ ( F @ vlookupATMap ) )
= ( D @ vsomeAType ) )
& ( C @ ( E @ vMC ) @ ( F @ vask @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) ) )
=> ( E
= ( B @ ( D @ ( F @ vatmbind ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(1273,plain,
! [F: vExp,E: vAType,D: vQID,C: vAType,B: vExp,A: vQID] :
( ( F = B )
| ( ( F @ ( C @ ( D @ vvalue ) ) )
!= ( B @ ( E @ ( A @ vvalue ) ) ) ) ),
inference(cnfConj,[status(thm)],[1270]) ).
thf(1280,plain,
! [F: vExp,E: vAType,D: vQID,C: vAType,B: vExp,A: vQID] :
( ( F = B )
| ( ( F @ ( C @ ( D @ vvalue ) ) )
!= ( B @ ( E @ ( A @ vvalue ) ) ) ) ),
inference(lifteq,[status(thm)],[1273]) ).
thf(1281,plain,
? [A: vQID > vAType > vEntry > vExp] :
! [B: vQID,C: vAType,D: vExp] :
( ( D @ ( C @ ( B @ vvalue ) ) @ ( C @ ( B @ A ) ) )
= D ),
inference(detectInverse,[status(thm)],[1280]) ).
thf(1282,plain,
! [C: vExp,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vvalue ) ) @ ( B @ ( A @ sk247 ) ) )
= C ),
inference(cnf,[status(esa)],[1281]) ).
thf(8919,plain,
! [C: vExp,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vvalue ) ) @ ( B @ ( A @ sk247 ) ) )
= C ),
inference(lifteq,[status(thm)],[1282]) ).
thf(105,axiom,
! [A: vExp] :
( ( A @ vexpIsValue )
=> ? [B: vAval] :
( A
= ( B @ vconstant ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','expIsValue-true-INV') ).
thf(949,plain,
! [A: vExp] :
( ( A @ vexpIsValue )
=> ? [B: vAval] :
( A
= ( B @ vconstant ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(426,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk47 ) )
| ( ( B @ ( A @ vecheck ) )
= ( A @ ( B @ sk51 ) @ vgetAType @ ( A @ ( B @ sk49 ) @ vgetAType @ ( A @ ( B @ sk53 ) @ vcheckBinOp ) ) ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(460,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk51 ) @ vgetAType @ ( A @ ( B @ sk49 ) @ vgetAType @ ( A @ ( B @ sk53 ) @ vcheckBinOp ) ) )
= ( B @ ( A @ vecheck ) ) ) ),
inference(lifteq,[status(thm)],[426]) ).
thf(209,axiom,
! [A: vQuestionnaire,B: vAnsMap,C: vQMap] :
( ( C @ ( B @ ( A @ ( vqempty @ vqseq ) @ vreduce ) ) )
= ( A @ ( C @ ( B @ vQC ) ) @ vsomeQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-8') ).
thf(4692,plain,
! [A: vQuestionnaire,B: vAnsMap,C: vQMap] :
( ( C @ ( B @ ( A @ ( vqempty @ vqseq ) @ vreduce ) ) )
= ( A @ ( C @ ( B @ vQC ) ) @ vsomeQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(783,plain,
~ ? [A: vQuestionnaire,B: vQuestionnaire,C: vGID,D: vQuestionnaire,E: vExp] :
( ( B @ ( D @ ( E @ vqcond ) ) )
= ( A @ ( C @ vqgroup ) ) ),
inference(miniscope,[status(thm)],[782]) ).
thf(784,plain,
! [E: vExp,D: vQuestionnaire,C: vGID,B: vQuestionnaire,A: vQuestionnaire] :
( ( B @ ( D @ ( E @ vqcond ) ) )
!= ( A @ ( C @ vqgroup ) ) ),
inference(cnf,[status(esa)],[783]) ).
thf(785,plain,
! [E: vExp,D: vQuestionnaire,C: vGID,B: vQuestionnaire,A: vQuestionnaire] :
( ( B @ ( D @ ( E @ vqcond ) ) )
!= ( A @ ( C @ vqgroup ) ) ),
inference(lifteq,[status(thm)],[784]) ).
thf(33,axiom,
! [A: vATMap,B: vExp,C: vExp,D: vBinOpT] :
( ~ ( ( C @ ( A @ vecheck ) @ visSomeAType )
& ( B @ ( A @ vecheck ) @ visSomeAType ) )
=> ( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= vnoAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','echeck-5') ).
thf(372,plain,
! [A: vATMap,B: vExp,C: vExp,D: vBinOpT] :
( ~ ( ( C @ ( A @ vecheck ) @ visSomeAType )
& ( B @ ( A @ vecheck ) @ visSomeAType ) )
=> ( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= vnoAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(67,axiom,
! [A: vUnOpT,B: vExp,C: vUnOpT,D: vExp] :
( ( ( B @ ( A @ vunop ) )
= ( D @ ( C @ vunop ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-unop') ).
thf(710,plain,
! [A: vUnOpT,B: vExp,C: vUnOpT,D: vExp] :
( ( ( B @ ( A @ vunop ) )
= ( D @ ( C @ vunop ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(711,plain,
! [D: vExp,C: vUnOpT,B: vExp,A: vUnOpT] :
( ( ( B = D )
| ( ( B @ ( A @ vunop ) )
!= ( D @ ( C @ vunop ) ) ) )
& ( ( A = C )
| ( ( B @ ( A @ vunop ) )
!= ( D @ ( C @ vunop ) ) ) ) ),
inference(cnf,[status(esa)],[710]) ).
thf(713,plain,
! [D: vExp,C: vUnOpT,B: vExp,A: vUnOpT] :
( ( B = D )
| ( ( B @ ( A @ vunop ) )
!= ( D @ ( C @ vunop ) ) ) ),
inference(cnfConj,[status(thm)],[711]) ).
thf(717,plain,
! [D: vExp,C: vUnOpT,B: vExp,A: vUnOpT] :
( ( B = D )
| ( ( B @ ( A @ vunop ) )
!= ( D @ ( C @ vunop ) ) ) ),
inference(lifteq,[status(thm)],[713]) ).
thf(718,plain,
? [A: vUnOpT > vExp > vExp] :
! [B: vUnOpT,C: vExp] :
( ( C @ ( B @ vunop ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[717]) ).
thf(719,plain,
! [B: vExp,A: vUnOpT] :
( ( B @ ( A @ vunop ) @ ( A @ sk137 ) )
= B ),
inference(cnf,[status(esa)],[718]) ).
thf(5910,plain,
! [B: vExp,A: vUnOpT] :
( ( B @ ( A @ vunop ) @ ( A @ sk137 ) )
= B ),
inference(lifteq,[status(thm)],[719]) ).
thf(64,axiom,
! [A: vYN,B: vYN] :
( ( B @ vB @ ( A @ vB @ ( vandop @ vevalBinOp ) ) )
= ( B @ ( A @ vand ) @ vB @ vconstant @ vsomeExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','evalBinOp-6') ).
thf(702,plain,
! [A: vYN,B: vYN] :
( ( B @ vB @ ( A @ vB @ ( vandop @ vevalBinOp ) ) )
= ( B @ ( A @ vand ) @ vB @ vconstant @ vsomeExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(73,axiom,
( ( vYesNo @ ( vnotop @ vcheckUnOp ) )
= ( vYesNo @ vsomeAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','checkUnOp-0') ).
thf(751,plain,
( ( vYesNo @ ( vnotop @ vcheckUnOp ) )
= ( vYesNo @ vsomeAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(28,axiom,
! [A: vOptExp] :
( ? [B: vExp] :
( A
= ( B @ vsomeExp ) )
| ( A = vnoExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-OptExp') ).
thf(357,plain,
! [A: vOptExp] :
( ? [B: vExp] :
( A
= ( B @ vsomeExp ) )
| ( A = vnoExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(234,axiom,
! [A: vQConf] :
? [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( ( A @ vgetAM )
= B )
& ( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getAM-INV') ).
thf(4798,plain,
! [A: vQConf] :
? [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( ( A @ vgetAM )
= B )
& ( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(4799,plain,
! [A: vQConf] :
? [B: vAnsMap] :
( ( ( A @ vgetAM )
= B )
& ? [C: vQMap,D: vQuestionnaire] :
( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ),
inference(miniscope,[status(thm)],[4798]) ).
thf(4800,plain,
! [A: vQConf] :
( ( ( A @ vgetAM )
= ( A @ sk386 ) )
& ( A
= ( A @ sk388 @ ( A @ sk387 @ ( A @ sk386 @ vQC ) ) ) ) ),
inference(cnf,[status(esa)],[4799]) ).
thf(4801,plain,
! [A: vQConf] :
( A
= ( A @ sk388 @ ( A @ sk387 @ ( A @ sk386 @ vQC ) ) ) ),
inference(cnfConj,[status(thm)],[4800]) ).
thf(4803,plain,
! [A: vQConf] :
( ( A @ sk388 @ ( A @ sk387 @ ( A @ sk386 @ vQC ) ) )
= A ),
inference(lifteq,[status(thm)],[4801]) ).
thf(4802,plain,
! [A: vQConf] :
( ( A @ vgetAM )
= ( A @ sk386 ) ),
inference(cnfConj,[status(thm)],[4800]) ).
thf(4804,plain,
! [A: vQConf] :
( ( A @ sk386 )
= ( A @ vgetAM ) ),
inference(lifteq,[status(thm)],[4802]) ).
thf(6421,plain,
! [A: vQConf] :
( ( A @ sk388 @ ( A @ sk387 @ ( A @ vgetAM @ vQC ) ) )
= A ),
inference(rewrite,[status(thm)],[4803,4804]) ).
thf(6432,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ sk388 @ ( A @ sk387 @ ( A @ vgetAM @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ vgetQM )
= C ) ),
inference(paramod_ordered,[status(thm)],[6421,4865]) ).
thf(6433,plain,
! [A: vQConf] :
( ( A @ sk387 )
= ( A @ vgetQM ) ),
inference(pattern_uni,[status(thm)],[6432:[bind(A,$thf( G )),bind(B,$thf( G @ vgetAM )),bind(C,$thf( G @ sk387 )),bind(D,$thf( G @ sk388 ))]]) ).
thf(6434,plain,
! [A: vQConf] :
( ( A @ sk387 )
= ( A @ vgetQM ) ),
inference(simp,[status(thm)],[6433]) ).
thf(228,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vdefquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( F = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tdefquestion_inv2') ).
thf(4766,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vdefquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( F = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(124,axiom,
( ( vyes @ ( vyes @ vand ) )
= vyes ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and-0') ).
thf(1058,plain,
( ( vyes @ ( vyes @ vand ) )
= vyes ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(1059,plain,
( ( vyes @ ( vyes @ vand ) )
= vyes ),
inference(lifteq,[status(thm)],[1058]) ).
thf(20,axiom,
! [A: vQID,B: vExp,C: vBinOpT,D: vExp] :
( ( A @ vqvar )
!= ( D @ ( C @ ( B @ vbinop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qvar-binop') ).
thf(322,plain,
! [A: vQID,B: vExp,C: vBinOpT,D: vExp] :
( ( A @ vqvar )
!= ( D @ ( C @ ( B @ vbinop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(323,plain,
~ ? [A: vQID,B: vExp,C: vBinOpT,D: vExp] :
( ( A @ vqvar )
= ( D @ ( C @ ( B @ vbinop ) ) ) ),
inference(miniscope,[status(thm)],[322]) ).
thf(324,plain,
! [D: vExp,C: vBinOpT,B: vExp,A: vQID] :
( ( A @ vqvar )
!= ( D @ ( C @ ( B @ vbinop ) ) ) ),
inference(cnf,[status(esa)],[323]) ).
thf(325,plain,
! [D: vExp,C: vBinOpT,B: vExp,A: vQID] :
( ( A @ vqvar )
!= ( D @ ( C @ ( B @ vbinop ) ) ) ),
inference(lifteq,[status(thm)],[324]) ).
thf(395,plain,
! [B: vAval,A: vUnOpT] :
( ( B @ ( A @ sk31 ) )
| ( B
= ( A @ ( B @ sk32 ) @ vB ) ) ),
inference(cnfConj,[status(thm)],[391]) ).
thf(403,plain,
! [B: vAval,A: vUnOpT] :
( ( B @ ( A @ sk31 ) )
| ( ( A @ ( B @ sk32 ) @ vB )
= B ) ),
inference(lifteq,[status(thm)],[395]) ).
thf(57,axiom,
! [A: vYN,B: vstring] :
( ( A @ vB )
!= ( B @ vT ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-B-T') ).
thf(679,plain,
! [A: vYN,B: vstring] :
( ( A @ vB )
!= ( B @ vT ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(680,plain,
~ ? [A: vYN,B: vstring] :
( ( A @ vB )
= ( B @ vT ) ),
inference(miniscope,[status(thm)],[679]) ).
thf(681,plain,
! [B: vstring,A: vYN] :
( ( A @ vB )
!= ( B @ vT ) ),
inference(cnf,[status(esa)],[680]) ).
thf(682,plain,
! [B: vstring,A: vYN] :
( ( A @ vB )
!= ( B @ vT ) ),
inference(lifteq,[status(thm)],[681]) ).
thf(6976,plain,
! [D: vstring,C: vYN,B: vAval,A: vUnOpT] :
( ( ( A @ ( B @ sk32 ) @ vB )
!= ( C @ vB ) )
| ( B
!= ( D @ vT ) )
| ( B @ ( A @ sk31 ) ) ),
inference(paramod_ordered,[status(thm)],[403,682]) ).
thf(6977,plain,
! [C: vUnOpT,B: vAval,A: vstring] :
( ( B
!= ( A @ vT ) )
| ( B @ ( C @ sk31 ) ) ),
inference(pattern_uni,[status(thm)],[6976:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk32 ) ))]]) ).
thf(7013,plain,
! [B: vUnOpT,A: vstring] : ( A @ vT @ ( B @ sk31 ) ),
inference(simp,[status(thm)],[6977]) ).
thf(7042,plain,
! [D: vAval,C: vUnOpT,B: vUnOpT,A: vstring] :
( ( ( A @ vT @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ~ $true
| ( ( C @ ( D @ sk34 ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[7013,401]) ).
thf(7043,plain,
! [D: vAval,C: vUnOpT,B: vUnOpT,A: vstring] :
( ( ( A @ vT @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ( ( C @ ( D @ sk34 ) )
= D ) ),
inference(simp,[status(thm)],[7042]) ).
thf(7044,plain,
! [B: vstring,A: vUnOpT] :
( ( A @ ( B @ vT @ sk34 ) )
= ( B @ vT ) ),
inference(pattern_uni,[status(thm)],[7043:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ vT ))]]) ).
thf(7047,plain,
! [B: vstring,A: vUnOpT] :
( ( A @ ( B @ vT @ sk34 ) )
= ( B @ vT ) ),
inference(simp,[status(thm)],[7044]) ).
thf(1255,plain,
! [F: vQMap,E: vQuestionnaire,D: vAnsMap,C: vQuestionnaire,B: vAnsMap,A: vQMap] :
( ( A = F )
| ( ( E @ ( A @ ( D @ vQC ) ) )
!= ( C @ ( F @ ( B @ vQC ) ) ) ) ),
inference(cnfConj,[status(thm)],[1253]) ).
thf(1260,plain,
! [F: vQMap,E: vQuestionnaire,D: vAnsMap,C: vQuestionnaire,B: vAnsMap,A: vQMap] :
( ( A = F )
| ( ( E @ ( A @ ( D @ vQC ) ) )
!= ( C @ ( F @ ( B @ vQC ) ) ) ) ),
inference(lifteq,[status(thm)],[1255]) ).
thf(1261,plain,
? [A: vAnsMap > vQuestionnaire > vQConf > vQMap] :
! [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vQC ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[1260]) ).
thf(1262,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ ( C @ ( A @ sk243 ) ) )
= B ),
inference(cnf,[status(esa)],[1261]) ).
thf(8674,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ ( C @ ( A @ sk243 ) ) )
= B ),
inference(lifteq,[status(thm)],[1262]) ).
thf(448,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk58 ) @ visSomeAType )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(1174,plain,
! [F: vAnsMap,E: vQID,D: vAval,C: vAval,B: vAnsMap,A: vQID] :
( ( ( F = B )
| ( ( F @ ( C @ ( E @ vabind ) ) )
!= ( B @ ( D @ ( A @ vabind ) ) ) ) )
& ( ( C = D )
| ( ( F @ ( C @ ( E @ vabind ) ) )
!= ( B @ ( D @ ( A @ vabind ) ) ) ) )
& ( ( E = A )
| ( ( F @ ( C @ ( E @ vabind ) ) )
!= ( B @ ( D @ ( A @ vabind ) ) ) ) ) ),
inference(cnf,[status(esa)],[1173]) ).
thf(1177,plain,
! [F: vAnsMap,E: vQID,D: vAval,C: vAval,B: vAnsMap,A: vQID] :
( ( F = B )
| ( ( F @ ( C @ ( E @ vabind ) ) )
!= ( B @ ( D @ ( A @ vabind ) ) ) ) ),
inference(cnfConj,[status(thm)],[1174]) ).
thf(1184,plain,
! [F: vAnsMap,E: vQID,D: vAval,C: vAval,B: vAnsMap,A: vQID] :
( ( F = B )
| ( ( F @ ( C @ ( E @ vabind ) ) )
!= ( B @ ( D @ ( A @ vabind ) ) ) ) ),
inference(lifteq,[status(thm)],[1177]) ).
thf(1185,plain,
? [A: vQID > vAval > vAnsMap > vAnsMap] :
! [B: vQID,C: vAval,D: vAnsMap] :
( ( D @ ( C @ ( B @ vabind ) ) @ ( C @ ( B @ A ) ) )
= D ),
inference(detectInverse,[status(thm)],[1184]) ).
thf(1186,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( C @ ( B @ ( A @ vabind ) ) @ ( B @ ( A @ sk227 ) ) )
= C ),
inference(cnf,[status(esa)],[1185]) ).
thf(8352,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( C @ ( B @ ( A @ vabind ) ) @ ( B @ ( A @ sk227 ) ) )
= C ),
inference(lifteq,[status(thm)],[1186]) ).
thf(231,axiom,
! [A: vQMap,B: vAType,C: vATMap,D: vATMap,E: vAnsMap,F: vQID,G: vExp] :
( ( ( D @ ( C @ vMC ) @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ ( A @ vtypeQM @ ( E @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ visValue )
& ( G @ vexpIsValue ) )
=> ? [H: vAnsMap,I: vQMap,J: vQuestionnaire] :
( ( A @ ( E @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( J @ ( I @ ( H @ vQC ) ) @ vsomeQConf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Progress-qsingle-value-expIsValue-True') ).
thf(4788,plain,
! [A: vQMap,B: vAType,C: vATMap,D: vATMap,E: vAnsMap,F: vQID,G: vExp] :
( ( ( D @ ( C @ vMC ) @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ ( A @ vtypeQM @ ( E @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ visValue )
& ( G @ vexpIsValue ) )
=> ? [H: vAnsMap,I: vQMap,J: vQuestionnaire] :
( ( A @ ( E @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( J @ ( I @ ( H @ vQC ) ) @ vsomeQConf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(12,axiom,
! [A: vOptAType] :
( ( A @ visSomeAType )
=> ? [B: vAType] :
( A
= ( B @ vsomeAType ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeAType-true-INV') ).
thf(282,plain,
! [A: vOptAType] :
( ( A @ visSomeAType )
=> ? [B: vAType] :
( A
= ( B @ vsomeAType ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(283,plain,
! [A: vOptAType] :
( ( A
= ( A @ sk8 @ vsomeAType ) )
| ~ ( A @ visSomeAType ) ),
inference(cnf,[status(esa)],[282]) ).
thf(284,plain,
! [A: vOptAType] :
( ~ ( A @ visSomeAType )
| ( ( A @ sk8 @ vsomeAType )
= A ) ),
inference(lifteq,[status(thm)],[283]) ).
thf(100,axiom,
! [A: vQID] :
( ( vatmempty @ ( A @ vlookupATMap ) )
= vnoAType ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookupATMap-0') ).
thf(908,plain,
! [A: vQID] :
( ( vatmempty @ ( A @ vlookupATMap ) )
= vnoAType ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(909,plain,
! [A: vQID] :
( ( vatmempty @ ( A @ vlookupATMap ) )
= vnoAType ),
inference(cnf,[status(esa)],[908]) ).
thf(910,plain,
! [A: vQID] :
( ( vatmempty @ ( A @ vlookupATMap ) )
= vnoAType ),
inference(lifteq,[status(thm)],[909]) ).
thf(5925,plain,
! [A: vQID] :
( ( A @ vqvar @ ( vatmempty @ vecheck ) )
= vnoAType ),
inference(rewrite,[status(thm)],[910,1138]) ).
thf(93,axiom,
! [A: vUnOpT,B: vAType] :
( ( ( B != vYesNo )
| ( A != vnotop ) )
=> ( ( B @ ( A @ vcheckUnOp ) )
= vnoAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','checkUnOp-1') ).
thf(881,plain,
! [A: vUnOpT,B: vAType] :
( ( ( B != vYesNo )
| ( A != vnotop ) )
=> ( ( B @ ( A @ vcheckUnOp ) )
= vnoAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(40,axiom,
! [A: vAval,B: vExp,C: vBinOpT,D: vExp] :
( ( A @ vconstant )
!= ( D @ ( C @ ( B @ vbinop ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-constant-binop') ).
thf(413,plain,
! [A: vAval,B: vExp,C: vBinOpT,D: vExp] :
( ( A @ vconstant )
!= ( D @ ( C @ ( B @ vbinop ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(414,plain,
~ ? [A: vAval,B: vExp,C: vBinOpT,D: vExp] :
( ( A @ vconstant )
= ( D @ ( C @ ( B @ vbinop ) ) ) ),
inference(miniscope,[status(thm)],[413]) ).
thf(415,plain,
! [D: vExp,C: vBinOpT,B: vExp,A: vAval] :
( ( A @ vconstant )
!= ( D @ ( C @ ( B @ vbinop ) ) ) ),
inference(cnf,[status(esa)],[414]) ).
thf(416,plain,
! [D: vExp,C: vBinOpT,B: vExp,A: vAval] :
( ( A @ vconstant )
!= ( D @ ( C @ ( B @ vbinop ) ) ) ),
inference(lifteq,[status(thm)],[415]) ).
thf(6963,plain,
! [D: vnat,C: vYN,B: vAval,A: vUnOpT] :
( ( ( A @ ( B @ sk32 ) @ vB )
!= ( C @ vB ) )
| ( B
!= ( D @ vNum ) )
| ( B @ ( A @ sk31 ) ) ),
inference(paramod_ordered,[status(thm)],[403,385]) ).
thf(6964,plain,
! [C: vUnOpT,B: vAval,A: vnat] :
( ( B
!= ( A @ vNum ) )
| ( B @ ( C @ sk31 ) ) ),
inference(pattern_uni,[status(thm)],[6963:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk32 ) ))]]) ).
thf(7020,plain,
! [B: vUnOpT,A: vnat] : ( A @ vNum @ ( B @ sk31 ) ),
inference(simp,[status(thm)],[6964]) ).
thf(7065,plain,
! [D: vAval,C: vUnOpT,B: vUnOpT,A: vnat] :
( ( ( A @ vNum @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ~ $true
| ( ( C @ ( D @ sk34 ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[7020,401]) ).
thf(7066,plain,
! [D: vAval,C: vUnOpT,B: vUnOpT,A: vnat] :
( ( ( A @ vNum @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ( ( C @ ( D @ sk34 ) )
= D ) ),
inference(simp,[status(thm)],[7065]) ).
thf(7067,plain,
! [B: vnat,A: vUnOpT] :
( ( A @ ( B @ vNum @ sk34 ) )
= ( B @ vNum ) ),
inference(pattern_uni,[status(thm)],[7066:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ vNum ))]]) ).
thf(7075,plain,
! [B: vnat,A: vUnOpT] :
( ( A @ ( B @ vNum @ sk34 ) )
= ( B @ vNum ) ),
inference(simp,[status(thm)],[7067]) ).
thf(117,axiom,
! [A: vQID,B: vLabel,C: vAType,D: vQID,E: vAType,F: vLabel] :
( ( ( C @ ( F @ ( D @ vquestion ) ) )
= ( E @ ( B @ ( A @ vquestion ) ) ) )
=> ( ( C = E )
& ( F = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-question') ).
thf(1023,plain,
! [A: vQID,B: vLabel,C: vAType,D: vQID,E: vAType,F: vLabel] :
( ( ( C @ ( F @ ( D @ vquestion ) ) )
= ( E @ ( B @ ( A @ vquestion ) ) ) )
=> ( ( C = E )
& ( F = B )
& ( D = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(1024,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( ( C = E )
| ( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vquestion ) ) ) ) )
& ( ( F = B )
| ( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vquestion ) ) ) ) )
& ( ( D = A )
| ( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vquestion ) ) ) ) ) ),
inference(cnf,[status(esa)],[1023]) ).
thf(1025,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( D = A )
| ( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vquestion ) ) ) ) ),
inference(cnfConj,[status(thm)],[1024]) ).
thf(1028,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( D = A )
| ( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vquestion ) ) ) ) ),
inference(lifteq,[status(thm)],[1025]) ).
thf(1029,plain,
? [A: vLabel > vAType > vEntry > vQID] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vquestion ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[1028]) ).
thf(1030,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vquestion ) ) @ ( C @ ( B @ sk203 ) ) )
= A ),
inference(cnf,[status(esa)],[1029]) ).
thf(6936,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vquestion ) ) @ ( C @ ( B @ sk203 ) ) )
= A ),
inference(lifteq,[status(thm)],[1030]) ).
thf(18,axiom,
! [A: vQID,B: vAnsMap] :
( ~ ( B @ ( A @ vlookupAnsMap ) @ visSomeAval )
=> ( ( B @ ( A @ vqvar @ vreduceExp ) )
= vnoExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-2') ).
thf(316,plain,
! [A: vQID,B: vAnsMap] :
( ~ ( B @ ( A @ vlookupAnsMap ) @ visSomeAval )
=> ( ( B @ ( A @ vqvar @ vreduceExp ) )
= vnoExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
! [A: vnat,B: vnat] :
( ( ( A @ vNum )
= ( B @ vNum ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-Num') ).
thf(290,plain,
! [A: vnat,B: vnat] :
( ( ( A @ vNum )
= ( B @ vNum ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(291,plain,
! [B: vnat,A: vnat] :
( ( A = B )
| ( ( A @ vNum )
!= ( B @ vNum ) ) ),
inference(cnf,[status(esa)],[290]) ).
thf(292,plain,
! [B: vnat,A: vnat] :
( ( A = B )
| ( ( A @ vNum )
!= ( B @ vNum ) ) ),
inference(lifteq,[status(thm)],[291]) ).
thf(293,plain,
? [A: vAval > vnat] :
! [B: vnat] :
( ( B @ vNum @ A )
= B ),
inference(detectInverse,[status(thm)],[292]) ).
thf(294,plain,
! [A: vnat] :
( ( A @ vNum @ sk10 )
= A ),
inference(cnf,[status(esa)],[293]) ).
thf(5076,plain,
! [A: vnat] :
( ( A @ vNum @ sk10 )
= A ),
inference(lifteq,[status(thm)],[294]) ).
thf(7034,plain,
! [E: vYN,D: vAval,C: vUnOpT,B: vUnOpT,A: vstring] :
( ( ( A @ vT @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ~ $true
| ( ( C @ ( D @ sk34 ) )
!= ( E @ vB ) ) ),
inference(paramod_ordered,[status(thm)],[7013,6784]) ).
thf(7035,plain,
! [E: vYN,D: vAval,C: vUnOpT,B: vUnOpT,A: vstring] :
( ( ( A @ vT @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ( ( C @ ( D @ sk34 ) )
!= ( E @ vB ) ) ),
inference(simp,[status(thm)],[7034]) ).
thf(7036,plain,
! [C: vstring,B: vYN,A: vUnOpT] :
( ( A @ ( C @ vT @ sk34 ) )
!= ( B @ vB ) ),
inference(pattern_uni,[status(thm)],[7035:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( F @ vT ))]]) ).
thf(7051,plain,
! [C: vstring,B: vYN,A: vUnOpT] :
( ( A @ ( C @ vT @ sk34 ) )
!= ( B @ vB ) ),
inference(simp,[status(thm)],[7036]) ).
thf(7126,plain,
! [E: vstring,D: vYN,C: vUnOpT,B: vAval,A: vUnOpT] :
( ( ( A @ ( B @ sk32 ) @ vB )
!= ( D @ vB ) )
| ( B
!= ( C @ ( E @ vT @ sk34 ) ) )
| ( B @ ( A @ sk31 ) ) ),
inference(paramod_ordered,[status(thm)],[403,7051]) ).
thf(7127,plain,
! [D: vUnOpT,C: vAval,B: vstring,A: vUnOpT] :
( ( C
!= ( A @ ( B @ vT @ sk34 ) ) )
| ( C @ ( D @ sk31 ) ) ),
inference(pattern_uni,[status(thm)],[7126:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G @ ( F @ sk32 ) ))]]) ).
thf(7139,plain,
! [C: vUnOpT,B: vstring,A: vUnOpT] : ( A @ ( B @ vT @ sk34 ) @ ( C @ sk31 ) ),
inference(simp,[status(thm)],[7127]) ).
thf(7509,plain,
! [B: vUnOpT,A: vstring] : ( A @ vT @ ( B @ sk31 ) ),
inference(rewrite,[status(thm)],[7139,7047]) ).
thf(4,axiom,
! [A: vAType,B: vAType] :
( ( B @ ( A @ ( veqop @ vcheckBinOp ) ) )
= ( vYesNo @ vsomeAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','checkBinOp-8') ).
thf(259,plain,
! [A: vAType,B: vAType] :
( ( B @ ( A @ ( veqop @ vcheckBinOp ) ) )
= ( vYesNo @ vsomeAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(260,plain,
! [B: vAType,A: vAType] :
( ( B @ ( A @ ( veqop @ vcheckBinOp ) ) )
= ( vYesNo @ vsomeAType ) ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [B: vAType,A: vAType] :
( ( B @ ( A @ ( veqop @ vcheckBinOp ) ) )
= ( vYesNo @ vsomeAType ) ),
inference(lifteq,[status(thm)],[260]) ).
thf(227,axiom,
! [A: vQMap] :
( ? [B: vQID,C: vLabel,D: vAType,E: vQMap] :
( ( ( A @ vtypeQM )
= ( E @ vtypeQM @ ( D @ ( B @ vatmbind ) ) ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ vqmbind ) ) ) ) ) )
| ( ( ( A @ vtypeQM )
= vatmempty )
& ( A = vqmempty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','typeQM-INV') ).
thf(4756,plain,
! [A: vQMap] :
( ? [B: vQID,C: vLabel,D: vAType,E: vQMap] :
( ( ( A @ vtypeQM )
= ( E @ vtypeQM @ ( D @ ( B @ vatmbind ) ) ) )
& ( A
= ( E @ ( D @ ( C @ ( B @ vqmbind ) ) ) ) ) )
| ( ( ( A @ vtypeQM )
= vatmempty )
& ( A = vqmempty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(5684,plain,
! [A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( vatmempty @ ( sk5 @ vtypeAM @ vMC ) ) )
| ( sk1 != vqmempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,4874]) ).
thf(5694,plain,
! [A: vMapConf] :
( ( ( A @ sk254 )
!= vatmempty )
| ( ( A @ sk253 )
!= ( sk5 @ vtypeAM ) )
| ( sk1 != vqmempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5684]) ).
thf(5791,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk4 @ ( sk3 @ vMC ) ) )
| ( ( B @ sk254 )
!= vatmempty )
| ( ( B @ sk253 )
!= ( sk5 @ vtypeAM ) )
| ( sk1 != vqmempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( B @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,5694]) ).
thf(5792,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 )
!= sk4 )
| ( ( A @ sk253 )
!= sk3 )
| ( ( B @ sk254 )
!= vatmempty )
| ( ( B @ sk253 )
!= ( sk5 @ vtypeAM ) )
| ( sk1 != vqmempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( B @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5791]) ).
thf(444,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk41 ) )
| ( B
= ( A @ ( B @ sk43 ) @ vT @ vconstant ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(475,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk43 ) @ vT @ vconstant )
= B ) ),
inference(lifteq,[status(thm)],[444]) ).
thf(53,axiom,
! [A: vQID,B: vQID] :
( ( ( A @ vqvar )
= ( B @ vqvar ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-qvar') ).
thf(664,plain,
! [A: vQID,B: vQID] :
( ( ( A @ vqvar )
= ( B @ vqvar ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(665,plain,
! [B: vQID,A: vQID] :
( ( A = B )
| ( ( A @ vqvar )
!= ( B @ vqvar ) ) ),
inference(cnf,[status(esa)],[664]) ).
thf(666,plain,
! [B: vQID,A: vQID] :
( ( A = B )
| ( ( A @ vqvar )
!= ( B @ vqvar ) ) ),
inference(lifteq,[status(thm)],[665]) ).
thf(667,plain,
? [A: vExp > vQID] :
! [B: vQID] :
( ( B @ vqvar @ A )
= B ),
inference(detectInverse,[status(thm)],[666]) ).
thf(668,plain,
! [A: vQID] :
( ( A @ vqvar @ sk135 )
= A ),
inference(cnf,[status(esa)],[667]) ).
thf(5084,plain,
! [A: vQID] :
( ( A @ vqvar @ sk135 )
= A ),
inference(lifteq,[status(thm)],[668]) ).
thf(218,axiom,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vATMap,G: vATMap,H: vExp,I: vQuestionnaire] :
( ( ( D @ ( F @ vMC ) @ ( I @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( D @ ( F @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( G @ ( E @ vMC ) @ ( I @ ( B @ ( H @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) )
=> ( E = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqcond_inv6') ).
thf(4724,plain,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vATMap,G: vATMap,H: vExp,I: vQuestionnaire] :
( ( ( D @ ( F @ vMC ) @ ( I @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( D @ ( F @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( G @ ( E @ vMC ) @ ( I @ ( B @ ( H @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) )
=> ( E = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(99,axiom,
! [A: vYN] :
( ( A = vno )
| ( A = vyes ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-YN') ).
thf(905,plain,
! [A: vYN] :
( ( A = vno )
| ( A = vyes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(906,plain,
! [A: vYN] :
( ( A = vno )
| ( A = vyes ) ),
inference(cnf,[status(esa)],[905]) ).
thf(907,plain,
! [A: vYN] :
( ( A = vno )
| ( A = vyes ) ),
inference(lifteq,[status(thm)],[906]) ).
thf(80,axiom,
( ( vno @ ( vno @ vor ) )
= vno ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','or-0') ).
thf(795,plain,
( ( vno @ ( vno @ vor ) )
= vno ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(796,plain,
( ( vno @ ( vno @ vor ) )
= vno ),
inference(lifteq,[status(thm)],[795]) ).
thf(5155,plain,
! [A: vYN] :
( ( vno != vno )
| ( ( A @ ( vno @ vor ) )
= vno )
| ( A = vyes ) ),
inference(paramod_ordered,[status(thm)],[907,796]) ).
thf(5156,plain,
! [A: vYN] :
( ( ( A @ ( vno @ vor ) )
= vno )
| ( A = vyes ) ),
inference(pattern_uni,[status(thm)],[5155:[]]) ).
thf(160,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( ( B @ ( G @ vlookupATMap ) )
= vnoAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tquestion_inv1') ).
thf(1283,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( ( B @ ( G @ vlookupATMap ) )
= vnoAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(122,axiom,
! [A: vQID,B: vQID,C: vAval,D: vAnsMap] :
( ( A != B )
=> ( ( D @ ( C @ ( B @ vabind ) ) @ ( A @ vlookupAnsMap ) )
= ( D @ ( A @ vlookupAnsMap ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookupAnsMap-2') ).
thf(1051,plain,
! [A: vQID,B: vQID,C: vAval,D: vAnsMap] :
( ( A != B )
=> ( ( D @ ( C @ ( B @ vabind ) ) @ ( A @ vlookupAnsMap ) )
= ( D @ ( A @ vlookupAnsMap ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(119,axiom,
! [A: vQID,B: vLabel,C: vAType,D: vQID,E: vAType,F: vLabel] :
( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-question-defquestion') ).
thf(1040,plain,
! [A: vQID,B: vLabel,C: vAType,D: vQID,E: vAType,F: vLabel] :
( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(19,axiom,
! [A: vExp] :
( ? [B: vUnOpT,C: vExp] :
( A
= ( C @ ( B @ vunop ) ) )
| ? [B: vExp,C: vBinOpT,D: vExp] :
( A
= ( D @ ( C @ ( B @ vbinop ) ) ) )
| ? [B: vQID] :
( A
= ( B @ vqvar ) )
| ? [B: vAval] :
( A
= ( B @ vconstant ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-Exp') ).
thf(319,plain,
! [A: vExp] :
( ? [B: vUnOpT,C: vExp] :
( A
= ( C @ ( B @ vunop ) ) )
| ? [B: vExp,C: vBinOpT,D: vExp] :
( A
= ( D @ ( C @ ( B @ vbinop ) ) ) )
| ? [B: vQID] :
( A
= ( B @ vqvar ) )
| ? [B: vAval] :
( A
= ( B @ vconstant ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(320,plain,
! [A: vExp] :
( ( A
= ( A @ sk24 @ ( A @ sk23 @ vunop ) ) )
| ( A
= ( A @ sk22 @ ( A @ sk21 @ ( A @ sk20 @ vbinop ) ) ) )
| ( A
= ( A @ sk19 @ vqvar ) )
| ( A
= ( A @ sk18 @ vconstant ) ) ),
inference(cnf,[status(esa)],[319]) ).
thf(321,plain,
! [A: vExp] :
( ( ( A @ sk24 @ ( A @ sk23 @ vunop ) )
= A )
| ( ( A @ sk22 @ ( A @ sk21 @ ( A @ sk20 @ vbinop ) ) )
= A )
| ( ( A @ sk19 @ vqvar )
= A )
| ( ( A @ sk18 @ vconstant )
= A ) ),
inference(lifteq,[status(thm)],[320]) ).
thf(42,axiom,
! [A: vstring,B: vstring] :
( ( ( A @ vT )
= ( B @ vT ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-T') ).
thf(485,plain,
! [A: vstring,B: vstring] :
( ( ( A @ vT )
= ( B @ vT ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(7578,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
( ( A
!= ( B @ sk354 ) )
| ( B @ visValue )
| ( vqempty != vqempty )
| ~ ( A @ visValue ) ),
inference(paramod_ordered,[status(thm)],[1374,4633]) ).
thf(7579,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
( ( A
!= ( B @ sk354 ) )
| ( B @ visValue )
| ~ ( A @ visValue ) ),
inference(simp,[status(thm)],[7578]) ).
thf(7580,plain,
! [A: vQuestionnaire] :
( ( A @ visValue )
| ~ ( A @ sk354 @ visValue ) ),
inference(pattern_uni,[status(thm)],[7579:[bind(A,$thf( C @ sk354 )),bind(B,$thf( C ))]]) ).
thf(7581,plain,
! [A: vQuestionnaire] :
( ( A @ visValue )
| ~ ( A @ sk354 @ visValue ) ),
inference(simp,[status(thm)],[7580]) ).
thf(6430,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ sk388 @ ( A @ sk387 @ ( A @ vgetAM @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ vgetQuest )
= D ) ),
inference(paramod_ordered,[status(thm)],[6421,4640]) ).
thf(6431,plain,
! [A: vQConf] :
( ( A @ sk388 )
= ( A @ vgetQuest ) ),
inference(pattern_uni,[status(thm)],[6430:[bind(A,$thf( G )),bind(B,$thf( G @ vgetAM )),bind(C,$thf( G @ sk387 )),bind(D,$thf( G @ sk388 ))]]) ).
thf(6438,plain,
! [A: vQConf] :
( ( A @ sk388 )
= ( A @ vgetQuest ) ),
inference(simp,[status(thm)],[6431]) ).
thf(84,axiom,
! [A: vQuestionnaire,B: vQuestionnaire] :
( vqempty
!= ( B @ ( A @ vqseq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qempty-qseq') ).
thf(819,plain,
! [A: vQuestionnaire,B: vQuestionnaire] :
( vqempty
!= ( B @ ( A @ vqseq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(820,plain,
~ ? [A: vQuestionnaire,B: vQuestionnaire] :
( vqempty
= ( B @ ( A @ vqseq ) ) ),
inference(miniscope,[status(thm)],[819]) ).
thf(821,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
( vqempty
!= ( B @ ( A @ vqseq ) ) ),
inference(cnf,[status(esa)],[820]) ).
thf(822,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
( ( B @ ( A @ vqseq ) )
!= vqempty ),
inference(lifteq,[status(thm)],[821]) ).
thf(5338,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vQuestionnaire] :
( ( A
!= ( C @ ( B @ vqseq ) ) )
| ( vqempty != vqempty )
| ~ ( A @ visValue ) ),
inference(paramod_ordered,[status(thm)],[1374,822]) ).
thf(5339,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vQuestionnaire] :
( ( A
!= ( C @ ( B @ vqseq ) ) )
| ~ ( A @ visValue ) ),
inference(simp,[status(thm)],[5338]) ).
thf(5340,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
~ ( B @ ( A @ vqseq ) @ visValue ),
inference(pattern_uni,[status(thm)],[5339:[bind(A,$thf( E @ ( D @ vqseq ) )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(5353,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
~ ( B @ ( A @ vqseq ) @ visValue ),
inference(simp,[status(thm)],[5340]) ).
thf(60,axiom,
! [A: vAval,B: vQID] :
( ( A @ vconstant )
!= ( B @ vqvar ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-constant-qvar') ).
thf(689,plain,
! [A: vAval,B: vQID] :
( ( A @ vconstant )
!= ( B @ vqvar ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(690,plain,
~ ? [A: vAval,B: vQID] :
( ( A @ vconstant )
= ( B @ vqvar ) ),
inference(miniscope,[status(thm)],[689]) ).
thf(691,plain,
! [B: vQID,A: vAval] :
( ( A @ vconstant )
!= ( B @ vqvar ) ),
inference(cnf,[status(esa)],[690]) ).
thf(692,plain,
! [B: vQID,A: vAval] :
( ( A @ vconstant )
!= ( B @ vqvar ) ),
inference(lifteq,[status(thm)],[691]) ).
thf(107,axiom,
! [A: vQID,B: vLabel,C: vAType] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ vgetQuestionLabel )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getQuestionLabel-0') ).
thf(956,plain,
! [A: vQID,B: vLabel,C: vAType] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ vgetQuestionLabel )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(7134,plain,
! [E: vstring,D: vYN,C: vUnOpT,B: vAval,A: vUnOpT] :
( ( ( A @ ( B @ sk34 ) )
!= ( C @ ( E @ vT @ sk34 ) ) )
| ( B
!= ( D @ vB ) )
| ~ ( B @ ( A @ sk31 ) ) ),
inference(paramod_ordered,[status(thm)],[401,7051]) ).
thf(7135,plain,
! [C: vstring,B: vYN,A: vUnOpT] :
( ( ( C @ vT )
!= ( B @ vB ) )
| ~ ( C @ vT @ ( A @ sk31 ) ) ),
inference(pattern_uni,[status(thm)],[7134:[bind(A,$thf( A )),bind(B,$thf( F @ vT )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( F ))]]) ).
thf(7143,plain,
! [C: vstring,B: vYN,A: vUnOpT] :
( ( ( C @ vT )
!= ( B @ vB ) )
| ~ ( C @ vT @ ( A @ sk31 ) ) ),
inference(simp,[status(thm)],[7135]) ).
thf(7335,plain,
! [B: vstring,A: vYN] :
( ( ( B @ vT )
!= ( A @ vB ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7143,7013]) ).
thf(7336,plain,
! [B: vstring,A: vYN] :
( ( B @ vT )
!= ( A @ vB ) ),
inference(simp,[status(thm)],[7335]) ).
thf(114,axiom,
! [A: vATMap,B: vATMap] :
( ? [C: vATMap,D: vATMap,E: vOptAType,F: vAType,G: vATMap,H: vQID] :
( ( ( B @ ( A @ vintersectATM ) )
= D )
& ( B = C )
& ( A
= ( G @ ( F @ ( H @ vatmbind ) ) ) )
& ~ ( ( ( E @ vgetAType )
= F )
& ( E @ visSomeAType ) )
& ( E
= ( C @ ( H @ vlookupATMap ) ) )
& ( D
= ( C @ ( G @ vintersectATM ) ) ) )
| ? [C: vATMap,D: vATMap,E: vOptAType,F: vAType,G: vATMap,H: vQID] :
( ( ( B @ ( A @ vintersectATM ) )
= ( D @ ( F @ ( H @ vatmbind ) ) ) )
& ( B = C )
& ( A
= ( G @ ( F @ ( H @ vatmbind ) ) ) )
& ( ( E @ vgetAType )
= F )
& ( E @ visSomeAType )
& ( E
= ( C @ ( H @ vlookupATMap ) ) )
& ( D
= ( C @ ( G @ vintersectATM ) ) ) )
| ? [C: vATMap] :
( ( ( B @ ( A @ vintersectATM ) )
= vatmempty )
& ( B = C )
& ( A = vatmempty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersectATM-INV') ).
thf(978,plain,
! [A: vATMap,B: vATMap] :
( ? [C: vATMap,D: vATMap,E: vOptAType,F: vAType,G: vATMap,H: vQID] :
( ( ( B @ ( A @ vintersectATM ) )
= D )
& ( B = C )
& ( A
= ( G @ ( F @ ( H @ vatmbind ) ) ) )
& ~ ( ( ( E @ vgetAType )
= F )
& ( E @ visSomeAType ) )
& ( E
= ( C @ ( H @ vlookupATMap ) ) )
& ( D
= ( C @ ( G @ vintersectATM ) ) ) )
| ? [C: vATMap,D: vATMap,E: vOptAType,F: vAType,G: vATMap,H: vQID] :
( ( ( B @ ( A @ vintersectATM ) )
= ( D @ ( F @ ( H @ vatmbind ) ) ) )
& ( B = C )
& ( A
= ( G @ ( F @ ( H @ vatmbind ) ) ) )
& ( ( E @ vgetAType )
= F )
& ( E @ visSomeAType )
& ( E
= ( C @ ( H @ vlookupATMap ) ) )
& ( D
= ( C @ ( G @ vintersectATM ) ) ) )
| ? [C: vATMap] :
( ( ( B @ ( A @ vintersectATM ) )
= vatmempty )
& ( B = C )
& ( A = vatmempty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(979,plain,
! [A: vATMap,B: vATMap] :
( ? [C: vATMap,D: vATMap,E: vOptAType,F: vAType,G: vATMap] :
( ? [H: vQID] :
( ( ( B @ ( A @ vintersectATM ) )
= D )
& ( B = C )
& ( A
= ( G @ ( F @ ( H @ vatmbind ) ) ) )
& ~ ( ( ( E @ vgetAType )
= F )
& ( E @ visSomeAType ) )
& ( E
= ( C @ ( H @ vlookupATMap ) ) ) )
& ( D
= ( C @ ( G @ vintersectATM ) ) ) )
| ? [C: vATMap,D: vATMap,E: vOptAType,F: vAType,G: vATMap] :
( ? [H: vQID] :
( ( ( B @ ( A @ vintersectATM ) )
= ( D @ ( F @ ( H @ vatmbind ) ) ) )
& ( B = C )
& ( A
= ( G @ ( F @ ( H @ vatmbind ) ) ) )
& ( ( E @ vgetAType )
= F )
& ( E @ visSomeAType )
& ( E
= ( C @ ( H @ vlookupATMap ) ) ) )
& ( D
= ( C @ ( G @ vintersectATM ) ) ) )
| ( ( ( B @ ( A @ vintersectATM ) )
= vatmempty )
& ? [C: vATMap] : ( B = C )
& ( A = vatmempty ) ) ),
inference(miniscope,[status(thm)],[978]) ).
thf(980,plain,
! [B: vATMap,A: vATMap] :
( ( ( ( B @ ( A @ vintersectATM ) )
= ( A @ ( B @ sk197 ) ) )
| ~ ( A @ ( B @ sk189 ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( B
= ( A @ ( B @ sk196 ) ) )
| ~ ( A @ ( B @ sk189 ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( A
= ( A @ ( B @ sk200 ) @ ( A @ ( B @ sk199 ) @ ( A @ ( B @ sk201 ) @ vatmbind ) ) ) )
| ~ ( A @ ( B @ sk189 ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( ( A @ ( B @ sk198 ) @ vgetAType )
!= ( A @ ( B @ sk199 ) ) )
| ~ ( A @ ( B @ sk198 ) @ visSomeAType )
| ~ ( A @ ( B @ sk189 ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( ( A @ ( B @ sk198 ) )
= ( A @ ( B @ sk196 ) @ ( A @ ( B @ sk201 ) @ vlookupATMap ) ) )
| ~ ( A @ ( B @ sk189 ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( ( A @ ( B @ sk197 ) )
= ( A @ ( B @ sk196 ) @ ( A @ ( B @ sk200 ) @ vintersectATM ) ) )
| ~ ( A @ ( B @ sk189 ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( A @ ( B @ sk189 ) )
| ( ( B @ ( A @ vintersectATM ) )
= ( A @ ( B @ sk191 ) @ ( A @ ( B @ sk193 ) @ ( A @ ( B @ sk195 ) @ vatmbind ) ) ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( A @ ( B @ sk189 ) )
| ( B
= ( A @ ( B @ sk190 ) ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( A @ ( B @ sk189 ) )
| ( A
= ( A @ ( B @ sk194 ) @ ( A @ ( B @ sk193 ) @ ( A @ ( B @ sk195 ) @ vatmbind ) ) ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( A @ ( B @ sk189 ) )
| ( ( A @ ( B @ sk192 ) @ vgetAType )
= ( A @ ( B @ sk193 ) ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( A @ ( B @ sk189 ) )
| ( A @ ( B @ sk192 ) @ visSomeAType )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( A @ ( B @ sk189 ) )
| ( ( A @ ( B @ sk192 ) )
= ( A @ ( B @ sk190 ) @ ( A @ ( B @ sk195 ) @ vlookupATMap ) ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( A @ ( B @ sk189 ) )
| ( ( A @ ( B @ sk191 ) )
= ( A @ ( B @ sk190 ) @ ( A @ ( B @ sk194 ) @ vintersectATM ) ) )
| ~ ( A @ ( B @ sk187 ) ) )
& ( ( A @ ( B @ sk187 ) )
| ( ( B @ ( A @ vintersectATM ) )
= vatmempty ) )
& ( ( A @ ( B @ sk187 ) )
| ( B
= ( A @ ( B @ sk188 ) ) ) )
& ( ( A @ ( B @ sk187 ) )
| ( A = vatmempty ) ) ),
inference(cnf,[status(esa)],[979]) ).
thf(993,plain,
! [B: vATMap,A: vATMap] :
( ( ( A @ ( B @ sk198 ) @ vgetAType )
!= ( A @ ( B @ sk199 ) ) )
| ~ ( A @ ( B @ sk198 ) @ visSomeAType )
| ~ ( A @ ( B @ sk189 ) )
| ~ ( A @ ( B @ sk187 ) ) ),
inference(cnfConj,[status(thm)],[980]) ).
thf(998,plain,
! [B: vATMap,A: vATMap] :
( ~ ( A @ ( B @ sk198 ) @ visSomeAType )
| ~ ( A @ ( B @ sk189 ) )
| ~ ( A @ ( B @ sk187 ) )
| ( ( A @ ( B @ sk199 ) )
!= ( A @ ( B @ sk198 ) @ vgetAType ) ) ),
inference(lifteq,[status(thm)],[993]) ).
thf(9588,plain,
! [E: vATMap,D: vAType,C: vQID,B: vstring,A: vQID] :
( ( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM @ ( D @ ( C @ sk224 ) ) )
= E ) ),
inference(paramod_ordered,[status(thm)],[9477,8152]) ).
thf(9589,plain,
! [B: vstring,A: vQID] :
( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM @ ( vText @ ( A @ sk224 ) ) )
= vatmempty ),
inference(pattern_uni,[status(thm)],[9588:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( vText )),bind(E,$thf( vatmempty ))]]) ).
thf(302,plain,
! [A: vAval] :
( ( ( ( A @ vtypeOf )
= vText )
& ? [B: vstring] :
( A
= ( B @ vT ) ) )
| ( ( ( A @ vtypeOf )
= vNumber )
& ? [B: vnat] :
( A
= ( B @ vNum ) ) )
| ( ( ( A @ vtypeOf )
= vYesNo )
& ? [B: vYN] :
( A
= ( B @ vB ) ) ) ),
inference(miniscope,[status(thm)],[301]) ).
thf(303,plain,
! [A: vAval] :
( ( ( ( A @ vtypeOf )
= vText )
| ( ( A @ vtypeOf )
= vNumber )
| ~ ( A @ sk14 ) )
& ( ( A
= ( A @ sk17 @ vT ) )
| ( ( A @ vtypeOf )
= vNumber )
| ~ ( A @ sk14 ) )
& ( ( ( A @ vtypeOf )
= vText )
| ( A
= ( A @ sk16 @ vNum ) )
| ~ ( A @ sk14 ) )
& ( ( A
= ( A @ sk17 @ vT ) )
| ( A
= ( A @ sk16 @ vNum ) )
| ~ ( A @ sk14 ) )
& ( ( A @ sk14 )
| ( ( A @ vtypeOf )
= vYesNo ) )
& ( ( A @ sk14 )
| ( A
= ( A @ sk15 @ vB ) ) ) ),
inference(cnf,[status(esa)],[302]) ).
thf(306,plain,
! [A: vAval] :
( ( A
= ( A @ sk17 @ vT ) )
| ( ( A @ vtypeOf )
= vNumber )
| ~ ( A @ sk14 ) ),
inference(cnfConj,[status(thm)],[303]) ).
thf(312,plain,
! [A: vAval] :
( ~ ( A @ sk14 )
| ( ( A @ sk17 @ vT )
= A )
| ( ( A @ vtypeOf )
= vNumber ) ),
inference(lifteq,[status(thm)],[306]) ).
thf(46,axiom,
! [A: vQID,B: vLabel,C: vAType,D: vQID,E: vAType,F: vLabel] :
( ( ( C @ ( F @ ( D @ vsomeQuestion ) ) )
= ( E @ ( B @ ( A @ vsomeQuestion ) ) ) )
=> ( ( C = E )
& ( F = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someQuestion') ).
thf(617,plain,
! [A: vQID,B: vLabel,C: vAType,D: vQID,E: vAType,F: vLabel] :
( ( ( C @ ( F @ ( D @ vsomeQuestion ) ) )
= ( E @ ( B @ ( A @ vsomeQuestion ) ) ) )
=> ( ( C = E )
& ( F = B )
& ( D = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(618,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( ( C = E )
| ( ( C @ ( F @ ( D @ vsomeQuestion ) ) )
!= ( E @ ( B @ ( A @ vsomeQuestion ) ) ) ) )
& ( ( F = B )
| ( ( C @ ( F @ ( D @ vsomeQuestion ) ) )
!= ( E @ ( B @ ( A @ vsomeQuestion ) ) ) ) )
& ( ( D = A )
| ( ( C @ ( F @ ( D @ vsomeQuestion ) ) )
!= ( E @ ( B @ ( A @ vsomeQuestion ) ) ) ) ) ),
inference(cnf,[status(esa)],[617]) ).
thf(621,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C = E )
| ( ( C @ ( F @ ( D @ vsomeQuestion ) ) )
!= ( E @ ( B @ ( A @ vsomeQuestion ) ) ) ) ),
inference(cnfConj,[status(thm)],[618]) ).
thf(628,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C = E )
| ( ( C @ ( F @ ( D @ vsomeQuestion ) ) )
!= ( E @ ( B @ ( A @ vsomeQuestion ) ) ) ) ),
inference(lifteq,[status(thm)],[621]) ).
thf(629,plain,
? [A: vQID > vLabel > vOptQuestion > vAType] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vsomeQuestion ) ) @ ( C @ ( B @ A ) ) )
= D ),
inference(detectInverse,[status(thm)],[628]) ).
thf(630,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ ( B @ ( A @ sk131 ) ) )
= C ),
inference(cnf,[status(esa)],[629]) ).
thf(6860,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ ( B @ ( A @ sk131 ) ) )
= C ),
inference(lifteq,[status(thm)],[630]) ).
thf(5685,plain,
! [A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk4 @ ( sk3 @ vMC ) ) )
| ( sk5 != vaempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( vatmempty @ vMC ) @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,4876]) ).
thf(5695,plain,
! [A: vMapConf] :
( ( ( A @ sk254 )
!= sk4 )
| ( ( A @ sk253 )
!= sk3 )
| ( sk5 != vaempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( vatmempty @ vMC ) @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5685]) ).
thf(51,axiom,
! [A: vQID,B: vLabel,C: vAType] :
( vnoQuestion
!= ( C @ ( B @ ( A @ vsomeQuestion ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noQuestion-someQuestion') ).
thf(657,plain,
! [A: vQID,B: vLabel,C: vAType] :
( vnoQuestion
!= ( C @ ( B @ ( A @ vsomeQuestion ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(658,plain,
~ ? [A: vQID,B: vLabel,C: vAType] :
( vnoQuestion
= ( C @ ( B @ ( A @ vsomeQuestion ) ) ) ),
inference(miniscope,[status(thm)],[657]) ).
thf(659,plain,
! [C: vAType,B: vLabel,A: vQID] :
( vnoQuestion
!= ( C @ ( B @ ( A @ vsomeQuestion ) ) ) ),
inference(cnf,[status(esa)],[658]) ).
thf(660,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) )
!= vnoQuestion ),
inference(lifteq,[status(thm)],[659]) ).
thf(240,axiom,
! [A: vEntry,B: vExp,C: vQuestionnaire,D: vQuestionnaire] :
( ( A @ vqsingle )
!= ( D @ ( C @ ( B @ vqcond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qsingle-qcond') ).
thf(4825,plain,
! [A: vEntry,B: vExp,C: vQuestionnaire,D: vQuestionnaire] :
( ( A @ vqsingle )
!= ( D @ ( C @ ( B @ vqcond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(7496,plain,
! [C: vExp,B: vATMap,A: vAType] :
( ( ( A @ vsomeAType @ visSomeAType )
!= ( B @ ( C @ sk68 ) @ visSomeAType ) )
| ~ $true
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[670,429]) ).
thf(7497,plain,
! [C: vExp,B: vATMap,A: vAType] :
( ( ( A @ vsomeAType @ visSomeAType )
!= ( B @ ( C @ sk68 ) @ visSomeAType ) )
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(simp,[status(thm)],[7496]) ).
thf(7505,plain,
! [C: vExp,B: vATMap,A: vAType] :
( ( ( A @ vsomeAType )
!= ( B @ ( C @ sk68 ) ) )
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(simp,[status(thm)],[7497]) ).
thf(89,axiom,
( ( vno @ vnot )
= vyes ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','not-1') ).
thf(849,plain,
( ( vno @ vnot )
= vyes ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(8,axiom,
veqop != vandop,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-eqop-andop') ).
thf(270,plain,
veqop != vandop,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(380,plain,
! [A: vAval] :
( ( A
= ( A @ sk30 @ vT ) )
| ( A
= ( A @ sk29 @ vNum ) )
| ( A
= ( A @ sk28 @ vB ) ) ),
inference(cnf,[status(esa)],[379]) ).
thf(381,plain,
! [A: vAval] :
( ( ( A @ sk30 @ vT )
= A )
| ( ( A @ sk29 @ vNum )
= A )
| ( ( A @ sk28 @ vB )
= A ) ),
inference(lifteq,[status(thm)],[380]) ).
thf(31,axiom,
~ ( vnoAType @ visSomeAType ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeAType-0') ).
thf(366,plain,
~ ( vnoAType @ visSomeAType ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(167,axiom,
! [A: vATMap,B: vATMap,C: vAType,D: vLabel,E: vQID] :
( ( ( A @ ( E @ vlookupATMap ) )
= vnoAType )
=> ( A @ ( C @ ( E @ vatmbind ) ) @ ( B @ vMC ) @ ( C @ ( D @ ( E @ vdefquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tdefquestion') ).
thf(1311,plain,
! [A: vATMap,B: vATMap,C: vAType,D: vLabel,E: vQID] :
( ( ( A @ ( E @ vlookupATMap ) )
= vnoAType )
=> ( A @ ( C @ ( E @ vatmbind ) ) @ ( B @ vMC ) @ ( C @ ( D @ ( E @ vdefquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(1063,plain,
! [A: vYN] :
( ( ( A @ vnot )
= vyes )
| ( A = vyes ) ),
inference(cnfConj,[status(thm)],[1061]) ).
thf(1067,plain,
! [A: vYN] :
( ( ( A @ vnot )
= vyes )
| ( A = vyes ) ),
inference(lifteq,[status(thm)],[1063]) ).
thf(104,axiom,
! [A: vAType,B: vAType] :
( ( ( A @ vsomeAType )
= ( B @ vsomeAType ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someAType') ).
thf(944,plain,
! [A: vAType,B: vAType] :
( ( ( A @ vsomeAType )
= ( B @ vsomeAType ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(945,plain,
! [B: vAType,A: vAType] :
( ( A = B )
| ( ( A @ vsomeAType )
!= ( B @ vsomeAType ) ) ),
inference(cnf,[status(esa)],[944]) ).
thf(946,plain,
! [B: vAType,A: vAType] :
( ( A = B )
| ( ( A @ vsomeAType )
!= ( B @ vsomeAType ) ) ),
inference(lifteq,[status(thm)],[945]) ).
thf(947,plain,
? [A: vOptAType > vAType] :
! [B: vAType] :
( ( B @ vsomeAType @ A )
= B ),
inference(detectInverse,[status(thm)],[946]) ).
thf(948,plain,
! [A: vAType] :
( ( A @ vsomeAType @ sk182 )
= A ),
inference(cnf,[status(esa)],[947]) ).
thf(5122,plain,
! [A: vAType] :
( ( A @ vsomeAType @ sk182 )
= A ),
inference(lifteq,[status(thm)],[948]) ).
thf(120,axiom,
! [A: vQuestionnaire,B: vQuestionnaire,C: vQuestionnaire,D: vQuestionnaire,E: vExp] :
( ( C @ ( D @ vqseq ) )
!= ( B @ ( A @ ( E @ vqcond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qseq-qcond') ).
thf(1044,plain,
! [A: vQuestionnaire,B: vQuestionnaire,C: vQuestionnaire,D: vQuestionnaire,E: vExp] :
( ( C @ ( D @ vqseq ) )
!= ( B @ ( A @ ( E @ vqcond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(1045,plain,
~ ? [A: vQuestionnaire,B: vQuestionnaire,C: vQuestionnaire,D: vQuestionnaire,E: vExp] :
( ( C @ ( D @ vqseq ) )
= ( B @ ( A @ ( E @ vqcond ) ) ) ),
inference(miniscope,[status(thm)],[1044]) ).
thf(1046,plain,
! [E: vExp,D: vQuestionnaire,C: vQuestionnaire,B: vQuestionnaire,A: vQuestionnaire] :
( ( C @ ( D @ vqseq ) )
!= ( B @ ( A @ ( E @ vqcond ) ) ) ),
inference(cnf,[status(esa)],[1045]) ).
thf(1047,plain,
! [E: vExp,D: vQuestionnaire,C: vQuestionnaire,B: vQuestionnaire,A: vQuestionnaire] :
( ( C @ ( D @ vqseq ) )
!= ( B @ ( A @ ( E @ vqcond ) ) ) ),
inference(lifteq,[status(thm)],[1046]) ).
thf(752,plain,
( ( vYesNo @ ( vnotop @ vcheckUnOp ) )
= ( vYesNo @ vsomeAType ) ),
inference(lifteq,[status(thm)],[751]) ).
thf(4887,plain,
! [A: vUnOpT] :
( ( vnotop != vnotop )
| ( ( vYesNo @ ( A @ vcheckUnOp ) )
= ( vYesNo @ vsomeAType ) ) ),
inference(paramod_ordered,[status(thm)],[356,752]) ).
thf(4888,plain,
! [A: vUnOpT] :
( ( vYesNo @ ( A @ vcheckUnOp ) )
= ( vYesNo @ vsomeAType ) ),
inference(pattern_uni,[status(thm)],[4887:[]]) ).
thf(52,axiom,
! [A: vYN,B: vYN] :
( ( B @ vB @ ( A @ vB @ ( vorop @ vevalBinOp ) ) )
= ( B @ ( A @ vor ) @ vB @ vconstant @ vsomeExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','evalBinOp-7') ).
thf(661,plain,
! [A: vYN,B: vYN] :
( ( B @ vB @ ( A @ vB @ ( vorop @ vevalBinOp ) ) )
= ( B @ ( A @ vor ) @ vB @ vconstant @ vsomeExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(148,axiom,
! [A: vGID,B: vQuestionnaire,C: vGID,D: vQuestionnaire] :
( ( ( B @ ( A @ vqgroup ) )
= ( D @ ( C @ vqgroup ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-qgroup') ).
thf(1192,plain,
! [A: vGID,B: vQuestionnaire,C: vGID,D: vQuestionnaire] :
( ( ( B @ ( A @ vqgroup ) )
= ( D @ ( C @ vqgroup ) ) )
=> ( ( B = D )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(1193,plain,
! [D: vQuestionnaire,C: vGID,B: vQuestionnaire,A: vGID] :
( ( ( B = D )
| ( ( B @ ( A @ vqgroup ) )
!= ( D @ ( C @ vqgroup ) ) ) )
& ( ( A = C )
| ( ( B @ ( A @ vqgroup ) )
!= ( D @ ( C @ vqgroup ) ) ) ) ),
inference(cnf,[status(esa)],[1192]) ).
thf(1194,plain,
! [D: vQuestionnaire,C: vGID,B: vQuestionnaire,A: vGID] :
( ( A = C )
| ( ( B @ ( A @ vqgroup ) )
!= ( D @ ( C @ vqgroup ) ) ) ),
inference(cnfConj,[status(thm)],[1193]) ).
thf(1196,plain,
! [D: vQuestionnaire,C: vGID,B: vQuestionnaire,A: vGID] :
( ( A = C )
| ( ( B @ ( A @ vqgroup ) )
!= ( D @ ( C @ vqgroup ) ) ) ),
inference(lifteq,[status(thm)],[1194]) ).
thf(1197,plain,
? [A: vQuestionnaire > vQuestionnaire > vGID] :
! [B: vGID,C: vQuestionnaire] :
( ( C @ ( B @ vqgroup ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[1196]) ).
thf(1198,plain,
! [B: vQuestionnaire,A: vGID] :
( ( B @ ( A @ vqgroup ) @ ( B @ sk228 ) )
= A ),
inference(cnf,[status(esa)],[1197]) ).
thf(5968,plain,
! [B: vQuestionnaire,A: vGID] :
( ( B @ ( A @ vqgroup ) @ ( B @ sk228 ) )
= A ),
inference(lifteq,[status(thm)],[1198]) ).
thf(798,plain,
! [B: vYN,A: vYN] :
( ( ( ( B @ ( A @ vor ) )
= vyes )
| ~ ( B @ ( A @ sk151 ) ) )
& ( ( B
= ( A @ ( B @ sk153 ) ) )
| ~ ( B @ ( A @ sk151 ) ) )
& ( ( A
= ( A @ ( B @ sk152 ) ) )
| ~ ( B @ ( A @ sk151 ) ) )
& ( ( ( A @ ( B @ sk153 ) )
!= vno )
| ( ( A @ ( B @ sk152 ) )
!= vno )
| ~ ( B @ ( A @ sk151 ) ) )
& ( ( B @ ( A @ sk151 ) )
| ( ( B @ ( A @ vor ) )
= vno ) )
& ( ( B @ ( A @ sk151 ) )
| ( B = vno ) )
& ( ( B @ ( A @ sk151 ) )
| ( A = vno ) ) ),
inference(cnf,[status(esa)],[797]) ).
thf(800,plain,
! [B: vYN,A: vYN] :
( ( ( A @ ( B @ sk153 ) )
!= vno )
| ( ( A @ ( B @ sk152 ) )
!= vno )
| ~ ( B @ ( A @ sk151 ) ) ),
inference(cnfConj,[status(thm)],[798]) ).
thf(810,plain,
! [B: vYN,A: vYN] :
( ~ ( B @ ( A @ sk151 ) )
| ( ( A @ ( B @ sk153 ) )
!= vno )
| ( ( A @ ( B @ sk152 ) )
!= vno ) ),
inference(lifteq,[status(thm)],[800]) ).
thf(1205,plain,
! [F: vExp,E: vQuestionnaire,D: vQuestionnaire,C: vExp,B: vQuestionnaire,A: vQuestionnaire] :
( ( E = A )
| ( ( D @ ( E @ ( F @ vqcond ) ) )
!= ( B @ ( A @ ( C @ vqcond ) ) ) ) ),
inference(cnfConj,[status(thm)],[1203]) ).
thf(1210,plain,
! [F: vExp,E: vQuestionnaire,D: vQuestionnaire,C: vExp,B: vQuestionnaire,A: vQuestionnaire] :
( ( E = A )
| ( ( D @ ( E @ ( F @ vqcond ) ) )
!= ( B @ ( A @ ( C @ vqcond ) ) ) ) ),
inference(lifteq,[status(thm)],[1205]) ).
thf(1211,plain,
? [A: vExp > vQuestionnaire > vQuestionnaire > vQuestionnaire] :
! [B: vExp,C: vQuestionnaire,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vqcond ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[1210]) ).
thf(1212,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vExp] :
( ( C @ ( B @ ( A @ vqcond ) ) @ ( C @ ( A @ sk231 ) ) )
= B ),
inference(cnf,[status(esa)],[1211]) ).
thf(8513,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vExp] :
( ( C @ ( B @ ( A @ vqcond ) ) @ ( C @ ( A @ sk231 ) ) )
= B ),
inference(lifteq,[status(thm)],[1212]) ).
thf(6894,plain,
! [B: vATMap,A: vATMap] :
( ( ( A @ ( B @ sk198 ) @ visSomeAType )
!= ( vYesNo @ vsomeAType @ visSomeAType ) )
| ~ $true
| ~ ( A @ ( B @ sk189 ) )
| ~ ( A @ ( B @ sk187 ) )
| ( ( A @ ( B @ sk199 ) )
!= ( A @ ( B @ sk198 ) @ vgetAType ) ) ),
inference(paramod_ordered,[status(thm)],[4997,998]) ).
thf(6895,plain,
! [B: vATMap,A: vATMap] :
( ( ( A @ ( B @ sk198 ) @ visSomeAType )
!= ( vYesNo @ vsomeAType @ visSomeAType ) )
| ~ ( A @ ( B @ sk189 ) )
| ~ ( A @ ( B @ sk187 ) )
| ( ( A @ ( B @ sk199 ) )
!= ( A @ ( B @ sk198 ) @ vgetAType ) ) ),
inference(simp,[status(thm)],[6894]) ).
thf(6897,plain,
! [B: vATMap,A: vATMap] :
( ( ( A @ ( B @ sk198 ) )
!= ( vYesNo @ vsomeAType ) )
| ~ ( A @ ( B @ sk189 ) )
| ~ ( A @ ( B @ sk187 ) )
| ( ( A @ ( B @ sk199 ) )
!= ( A @ ( B @ sk198 ) @ vgetAType ) ) ),
inference(simp,[status(thm)],[6895]) ).
thf(76,axiom,
! [A: vQID,B: vLabel,C: vAType,D: vQID] :
( ( C @ ( B @ ( A @ vdefquestion ) ) )
!= ( D @ vask ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-defquestion-ask') ).
thf(778,plain,
! [A: vQID,B: vLabel,C: vAType,D: vQID] :
( ( C @ ( B @ ( A @ vdefquestion ) ) )
!= ( D @ vask ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(106,axiom,
! [A: vQID,B: vQID,C: vAType,D: vATMap] :
( ( A != B )
=> ( ( D @ ( C @ ( B @ vatmbind ) ) @ ( A @ vlookupATMap ) )
= ( D @ ( A @ vlookupATMap ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookupATMap-2') ).
thf(952,plain,
! [A: vQID,B: vQID,C: vAType,D: vATMap] :
( ( A != B )
=> ( ( D @ ( C @ ( B @ vatmbind ) ) @ ( A @ vlookupATMap ) )
= ( D @ ( A @ vlookupATMap ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(182,axiom,
! [A: vEntry] :
( vqempty
!= ( A @ vqsingle ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qempty-qsingle') ).
thf(1365,plain,
! [A: vEntry] :
( vqempty
!= ( A @ vqsingle ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1366,plain,
~ ? [A: vEntry] :
( vqempty
= ( A @ vqsingle ) ),
inference(miniscope,[status(thm)],[1365]) ).
thf(1367,plain,
! [A: vEntry] :
( vqempty
!= ( A @ vqsingle ) ),
inference(cnf,[status(esa)],[1366]) ).
thf(1368,plain,
! [A: vEntry] :
( ( A @ vqsingle )
!= vqempty ),
inference(lifteq,[status(thm)],[1367]) ).
thf(5329,plain,
! [B: vEntry,A: vQuestionnaire] :
( ( A
!= ( B @ vqsingle ) )
| ( vqempty != vqempty )
| ~ ( A @ visValue ) ),
inference(paramod_ordered,[status(thm)],[1374,1368]) ).
thf(5330,plain,
! [B: vEntry,A: vQuestionnaire] :
( ( A
!= ( B @ vqsingle ) )
| ~ ( A @ visValue ) ),
inference(simp,[status(thm)],[5329]) ).
thf(5331,plain,
! [A: vEntry] :
~ ( A @ vqsingle @ visValue ),
inference(pattern_uni,[status(thm)],[5330:[bind(A,$thf( C @ vqsingle )),bind(B,$thf( C ))]]) ).
thf(5349,plain,
! [A: vEntry] :
~ ( A @ vqsingle @ visValue ),
inference(simp,[status(thm)],[5331]) ).
thf(5716,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk1 @ vtypeQM @ ( sk5 @ vtypeAM @ vMC ) ) )
| ( ( B @ sk254 )
!= sk4 )
| ( ( B @ sk253 )
!= sk3 )
| ( B @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,5691]) ).
thf(5719,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 )
!= ( sk1 @ vtypeQM ) )
| ( ( A @ sk253 )
!= ( sk5 @ vtypeAM ) )
| ( ( B @ sk254 )
!= sk4 )
| ( ( B @ sk253 )
!= sk3 )
| ( B @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5716]) ).
thf(61,axiom,
! [A: vLabel] :
( ( vNumber @ ( A @ vgetAnswer ) )
= ( A @ vaskNumber @ vNum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getAnswer-1') ).
thf(693,plain,
! [A: vLabel] :
( ( vNumber @ ( A @ vgetAnswer ) )
= ( A @ vaskNumber @ vNum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(230,axiom,
! [A: vOptQConf] :
( ( A @ visSomeQC )
=> ? [B: vQConf] :
( A
= ( B @ vsomeQConf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeQC-true-INV') ).
thf(4785,plain,
! [A: vOptQConf] :
( ( A @ visSomeQC )
=> ? [B: vQConf] :
( A
= ( B @ vsomeQConf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(243,axiom,
! [A: vQuestionnaire] :
( ? [B: vGID,C: vQuestionnaire] :
( A
= ( C @ ( B @ vqgroup ) ) )
| ? [B: vExp,C: vQuestionnaire,D: vQuestionnaire] :
( A
= ( D @ ( C @ ( B @ vqcond ) ) ) )
| ? [B: vQuestionnaire,C: vQuestionnaire] :
( A
= ( C @ ( B @ vqseq ) ) )
| ? [B: vEntry] :
( A
= ( B @ vqsingle ) )
| ( A = vqempty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-Questionnaire') ).
thf(4836,plain,
! [A: vQuestionnaire] :
( ? [B: vGID,C: vQuestionnaire] :
( A
= ( C @ ( B @ vqgroup ) ) )
| ? [B: vExp,C: vQuestionnaire,D: vQuestionnaire] :
( A
= ( D @ ( C @ ( B @ vqcond ) ) ) )
| ? [B: vQuestionnaire,C: vQuestionnaire] :
( A
= ( C @ ( B @ vqseq ) ) )
| ? [B: vEntry] :
( A
= ( B @ vqsingle ) )
| ( A = vqempty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(204,axiom,
! [A: vQMap,B: vQuestionnaire,C: vExp,D: vAnsMap,E: vQuestionnaire] :
( ( ~ ( D @ ( C @ vreduceExp ) @ visSomeExp )
& ! [F: vQuestionnaire,G: vQuestionnaire] :
( ( E != G )
| ( B != F )
| ( C
!= ( vno @ vB @ vconstant ) ) )
& ! [F: vQuestionnaire,G: vQuestionnaire] :
( ( E != G )
| ( B != F )
| ( C
!= ( vyes @ vB @ vconstant ) ) ) )
=> ( ( A @ ( D @ ( E @ ( B @ ( C @ vqcond ) ) @ vreduce ) ) )
= vnoQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-14') ).
thf(4661,plain,
! [A: vQMap,B: vQuestionnaire,C: vExp,D: vAnsMap,E: vQuestionnaire] :
( ( ~ ( D @ ( C @ vreduceExp ) @ visSomeExp )
& ! [F: vQuestionnaire,G: vQuestionnaire] :
( ( E != G )
| ( B != F )
| ( C
!= ( vno @ vB @ vconstant ) ) )
& ! [F: vQuestionnaire,G: vQuestionnaire] :
( ( E != G )
| ( B != F )
| ( C
!= ( vyes @ vB @ vconstant ) ) ) )
=> ( ( A @ ( D @ ( E @ ( B @ ( C @ vqcond ) ) @ vreduce ) ) )
= vnoQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(189,axiom,
! [A: vQID,B: vQMap,C: vAnsMap] :
( ( B @ ( A @ vlookupQMap ) @ visSomeQuestion )
=> ( ( B @ ( C @ ( A @ vask @ vqsingle @ vreduce ) ) )
= ( B @ ( A @ vlookupQMap ) @ vgetQuestionAType @ ( B @ ( A @ vlookupQMap ) @ vgetQuestionLabel @ ( A @ vquestion ) ) @ vqsingle @ ( B @ ( C @ vQC ) ) @ vsomeQConf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-6') ).
thf(1387,plain,
! [A: vQID,B: vQMap,C: vAnsMap] :
( ( B @ ( A @ vlookupQMap ) @ visSomeQuestion )
=> ( ( B @ ( C @ ( A @ vask @ vqsingle @ vreduce ) ) )
= ( B @ ( A @ vlookupQMap ) @ vgetQuestionAType @ ( B @ ( A @ vlookupQMap ) @ vgetQuestionLabel @ ( A @ vquestion ) ) @ vqsingle @ ( B @ ( C @ vQC ) ) @ vsomeQConf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(12105,plain,
! [D: vAval,C: vQID,B: vYN,A: vQID] :
( ( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ ( D @ ( C @ vabind ) ) @ vtypeAM ) )
| ( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( vatmempty @ ( D @ vtypeOf @ sk222 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[9480,9484]) ).
thf(12106,plain,
! [B: vYN,A: vQID] :
( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( vatmempty @ ( B @ vB @ vtypeOf @ sk222 ) ) )
= A ),
inference(pattern_uni,[status(thm)],[12105:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vB ))]]) ).
thf(12146,plain,
! [B: vYN,A: vQID] :
( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( vatmempty @ ( B @ vB @ vtypeOf @ sk222 ) ) )
= A ),
inference(simp,[status(thm)],[12106]) ).
thf(12159,plain,
! [A: vQID] :
( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( vatmempty @ ( vYesNo @ sk222 ) ) )
= A ),
inference(rewrite,[status(thm)],[12146,1135]) ).
thf(152,axiom,
! [A: vATMap] :
( ( A @ ( vatmempty @ vintersectATM ) )
= vatmempty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersectATM-0') ).
thf(1223,plain,
! [A: vATMap] :
( ( A @ ( vatmempty @ vintersectATM ) )
= vatmempty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(214,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap] :
( ( D @ ( C @ vMC ) @ ( vqempty @ ( B @ ( A @ vMC ) @ vptcheck ) ) )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqempty_inv1') ).
thf(4712,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap] :
( ( D @ ( C @ vMC ) @ ( vqempty @ ( B @ ( A @ vMC ) @ vptcheck ) ) )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(95,axiom,
! [A: vQID,B: vAval,C: vAnsMap] :
( vaempty
!= ( C @ ( B @ ( A @ vabind ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-aempty-abind') ).
thf(891,plain,
! [A: vQID,B: vAval,C: vAnsMap] :
( vaempty
!= ( C @ ( B @ ( A @ vabind ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(892,plain,
~ ? [A: vQID,B: vAval,C: vAnsMap] :
( vaempty
= ( C @ ( B @ ( A @ vabind ) ) ) ),
inference(miniscope,[status(thm)],[891]) ).
thf(893,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( vaempty
!= ( C @ ( B @ ( A @ vabind ) ) ) ),
inference(cnf,[status(esa)],[892]) ).
thf(894,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( C @ ( B @ ( A @ vabind ) ) )
!= vaempty ),
inference(lifteq,[status(thm)],[893]) ).
thf(70,axiom,
! [A: vYN,B: vYN] :
( ( ( A @ vB )
= ( B @ vB ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-B') ).
thf(726,plain,
! [A: vYN,B: vYN] :
( ( ( A @ vB )
= ( B @ vB ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(727,plain,
! [B: vYN,A: vYN] :
( ( A = B )
| ( ( A @ vB )
!= ( B @ vB ) ) ),
inference(cnf,[status(esa)],[726]) ).
thf(728,plain,
! [B: vYN,A: vYN] :
( ( A = B )
| ( ( A @ vB )
!= ( B @ vB ) ) ),
inference(lifteq,[status(thm)],[727]) ).
thf(729,plain,
? [A: vAval > vYN] :
! [B: vYN] :
( ( B @ vB @ A )
= B ),
inference(detectInverse,[status(thm)],[728]) ).
thf(730,plain,
! [A: vYN] :
( ( A @ vB @ sk138 )
= A ),
inference(cnf,[status(esa)],[729]) ).
thf(5085,plain,
! [A: vYN] :
( ( A @ vB @ sk138 )
= A ),
inference(lifteq,[status(thm)],[730]) ).
thf(9,axiom,
vandop != vorop,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-andop-orop') ).
thf(273,plain,
vandop != vorop,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(274,plain,
vandop != vorop,
inference(polarity_switch,[status(thm)],[273]) ).
thf(275,plain,
vorop != vandop,
inference(lifteq,[status(thm)],[274]) ).
thf(255,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( C @ ( B @ ( A @ vQC ) ) @ vsomeQConf ) ),
inference(cnfConj,[status(thm)],[252]) ).
thf(256,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( C @ ( B @ ( A @ vQC ) ) @ vsomeQConf ) ),
inference(lifteq,[status(thm)],[255]) ).
thf(7871,plain,
! [E: vQuestionnaire,D: vQMap,C: vAnsMap,B: vAType,A: vLabel] :
( ( B != sk2 )
| ( ( sk1 @ ( sk5 @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( E @ ( D @ ( C @ vQC ) ) @ vsomeQConf ) )
| ( B @ ( A @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[610,256]) ).
thf(7872,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vLabel] :
( ( ( sk1 @ ( sk5 @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) @ vsomeQConf ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(pattern_uni,[status(thm)],[7871:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(7984,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vLabel] :
( ( ( sk1 @ ( sk5 @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) @ vsomeQConf ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(simp,[status(thm)],[7872]) ).
thf(13146,plain,
! [D: vAnsMap,C: vQID,B: vnat,A: vQID] :
( ( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( D @ vtypeAM ) )
| ( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) @ ( vNumber @ ( C @ vatmbind ) ) )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9478,12863]) ).
thf(13147,plain,
! [B: vQID,A: vQID] :
( ( vatmempty @ ( vNumber @ ( B @ vatmbind ) ) @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[13146:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( vaempty @ ( H @ vNum @ ( E @ vabind ) ) ))]]) ).
thf(13158,plain,
! [B: vQID,A: vQID] :
( ( vatmempty @ ( vNumber @ ( B @ vatmbind ) ) @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(simp,[status(thm)],[13147]) ).
thf(421,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk54 ) )
| ( ( A @ ( B @ sk56 ) )
= ( A @ ( B @ sk57 ) @ ( A @ ( B @ sk55 ) @ vecheck ) ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(467,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk56 ) )
= ( A @ ( B @ sk57 ) @ ( A @ ( B @ sk55 ) @ vecheck ) ) ) ),
inference(lifteq,[status(thm)],[421]) ).
thf(10037,plain,
! [E: vATMap,D: vAType,C: vQID,B: vYN,A: vQID] :
( ( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9480,1229]) ).
thf(10038,plain,
! [B: vYN,A: vQID] :
( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[10037:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( vYesNo )),bind(E,$thf( vatmempty ))]]) ).
thf(92,axiom,
! [A: vAval] : ( A @ vconstant @ vexpIsValue ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','expIsValue-0') ).
thf(879,plain,
! [A: vAval] : ( A @ vconstant @ vexpIsValue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(435,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk47 ) )
| ( A @ ( B @ sk49 ) @ visSomeAType )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(5682,plain,
! [A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( vatmempty @ ( vatmempty @ vMC ) ) )
| ( sk5 != vaempty )
| ( sk1 != vqmempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,4878]) ).
thf(5690,plain,
! [A: vMapConf] :
( ( ( A @ sk254 )
!= vatmempty )
| ( ( A @ sk253 )
!= vatmempty )
| ( sk5 != vaempty )
| ( sk1 != vqmempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5682]) ).
thf(164,axiom,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vGID,F: vATMap] :
( ( D @ ( F @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ( D @ ( F @ vMC ) @ ( B @ ( E @ vqgroup ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqgroup') ).
thf(1296,plain,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vGID,F: vATMap] :
( ( D @ ( F @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ( D @ ( F @ vMC ) @ ( B @ ( E @ vqgroup ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(441,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk61 ) )
| ( ( A @ ( B @ sk64 ) )
= ( A @ ( B @ sk63 ) @ ( A @ ( B @ sk65 ) @ vecheck ) ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(461,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk64 ) )
= ( A @ ( B @ sk63 ) @ ( A @ ( B @ sk65 ) @ vecheck ) ) ) ),
inference(lifteq,[status(thm)],[441]) ).
thf(191,axiom,
! [A: vQID,B: vAType,C: vQID,D: vAType,E: vExp,F: vLabel] :
( ( E @ ( B @ ( C @ vvalue ) ) )
!= ( D @ ( F @ ( A @ vdefquestion ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-value-defquestion') ).
thf(1392,plain,
! [A: vQID,B: vAType,C: vQID,D: vAType,E: vExp,F: vLabel] :
( ( E @ ( B @ ( C @ vvalue ) ) )
!= ( D @ ( F @ ( A @ vdefquestion ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(443,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk41 ) )
| ( A
= ( A @ ( B @ sk42 ) ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(456,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk42 ) )
= A ) ),
inference(lifteq,[status(thm)],[443]) ).
thf(29,axiom,
~ ( vnoExp @ visSomeExp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeExp-0') ).
thf(360,plain,
~ ( vnoExp @ visSomeExp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(361,plain,
~ ( vnoExp @ visSomeExp ),
inference(polarity_switch,[status(thm)],[360]) ).
thf(206,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vATMap,F: vQID,G: vExp] :
( ( C @ ( E @ vMC ) @ ( G @ ( D @ ( F @ vvalue ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tvalue_inv4') ).
thf(4680,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vATMap,F: vQID,G: vExp] :
( ( C @ ( E @ vMC ) @ ( G @ ( D @ ( F @ vvalue ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(112,axiom,
vyes != vno,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-yes-no') ).
thf(972,plain,
vyes != vno,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(973,plain,
vyes != vno,
inference(polarity_switch,[status(thm)],[972]) ).
thf(974,plain,
vno != vyes,
inference(lifteq,[status(thm)],[973]) ).
thf(115,axiom,
! [A: vExp,B: vAnsMap,C: vBinOpT,D: vExp] :
( ( ~ ( B @ ( A @ vreduceExp ) @ visSomeExp )
& ~ ( A @ vexpIsValue ) )
=> ( ( B @ ( D @ ( C @ ( A @ vbinop ) ) @ vreduceExp ) )
= vnoExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-7') ).
thf(1012,plain,
! [A: vExp,B: vAnsMap,C: vBinOpT,D: vExp] :
( ( ~ ( B @ ( A @ vreduceExp ) @ visSomeExp )
& ~ ( A @ vexpIsValue ) )
=> ( ( B @ ( D @ ( C @ ( A @ vbinop ) ) @ vreduceExp ) )
= vnoExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(6226,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ sk263 @ ( A @ sk262 @ ( A @ sk261 @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ vsomeQConf )
!= ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1339,256]) ).
thf(6227,plain,
! [A: vQConf] :
( ( A @ vsomeQConf )
!= ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) ) ),
inference(pattern_uni,[status(thm)],[6226:[bind(A,$thf( G )),bind(B,$thf( G @ sk261 )),bind(C,$thf( G @ sk262 )),bind(D,$thf( G @ sk263 ))]]) ).
thf(6235,plain,
! [A: vQConf] :
( ( A @ vsomeQConf )
!= ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) ) ),
inference(simp,[status(thm)],[6227]) ).
thf(7867,plain,
! [C: vQConf,B: vAType,A: vLabel] :
( ( B != sk2 )
| ( ( sk1 @ ( sk5 @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( C @ vsomeQConf ) )
| ( B @ ( A @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[610,6235]) ).
thf(7868,plain,
! [B: vQConf,A: vLabel] :
( ( ( sk1 @ ( sk5 @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( B @ vsomeQConf ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(pattern_uni,[status(thm)],[7867:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(7982,plain,
! [B: vQConf,A: vLabel] :
( ( ( sk1 @ ( sk5 @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( B @ vsomeQConf ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(simp,[status(thm)],[7868]) ).
thf(8072,plain,
! [D: vQConf,C: vLabel,B: vAType,A: vLabel] :
( ( vYesNo != vYesNo )
| ( ( sk1 @ ( sk5 @ ( sk7 @ ( B @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( D @ vsomeQConf ) )
| ( sk2 @ ( C @ sk124 ) )
| ( B @ ( A @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[610,7982]) ).
thf(8073,plain,
! [D: vQConf,C: vLabel,B: vAType,A: vLabel] :
( ( ( sk1 @ ( sk5 @ ( sk7 @ ( B @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( D @ vsomeQConf ) )
| ( sk2 @ ( C @ sk124 ) )
| ( B @ ( A @ sk124 ) ) ),
inference(pattern_uni,[status(thm)],[8072:[]]) ).
thf(13,axiom,
! [A: vExp,B: vExp] :
( ( ( A @ vsomeExp )
= ( B @ vsomeExp ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someExp') ).
thf(285,plain,
! [A: vExp,B: vExp] :
( ( ( A @ vsomeExp )
= ( B @ vsomeExp ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(139,axiom,
! [A: vATMap] :
( ( A @ ( vatmempty @ vappendATMap ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','appendATMap-0') ).
thf(1143,plain,
! [A: vATMap] :
( ( A @ ( vatmempty @ vappendATMap ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(9803,plain,
! [E: vATMap,D: vAType,C: vQID,B: vnat,A: vQID] :
( ( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM @ ( E @ ( D @ sk222 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[9478,8147]) ).
thf(9804,plain,
! [B: vnat,A: vQID] :
( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM @ ( vatmempty @ ( vNumber @ sk222 ) ) )
= A ),
inference(pattern_uni,[status(thm)],[9803:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( vNumber )),bind(E,$thf( vatmempty ))]]) ).
thf(367,plain,
~ ( vnoAType @ visSomeAType ),
inference(polarity_switch,[status(thm)],[366]) ).
thf(5004,plain,
( ( ( vYesNo @ vsomeAType @ visSomeAType )
!= ( vnoAType @ visSomeAType ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4997,367]) ).
thf(5005,plain,
( ( vYesNo @ vsomeAType @ visSomeAType )
!= ( vnoAType @ visSomeAType ) ),
inference(simp,[status(thm)],[5004]) ).
thf(5006,plain,
( ( vYesNo @ vsomeAType )
!= vnoAType ),
inference(simp,[status(thm)],[5005]) ).
thf(8988,plain,
! [F: vExp,E: vBinOpT,D: vExp,C: vAval,B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk37 ) @ vB @ vconstant )
!= ( C @ vconstant ) )
| ( B
!= ( F @ ( E @ ( D @ vbinop ) ) ) )
| ( B @ ( A @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[458,416]) ).
thf(8989,plain,
! [E: vATMap,D: vExp,C: vExp,B: vBinOpT,A: vExp] :
( ( D
!= ( C @ ( B @ ( A @ vbinop ) ) ) )
| ( D @ ( E @ sk35 ) ) ),
inference(pattern_uni,[status(thm)],[8988:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ sk37 ) @ vB )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F ))]]) ).
thf(9073,plain,
! [D: vATMap,C: vExp,B: vBinOpT,A: vExp] : ( C @ ( B @ ( A @ vbinop ) ) @ ( D @ sk35 ) ),
inference(simp,[status(thm)],[8989]) ).
thf(94,axiom,
! [A: vExp,B: vQuestionnaire,C: vQuestionnaire] :
( vqempty
!= ( C @ ( B @ ( A @ vqcond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qempty-qcond') ).
thf(887,plain,
! [A: vExp,B: vQuestionnaire,C: vQuestionnaire] :
( vqempty
!= ( C @ ( B @ ( A @ vqcond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(888,plain,
~ ? [A: vExp,B: vQuestionnaire,C: vQuestionnaire] :
( vqempty
= ( C @ ( B @ ( A @ vqcond ) ) ) ),
inference(miniscope,[status(thm)],[887]) ).
thf(889,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vExp] :
( vqempty
!= ( C @ ( B @ ( A @ vqcond ) ) ) ),
inference(cnf,[status(esa)],[888]) ).
thf(890,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vExp] :
( ( C @ ( B @ ( A @ vqcond ) ) )
!= vqempty ),
inference(lifteq,[status(thm)],[889]) ).
thf(5319,plain,
! [D: vQuestionnaire,C: vQuestionnaire,B: vExp,A: vQuestionnaire] :
( ( A
!= ( D @ ( C @ ( B @ vqcond ) ) ) )
| ( vqempty != vqempty )
| ~ ( A @ visValue ) ),
inference(paramod_ordered,[status(thm)],[1374,890]) ).
thf(5320,plain,
! [D: vQuestionnaire,C: vQuestionnaire,B: vExp,A: vQuestionnaire] :
( ( A
!= ( D @ ( C @ ( B @ vqcond ) ) ) )
| ~ ( A @ visValue ) ),
inference(simp,[status(thm)],[5319]) ).
thf(5321,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vExp] :
~ ( C @ ( B @ ( A @ vqcond ) ) @ visValue ),
inference(pattern_uni,[status(thm)],[5320:[bind(A,$thf( G @ ( F @ ( E @ vqcond ) ) )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( G ))]]) ).
thf(5345,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vExp] :
~ ( C @ ( B @ ( A @ vqcond ) ) @ visValue ),
inference(simp,[status(thm)],[5321]) ).
thf(185,axiom,
! [A: vGID,B: vQuestionnaire,C: vAnsMap,D: vQMap] :
( ( D @ ( C @ ( B @ ( A @ vqgroup ) @ vreduce ) ) )
= ( B @ ( D @ ( C @ vQC ) ) @ vsomeQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-15') ).
thf(1375,plain,
! [A: vGID,B: vQuestionnaire,C: vAnsMap,D: vQMap] :
( ( D @ ( C @ ( B @ ( A @ vqgroup ) @ vreduce ) ) )
= ( B @ ( D @ ( C @ vQC ) ) @ vsomeQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(237,axiom,
! [A: vQConf] :
? [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( ( A @ vgetQM )
= C )
& ( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getQM-INV') ).
thf(4811,plain,
! [A: vQConf] :
? [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( ( A @ vgetQM )
= C )
& ( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(4812,plain,
! [A: vQConf] :
? [B: vAnsMap,C: vQMap] :
( ( ( A @ vgetQM )
= C )
& ? [D: vQuestionnaire] :
( A
= ( D @ ( C @ ( B @ vQC ) ) ) ) ),
inference(miniscope,[status(thm)],[4811]) ).
thf(4813,plain,
! [A: vQConf] :
( ( ( A @ vgetQM )
= ( A @ sk400 ) )
& ( A
= ( A @ sk401 @ ( A @ sk400 @ ( A @ sk399 @ vQC ) ) ) ) ),
inference(cnf,[status(esa)],[4812]) ).
thf(4814,plain,
! [A: vQConf] :
( A
= ( A @ sk401 @ ( A @ sk400 @ ( A @ sk399 @ vQC ) ) ) ),
inference(cnfConj,[status(thm)],[4813]) ).
thf(4816,plain,
! [A: vQConf] :
( ( A @ sk401 @ ( A @ sk400 @ ( A @ sk399 @ vQC ) ) )
= A ),
inference(lifteq,[status(thm)],[4814]) ).
thf(4815,plain,
! [A: vQConf] :
( ( A @ vgetQM )
= ( A @ sk400 ) ),
inference(cnfConj,[status(thm)],[4813]) ).
thf(4817,plain,
! [A: vQConf] :
( ( A @ sk400 )
= ( A @ vgetQM ) ),
inference(lifteq,[status(thm)],[4815]) ).
thf(6443,plain,
! [A: vQConf] :
( ( A @ sk401 @ ( A @ vgetQM @ ( A @ sk399 @ vQC ) ) )
= A ),
inference(rewrite,[status(thm)],[4816,4817]) ).
thf(6444,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ sk401 @ ( A @ vgetQM @ ( A @ sk399 @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ vgetAM )
= B ) ),
inference(paramod_ordered,[status(thm)],[6443,1347]) ).
thf(6445,plain,
! [A: vQConf] :
( ( A @ sk399 )
= ( A @ vgetAM ) ),
inference(pattern_uni,[status(thm)],[6444:[bind(A,$thf( G )),bind(B,$thf( G @ sk399 )),bind(C,$thf( G @ vgetQM )),bind(D,$thf( G @ sk401 ))]]) ).
thf(6459,plain,
! [A: vQConf] :
( ( A @ sk399 )
= ( A @ vgetAM ) ),
inference(simp,[status(thm)],[6445]) ).
thf(69,axiom,
! [A: vAval] :
( ( A @ vconstant @ vgetExpValue )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getExpValue-0') ).
thf(723,plain,
! [A: vAval] :
( ( A @ vconstant @ vgetExpValue )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(724,plain,
! [A: vAval] :
( ( A @ vconstant @ vgetExpValue )
= A ),
inference(cnf,[status(esa)],[723]) ).
thf(725,plain,
! [A: vAval] :
( ( A @ vconstant @ vgetExpValue )
= A ),
inference(lifteq,[status(thm)],[724]) ).
thf(9602,plain,
! [E: vATMap,D: vAType,C: vQID,B: vstring,A: vQID] :
( ( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM @ ( E @ ( D @ sk222 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[9477,8147]) ).
thf(9603,plain,
! [B: vstring,A: vQID] :
( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM @ ( vatmempty @ ( vText @ sk222 ) ) )
= A ),
inference(pattern_uni,[status(thm)],[9602:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( vText )),bind(E,$thf( vatmempty ))]]) ).
thf(8101,plain,
! [D: vExp,C: vATMap,B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk54 ) )
!= ( C @ ( D @ sk54 ) ) )
| ~ ( C @ ( D @ sk68 ) @ visSomeAType )
| ~ ( C @ ( D @ sk61 ) )
| ~ $true
| ~ ( C @ ( D @ sk47 ) )
| ~ ( C @ ( D @ sk44 ) )
| ~ ( D @ ( C @ sk41 ) )
| ~ ( D @ ( C @ sk38 ) )
| ~ ( D @ ( C @ sk35 ) )
| ~ ( A @ ( B @ sk58 ) @ visSomeAType )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[448,429]) ).
thf(8102,plain,
! [D: vExp,C: vATMap,B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk54 ) )
!= ( C @ ( D @ sk54 ) ) )
| ~ ( C @ ( D @ sk68 ) @ visSomeAType )
| ~ ( C @ ( D @ sk61 ) )
| ~ ( C @ ( D @ sk47 ) )
| ~ ( C @ ( D @ sk44 ) )
| ~ ( D @ ( C @ sk41 ) )
| ~ ( D @ ( C @ sk38 ) )
| ~ ( D @ ( C @ sk35 ) )
| ~ ( A @ ( B @ sk58 ) @ visSomeAType )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(simp,[status(thm)],[8101]) ).
thf(8103,plain,
! [B: vExp,A: vATMap] :
( ~ ( A @ ( B @ sk68 ) @ visSomeAType )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ~ ( A @ ( B @ sk58 ) @ visSomeAType )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(pattern_uni,[status(thm)],[8102:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(8138,plain,
! [B: vExp,A: vATMap] :
( ~ ( A @ ( B @ sk68 ) @ visSomeAType )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk58 ) @ visSomeAType )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(simp,[status(thm)],[8103]) ).
thf(236,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vdefquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( ( A @ ( G @ vlookupATMap ) )
= vnoAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tdefquestion_inv1') ).
thf(4808,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vdefquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( ( A @ ( G @ vlookupATMap ) )
= vnoAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(178,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap,E: vQID] :
( ( C @ ( D @ vMC ) @ ( E @ vask @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Task_inv4') ).
thf(1350,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap,E: vQID] :
( ( C @ ( D @ vMC ) @ ( E @ vask @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(71,axiom,
! [A: vYN,B: vYN] :
( ? [C: vYN,D: vYN] :
( ( ( B @ ( A @ vand ) )
= vno )
& ( B = D )
& ( A = C )
& ( ( D != vyes )
| ( C != vyes ) ) )
| ( ( ( B @ ( A @ vand ) )
= vyes )
& ( B = vyes )
& ( A = vyes ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and-INV') ).
thf(731,plain,
! [A: vYN,B: vYN] :
( ? [C: vYN,D: vYN] :
( ( ( B @ ( A @ vand ) )
= vno )
& ( B = D )
& ( A = C )
& ( ( D != vyes )
| ( C != vyes ) ) )
| ( ( ( B @ ( A @ vand ) )
= vyes )
& ( B = vyes )
& ( A = vyes ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(732,plain,
! [B: vYN,A: vYN] :
( ( ( ( B @ ( A @ vand ) )
= vno )
| ~ ( B @ ( A @ sk139 ) ) )
& ( ( B
= ( A @ ( B @ sk141 ) ) )
| ~ ( B @ ( A @ sk139 ) ) )
& ( ( A
= ( A @ ( B @ sk140 ) ) )
| ~ ( B @ ( A @ sk139 ) ) )
& ( ( ( A @ ( B @ sk141 ) )
!= vyes )
| ( ( A @ ( B @ sk140 ) )
!= vyes )
| ~ ( B @ ( A @ sk139 ) ) )
& ( ( B @ ( A @ sk139 ) )
| ( ( B @ ( A @ vand ) )
= vyes ) )
& ( ( B @ ( A @ sk139 ) )
| ( B = vyes ) )
& ( ( B @ ( A @ sk139 ) )
| ( A = vyes ) ) ),
inference(cnf,[status(esa)],[731]) ).
thf(733,plain,
! [B: vYN,A: vYN] :
( ( ( A @ ( B @ sk141 ) )
!= vyes )
| ( ( A @ ( B @ sk140 ) )
!= vyes )
| ~ ( B @ ( A @ sk139 ) ) ),
inference(cnfConj,[status(thm)],[732]) ).
thf(742,plain,
! [B: vYN,A: vYN] :
( ~ ( B @ ( A @ sk139 ) )
| ( ( A @ ( B @ sk141 ) )
!= vyes )
| ( ( A @ ( B @ sk140 ) )
!= vyes ) ),
inference(lifteq,[status(thm)],[733]) ).
thf(1254,plain,
! [F: vQMap,E: vQuestionnaire,D: vAnsMap,C: vQuestionnaire,B: vAnsMap,A: vQMap] :
( ( D = B )
| ( ( E @ ( A @ ( D @ vQC ) ) )
!= ( C @ ( F @ ( B @ vQC ) ) ) ) ),
inference(cnfConj,[status(thm)],[1253]) ).
thf(1257,plain,
! [F: vQMap,E: vQuestionnaire,D: vAnsMap,C: vQuestionnaire,B: vAnsMap,A: vQMap] :
( ( D = B )
| ( ( E @ ( A @ ( D @ vQC ) ) )
!= ( C @ ( F @ ( B @ vQC ) ) ) ) ),
inference(lifteq,[status(thm)],[1254]) ).
thf(1258,plain,
? [A: vQMap > vQuestionnaire > vQConf > vAnsMap] :
! [B: vAnsMap,C: vQMap,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vQC ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[1257]) ).
thf(1259,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ ( C @ ( B @ sk242 ) ) )
= A ),
inference(cnf,[status(esa)],[1258]) ).
thf(8527,plain,
! [C: vQuestionnaire,B: vQMap,A: vAnsMap] :
( ( C @ ( B @ ( A @ vQC ) ) @ ( C @ ( B @ sk242 ) ) )
= A ),
inference(lifteq,[status(thm)],[1259]) ).
thf(8528,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ vgetQuest @ ( A @ vgetQM @ ( A @ vgetAM @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ ( D @ ( C @ sk242 ) ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[6513,8527]) ).
thf(8529,plain,
! [A: vQConf] :
( ( A @ ( A @ vgetQuest @ ( A @ vgetQM @ sk242 ) ) )
= ( A @ vgetAM ) ),
inference(pattern_uni,[status(thm)],[8528:[bind(A,$thf( G )),bind(B,$thf( G @ vgetAM )),bind(C,$thf( G @ vgetQM )),bind(D,$thf( G @ vgetQuest ))]]) ).
thf(8530,plain,
! [A: vQConf] :
( ( A @ ( A @ vgetQuest @ ( A @ vgetQM @ sk242 ) ) )
= ( A @ vgetAM ) ),
inference(simp,[status(thm)],[8529]) ).
thf(155,axiom,
! [A: vAnsMap,B: vAnsMap] :
( ? [C: vQID,D: vAval,E: vAnsMap,F: vAnsMap] :
( ( ( B @ ( A @ vappendAnsMap ) )
= ( F @ ( E @ vappendAnsMap ) @ ( D @ ( C @ vabind ) ) ) )
& ( B = F )
& ( A
= ( E @ ( D @ ( C @ vabind ) ) ) ) )
| ? [C: vAnsMap] :
( ( ( B @ ( A @ vappendAnsMap ) )
= C )
& ( B = C )
& ( A = vaempty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','appendAnsMap-INV') ).
thf(1234,plain,
! [A: vAnsMap,B: vAnsMap] :
( ? [C: vQID,D: vAval,E: vAnsMap,F: vAnsMap] :
( ( ( B @ ( A @ vappendAnsMap ) )
= ( F @ ( E @ vappendAnsMap ) @ ( D @ ( C @ vabind ) ) ) )
& ( B = F )
& ( A
= ( E @ ( D @ ( C @ vabind ) ) ) ) )
| ? [C: vAnsMap] :
( ( ( B @ ( A @ vappendAnsMap ) )
= C )
& ( B = C )
& ( A = vaempty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(4693,plain,
! [C: vQMap,B: vAnsMap,A: vQuestionnaire] :
( ( C @ ( B @ ( A @ ( vqempty @ vqseq ) @ vreduce ) ) )
= ( A @ ( C @ ( B @ vQC ) ) @ vsomeQConf ) ),
inference(cnf,[status(esa)],[4692]) ).
thf(4694,plain,
! [C: vQMap,B: vAnsMap,A: vQuestionnaire] :
( ( C @ ( B @ ( A @ ( vqempty @ vqseq ) @ vreduce ) ) )
= ( A @ ( C @ ( B @ vQC ) ) @ vsomeQConf ) ),
inference(lifteq,[status(thm)],[4693]) ).
thf(12527,plain,
! [G: vQConf,F: vLabel,E: vAType,D: vLabel,C: vQMap,B: vAnsMap,A: vQuestionnaire] :
( ( ( C @ ( B @ ( A @ ( vqempty @ vqseq ) @ vreduce ) ) )
!= ( sk1 @ ( sk5 @ ( sk7 @ ( E @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) ) )
| ( ( A @ ( C @ ( B @ vQC ) ) @ vsomeQConf )
!= ( G @ vsomeQConf ) )
| ( sk2 @ ( F @ sk124 ) )
| ( E @ ( D @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[4694,8073]) ).
thf(12533,plain,
! [G: vQConf,F: vLabel,E: vAType,D: vLabel,C: vQMap,B: vAnsMap,A: vQuestionnaire] :
( ( C != sk1 )
| ( B != sk5 )
| ( ( A @ ( vqempty @ vqseq ) )
!= ( sk7 @ ( E @ ( sk6 @ vvalue ) ) @ vqsingle ) )
| ( ( A @ ( C @ ( B @ vQC ) ) )
!= G )
| ( sk2 @ ( F @ sk124 ) )
| ( E @ ( D @ sk124 ) ) ),
inference(simp,[status(thm)],[12527]) ).
thf(12538,plain,
! [D: vLabel,C: vAType,B: vLabel,A: vQuestionnaire] :
( ( ( A @ ( vqempty @ vqseq ) )
!= ( sk7 @ ( C @ ( sk6 @ vvalue ) ) @ vqsingle ) )
| ( sk2 @ ( D @ sk124 ) )
| ( C @ ( B @ sk124 ) ) ),
inference(simp,[status(thm)],[12533]) ).
thf(8675,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ vgetQuest @ ( A @ vgetQM @ ( A @ vgetAM @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ ( D @ ( B @ sk243 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[6513,8674]) ).
thf(8676,plain,
! [A: vQConf] :
( ( A @ ( A @ vgetQuest @ ( A @ vgetAM @ sk243 ) ) )
= ( A @ vgetQM ) ),
inference(pattern_uni,[status(thm)],[8675:[bind(A,$thf( G )),bind(B,$thf( G @ vgetAM )),bind(C,$thf( G @ vgetQM )),bind(D,$thf( G @ vgetQuest ))]]) ).
thf(8677,plain,
! [A: vQConf] :
( ( A @ ( A @ vgetQuest @ ( A @ vgetAM @ sk243 ) ) )
= ( A @ vgetQM ) ),
inference(simp,[status(thm)],[8676]) ).
thf(171,axiom,
! [A: vATMap,B: vATMap,C: vAType,D: vQID,E: vExp] :
( ( ( ( E @ ( B @ vecheck ) )
= ( C @ vsomeAType ) )
& ( ( B @ ( D @ vlookupATMap ) )
= vnoAType ) )
=> ( A @ ( B @ ( C @ ( D @ vatmbind ) ) @ vMC ) @ ( E @ ( C @ ( D @ vvalue ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tvalue') ).
thf(1329,plain,
! [A: vATMap,B: vATMap,C: vAType,D: vQID,E: vExp] :
( ( ( ( E @ ( B @ vecheck ) )
= ( C @ vsomeAType ) )
& ( ( B @ ( D @ vlookupATMap ) )
= vnoAType ) )
=> ( A @ ( B @ ( C @ ( D @ vatmbind ) ) @ vMC ) @ ( E @ ( C @ ( D @ vvalue ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(141,axiom,
! [A: vQID,B: vLabel,C: vAType] : ( C @ ( B @ ( A @ vsomeQuestion ) ) @ visSomeQuestion ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeQuestion-1') ).
thf(1160,plain,
! [A: vQID,B: vLabel,C: vAType] : ( C @ ( B @ ( A @ vsomeQuestion ) ) @ visSomeQuestion ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(181,axiom,
! [A: vEntry,B: vQuestionnaire,C: vQuestionnaire] :
( ( A @ vqsingle )
!= ( C @ ( B @ vqseq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qsingle-qseq') ).
thf(1361,plain,
! [A: vEntry,B: vQuestionnaire,C: vQuestionnaire] :
( ( A @ vqsingle )
!= ( C @ ( B @ vqseq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(712,plain,
! [D: vExp,C: vUnOpT,B: vExp,A: vUnOpT] :
( ( A = C )
| ( ( B @ ( A @ vunop ) )
!= ( D @ ( C @ vunop ) ) ) ),
inference(cnfConj,[status(thm)],[711]) ).
thf(714,plain,
! [D: vExp,C: vUnOpT,B: vExp,A: vUnOpT] :
( ( A = C )
| ( ( B @ ( A @ vunop ) )
!= ( D @ ( C @ vunop ) ) ) ),
inference(lifteq,[status(thm)],[712]) ).
thf(715,plain,
? [A: vExp > vExp > vUnOpT] :
! [B: vUnOpT,C: vExp] :
( ( C @ ( B @ vunop ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[714]) ).
thf(716,plain,
! [B: vExp,A: vUnOpT] :
( ( B @ ( A @ vunop ) @ ( B @ sk136 ) )
= A ),
inference(cnf,[status(esa)],[715]) ).
thf(5818,plain,
! [B: vExp,A: vUnOpT] :
( ( B @ ( A @ vunop ) @ ( B @ sk136 ) )
= A ),
inference(lifteq,[status(thm)],[716]) ).
thf(334,plain,
! [A: vUnOpT,B: vAval] :
( ( ~ ? [C: vYN] :
( B
= ( C @ vB ) )
| ( A != vnotop ) )
=> ( ( B @ ( A @ vevalUnOp ) )
= vnoExp ) ),
inference(miniscope,[status(thm)],[333]) ).
thf(335,plain,
! [B: vAval,A: vUnOpT] :
( ( ( ( B @ ( A @ vevalUnOp ) )
= vnoExp )
| ( B
= ( A @ ( B @ sk25 ) @ vB ) ) )
& ( ( ( B @ ( A @ vevalUnOp ) )
= vnoExp )
| ( A = vnotop ) ) ),
inference(cnf,[status(esa)],[334]) ).
thf(337,plain,
! [B: vAval,A: vUnOpT] :
( ( ( B @ ( A @ vevalUnOp ) )
= vnoExp )
| ( B
= ( A @ ( B @ sk25 ) @ vB ) ) ),
inference(cnfConj,[status(thm)],[335]) ).
thf(339,plain,
! [B: vAval,A: vUnOpT] :
( ( ( B @ ( A @ vevalUnOp ) )
= vnoExp )
| ( ( A @ ( B @ sk25 ) @ vB )
= B ) ),
inference(lifteq,[status(thm)],[337]) ).
thf(217,axiom,
! [A: vQConf] :
( ( A @ vsomeQConf @ vgetQC )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getQC-0') ).
thf(4721,plain,
! [A: vQConf] :
( ( A @ vsomeQConf @ vgetQC )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(150,axiom,
! [A: vATMap,B: vnat] :
( ( B @ vNum @ vconstant @ ( A @ vecheck ) )
= ( vNumber @ vsomeAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','echeck-1') ).
thf(1216,plain,
! [A: vATMap,B: vnat] :
( ( B @ vNum @ vconstant @ ( A @ vecheck ) )
= ( vNumber @ vsomeAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1217,plain,
! [B: vnat,A: vATMap] :
( ( B @ vNum @ vconstant @ ( A @ vecheck ) )
= ( vNumber @ vsomeAType ) ),
inference(cnf,[status(esa)],[1216]) ).
thf(1218,plain,
! [B: vnat,A: vATMap] :
( ( B @ vNum @ vconstant @ ( A @ vecheck ) )
= ( vNumber @ vsomeAType ) ),
inference(lifteq,[status(thm)],[1217]) ).
thf(8573,plain,
! [D: vExp,C: vATMap,B: vnat,A: vATMap] :
( ( ( B @ vNum @ vconstant @ ( A @ vecheck ) )
!= ( C @ ( D @ sk67 ) @ ( C @ ( D @ sk69 ) @ vecheck ) ) )
| ~ ( vNumber @ vsomeAType @ visSomeAType )
| ~ ( C @ ( D @ sk61 ) )
| ~ ( C @ ( D @ sk54 ) )
| ~ ( C @ ( D @ sk47 ) )
| ~ ( C @ ( D @ sk44 ) )
| ~ ( D @ ( C @ sk41 ) )
| ~ ( D @ ( C @ sk38 ) )
| ~ ( D @ ( C @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[1218,8488]) ).
thf(8591,plain,
! [D: vExp,C: vATMap,B: vnat,A: vATMap] :
( ( ( B @ vNum @ vconstant )
!= ( C @ ( D @ sk67 ) ) )
| ( A
!= ( C @ ( D @ sk69 ) ) )
| ~ ( vNumber @ vsomeAType @ visSomeAType )
| ~ ( C @ ( D @ sk61 ) )
| ~ ( C @ ( D @ sk54 ) )
| ~ ( C @ ( D @ sk47 ) )
| ~ ( C @ ( D @ sk44 ) )
| ~ ( D @ ( C @ sk41 ) )
| ~ ( D @ ( C @ sk38 ) )
| ~ ( D @ ( C @ sk35 ) ) ),
inference(simp,[status(thm)],[8573]) ).
thf(8601,plain,
! [C: vExp,B: vATMap,A: vnat] :
( ( ( A @ vNum @ vconstant )
!= ( B @ ( C @ sk67 ) ) )
| ~ ( vNumber @ vsomeAType @ visSomeAType )
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(simp,[status(thm)],[8591]) ).
thf(8742,plain,
! [C: vExp,B: vATMap,A: vnat] :
( ( ( A @ vNum @ vconstant )
!= ( B @ ( C @ sk67 ) ) )
| ~ $true
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(rewrite,[status(thm)],[8601,670]) ).
thf(8743,plain,
! [C: vExp,B: vATMap,A: vnat] :
( ( ( A @ vNum @ vconstant )
!= ( B @ ( C @ sk67 ) ) )
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(simp,[status(thm)],[8742]) ).
thf(305,plain,
! [A: vAval] :
( ( A @ sk14 )
| ( A
= ( A @ sk15 @ vB ) ) ),
inference(cnfConj,[status(thm)],[303]) ).
thf(314,plain,
! [A: vAval] :
( ( A @ sk14 )
| ( ( A @ sk15 @ vB )
= A ) ),
inference(lifteq,[status(thm)],[305]) ).
thf(5535,plain,
! [C: vstring,B: vYN,A: vAval] :
( ( ( A @ sk15 @ vB )
!= ( B @ vB ) )
| ( A
!= ( C @ vT ) )
| ( A @ sk14 ) ),
inference(paramod_ordered,[status(thm)],[314,682]) ).
thf(5536,plain,
! [B: vAval,A: vstring] :
( ( B
!= ( A @ vT ) )
| ( B @ sk14 ) ),
inference(pattern_uni,[status(thm)],[5535:[bind(A,$thf( D )),bind(B,$thf( D @ sk15 ))]]) ).
thf(5547,plain,
! [A: vstring] : ( A @ vT @ sk14 ),
inference(simp,[status(thm)],[5536]) ).
thf(8922,plain,
! [D: vQConf,C: vQMap,B: vAnsMap,A: vQuestionnaire] :
( ( ( C @ ( B @ ( A @ ( vqempty @ vqseq ) @ vreduce ) ) )
!= ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) ) )
| ( ( A @ ( C @ ( B @ vQC ) ) @ vsomeQConf )
!= ( D @ vsomeQConf ) ) ),
inference(paramod_ordered,[status(thm)],[4694,6235]) ).
thf(8941,plain,
! [D: vQConf,C: vQMap,B: vAnsMap,A: vQuestionnaire] :
( ( ( C @ ( B @ ( A @ ( vqempty @ vqseq ) @ vreduce ) ) )
!= ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) ) )
| ( ( A @ ( C @ ( B @ vQC ) ) )
!= D ) ),
inference(simp,[status(thm)],[8922]) ).
thf(8951,plain,
! [C: vQMap,B: vAnsMap,A: vQuestionnaire] :
( ( C @ ( B @ ( A @ ( vqempty @ vqseq ) @ vreduce ) ) )
!= ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) ) ),
inference(simp,[status(thm)],[8941]) ).
thf(9288,plain,
! [C: vQMap,B: vAnsMap,A: vQuestionnaire] :
( ( A @ ( C @ ( B @ vQC ) ) @ vsomeQConf )
!= ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) ) ),
inference(rewrite,[status(thm)],[8951,4694]) ).
thf(116,axiom,
! [A: vExp] :
( ~ ( A @ vexpIsValue )
=> ? [B: vExp] :
( ( A = B )
& ! [C: vAval] :
( B
!= ( C @ vconstant ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','expIsValue-false-INV') ).
thf(1016,plain,
! [A: vExp] :
( ~ ( A @ vexpIsValue )
=> ? [B: vExp] :
( ( A = B )
& ! [C: vAval] :
( B
!= ( C @ vconstant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(277,plain,
vYesNo != vText,
inference(polarity_switch,[status(thm)],[276]) ).
thf(278,plain,
vText != vYesNo,
inference(lifteq,[status(thm)],[277]) ).
thf(7893,plain,
! [B: vAType,A: vLabel] :
( ( B != vText )
| ( vYesNo != vYesNo )
| ( B @ ( A @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[610,278]) ).
thf(7894,plain,
! [B: vAType,A: vLabel] :
( ( B != vText )
| ( B @ ( A @ sk124 ) ) ),
inference(simp,[status(thm)],[7893]) ).
thf(7895,plain,
! [A: vLabel] : ( vText @ ( A @ sk124 ) ),
inference(pattern_uni,[status(thm)],[7894:[bind(A,$thf( A )),bind(B,$thf( vText ))]]) ).
thf(65,axiom,
! [A: vExp] : ( A @ vsomeExp @ visSomeExp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeExp-1') ).
thf(705,plain,
! [A: vExp] : ( A @ vsomeExp @ visSomeExp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(706,plain,
! [A: vExp] : ( A @ vsomeExp @ visSomeExp ),
inference(cnf,[status(esa)],[705]) ).
thf(205,axiom,
! [A: vQID,B: vQMap,C: vAnsMap] :
( ~ ( B @ ( A @ vlookupQMap ) @ visSomeQuestion )
=> ( ( B @ ( C @ ( A @ vask @ vqsingle @ vreduce ) ) )
= vnoQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-7') ).
thf(4676,plain,
! [A: vQID,B: vQMap,C: vAnsMap] :
( ~ ( B @ ( A @ vlookupQMap ) @ visSomeQuestion )
=> ( ( B @ ( C @ ( A @ vask @ vqsingle @ vreduce ) ) )
= vnoQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(439,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk54 ) )
| ( B
= ( A @ ( B @ sk59 ) @ ( A @ ( B @ sk60 ) @ ( A @ ( B @ sk57 ) @ vbinop ) ) ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(471,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk59 ) @ ( A @ ( B @ sk60 ) @ ( A @ ( B @ sk57 ) @ vbinop ) ) )
= B ) ),
inference(lifteq,[status(thm)],[439]) ).
thf(98,axiom,
! [A: vExp,B: vAnsMap,C: vBinOpT,D: vExp] :
( ( ( B @ ( A @ vreduceExp ) @ visSomeExp )
& ~ ( A @ vexpIsValue ) )
=> ( ( B @ ( D @ ( C @ ( A @ vbinop ) ) @ vreduceExp ) )
= ( D @ ( C @ ( B @ ( A @ vreduceExp ) @ vgetExp @ vbinop ) ) @ vsomeExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-6') ).
thf(901,plain,
! [A: vExp,B: vAnsMap,C: vBinOpT,D: vExp] :
( ( ( B @ ( A @ vreduceExp ) @ visSomeExp )
& ~ ( A @ vexpIsValue ) )
=> ( ( B @ ( D @ ( C @ ( A @ vbinop ) ) @ vreduceExp ) )
= ( D @ ( C @ ( B @ ( A @ vreduceExp ) @ vgetExp @ vbinop ) ) @ vsomeExp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(59,axiom,
! [A: vAType] :
( ( A = vText )
| ( A = vNumber )
| ( A = vYesNo ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-AType') ).
thf(686,plain,
! [A: vAType] :
( ( A = vText )
| ( A = vNumber )
| ( A = vYesNo ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(127,axiom,
! [A: vATMap] :
( ? [B: vQID,C: vAType,D: vATMap] :
( A
= ( D @ ( C @ ( B @ vatmbind ) ) ) )
| ( A = vatmempty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-ATMap') ).
thf(1075,plain,
! [A: vATMap] :
( ? [B: vQID,C: vAType,D: vATMap] :
( A
= ( D @ ( C @ ( B @ vatmbind ) ) ) )
| ( A = vatmempty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(451,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk38 ) )
| ( A
= ( A @ ( B @ sk39 ) ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(476,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk39 ) )
= A ) ),
inference(lifteq,[status(thm)],[451]) ).
thf(200,axiom,
! [A: vQConf] :
( vnoQConf
!= ( A @ vsomeQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noQConf-someQConf') ).
thf(4648,plain,
! [A: vQConf] :
( vnoQConf
!= ( A @ vsomeQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(86,axiom,
! [A: vQID,B: vLabel,C: vAType,D: vQID,E: vAType,F: vLabel] :
( ( ( C @ ( F @ ( D @ vdefquestion ) ) )
= ( E @ ( B @ ( A @ vdefquestion ) ) ) )
=> ( ( C = E )
& ( F = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-defquestion') ).
thf(826,plain,
! [A: vQID,B: vLabel,C: vAType,D: vQID,E: vAType,F: vLabel] :
( ( ( C @ ( F @ ( D @ vdefquestion ) ) )
= ( E @ ( B @ ( A @ vdefquestion ) ) ) )
=> ( ( C = E )
& ( F = B )
& ( D = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(827,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( ( C = E )
| ( ( C @ ( F @ ( D @ vdefquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ) )
& ( ( F = B )
| ( ( C @ ( F @ ( D @ vdefquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ) )
& ( ( D = A )
| ( ( C @ ( F @ ( D @ vdefquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ) ) ),
inference(cnf,[status(esa)],[826]) ).
thf(830,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C = E )
| ( ( C @ ( F @ ( D @ vdefquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ) ),
inference(cnfConj,[status(thm)],[827]) ).
thf(837,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C = E )
| ( ( C @ ( F @ ( D @ vdefquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ) ),
inference(lifteq,[status(thm)],[830]) ).
thf(838,plain,
? [A: vQID > vLabel > vEntry > vAType] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vdefquestion ) ) @ ( C @ ( B @ A ) ) )
= D ),
inference(detectInverse,[status(thm)],[837]) ).
thf(839,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vdefquestion ) ) @ ( B @ ( A @ sk156 ) ) )
= C ),
inference(cnf,[status(esa)],[838]) ).
thf(6935,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vdefquestion ) ) @ ( B @ ( A @ sk156 ) ) )
= C ),
inference(lifteq,[status(thm)],[839]) ).
thf(118,axiom,
! [A: vATMap,B: vstring] :
( ( B @ vT @ vconstant @ ( A @ vecheck ) )
= ( vText @ vsomeAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','echeck-2') ).
thf(1037,plain,
! [A: vATMap,B: vstring] :
( ( B @ vT @ vconstant @ ( A @ vecheck ) )
= ( vText @ vsomeAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1038,plain,
! [B: vstring,A: vATMap] :
( ( B @ vT @ vconstant @ ( A @ vecheck ) )
= ( vText @ vsomeAType ) ),
inference(cnf,[status(esa)],[1037]) ).
thf(1039,plain,
! [B: vstring,A: vATMap] :
( ( B @ vT @ vconstant @ ( A @ vecheck ) )
= ( vText @ vsomeAType ) ),
inference(lifteq,[status(thm)],[1038]) ).
thf(169,axiom,
! [A: vQConf,B: vQuestionnaire] :
? [C: vAnsMap,D: vQMap,E: vQuestionnaire,F: vQuestionnaire] :
( ( ( B @ ( A @ vqcappend ) )
= ( F @ ( E @ vqseq ) @ ( D @ ( C @ vQC ) ) ) )
& ( B = F )
& ( A
= ( E @ ( D @ ( C @ vQC ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qcappend-INV') ).
thf(1317,plain,
! [A: vQConf,B: vQuestionnaire] :
? [C: vAnsMap,D: vQMap,E: vQuestionnaire,F: vQuestionnaire] :
( ( ( B @ ( A @ vqcappend ) )
= ( F @ ( E @ vqseq ) @ ( D @ ( C @ vQC ) ) ) )
& ( B = F )
& ( A
= ( E @ ( D @ ( C @ vQC ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(1318,plain,
! [A: vQConf,B: vQuestionnaire] :
? [C: vAnsMap,D: vQMap,E: vQuestionnaire] :
( ? [F: vQuestionnaire] :
( ( ( B @ ( A @ vqcappend ) )
= ( F @ ( E @ vqseq ) @ ( D @ ( C @ vQC ) ) ) )
& ( B = F ) )
& ( A
= ( E @ ( D @ ( C @ vQC ) ) ) ) ),
inference(miniscope,[status(thm)],[1317]) ).
thf(1319,plain,
! [B: vQuestionnaire,A: vQConf] :
( ( ( B @ ( A @ vqcappend ) )
= ( A @ ( B @ sk258 ) @ ( A @ ( B @ sk257 ) @ vqseq ) @ ( A @ ( B @ sk256 ) @ ( A @ ( B @ sk255 ) @ vQC ) ) ) )
& ( B
= ( A @ ( B @ sk258 ) ) )
& ( A
= ( A @ ( B @ sk257 ) @ ( A @ ( B @ sk256 ) @ ( A @ ( B @ sk255 ) @ vQC ) ) ) ) ),
inference(cnf,[status(esa)],[1318]) ).
thf(1321,plain,
! [B: vQuestionnaire,A: vQConf] :
( B
= ( A @ ( B @ sk258 ) ) ),
inference(cnfConj,[status(thm)],[1319]) ).
thf(1324,plain,
! [B: vQuestionnaire,A: vQConf] :
( ( A @ ( B @ sk258 ) )
= B ),
inference(lifteq,[status(thm)],[1321]) ).
thf(246,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vQuestionnaire,E: vATMap,F: vATMap,G: vATMap,H: vQuestionnaire] :
( ( ( C @ ( B @ vMC ) @ ( H @ ( F @ ( G @ vMC ) @ vptcheck ) ) )
& ( F @ ( G @ vMC ) @ ( D @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) )
=> ( C @ ( B @ vMC ) @ ( H @ ( D @ vqseq ) @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqseq') ).
thf(4846,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vQuestionnaire,E: vATMap,F: vATMap,G: vATMap,H: vQuestionnaire] :
( ( ( C @ ( B @ vMC ) @ ( H @ ( F @ ( G @ vMC ) @ vptcheck ) ) )
& ( F @ ( G @ vMC ) @ ( D @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) )
=> ( C @ ( B @ vMC ) @ ( H @ ( D @ vqseq ) @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(130,axiom,
! [A: vQID,B: vAType,C: vATMap,D: vATMap] :
( ( D @ ( C @ ( B @ ( A @ vatmbind ) ) @ vappendATMap ) )
= ( D @ ( C @ vappendATMap ) @ ( B @ ( A @ vatmbind ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','appendATMap-1') ).
thf(1099,plain,
! [A: vQID,B: vAType,C: vATMap,D: vATMap] :
( ( D @ ( C @ ( B @ ( A @ vatmbind ) ) @ vappendATMap ) )
= ( D @ ( C @ vappendATMap ) @ ( B @ ( A @ vatmbind ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(156,axiom,
! [A: vOptQuestion] :
( ( A @ visSomeQuestion )
=> ? [B: vQID,C: vLabel,D: vAType] :
( A
= ( D @ ( C @ ( B @ vsomeQuestion ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeQuestion-true-INV') ).
thf(1249,plain,
! [A: vOptQuestion] :
( ( A @ visSomeQuestion )
=> ? [B: vQID,C: vLabel,D: vAType] :
( A
= ( D @ ( C @ ( B @ vsomeQuestion ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(1176,plain,
! [F: vAnsMap,E: vQID,D: vAval,C: vAval,B: vAnsMap,A: vQID] :
( ( C = D )
| ( ( F @ ( C @ ( E @ vabind ) ) )
!= ( B @ ( D @ ( A @ vabind ) ) ) ) ),
inference(cnfConj,[status(thm)],[1174]) ).
thf(1181,plain,
! [F: vAnsMap,E: vQID,D: vAval,C: vAval,B: vAnsMap,A: vQID] :
( ( C = D )
| ( ( F @ ( C @ ( E @ vabind ) ) )
!= ( B @ ( D @ ( A @ vabind ) ) ) ) ),
inference(lifteq,[status(thm)],[1176]) ).
thf(1182,plain,
? [A: vQID > vAnsMap > vAnsMap > vAval] :
! [B: vQID,C: vAval,D: vAnsMap] :
( ( D @ ( C @ ( B @ vabind ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[1181]) ).
thf(1183,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( C @ ( B @ ( A @ vabind ) ) @ ( C @ ( A @ sk226 ) ) )
= B ),
inference(cnf,[status(esa)],[1182]) ).
thf(8351,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( C @ ( B @ ( A @ vabind ) ) @ ( C @ ( A @ sk226 ) ) )
= B ),
inference(lifteq,[status(thm)],[1183]) ).
thf(158,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( F
= ( B @ ( D @ ( G @ vatmbind ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tquestion_inv2') ).
thf(1266,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( F
= ( B @ ( D @ ( G @ vatmbind ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(341,plain,
! [A: vOptExp] :
( ( A
= ( A @ sk26 @ vsomeExp ) )
| ~ ( A @ visSomeExp ) ),
inference(cnf,[status(esa)],[340]) ).
thf(342,plain,
! [A: vOptExp] :
( ~ ( A @ visSomeExp )
| ( ( A @ sk26 @ vsomeExp )
= A ) ),
inference(lifteq,[status(thm)],[341]) ).
thf(6095,plain,
! [B: vOptExp,A: vExp] :
( ( ( A @ vsomeExp @ visSomeExp )
!= ( B @ visSomeExp ) )
| ~ $true
| ( ( B @ sk26 @ vsomeExp )
= B ) ),
inference(paramod_ordered,[status(thm)],[706,342]) ).
thf(6096,plain,
! [B: vOptExp,A: vExp] :
( ( ( A @ vsomeExp @ visSomeExp )
!= ( B @ visSomeExp ) )
| ( ( B @ sk26 @ vsomeExp )
= B ) ),
inference(simp,[status(thm)],[6095]) ).
thf(6097,plain,
! [A: vExp] :
( ( A @ vsomeExp @ sk26 @ vsomeExp )
= ( A @ vsomeExp ) ),
inference(pattern_uni,[status(thm)],[6096:[bind(A,$thf( C )),bind(B,$thf( C @ vsomeExp ))]]) ).
thf(6114,plain,
! [A: vExp] :
( ( A @ vsomeExp @ sk26 @ vsomeExp )
= ( A @ vsomeExp ) ),
inference(simp,[status(thm)],[6097]) ).
thf(286,plain,
! [B: vExp,A: vExp] :
( ( A = B )
| ( ( A @ vsomeExp )
!= ( B @ vsomeExp ) ) ),
inference(cnf,[status(esa)],[285]) ).
thf(287,plain,
! [B: vExp,A: vExp] :
( ( A = B )
| ( ( A @ vsomeExp )
!= ( B @ vsomeExp ) ) ),
inference(lifteq,[status(thm)],[286]) ).
thf(288,plain,
? [A: vOptExp > vExp] :
! [B: vExp] :
( ( B @ vsomeExp @ A )
= B ),
inference(detectInverse,[status(thm)],[287]) ).
thf(289,plain,
! [A: vExp] :
( ( A @ vsomeExp @ sk9 )
= A ),
inference(cnf,[status(esa)],[288]) ).
thf(5015,plain,
! [A: vExp] :
( ( A @ vsomeExp @ sk9 )
= A ),
inference(lifteq,[status(thm)],[289]) ).
thf(6134,plain,
! [B: vExp,A: vExp] :
( ( ( A @ vsomeExp @ sk26 @ vsomeExp )
!= ( B @ vsomeExp ) )
| ( ( A @ vsomeExp @ sk9 )
= B ) ),
inference(paramod_ordered,[status(thm)],[6114,5015]) ).
thf(6135,plain,
! [A: vExp] :
( ( A @ vsomeExp @ sk26 )
= ( A @ vsomeExp @ sk9 ) ),
inference(pattern_uni,[status(thm)],[6134:[bind(A,$thf( D )),bind(B,$thf( D @ vsomeExp @ sk26 ))]]) ).
thf(6144,plain,
! [A: vExp] :
( ( A @ vsomeExp @ sk26 )
= ( A @ vsomeExp @ sk9 ) ),
inference(simp,[status(thm)],[6135]) ).
thf(6152,plain,
! [A: vExp] :
( ( A @ vsomeExp @ sk26 )
= A ),
inference(rewrite,[status(thm)],[6144,5015]) ).
thf(32,axiom,
! [A: vExp,B: vUnOpT,C: vExp,D: vExp,E: vBinOpT] :
( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( C @ ( B @ vunop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-binop-unop') ).
thf(368,plain,
! [A: vExp,B: vUnOpT,C: vExp,D: vExp,E: vBinOpT] :
( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( C @ ( B @ vunop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(369,plain,
~ ? [A: vExp,B: vUnOpT,C: vExp,D: vExp,E: vBinOpT] :
( ( A @ ( E @ ( D @ vbinop ) ) )
= ( C @ ( B @ vunop ) ) ),
inference(miniscope,[status(thm)],[368]) ).
thf(370,plain,
! [E: vBinOpT,D: vExp,C: vExp,B: vUnOpT,A: vExp] :
( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( C @ ( B @ vunop ) ) ),
inference(cnf,[status(esa)],[369]) ).
thf(371,plain,
! [E: vBinOpT,D: vExp,C: vExp,B: vUnOpT,A: vExp] :
( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( C @ ( B @ vunop ) ) ),
inference(lifteq,[status(thm)],[370]) ).
thf(420,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk41 ) )
| ( ( B @ ( A @ vecheck ) )
= ( vText @ vsomeAType ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(457,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( B @ ( A @ vecheck ) )
= ( vText @ vsomeAType ) ) ),
inference(lifteq,[status(thm)],[420]) ).
thf(101,axiom,
! [A: vExp] :
( ! [B: vAval] :
( A
!= ( B @ vconstant ) )
=> ~ ( A @ vexpIsValue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','expIsValue-1') ).
thf(911,plain,
! [A: vExp] :
( ! [B: vAval] :
( A
!= ( B @ vconstant ) )
=> ~ ( A @ vexpIsValue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(241,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vATMap,F: vQID,G: vExp] :
( ( C @ ( E @ vMC ) @ ( G @ ( D @ ( F @ vvalue ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( ( B @ ( F @ vlookupATMap ) )
= vnoAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tvalue_inv1') ).
thf(4829,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vATMap,F: vQID,G: vExp] :
( ( C @ ( E @ vMC ) @ ( G @ ( D @ ( F @ vvalue ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( ( B @ ( F @ vlookupATMap ) )
= vnoAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(78,axiom,
! [A: vQID,B: vQID] :
( ( ( A @ vask )
= ( B @ vask ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-ask') ).
thf(786,plain,
! [A: vQID,B: vQID] :
( ( ( A @ vask )
= ( B @ vask ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(787,plain,
! [B: vQID,A: vQID] :
( ( A = B )
| ( ( A @ vask )
!= ( B @ vask ) ) ),
inference(cnf,[status(esa)],[786]) ).
thf(788,plain,
! [B: vQID,A: vQID] :
( ( A = B )
| ( ( A @ vask )
!= ( B @ vask ) ) ),
inference(lifteq,[status(thm)],[787]) ).
thf(789,plain,
? [A: vEntry > vQID] :
! [B: vQID] :
( ( B @ vask @ A )
= B ),
inference(detectInverse,[status(thm)],[788]) ).
thf(790,plain,
! [A: vQID] :
( ( A @ vask @ sk150 )
= A ),
inference(cnf,[status(esa)],[789]) ).
thf(5112,plain,
! [A: vQID] :
( ( A @ vask @ sk150 )
= A ),
inference(lifteq,[status(thm)],[790]) ).
thf(24,axiom,
! [A: vExp] :
( vnoExp
!= ( A @ vsomeExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).
thf(343,plain,
! [A: vExp] :
( vnoExp
!= ( A @ vsomeExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,axiom,
! [A: vQID,B: vAnsMap] :
( ( B @ ( A @ vlookupAnsMap ) @ visSomeAval )
=> ( ( B @ ( A @ vqvar @ vreduceExp ) )
= ( B @ ( A @ vlookupAnsMap ) @ vgetAval @ vconstant @ vsomeExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-1') ).
thf(264,plain,
! [A: vQID,B: vAnsMap] :
( ( B @ ( A @ vlookupAnsMap ) @ visSomeAval )
=> ( ( B @ ( A @ vqvar @ vreduceExp ) )
= ( B @ ( A @ vlookupAnsMap ) @ vgetAval @ vconstant @ vsomeExp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(265,plain,
! [B: vAnsMap,A: vQID] :
( ( ( B @ ( A @ vqvar @ vreduceExp ) )
= ( B @ ( A @ vlookupAnsMap ) @ vgetAval @ vconstant @ vsomeExp ) )
| ~ ( B @ ( A @ vlookupAnsMap ) @ visSomeAval ) ),
inference(cnf,[status(esa)],[264]) ).
thf(266,plain,
! [B: vAnsMap,A: vQID] :
( ~ ( B @ ( A @ vlookupAnsMap ) @ visSomeAval )
| ( ( B @ ( A @ vqvar @ vreduceExp ) )
= ( B @ ( A @ vlookupAnsMap ) @ vgetAval @ vconstant @ vsomeExp ) ) ),
inference(lifteq,[status(thm)],[265]) ).
thf(1169,plain,
! [A: vAnsMap] :
( ( A @ ( vaempty @ vappendAnsMap ) )
= A ),
inference(cnf,[status(esa)],[1168]) ).
thf(1170,plain,
! [A: vAnsMap] :
( ( A @ ( vaempty @ vappendAnsMap ) )
= A ),
inference(lifteq,[status(thm)],[1169]) ).
thf(161,axiom,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vATMap,G: vATMap,H: vQuestionnaire] :
( ( ( D @ ( F @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( G @ ( E @ vMC ) @ ( H @ ( B @ vqseq ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) )
=> ? [I: vATMap,J: vATMap] : ( J @ ( I @ vMC ) @ ( H @ ( D @ ( F @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqseq_inv2') ).
thf(1286,plain,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vATMap,G: vATMap,H: vQuestionnaire] :
( ( ( D @ ( F @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( G @ ( E @ vMC ) @ ( H @ ( B @ vqseq ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) )
=> ? [I: vATMap,J: vATMap] : ( J @ ( I @ vMC ) @ ( H @ ( D @ ( F @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(146,axiom,
~ ( vnoQConf @ visSomeQC ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeQC-0') ).
thf(1187,plain,
~ ( vnoQConf @ visSomeQC ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(102,axiom,
! [A: vQID,B: vQMap] :
( ? [C: vQMap,D: vQID,E: vAType,F: vLabel,G: vQID] :
( ( ( B @ ( A @ vlookupQMap ) )
= ( C @ ( G @ vlookupQMap ) ) )
& ( B
= ( C @ ( E @ ( F @ ( D @ vqmbind ) ) ) ) )
& ( A = G )
& ( G != D ) )
| ? [C: vQMap,D: vQID,E: vAType,F: vLabel,G: vQID] :
( ( ( B @ ( A @ vlookupQMap ) )
= ( E @ ( F @ ( G @ vsomeQuestion ) ) ) )
& ( B
= ( C @ ( E @ ( F @ ( D @ vqmbind ) ) ) ) )
& ( A = G )
& ( G = D ) )
| ? [C: vQID] :
( ( ( B @ ( A @ vlookupQMap ) )
= vnoQuestion )
& ( B = vqmempty )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookupQMap-INV') ).
thf(915,plain,
! [A: vQID,B: vQMap] :
( ? [C: vQMap,D: vQID,E: vAType,F: vLabel,G: vQID] :
( ( ( B @ ( A @ vlookupQMap ) )
= ( C @ ( G @ vlookupQMap ) ) )
& ( B
= ( C @ ( E @ ( F @ ( D @ vqmbind ) ) ) ) )
& ( A = G )
& ( G != D ) )
| ? [C: vQMap,D: vQID,E: vAType,F: vLabel,G: vQID] :
( ( ( B @ ( A @ vlookupQMap ) )
= ( E @ ( F @ ( G @ vsomeQuestion ) ) ) )
& ( B
= ( C @ ( E @ ( F @ ( D @ vqmbind ) ) ) ) )
& ( A = G )
& ( G = D ) )
| ? [C: vQID] :
( ( ( B @ ( A @ vlookupQMap ) )
= vnoQuestion )
& ( B = vqmempty )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(916,plain,
! [A: vQID,B: vQMap] :
( ? [C: vQMap,D: vQID,E: vAType,F: vLabel,G: vQID] :
( ( ( B @ ( A @ vlookupQMap ) )
= ( C @ ( G @ vlookupQMap ) ) )
& ( B
= ( C @ ( E @ ( F @ ( D @ vqmbind ) ) ) ) )
& ( A = G )
& ( G != D ) )
| ? [C: vQMap,D: vQID,E: vAType,F: vLabel,G: vQID] :
( ( ( B @ ( A @ vlookupQMap ) )
= ( E @ ( F @ ( G @ vsomeQuestion ) ) ) )
& ( B
= ( C @ ( E @ ( F @ ( D @ vqmbind ) ) ) ) )
& ( A = G )
& ( G = D ) )
| ( ( ( B @ ( A @ vlookupQMap ) )
= vnoQuestion )
& ( B = vqmempty )
& ? [C: vQID] : ( A = C ) ) ),
inference(miniscope,[status(thm)],[915]) ).
thf(917,plain,
! [B: vQMap,A: vQID] :
( ( ( ( B @ ( A @ vlookupQMap ) )
= ( A @ ( B @ sk177 ) @ ( A @ ( B @ sk181 ) @ vlookupQMap ) ) )
| ~ ( B @ ( A @ sk171 ) )
| ~ ( B @ ( A @ sk169 ) ) )
& ( ( B
= ( A @ ( B @ sk177 ) @ ( A @ ( B @ sk179 ) @ ( A @ ( B @ sk180 ) @ ( A @ ( B @ sk178 ) @ vqmbind ) ) ) ) )
| ~ ( B @ ( A @ sk171 ) )
| ~ ( B @ ( A @ sk169 ) ) )
& ( ( A
= ( A @ ( B @ sk181 ) ) )
| ~ ( B @ ( A @ sk171 ) )
| ~ ( B @ ( A @ sk169 ) ) )
& ( ( ( A @ ( B @ sk181 ) )
!= ( A @ ( B @ sk178 ) ) )
| ~ ( B @ ( A @ sk171 ) )
| ~ ( B @ ( A @ sk169 ) ) )
& ( ( B @ ( A @ sk171 ) )
| ( ( B @ ( A @ vlookupQMap ) )
= ( A @ ( B @ sk174 ) @ ( A @ ( B @ sk175 ) @ ( A @ ( B @ sk176 ) @ vsomeQuestion ) ) ) )
| ~ ( B @ ( A @ sk169 ) ) )
& ( ( B @ ( A @ sk171 ) )
| ( B
= ( A @ ( B @ sk172 ) @ ( A @ ( B @ sk174 ) @ ( A @ ( B @ sk175 ) @ ( A @ ( B @ sk173 ) @ vqmbind ) ) ) ) )
| ~ ( B @ ( A @ sk169 ) ) )
& ( ( B @ ( A @ sk171 ) )
| ( A
= ( A @ ( B @ sk176 ) ) )
| ~ ( B @ ( A @ sk169 ) ) )
& ( ( B @ ( A @ sk171 ) )
| ( ( A @ ( B @ sk176 ) )
= ( A @ ( B @ sk173 ) ) )
| ~ ( B @ ( A @ sk169 ) ) )
& ( ( B @ ( A @ sk169 ) )
| ( ( B @ ( A @ vlookupQMap ) )
= vnoQuestion ) )
& ( ( B @ ( A @ sk169 ) )
| ( B = vqmempty ) )
& ( ( B @ ( A @ sk169 ) )
| ( A
= ( A @ ( B @ sk170 ) ) ) ) ),
inference(cnf,[status(esa)],[916]) ).
thf(918,plain,
! [B: vQMap,A: vQID] :
( ( ( A @ ( B @ sk181 ) )
!= ( A @ ( B @ sk178 ) ) )
| ~ ( B @ ( A @ sk171 ) )
| ~ ( B @ ( A @ sk169 ) ) ),
inference(cnfConj,[status(thm)],[917]) ).
thf(938,plain,
! [B: vQMap,A: vQID] :
( ~ ( B @ ( A @ sk171 ) )
| ~ ( B @ ( A @ sk169 ) )
| ( ( A @ ( B @ sk181 ) )
!= ( A @ ( B @ sk178 ) ) ) ),
inference(lifteq,[status(thm)],[918]) ).
thf(198,axiom,
! [A: vEntry,B: vGID,C: vQuestionnaire] :
( ( A @ vqsingle )
!= ( C @ ( B @ vqgroup ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qsingle-qgroup') ).
thf(4641,plain,
! [A: vEntry,B: vGID,C: vQuestionnaire] :
( ( A @ vqsingle )
!= ( C @ ( B @ vqgroup ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(4642,plain,
~ ? [A: vEntry,B: vGID,C: vQuestionnaire] :
( ( A @ vqsingle )
= ( C @ ( B @ vqgroup ) ) ),
inference(miniscope,[status(thm)],[4641]) ).
thf(4643,plain,
! [C: vQuestionnaire,B: vGID,A: vEntry] :
( ( A @ vqsingle )
!= ( C @ ( B @ vqgroup ) ) ),
inference(cnf,[status(esa)],[4642]) ).
thf(4644,plain,
! [C: vQuestionnaire,B: vGID,A: vEntry] :
( ( A @ vqsingle )
!= ( C @ ( B @ vqgroup ) ) ),
inference(lifteq,[status(thm)],[4643]) ).
thf(47,axiom,
! [A: vExp] :
( ( A @ vsomeExp @ vgetExp )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getExp-0') ).
thf(631,plain,
! [A: vExp] :
( ( A @ vsomeExp @ vgetExp )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(632,plain,
! [A: vExp] :
( ( A @ vsomeExp @ vgetExp )
= A ),
inference(cnf,[status(esa)],[631]) ).
thf(633,plain,
! [A: vExp] :
( ( A @ vsomeExp @ vgetExp )
= A ),
inference(lifteq,[status(thm)],[632]) ).
thf(8185,plain,
! [B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk58 ) @ visSomeAType )
!= ( vYesNo @ vsomeAType @ visSomeAType ) )
| ~ ( A @ ( B @ sk68 ) @ visSomeAType )
| ~ ( A @ ( B @ sk61 ) )
| ~ $true
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[4997,8138]) ).
thf(8186,plain,
! [B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk58 ) @ visSomeAType )
!= ( vYesNo @ vsomeAType @ visSomeAType ) )
| ~ ( A @ ( B @ sk68 ) @ visSomeAType )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(simp,[status(thm)],[8185]) ).
thf(8205,plain,
! [B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk58 ) )
!= ( vYesNo @ vsomeAType ) )
| ~ ( A @ ( B @ sk68 ) @ visSomeAType )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(simp,[status(thm)],[8186]) ).
thf(307,plain,
! [A: vAval] :
( ( ( A @ vtypeOf )
= vText )
| ( ( A @ vtypeOf )
= vNumber )
| ~ ( A @ sk14 ) ),
inference(cnfConj,[status(thm)],[303]) ).
thf(311,plain,
! [A: vAval] :
( ~ ( A @ sk14 )
| ( ( A @ vtypeOf )
= vText )
| ( ( A @ vtypeOf )
= vNumber ) ),
inference(lifteq,[status(thm)],[307]) ).
thf(16,axiom,
! [A: vOptQuestion] :
( ? [B: vQID,C: vLabel,D: vAType] :
( A
= ( D @ ( C @ ( B @ vsomeQuestion ) ) ) )
| ( A = vnoQuestion ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-OptQuestion') ).
thf(298,plain,
! [A: vOptQuestion] :
( ? [B: vQID,C: vLabel,D: vAType] :
( A
= ( D @ ( C @ ( B @ vsomeQuestion ) ) ) )
| ( A = vnoQuestion ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(748,plain,
~ ? [A: vQuestionnaire,B: vQuestionnaire,C: vGID,D: vQuestionnaire] :
( ( B @ ( A @ vqseq ) )
= ( D @ ( C @ vqgroup ) ) ),
inference(miniscope,[status(thm)],[747]) ).
thf(749,plain,
! [D: vQuestionnaire,C: vGID,B: vQuestionnaire,A: vQuestionnaire] :
( ( B @ ( A @ vqseq ) )
!= ( D @ ( C @ vqgroup ) ) ),
inference(cnf,[status(esa)],[748]) ).
thf(750,plain,
! [D: vQuestionnaire,C: vGID,B: vQuestionnaire,A: vQuestionnaire] :
( ( B @ ( A @ vqseq ) )
!= ( D @ ( C @ vqgroup ) ) ),
inference(lifteq,[status(thm)],[749]) ).
thf(11616,plain,
! [D: vAval,C: vQID,B: vnat,A: vQID] :
( ( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ ( D @ ( C @ vabind ) ) @ vtypeAM ) )
| ( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) @ ( D @ vtypeOf @ ( C @ sk224 ) ) )
= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9478,9481]) ).
thf(11617,plain,
! [B: vnat,A: vQID] :
( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) @ ( B @ vNum @ vtypeOf @ ( A @ sk224 ) ) )
= vatmempty ),
inference(pattern_uni,[status(thm)],[11616:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vNum ))]]) ).
thf(11629,plain,
! [B: vnat,A: vQID] :
( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) @ ( B @ vNum @ vtypeOf @ ( A @ sk224 ) ) )
= vatmempty ),
inference(simp,[status(thm)],[11617]) ).
thf(11638,plain,
! [A: vQID] :
( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) @ ( vNumber @ ( A @ sk224 ) ) )
= vatmempty ),
inference(rewrite,[status(thm)],[11629,388]) ).
thf(151,axiom,
! [A: vExp,B: vAnsMap,C: vUnOpT] :
( ( ( B @ ( A @ vreduceExp ) @ visSomeExp )
& ~ ( A @ vexpIsValue ) )
=> ( ( B @ ( A @ ( C @ vunop ) @ vreduceExp ) )
= ( B @ ( A @ vreduceExp ) @ vgetExp @ ( C @ vunop ) @ vsomeExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-9') ).
thf(1219,plain,
! [A: vExp,B: vAnsMap,C: vUnOpT] :
( ( ( B @ ( A @ vreduceExp ) @ visSomeExp )
& ~ ( A @ vexpIsValue ) )
=> ( ( B @ ( A @ ( C @ vunop ) @ vreduceExp ) )
= ( B @ ( A @ vreduceExp ) @ vgetExp @ ( C @ vunop ) @ vsomeExp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(11,axiom,
vNumber != vText,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-Number-Text') ).
thf(279,plain,
vNumber != vText,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(166,axiom,
! [A: vAnsMap] :
( ? [B: vQID,C: vAval,D: vAnsMap] :
( ( ( A @ vtypeAM )
= ( D @ vtypeAM @ ( C @ vtypeOf @ ( B @ vatmbind ) ) ) )
& ( A
= ( D @ ( C @ ( B @ vabind ) ) ) ) )
| ( ( ( A @ vtypeAM )
= vatmempty )
& ( A = vaempty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','typeAM-INV') ).
thf(1301,plain,
! [A: vAnsMap] :
( ? [B: vQID,C: vAval,D: vAnsMap] :
( ( ( A @ vtypeAM )
= ( D @ vtypeAM @ ( C @ vtypeOf @ ( B @ vatmbind ) ) ) )
& ( A
= ( D @ ( C @ ( B @ vabind ) ) ) ) )
| ( ( ( A @ vtypeAM )
= vatmempty )
& ( A = vaempty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(7952,plain,
! [B: vAType,A: vLabel] :
( ( B != sk2 )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) )
| ( B @ ( A @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[610,254]) ).
thf(7953,plain,
! [A: vLabel] :
( ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(pattern_uni,[status(thm)],[7952:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(39,axiom,
! [A: vQID,B: vUnOpT,C: vExp] :
( ( A @ vqvar )
!= ( C @ ( B @ vunop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qvar-unop') ).
thf(409,plain,
! [A: vQID,B: vUnOpT,C: vExp] :
( ( A @ vqvar )
!= ( C @ ( B @ vunop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(410,plain,
~ ? [A: vQID,B: vUnOpT,C: vExp] :
( ( A @ vqvar )
= ( C @ ( B @ vunop ) ) ),
inference(miniscope,[status(thm)],[409]) ).
thf(411,plain,
! [C: vExp,B: vUnOpT,A: vQID] :
( ( A @ vqvar )
!= ( C @ ( B @ vunop ) ) ),
inference(cnf,[status(esa)],[410]) ).
thf(412,plain,
! [C: vExp,B: vUnOpT,A: vQID] :
( ( A @ vqvar )
!= ( C @ ( B @ vunop ) ) ),
inference(lifteq,[status(thm)],[411]) ).
thf(113,axiom,
! [A: vAnsMap] :
( ? [B: vQID,C: vAval,D: vAnsMap] :
( A
= ( D @ ( C @ ( B @ vabind ) ) ) )
| ( A = vaempty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-AnsMap') ).
thf(975,plain,
! [A: vAnsMap] :
( ? [B: vQID,C: vAval,D: vAnsMap] :
( A
= ( D @ ( C @ ( B @ vabind ) ) ) )
| ( A = vaempty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(7831,plain,
! [B: vAType,A: vLabel] :
( ( vYesNo != vYesNo )
| ( B != vNumber )
| ( B @ ( A @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[610,698]) ).
thf(7832,plain,
! [B: vAType,A: vLabel] :
( ( B != vNumber )
| ( B @ ( A @ sk124 ) ) ),
inference(pattern_uni,[status(thm)],[7831:[]]) ).
thf(7968,plain,
! [A: vLabel] : ( vNumber @ ( A @ sk124 ) ),
inference(simp,[status(thm)],[7832]) ).
thf(638,plain,
! [F: vBinOpT,E: vBinOpT,D: vExp,C: vExp,B: vExp,A: vExp] :
( ( A = B )
| ( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( B @ ( F @ ( C @ vbinop ) ) ) ) ),
inference(cnfConj,[status(thm)],[635]) ).
thf(645,plain,
! [F: vBinOpT,E: vBinOpT,D: vExp,C: vExp,B: vExp,A: vExp] :
( ( A = B )
| ( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( B @ ( F @ ( C @ vbinop ) ) ) ) ),
inference(lifteq,[status(thm)],[638]) ).
thf(646,plain,
? [A: vExp > vBinOpT > vExp > vExp] :
! [B: vExp,C: vBinOpT,D: vExp] :
( ( D @ ( C @ ( B @ vbinop ) ) @ ( C @ ( B @ A ) ) )
= D ),
inference(detectInverse,[status(thm)],[645]) ).
thf(647,plain,
! [C: vExp,B: vBinOpT,A: vExp] :
( ( C @ ( B @ ( A @ vbinop ) ) @ ( B @ ( A @ sk134 ) ) )
= C ),
inference(cnf,[status(esa)],[646]) ).
thf(6881,plain,
! [C: vExp,B: vBinOpT,A: vExp] :
( ( C @ ( B @ ( A @ vbinop ) ) @ ( B @ ( A @ sk134 ) ) )
= C ),
inference(lifteq,[status(thm)],[647]) ).
thf(957,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ vgetQuestionLabel )
= B ),
inference(cnf,[status(esa)],[956]) ).
thf(958,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ vgetQuestionLabel )
= B ),
inference(lifteq,[status(thm)],[957]) ).
thf(9584,plain,
! [E: vAnsMap,D: vAval,C: vQID,B: vstring,A: vQID] :
( ( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM )
!= ( E @ ( D @ ( C @ vabind ) ) @ vtypeAM ) )
| ( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9477,9436]) ).
thf(9585,plain,
! [A: vQID] :
( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[9584:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ vT )),bind(E,$thf( vaempty ))]]) ).
thf(13143,plain,
! [D: vAnsMap,C: vQID,B: vstring,A: vQID] :
( ( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM )
!= ( D @ vtypeAM ) )
| ( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) @ ( vNumber @ ( C @ vatmbind ) ) )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9477,12863]) ).
thf(13144,plain,
! [B: vQID,A: vQID] :
( ( vatmempty @ ( vText @ ( B @ vatmbind ) ) @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[13143:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( vaempty @ ( H @ vT @ ( E @ vabind ) ) ))]]) ).
thf(13157,plain,
! [B: vQID,A: vQID] :
( ( vatmempty @ ( vText @ ( B @ vatmbind ) ) @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(simp,[status(thm)],[13144]) ).
thf(5939,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk4 @ ( sk3 @ vMC ) ) )
| ( ( B @ sk254 )
!= vatmempty )
| ( ( B @ sk253 )
!= vatmempty )
| ( sk5 != vaempty )
| ( sk1 != vqmempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( B @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,5690]) ).
thf(5940,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 )
!= sk4 )
| ( ( A @ sk253 )
!= sk3 )
| ( ( B @ sk254 )
!= vatmempty )
| ( ( B @ sk253 )
!= vatmempty )
| ( sk5 != vaempty )
| ( sk1 != vqmempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( B @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5939]) ).
thf(213,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap] :
( ( D @ ( C @ vMC ) @ ( vqempty @ ( B @ ( A @ vMC ) @ vptcheck ) ) )
=> ( D = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqempty_inv2') ).
thf(4709,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap] :
( ( D @ ( C @ vMC ) @ ( vqempty @ ( B @ ( A @ vMC ) @ vptcheck ) ) )
=> ( D = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(5797,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk1 @ vtypeQM @ ( vatmempty @ vMC ) ) )
| ( ( B @ sk254 )
!= sk4 )
| ( ( B @ sk253 )
!= sk3 )
| ( sk5 != vaempty )
| ( B @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,5695]) ).
thf(5799,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 )
!= ( sk1 @ vtypeQM ) )
| ( ( A @ sk253 )
!= vatmempty )
| ( ( B @ sk254 )
!= sk4 )
| ( ( B @ sk253 )
!= sk3 )
| ( sk5 != vaempty )
| ( B @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5797]) ).
thf(280,plain,
vNumber != vText,
inference(polarity_switch,[status(thm)],[279]) ).
thf(281,plain,
vText != vNumber,
inference(lifteq,[status(thm)],[280]) ).
thf(12895,plain,
! [F: vATMap,E: vAType,D: vQID,C: vnat,B: vAnsMap,A: vQID] :
( ( ( B @ vtypeAM @ ( vNumber @ ( A @ vatmbind ) ) )
!= ( F @ ( E @ ( D @ vatmbind ) ) ) )
| ( ( B @ ( C @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9428,1229]) ).
thf(12896,plain,
! [C: vAnsMap,B: vnat,A: vQID] :
( ( C @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[12895:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( vNumber )),bind(F,$thf( G @ vtypeAM ))]]) ).
thf(12964,plain,
! [C: vAnsMap,B: vnat,A: vQID] :
( ( C @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ),
inference(simp,[status(thm)],[12896]) ).
thf(13131,plain,
! [E: vAnsMap,D: vQID,C: vnat,B: vAnsMap,A: vQID] :
( ( ( B @ vtypeAM @ ( vNumber @ ( A @ vatmbind ) ) )
!= ( E @ vtypeAM @ ( vNumber @ ( D @ vatmbind ) ) ) )
| ( ( B @ ( C @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9428,12863]) ).
thf(13132,plain,
! [C: vnat,B: vAnsMap,A: vQID] :
( ( B @ ( C @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[13131:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( A )),bind(E,$thf( B ))]]) ).
thf(138,axiom,
! [A: vExp,B: vExp,C: vAnsMap,D: vBinOpT] :
( ( ~ ( C @ ( B @ vreduceExp ) @ visSomeExp )
& ~ ( B @ vexpIsValue )
& ( A @ vexpIsValue ) )
=> ( ( C @ ( B @ ( D @ ( A @ vbinop ) ) @ vreduceExp ) )
= vnoExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-5') ).
thf(1139,plain,
! [A: vExp,B: vExp,C: vAnsMap,D: vBinOpT] :
( ( ~ ( C @ ( B @ vreduceExp ) @ visSomeExp )
& ~ ( B @ vexpIsValue )
& ( A @ vexpIsValue ) )
=> ( ( C @ ( B @ ( D @ ( A @ vbinop ) ) @ vreduceExp ) )
= vnoExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(440,plain,
! [B: vExp,A: vATMap] :
( ( ( B @ ( A @ vecheck ) )
= vnoAType )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(466,plain,
! [B: vExp,A: vATMap] :
( ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( B @ ( A @ vecheck ) )
= vnoAType ) ),
inference(lifteq,[status(thm)],[440]) ).
thf(703,plain,
! [B: vYN,A: vYN] :
( ( B @ vB @ ( A @ vB @ ( vandop @ vevalBinOp ) ) )
= ( B @ ( A @ vand ) @ vB @ vconstant @ vsomeExp ) ),
inference(cnf,[status(esa)],[702]) ).
thf(704,plain,
! [B: vYN,A: vYN] :
( ( B @ vB @ ( A @ vB @ ( vandop @ vevalBinOp ) ) )
= ( B @ ( A @ vand ) @ vB @ vconstant @ vsomeExp ) ),
inference(lifteq,[status(thm)],[703]) ).
thf(1355,plain,
! [B: vQMap,A: vAnsMap] :
( ( B @ ( A @ ( vqempty @ vreduce ) ) )
= vnoQConf ),
inference(cnf,[status(esa)],[1354]) ).
thf(1356,plain,
! [B: vQMap,A: vAnsMap] :
( ( B @ ( A @ ( vqempty @ vreduce ) ) )
= vnoQConf ),
inference(lifteq,[status(thm)],[1355]) ).
thf(304,plain,
! [A: vAval] :
( ( A
= ( A @ sk17 @ vT ) )
| ( A
= ( A @ sk16 @ vNum ) )
| ~ ( A @ sk14 ) ),
inference(cnfConj,[status(thm)],[303]) ).
thf(313,plain,
! [A: vAval] :
( ~ ( A @ sk14 )
| ( ( A @ sk17 @ vT )
= A )
| ( ( A @ sk16 @ vNum )
= A ) ),
inference(lifteq,[status(thm)],[304]) ).
thf(1026,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( F = B )
| ( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vquestion ) ) ) ) ),
inference(cnfConj,[status(thm)],[1024]) ).
thf(1031,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( F = B )
| ( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vquestion ) ) ) ) ),
inference(lifteq,[status(thm)],[1026]) ).
thf(1032,plain,
? [A: vQID > vAType > vEntry > vLabel] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vquestion ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[1031]) ).
thf(1033,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vquestion ) ) @ ( C @ ( A @ sk204 ) ) )
= B ),
inference(cnf,[status(esa)],[1032]) ).
thf(6937,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vquestion ) ) @ ( C @ ( A @ sk204 ) ) )
= B ),
inference(lifteq,[status(thm)],[1033]) ).
thf(199,axiom,
! [A: vQID,B: vLabel,C: vAType,D: vQMap] :
( ( D @ ( C @ ( B @ ( A @ vqmbind ) ) ) @ vtypeQM )
= ( D @ vtypeQM @ ( C @ ( A @ vatmbind ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','typeQM-1') ).
thf(4645,plain,
! [A: vQID,B: vLabel,C: vAType,D: vQMap] :
( ( D @ ( C @ ( B @ ( A @ vqmbind ) ) ) @ vtypeQM )
= ( D @ vtypeQM @ ( C @ ( A @ vatmbind ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(7950,plain,
! [B: vAType,A: vLabel] :
( ( B != sk2 )
| ( sk5 != vaempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( vatmempty @ vMC ) @ vptcheck ) ) )
| ( B @ ( A @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[610,4876]) ).
thf(7951,plain,
! [A: vLabel] :
( ( sk5 != vaempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ ( sk1 @ vtypeQM @ ( vatmempty @ vMC ) @ vptcheck ) ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(pattern_uni,[status(thm)],[7950:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(172,axiom,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vQuestionnaire] :
( ( E @ ( D @ vMC ) @ ( F @ ( B @ vqseq ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ? [G: vATMap,H: vATMap] : ( H @ ( G @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqseq_inv1') ).
thf(1332,plain,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vQuestionnaire] :
( ( E @ ( D @ vMC ) @ ( F @ ( B @ vqseq ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ? [G: vATMap,H: vATMap] : ( H @ ( G @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(9468,plain,
! [E: vATMap,D: vAType,C: vQID,B: vAval,A: vQID] :
( ( ( vatmempty @ ( B @ vtypeOf @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9403,1229]) ).
thf(9469,plain,
! [B: vAval,A: vQID] :
( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[9468:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ vtypeOf )),bind(E,$thf( vatmempty ))]]) ).
thf(9483,plain,
! [B: vAval,A: vQID] :
( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ),
inference(simp,[status(thm)],[9469]) ).
thf(215,axiom,
! [A: vQMap,B: vAType,C: vAnsMap,D: vQID,E: vExp] :
( ( E @ vexpIsValue )
=> ( ( A @ ( C @ ( E @ ( B @ ( D @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( vqempty @ ( A @ ( C @ ( E @ vgetExpValue @ ( D @ vabind ) ) @ vQC ) ) @ vsomeQConf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-2') ).
thf(4716,plain,
! [A: vQMap,B: vAType,C: vAnsMap,D: vQID,E: vExp] :
( ( E @ vexpIsValue )
=> ( ( A @ ( C @ ( E @ ( B @ ( D @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( vqempty @ ( A @ ( C @ ( E @ vgetExpValue @ ( D @ vabind ) ) @ vQC ) ) @ vsomeQConf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(9293,plain,
! [E: vQMap,D: vAnsMap,C: vQuestionnaire,B: vAType,A: vLabel] :
( ( B != sk2 )
| ( ( sk1 @ ( sk5 @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( C @ ( E @ ( D @ vQC ) ) @ vsomeQConf ) )
| ( B @ ( A @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[610,9288]) ).
thf(9294,plain,
! [D: vQMap,C: vAnsMap,B: vQuestionnaire,A: vLabel] :
( ( ( sk1 @ ( sk5 @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( B @ ( D @ ( C @ vQC ) ) @ vsomeQConf ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(pattern_uni,[status(thm)],[9293:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(9312,plain,
! [D: vQMap,C: vAnsMap,B: vQuestionnaire,A: vLabel] :
( ( ( sk1 @ ( sk5 @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( B @ ( D @ ( C @ vQC ) ) @ vsomeQConf ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(simp,[status(thm)],[9294]) ).
thf(7053,plain,
! [D: vYN,C: vUnOpT,B: vUnOpT,A: vnat] :
( ( ( A @ vNum @ ( B @ sk31 ) )
!= ( D @ vB @ ( C @ sk31 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7020,6939]) ).
thf(7054,plain,
! [D: vYN,C: vUnOpT,B: vUnOpT,A: vnat] :
( ( A @ vNum @ ( B @ sk31 ) )
!= ( D @ vB @ ( C @ sk31 ) ) ),
inference(simp,[status(thm)],[7053]) ).
thf(7070,plain,
! [D: vYN,C: vUnOpT,B: vUnOpT,A: vnat] :
( ( ( A @ vNum )
!= ( D @ vB ) )
| ( B != C ) ),
inference(simp,[status(thm)],[7054]) ).
thf(7077,plain,
! [B: vYN,A: vnat] :
( ( A @ vNum )
!= ( B @ vB ) ),
inference(simp,[status(thm)],[7070]) ).
thf(4826,plain,
~ ? [A: vEntry,B: vExp,C: vQuestionnaire,D: vQuestionnaire] :
( ( A @ vqsingle )
= ( D @ ( C @ ( B @ vqcond ) ) ) ),
inference(miniscope,[status(thm)],[4825]) ).
thf(4827,plain,
! [D: vQuestionnaire,C: vQuestionnaire,B: vExp,A: vEntry] :
( ( A @ vqsingle )
!= ( D @ ( C @ ( B @ vqcond ) ) ) ),
inference(cnf,[status(esa)],[4826]) ).
thf(4828,plain,
! [D: vQuestionnaire,C: vQuestionnaire,B: vExp,A: vEntry] :
( ( A @ vqsingle )
!= ( D @ ( C @ ( B @ vqcond ) ) ) ),
inference(lifteq,[status(thm)],[4827]) ).
thf(121,axiom,
! [A: vOptAType] :
( ? [B: vAType] :
( A
= ( B @ vsomeAType ) )
| ( A = vnoAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-OptAType') ).
thf(1048,plain,
! [A: vOptAType] :
( ? [B: vAType] :
( A
= ( B @ vsomeAType ) )
| ( A = vnoAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(373,plain,
! [A: vATMap,B: vExp,C: vExp] :
( ~ ( ( C @ ( A @ vecheck ) @ visSomeAType )
& ( B @ ( A @ vecheck ) @ visSomeAType ) )
=> ! [D: vBinOpT] :
( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= vnoAType ) ),
inference(miniscope,[status(thm)],[372]) ).
thf(374,plain,
! [D: vBinOpT,C: vExp,B: vExp,A: vATMap] :
( ( ( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= vnoAType )
| ( C @ ( A @ vecheck ) @ visSomeAType ) )
& ( ( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= vnoAType )
| ( B @ ( A @ vecheck ) @ visSomeAType ) ) ),
inference(cnf,[status(esa)],[373]) ).
thf(375,plain,
! [D: vBinOpT,C: vExp,B: vExp,A: vATMap] :
( ( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= vnoAType )
| ( B @ ( A @ vecheck ) @ visSomeAType ) ),
inference(cnfConj,[status(thm)],[374]) ).
thf(377,plain,
! [D: vBinOpT,C: vExp,B: vExp,A: vATMap] :
( ( B @ ( A @ vecheck ) @ visSomeAType )
| ( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= vnoAType ) ),
inference(lifteq,[status(thm)],[375]) ).
thf(235,axiom,
! [A: vEntry] :
( ? [B: vQID] :
( A
= ( B @ vask ) )
| ? [B: vQID,C: vLabel,D: vAType] :
( A
= ( D @ ( C @ ( B @ vdefquestion ) ) ) )
| ? [B: vQID,C: vAType,D: vExp] :
( A
= ( D @ ( C @ ( B @ vvalue ) ) ) )
| ? [B: vQID,C: vLabel,D: vAType] :
( A
= ( D @ ( C @ ( B @ vquestion ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-Entry') ).
thf(4805,plain,
! [A: vEntry] :
( ? [B: vQID] :
( A
= ( B @ vask ) )
| ? [B: vQID,C: vLabel,D: vAType] :
( A
= ( D @ ( C @ ( B @ vdefquestion ) ) ) )
| ? [B: vQID,C: vAType,D: vExp] :
( A
= ( D @ ( C @ ( B @ vvalue ) ) ) )
| ? [B: vQID,C: vLabel,D: vAType] :
( A
= ( D @ ( C @ ( B @ vquestion ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(317,plain,
! [B: vAnsMap,A: vQID] :
( ( ( B @ ( A @ vqvar @ vreduceExp ) )
= vnoExp )
| ( B @ ( A @ vlookupAnsMap ) @ visSomeAval ) ),
inference(cnf,[status(esa)],[316]) ).
thf(318,plain,
! [B: vAnsMap,A: vQID] :
( ( B @ ( A @ vlookupAnsMap ) @ visSomeAval )
| ( ( B @ ( A @ vqvar @ vreduceExp ) )
= vnoExp ) ),
inference(lifteq,[status(thm)],[317]) ).
thf(1195,plain,
! [D: vQuestionnaire,C: vGID,B: vQuestionnaire,A: vGID] :
( ( B = D )
| ( ( B @ ( A @ vqgroup ) )
!= ( D @ ( C @ vqgroup ) ) ) ),
inference(cnfConj,[status(thm)],[1193]) ).
thf(1199,plain,
! [D: vQuestionnaire,C: vGID,B: vQuestionnaire,A: vGID] :
( ( B = D )
| ( ( B @ ( A @ vqgroup ) )
!= ( D @ ( C @ vqgroup ) ) ) ),
inference(lifteq,[status(thm)],[1195]) ).
thf(1200,plain,
? [A: vGID > vQuestionnaire > vQuestionnaire] :
! [B: vGID,C: vQuestionnaire] :
( ( C @ ( B @ vqgroup ) @ ( B @ A ) )
= C ),
inference(detectInverse,[status(thm)],[1199]) ).
thf(1201,plain,
! [B: vQuestionnaire,A: vGID] :
( ( B @ ( A @ vqgroup ) @ ( A @ sk229 ) )
= B ),
inference(cnf,[status(esa)],[1200]) ).
thf(5972,plain,
! [B: vQuestionnaire,A: vGID] :
( ( B @ ( A @ vqgroup ) @ ( A @ sk229 ) )
= B ),
inference(lifteq,[status(thm)],[1201]) ).
thf(173,axiom,
! [A: vATMap,B: vATMap] : ( B @ ( A @ vMC ) @ ( vqempty @ ( B @ ( A @ vMC ) @ vptcheck ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqempty') ).
thf(1335,plain,
! [A: vATMap,B: vATMap] : ( B @ ( A @ vMC ) @ ( vqempty @ ( B @ ( A @ vMC ) @ vptcheck ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(1336,plain,
! [B: vATMap,A: vATMap] : ( B @ ( A @ vMC ) @ ( vqempty @ ( B @ ( A @ vMC ) @ vptcheck ) ) ),
inference(cnf,[status(esa)],[1335]) ).
thf(6209,plain,
! [C: vATMap,B: vATMap,A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( C @ ( B @ vMC ) ) )
| ( C @ ( B @ vMC ) @ ( vqempty @ ( A @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,1336]) ).
thf(6210,plain,
! [A: vMapConf] : ( A @ sk254 @ ( A @ sk253 @ vMC ) @ ( vqempty @ ( A @ vptcheck ) ) ),
inference(pattern_uni,[status(thm)],[6209:[bind(A,$thf( E )),bind(B,$thf( E @ sk253 )),bind(C,$thf( E @ sk254 ))]]) ).
thf(6213,plain,
! [A: vMapConf] : ( A @ sk254 @ ( A @ sk253 @ vMC ) @ ( vqempty @ ( A @ vptcheck ) ) ),
inference(simp,[status(thm)],[6210]) ).
thf(6216,plain,
! [A: vMapConf] : ( A @ ( vqempty @ ( A @ vptcheck ) ) ),
inference(rewrite,[status(thm)],[6213,1316]) ).
thf(899,plain,
! [A: vOptQuestion] :
( ( A = vnoQuestion )
| ( A @ visSomeQuestion ) ),
inference(cnf,[status(esa)],[898]) ).
thf(900,plain,
! [A: vOptQuestion] :
( ( A @ visSomeQuestion )
| ( A = vnoQuestion ) ),
inference(lifteq,[status(thm)],[899]) ).
thf(880,plain,
! [A: vAval] : ( A @ vconstant @ vexpIsValue ),
inference(cnf,[status(esa)],[879]) ).
thf(1041,plain,
~ ? [A: vQID,B: vLabel,C: vAType,D: vQID,E: vAType,F: vLabel] :
( ( C @ ( F @ ( D @ vquestion ) ) )
= ( E @ ( B @ ( A @ vdefquestion ) ) ) ),
inference(miniscope,[status(thm)],[1040]) ).
thf(1042,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ),
inference(cnf,[status(esa)],[1041]) ).
thf(1043,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ),
inference(lifteq,[status(thm)],[1042]) ).
thf(196,axiom,
! [A: vQuestionnaire,B: vQuestionnaire,C: vAnsMap,D: vQMap] :
( ( D @ ( C @ ( B @ ( A @ ( vyes @ vB @ vconstant @ vqcond ) ) @ vreduce ) ) )
= ( A @ ( D @ ( C @ vQC ) ) @ vsomeQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-11') ).
thf(4635,plain,
! [A: vQuestionnaire,B: vQuestionnaire,C: vAnsMap,D: vQMap] :
( ( D @ ( C @ ( B @ ( A @ ( vyes @ vB @ vconstant @ vqcond ) ) @ vreduce ) ) )
= ( A @ ( D @ ( C @ vQC ) ) @ vsomeQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(242,axiom,
! [A: vQMap,B: vAType,C: vAnsMap,D: vQID,E: vExp] :
( ( ~ ( C @ ( E @ vreduceExp ) @ visSomeExp )
& ~ ( E @ vexpIsValue ) )
=> ( ( A @ ( C @ ( E @ ( B @ ( D @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= vnoQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-4') ).
thf(4833,plain,
! [A: vQMap,B: vAType,C: vAnsMap,D: vQID,E: vExp] :
( ( ~ ( C @ ( E @ vreduceExp ) @ visSomeExp )
& ~ ( E @ vexpIsValue ) )
=> ( ( A @ ( C @ ( E @ ( B @ ( D @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= vnoQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(83,axiom,
! [A: vAval,B: vAnsMap] :
( ( B @ ( A @ vconstant @ vreduceExp ) )
= vnoExp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-0') ).
thf(816,plain,
! [A: vAval,B: vAnsMap] :
( ( B @ ( A @ vconstant @ vreduceExp ) )
= vnoExp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(238,axiom,
! [A: vOptQConf] :
( ? [B: vQConf] :
( A
= ( B @ vsomeQConf ) )
| ( A = vnoQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-OptQConf') ).
thf(4818,plain,
! [A: vOptQConf] :
( ? [B: vQConf] :
( A
= ( B @ vsomeQConf ) )
| ( A = vnoQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(220,axiom,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vExp,G: vQuestionnaire] :
( ( E @ ( D @ vMC ) @ ( G @ ( B @ ( F @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ( ( F @ ( C @ vecheck ) )
= ( vYesNo @ vsomeAType ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqcond_inv1') ).
thf(4731,plain,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vExp,G: vQuestionnaire] :
( ( E @ ( D @ vMC ) @ ( G @ ( B @ ( F @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ( ( F @ ( C @ vecheck ) )
= ( vYesNo @ vsomeAType ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(44,axiom,
! [A: vAType] :
( ( A @ vsomeAType @ vgetAType )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getAType-0') ).
thf(594,plain,
! [A: vAType] :
( ( A @ vsomeAType @ vgetAType )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(96,axiom,
! [A: vLabel] :
( ( vYesNo @ ( A @ vgetAnswer ) )
= ( A @ vaskYesNo @ vB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getAnswer-0') ).
thf(895,plain,
! [A: vLabel] :
( ( vYesNo @ ( A @ vgetAnswer ) )
= ( A @ vaskYesNo @ vB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(103,axiom,
! [A: vQID,B: vLabel,C: vAType,D: vQMap] :
( vqmempty
!= ( D @ ( C @ ( B @ ( A @ vqmbind ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-qmempty-qmbind') ).
thf(940,plain,
! [A: vQID,B: vLabel,C: vAType,D: vQMap] :
( vqmempty
!= ( D @ ( C @ ( B @ ( A @ vqmbind ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(941,plain,
~ ? [A: vQID,B: vLabel,C: vAType,D: vQMap] :
( vqmempty
= ( D @ ( C @ ( B @ ( A @ vqmbind ) ) ) ) ),
inference(miniscope,[status(thm)],[940]) ).
thf(942,plain,
! [D: vQMap,C: vAType,B: vLabel,A: vQID] :
( vqmempty
!= ( D @ ( C @ ( B @ ( A @ vqmbind ) ) ) ) ),
inference(cnf,[status(esa)],[941]) ).
thf(943,plain,
! [D: vQMap,C: vAType,B: vLabel,A: vQID] :
( ( D @ ( C @ ( B @ ( A @ vqmbind ) ) ) )
!= vqmempty ),
inference(lifteq,[status(thm)],[942]) ).
thf(8990,plain,
! [D: vQID,C: vAval,B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk37 ) @ vB @ vconstant )
!= ( C @ vconstant ) )
| ( B
!= ( D @ vqvar ) )
| ( B @ ( A @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[458,692]) ).
thf(8991,plain,
! [C: vATMap,B: vExp,A: vQID] :
( ( B
!= ( A @ vqvar ) )
| ( B @ ( C @ sk35 ) ) ),
inference(pattern_uni,[status(thm)],[8990:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ sk37 ) @ vB )),bind(D,$thf( D ))]]) ).
thf(9074,plain,
! [B: vATMap,A: vQID] : ( A @ vqvar @ ( B @ sk35 ) ),
inference(simp,[status(thm)],[8991]) ).
thf(187,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tquestion_inv3') ).
thf(1381,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( C = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(142,axiom,
! [A: vYN,B: vYN] :
( ( ( B != vno )
| ( A != vno ) )
=> ( ( B @ ( A @ vor ) )
= vyes ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','or-1') ).
thf(1162,plain,
! [A: vYN,B: vYN] :
( ( ( B != vno )
| ( A != vno ) )
=> ( ( B @ ( A @ vor ) )
= vyes ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(847,plain,
! [A: vQID] :
( ( vqmempty @ ( A @ vlookupQMap ) )
= vnoQuestion ),
inference(cnf,[status(esa)],[846]) ).
thf(848,plain,
! [A: vQID] :
( ( vqmempty @ ( A @ vlookupQMap ) )
= vnoQuestion ),
inference(lifteq,[status(thm)],[847]) ).
thf(9485,plain,
! [B: vAval,A: vQID] :
( ( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) )
| ( vatmempty != vatmempty ) ),
inference(paramod_ordered,[status(thm)],[4862,9483]) ).
thf(9486,plain,
! [B: vAval,A: vQID] :
( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) ),
inference(simp,[status(thm)],[9485]) ).
thf(9487,plain,
! [B: vAval,A: vQID] :
( ( vaempty @ ( B @ ( A @ vabind ) ) )
!= vaempty ),
inference(simp,[status(thm)],[9486]) ).
thf(110,axiom,
! [A: vExp,B: vAnsMap,C: vUnOpT] :
( ( ~ ( B @ ( A @ vreduceExp ) @ visSomeExp )
& ~ ( A @ vexpIsValue ) )
=> ( ( B @ ( A @ ( C @ vunop ) @ vreduceExp ) )
= vnoExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-10') ).
thf(964,plain,
! [A: vExp,B: vAnsMap,C: vUnOpT] :
( ( ~ ( B @ ( A @ vreduceExp ) @ visSomeExp )
& ~ ( A @ vexpIsValue ) )
=> ( ( B @ ( A @ ( C @ vunop ) @ vreduceExp ) )
= vnoExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(201,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vdefquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( C
= ( A @ ( D @ ( G @ vatmbind ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tdefquestion_inv3') ).
thf(4652,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vLabel,F: vATMap,G: vQID] :
( ( C @ ( F @ vMC ) @ ( D @ ( E @ ( G @ vdefquestion ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( C
= ( A @ ( D @ ( G @ vatmbind ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(207,axiom,
! [A: vQMap,B: vAType,C: vATMap,D: vATMap,E: vAnsMap,F: vQID,G: vExp] :
( ( ( D @ ( C @ vMC ) @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ ( A @ vtypeQM @ ( E @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ visValue )
& ~ ( G @ vexpIsValue ) )
=> ? [H: vAnsMap,I: vQMap,J: vQuestionnaire] :
( ( A @ ( E @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( J @ ( I @ ( H @ vQC ) ) @ vsomeQConf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Progress-qsingle-value-expIsValue-False') ).
thf(4684,plain,
! [A: vQMap,B: vAType,C: vATMap,D: vATMap,E: vAnsMap,F: vQID,G: vExp] :
( ( ( D @ ( C @ vMC ) @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ ( A @ vtypeQM @ ( E @ vtypeAM @ vMC ) @ vptcheck ) ) )
& ~ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ visValue )
& ~ ( G @ vexpIsValue ) )
=> ? [H: vAnsMap,I: vQMap,J: vQuestionnaire] :
( ( A @ ( E @ ( G @ ( B @ ( F @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( J @ ( I @ ( H @ vQC ) ) @ vsomeQConf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(446,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk61 ) )
| ( B
= ( A @ ( B @ sk63 ) @ ( A @ ( B @ sk62 ) @ vunop ) ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(462,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk63 ) @ ( A @ ( B @ sk62 ) @ vunop ) )
= B ) ),
inference(lifteq,[status(thm)],[446]) ).
thf(192,axiom,
! [A: vQuestionnaire,B: vAnsMap,C: vQMap] :
( ? [D: vGID,E: vQuestionnaire,F: vAnsMap,G: vQMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( E @ ( G @ ( F @ vQC ) ) @ vsomeQConf ) )
& ( C = G )
& ( B = F )
& ( A
= ( E @ ( D @ vqgroup ) ) ) )
| ? [D: vQMap,E: vOptExp,F: vQuestionnaire,G: vExp,H: vAnsMap,I: vQuestionnaire] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= vnoQConf )
& ( C = D )
& ( B = H )
& ( A
= ( I @ ( F @ ( G @ vqcond ) ) ) )
& ~ ( E @ visSomeExp )
& ( E
= ( H @ ( G @ vreduceExp ) ) )
& ! [J: vQuestionnaire,K: vQuestionnaire] :
( ( I != K )
| ( F != J )
| ( G
!= ( vno @ vB @ vconstant ) ) )
& ! [J: vQuestionnaire,K: vQuestionnaire] :
( ( I != K )
| ( F != J )
| ( G
!= ( vyes @ vB @ vconstant ) ) ) )
| ? [D: vQMap,E: vOptExp,F: vQuestionnaire,G: vExp,H: vAnsMap,I: vQuestionnaire] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( I @ ( F @ ( E @ vgetExp @ vqcond ) ) @ ( D @ ( H @ vQC ) ) @ vsomeQConf ) )
& ( C = D )
& ( B = H )
& ( A
= ( I @ ( F @ ( G @ vqcond ) ) ) )
& ( E @ visSomeExp )
& ( E
= ( H @ ( G @ vreduceExp ) ) )
& ! [J: vQuestionnaire,K: vQuestionnaire] :
( ( I != K )
| ( F != J )
| ( G
!= ( vno @ vB @ vconstant ) ) )
& ! [J: vQuestionnaire,K: vQuestionnaire] :
( ( I != K )
| ( F != J )
| ( G
!= ( vyes @ vB @ vconstant ) ) ) )
| ? [D: vQuestionnaire,E: vQuestionnaire,F: vAnsMap,G: vQMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( E @ ( G @ ( F @ vQC ) ) @ vsomeQConf ) )
& ( C = G )
& ( B = F )
& ( A
= ( E @ ( D @ ( vno @ vB @ vconstant @ vqcond ) ) ) ) )
| ? [D: vQuestionnaire,E: vQuestionnaire,F: vAnsMap,G: vQMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( D @ ( G @ ( F @ vQC ) ) @ vsomeQConf ) )
& ( C = G )
& ( B = F )
& ( A
= ( E @ ( D @ ( vyes @ vB @ vconstant @ vqcond ) ) ) ) )
| ? [D: vQMap,E: vQuestionnaire,F: vAnsMap,G: vQuestionnaire,H: vOptQConf] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= vnoQConf )
& ( C = D )
& ( B = F )
& ( A
= ( G @ ( E @ vqseq ) ) )
& ~ ( H @ visSomeQC )
& ( H
= ( D @ ( F @ ( E @ vreduce ) ) ) )
& ! [I: vQuestionnaire] :
( ( G != I )
| ( E != vqempty ) ) )
| ? [D: vQMap,E: vQuestionnaire,F: vAnsMap,G: vQuestionnaire,H: vOptQConf] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( G @ ( H @ vgetQC @ vqcappend ) @ vsomeQConf ) )
& ( C = D )
& ( B = F )
& ( A
= ( G @ ( E @ vqseq ) ) )
& ( H @ visSomeQC )
& ( H
= ( D @ ( F @ ( E @ vreduce ) ) ) )
& ! [I: vQuestionnaire] :
( ( G != I )
| ( E != vqempty ) ) )
| ? [D: vQuestionnaire,E: vAnsMap,F: vQMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( D @ ( F @ ( E @ vQC ) ) @ vsomeQConf ) )
& ( C = F )
& ( B = E )
& ( A
= ( D @ ( vqempty @ vqseq ) ) ) )
| ? [D: vQID,E: vOptQuestion,F: vQMap,G: vAnsMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= vnoQConf )
& ( C = F )
& ( B = G )
& ( A
= ( D @ vask @ vqsingle ) )
& ~ ( E @ visSomeQuestion )
& ( E
= ( F @ ( D @ vlookupQMap ) ) ) )
| ? [D: vQID,E: vOptQuestion,F: vQMap,G: vAnsMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( E @ vgetQuestionAType @ ( E @ vgetQuestionLabel @ ( D @ vquestion ) ) @ vqsingle @ ( F @ ( G @ vQC ) ) @ vsomeQConf ) )
& ( C = F )
& ( B = G )
& ( A
= ( D @ vask @ vqsingle ) )
& ( E @ visSomeQuestion )
& ( E
= ( F @ ( D @ vlookupQMap ) ) ) )
| ? [D: vQMap,E: vAType,F: vLabel,G: vAnsMap,H: vQID] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( vqempty @ ( D @ ( E @ ( F @ ( H @ vqmbind ) ) ) @ ( G @ vQC ) ) @ vsomeQConf ) )
& ( C = D )
& ( B = G )
& ( A
= ( E @ ( F @ ( H @ vdefquestion ) ) @ vqsingle ) ) )
| ? [D: vQMap,E: vAType,F: vOptExp,G: vAnsMap,H: vQID,I: vExp] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= vnoQConf )
& ( C = D )
& ( B = G )
& ( A
= ( I @ ( E @ ( H @ vvalue ) ) @ vqsingle ) )
& ~ ( F @ visSomeExp )
& ( F
= ( G @ ( I @ vreduceExp ) ) )
& ~ ( I @ vexpIsValue ) )
| ? [D: vQMap,E: vAType,F: vOptExp,G: vAnsMap,H: vQID,I: vExp] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( F @ vgetExp @ ( E @ ( H @ vvalue ) ) @ vqsingle @ ( D @ ( G @ vQC ) ) @ vsomeQConf ) )
& ( C = D )
& ( B = G )
& ( A
= ( I @ ( E @ ( H @ vvalue ) ) @ vqsingle ) )
& ( F @ visSomeExp )
& ( F
= ( G @ ( I @ vreduceExp ) ) )
& ~ ( I @ vexpIsValue ) )
| ? [D: vQMap,E: vAType,F: vAnsMap,G: vQID,H: vExp] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( vqempty @ ( D @ ( F @ ( H @ vgetExpValue @ ( G @ vabind ) ) @ vQC ) ) @ vsomeQConf ) )
& ( C = D )
& ( B = F )
& ( A
= ( H @ ( E @ ( G @ vvalue ) ) @ vqsingle ) )
& ( H @ vexpIsValue ) )
| ? [D: vQMap,E: vAType,F: vLabel,G: vAval,H: vAnsMap,I: vQID] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( vqempty @ ( D @ ( H @ ( G @ ( I @ vabind ) ) @ vQC ) ) @ vsomeQConf ) )
& ( C = D )
& ( B = H )
& ( A
= ( E @ ( F @ ( I @ vquestion ) ) @ vqsingle ) )
& ( G
= ( E @ ( F @ vgetAnswer ) ) ) )
| ? [D: vAnsMap,E: vQMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= vnoQConf )
& ( C = E )
& ( B = D )
& ( A = vqempty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-INV') ).
thf(1396,plain,
! [A: vQuestionnaire,B: vAnsMap,C: vQMap] :
( ? [D: vGID,E: vQuestionnaire,F: vAnsMap,G: vQMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( E @ ( G @ ( F @ vQC ) ) @ vsomeQConf ) )
& ( C = G )
& ( B = F )
& ( A
= ( E @ ( D @ vqgroup ) ) ) )
| ? [D: vQMap,E: vOptExp,F: vQuestionnaire,G: vExp,H: vAnsMap,I: vQuestionnaire] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= vnoQConf )
& ( C = D )
& ( B = H )
& ( A
= ( I @ ( F @ ( G @ vqcond ) ) ) )
& ~ ( E @ visSomeExp )
& ( E
= ( H @ ( G @ vreduceExp ) ) )
& ! [J: vQuestionnaire,K: vQuestionnaire] :
( ( I != K )
| ( F != J )
| ( G
!= ( vno @ vB @ vconstant ) ) )
& ! [J: vQuestionnaire,K: vQuestionnaire] :
( ( I != K )
| ( F != J )
| ( G
!= ( vyes @ vB @ vconstant ) ) ) )
| ? [D: vQMap,E: vOptExp,F: vQuestionnaire,G: vExp,H: vAnsMap,I: vQuestionnaire] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( I @ ( F @ ( E @ vgetExp @ vqcond ) ) @ ( D @ ( H @ vQC ) ) @ vsomeQConf ) )
& ( C = D )
& ( B = H )
& ( A
= ( I @ ( F @ ( G @ vqcond ) ) ) )
& ( E @ visSomeExp )
& ( E
= ( H @ ( G @ vreduceExp ) ) )
& ! [J: vQuestionnaire,K: vQuestionnaire] :
( ( I != K )
| ( F != J )
| ( G
!= ( vno @ vB @ vconstant ) ) )
& ! [J: vQuestionnaire,K: vQuestionnaire] :
( ( I != K )
| ( F != J )
| ( G
!= ( vyes @ vB @ vconstant ) ) ) )
| ? [D: vQuestionnaire,E: vQuestionnaire,F: vAnsMap,G: vQMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( E @ ( G @ ( F @ vQC ) ) @ vsomeQConf ) )
& ( C = G )
& ( B = F )
& ( A
= ( E @ ( D @ ( vno @ vB @ vconstant @ vqcond ) ) ) ) )
| ? [D: vQuestionnaire,E: vQuestionnaire,F: vAnsMap,G: vQMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( D @ ( G @ ( F @ vQC ) ) @ vsomeQConf ) )
& ( C = G )
& ( B = F )
& ( A
= ( E @ ( D @ ( vyes @ vB @ vconstant @ vqcond ) ) ) ) )
| ? [D: vQMap,E: vQuestionnaire,F: vAnsMap,G: vQuestionnaire,H: vOptQConf] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= vnoQConf )
& ( C = D )
& ( B = F )
& ( A
= ( G @ ( E @ vqseq ) ) )
& ~ ( H @ visSomeQC )
& ( H
= ( D @ ( F @ ( E @ vreduce ) ) ) )
& ! [I: vQuestionnaire] :
( ( G != I )
| ( E != vqempty ) ) )
| ? [D: vQMap,E: vQuestionnaire,F: vAnsMap,G: vQuestionnaire,H: vOptQConf] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( G @ ( H @ vgetQC @ vqcappend ) @ vsomeQConf ) )
& ( C = D )
& ( B = F )
& ( A
= ( G @ ( E @ vqseq ) ) )
& ( H @ visSomeQC )
& ( H
= ( D @ ( F @ ( E @ vreduce ) ) ) )
& ! [I: vQuestionnaire] :
( ( G != I )
| ( E != vqempty ) ) )
| ? [D: vQuestionnaire,E: vAnsMap,F: vQMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( D @ ( F @ ( E @ vQC ) ) @ vsomeQConf ) )
& ( C = F )
& ( B = E )
& ( A
= ( D @ ( vqempty @ vqseq ) ) ) )
| ? [D: vQID,E: vOptQuestion,F: vQMap,G: vAnsMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= vnoQConf )
& ( C = F )
& ( B = G )
& ( A
= ( D @ vask @ vqsingle ) )
& ~ ( E @ visSomeQuestion )
& ( E
= ( F @ ( D @ vlookupQMap ) ) ) )
| ? [D: vQID,E: vOptQuestion,F: vQMap,G: vAnsMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( E @ vgetQuestionAType @ ( E @ vgetQuestionLabel @ ( D @ vquestion ) ) @ vqsingle @ ( F @ ( G @ vQC ) ) @ vsomeQConf ) )
& ( C = F )
& ( B = G )
& ( A
= ( D @ vask @ vqsingle ) )
& ( E @ visSomeQuestion )
& ( E
= ( F @ ( D @ vlookupQMap ) ) ) )
| ? [D: vQMap,E: vAType,F: vLabel,G: vAnsMap,H: vQID] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( vqempty @ ( D @ ( E @ ( F @ ( H @ vqmbind ) ) ) @ ( G @ vQC ) ) @ vsomeQConf ) )
& ( C = D )
& ( B = G )
& ( A
= ( E @ ( F @ ( H @ vdefquestion ) ) @ vqsingle ) ) )
| ? [D: vQMap,E: vAType,F: vOptExp,G: vAnsMap,H: vQID,I: vExp] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= vnoQConf )
& ( C = D )
& ( B = G )
& ( A
= ( I @ ( E @ ( H @ vvalue ) ) @ vqsingle ) )
& ~ ( F @ visSomeExp )
& ( F
= ( G @ ( I @ vreduceExp ) ) )
& ~ ( I @ vexpIsValue ) )
| ? [D: vQMap,E: vAType,F: vOptExp,G: vAnsMap,H: vQID,I: vExp] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( F @ vgetExp @ ( E @ ( H @ vvalue ) ) @ vqsingle @ ( D @ ( G @ vQC ) ) @ vsomeQConf ) )
& ( C = D )
& ( B = G )
& ( A
= ( I @ ( E @ ( H @ vvalue ) ) @ vqsingle ) )
& ( F @ visSomeExp )
& ( F
= ( G @ ( I @ vreduceExp ) ) )
& ~ ( I @ vexpIsValue ) )
| ? [D: vQMap,E: vAType,F: vAnsMap,G: vQID,H: vExp] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( vqempty @ ( D @ ( F @ ( H @ vgetExpValue @ ( G @ vabind ) ) @ vQC ) ) @ vsomeQConf ) )
& ( C = D )
& ( B = F )
& ( A
= ( H @ ( E @ ( G @ vvalue ) ) @ vqsingle ) )
& ( H @ vexpIsValue ) )
| ? [D: vQMap,E: vAType,F: vLabel,G: vAval,H: vAnsMap,I: vQID] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= ( vqempty @ ( D @ ( H @ ( G @ ( I @ vabind ) ) @ vQC ) ) @ vsomeQConf ) )
& ( C = D )
& ( B = H )
& ( A
= ( E @ ( F @ ( I @ vquestion ) ) @ vqsingle ) )
& ( G
= ( E @ ( F @ vgetAnswer ) ) ) )
| ? [D: vAnsMap,E: vQMap] :
( ( ( C @ ( B @ ( A @ vreduce ) ) )
= vnoQConf )
& ( C = E )
& ( B = D )
& ( A = vqempty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(392,plain,
! [B: vAval,A: vUnOpT] :
( ( ( B @ ( A @ vevalUnOp ) )
= vnoExp )
| ~ ( B @ ( A @ sk31 ) ) ),
inference(cnfConj,[status(thm)],[391]) ).
thf(399,plain,
! [B: vAval,A: vUnOpT] :
( ~ ( B @ ( A @ sk31 ) )
| ( ( B @ ( A @ vevalUnOp ) )
= vnoExp ) ),
inference(lifteq,[status(thm)],[392]) ).
thf(108,axiom,
! [A: vQID,B: vLabel,C: vAType] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ vgetQuestionAType )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getQuestionAType-0') ).
thf(959,plain,
! [A: vQID,B: vLabel,C: vAType] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ vgetQuestionAType )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1362,plain,
~ ? [A: vEntry,B: vQuestionnaire,C: vQuestionnaire] :
( ( A @ vqsingle )
= ( C @ ( B @ vqseq ) ) ),
inference(miniscope,[status(thm)],[1361]) ).
thf(1363,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vEntry] :
( ( A @ vqsingle )
!= ( C @ ( B @ vqseq ) ) ),
inference(cnf,[status(esa)],[1362]) ).
thf(1364,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vEntry] :
( ( A @ vqsingle )
!= ( C @ ( B @ vqseq ) ) ),
inference(lifteq,[status(thm)],[1363]) ).
thf(5688,plain,
! [A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk1 @ vtypeQM @ ( sk5 @ vtypeAM @ vMC ) ) )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,254]) ).
thf(5693,plain,
! [A: vMapConf] :
( ( ( A @ sk254 )
!= ( sk1 @ vtypeQM ) )
| ( ( A @ sk253 )
!= ( sk5 @ vtypeAM ) )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5688]) ).
thf(684,plain,
! [A: vOptExp] :
( ( A = vnoExp )
| ( A @ visSomeExp ) ),
inference(cnf,[status(esa)],[683]) ).
thf(685,plain,
! [A: vOptExp] :
( ( A @ visSomeExp )
| ( A = vnoExp ) ),
inference(lifteq,[status(thm)],[684]) ).
thf(144,axiom,
( ( vyes @ vnot )
= vno ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','not-0') ).
thf(1171,plain,
( ( vyes @ vnot )
= vno ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(694,plain,
! [A: vLabel] :
( ( vNumber @ ( A @ vgetAnswer ) )
= ( A @ vaskNumber @ vNum ) ),
inference(cnf,[status(esa)],[693]) ).
thf(695,plain,
! [A: vLabel] :
( ( vNumber @ ( A @ vgetAnswer ) )
= ( A @ vaskNumber @ vNum ) ),
inference(lifteq,[status(thm)],[694]) ).
thf(1111,plain,
! [B: vAType,A: vUnOpT] :
( ( ( ( B @ ( A @ vcheckUnOp ) )
= vnoAType )
| ~ ( B @ ( A @ sk215 ) ) )
& ( ( B
= ( A @ ( B @ sk217 ) ) )
| ~ ( B @ ( A @ sk215 ) ) )
& ( ( A
= ( A @ ( B @ sk216 ) ) )
| ~ ( B @ ( A @ sk215 ) ) )
& ( ( ( A @ ( B @ sk217 ) )
!= vYesNo )
| ( ( A @ ( B @ sk216 ) )
!= vnotop )
| ~ ( B @ ( A @ sk215 ) ) )
& ( ( B @ ( A @ sk215 ) )
| ( ( B @ ( A @ vcheckUnOp ) )
= ( vYesNo @ vsomeAType ) ) )
& ( ( B @ ( A @ sk215 ) )
| ( B = vYesNo ) )
& ( ( B @ ( A @ sk215 ) )
| ( A = vnotop ) ) ),
inference(cnf,[status(esa)],[1110]) ).
thf(1117,plain,
! [B: vAType,A: vUnOpT] :
( ( ( A @ ( B @ sk217 ) )
!= vYesNo )
| ( ( A @ ( B @ sk216 ) )
!= vnotop )
| ~ ( B @ ( A @ sk215 ) ) ),
inference(cnfConj,[status(thm)],[1111]) ).
thf(1122,plain,
! [B: vAType,A: vUnOpT] :
( ~ ( B @ ( A @ sk215 ) )
| ( ( A @ ( B @ sk217 ) )
!= vYesNo )
| ( ( A @ ( B @ sk216 ) )
!= vnotop ) ),
inference(lifteq,[status(thm)],[1117]) ).
thf(6783,plain,
! [B: vAType,A: vUnOpT] :
( ~ ( B @ ( A @ sk215 ) )
| ( ( A @ ( B @ sk217 ) )
!= vYesNo ) ),
inference(simplifyReflect,[status(thm)],[1122,356]) ).
thf(90,axiom,
! [A: vQID,B: vATMap] :
( ? [C: vQID,D: vAType,E: vATMap,F: vQID] :
( ( ( B @ ( A @ vlookupATMap ) )
= ( E @ ( F @ vlookupATMap ) ) )
& ( B
= ( E @ ( D @ ( C @ vatmbind ) ) ) )
& ( A = F )
& ( F != C ) )
| ? [C: vQID,D: vAType,E: vATMap,F: vQID] :
( ( ( B @ ( A @ vlookupATMap ) )
= ( D @ vsomeAType ) )
& ( B
= ( E @ ( D @ ( C @ vatmbind ) ) ) )
& ( A = F )
& ( F = C ) )
| ? [C: vQID] :
( ( ( B @ ( A @ vlookupATMap ) )
= vnoAType )
& ( B = vatmempty )
& ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookupATMap-INV') ).
thf(851,plain,
! [A: vQID,B: vATMap] :
( ? [C: vQID,D: vAType,E: vATMap,F: vQID] :
( ( ( B @ ( A @ vlookupATMap ) )
= ( E @ ( F @ vlookupATMap ) ) )
& ( B
= ( E @ ( D @ ( C @ vatmbind ) ) ) )
& ( A = F )
& ( F != C ) )
| ? [C: vQID,D: vAType,E: vATMap,F: vQID] :
( ( ( B @ ( A @ vlookupATMap ) )
= ( D @ vsomeAType ) )
& ( B
= ( E @ ( D @ ( C @ vatmbind ) ) ) )
& ( A = F )
& ( F = C ) )
| ? [C: vQID] :
( ( ( B @ ( A @ vlookupATMap ) )
= vnoAType )
& ( B = vatmempty )
& ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(131,axiom,
! [A: vExp,B: vExp,C: vBinOpT,D: vAnsMap] :
( ( ( B @ vexpIsValue )
& ( A @ vexpIsValue ) )
=> ( ( D @ ( B @ ( C @ ( A @ vbinop ) ) @ vreduceExp ) )
= ( B @ vgetExpValue @ ( A @ vgetExpValue @ ( C @ vevalBinOp ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-3') ).
thf(1102,plain,
! [A: vExp,B: vExp,C: vBinOpT,D: vAnsMap] :
( ( ( B @ vexpIsValue )
& ( A @ vexpIsValue ) )
=> ( ( D @ ( B @ ( C @ ( A @ vbinop ) ) @ vreduceExp ) )
= ( B @ vgetExpValue @ ( A @ vgetExpValue @ ( C @ vevalBinOp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(194,axiom,
! [A: vAnsMap,B: vQMap,C: vQuestionnaire,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ ( A @ vQC ) ) @ vqcappend ) )
= ( D @ ( C @ vqseq ) @ ( B @ ( A @ vQC ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qcappend-0') ).
thf(4626,plain,
! [A: vAnsMap,B: vQMap,C: vQuestionnaire,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ ( A @ vQC ) ) @ vqcappend ) )
= ( D @ ( C @ vqseq ) @ ( B @ ( A @ vQC ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(425,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk38 ) )
| ( ( B @ ( A @ vecheck ) )
= ( vNumber @ vsomeAType ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(473,plain,
! [B: vExp,A: vATMap] :
( ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( B @ ( A @ vecheck ) )
= ( vNumber @ vsomeAType ) ) ),
inference(lifteq,[status(thm)],[425]) ).
thf(223,axiom,
! [A: vQConf] : ( A @ vsomeQConf @ visSomeQC ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeQC-1') ).
thf(4741,plain,
! [A: vQConf] : ( A @ vsomeQConf @ visSomeQC ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(662,plain,
! [B: vYN,A: vYN] :
( ( B @ vB @ ( A @ vB @ ( vorop @ vevalBinOp ) ) )
= ( B @ ( A @ vor ) @ vB @ vconstant @ vsomeExp ) ),
inference(cnf,[status(esa)],[661]) ).
thf(663,plain,
! [B: vYN,A: vYN] :
( ( B @ vB @ ( A @ vB @ ( vorop @ vevalBinOp ) ) )
= ( B @ ( A @ vor ) @ vB @ vconstant @ vsomeExp ) ),
inference(lifteq,[status(thm)],[662]) ).
thf(221,axiom,
! [A: vQMap,B: vAType,C: vAnsMap,D: vQID,E: vExp] :
( ( ( C @ ( E @ vreduceExp ) @ visSomeExp )
& ~ ( E @ vexpIsValue ) )
=> ( ( A @ ( C @ ( E @ ( B @ ( D @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( C @ ( E @ vreduceExp ) @ vgetExp @ ( B @ ( D @ vvalue ) ) @ vqsingle @ ( A @ ( C @ vQC ) ) @ vsomeQConf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-3') ).
thf(4735,plain,
! [A: vQMap,B: vAType,C: vAnsMap,D: vQID,E: vExp] :
( ( ( C @ ( E @ vreduceExp ) @ visSomeExp )
& ~ ( E @ vexpIsValue ) )
=> ( ( A @ ( C @ ( E @ ( B @ ( D @ vvalue ) ) @ vqsingle @ vreduce ) ) )
= ( C @ ( E @ vreduceExp ) @ vgetExp @ ( B @ ( D @ vvalue ) ) @ vqsingle @ ( A @ ( C @ vQC ) ) @ vsomeQConf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(5683,plain,
! [A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk4 @ ( sk3 @ vMC ) ) )
| ( sk1 != vqmempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,4874]) ).
thf(5692,plain,
! [A: vMapConf] :
( ( ( A @ sk254 )
!= sk4 )
| ( ( A @ sk253 )
!= sk3 )
| ( sk1 != vqmempty )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5683]) ).
thf(5755,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( vatmempty @ ( sk5 @ vtypeAM @ vMC ) ) )
| ( ( B @ sk254 )
!= sk4 )
| ( ( B @ sk253 )
!= sk3 )
| ( sk1 != vqmempty )
| ( B @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,5692]) ).
thf(5757,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 )
!= vatmempty )
| ( ( A @ sk253 )
!= ( sk5 @ vtypeAM ) )
| ( ( B @ sk254 )
!= sk4 )
| ( ( B @ sk253 )
!= sk3 )
| ( sk1 != vqmempty )
| ( B @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5755]) ).
thf(6086,plain,
! [C: vATMap,B: vATMap,A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( C @ ( B @ vMC ) ) )
| ( ( A @ ( B @ sk412 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[1316,6085]) ).
thf(6087,plain,
! [A: vMapConf] :
( ( A @ ( A @ sk253 @ sk412 ) )
= ( A @ sk254 ) ),
inference(pattern_uni,[status(thm)],[6086:[bind(A,$thf( E )),bind(B,$thf( E @ sk253 )),bind(C,$thf( E @ sk254 ))]]) ).
thf(6088,plain,
! [A: vMapConf] :
( ( A @ ( A @ sk253 @ sk412 ) )
= ( A @ sk254 ) ),
inference(simp,[status(thm)],[6087]) ).
thf(129,axiom,
! [A: vQMap,B: vQID,C: vLabel,D: vAType,E: vQID,F: vAType,G: vQMap,H: vLabel] :
( ( ( A @ ( D @ ( H @ ( E @ vqmbind ) ) ) )
= ( G @ ( F @ ( C @ ( B @ vqmbind ) ) ) ) )
=> ( ( A = G )
& ( D = F )
& ( H = C )
& ( E = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-qmbind') ).
thf(1081,plain,
! [A: vQMap,B: vQID,C: vLabel,D: vAType,E: vQID,F: vAType,G: vQMap,H: vLabel] :
( ( ( A @ ( D @ ( H @ ( E @ vqmbind ) ) ) )
= ( G @ ( F @ ( C @ ( B @ vqmbind ) ) ) ) )
=> ( ( A = G )
& ( D = F )
& ( H = C )
& ( E = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(1144,plain,
! [A: vATMap] :
( ( A @ ( vatmempty @ vappendATMap ) )
= A ),
inference(cnf,[status(esa)],[1143]) ).
thf(1145,plain,
! [A: vATMap] :
( ( A @ ( vatmempty @ vappendATMap ) )
= A ),
inference(lifteq,[status(thm)],[1144]) ).
thf(9782,plain,
! [E: vAnsMap,D: vAval,C: vQID,B: vnat,A: vQID] :
( ( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( E @ ( D @ ( C @ vabind ) ) @ vtypeAM ) )
| ( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9478,9436]) ).
thf(9783,plain,
! [A: vQID] :
( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[9782:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ vNum )),bind(E,$thf( vaempty ))]]) ).
thf(56,axiom,
! [A: vATMap,B: vExp,C: vUnOpT] :
( ( B @ ( A @ vecheck ) @ visSomeAType )
=> ( ( B @ ( C @ vunop ) @ ( A @ vecheck ) )
= ( B @ ( A @ vecheck ) @ vgetAType @ ( C @ vcheckUnOp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','echeck-6') ).
thf(675,plain,
! [A: vATMap,B: vExp,C: vUnOpT] :
( ( B @ ( A @ vecheck ) @ visSomeAType )
=> ( ( B @ ( C @ vunop ) @ ( A @ vecheck ) )
= ( B @ ( A @ vecheck ) @ vgetAType @ ( C @ vcheckUnOp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(253,plain,
~ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ visValue ),
inference(cnfConj,[status(thm)],[252]) ).
thf(4866,plain,
( ( ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ visValue )
!= ( vqempty @ visValue ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1391,253]) ).
thf(4867,plain,
( ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ visValue )
!= ( vqempty @ visValue ) ),
inference(simp,[status(thm)],[4866]) ).
thf(4868,plain,
( ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle )
!= vqempty ),
inference(simp,[status(thm)],[4867]) ).
thf(175,axiom,
! [A: vQConf,B: vQConf] :
( ( ( A @ vsomeQConf )
= ( B @ vsomeQConf ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someQConf') ).
thf(1340,plain,
! [A: vQConf,B: vQConf] :
( ( ( A @ vsomeQConf )
= ( B @ vsomeQConf ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(620,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( F = B )
| ( ( C @ ( F @ ( D @ vsomeQuestion ) ) )
!= ( E @ ( B @ ( A @ vsomeQuestion ) ) ) ) ),
inference(cnfConj,[status(thm)],[618]) ).
thf(625,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( F = B )
| ( ( C @ ( F @ ( D @ vsomeQuestion ) ) )
!= ( E @ ( B @ ( A @ vsomeQuestion ) ) ) ) ),
inference(lifteq,[status(thm)],[620]) ).
thf(626,plain,
? [A: vQID > vAType > vOptQuestion > vLabel] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vsomeQuestion ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[625]) ).
thf(627,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ ( C @ ( A @ sk130 ) ) )
= B ),
inference(cnf,[status(esa)],[626]) ).
thf(6853,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ ( C @ ( A @ sk130 ) ) )
= B ),
inference(lifteq,[status(thm)],[627]) ).
thf(111,axiom,
! [A: vExp,B: vUnOpT,C: vAnsMap] :
( ( A @ vexpIsValue )
=> ( ( C @ ( A @ ( B @ vunop ) @ vreduceExp ) )
= ( A @ vgetExpValue @ ( B @ vevalUnOp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-8') ).
thf(968,plain,
! [A: vExp,B: vUnOpT,C: vAnsMap] :
( ( A @ vexpIsValue )
=> ( ( C @ ( A @ ( B @ vunop ) @ vreduceExp ) )
= ( A @ vgetExpValue @ ( B @ vevalUnOp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(203,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vATMap,F: vQID,G: vExp] :
( ( C @ ( E @ vMC ) @ ( G @ ( D @ ( F @ vvalue ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( ( G @ ( B @ vecheck ) )
= ( D @ vsomeAType ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tvalue_inv2') ).
thf(4658,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vATMap,F: vQID,G: vExp] :
( ( C @ ( E @ vMC ) @ ( G @ ( D @ ( F @ vvalue ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( ( G @ ( B @ vecheck ) )
= ( D @ vsomeAType ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(225,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap,E: vQID] :
( ( C @ ( D @ vMC ) @ ( E @ vask @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ? [F: vAType] :
( ( A @ ( E @ vlookupATMap ) )
= ( F @ vsomeAType ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Task_inv2') ).
thf(4749,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap,E: vQID] :
( ( C @ ( D @ vMC ) @ ( E @ vask @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ? [F: vAType] :
( ( A @ ( E @ vlookupATMap ) )
= ( F @ vsomeAType ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(1175,plain,
! [F: vAnsMap,E: vQID,D: vAval,C: vAval,B: vAnsMap,A: vQID] :
( ( E = A )
| ( ( F @ ( C @ ( E @ vabind ) ) )
!= ( B @ ( D @ ( A @ vabind ) ) ) ) ),
inference(cnfConj,[status(thm)],[1174]) ).
thf(1178,plain,
! [F: vAnsMap,E: vQID,D: vAval,C: vAval,B: vAnsMap,A: vQID] :
( ( E = A )
| ( ( F @ ( C @ ( E @ vabind ) ) )
!= ( B @ ( D @ ( A @ vabind ) ) ) ) ),
inference(lifteq,[status(thm)],[1175]) ).
thf(1179,plain,
? [A: vAval > vAnsMap > vAnsMap > vQID] :
! [B: vQID,C: vAval,D: vAnsMap] :
( ( D @ ( C @ ( B @ vabind ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[1178]) ).
thf(1180,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( C @ ( B @ ( A @ vabind ) ) @ ( C @ ( B @ sk225 ) ) )
= A ),
inference(cnf,[status(esa)],[1179]) ).
thf(8350,plain,
! [C: vAnsMap,B: vAval,A: vQID] :
( ( C @ ( B @ ( A @ vabind ) ) @ ( C @ ( B @ sk225 ) ) )
= A ),
inference(lifteq,[status(thm)],[1180]) ).
thf(7503,plain,
! [B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk68 ) @ visSomeAType )
!= ( vYesNo @ vsomeAType @ visSomeAType ) )
| ~ $true
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[4997,429]) ).
thf(7504,plain,
! [B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk68 ) @ visSomeAType )
!= ( vYesNo @ vsomeAType @ visSomeAType ) )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(simp,[status(thm)],[7503]) ).
thf(7506,plain,
! [B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk68 ) )
!= ( vYesNo @ vsomeAType ) )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(simp,[status(thm)],[7504]) ).
thf(8122,plain,
! [D: vExp,C: vATMap,B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk54 ) )
!= ( C @ ( D @ sk54 ) ) )
| ( ( C @ ( D @ sk68 ) )
!= ( vYesNo @ vsomeAType ) )
| ~ ( C @ ( D @ sk61 ) )
| ~ $true
| ~ ( C @ ( D @ sk47 ) )
| ~ ( C @ ( D @ sk44 ) )
| ~ ( D @ ( C @ sk41 ) )
| ~ ( D @ ( C @ sk38 ) )
| ~ ( D @ ( C @ sk35 ) )
| ~ ( A @ ( B @ sk58 ) @ visSomeAType )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[448,7506]) ).
thf(8123,plain,
! [D: vExp,C: vATMap,B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk54 ) )
!= ( C @ ( D @ sk54 ) ) )
| ( ( C @ ( D @ sk68 ) )
!= ( vYesNo @ vsomeAType ) )
| ~ ( C @ ( D @ sk61 ) )
| ~ ( C @ ( D @ sk47 ) )
| ~ ( C @ ( D @ sk44 ) )
| ~ ( D @ ( C @ sk41 ) )
| ~ ( D @ ( C @ sk38 ) )
| ~ ( D @ ( C @ sk35 ) )
| ~ ( A @ ( B @ sk58 ) @ visSomeAType )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(simp,[status(thm)],[8122]) ).
thf(8124,plain,
! [B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk68 ) )
!= ( vYesNo @ vsomeAType ) )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ~ ( A @ ( B @ sk58 ) @ visSomeAType )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(pattern_uni,[status(thm)],[8123:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(8143,plain,
! [B: vExp,A: vATMap] :
( ( ( A @ ( B @ sk68 ) )
!= ( vYesNo @ vsomeAType ) )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk58 ) @ visSomeAType )
| ~ ( A @ ( B @ sk56 ) @ visSomeAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(simp,[status(thm)],[8124]) ).
thf(126,axiom,
! [A: vAval,B: vAval] :
( ( ( A @ vconstant )
= ( B @ vconstant ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-constant') ).
thf(1070,plain,
! [A: vAval,B: vAval] :
( ( ( A @ vconstant )
= ( B @ vconstant ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1224,plain,
! [A: vATMap] :
( ( A @ ( vatmempty @ vintersectATM ) )
= vatmempty ),
inference(cnf,[status(esa)],[1223]) ).
thf(1225,plain,
! [A: vATMap] :
( ( A @ ( vatmempty @ vintersectATM ) )
= vatmempty ),
inference(lifteq,[status(thm)],[1224]) ).
thf(828,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( D = A )
| ( ( C @ ( F @ ( D @ vdefquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ) ),
inference(cnfConj,[status(thm)],[827]) ).
thf(831,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( D = A )
| ( ( C @ ( F @ ( D @ vdefquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ) ),
inference(lifteq,[status(thm)],[828]) ).
thf(832,plain,
? [A: vLabel > vAType > vEntry > vQID] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vdefquestion ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[831]) ).
thf(833,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vdefquestion ) ) @ ( C @ ( B @ sk154 ) ) )
= A ),
inference(cnf,[status(esa)],[832]) ).
thf(6885,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vdefquestion ) ) @ ( C @ ( B @ sk154 ) ) )
= A ),
inference(lifteq,[status(thm)],[833]) ).
thf(308,plain,
! [A: vAval] :
( ( A @ sk14 )
| ( ( A @ vtypeOf )
= vYesNo ) ),
inference(cnfConj,[status(thm)],[303]) ).
thf(310,plain,
! [A: vAval] :
( ( A @ sk14 )
| ( ( A @ vtypeOf )
= vYesNo ) ),
inference(lifteq,[status(thm)],[308]) ).
thf(79,axiom,
! [A: vExp,B: vExp,C: vAnsMap,D: vBinOpT] :
( ( ( C @ ( B @ vreduceExp ) @ visSomeExp )
& ~ ( B @ vexpIsValue )
& ( A @ vexpIsValue ) )
=> ( ( C @ ( B @ ( D @ ( A @ vbinop ) ) @ vreduceExp ) )
= ( C @ ( B @ vreduceExp ) @ vgetExp @ ( D @ ( A @ vbinop ) ) @ vsomeExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduceExp-4') ).
thf(791,plain,
! [A: vExp,B: vExp,C: vAnsMap,D: vBinOpT] :
( ( ( C @ ( B @ vreduceExp ) @ visSomeExp )
& ~ ( B @ vexpIsValue )
& ( A @ vexpIsValue ) )
=> ( ( C @ ( B @ ( D @ ( A @ vbinop ) ) @ vreduceExp ) )
= ( C @ ( B @ vreduceExp ) @ vgetExp @ ( D @ ( A @ vbinop ) ) @ vsomeExp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(1188,plain,
~ ( vnoQConf @ visSomeQC ),
inference(polarity_switch,[status(thm)],[1187]) ).
thf(87,axiom,
! [A: vYN,B: vYN] :
( ( ( B != vyes )
| ( A != vyes ) )
=> ( ( B @ ( A @ vand ) )
= vno ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','and-1') ).
thf(840,plain,
! [A: vYN,B: vYN] :
( ( ( B != vyes )
| ( A != vyes ) )
=> ( ( B @ ( A @ vand ) )
= vno ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(450,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk47 ) )
| ( B
= ( A @ ( B @ sk52 ) @ ( A @ ( B @ sk53 ) @ ( A @ ( B @ sk50 ) @ vbinop ) ) ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(463,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk52 ) @ ( A @ ( B @ sk53 ) @ ( A @ ( B @ sk50 ) @ vbinop ) ) )
= B ) ),
inference(lifteq,[status(thm)],[450]) ).
thf(5153,plain,
! [A: vYN] :
( ( vno != vno )
| ( ( vno @ ( A @ vor ) )
= vno )
| ( A = vyes ) ),
inference(paramod_ordered,[status(thm)],[907,796]) ).
thf(5154,plain,
! [A: vYN] :
( ( ( vno @ ( A @ vor ) )
= vno )
| ( A = vyes ) ),
inference(pattern_uni,[status(thm)],[5153:[]]) ).
thf(1149,plain,
! [F: vAType,E: vQID,D: vAType,C: vATMap,B: vATMap,A: vQID] :
( ( D = F )
| ( ( C @ ( D @ ( E @ vatmbind ) ) )
!= ( B @ ( F @ ( A @ vatmbind ) ) ) ) ),
inference(cnfConj,[status(thm)],[1147]) ).
thf(1154,plain,
! [F: vAType,E: vQID,D: vAType,C: vATMap,B: vATMap,A: vQID] :
( ( D = F )
| ( ( C @ ( D @ ( E @ vatmbind ) ) )
!= ( B @ ( F @ ( A @ vatmbind ) ) ) ) ),
inference(lifteq,[status(thm)],[1149]) ).
thf(1155,plain,
? [A: vQID > vATMap > vATMap > vAType] :
! [B: vQID,C: vAType,D: vATMap] :
( ( D @ ( C @ ( B @ vatmbind ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[1154]) ).
thf(1156,plain,
! [C: vATMap,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vatmbind ) ) @ ( C @ ( A @ sk223 ) ) )
= B ),
inference(cnf,[status(esa)],[1155]) ).
thf(8148,plain,
! [C: vATMap,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vatmbind ) ) @ ( C @ ( A @ sk223 ) ) )
= B ),
inference(lifteq,[status(thm)],[1156]) ).
thf(358,plain,
! [A: vOptExp] :
( ( A
= ( A @ sk27 @ vsomeExp ) )
| ( A = vnoExp ) ),
inference(cnf,[status(esa)],[357]) ).
thf(359,plain,
! [A: vOptExp] :
( ( ( A @ sk27 @ vsomeExp )
= A )
| ( A = vnoExp ) ),
inference(lifteq,[status(thm)],[358]) ).
thf(135,axiom,
! [A: vQMap] :
( ? [B: vQID,C: vLabel,D: vAType,E: vQMap] :
( A
= ( E @ ( D @ ( C @ ( B @ vqmbind ) ) ) ) )
| ( A = vqmempty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dom-QMap') ).
thf(1130,plain,
! [A: vQMap] :
( ? [B: vQID,C: vLabel,D: vAType,E: vQMap] :
( A
= ( E @ ( D @ ( C @ ( B @ vqmbind ) ) ) ) )
| ( A = vqmempty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(396,plain,
! [B: vAval,A: vUnOpT] :
( ( A
= ( A @ ( B @ sk33 ) ) )
| ~ ( B @ ( A @ sk31 ) ) ),
inference(cnfConj,[status(thm)],[391]) ).
thf(405,plain,
! [B: vAval,A: vUnOpT] :
( ~ ( B @ ( A @ sk31 ) )
| ( ( A @ ( B @ sk33 ) )
= A ) ),
inference(lifteq,[status(thm)],[396]) ).
thf(7392,plain,
! [D: vAval,C: vUnOpT,B: vUnOpT,A: vnat] :
( ( ( A @ vNum @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ~ $true
| ( ( C @ ( D @ sk33 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[7020,405]) ).
thf(7393,plain,
! [D: vAval,C: vUnOpT,B: vUnOpT,A: vnat] :
( ( ( A @ vNum @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ( ( C @ ( D @ sk33 ) )
= C ) ),
inference(simp,[status(thm)],[7392]) ).
thf(7394,plain,
! [B: vnat,A: vUnOpT] :
( ( A @ ( B @ vNum @ sk33 ) )
= A ),
inference(pattern_uni,[status(thm)],[7393:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ vNum ))]]) ).
thf(7398,plain,
! [B: vnat,A: vUnOpT] :
( ( A @ ( B @ vNum @ sk33 ) )
= A ),
inference(simp,[status(thm)],[7394]) ).
thf(1341,plain,
! [B: vQConf,A: vQConf] :
( ( A = B )
| ( ( A @ vsomeQConf )
!= ( B @ vsomeQConf ) ) ),
inference(cnf,[status(esa)],[1340]) ).
thf(1342,plain,
! [B: vQConf,A: vQConf] :
( ( A = B )
| ( ( A @ vsomeQConf )
!= ( B @ vsomeQConf ) ) ),
inference(lifteq,[status(thm)],[1341]) ).
thf(1343,plain,
? [A: vOptQConf > vQConf] :
! [B: vQConf] :
( ( B @ vsomeQConf @ A )
= B ),
inference(detectInverse,[status(thm)],[1342]) ).
thf(1344,plain,
! [A: vQConf] :
( ( A @ vsomeQConf @ sk264 )
= A ),
inference(cnf,[status(esa)],[1343]) ).
thf(5186,plain,
! [A: vQConf] :
( ( A @ vsomeQConf @ sk264 )
= A ),
inference(lifteq,[status(thm)],[1344]) ).
thf(4920,plain,
! [B: vOptAType,A: vAType] :
( ( ( A @ vsomeAType @ visSomeAType )
!= ( B @ visSomeAType ) )
| ~ $true
| ( ( B @ sk8 @ vsomeAType )
= B ) ),
inference(paramod_ordered,[status(thm)],[670,284]) ).
thf(4921,plain,
! [B: vOptAType,A: vAType] :
( ( ( A @ vsomeAType @ visSomeAType )
!= ( B @ visSomeAType ) )
| ( ( B @ sk8 @ vsomeAType )
= B ) ),
inference(simp,[status(thm)],[4920]) ).
thf(4922,plain,
! [A: vAType] :
( ( A @ vsomeAType @ sk8 @ vsomeAType )
= ( A @ vsomeAType ) ),
inference(pattern_uni,[status(thm)],[4921:[bind(A,$thf( C )),bind(B,$thf( C @ vsomeAType ))]]) ).
thf(4925,plain,
! [A: vAType] :
( ( A @ vsomeAType @ sk8 @ vsomeAType )
= ( A @ vsomeAType ) ),
inference(simp,[status(thm)],[4922]) ).
thf(595,plain,
! [A: vAType] :
( ( A @ vsomeAType @ vgetAType )
= A ),
inference(cnf,[status(esa)],[594]) ).
thf(596,plain,
! [A: vAType] :
( ( A @ vsomeAType @ vgetAType )
= A ),
inference(lifteq,[status(thm)],[595]) ).
thf(5266,plain,
! [B: vAType,A: vAType] :
( ( ( A @ vsomeAType @ sk8 @ vsomeAType )
!= ( B @ vsomeAType ) )
| ( ( A @ vsomeAType @ vgetAType )
= B ) ),
inference(paramod_ordered,[status(thm)],[4925,596]) ).
thf(5267,plain,
! [A: vAType] :
( ( A @ vsomeAType @ sk8 )
= ( A @ vsomeAType @ vgetAType ) ),
inference(pattern_uni,[status(thm)],[5266:[bind(A,$thf( D )),bind(B,$thf( D @ vsomeAType @ sk8 ))]]) ).
thf(5271,plain,
! [A: vAType] :
( ( A @ vsomeAType @ sk8 )
= ( A @ vsomeAType @ vgetAType ) ),
inference(simp,[status(thm)],[5267]) ).
thf(5277,plain,
! [A: vAType] :
( ( A @ vsomeAType @ sk8 )
= A ),
inference(rewrite,[status(thm)],[5271,596]) ).
thf(7057,plain,
! [E: vYN,D: vAval,C: vUnOpT,B: vUnOpT,A: vnat] :
( ( ( A @ vNum @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ~ $true
| ( ( C @ ( D @ sk34 ) )
!= ( E @ vB ) ) ),
inference(paramod_ordered,[status(thm)],[7020,6784]) ).
thf(7058,plain,
! [E: vYN,D: vAval,C: vUnOpT,B: vUnOpT,A: vnat] :
( ( ( A @ vNum @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ( ( C @ ( D @ sk34 ) )
!= ( E @ vB ) ) ),
inference(simp,[status(thm)],[7057]) ).
thf(7059,plain,
! [C: vnat,B: vYN,A: vUnOpT] :
( ( A @ ( C @ vNum @ sk34 ) )
!= ( B @ vB ) ),
inference(pattern_uni,[status(thm)],[7058:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( F @ vNum ))]]) ).
thf(7072,plain,
! [C: vnat,B: vYN,A: vUnOpT] :
( ( A @ ( C @ vNum @ sk34 ) )
!= ( B @ vB ) ),
inference(simp,[status(thm)],[7059]) ).
thf(7150,plain,
! [E: vnat,D: vYN,C: vUnOpT,B: vAval,A: vUnOpT] :
( ( ( A @ ( B @ sk25 ) @ vB )
!= ( D @ vB ) )
| ( B
!= ( C @ ( E @ vNum @ sk34 ) ) )
| ( ( B @ ( A @ vevalUnOp ) )
= vnoExp ) ),
inference(paramod_ordered,[status(thm)],[339,7072]) ).
thf(7151,plain,
! [D: vUnOpT,C: vAval,B: vnat,A: vUnOpT] :
( ( C
!= ( A @ ( B @ vNum @ sk34 ) ) )
| ( ( C @ ( D @ vevalUnOp ) )
= vnoExp ) ),
inference(pattern_uni,[status(thm)],[7150:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G @ ( F @ sk25 ) ))]]) ).
thf(7167,plain,
! [C: vUnOpT,B: vnat,A: vUnOpT] :
( ( A @ ( B @ vNum @ sk34 ) @ ( C @ vevalUnOp ) )
= vnoExp ),
inference(simp,[status(thm)],[7151]) ).
thf(7737,plain,
! [B: vUnOpT,A: vnat] :
( ( A @ vNum @ ( B @ vevalUnOp ) )
= vnoExp ),
inference(rewrite,[status(thm)],[7167,7075]) ).
thf(6450,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ sk401 @ ( A @ vgetQM @ ( A @ sk399 @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ vgetQuest )
= D ) ),
inference(paramod_ordered,[status(thm)],[6443,4640]) ).
thf(6451,plain,
! [A: vQConf] :
( ( A @ sk401 )
= ( A @ vgetQuest ) ),
inference(pattern_uni,[status(thm)],[6450:[bind(A,$thf( G )),bind(B,$thf( G @ sk399 )),bind(C,$thf( G @ vgetQM )),bind(D,$thf( G @ sk401 ))]]) ).
thf(6457,plain,
! [A: vQConf] :
( ( A @ sk401 )
= ( A @ vgetQuest ) ),
inference(simp,[status(thm)],[6451]) ).
thf(8932,plain,
! [E: vQConf,D: vLabel,C: vQMap,B: vAnsMap,A: vQuestionnaire] :
( ( ( C @ ( B @ ( A @ ( vqempty @ vqseq ) @ vreduce ) ) )
!= ( sk1 @ ( sk5 @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) ) )
| ( ( A @ ( C @ ( B @ vQC ) ) @ vsomeQConf )
!= ( E @ vsomeQConf ) )
| ( sk2 @ ( D @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[4694,7982]) ).
thf(8940,plain,
! [E: vQConf,D: vLabel,C: vQMap,B: vAnsMap,A: vQuestionnaire] :
( ( C != sk1 )
| ( B != sk5 )
| ( ( A @ ( vqempty @ vqseq ) )
!= ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle ) )
| ( ( A @ ( C @ ( B @ vQC ) ) )
!= E )
| ( sk2 @ ( D @ sk124 ) ) ),
inference(simp,[status(thm)],[8932]) ).
thf(8950,plain,
! [B: vLabel,A: vQuestionnaire] :
( ( ( A @ ( vqempty @ vqseq ) )
!= ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle ) )
| ( sk2 @ ( B @ sk124 ) ) ),
inference(simp,[status(thm)],[8940]) ).
thf(9352,plain,
! [C: vLabel,B: vQuestionnaire,A: vQuestionnaire] :
( ( vqempty != vqempty )
| ( ( B @ ( A @ vqseq ) )
!= ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle ) )
| ( sk2 @ ( C @ sk124 ) )
| ~ ( A @ visValue ) ),
inference(paramod_ordered,[status(thm)],[1374,8950]) ).
thf(9353,plain,
! [C: vLabel,B: vQuestionnaire,A: vQuestionnaire] :
( ( ( B @ ( A @ vqseq ) )
!= ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle ) )
| ( sk2 @ ( C @ sk124 ) )
| ~ ( A @ visValue ) ),
inference(pattern_uni,[status(thm)],[9352:[]]) ).
thf(210,axiom,
! [A: vQID,B: vATMap,C: vAType,D: vATMap] :
( ( ( ( D @ ( A @ vlookupATMap ) )
= vnoAType )
& ( ( B @ ( A @ vlookupATMap ) )
= ( C @ vsomeAType ) ) )
=> ( B @ ( D @ ( C @ ( A @ vatmbind ) ) @ vMC ) @ ( A @ vask @ vqsingle @ ( B @ ( D @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Task') ).
thf(4695,plain,
! [A: vQID,B: vATMap,C: vAType,D: vATMap] :
( ( ( ( D @ ( A @ vlookupATMap ) )
= vnoAType )
& ( ( B @ ( A @ vlookupATMap ) )
= ( C @ vsomeAType ) ) )
=> ( B @ ( D @ ( C @ ( A @ vatmbind ) ) @ vMC ) @ ( A @ vask @ vqsingle @ ( B @ ( D @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(233,axiom,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vExp,G: vQuestionnaire] :
( ( E @ ( D @ vMC ) @ ( G @ ( B @ ( F @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ? [H: vATMap,I: vATMap] : ( I @ ( H @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqcond_inv2') ).
thf(4795,plain,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vExp,G: vQuestionnaire] :
( ( E @ ( D @ vMC ) @ ( G @ ( B @ ( F @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ? [H: vATMap,I: vATMap] : ( I @ ( H @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(1271,plain,
! [F: vExp,E: vAType,D: vQID,C: vAType,B: vExp,A: vQID] :
( ( D = A )
| ( ( F @ ( C @ ( D @ vvalue ) ) )
!= ( B @ ( E @ ( A @ vvalue ) ) ) ) ),
inference(cnfConj,[status(thm)],[1270]) ).
thf(1274,plain,
! [F: vExp,E: vAType,D: vQID,C: vAType,B: vExp,A: vQID] :
( ( D = A )
| ( ( F @ ( C @ ( D @ vvalue ) ) )
!= ( B @ ( E @ ( A @ vvalue ) ) ) ) ),
inference(lifteq,[status(thm)],[1271]) ).
thf(1275,plain,
? [A: vAType > vExp > vEntry > vQID] :
! [B: vQID,C: vAType,D: vExp] :
( ( D @ ( C @ ( B @ vvalue ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[1274]) ).
thf(1276,plain,
! [C: vExp,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vvalue ) ) @ ( C @ ( B @ sk245 ) ) )
= A ),
inference(cnf,[status(esa)],[1275]) ).
thf(8914,plain,
! [C: vExp,B: vAType,A: vQID] :
( ( C @ ( B @ ( A @ vvalue ) ) @ ( C @ ( B @ sk245 ) ) )
= A ),
inference(lifteq,[status(thm)],[1276]) ).
thf(486,plain,
! [B: vstring,A: vstring] :
( ( A = B )
| ( ( A @ vT )
!= ( B @ vT ) ) ),
inference(cnf,[status(esa)],[485]) ).
thf(487,plain,
! [B: vstring,A: vstring] :
( ( A = B )
| ( ( A @ vT )
!= ( B @ vT ) ) ),
inference(lifteq,[status(thm)],[486]) ).
thf(488,plain,
? [A: vAval > vstring] :
! [B: vstring] :
( ( B @ vT @ A )
= B ),
inference(detectInverse,[status(thm)],[487]) ).
thf(489,plain,
! [A: vstring] :
( ( A @ vT @ sk70 )
= A ),
inference(cnf,[status(esa)],[488]) ).
thf(5083,plain,
! [A: vstring] :
( ( A @ vT @ sk70 )
= A ),
inference(lifteq,[status(thm)],[489]) ).
thf(13133,plain,
! [E: vAnsMap,D: vQID,C: vnat,B: vAnsMap,A: vQID] :
( ( ( B @ ( C @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( E @ vtypeAM ) )
| ( ( B @ vtypeAM @ ( vNumber @ ( A @ vatmbind ) ) @ ( vNumber @ ( D @ vatmbind ) ) )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9428,12863]) ).
thf(13134,plain,
! [C: vAnsMap,B: vQID,A: vQID] :
( ( C @ vtypeAM @ ( vNumber @ ( B @ vatmbind ) ) @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[13133:[bind(A,$thf( F )),bind(B,$thf( H )),bind(C,$thf( I )),bind(D,$thf( D )),bind(E,$thf( H @ ( I @ vNum @ ( F @ vabind ) ) ))]]) ).
thf(13160,plain,
! [C: vAnsMap,B: vQID,A: vQID] :
( ( C @ vtypeAM @ ( vNumber @ ( B @ vatmbind ) ) @ ( vNumber @ ( A @ vatmbind ) ) )
!= vatmempty ),
inference(simp,[status(thm)],[13134]) ).
thf(454,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk61 ) )
| ( ( B @ ( A @ vecheck ) )
= ( A @ ( B @ sk64 ) @ vgetAType @ ( A @ ( B @ sk62 ) @ vcheckUnOp ) ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(465,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk64 ) @ vgetAType @ ( A @ ( B @ sk62 ) @ vcheckUnOp ) )
= ( B @ ( A @ vecheck ) ) ) ),
inference(lifteq,[status(thm)],[454]) ).
thf(4649,plain,
~ ? [A: vQConf] :
( vnoQConf
= ( A @ vsomeQConf ) ),
inference(miniscope,[status(thm)],[4648]) ).
thf(4650,plain,
! [A: vQConf] :
( vnoQConf
!= ( A @ vsomeQConf ) ),
inference(cnf,[status(esa)],[4649]) ).
thf(4651,plain,
! [A: vQConf] :
( ( A @ vsomeQConf )
!= vnoQConf ),
inference(lifteq,[status(thm)],[4650]) ).
thf(229,axiom,
! [A: vQMap,B: vQuestionnaire,C: vExp,D: vAnsMap,E: vQuestionnaire] :
( ( ( D @ ( C @ vreduceExp ) @ visSomeExp )
& ! [F: vQuestionnaire,G: vQuestionnaire] :
( ( E != G )
| ( B != F )
| ( C
!= ( vno @ vB @ vconstant ) ) )
& ! [F: vQuestionnaire,G: vQuestionnaire] :
( ( E != G )
| ( B != F )
| ( C
!= ( vyes @ vB @ vconstant ) ) ) )
=> ( ( A @ ( D @ ( E @ ( B @ ( C @ vqcond ) ) @ vreduce ) ) )
= ( E @ ( B @ ( D @ ( C @ vreduceExp ) @ vgetExp @ vqcond ) ) @ ( A @ ( D @ vQC ) ) @ vsomeQConf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-13') ).
thf(4770,plain,
! [A: vQMap,B: vQuestionnaire,C: vExp,D: vAnsMap,E: vQuestionnaire] :
( ( ( D @ ( C @ vreduceExp ) @ visSomeExp )
& ! [F: vQuestionnaire,G: vQuestionnaire] :
( ( E != G )
| ( B != F )
| ( C
!= ( vno @ vB @ vconstant ) ) )
& ! [F: vQuestionnaire,G: vQuestionnaire] :
( ( E != G )
| ( B != F )
| ( C
!= ( vyes @ vB @ vconstant ) ) ) )
=> ( ( A @ ( D @ ( E @ ( B @ ( C @ vqcond ) ) @ vreduce ) ) )
= ( E @ ( B @ ( D @ ( C @ vreduceExp ) @ vgetExp @ vqcond ) ) @ ( A @ ( D @ vQC ) ) @ vsomeQConf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(55,axiom,
! [A: vATMap,B: vExp,C: vUnOpT] :
( ~ ( B @ ( A @ vecheck ) @ visSomeAType )
=> ( ( B @ ( C @ vunop ) @ ( A @ vecheck ) )
= vnoAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','echeck-7') ).
thf(671,plain,
! [A: vATMap,B: vExp,C: vUnOpT] :
( ~ ( B @ ( A @ vecheck ) @ visSomeAType )
=> ( ( B @ ( C @ vunop ) @ ( A @ vecheck ) )
= vnoAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(222,axiom,
! [A: vQMap,B: vAType,C: vLabel,D: vAnsMap,E: vQID] :
( ( A @ ( D @ ( B @ ( C @ ( E @ vdefquestion ) ) @ vqsingle @ vreduce ) ) )
= ( vqempty @ ( A @ ( B @ ( C @ ( E @ vqmbind ) ) ) @ ( D @ vQC ) ) @ vsomeQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-5') ).
thf(4738,plain,
! [A: vQMap,B: vAType,C: vLabel,D: vAnsMap,E: vQID] :
( ( A @ ( D @ ( B @ ( C @ ( E @ vdefquestion ) ) @ vqsingle @ vreduce ) ) )
= ( vqempty @ ( A @ ( B @ ( C @ ( E @ vqmbind ) ) ) @ ( D @ vQC ) ) @ vsomeQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(134,axiom,
! [A: vQID,B: vLabel,C: vAType,D: vQID] :
( ( C @ ( B @ ( A @ vquestion ) ) )
!= ( D @ vask ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-question-ask') ).
thf(1126,plain,
! [A: vQID,B: vLabel,C: vAType,D: vQID] :
( ( C @ ( B @ ( A @ vquestion ) ) )
!= ( D @ vask ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(9599,plain,
! [E: vATMap,D: vAType,C: vQID,B: vstring,A: vQID] :
( ( ( vatmempty @ ( vText @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9477,1229]) ).
thf(9600,plain,
! [B: vstring,A: vQID] :
( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM )
!= vatmempty ),
inference(pattern_uni,[status(thm)],[9599:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( vText )),bind(E,$thf( vatmempty ))]]) ).
thf(9637,plain,
! [B: vstring,A: vQID] :
( ( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) )
| ( vatmempty != vatmempty ) ),
inference(paramod_ordered,[status(thm)],[4862,9600]) ).
thf(9638,plain,
! [B: vstring,A: vQID] :
( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) ),
inference(simp,[status(thm)],[9637]) ).
thf(9647,plain,
! [B: vstring,A: vQID] :
( ( vaempty @ ( B @ vT @ ( A @ vabind ) ) )
!= vaempty ),
inference(simp,[status(thm)],[9638]) ).
thf(619,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( D = A )
| ( ( C @ ( F @ ( D @ vsomeQuestion ) ) )
!= ( E @ ( B @ ( A @ vsomeQuestion ) ) ) ) ),
inference(cnfConj,[status(thm)],[618]) ).
thf(622,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( D = A )
| ( ( C @ ( F @ ( D @ vsomeQuestion ) ) )
!= ( E @ ( B @ ( A @ vsomeQuestion ) ) ) ) ),
inference(lifteq,[status(thm)],[619]) ).
thf(623,plain,
? [A: vLabel > vAType > vOptQuestion > vQID] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vsomeQuestion ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[622]) ).
thf(624,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ ( C @ ( B @ sk129 ) ) )
= A ),
inference(cnf,[status(esa)],[623]) ).
thf(6846,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ ( C @ ( B @ sk129 ) ) )
= A ),
inference(lifteq,[status(thm)],[624]) ).
thf(211,axiom,
! [A: vQuestionnaire,B: vQuestionnaire,C: vAnsMap,D: vQMap] :
( ( ( D @ ( C @ ( A @ vreduce ) ) @ visSomeQC )
& ! [E: vQuestionnaire] :
( ( B != E )
| ( A != vqempty ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ vqseq ) @ vreduce ) ) )
= ( B @ ( D @ ( C @ ( A @ vreduce ) ) @ vgetQC @ vqcappend ) @ vsomeQConf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-9') ).
thf(4698,plain,
! [A: vQuestionnaire,B: vQuestionnaire,C: vAnsMap,D: vQMap] :
( ( ( D @ ( C @ ( A @ vreduce ) ) @ visSomeQC )
& ! [E: vQuestionnaire] :
( ( B != E )
| ( A != vqempty ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ vqseq ) @ vreduce ) ) )
= ( B @ ( D @ ( C @ ( A @ vreduce ) ) @ vgetQC @ vqcappend ) @ vsomeQConf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1027,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C = E )
| ( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vquestion ) ) ) ) ),
inference(cnfConj,[status(thm)],[1024]) ).
thf(1034,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C = E )
| ( ( C @ ( F @ ( D @ vquestion ) ) )
!= ( E @ ( B @ ( A @ vquestion ) ) ) ) ),
inference(lifteq,[status(thm)],[1027]) ).
thf(1035,plain,
? [A: vQID > vLabel > vEntry > vAType] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vquestion ) ) @ ( C @ ( B @ A ) ) )
= D ),
inference(detectInverse,[status(thm)],[1034]) ).
thf(1036,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vquestion ) ) @ ( B @ ( A @ sk205 ) ) )
= C ),
inference(cnf,[status(esa)],[1035]) ).
thf(6938,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vquestion ) ) @ ( B @ ( A @ sk205 ) ) )
= C ),
inference(lifteq,[status(thm)],[1036]) ).
thf(147,axiom,
! [A: vQID,B: vAval,C: vAnsMap,D: vAnsMap] :
( ( D @ ( C @ ( B @ ( A @ vabind ) ) @ vappendAnsMap ) )
= ( D @ ( C @ vappendAnsMap ) @ ( B @ ( A @ vabind ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','appendAnsMap-1') ).
thf(1189,plain,
! [A: vQID,B: vAval,C: vAnsMap,D: vAnsMap] :
( ( D @ ( C @ ( B @ ( A @ vabind ) ) @ vappendAnsMap ) )
= ( D @ ( C @ vappendAnsMap ) @ ( B @ ( A @ vabind ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(636,plain,
! [F: vBinOpT,E: vBinOpT,D: vExp,C: vExp,B: vExp,A: vExp] :
( ( D = C )
| ( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( B @ ( F @ ( C @ vbinop ) ) ) ) ),
inference(cnfConj,[status(thm)],[635]) ).
thf(639,plain,
! [F: vBinOpT,E: vBinOpT,D: vExp,C: vExp,B: vExp,A: vExp] :
( ( D = C )
| ( ( A @ ( E @ ( D @ vbinop ) ) )
!= ( B @ ( F @ ( C @ vbinop ) ) ) ) ),
inference(lifteq,[status(thm)],[636]) ).
thf(640,plain,
? [A: vBinOpT > vExp > vExp > vExp] :
! [B: vExp,C: vBinOpT,D: vExp] :
( ( D @ ( C @ ( B @ vbinop ) ) @ ( D @ ( C @ A ) ) )
= B ),
inference(detectInverse,[status(thm)],[639]) ).
thf(641,plain,
! [C: vExp,B: vBinOpT,A: vExp] :
( ( C @ ( B @ ( A @ vbinop ) ) @ ( C @ ( B @ sk132 ) ) )
= A ),
inference(cnf,[status(esa)],[640]) ).
thf(6867,plain,
! [C: vExp,B: vBinOpT,A: vExp] :
( ( C @ ( B @ ( A @ vbinop ) ) @ ( C @ ( B @ sk132 ) ) )
= A ),
inference(lifteq,[status(thm)],[641]) ).
thf(170,axiom,
! [A: vQMap,B: vAType,C: vLabel,D: vAnsMap,E: vQID] :
( ( A @ ( D @ ( B @ ( C @ ( E @ vquestion ) ) @ vqsingle @ vreduce ) ) )
= ( vqempty @ ( A @ ( D @ ( B @ ( C @ vgetAnswer ) @ ( E @ vabind ) ) @ vQC ) ) @ vsomeQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-1') ).
thf(1326,plain,
! [A: vQMap,B: vAType,C: vLabel,D: vAnsMap,E: vQID] :
( ( A @ ( D @ ( B @ ( C @ ( E @ vquestion ) ) @ vqsingle @ vreduce ) ) )
= ( vqempty @ ( A @ ( D @ ( B @ ( C @ vgetAnswer ) @ ( E @ vabind ) ) @ vQC ) ) @ vsomeQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(63,axiom,
! [A: vYN] :
( ( A @ vB @ ( vnotop @ vevalUnOp ) )
= ( A @ vnot @ vB @ vconstant @ vsomeExp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','evalUnOp-0') ).
thf(699,plain,
! [A: vYN] :
( ( A @ vB @ ( vnotop @ vevalUnOp ) )
= ( A @ vnot @ vB @ vconstant @ vsomeExp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(963,plain,
~ ( vnoQuestion @ visSomeQuestion ),
inference(polarity_switch,[status(thm)],[962]) ).
thf(7156,plain,
! [E: vnat,D: vYN,C: vUnOpT,B: vAval,A: vUnOpT] :
( ( ( A @ ( B @ sk34 ) )
!= ( C @ ( E @ vNum @ sk34 ) ) )
| ( B
!= ( D @ vB ) )
| ~ ( B @ ( A @ sk31 ) ) ),
inference(paramod_ordered,[status(thm)],[401,7072]) ).
thf(7157,plain,
! [C: vnat,B: vYN,A: vUnOpT] :
( ( ( C @ vNum )
!= ( B @ vB ) )
| ~ ( C @ vNum @ ( A @ sk31 ) ) ),
inference(pattern_uni,[status(thm)],[7156:[bind(A,$thf( A )),bind(B,$thf( F @ vNum )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( F ))]]) ).
thf(7162,plain,
! [C: vnat,B: vYN,A: vUnOpT] :
( ( ( C @ vNum )
!= ( B @ vB ) )
| ~ ( C @ vNum @ ( A @ sk31 ) ) ),
inference(simp,[status(thm)],[7157]) ).
thf(7358,plain,
! [B: vnat,A: vYN] :
( ( ( B @ vNum )
!= ( A @ vB ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7162,7020]) ).
thf(7359,plain,
! [B: vnat,A: vYN] :
( ( B @ vNum )
!= ( A @ vB ) ),
inference(simp,[status(thm)],[7358]) ).
thf(232,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vATMap,F: vQID,G: vExp] :
( ( C @ ( E @ vMC ) @ ( G @ ( D @ ( F @ vvalue ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( E
= ( B @ ( D @ ( F @ vatmbind ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tvalue_inv3') ).
thf(4791,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vAType,E: vATMap,F: vQID,G: vExp] :
( ( C @ ( E @ vMC ) @ ( G @ ( D @ ( F @ vvalue ) ) @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( E
= ( B @ ( D @ ( F @ vatmbind ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(212,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vQuestionnaire,E: vATMap,F: vATMap,G: vATMap,H: vATMap,I: vATMap,J: vQuestionnaire] :
( ( ( C @ ( B @ vMC ) @ ( J @ ( F @ ( H @ vMC ) @ vptcheck ) ) )
& ( F @ ( H @ vMC ) @ ( D @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( I @ ( G @ vMC ) @ ( J @ ( D @ vqseq ) @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) )
=> ( I = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqseq_inv4') ).
thf(4705,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vQuestionnaire,E: vATMap,F: vATMap,G: vATMap,H: vATMap,I: vATMap,J: vQuestionnaire] :
( ( ( C @ ( B @ vMC ) @ ( J @ ( F @ ( H @ vMC ) @ vptcheck ) ) )
& ( F @ ( H @ vMC ) @ ( D @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( I @ ( G @ vMC ) @ ( J @ ( D @ vqseq ) @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) )
=> ( I = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(960,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ vgetQuestionAType )
= C ),
inference(cnf,[status(esa)],[959]) ).
thf(961,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vsomeQuestion ) ) @ vgetQuestionAType )
= C ),
inference(lifteq,[status(thm)],[960]) ).
thf(82,axiom,
! [A: vQID,B: vLabel,C: vAType,D: vQMap] :
( ( D @ ( C @ ( B @ ( A @ vqmbind ) ) ) @ ( A @ vlookupQMap ) )
= ( C @ ( B @ ( A @ vsomeQuestion ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookupQMap-1') ).
thf(813,plain,
! [A: vQID,B: vLabel,C: vAType,D: vQMap] :
( ( D @ ( C @ ( B @ ( A @ vqmbind ) ) ) @ ( A @ vlookupQMap ) )
= ( C @ ( B @ ( A @ vsomeQuestion ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(188,axiom,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vGID,F: vATMap] :
( ( D @ ( F @ vMC ) @ ( B @ ( E @ vqgroup ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ( D @ ( F @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqgroup_inv') ).
thf(1385,plain,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vGID,F: vATMap] :
( ( D @ ( F @ vMC ) @ ( B @ ( E @ vqgroup ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ( D @ ( F @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(5723,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( sk4 @ ( sk3 @ vMC ) ) )
| ( ( B @ sk254 )
!= ( sk1 @ vtypeQM ) )
| ( ( B @ sk253 )
!= ( sk5 @ vtypeAM ) )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( B @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,5693]) ).
thf(5724,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 )
!= sk4 )
| ( ( A @ sk253 )
!= sk3 )
| ( ( B @ sk254 )
!= ( sk1 @ vtypeQM ) )
| ( ( B @ sk253 )
!= ( sk5 @ vtypeAM ) )
| ( A @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( B @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5723]) ).
thf(9464,plain,
! [E: vATMap,D: vAType,C: vQID,B: vAval,A: vQID] :
( ( ( vatmempty @ ( B @ vtypeOf @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ ( E @ ( C @ sk223 ) ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[9403,8148]) ).
thf(9465,plain,
! [B: vAval,A: vQID] :
( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ ( vatmempty @ ( A @ sk223 ) ) )
= ( B @ vtypeOf ) ),
inference(pattern_uni,[status(thm)],[9464:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( A )),bind(D,$thf( F @ vtypeOf )),bind(E,$thf( vatmempty ))]]) ).
thf(9482,plain,
! [B: vAval,A: vQID] :
( ( vaempty @ ( B @ ( A @ vabind ) ) @ vtypeAM @ ( vatmempty @ ( A @ sk223 ) ) )
= ( B @ vtypeOf ) ),
inference(simp,[status(thm)],[9465]) ).
thf(258,plain,
( ( vYesNo @ ( vYesNo @ ( vorop @ vcheckBinOp ) ) )
= ( vYesNo @ vsomeAType ) ),
inference(lifteq,[status(thm)],[257]) ).
thf(50,axiom,
! [A: vQID,B: vATMap,C: vAType,D: vATMap] :
( ( ( ( B @ ( A @ vlookupATMap ) @ vgetAType )
= C )
& ( B @ ( A @ vlookupATMap ) @ visSomeAType ) )
=> ( ( B @ ( D @ ( C @ ( A @ vatmbind ) ) @ vintersectATM ) )
= ( B @ ( D @ vintersectATM ) @ ( C @ ( A @ vatmbind ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersectATM-1') ).
thf(652,plain,
! [A: vQID,B: vATMap,C: vAType,D: vATMap] :
( ( ( ( B @ ( A @ vlookupATMap ) @ vgetAType )
= C )
& ( B @ ( A @ vlookupATMap ) @ visSomeAType ) )
=> ( ( B @ ( D @ ( C @ ( A @ vatmbind ) ) @ vintersectATM ) )
= ( B @ ( D @ vintersectATM ) @ ( C @ ( A @ vatmbind ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(8569,plain,
! [D: vExp,C: vATMap,B: vstring,A: vATMap] :
( ( ( B @ vT @ vconstant @ ( A @ vecheck ) )
!= ( C @ ( D @ sk67 ) @ ( C @ ( D @ sk69 ) @ vecheck ) ) )
| ~ ( vText @ vsomeAType @ visSomeAType )
| ~ ( C @ ( D @ sk61 ) )
| ~ ( C @ ( D @ sk54 ) )
| ~ ( C @ ( D @ sk47 ) )
| ~ ( C @ ( D @ sk44 ) )
| ~ ( D @ ( C @ sk41 ) )
| ~ ( D @ ( C @ sk38 ) )
| ~ ( D @ ( C @ sk35 ) ) ),
inference(paramod_ordered,[status(thm)],[1039,8488]) ).
thf(8586,plain,
! [D: vExp,C: vATMap,B: vstring,A: vATMap] :
( ( ( B @ vT @ vconstant )
!= ( C @ ( D @ sk67 ) ) )
| ( A
!= ( C @ ( D @ sk69 ) ) )
| ~ ( vText @ vsomeAType @ visSomeAType )
| ~ ( C @ ( D @ sk61 ) )
| ~ ( C @ ( D @ sk54 ) )
| ~ ( C @ ( D @ sk47 ) )
| ~ ( C @ ( D @ sk44 ) )
| ~ ( D @ ( C @ sk41 ) )
| ~ ( D @ ( C @ sk38 ) )
| ~ ( D @ ( C @ sk35 ) ) ),
inference(simp,[status(thm)],[8569]) ).
thf(8598,plain,
! [C: vExp,B: vATMap,A: vstring] :
( ( ( A @ vT @ vconstant )
!= ( B @ ( C @ sk67 ) ) )
| ~ ( vText @ vsomeAType @ visSomeAType )
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(simp,[status(thm)],[8586]) ).
thf(8715,plain,
! [C: vExp,B: vATMap,A: vstring] :
( ( ( A @ vT @ vconstant )
!= ( B @ ( C @ sk67 ) ) )
| ~ $true
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(rewrite,[status(thm)],[8598,670]) ).
thf(8716,plain,
! [C: vExp,B: vATMap,A: vstring] :
( ( ( A @ vT @ vconstant )
!= ( B @ ( C @ sk67 ) ) )
| ~ ( B @ ( C @ sk61 ) )
| ~ ( B @ ( C @ sk54 ) )
| ~ ( B @ ( C @ sk47 ) )
| ~ ( B @ ( C @ sk44 ) )
| ~ ( C @ ( B @ sk41 ) )
| ~ ( C @ ( B @ sk38 ) )
| ~ ( C @ ( B @ sk35 ) ) ),
inference(simp,[status(thm)],[8715]) ).
thf(779,plain,
~ ? [A: vQID,B: vLabel,C: vAType,D: vQID] :
( ( C @ ( B @ ( A @ vdefquestion ) ) )
= ( D @ vask ) ),
inference(miniscope,[status(thm)],[778]) ).
thf(780,plain,
! [D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vdefquestion ) ) )
!= ( D @ vask ) ),
inference(cnf,[status(esa)],[779]) ).
thf(781,plain,
! [D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vdefquestion ) ) )
!= ( D @ vask ) ),
inference(lifteq,[status(thm)],[780]) ).
thf(7395,plain,
! [D: vAval,C: vUnOpT,B: vUnOpT,A: vstring] :
( ( ( A @ vT @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ~ $true
| ( ( C @ ( D @ sk33 ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[7013,405]) ).
thf(7396,plain,
! [D: vAval,C: vUnOpT,B: vUnOpT,A: vstring] :
( ( ( A @ vT @ ( B @ sk31 ) )
!= ( D @ ( C @ sk31 ) ) )
| ( ( C @ ( D @ sk33 ) )
= C ) ),
inference(simp,[status(thm)],[7395]) ).
thf(7397,plain,
! [B: vstring,A: vUnOpT] :
( ( A @ ( B @ vT @ sk33 ) )
= A ),
inference(pattern_uni,[status(thm)],[7396:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ vT ))]]) ).
thf(7399,plain,
! [B: vstring,A: vUnOpT] :
( ( A @ ( B @ vT @ sk33 ) )
= A ),
inference(simp,[status(thm)],[7397]) ).
thf(5526,plain,
! [C: vnat,B: vYN,A: vAval] :
( ( ( A @ sk15 @ vB )
!= ( B @ vB ) )
| ( A
!= ( C @ vNum ) )
| ( A @ sk14 ) ),
inference(paramod_ordered,[status(thm)],[314,385]) ).
thf(5527,plain,
! [B: vAval,A: vnat] :
( ( B
!= ( A @ vNum ) )
| ( B @ sk14 ) ),
inference(pattern_uni,[status(thm)],[5526:[bind(A,$thf( D )),bind(B,$thf( D @ sk15 ))]]) ).
thf(5549,plain,
! [A: vnat] : ( A @ vNum @ sk14 ),
inference(simp,[status(thm)],[5527]) ).
thf(8943,plain,
! [D: vQConf,C: vQMap,B: vAnsMap,A: vQuestionnaire] :
( ( C != sk1 )
| ( B != sk5 )
| ( ( A @ ( vqempty @ vqseq ) )
!= ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle ) )
| ( ( A @ ( C @ ( B @ vQC ) ) )
!= D ) ),
inference(simp,[status(thm)],[8922]) ).
thf(8953,plain,
! [A: vQuestionnaire] :
( ( A @ ( vqempty @ vqseq ) )
!= ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle ) ),
inference(simp,[status(thm)],[8943]) ).
thf(344,plain,
~ ? [A: vExp] :
( vnoExp
= ( A @ vsomeExp ) ),
inference(miniscope,[status(thm)],[343]) ).
thf(345,plain,
! [A: vExp] :
( vnoExp
!= ( A @ vsomeExp ) ),
inference(cnf,[status(esa)],[344]) ).
thf(346,plain,
! [A: vExp] :
( ( A @ vsomeExp )
!= vnoExp ),
inference(lifteq,[status(thm)],[345]) ).
thf(208,axiom,
! [A: vEntry,B: vEntry] :
( ( ( A @ vqsingle )
= ( B @ vqsingle ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-qsingle') ).
thf(4687,plain,
! [A: vEntry,B: vEntry] :
( ( ( A @ vqsingle )
= ( B @ vqsingle ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(4688,plain,
! [B: vEntry,A: vEntry] :
( ( A = B )
| ( ( A @ vqsingle )
!= ( B @ vqsingle ) ) ),
inference(cnf,[status(esa)],[4687]) ).
thf(4689,plain,
! [B: vEntry,A: vEntry] :
( ( A = B )
| ( ( A @ vqsingle )
!= ( B @ vqsingle ) ) ),
inference(lifteq,[status(thm)],[4688]) ).
thf(4690,plain,
? [A: vQuestionnaire > vEntry] :
! [B: vEntry] :
( ( B @ vqsingle @ A )
= B ),
inference(detectInverse,[status(thm)],[4689]) ).
thf(4691,plain,
! [A: vEntry] :
( ( A @ vqsingle @ sk363 )
= A ),
inference(cnf,[status(esa)],[4690]) ).
thf(5196,plain,
! [A: vEntry] :
( ( A @ vqsingle @ sk363 )
= A ),
inference(lifteq,[status(thm)],[4691]) ).
thf(1206,plain,
! [F: vExp,E: vQuestionnaire,D: vQuestionnaire,C: vExp,B: vQuestionnaire,A: vQuestionnaire] :
( ( D = B )
| ( ( D @ ( E @ ( F @ vqcond ) ) )
!= ( B @ ( A @ ( C @ vqcond ) ) ) ) ),
inference(cnfConj,[status(thm)],[1203]) ).
thf(1213,plain,
! [F: vExp,E: vQuestionnaire,D: vQuestionnaire,C: vExp,B: vQuestionnaire,A: vQuestionnaire] :
( ( D = B )
| ( ( D @ ( E @ ( F @ vqcond ) ) )
!= ( B @ ( A @ ( C @ vqcond ) ) ) ) ),
inference(lifteq,[status(thm)],[1206]) ).
thf(1214,plain,
? [A: vExp > vQuestionnaire > vQuestionnaire > vQuestionnaire] :
! [B: vExp,C: vQuestionnaire,D: vQuestionnaire] :
( ( D @ ( C @ ( B @ vqcond ) ) @ ( C @ ( B @ A ) ) )
= D ),
inference(detectInverse,[status(thm)],[1213]) ).
thf(1215,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vExp] :
( ( C @ ( B @ ( A @ vqcond ) ) @ ( B @ ( A @ sk232 ) ) )
= C ),
inference(cnf,[status(esa)],[1214]) ).
thf(8520,plain,
! [C: vQuestionnaire,B: vQuestionnaire,A: vExp] :
( ( C @ ( B @ ( A @ vqcond ) ) @ ( B @ ( A @ sk232 ) ) )
= C ),
inference(lifteq,[status(thm)],[1215]) ).
thf(193,axiom,
! [A: vQuestionnaire,B: vQuestionnaire,C: vAnsMap,D: vQMap] :
( ( ~ ( D @ ( C @ ( A @ vreduce ) ) @ visSomeQC )
& ! [E: vQuestionnaire] :
( ( B != E )
| ( A != vqempty ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ vqseq ) @ vreduce ) ) )
= vnoQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-10') ).
thf(4619,plain,
! [A: vQuestionnaire,B: vQuestionnaire,C: vAnsMap,D: vQMap] :
( ( ~ ( D @ ( C @ ( A @ vreduce ) ) @ visSomeQC )
& ! [E: vQuestionnaire] :
( ( B != E )
| ( A != vqempty ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ vqseq ) @ vreduce ) ) )
= vnoQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(376,plain,
! [D: vBinOpT,C: vExp,B: vExp,A: vATMap] :
( ( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= vnoAType )
| ( C @ ( A @ vecheck ) @ visSomeAType ) ),
inference(cnfConj,[status(thm)],[374]) ).
thf(378,plain,
! [D: vBinOpT,C: vExp,B: vExp,A: vATMap] :
( ( C @ ( A @ vecheck ) @ visSomeAType )
| ( ( C @ ( D @ ( B @ vbinop ) ) @ ( A @ vecheck ) )
= vnoAType ) ),
inference(lifteq,[status(thm)],[376]) ).
thf(75,axiom,
! [A: vATMap,B: vATMap] :
( ? [C: vQID,D: vAType,E: vATMap,F: vATMap] :
( ( ( B @ ( A @ vappendATMap ) )
= ( F @ ( E @ vappendATMap ) @ ( D @ ( C @ vatmbind ) ) ) )
& ( B = F )
& ( A
= ( E @ ( D @ ( C @ vatmbind ) ) ) ) )
| ? [C: vATMap] :
( ( ( B @ ( A @ vappendATMap ) )
= C )
& ( B = C )
& ( A = vatmempty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','appendATMap-INV') ).
thf(763,plain,
! [A: vATMap,B: vATMap] :
( ? [C: vQID,D: vAType,E: vATMap,F: vATMap] :
( ( ( B @ ( A @ vappendATMap ) )
= ( F @ ( E @ vappendATMap ) @ ( D @ ( C @ vatmbind ) ) ) )
& ( B = F )
& ( A
= ( E @ ( D @ ( C @ vatmbind ) ) ) ) )
| ? [C: vATMap] :
( ( ( B @ ( A @ vappendATMap ) )
= C )
& ( B = C )
& ( A = vatmempty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(271,plain,
veqop != vandop,
inference(polarity_switch,[status(thm)],[270]) ).
thf(272,plain,
veqop != vandop,
inference(lifteq,[status(thm)],[271]) ).
thf(1161,plain,
! [C: vAType,B: vLabel,A: vQID] : ( C @ ( B @ ( A @ vsomeQuestion ) ) @ visSomeQuestion ),
inference(cnf,[status(esa)],[1160]) ).
thf(7148,plain,
! [E: vnat,D: vYN,C: vUnOpT,B: vAval,A: vUnOpT] :
( ( ( A @ ( B @ sk32 ) @ vB )
!= ( D @ vB ) )
| ( B
!= ( C @ ( E @ vNum @ sk34 ) ) )
| ( B @ ( A @ sk31 ) ) ),
inference(paramod_ordered,[status(thm)],[403,7072]) ).
thf(7149,plain,
! [D: vUnOpT,C: vAval,B: vnat,A: vUnOpT] :
( ( C
!= ( A @ ( B @ vNum @ sk34 ) ) )
| ( C @ ( D @ sk31 ) ) ),
inference(pattern_uni,[status(thm)],[7148:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G @ ( F @ sk32 ) ))]]) ).
thf(7166,plain,
! [C: vUnOpT,B: vnat,A: vUnOpT] : ( A @ ( B @ vNum @ sk34 ) @ ( C @ sk31 ) ),
inference(simp,[status(thm)],[7149]) ).
thf(7542,plain,
! [B: vUnOpT,A: vnat] : ( A @ vNum @ ( B @ sk31 ) ),
inference(rewrite,[status(thm)],[7166,7075]) ).
thf(309,plain,
! [A: vAval] :
( ( ( A @ vtypeOf )
= vText )
| ( A
= ( A @ sk16 @ vNum ) )
| ~ ( A @ sk14 ) ),
inference(cnfConj,[status(thm)],[303]) ).
thf(315,plain,
! [A: vAval] :
( ~ ( A @ sk14 )
| ( ( A @ vtypeOf )
= vText )
| ( ( A @ sk16 @ vNum )
= A ) ),
inference(lifteq,[status(thm)],[309]) ).
thf(12125,plain,
! [D: vAval,C: vQID,B: vnat,A: vQID] :
( ( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ ( D @ ( C @ vabind ) ) @ vtypeAM ) )
| ( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) @ ( vatmempty @ ( D @ vtypeOf @ sk222 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[9478,9484]) ).
thf(12126,plain,
! [B: vnat,A: vQID] :
( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) @ ( vatmempty @ ( B @ vNum @ vtypeOf @ sk222 ) ) )
= A ),
inference(pattern_uni,[status(thm)],[12125:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vNum ))]]) ).
thf(12158,plain,
! [B: vnat,A: vQID] :
( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) @ ( vatmempty @ ( B @ vNum @ vtypeOf @ sk222 ) ) )
= A ),
inference(simp,[status(thm)],[12126]) ).
thf(12267,plain,
! [A: vQID] :
( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) @ ( vatmempty @ ( vNumber @ sk222 ) ) )
= A ),
inference(rewrite,[status(thm)],[12158,388]) ).
thf(10040,plain,
! [E: vATMap,D: vAType,C: vQID,B: vYN,A: vQID] :
( ( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM @ ( E @ ( D @ sk222 ) ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[9480,8147]) ).
thf(10041,plain,
! [B: vYN,A: vQID] :
( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM @ ( vatmempty @ ( vYesNo @ sk222 ) ) )
= A ),
inference(pattern_uni,[status(thm)],[10040:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( vYesNo )),bind(E,$thf( vatmempty ))]]) ).
thf(1393,plain,
~ ? [A: vQID,B: vAType,C: vQID,D: vAType,E: vExp,F: vLabel] :
( ( E @ ( B @ ( C @ vvalue ) ) )
= ( D @ ( F @ ( A @ vdefquestion ) ) ) ),
inference(miniscope,[status(thm)],[1392]) ).
thf(1394,plain,
! [F: vLabel,E: vExp,D: vAType,C: vQID,B: vAType,A: vQID] :
( ( E @ ( B @ ( C @ vvalue ) ) )
!= ( D @ ( F @ ( A @ vdefquestion ) ) ) ),
inference(cnf,[status(esa)],[1393]) ).
thf(1395,plain,
! [F: vLabel,E: vExp,D: vAType,C: vQID,B: vAType,A: vQID] :
( ( E @ ( B @ ( C @ vvalue ) ) )
!= ( D @ ( F @ ( A @ vdefquestion ) ) ) ),
inference(lifteq,[status(thm)],[1394]) ).
thf(817,plain,
! [B: vAnsMap,A: vAval] :
( ( B @ ( A @ vconstant @ vreduceExp ) )
= vnoExp ),
inference(cnf,[status(esa)],[816]) ).
thf(818,plain,
! [B: vAnsMap,A: vAval] :
( ( B @ ( A @ vconstant @ vreduceExp ) )
= vnoExp ),
inference(lifteq,[status(thm)],[817]) ).
thf(216,axiom,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vExp,G: vQuestionnaire] :
( ( E @ ( D @ vMC ) @ ( G @ ( B @ ( F @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ? [H: vATMap,I: vATMap] : ( I @ ( H @ vMC ) @ ( G @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqcond_inv3') ).
thf(4719,plain,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vExp,G: vQuestionnaire] :
( ( E @ ( D @ vMC ) @ ( G @ ( B @ ( F @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
=> ? [H: vATMap,I: vATMap] : ( I @ ( H @ vMC ) @ ( G @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(13282,plain,
! [C: vAnsMap,B: vnat,A: vQID] :
( ( ( C @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) )
| ( vatmempty != vatmempty ) ),
inference(paramod_ordered,[status(thm)],[4862,12964]) ).
thf(13283,plain,
! [C: vAnsMap,B: vnat,A: vQID] :
( ( C @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) ),
inference(simp,[status(thm)],[13282]) ).
thf(13294,plain,
! [C: vAnsMap,B: vnat,A: vQID] :
( ( C @ ( B @ vNum @ ( A @ vabind ) ) )
!= vaempty ),
inference(simp,[status(thm)],[13283]) ).
thf(7028,plain,
! [D: vYN,C: vUnOpT,B: vUnOpT,A: vstring] :
( ( ( A @ vT @ ( B @ sk31 ) )
!= ( D @ vB @ ( C @ sk31 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7013,6939]) ).
thf(7029,plain,
! [D: vYN,C: vUnOpT,B: vUnOpT,A: vstring] :
( ( A @ vT @ ( B @ sk31 ) )
!= ( D @ vB @ ( C @ sk31 ) ) ),
inference(simp,[status(thm)],[7028]) ).
thf(7045,plain,
! [D: vYN,C: vUnOpT,B: vUnOpT,A: vstring] :
( ( ( A @ vT )
!= ( D @ vB ) )
| ( B != C ) ),
inference(simp,[status(thm)],[7029]) ).
thf(7048,plain,
! [B: vYN,A: vstring] :
( ( A @ vT )
!= ( B @ vB ) ),
inference(simp,[status(thm)],[7045]) ).
thf(299,plain,
! [A: vOptQuestion] :
( ( A
= ( A @ sk13 @ ( A @ sk12 @ ( A @ sk11 @ vsomeQuestion ) ) ) )
| ( A = vnoQuestion ) ),
inference(cnf,[status(esa)],[298]) ).
thf(300,plain,
! [A: vOptQuestion] :
( ( ( A @ sk13 @ ( A @ sk12 @ ( A @ sk11 @ vsomeQuestion ) ) )
= A )
| ( A = vnoQuestion ) ),
inference(lifteq,[status(thm)],[299]) ).
thf(1071,plain,
! [B: vAval,A: vAval] :
( ( A = B )
| ( ( A @ vconstant )
!= ( B @ vconstant ) ) ),
inference(cnf,[status(esa)],[1070]) ).
thf(1072,plain,
! [B: vAval,A: vAval] :
( ( A = B )
| ( ( A @ vconstant )
!= ( B @ vconstant ) ) ),
inference(lifteq,[status(thm)],[1071]) ).
thf(1073,plain,
? [A: vExp > vAval] :
! [B: vAval] :
( ( B @ vconstant @ A )
= B ),
inference(detectInverse,[status(thm)],[1072]) ).
thf(1074,plain,
! [A: vAval] :
( ( A @ vconstant @ sk207 )
= A ),
inference(cnf,[status(esa)],[1073]) ).
thf(5129,plain,
! [A: vAval] :
( ( A @ vconstant @ sk207 )
= A ),
inference(lifteq,[status(thm)],[1074]) ).
thf(852,plain,
! [A: vQID,B: vATMap] :
( ? [C: vQID,D: vAType,E: vATMap,F: vQID] :
( ( ( B @ ( A @ vlookupATMap ) )
= ( E @ ( F @ vlookupATMap ) ) )
& ( B
= ( E @ ( D @ ( C @ vatmbind ) ) ) )
& ( A = F )
& ( F != C ) )
| ? [C: vQID,D: vAType,E: vATMap,F: vQID] :
( ( ( B @ ( A @ vlookupATMap ) )
= ( D @ vsomeAType ) )
& ( B
= ( E @ ( D @ ( C @ vatmbind ) ) ) )
& ( A = F )
& ( F = C ) )
| ( ( ( B @ ( A @ vlookupATMap ) )
= vnoAType )
& ( B = vatmempty )
& ? [C: vQID] : ( A = C ) ) ),
inference(miniscope,[status(thm)],[851]) ).
thf(853,plain,
! [B: vATMap,A: vQID] :
( ( ( ( B @ ( A @ vlookupATMap ) )
= ( A @ ( B @ sk166 ) @ ( A @ ( B @ sk167 ) @ vlookupATMap ) ) )
| ~ ( A @ ( B @ sk159 ) )
| ~ ( A @ ( B @ sk157 ) ) )
& ( ( B
= ( A @ ( B @ sk166 ) @ ( A @ ( B @ sk165 ) @ ( A @ ( B @ sk164 ) @ vatmbind ) ) ) )
| ~ ( A @ ( B @ sk159 ) )
| ~ ( A @ ( B @ sk157 ) ) )
& ( ( A
= ( A @ ( B @ sk167 ) ) )
| ~ ( A @ ( B @ sk159 ) )
| ~ ( A @ ( B @ sk157 ) ) )
& ( ( ( A @ ( B @ sk167 ) )
!= ( A @ ( B @ sk164 ) ) )
| ~ ( A @ ( B @ sk159 ) )
| ~ ( A @ ( B @ sk157 ) ) )
& ( ( A @ ( B @ sk159 ) )
| ( ( B @ ( A @ vlookupATMap ) )
= ( A @ ( B @ sk161 ) @ vsomeAType ) )
| ~ ( A @ ( B @ sk157 ) ) )
& ( ( A @ ( B @ sk159 ) )
| ( B
= ( A @ ( B @ sk162 ) @ ( A @ ( B @ sk161 ) @ ( A @ ( B @ sk160 ) @ vatmbind ) ) ) )
| ~ ( A @ ( B @ sk157 ) ) )
& ( ( A @ ( B @ sk159 ) )
| ( A
= ( A @ ( B @ sk163 ) ) )
| ~ ( A @ ( B @ sk157 ) ) )
& ( ( A @ ( B @ sk159 ) )
| ( ( A @ ( B @ sk163 ) )
= ( A @ ( B @ sk160 ) ) )
| ~ ( A @ ( B @ sk157 ) ) )
& ( ( A @ ( B @ sk157 ) )
| ( ( B @ ( A @ vlookupATMap ) )
= vnoAType ) )
& ( ( A @ ( B @ sk157 ) )
| ( B = vatmempty ) )
& ( ( A @ ( B @ sk157 ) )
| ( A
= ( A @ ( B @ sk158 ) ) ) ) ),
inference(cnf,[status(esa)],[852]) ).
thf(857,plain,
! [B: vATMap,A: vQID] :
( ( ( A @ ( B @ sk167 ) )
!= ( A @ ( B @ sk164 ) ) )
| ~ ( A @ ( B @ sk159 ) )
| ~ ( A @ ( B @ sk157 ) ) ),
inference(cnfConj,[status(thm)],[853]) ).
thf(867,plain,
! [B: vATMap,A: vQID] :
( ~ ( A @ ( B @ sk159 ) )
| ~ ( A @ ( B @ sk157 ) )
| ( ( A @ ( B @ sk167 ) )
!= ( A @ ( B @ sk164 ) ) ) ),
inference(lifteq,[status(thm)],[857]) ).
thf(700,plain,
! [A: vYN] :
( ( A @ vB @ ( vnotop @ vevalUnOp ) )
= ( A @ vnot @ vB @ vconstant @ vsomeExp ) ),
inference(cnf,[status(esa)],[699]) ).
thf(701,plain,
! [A: vYN] :
( ( A @ vB @ ( vnotop @ vevalUnOp ) )
= ( A @ vnot @ vB @ vconstant @ vsomeExp ) ),
inference(lifteq,[status(thm)],[700]) ).
thf(5699,plain,
! [B: vYN,A: vUnOpT] :
( ( vnotop != vnotop )
| ( ( B @ vB @ ( A @ vevalUnOp ) )
= ( B @ vnot @ vB @ vconstant @ vsomeExp ) ) ),
inference(paramod_ordered,[status(thm)],[356,701]) ).
thf(5700,plain,
! [B: vYN,A: vUnOpT] :
( ( B @ vB @ ( A @ vevalUnOp ) )
= ( B @ vnot @ vB @ vconstant @ vsomeExp ) ),
inference(pattern_uni,[status(thm)],[5699:[]]) ).
thf(21,axiom,
! [A: vQID,B: vATMap,C: vAType,D: vATMap] :
( ~ ( ( ( B @ ( A @ vlookupATMap ) @ vgetAType )
= C )
& ( B @ ( A @ vlookupATMap ) @ visSomeAType ) )
=> ( ( B @ ( D @ ( C @ ( A @ vatmbind ) ) @ vintersectATM ) )
= ( B @ ( D @ vintersectATM ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','intersectATM-2') ).
thf(326,plain,
! [A: vQID,B: vATMap,C: vAType,D: vATMap] :
( ~ ( ( ( B @ ( A @ vlookupATMap ) @ vgetAType )
= C )
& ( B @ ( A @ vlookupATMap ) @ visSomeAType ) )
=> ( ( B @ ( D @ ( C @ ( A @ vatmbind ) ) @ vintersectATM ) )
= ( B @ ( D @ vintersectATM ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9787,plain,
! [E: vATMap,D: vAType,C: vQID,B: vnat,A: vQID] :
( ( ( vatmempty @ ( vNumber @ ( A @ vatmbind ) ) )
!= ( E @ ( D @ ( C @ vatmbind ) ) ) )
| ( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM @ ( D @ ( C @ sk224 ) ) )
= E ) ),
inference(paramod_ordered,[status(thm)],[9478,8152]) ).
thf(9788,plain,
! [B: vnat,A: vQID] :
( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM @ ( vNumber @ ( A @ sk224 ) ) )
= vatmempty ),
inference(pattern_uni,[status(thm)],[9787:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( vNumber )),bind(E,$thf( vatmempty ))]]) ).
thf(162,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vQuestionnaire,E: vATMap,F: vATMap,G: vATMap,H: vATMap,I: vATMap,J: vExp,K: vQuestionnaire] :
( ( ( C @ ( B @ vMC ) @ ( K @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( F @ ( H @ vMC ) @ ( D @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( I @ ( G @ vMC ) @ ( K @ ( D @ ( J @ vqcond ) ) @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) )
=> ( F = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqcond_inv5') ).
thf(1288,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vQuestionnaire,E: vATMap,F: vATMap,G: vATMap,H: vATMap,I: vATMap,J: vExp,K: vQuestionnaire] :
( ( ( C @ ( B @ vMC ) @ ( K @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( F @ ( H @ vMC ) @ ( D @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( I @ ( G @ vMC ) @ ( K @ ( D @ ( J @ vqcond ) ) @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) )
=> ( F = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(452,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk44 ) )
| ( ( B @ ( A @ vecheck ) )
= ( A @ ( B @ sk46 ) @ ( A @ ( B @ sk45 ) @ vlookupATMap ) ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(470,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk46 ) @ ( A @ ( B @ sk45 ) @ vlookupATMap ) )
= ( B @ ( A @ vecheck ) ) ) ),
inference(lifteq,[status(thm)],[452]) ).
thf(11776,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk45 ) @ vqvar @ ( A @ ( B @ sk46 ) @ vecheck ) )
= ( B @ ( A @ vecheck ) ) ) ),
inference(rewrite,[status(thm)],[470,1138]) ).
thf(68,axiom,
! [A: vAval,B: vAval] :
( ( A != B )
=> ( ( B @ ( A @ ( veqop @ vevalBinOp ) ) )
= ( vno @ vB @ vconstant @ vsomeExp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','evalBinOp-9') ).
thf(720,plain,
! [A: vAval,B: vAval] :
( ( A != B )
=> ( ( B @ ( A @ ( veqop @ vevalBinOp ) ) )
= ( vno @ vB @ vconstant @ vsomeExp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(437,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk47 ) )
| ( A @ ( B @ sk51 ) @ visSomeAType )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(1172,plain,
( ( vyes @ vnot )
= vno ),
inference(lifteq,[status(thm)],[1171]) ).
thf(896,plain,
! [A: vLabel] :
( ( vYesNo @ ( A @ vgetAnswer ) )
= ( A @ vaskYesNo @ vB ) ),
inference(cnf,[status(esa)],[895]) ).
thf(897,plain,
! [A: vLabel] :
( ( vYesNo @ ( A @ vgetAnswer ) )
= ( A @ vaskYesNo @ vB ) ),
inference(lifteq,[status(thm)],[896]) ).
thf(430,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk47 ) )
| ( ( A @ ( B @ sk49 ) )
= ( A @ ( B @ sk50 ) @ ( A @ ( B @ sk48 ) @ vecheck ) ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(474,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk49 ) )
= ( A @ ( B @ sk50 ) @ ( A @ ( B @ sk48 ) @ vecheck ) ) ) ),
inference(lifteq,[status(thm)],[430]) ).
thf(433,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk54 ) )
| ( ( B @ ( A @ vecheck ) )
= vnoAType )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(464,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( B @ ( A @ vecheck ) )
= vnoAType ) ),
inference(lifteq,[status(thm)],[433]) ).
thf(7879,plain,
! [B: vAType,A: vLabel] :
( ( B != sk2 )
| ( sk1 != vqmempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) )
| ( B @ ( A @ sk124 ) ) ),
inference(paramod_ordered,[status(thm)],[610,4874]) ).
thf(7880,plain,
! [A: vLabel] :
( ( sk1 != vqmempty )
| ( sk4 @ ( sk3 @ vMC ) @ ( sk7 @ ( vYesNo @ ( sk6 @ vvalue ) ) @ vqsingle @ ( vatmempty @ ( sk5 @ vtypeAM @ vMC ) @ vptcheck ) ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(pattern_uni,[status(thm)],[7879:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(6370,plain,
! [D: vQuestionnaire,C: vQMap,B: vAnsMap,A: vQConf] :
( ( ( A @ vgetQuest @ ( A @ sk368 @ ( A @ sk367 @ vQC ) ) )
!= ( D @ ( C @ ( B @ vQC ) ) ) )
| ( ( A @ vgetQM )
= C ) ),
inference(paramod_ordered,[status(thm)],[6359,4865]) ).
thf(6371,plain,
! [A: vQConf] :
( ( A @ sk368 )
= ( A @ vgetQM ) ),
inference(pattern_uni,[status(thm)],[6370:[bind(A,$thf( G )),bind(B,$thf( G @ sk367 )),bind(C,$thf( G @ sk368 )),bind(D,$thf( G @ vgetQuest ))]]) ).
thf(6373,plain,
! [A: vQConf] :
( ( A @ sk368 )
= ( A @ vgetQM ) ),
inference(simp,[status(thm)],[6371]) ).
thf(6967,plain,
! [D: vYN,C: vUnOpT,B: vAval,A: vUnOpT] :
( ( ( B @ ( A @ sk31 ) )
!= ( D @ vB @ ( C @ sk31 ) ) )
| ~ $true
| ( ( A @ ( B @ sk32 ) @ vB )
= B ) ),
inference(paramod_ordered,[status(thm)],[403,6939]) ).
thf(6968,plain,
! [D: vYN,C: vUnOpT,B: vAval,A: vUnOpT] :
( ( ( B @ ( A @ sk31 ) )
!= ( D @ vB @ ( C @ sk31 ) ) )
| ( ( A @ ( B @ sk32 ) @ vB )
= B ) ),
inference(simp,[status(thm)],[6967]) ).
thf(6969,plain,
! [B: vYN,A: vUnOpT] :
( ( A @ ( B @ vB @ sk32 ) @ vB )
= ( B @ vB ) ),
inference(pattern_uni,[status(thm)],[6968:[bind(A,$thf( A )),bind(B,$thf( E @ vB )),bind(C,$thf( A )),bind(D,$thf( E ))]]) ).
thf(7024,plain,
! [B: vYN,A: vUnOpT] :
( ( A @ ( B @ vB @ sk32 ) @ vB )
= ( B @ vB ) ),
inference(simp,[status(thm)],[6969]) ).
thf(7623,plain,
! [C: vYN,B: vYN,A: vUnOpT] :
( ( ( A @ ( B @ vB @ sk32 ) @ vB )
!= ( C @ vB ) )
| ( ( B @ vB @ sk138 )
= C ) ),
inference(paramod_ordered,[status(thm)],[7024,5085]) ).
thf(7624,plain,
! [B: vYN,A: vUnOpT] :
( ( A @ ( B @ vB @ sk32 ) )
= ( B @ vB @ sk138 ) ),
inference(pattern_uni,[status(thm)],[7623:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E @ ( F @ vB @ sk32 ) ))]]) ).
thf(7675,plain,
! [B: vYN,A: vUnOpT] :
( ( A @ ( B @ vB @ sk32 ) )
= ( B @ vB @ sk138 ) ),
inference(simp,[status(thm)],[7624]) ).
thf(7780,plain,
! [B: vYN,A: vUnOpT] :
( ( A @ ( B @ vB @ sk32 ) )
= B ),
inference(rewrite,[status(thm)],[7675,5085]) ).
thf(850,plain,
( ( vno @ vnot )
= vyes ),
inference(lifteq,[status(thm)],[849]) ).
thf(5944,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 @ ( A @ sk253 @ vMC ) )
!= ( vatmempty @ ( vatmempty @ vMC ) ) )
| ( ( B @ sk254 )
!= sk4 )
| ( ( B @ sk253 )
!= sk3 )
| ( sk5 != vaempty )
| ( sk1 != vqmempty )
| ( B @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(paramod_ordered,[status(thm)],[1316,5696]) ).
thf(5945,plain,
! [B: vMapConf,A: vMapConf] :
( ( ( A @ sk254 )
!= vatmempty )
| ( ( A @ sk253 )
!= vatmempty )
| ( ( B @ sk254 )
!= sk4 )
| ( ( B @ sk253 )
!= sk3 )
| ( sk5 != vaempty )
| ( sk1 != vqmempty )
| ( B @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ ( A @ vptcheck ) ) ) ),
inference(simp,[status(thm)],[5944]) ).
thf(247,axiom,
! [A: vQuestionnaire,B: vQuestionnaire,C: vAnsMap,D: vQMap] :
( ( D @ ( C @ ( B @ ( A @ ( vno @ vB @ vconstant @ vqcond ) ) @ vreduce ) ) )
= ( B @ ( D @ ( C @ vQC ) ) @ vsomeQConf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-12') ).
thf(4848,plain,
! [A: vQuestionnaire,B: vQuestionnaire,C: vAnsMap,D: vQMap] :
( ( D @ ( C @ ( B @ ( A @ ( vno @ vB @ vconstant @ vqcond ) ) @ vreduce ) ) )
= ( B @ ( D @ ( C @ vQC ) ) @ vsomeQConf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(9848,plain,
! [B: vnat,A: vQID] :
( ( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) )
| ( vatmempty != vatmempty ) ),
inference(paramod_ordered,[status(thm)],[4862,9801]) ).
thf(9849,plain,
! [B: vnat,A: vQID] :
( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) ),
inference(simp,[status(thm)],[9848]) ).
thf(9859,plain,
! [B: vnat,A: vQID] :
( ( vaempty @ ( B @ vNum @ ( A @ vabind ) ) )
!= vaempty ),
inference(simp,[status(thm)],[9849]) ).
thf(1127,plain,
~ ? [A: vQID,B: vLabel,C: vAType,D: vQID] :
( ( C @ ( B @ ( A @ vquestion ) ) )
= ( D @ vask ) ),
inference(miniscope,[status(thm)],[1126]) ).
thf(1128,plain,
! [D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vquestion ) ) )
!= ( D @ vask ) ),
inference(cnf,[status(esa)],[1127]) ).
thf(1129,plain,
! [D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vquestion ) ) )
!= ( D @ vask ) ),
inference(lifteq,[status(thm)],[1128]) ).
thf(186,axiom,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vExp,G: vQuestionnaire] :
( ( ( D @ ( E @ vMC ) @ ( G @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( D @ ( E @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( ( F @ ( C @ vecheck ) )
= ( vYesNo @ vsomeAType ) ) )
=> ( D @ ( E @ vMC ) @ ( G @ ( B @ ( F @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqcond') ).
thf(1378,plain,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vExp,G: vQuestionnaire] :
( ( ( D @ ( E @ vMC ) @ ( G @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( D @ ( E @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( ( F @ ( C @ vecheck ) )
= ( vYesNo @ vsomeAType ) ) )
=> ( D @ ( E @ vMC ) @ ( G @ ( B @ ( F @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(180,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vQuestionnaire,E: vATMap,F: vATMap,G: vATMap,H: vATMap,I: vATMap,J: vExp,K: vQuestionnaire] :
( ( ( C @ ( B @ vMC ) @ ( K @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( F @ ( H @ vMC ) @ ( D @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( I @ ( G @ vMC ) @ ( K @ ( D @ ( J @ vqcond ) ) @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) )
=> ( H = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqcond_inv4') ).
thf(1357,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vQuestionnaire,E: vATMap,F: vATMap,G: vATMap,H: vATMap,I: vATMap,J: vExp,K: vQuestionnaire] :
( ( ( C @ ( B @ vMC ) @ ( K @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( F @ ( H @ vMC ) @ ( D @ ( A @ ( E @ vMC ) @ vptcheck ) ) )
& ( I @ ( G @ vMC ) @ ( K @ ( D @ ( J @ vqcond ) ) @ ( A @ ( E @ vMC ) @ vptcheck ) ) ) )
=> ( H = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(445,plain,
! [B: vExp,A: vATMap] :
( ( A
= ( A @ ( B @ sk69 ) ) )
| ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(459,plain,
! [B: vExp,A: vATMap] :
( ~ ( A @ ( B @ sk61 ) )
| ~ ( A @ ( B @ sk54 ) )
| ~ ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk69 ) )
= A ) ),
inference(lifteq,[status(thm)],[445]) ).
thf(12528,plain,
! [D: vQConf,C: vLabel,B: vAType,A: vLabel] :
( ~ $true
| ( ( sk2 @ ( C @ sk124 ) )
!= ( B @ ( A @ sk124 ) ) )
| ( ( sk1 @ ( sk5 @ ( sk7 @ ( B @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( D @ vsomeQConf ) )
| ( B @ ( A @ sk124 ) ) ),
inference(eqfactor_ordered,[status(thm)],[8073]) ).
thf(12530,plain,
! [B: vQConf,A: vLabel] :
( ( ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( B @ vsomeQConf ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(pattern_uni,[status(thm)],[12528:[bind(A,$thf( C )),bind(B,$thf( sk2 ))]]) ).
thf(12535,plain,
! [B: vQConf,A: vLabel] :
( ( ( sk1 @ ( sk5 @ ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle @ vreduce ) ) )
!= ( B @ vsomeQConf ) )
| ( sk2 @ ( A @ sk124 ) ) ),
inference(simp,[status(thm)],[12530]) ).
thf(7128,plain,
! [E: vstring,D: vYN,C: vUnOpT,B: vAval,A: vUnOpT] :
( ( ( A @ ( B @ sk25 ) @ vB )
!= ( D @ vB ) )
| ( B
!= ( C @ ( E @ vT @ sk34 ) ) )
| ( ( B @ ( A @ vevalUnOp ) )
= vnoExp ) ),
inference(paramod_ordered,[status(thm)],[339,7051]) ).
thf(7129,plain,
! [D: vUnOpT,C: vAval,B: vstring,A: vUnOpT] :
( ( C
!= ( A @ ( B @ vT @ sk34 ) ) )
| ( ( C @ ( D @ vevalUnOp ) )
= vnoExp ) ),
inference(pattern_uni,[status(thm)],[7128:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G @ ( F @ sk25 ) ))]]) ).
thf(7140,plain,
! [C: vUnOpT,B: vstring,A: vUnOpT] :
( ( A @ ( B @ vT @ sk34 ) @ ( C @ vevalUnOp ) )
= vnoExp ),
inference(simp,[status(thm)],[7129]) ).
thf(7694,plain,
! [B: vUnOpT,A: vstring] :
( ( A @ vT @ ( B @ vevalUnOp ) )
= vnoExp ),
inference(rewrite,[status(thm)],[7140,7047]) ).
thf(10103,plain,
! [B: vYN,A: vQID] :
( ( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) )
| ( vatmempty != vatmempty ) ),
inference(paramod_ordered,[status(thm)],[4862,10038]) ).
thf(10104,plain,
! [B: vYN,A: vQID] :
( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) ),
inference(simp,[status(thm)],[10103]) ).
thf(10118,plain,
! [B: vYN,A: vQID] :
( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) )
!= vaempty ),
inference(simp,[status(thm)],[10104]) ).
thf(4722,plain,
! [A: vQConf] :
( ( A @ vsomeQConf @ vgetQC )
= A ),
inference(cnf,[status(esa)],[4721]) ).
thf(4723,plain,
! [A: vQConf] :
( ( A @ vsomeQConf @ vgetQC )
= A ),
inference(lifteq,[status(thm)],[4722]) ).
thf(8965,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
( ( vqempty != vqempty )
| ( ( B @ ( A @ vqseq ) )
!= ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle ) )
| ~ ( A @ visValue ) ),
inference(paramod_ordered,[status(thm)],[1374,8953]) ).
thf(8966,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
( ( ( B @ ( A @ vqseq ) )
!= ( sk7 @ ( sk2 @ ( sk6 @ vvalue ) ) @ vqsingle ) )
| ~ ( A @ visValue ) ),
inference(pattern_uni,[status(thm)],[8965:[]]) ).
thf(1065,plain,
! [A: vYN] :
( ( ( A @ vnot )
= vyes )
| ( ( A @ vnot )
= vno ) ),
inference(cnfConj,[status(thm)],[1061]) ).
thf(1069,plain,
! [A: vYN] :
( ( ( A @ vnot )
= vyes )
| ( ( A @ vnot )
= vno ) ),
inference(lifteq,[status(thm)],[1065]) ).
thf(13511,plain,
! [C: vnat,B: vAnsMap,A: vQID] :
( ( ( B @ ( C @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) )
| ( vatmempty != vatmempty ) ),
inference(paramod_ordered,[status(thm)],[4862,13132]) ).
thf(13512,plain,
! [C: vnat,B: vAnsMap,A: vQID] :
( ( B @ ( C @ vNum @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ vtypeAM ) ),
inference(simp,[status(thm)],[13511]) ).
thf(13524,plain,
! [C: vnat,B: vAnsMap,A: vQID] :
( ( B @ ( C @ vNum @ ( A @ vabind ) ) )
!= vaempty ),
inference(simp,[status(thm)],[13512]) ).
thf(202,axiom,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap,E: vQID] :
( ( C @ ( D @ vMC ) @ ( E @ vask @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( ( B @ ( E @ vlookupATMap ) )
= vnoAType ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Task_inv1') ).
thf(4655,plain,
! [A: vATMap,B: vATMap,C: vATMap,D: vATMap,E: vQID] :
( ( C @ ( D @ vMC ) @ ( E @ vask @ vqsingle @ ( A @ ( B @ vMC ) @ vptcheck ) ) )
=> ( ( B @ ( E @ vlookupATMap ) )
= vnoAType ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(11594,plain,
! [D: vAval,C: vQID,B: vYN,A: vQID] :
( ( ( vaempty @ ( B @ vB @ ( A @ vabind ) ) @ vtypeAM )
!= ( vaempty @ ( D @ ( C @ vabind ) ) @ vtypeAM ) )
| ( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( D @ vtypeOf @ ( C @ sk224 ) ) )
= vatmempty ) ),
inference(paramod_ordered,[status(thm)],[9480,9481]) ).
thf(11595,plain,
! [B: vYN,A: vQID] :
( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( B @ vB @ vtypeOf @ ( A @ sk224 ) ) )
= vatmempty ),
inference(pattern_uni,[status(thm)],[11594:[bind(A,$thf( A )),bind(B,$thf( E )),bind(C,$thf( A )),bind(D,$thf( E @ vB ))]]) ).
thf(11631,plain,
! [B: vYN,A: vQID] :
( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( B @ vB @ vtypeOf @ ( A @ sk224 ) ) )
= vatmempty ),
inference(simp,[status(thm)],[11595]) ).
thf(11675,plain,
! [A: vQID] :
( ( vatmempty @ ( vYesNo @ ( A @ vatmbind ) ) @ ( vYesNo @ ( A @ sk224 ) ) )
= vatmempty ),
inference(rewrite,[status(thm)],[11631,1135]) ).
thf(428,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk47 ) )
| ( A
= ( A @ ( B @ sk48 ) ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) ) ),
inference(cnfConj,[status(thm)],[419]) ).
thf(469,plain,
! [B: vExp,A: vATMap] :
( ( A @ ( B @ sk47 ) )
| ~ ( A @ ( B @ sk44 ) )
| ~ ( B @ ( A @ sk41 ) )
| ~ ( B @ ( A @ sk38 ) )
| ~ ( B @ ( A @ sk35 ) )
| ( ( A @ ( B @ sk48 ) )
= A ) ),
inference(lifteq,[status(thm)],[428]) ).
thf(226,axiom,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vATMap,G: vATMap,H: vExp,I: vQuestionnaire] :
( ( ( D @ ( F @ vMC ) @ ( I @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( D @ ( F @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( G @ ( E @ vMC ) @ ( I @ ( B @ ( H @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) )
=> ( G = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Tqcond_inv7') ).
thf(4752,plain,
! [A: vATMap,B: vQuestionnaire,C: vATMap,D: vATMap,E: vATMap,F: vATMap,G: vATMap,H: vExp,I: vQuestionnaire] :
( ( ( D @ ( F @ vMC ) @ ( I @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( D @ ( F @ vMC ) @ ( B @ ( A @ ( C @ vMC ) @ vptcheck ) ) )
& ( G @ ( E @ vMC ) @ ( I @ ( B @ ( H @ vqcond ) ) @ ( A @ ( C @ vMC ) @ vptcheck ) ) ) )
=> ( G = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(4742,plain,
! [A: vQConf] : ( A @ vsomeQConf @ visSomeQC ),
inference(cnf,[status(esa)],[4741]) ).
thf(6887,plain,
! [C: vATMap,B: vATMap,A: vAType] :
( ( ( A @ vsomeAType @ visSomeAType )
!= ( B @ ( C @ sk198 ) @ visSomeAType ) )
| ~ $true
| ~ ( B @ ( C @ sk189 ) )
| ~ ( B @ ( C @ sk187 ) )
| ( ( B @ ( C @ sk199 ) )
!= ( B @ ( C @ sk198 ) @ vgetAType ) ) ),
inference(paramod_ordered,[status(thm)],[670,998]) ).
thf(6888,plain,
! [C: vATMap,B: vATMap,A: vAType] :
( ( ( A @ vsomeAType @ visSomeAType )
!= ( B @ ( C @ sk198 ) @ visSomeAType ) )
| ~ ( B @ ( C @ sk189 ) )
| ~ ( B @ ( C @ sk187 ) )
| ( ( B @ ( C @ sk199 ) )
!= ( B @ ( C @ sk198 ) @ vgetAType ) ) ),
inference(simp,[status(thm)],[6887]) ).
thf(6896,plain,
! [C: vATMap,B: vATMap,A: vAType] :
( ( ( A @ vsomeAType )
!= ( B @ ( C @ sk198 ) ) )
| ~ ( B @ ( C @ sk189 ) )
| ~ ( B @ ( C @ sk187 ) )
| ( ( B @ ( C @ sk199 ) )
!= ( B @ ( C @ sk198 ) @ vgetAType ) ) ),
inference(simp,[status(thm)],[6888]) ).
thf(755,plain,
! [D: vQuestionnaire,C: vQuestionnaire,B: vQuestionnaire,A: vQuestionnaire] :
( ( A = C )
| ( ( B @ ( A @ vqseq ) )
!= ( D @ ( C @ vqseq ) ) ) ),
inference(cnfConj,[status(thm)],[754]) ).
thf(757,plain,
! [D: vQuestionnaire,C: vQuestionnaire,B: vQuestionnaire,A: vQuestionnaire] :
( ( A = C )
| ( ( B @ ( A @ vqseq ) )
!= ( D @ ( C @ vqseq ) ) ) ),
inference(lifteq,[status(thm)],[755]) ).
thf(758,plain,
? [A: vQuestionnaire > vQuestionnaire > vQuestionnaire] :
! [B: vQuestionnaire,C: vQuestionnaire] :
( ( C @ ( B @ vqseq ) @ ( C @ A ) )
= B ),
inference(detectInverse,[status(thm)],[757]) ).
thf(759,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
( ( B @ ( A @ vqseq ) @ ( B @ sk142 ) )
= A ),
inference(cnf,[status(esa)],[758]) ).
thf(5911,plain,
! [B: vQuestionnaire,A: vQuestionnaire] :
( ( B @ ( A @ vqseq ) @ ( B @ sk142 ) )
= A ),
inference(lifteq,[status(thm)],[759]) ).
thf(829,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( F = B )
| ( ( C @ ( F @ ( D @ vdefquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ) ),
inference(cnfConj,[status(thm)],[827]) ).
thf(834,plain,
! [F: vLabel,E: vAType,D: vQID,C: vAType,B: vLabel,A: vQID] :
( ( F = B )
| ( ( C @ ( F @ ( D @ vdefquestion ) ) )
!= ( E @ ( B @ ( A @ vdefquestion ) ) ) ) ),
inference(lifteq,[status(thm)],[829]) ).
thf(835,plain,
? [A: vQID > vAType > vEntry > vLabel] :
! [B: vQID,C: vLabel,D: vAType] :
( ( D @ ( C @ ( B @ vdefquestion ) ) @ ( D @ ( B @ A ) ) )
= C ),
inference(detectInverse,[status(thm)],[834]) ).
thf(836,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vdefquestion ) ) @ ( C @ ( A @ sk155 ) ) )
= B ),
inference(cnf,[status(esa)],[835]) ).
thf(6886,plain,
! [C: vAType,B: vLabel,A: vQID] :
( ( C @ ( B @ ( A @ vdefquestion ) ) @ ( C @ ( A @ sk155 ) ) )
= B ),
inference(lifteq,[status(thm)],[836]) ).
thf(23740,plain,
$false,
inference(e,[status(thm)],[8607,6085,1337,5918,1168,4824,347,846,333,4728,1295,6374,1110,365,1369,962,468,408,683,276,1068,5696,878,5691,269,597,1173,5982,10017,449,379,1269,5348,11724,1078,6939,8915,500,1233,698,747,9801,340,1354,6877,4633,385,4839,6675,797,8353,9428,4638,472,9481,670,898,9476,10022,1391,782,417,301,8699,5750,7858,404,709,12212,651,257,389,1055,13658,4743,9067,1298,8919,949,460,4692,785,372,5910,702,751,357,6434,4766,1059,9480,1347,325,7047,8674,448,8352,4862,4788,284,5925,881,416,7075,6936,316,5076,7509,261,4756,5792,475,13166,5084,4724,5156,1283,1051,905,1040,1109,321,485,1136,4798,7581,353,6438,5353,634,692,956,7336,998,1345,9589,312,6860,5695,660,4825,7505,849,292,4629,270,381,366,1311,1067,5122,1047,4888,661,5968,810,8513,6897,825,778,952,4878,5349,5719,297,693,4785,4821,4836,4661,1387,12159,1223,4712,894,429,5085,275,7984,13158,467,10038,879,435,5690,1296,461,682,1392,710,456,361,1365,4680,974,1012,8073,285,1106,1143,9804,5006,9073,5345,1375,6459,725,403,388,610,9603,8138,4817,4808,1350,742,8530,12863,1234,12538,8677,6235,4845,1138,356,1329,1160,1361,5818,5694,339,1292,753,4721,669,8743,9477,5547,9288,1016,7895,706,256,4676,471,901,686,1075,476,4861,4648,6935,679,1039,4804,1324,4846,1099,1249,8351,1266,1192,6784,6152,371,1060,457,911,4829,5112,343,8527,1202,266,657,1170,1286,1187,938,4644,360,633,8205,311,9436,298,750,1146,11638,1219,4874,264,279,1301,7953,1374,1135,412,9484,689,5979,975,7968,6881,958,9585,1226,413,6234,819,13157,5940,826,4709,5799,281,259,12964,13132,1139,382,1058,466,4640,704,1356,313,6937,8152,4645,7951,1332,350,9483,4716,9312,7077,4828,1048,1349,377,8693,362,4805,318,5689,5972,6216,900,406,880,1043,890,4694,4635,631,367,4833,816,4818,4731,594,251,895,915,943,9074,1381,1162,726,848,9487,964,4652,4684,462,1396,399,9478,959,278,1364,5693,685,1171,1044,695,6783,455,267,851,1102,4626,473,4741,9403,795,663,4735,5757,6088,648,1081,617,342,1145,9783,7982,490,675,944,4868,1340,6853,968,458,823,4658,4749,6238,295,887,1252,8350,8143,1070,705,282,1225,6885,707,1368,4641,409,1230,263,310,791,1188,5015,840,6513,463,5154,1317,8148,359,1130,1218,7398,5186,5277,907,7737,6457,1023,9353,4748,4695,314,4795,876,8914,978,386,1372,5083,13160,465,4651,4851,4770,671,4997,4738,1126,368,9647,1316,6846,4698,6938,1216,891,1189,6867,1326,699,963,7359,4791,401,4705,961,813,1385,5724,319,9482,258,652,351,731,786,8716,781,8488,5692,7399,5549,8953,346,5196,8520,4619,290,378,763,272,1161,287,1133,7542,315,12267,1229,10041,1395,818,4719,405,13294,7048,300,1348,5129,4687,262,4811,6237,4843,867,273,5700,326,1314,9788,664,1288,4865,11776,696,720,796,437,1335,1172,897,474,464,7880,7506,6373,4876,908,723,822,7780,850,8147,9600,5945,4848,9859,1129,596,1378,1357,459,12535,7694,322,10118,354,4723,13156,8966,4863,1069,972,13524,254,4655,8950,11675,469,940,4752,1037,4742,6896,5911,6886]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM268_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n013.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 23:50:06 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.96/1.39 % [INFO] Parsing done (410ms).
% 2.45/1.41 % [INFO] Running in sequential loop mode.
% 3.07/1.79 % [INFO] eprover registered as external prover.
% 3.07/1.79 % [INFO] Scanning for conjecture ...
% 3.81/2.03 % [INFO] Found a conjecture (or negated_conjecture) and 361 axioms. Running axiom selection ...
% 4.39/2.24 % [INFO] Axiom selection finished. Selected 248 axioms (removed 113 axioms).
% 5.56/2.59 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.88/2.62 % [INFO] Type checking passed.
% 5.88/2.62 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 7.96/3.14 % [INFO] [Domain constraints] Detected constraint on vUnOpT
% 7.96/3.15 % [INFO] [Domain constraints] dom(vUnOpT) ⊆ {vnotop}
% 9.84/3.76 % [INFO] [Domain constraints] Detected constraint on vAType
% 9.84/3.76 % [INFO] [Domain constraints] dom(vAType) ⊆ {vYesNo,vNumber,vText}
% 10.52/3.93 % [INFO] [Domain constraints] Detected constraint on vYN
% 10.52/3.93 % [INFO] [Domain constraints] dom(vYN) ⊆ {vyes,vno}
% 11.05/4.09 % [INFO] [Domain constraints] Detected constraint on vYN
% 11.05/4.09 % [INFO] [Domain constraints] dom(vYN) ⊆ {vyes,vno}
% 185.82/94.34 % External prover 'e' found a proof!
% 185.82/94.34 % [INFO] Killing All external provers ...
% 185.82/94.34 % Time passed: 93796ms (effective reasoning time: 92925ms)
% 185.82/94.34 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 185.82/94.34 % Axioms used in derivation (248): Task_inv2, getQC-0, reduceExp-10, intersectATM-INV, checkBinOp-6, dom-AType, typeAM-INV, dom-Entry, isSomeAType-1, EQ-qvar, Tdefquestion_inv3, echeck-0, reduceExp-7, reduce-7, DIFF-value-defquestion, isValue-true-INV, Tqcond_inv5, reduce-0, DIFF-eqop-andop, Task_inv3, echeck-4, isSomeAType-false-INV, typeOf-0, Tvalue_inv2, DIFF-qempty-qsingle, EQ-B, dom-OptQConf, getExp-0, reduceExp-6, reduce-INV, reduceExp-INV, typeQM-0, evalBinOp-6, DIFF-eqop-orop, getAType-0, DIFF-qsingle-qseq, lookupQMap-1, reduceExp-2, isSomeQC-0, isSomeQuestion-1, dom-YN, getAnswer-1, Tqseq, getAM-0, reduce-13, appendAnsMap-0, evalUnOp-0, isSomeQC-false-INV, intersectATM-1, dom-AnsMap, appendATMap-0, DIFF-value-ask, reduce-11, EQ-qsingle, lookupATMap-0, isSomeQuestion-false-INV, lookupATMap-INV, isSomeExp-true-INV, expIsValue-false-INV, reduce-4, EQ-unop, reduceExp-8, getAnswer-0, or-0, EQ-someQConf, reduce-15, reduce-1, getExpValue-0, EQ-value, dom-OptExp, isValue-1, EQ-someExp, dom-Questionnaire, DIFF-qseq-qcond, EQ-Num, reduceExp-5, dom-OptQuestion, DIFF-B-Num, Tvalue_inv1, dom-OptAType, getQuest-INV, echeck-3, checkUnOp-1, appendAnsMap-INV, DIFF-andop-orop, intersectATM-0, reduce-10, and-INV, reduceExp-1, evalBinOp-9, isSomeQuestion-0, dom-QMap, typeOf-1, Progress-qsingle-value-expIsValue-False, Tqgroup, Tqseq_inv3, DIFF-qsingle-qcond, isSomeAType-true-INV, isValue-false-INV, EQ-someAType, DIFF-YesNo-Text, typeOf-INV, DIFF-question-defquestion, dom-ATMap, echeck-7, DIFF-Number-Text, Tqempty_inv2, reduce-9, EQ-qseq, reduce-14, appendAnsMap-1, EQ-question, lookupQMap-2, Tquestion_inv2, dom-Aval, EQ-binop, typeQM-1, DIFF-qempty-qgroup, lookupQMap-INV, typeAM-1, DIFF-defquestion-ask, dom-UnOpT, Tqempty, getAnswer-2, reduce-5, isValue-0, reduceExp-4, getQM-INV, reduce-12, reduce-2, Tquestion_inv1, DIFF-noQConf-someQConf, and-1, EQ-ask, checkBinOp-8, EQ-abind, or-INV, reduceExp-9, EQ-constant, Task_inv4, DIFF-qvar-unop, or-1, checkUnOp-0, Tqcond, EQ-qmbind, echeck-INV, DIFF-yes-no, DIFF-qsingle-qgroup, DIFF-YesNo-Number, not-0, Tqcond_inv4, getAM-INV, EQ-qcond, isSomeQuestion-true-INV, DIFF-qcond-qgroup, DIFF-qseq-qgroup, echeck-1, lookupATMap-1, Tvalue_inv4, evalBinOp-8, not-INV, getQuestionAType-0, Tquestion_inv3, DIFF-qempty-qseq, DIFF-noQuestion-someQuestion, dom-QConf, dom-Exp, typeOf-2, reduce-8, EQ-atmbind, DIFF-aempty-abind, DIFF-qmempty-qmbind, checkBinOp-7, Tqempty_inv1, isSomeAType-0, qcappend-0, reduceExp-0, DIFF-Num-T, isSomeExp-1, Tqseq_inv2, evalUnOp-INV, DIFF-question-ask, DIFF-question-value, DIFF-constant-binop, Tvalue, reduce-6, not-1, Tquestion, Tdefquestion, EQ-qgroup, getQuestionLabel-0, Tqcond_inv7, getQM-0, appendATMap-INV, reduceExp-3, typeAM-0, Tqgroup_inv, Tvalue_inv3, Tdefquestion_inv2, echeck-5, expIsValue-0, Tqseq_inv4, isSomeQC-true-INV, Tqcond_inv2, DIFF-qvar-binop, isSomeExp-false-INV, DIFF-atmempty-atmbind, checkUnOp-INV, and-0, EQ-T, expIsValue-1, appendATMap-1, Tqseq_inv1, echeck-6, DIFF-constant-qvar, getQuest-0, isSomeExp-0, DIFF-binop-unop, Tqcond_inv6, getAnswer-INV, lookupATMap-2, lookupAnsMap-2, EQ-defquestion, evalBinOp-7, DIFF-noAType-someAType, DIFF-qempty-qcond, Task_inv1, Task, echeck-2, Tdefquestion_inv1, DIFF-noExp-someExp, DIFF-constant-unop, Progress-qsingle-value-expIsValue-True, qcappend-INV, evalUnOp-1, EQ-MC, intersectATM-2, reduce-3, Tqcond_inv1, lookupQMap-0, dom-MapConf, isSomeQC-1, expIsValue-true-INV, EQ-QC, DIFF-B-T, EQ-someQuestion, Tqcond_inv3, typeQM-INV
% 185.82/94.34 % No. of inferences in proof: 1573
% 185.82/94.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 93796 ms resp. 92925 ms w/o parsing
% 177.04/94.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 177.04/94.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------