%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV568-1.030 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:35:36 AM UTC 2025
% Result : Unsatisfiable 0.59s 0.78s
% Output : Proof 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 776
% Syntax : Number of formulae : 2531 (1919 unt; 0 typ; 0 def)
% Number of atoms : 3391 (3363 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 1397 ( 564 ~; 432 |; 0 &)
% ( 401 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 21 ( 3 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 286 ( 286 usr; 277 con; 0-3 aty)
% Number of variables : 1011 ( 976 !; 0 ?;1011 :)
% Comments :
%------------------------------------------------------------------------------
tff(rselect_tail_type,type,
rselect_tail: $i > $i ).
tff(q10_type,type,
q10: $i ).
tff(q11_type,type,
q11: $i ).
tff(s_type,type,
s: $i > $i ).
tff(index_15_type,type,
index_15: $i ).
tff(rstore_tail_type,type,
rstore_tail: ( $i * $i ) > $i ).
tff(rstore_seq_type,type,
rstore_seq: ( $i * $i ) > $i ).
tff(earray_16_type,type,
earray_16: $i ).
tff(queue_19_type,type,
queue_19: $i ).
tff(index_18_type,type,
index_18: $i ).
tff(queue_17_type,type,
queue_17: $i ).
tff(select_type,type,
select: ( $i * $i ) > $i ).
tff(store_type,type,
store: ( $i * $i * $i ) > $i ).
tff(e10_type,type,
e10: $i ).
tff(earray_14_type,type,
earray_14: $i ).
tff(e11_type,type,
e11: $i ).
tff(elem_214_type,type,
elem_214: $i ).
tff(rselect_seq_type,type,
rselect_seq: $i > $i ).
tff(index_213_type,type,
index_213: $i ).
tff(earray_212_type,type,
earray_212: $i ).
tff(e29_type,type,
e29: $i ).
tff(q29_type,type,
q29: $i ).
tff(e28_type,type,
e28: $i ).
tff(index_147_type,type,
index_147: $i ).
tff(earray_146_type,type,
earray_146: $i ).
tff(rselect_head_type,type,
rselect_head: $i > $i ).
tff(q30_type,type,
q30: $i ).
tff(rstore_head_type,type,
rstore_head: ( $i * $i ) > $i ).
tff(index_167_type,type,
index_167: $i ).
tff(index_165_type,type,
index_165: $i ).
tff(queue_164_type,type,
queue_164: $i ).
tff(index_168_type,type,
index_168: $i ).
tff(queue_166_type,type,
queue_166: $i ).
tff(queue_169_type,type,
queue_169: $i ).
tff(queue_136_type,type,
queue_136: $i ).
tff(index_137_type,type,
index_137: $i ).
tff(index_135_type,type,
index_135: $i ).
tff(queue_134_type,type,
queue_134: $i ).
tff(index_138_type,type,
index_138: $i ).
tff(e27_type,type,
e27: $i ).
tff(index_141_type,type,
index_141: $i ).
tff(earray_140_type,type,
earray_140: $i ).
tff(earray_142_type,type,
earray_142: $i ).
tff(q27_type,type,
q27: $i ).
tff(queue_139_type,type,
queue_139: $i ).
tff(index_144_type,type,
index_144: $i ).
tff(queue_143_type,type,
queue_143: $i ).
tff(earray_148_type,type,
earray_148: $i ).
tff(q28_type,type,
q28: $i ).
tff(queue_145_type,type,
queue_145: $i ).
tff(index_150_type,type,
index_150: $i ).
tff(queue_149_type,type,
queue_149: $i ).
tff(index_162_type,type,
index_162: $i ).
tff(earray_161_type,type,
earray_161: $i ).
tff(earray_163_type,type,
earray_163: $i ).
tff(queue_151_type,type,
queue_151: $i ).
tff(index_9_type,type,
index_9: $i ).
tff(q9_type,type,
q9: $i ).
tff(index_209_type,type,
index_209: $i ).
tff(index_207_type,type,
index_207: $i ).
tff(queue_206_type,type,
queue_206: $i ).
tff(index_210_type,type,
index_210: $i ).
tff(queue_208_type,type,
queue_208: $i ).
tff(queue_211_type,type,
queue_211: $i ).
tff(index_204_type,type,
index_204: $i ).
tff(earray_205_type,type,
earray_205: $i ).
tff(q8_type,type,
q8: $i ).
tff(queue_115_type,type,
queue_115: $i ).
tff(index_116_type,type,
index_116: $i ).
tff(queue_94_type,type,
queue_94: $i ).
tff(index_111_type,type,
index_111: $i ).
tff(earray_112_type,type,
earray_112: $i ).
tff(q23_type,type,
q23: $i ).
tff(index_114_type,type,
index_114: $i ).
tff(queue_113_type,type,
queue_113: $i ).
tff(e23_type,type,
e23: $i ).
tff(earray_110_type,type,
earray_110: $i ).
tff(index_108_type,type,
index_108: $i ).
tff(queue_107_type,type,
queue_107: $i ).
tff(queue_109_type,type,
queue_109: $i ).
tff(index_105_type,type,
index_105: $i ).
tff(earray_106_type,type,
earray_106: $i ).
tff(q22_type,type,
q22: $i ).
tff(e22_type,type,
e22: $i ).
tff(earray_104_type,type,
earray_104: $i ).
tff(index_102_type,type,
index_102: $i ).
tff(queue_101_type,type,
queue_101: $i ).
tff(queue_103_type,type,
queue_103: $i ).
tff(index_99_type,type,
index_99: $i ).
tff(earray_100_type,type,
earray_100: $i ).
tff(q21_type,type,
q21: $i ).
tff(e21_type,type,
e21: $i ).
tff(earray_98_type,type,
earray_98: $i ).
tff(index_96_type,type,
index_96: $i ).
tff(queue_97_type,type,
queue_97: $i ).
tff(index_95_type,type,
index_95: $i ).
tff(index_93_type,type,
index_93: $i ).
tff(queue_92_type,type,
queue_92: $i ).
tff(index_198_type,type,
index_198: $i ).
tff(queue_67_type,type,
queue_67: $i ).
tff(index_90_type,type,
index_90: $i ).
tff(earray_91_type,type,
earray_91: $i ).
tff(q20_type,type,
q20: $i ).
tff(e20_type,type,
e20: $i ).
tff(earray_89_type,type,
earray_89: $i ).
tff(index_87_type,type,
index_87: $i ).
tff(queue_86_type,type,
queue_86: $i ).
tff(queue_88_type,type,
queue_88: $i ).
tff(index_84_type,type,
index_84: $i ).
tff(earray_85_type,type,
earray_85: $i ).
tff(q19_type,type,
q19: $i ).
tff(e19_type,type,
e19: $i ).
tff(earray_83_type,type,
earray_83: $i ).
tff(index_75_type,type,
index_75: $i ).
tff(queue_74_type,type,
queue_74: $i ).
tff(queue_76_type,type,
queue_76: $i ).
tff(index_72_type,type,
index_72: $i ).
tff(earray_73_type,type,
earray_73: $i ).
tff(q18_type,type,
q18: $i ).
tff(e18_type,type,
e18: $i ).
tff(earray_71_type,type,
earray_71: $i ).
tff(index_69_type,type,
index_69: $i ).
tff(queue_70_type,type,
queue_70: $i ).
tff(index_68_type,type,
index_68: $i ).
tff(index_66_type,type,
index_66: $i ).
tff(queue_65_type,type,
queue_65: $i ).
tff(index_192_type,type,
index_192: $i ).
tff(queue_46_type,type,
queue_46: $i ).
tff(index_63_type,type,
index_63: $i ).
tff(earray_64_type,type,
earray_64: $i ).
tff(q17_type,type,
q17: $i ).
tff(e17_type,type,
e17: $i ).
tff(earray_62_type,type,
earray_62: $i ).
tff(index_60_type,type,
index_60: $i ).
tff(queue_59_type,type,
queue_59: $i ).
tff(queue_61_type,type,
queue_61: $i ).
tff(index_57_type,type,
index_57: $i ).
tff(earray_58_type,type,
earray_58: $i ).
tff(q16_type,type,
q16: $i ).
tff(e16_type,type,
e16: $i ).
tff(earray_56_type,type,
earray_56: $i ).
tff(index_54_type,type,
index_54: $i ).
tff(queue_53_type,type,
queue_53: $i ).
tff(queue_55_type,type,
queue_55: $i ).
tff(index_51_type,type,
index_51: $i ).
tff(earray_52_type,type,
earray_52: $i ).
tff(q15_type,type,
q15: $i ).
tff(e15_type,type,
e15: $i ).
tff(earray_50_type,type,
earray_50: $i ).
tff(index_48_type,type,
index_48: $i ).
tff(queue_49_type,type,
queue_49: $i ).
tff(index_47_type,type,
index_47: $i ).
tff(index_45_type,type,
index_45: $i ).
tff(queue_44_type,type,
queue_44: $i ).
tff(index_183_type,type,
index_183: $i ).
tff(queue_25_type,type,
queue_25: $i ).
tff(index_42_type,type,
index_42: $i ).
tff(earray_43_type,type,
earray_43: $i ).
tff(q14_type,type,
q14: $i ).
tff(e14_type,type,
e14: $i ).
tff(earray_41_type,type,
earray_41: $i ).
tff(index_39_type,type,
index_39: $i ).
tff(queue_38_type,type,
queue_38: $i ).
tff(queue_40_type,type,
queue_40: $i ).
tff(index_36_type,type,
index_36: $i ).
tff(earray_37_type,type,
earray_37: $i ).
tff(q13_type,type,
q13: $i ).
tff(e13_type,type,
e13: $i ).
tff(earray_35_type,type,
earray_35: $i ).
tff(index_33_type,type,
index_33: $i ).
tff(queue_32_type,type,
queue_32: $i ).
tff(queue_34_type,type,
queue_34: $i ).
tff(index_30_type,type,
index_30: $i ).
tff(earray_31_type,type,
earray_31: $i ).
tff(q12_type,type,
q12: $i ).
tff(e12_type,type,
e12: $i ).
tff(earray_29_type,type,
earray_29: $i ).
tff(index_27_type,type,
index_27: $i ).
tff(queue_28_type,type,
queue_28: $i ).
tff(index_26_type,type,
index_26: $i ).
tff(index_24_type,type,
index_24: $i ).
tff(queue_23_type,type,
queue_23: $i ).
tff(index_177_type,type,
index_177: $i ).
tff(index_21_type,type,
index_21: $i ).
tff(earray_22_type,type,
earray_22: $i ).
tff(earray_20_type,type,
earray_20: $i ).
tff(index_12_type,type,
index_12: $i ).
tff(queue_11_type,type,
queue_11: $i ).
tff(queue_13_type,type,
queue_13: $i ).
tff(earray_10_type,type,
earray_10: $i ).
tff(e9_type,type,
e9: $i ).
tff(earray_8_type,type,
earray_8: $i ).
tff(index_171_type,type,
index_171: $i ).
tff(queue_187_type,type,
queue_187: $i ).
tff(e8_type,type,
e8: $i ).
tff(earray_203_type,type,
earray_203: $i ).
tff(index_201_type,type,
index_201: $i ).
tff(queue_200_type,type,
queue_200: $i ).
tff(queue_202_type,type,
queue_202: $i ).
tff(earray_199_type,type,
earray_199: $i ).
tff(q7_type,type,
q7: $i ).
tff(e7_type,type,
e7: $i ).
tff(earray_197_type,type,
earray_197: $i ).
tff(index_195_type,type,
index_195: $i ).
tff(queue_194_type,type,
queue_194: $i ).
tff(queue_196_type,type,
queue_196: $i ).
tff(earray_193_type,type,
earray_193: $i ).
tff(q6_type,type,
q6: $i ).
tff(e6_type,type,
e6: $i ).
tff(earray_191_type,type,
earray_191: $i ).
tff(index_189_type,type,
index_189: $i ).
tff(queue_190_type,type,
queue_190: $i ).
tff(index_188_type,type,
index_188: $i ).
tff(index_186_type,type,
index_186: $i ).
tff(queue_185_type,type,
queue_185: $i ).
tff(index_153_type,type,
index_153: $i ).
tff(queue_157_type,type,
queue_157: $i ).
tff(earray_184_type,type,
earray_184: $i ).
tff(q5_type,type,
q5: $i ).
tff(e5_type,type,
e5: $i ).
tff(earray_182_type,type,
earray_182: $i ).
tff(index_180_type,type,
index_180: $i ).
tff(queue_179_type,type,
queue_179: $i ).
tff(queue_181_type,type,
queue_181: $i ).
tff(earray_178_type,type,
earray_178: $i ).
tff(q4_type,type,
q4: $i ).
tff(e4_type,type,
e4: $i ).
tff(earray_176_type,type,
earray_176: $i ).
tff(index_174_type,type,
index_174: $i ).
tff(queue_173_type,type,
queue_173: $i ).
tff(queue_175_type,type,
queue_175: $i ).
tff(earray_172_type,type,
earray_172: $i ).
tff(q3_type,type,
q3: $i ).
tff(e3_type,type,
e3: $i ).
tff(earray_170_type,type,
earray_170: $i ).
tff(index_159_type,type,
index_159: $i ).
tff(queue_160_type,type,
queue_160: $i ).
tff(index_158_type,type,
index_158: $i ).
tff(index_156_type,type,
index_156: $i ).
tff(queue_155_type,type,
queue_155: $i ).
tff(index_78_type,type,
index_78: $i ).
tff(index_3_type,type,
index_3: $i ).
tff(earray_154_type,type,
earray_154: $i ).
tff(q2_type,type,
q2: $i ).
tff(e2_type,type,
e2: $i ).
tff(earray_152_type,type,
earray_152: $i ).
tff(index_81_type,type,
index_81: $i ).
tff(queue_80_type,type,
queue_80: $i ).
tff(queue_82_type,type,
queue_82: $i ).
tff(earray_79_type,type,
earray_79: $i ).
tff(q1_type,type,
q1: $i ).
tff(e1_type,type,
e1: $i ).
tff(earray_77_type,type,
earray_77: $i ).
tff(index_6_type,type,
index_6: $i ).
tff(queue_5_type,type,
queue_5: $i ).
tff(queue_7_type,type,
queue_7: $i ).
tff(earray_4_type,type,
earray_4: $i ).
tff(q0_type,type,
q0: $i ).
tff(e0_type,type,
e0: $i ).
tff(earray_2_type,type,
earray_2: $i ).
tff(index_0_type,type,
index_0: $i ).
tff(q_type,type,
q: $i ).
tff(queue_1_type,type,
queue_1: $i ).
tff(index_132_type,type,
index_132: $i ).
tff(earray_133_type,type,
earray_133: $i ).
tff(q26_type,type,
q26: $i ).
tff(e26_type,type,
e26: $i ).
tff(earray_131_type,type,
earray_131: $i ).
tff(index_129_type,type,
index_129: $i ).
tff(queue_128_type,type,
queue_128: $i ).
tff(queue_130_type,type,
queue_130: $i ).
tff(index_126_type,type,
index_126: $i ).
tff(earray_127_type,type,
earray_127: $i ).
tff(q25_type,type,
q25: $i ).
tff(e25_type,type,
e25: $i ).
tff(earray_125_type,type,
earray_125: $i ).
tff(index_123_type,type,
index_123: $i ).
tff(queue_122_type,type,
queue_122: $i ).
tff(queue_124_type,type,
queue_124: $i ).
tff(index_120_type,type,
index_120: $i ).
tff(earray_121_type,type,
earray_121: $i ).
tff(q24_type,type,
q24: $i ).
tff(e24_type,type,
e24: $i ).
tff(earray_119_type,type,
earray_119: $i ).
tff(index_117_type,type,
index_117: $i ).
tff(queue_118_type,type,
queue_118: $i ).
tff(1,plain,
( ( index_15 = rselect_tail(q10) )
<=> ( index_15 = rselect_tail(q10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
index_15 = rselect_tail(q10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp82) ).
tff(3,plain,
index_15 = rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
rselect_tail(q10) = index_15,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
s(rselect_tail(q10)) = s(index_15),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
s(index_15) = s(rselect_tail(q10)),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_tail(rstore_tail(A,E)) = E )
<=> ( rselect_tail(rstore_tail(A,E)) = E ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_tail) ).
tff(11,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = s(index_15) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = s(index_15),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
( ( q11 = queue_19 )
<=> ( q11 = queue_19 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,axiom,
q11 = queue_19,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp218) ).
tff(18,plain,
q11 = queue_19,
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
queue_19 = q11,
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
( ( queue_19 = rstore_tail(queue_17,index_18) )
<=> ( queue_19 = rstore_tail(queue_17,index_18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
queue_19 = rstore_tail(queue_17,index_18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp178) ).
tff(22,plain,
queue_19 = rstore_tail(queue_17,index_18),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
rstore_tail(queue_17,index_18) = queue_19,
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
( ( index_18 = s(index_15) )
<=> ( index_18 = s(index_15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
index_18 = s(index_15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp95) ).
tff(26,plain,
index_18 = s(index_15),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
s(index_15) = index_18,
inference(symmetry,[status(thm)],[26]) ).
tff(28,plain,
( ( queue_17 = rstore_seq(q10,earray_16) )
<=> ( queue_17 = rstore_seq(q10,earray_16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,axiom,
queue_17 = rstore_seq(q10,earray_16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp171) ).
tff(30,plain,
queue_17 = rstore_seq(q10,earray_16),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
rstore_seq(q10,earray_16) = queue_17,
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
rstore_tail(rstore_seq(q10,earray_16),s(index_15)) = rstore_tail(queue_17,index_18),
inference(monotonicity,[status(thm)],[31,27]) ).
tff(33,plain,
rstore_tail(rstore_seq(q10,earray_16),s(index_15)) = q11,
inference(transitivity,[status(thm)],[32,23,19]) ).
tff(34,plain,
rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_tail(q11),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
rselect_tail(q11) = rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
rselect_tail(q11) = s(rselect_tail(q10)),
inference(transitivity,[status(thm)],[35,15,6]) ).
tff(37,plain,
( ( rselect_tail(q11) = rselect_tail(q10) )
<=> ( s(rselect_tail(q10)) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( ( s(rselect_tail(q10)) = rselect_tail(q10) )
<=> ( rselect_tail(q11) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( ( s(rselect_tail(q10)) != rselect_tail(q10) )
<=> ( rselect_tail(q11) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
^ [X: $i] :
refl(( ( s(X) != X )
<=> ( s(X) != X ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [X: $i] : ( s(X) != X )
<=> ! [X: $i] : ( s(X) != X ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [X: $i] : ( s(X) != X )
<=> ! [X: $i] : ( s(X) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,axiom,
! [X: $i] : ( s(X) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as1) ).
tff(44,plain,
! [X: $i] : ( s(X) != X ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] : ( s(X) != X ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [X: $i] : ( s(X) != X ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
( ~ ! [X: $i] : ( s(X) != X )
| ( s(rselect_tail(q10)) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
s(rselect_tail(q10)) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
rselect_tail(q11) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[48,39]) ).
tff(50,plain,
( ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
<=> ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
<=> ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,axiom,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
tff(53,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E ),
inference(modus_ponens,[status(thm)],[54,50]) ).
tff(56,plain,
( ~ ! [I: $i,E: $i,A: $i] : ( select(store(A,I,E),I) = E )
| ( select(store(rselect_seq(q10),rselect_tail(q10),e10),rselect_tail(q10)) = e10 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(57,plain,
select(store(rselect_seq(q10),rselect_tail(q10),e10),rselect_tail(q10)) = e10,
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
( ( earray_14 = rselect_seq(q10) )
<=> ( earray_14 = rselect_seq(q10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
earray_14 = rselect_seq(q10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp12) ).
tff(60,plain,
earray_14 = rselect_seq(q10),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
rselect_seq(q10) = earray_14,
inference(symmetry,[status(thm)],[60]) ).
tff(62,plain,
store(rselect_seq(q10),rselect_tail(q10),e10) = store(earray_14,index_15,e10),
inference(monotonicity,[status(thm)],[61,4]) ).
tff(63,plain,
store(earray_14,index_15,e10) = store(rselect_seq(q10),rselect_tail(q10),e10),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
select(store(earray_14,index_15,e10),rselect_tail(q10)) = select(store(rselect_seq(q10),rselect_tail(q10),e10),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
select(store(earray_14,index_15,e10),rselect_tail(q10)) = e10,
inference(transitivity,[status(thm)],[64,57]) ).
tff(66,plain,
( ( elem_214 = select(earray_212,index_213) )
<=> ( elem_214 = select(earray_212,index_213) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
elem_214 = select(earray_212,index_213),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp61) ).
tff(68,plain,
elem_214 = select(earray_212,index_213),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
select(earray_212,index_213) = elem_214,
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
( ( index_213 = rselect_head(q30) )
<=> ( index_213 = rselect_head(q30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
index_213 = rselect_head(q30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp110) ).
tff(72,plain,
index_213 = rselect_head(q30),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
rselect_head(q30) = index_213,
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ( index_168 = s(index_167) )
<=> ( index_168 = s(index_167) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,axiom,
index_168 = s(index_167),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp91) ).
tff(76,plain,
index_168 = s(index_167),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
s(index_167) = index_168,
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
( ( queue_166 = rstore_tail(queue_164,index_165) )
<=> ( queue_166 = rstore_tail(queue_164,index_165) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
queue_166 = rstore_tail(queue_164,index_165),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp169) ).
tff(80,plain,
queue_166 = rstore_tail(queue_164,index_165),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
rstore_tail(queue_164,index_165) = queue_166,
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
rstore_head(rstore_tail(queue_164,index_165),s(index_167)) = rstore_head(queue_166,index_168),
inference(monotonicity,[status(thm)],[81,77]) ).
tff(83,plain,
rstore_head(queue_166,index_168) = rstore_head(rstore_tail(queue_164,index_165),s(index_167)),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
( ( queue_169 = rstore_head(queue_166,index_168) )
<=> ( queue_169 = rstore_head(queue_166,index_168) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,axiom,
queue_169 = rstore_head(queue_166,index_168),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp170) ).
tff(86,plain,
queue_169 = rstore_head(queue_166,index_168),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ( q30 = queue_169 )
<=> ( q30 = queue_169 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
q30 = queue_169,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp239) ).
tff(89,plain,
q30 = queue_169,
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
q30 = rstore_head(rstore_tail(queue_164,index_165),s(index_167)),
inference(transitivity,[status(thm)],[89,86,83]) ).
tff(91,plain,
rselect_head(q30) = rselect_head(rstore_head(rstore_tail(queue_164,index_165),s(index_167))),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
rselect_head(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = rselect_head(q30),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_head(rstore_head(A,E)) = E )
<=> ( rselect_head(rstore_head(A,E)) = E ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,axiom,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_head) ).
tff(97,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
inference(skolemize,[status(sab)],[97]) ).
tff(99,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = s(index_167) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
rselect_head(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = s(index_167),
inference(unit_resolution,[status(thm)],[100,99]) ).
tff(102,plain,
s(index_167) = rselect_head(rstore_head(rstore_tail(queue_164,index_165),s(index_167))),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ( index_137 = rselect_head(queue_136) )
<=> ( index_137 = rselect_head(queue_136) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,axiom,
index_137 = rselect_head(queue_136),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp77) ).
tff(105,plain,
index_137 = rselect_head(queue_136),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
rselect_head(queue_136) = index_137,
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
s(rselect_head(queue_136)) = s(index_137),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
s(index_137) = s(rselect_head(queue_136)),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = s(index_137) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(110,plain,
rselect_head(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = s(index_137),
inference(unit_resolution,[status(thm)],[109,99]) ).
tff(111,plain,
( ( index_138 = s(index_137) )
<=> ( index_138 = s(index_137) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,axiom,
index_138 = s(index_137),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp78) ).
tff(113,plain,
index_138 = s(index_137),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
s(index_137) = index_138,
inference(symmetry,[status(thm)],[113]) ).
tff(115,plain,
( ( queue_136 = rstore_tail(queue_134,index_135) )
<=> ( queue_136 = rstore_tail(queue_134,index_135) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,axiom,
queue_136 = rstore_tail(queue_134,index_135),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp159) ).
tff(117,plain,
queue_136 = rstore_tail(queue_134,index_135),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
rstore_tail(queue_134,index_135) = queue_136,
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
rstore_head(rstore_tail(queue_134,index_135),s(index_137)) = rstore_head(queue_136,index_138),
inference(monotonicity,[status(thm)],[118,114]) ).
tff(120,plain,
rselect_head(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_head(rstore_head(queue_136,index_138)),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
rselect_head(rstore_head(queue_136,index_138)) = rselect_head(rstore_head(rstore_tail(queue_134,index_135),s(index_137))),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
<=> ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,axiom,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_head_seq) ).
tff(126,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = rselect_head(rstore_head(queue_136,index_138)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(130,plain,
rselect_head(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = rselect_head(rstore_head(queue_136,index_138)),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
( ( earray_142 = store(earray_140,index_141,e27) )
<=> ( earray_142 = store(earray_140,index_141,e27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,axiom,
earray_142 = store(earray_140,index_141,e27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp14) ).
tff(133,plain,
earray_142 = store(earray_140,index_141,e27),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
store(earray_140,index_141,e27) = earray_142,
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ( q27 = queue_139 )
<=> ( q27 = queue_139 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(136,axiom,
q27 = queue_139,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp235) ).
tff(137,plain,
q27 = queue_139,
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
queue_139 = q27,
inference(symmetry,[status(thm)],[137]) ).
tff(139,plain,
( ( queue_139 = rstore_head(queue_136,index_138) )
<=> ( queue_139 = rstore_head(queue_136,index_138) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,axiom,
queue_139 = rstore_head(queue_136,index_138),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp160) ).
tff(141,plain,
queue_139 = rstore_head(queue_136,index_138),
inference(modus_ponens,[status(thm)],[140,139]) ).
tff(142,plain,
rstore_head(queue_136,index_138) = queue_139,
inference(symmetry,[status(thm)],[141]) ).
tff(143,plain,
rstore_head(queue_136,index_138) = q27,
inference(transitivity,[status(thm)],[142,138]) ).
tff(144,plain,
rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27)) = rstore_seq(q27,earray_142),
inference(monotonicity,[status(thm)],[143,134]) ).
tff(145,plain,
rselect_head(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = rselect_head(rstore_seq(q27,earray_142)),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
rselect_head(rstore_seq(q27,earray_142)) = rselect_head(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
<=> ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,plain,
( ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
<=> ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,axiom,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_head_tail) ).
tff(151,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) ),
inference(modus_ponens,[status(thm)],[152,148]) ).
tff(154,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_head(rstore_seq(q27,earray_142)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(155,plain,
rselect_head(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_head(rstore_seq(q27,earray_142)),
inference(unit_resolution,[status(thm)],[154,153]) ).
tff(156,plain,
( ( index_144 = s(index_141) )
<=> ( index_144 = s(index_141) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,axiom,
index_144 = s(index_141),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp80) ).
tff(158,plain,
index_144 = s(index_141),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
s(index_141) = index_144,
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
( ( queue_143 = rstore_seq(q27,earray_142) )
<=> ( queue_143 = rstore_seq(q27,earray_142) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(161,axiom,
queue_143 = rstore_seq(q27,earray_142),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp161) ).
tff(162,plain,
queue_143 = rstore_seq(q27,earray_142),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
rstore_seq(q27,earray_142) = queue_143,
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
rstore_tail(rstore_seq(q27,earray_142),s(index_141)) = rstore_tail(queue_143,index_144),
inference(monotonicity,[status(thm)],[163,159]) ).
tff(165,plain,
rstore_tail(queue_143,index_144) = rstore_tail(rstore_seq(q27,earray_142),s(index_141)),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
rselect_head(rstore_tail(queue_143,index_144)) = rselect_head(rstore_tail(rstore_seq(q27,earray_142),s(index_141))),
inference(monotonicity,[status(thm)],[165]) ).
tff(167,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))) = rselect_head(rstore_tail(queue_143,index_144)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(168,plain,
rselect_head(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))) = rselect_head(rstore_tail(queue_143,index_144)),
inference(unit_resolution,[status(thm)],[167,128]) ).
tff(169,plain,
( ( earray_148 = store(earray_146,index_147,e28) )
<=> ( earray_148 = store(earray_146,index_147,e28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,axiom,
earray_148 = store(earray_146,index_147,e28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp16) ).
tff(171,plain,
earray_148 = store(earray_146,index_147,e28),
inference(modus_ponens,[status(thm)],[170,169]) ).
tff(172,plain,
store(earray_146,index_147,e28) = earray_148,
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
( ( q28 = queue_145 )
<=> ( q28 = queue_145 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,axiom,
q28 = queue_145,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp236) ).
tff(175,plain,
q28 = queue_145,
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
queue_145 = q28,
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
( ( queue_145 = rstore_tail(queue_143,index_144) )
<=> ( queue_145 = rstore_tail(queue_143,index_144) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(178,axiom,
queue_145 = rstore_tail(queue_143,index_144),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp162) ).
tff(179,plain,
queue_145 = rstore_tail(queue_143,index_144),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
rstore_tail(queue_143,index_144) = queue_145,
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
rstore_tail(queue_143,index_144) = q28,
inference(transitivity,[status(thm)],[180,176]) ).
tff(182,plain,
rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28)) = rstore_seq(q28,earray_148),
inference(monotonicity,[status(thm)],[181,172]) ).
tff(183,plain,
rstore_seq(q28,earray_148) = rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28)),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
rselect_head(rstore_seq(q28,earray_148)) = rselect_head(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_head(rstore_seq(q28,earray_148)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
rselect_head(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_head(rstore_seq(q28,earray_148)),
inference(unit_resolution,[status(thm)],[185,153]) ).
tff(187,plain,
( ( index_150 = s(index_147) )
<=> ( index_150 = s(index_147) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,axiom,
index_150 = s(index_147),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp83) ).
tff(189,plain,
index_150 = s(index_147),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
s(index_147) = index_150,
inference(symmetry,[status(thm)],[189]) ).
tff(191,plain,
( ( queue_149 = rstore_seq(q28,earray_148) )
<=> ( queue_149 = rstore_seq(q28,earray_148) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(192,axiom,
queue_149 = rstore_seq(q28,earray_148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp163) ).
tff(193,plain,
queue_149 = rstore_seq(q28,earray_148),
inference(modus_ponens,[status(thm)],[192,191]) ).
tff(194,plain,
rstore_seq(q28,earray_148) = queue_149,
inference(symmetry,[status(thm)],[193]) ).
tff(195,plain,
rstore_tail(rstore_seq(q28,earray_148),s(index_147)) = rstore_tail(queue_149,index_150),
inference(monotonicity,[status(thm)],[194,190]) ).
tff(196,plain,
rstore_tail(queue_149,index_150) = rstore_tail(rstore_seq(q28,earray_148),s(index_147)),
inference(symmetry,[status(thm)],[195]) ).
tff(197,plain,
rselect_head(rstore_tail(queue_149,index_150)) = rselect_head(rstore_tail(rstore_seq(q28,earray_148),s(index_147))),
inference(monotonicity,[status(thm)],[196]) ).
tff(198,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))) = rselect_head(rstore_tail(queue_149,index_150)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(199,plain,
rselect_head(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))) = rselect_head(rstore_tail(queue_149,index_150)),
inference(unit_resolution,[status(thm)],[198,128]) ).
tff(200,plain,
( ( earray_163 = store(earray_161,index_162,e29) )
<=> ( earray_163 = store(earray_161,index_162,e29) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(201,axiom,
earray_163 = store(earray_161,index_162,e29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp21) ).
tff(202,plain,
earray_163 = store(earray_161,index_162,e29),
inference(modus_ponens,[status(thm)],[201,200]) ).
tff(203,plain,
store(earray_161,index_162,e29) = earray_163,
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
( ( q29 = queue_151 )
<=> ( q29 = queue_151 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(205,axiom,
q29 = queue_151,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp237) ).
tff(206,plain,
q29 = queue_151,
inference(modus_ponens,[status(thm)],[205,204]) ).
tff(207,plain,
queue_151 = q29,
inference(symmetry,[status(thm)],[206]) ).
tff(208,plain,
( ( queue_151 = rstore_tail(queue_149,index_150) )
<=> ( queue_151 = rstore_tail(queue_149,index_150) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(209,axiom,
queue_151 = rstore_tail(queue_149,index_150),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp164) ).
tff(210,plain,
queue_151 = rstore_tail(queue_149,index_150),
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
rstore_tail(queue_149,index_150) = queue_151,
inference(symmetry,[status(thm)],[210]) ).
tff(212,plain,
rstore_tail(queue_149,index_150) = q29,
inference(transitivity,[status(thm)],[211,207]) ).
tff(213,plain,
rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29)) = rstore_seq(q29,earray_163),
inference(monotonicity,[status(thm)],[212,203]) ).
tff(214,plain,
rstore_seq(q29,earray_163) = rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29)),
inference(symmetry,[status(thm)],[213]) ).
tff(215,plain,
rselect_head(rstore_seq(q29,earray_163)) = rselect_head(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))),
inference(monotonicity,[status(thm)],[214]) ).
tff(216,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_head(rstore_seq(q29,earray_163)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
rselect_head(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_head(rstore_seq(q29,earray_163)),
inference(unit_resolution,[status(thm)],[216,153]) ).
tff(218,plain,
( ( index_165 = s(index_162) )
<=> ( index_165 = s(index_162) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(219,axiom,
index_165 = s(index_162),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp89) ).
tff(220,plain,
index_165 = s(index_162),
inference(modus_ponens,[status(thm)],[219,218]) ).
tff(221,plain,
s(index_162) = index_165,
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
( ( queue_164 = rstore_seq(q29,earray_163) )
<=> ( queue_164 = rstore_seq(q29,earray_163) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(223,axiom,
queue_164 = rstore_seq(q29,earray_163),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp168) ).
tff(224,plain,
queue_164 = rstore_seq(q29,earray_163),
inference(modus_ponens,[status(thm)],[223,222]) ).
tff(225,plain,
rstore_seq(q29,earray_163) = queue_164,
inference(symmetry,[status(thm)],[224]) ).
tff(226,plain,
rstore_tail(rstore_seq(q29,earray_163),s(index_162)) = rstore_tail(queue_164,index_165),
inference(monotonicity,[status(thm)],[225,221]) ).
tff(227,plain,
rstore_tail(queue_164,index_165) = rstore_tail(rstore_seq(q29,earray_163),s(index_162)),
inference(symmetry,[status(thm)],[226]) ).
tff(228,plain,
queue_166 = rstore_tail(rstore_seq(q29,earray_163),s(index_162)),
inference(transitivity,[status(thm)],[80,227]) ).
tff(229,plain,
rselect_head(queue_166) = rselect_head(rstore_tail(rstore_seq(q29,earray_163),s(index_162))),
inference(monotonicity,[status(thm)],[228]) ).
tff(230,plain,
( ( index_167 = rselect_head(queue_166) )
<=> ( index_167 = rselect_head(queue_166) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(231,axiom,
index_167 = rselect_head(queue_166),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp90) ).
tff(232,plain,
index_167 = rselect_head(queue_166),
inference(modus_ponens,[status(thm)],[231,230]) ).
tff(233,plain,
index_167 = s(rselect_head(queue_136)),
inference(transitivity,[status(thm)],[232,229,217,215,199,197,186,184,168,166,155,146,130,121,110,108]) ).
tff(234,plain,
s(index_167) = s(s(rselect_head(queue_136))),
inference(monotonicity,[status(thm)],[233]) ).
tff(235,plain,
s(s(rselect_head(queue_136))) = s(index_167),
inference(symmetry,[status(thm)],[234]) ).
tff(236,plain,
( ( index_9 = rselect_tail(q9) )
<=> ( index_9 = rselect_tail(q9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(237,axiom,
index_9 = rselect_tail(q9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp138) ).
tff(238,plain,
index_9 = rselect_tail(q9),
inference(modus_ponens,[status(thm)],[237,236]) ).
tff(239,plain,
rselect_tail(q9) = index_9,
inference(symmetry,[status(thm)],[238]) ).
tff(240,plain,
( ( index_210 = s(index_209) )
<=> ( index_210 = s(index_209) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(241,axiom,
index_210 = s(index_209),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp109) ).
tff(242,plain,
index_210 = s(index_209),
inference(modus_ponens,[status(thm)],[241,240]) ).
tff(243,plain,
s(index_209) = index_210,
inference(symmetry,[status(thm)],[242]) ).
tff(244,plain,
( ( queue_208 = rstore_tail(queue_206,index_207) )
<=> ( queue_208 = rstore_tail(queue_206,index_207) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(245,axiom,
queue_208 = rstore_tail(queue_206,index_207),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp185) ).
tff(246,plain,
queue_208 = rstore_tail(queue_206,index_207),
inference(modus_ponens,[status(thm)],[245,244]) ).
tff(247,plain,
rstore_tail(queue_206,index_207) = queue_208,
inference(symmetry,[status(thm)],[246]) ).
tff(248,plain,
rstore_head(rstore_tail(queue_206,index_207),s(index_209)) = rstore_head(queue_208,index_210),
inference(monotonicity,[status(thm)],[247,243]) ).
tff(249,plain,
rstore_head(queue_208,index_210) = rstore_head(rstore_tail(queue_206,index_207),s(index_209)),
inference(symmetry,[status(thm)],[248]) ).
tff(250,plain,
( ( queue_211 = rstore_head(queue_208,index_210) )
<=> ( queue_211 = rstore_head(queue_208,index_210) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(251,axiom,
queue_211 = rstore_head(queue_208,index_210),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp186) ).
tff(252,plain,
queue_211 = rstore_head(queue_208,index_210),
inference(modus_ponens,[status(thm)],[251,250]) ).
tff(253,plain,
( ( q9 = queue_211 )
<=> ( q9 = queue_211 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(254,axiom,
q9 = queue_211,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp245) ).
tff(255,plain,
q9 = queue_211,
inference(modus_ponens,[status(thm)],[254,253]) ).
tff(256,plain,
q9 = rstore_head(rstore_tail(queue_206,index_207),s(index_209)),
inference(transitivity,[status(thm)],[255,252,249]) ).
tff(257,plain,
rselect_tail(q9) = rselect_tail(rstore_head(rstore_tail(queue_206,index_207),s(index_209))),
inference(monotonicity,[status(thm)],[256]) ).
tff(258,plain,
rselect_tail(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = rselect_tail(q9),
inference(symmetry,[status(thm)],[257]) ).
tff(259,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
<=> ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ) )),
inference(bind,[status(th)],[]) ).
tff(260,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ) ),
inference(quant_intro,[status(thm)],[259]) ).
tff(261,plain,
( ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
<=> ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(262,axiom,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_tail_head) ).
tff(263,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
inference(modus_ponens,[status(thm)],[262,261]) ).
tff(264,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
inference(skolemize,[status(sab)],[263]) ).
tff(265,plain,
! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) ),
inference(modus_ponens,[status(thm)],[264,260]) ).
tff(266,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = rselect_tail(rstore_tail(queue_206,index_207)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(267,plain,
rselect_tail(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = rselect_tail(rstore_tail(queue_206,index_207)),
inference(unit_resolution,[status(thm)],[266,265]) ).
tff(268,plain,
rselect_tail(rstore_tail(queue_206,index_207)) = rselect_tail(rstore_head(rstore_tail(queue_206,index_207),s(index_209))),
inference(symmetry,[status(thm)],[267]) ).
tff(269,plain,
( ( index_207 = s(index_204) )
<=> ( index_207 = s(index_204) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(270,axiom,
index_207 = s(index_204),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp106) ).
tff(271,plain,
index_207 = s(index_204),
inference(modus_ponens,[status(thm)],[270,269]) ).
tff(272,plain,
s(index_204) = index_207,
inference(symmetry,[status(thm)],[271]) ).
tff(273,plain,
( ( queue_206 = rstore_seq(q8,earray_205) )
<=> ( queue_206 = rstore_seq(q8,earray_205) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(274,axiom,
queue_206 = rstore_seq(q8,earray_205),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp184) ).
tff(275,plain,
queue_206 = rstore_seq(q8,earray_205),
inference(modus_ponens,[status(thm)],[274,273]) ).
tff(276,plain,
rstore_seq(q8,earray_205) = queue_206,
inference(symmetry,[status(thm)],[275]) ).
tff(277,plain,
rstore_tail(rstore_seq(q8,earray_205),s(index_204)) = rstore_tail(queue_206,index_207),
inference(monotonicity,[status(thm)],[276,272]) ).
tff(278,plain,
rstore_tail(queue_206,index_207) = rstore_tail(rstore_seq(q8,earray_205),s(index_204)),
inference(symmetry,[status(thm)],[277]) ).
tff(279,plain,
rselect_tail(rstore_tail(queue_206,index_207)) = rselect_tail(rstore_tail(rstore_seq(q8,earray_205),s(index_204))),
inference(monotonicity,[status(thm)],[278]) ).
tff(280,plain,
rselect_tail(rstore_tail(rstore_seq(q8,earray_205),s(index_204))) = rselect_tail(rstore_tail(queue_206,index_207)),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q8,earray_205),s(index_204))) = s(index_204) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(282,plain,
rselect_tail(rstore_tail(rstore_seq(q8,earray_205),s(index_204))) = s(index_204),
inference(unit_resolution,[status(thm)],[281,13]) ).
tff(283,plain,
s(index_204) = rselect_tail(rstore_tail(rstore_seq(q8,earray_205),s(index_204))),
inference(symmetry,[status(thm)],[282]) ).
tff(284,plain,
( ( index_116 = rselect_head(queue_115) )
<=> ( index_116 = rselect_head(queue_115) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(285,axiom,
index_116 = rselect_head(queue_115),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp68) ).
tff(286,plain,
index_116 = rselect_head(queue_115),
inference(modus_ponens,[status(thm)],[285,284]) ).
tff(287,plain,
rselect_head(queue_115) = index_116,
inference(symmetry,[status(thm)],[286]) ).
tff(288,plain,
s(rselect_head(queue_115)) = s(index_116),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
s(index_116) = s(rselect_head(queue_115)),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
( ( index_114 = s(index_111) )
<=> ( index_114 = s(index_111) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(291,axiom,
index_114 = s(index_111),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp67) ).
tff(292,plain,
index_114 = s(index_111),
inference(modus_ponens,[status(thm)],[291,290]) ).
tff(293,plain,
s(index_111) = index_114,
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
( ( queue_113 = rstore_seq(q23,earray_112) )
<=> ( queue_113 = rstore_seq(q23,earray_112) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(295,axiom,
queue_113 = rstore_seq(q23,earray_112),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp150) ).
tff(296,plain,
queue_113 = rstore_seq(q23,earray_112),
inference(modus_ponens,[status(thm)],[295,294]) ).
tff(297,plain,
rstore_seq(q23,earray_112) = queue_113,
inference(symmetry,[status(thm)],[296]) ).
tff(298,plain,
rstore_tail(rstore_seq(q23,earray_112),s(index_111)) = rstore_tail(queue_113,index_114),
inference(monotonicity,[status(thm)],[297,293]) ).
tff(299,plain,
rstore_tail(queue_113,index_114) = rstore_tail(rstore_seq(q23,earray_112),s(index_111)),
inference(symmetry,[status(thm)],[298]) ).
tff(300,plain,
( ( queue_115 = rstore_tail(queue_113,index_114) )
<=> ( queue_115 = rstore_tail(queue_113,index_114) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(301,axiom,
queue_115 = rstore_tail(queue_113,index_114),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp151) ).
tff(302,plain,
queue_115 = rstore_tail(queue_113,index_114),
inference(modus_ponens,[status(thm)],[301,300]) ).
tff(303,plain,
queue_115 = rstore_tail(rstore_seq(q23,earray_112),s(index_111)),
inference(transitivity,[status(thm)],[302,299]) ).
tff(304,plain,
rselect_head(queue_115) = rselect_head(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(monotonicity,[status(thm)],[303]) ).
tff(305,plain,
rselect_head(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_head(queue_115),
inference(symmetry,[status(thm)],[304]) ).
tff(306,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_head(rstore_seq(q23,earray_112)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(307,plain,
rselect_head(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_head(rstore_seq(q23,earray_112)),
inference(unit_resolution,[status(thm)],[306,153]) ).
tff(308,plain,
rselect_head(rstore_seq(q23,earray_112)) = rselect_head(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(symmetry,[status(thm)],[307]) ).
tff(309,plain,
( ( earray_112 = store(earray_110,index_111,e23) )
<=> ( earray_112 = store(earray_110,index_111,e23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(310,axiom,
earray_112 = store(earray_110,index_111,e23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp5) ).
tff(311,plain,
earray_112 = store(earray_110,index_111,e23),
inference(modus_ponens,[status(thm)],[310,309]) ).
tff(312,plain,
store(earray_110,index_111,e23) = earray_112,
inference(symmetry,[status(thm)],[311]) ).
tff(313,plain,
( ( q23 = queue_109 )
<=> ( q23 = queue_109 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(314,axiom,
q23 = queue_109,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp231) ).
tff(315,plain,
q23 = queue_109,
inference(modus_ponens,[status(thm)],[314,313]) ).
tff(316,plain,
queue_109 = q23,
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
( ( queue_109 = rstore_tail(queue_107,index_108) )
<=> ( queue_109 = rstore_tail(queue_107,index_108) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(318,axiom,
queue_109 = rstore_tail(queue_107,index_108),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp148) ).
tff(319,plain,
queue_109 = rstore_tail(queue_107,index_108),
inference(modus_ponens,[status(thm)],[318,317]) ).
tff(320,plain,
rstore_tail(queue_107,index_108) = queue_109,
inference(symmetry,[status(thm)],[319]) ).
tff(321,plain,
rstore_tail(queue_107,index_108) = q23,
inference(transitivity,[status(thm)],[320,316]) ).
tff(322,plain,
rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23)) = rstore_seq(q23,earray_112),
inference(monotonicity,[status(thm)],[321,312]) ).
tff(323,plain,
rstore_seq(q23,earray_112) = rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23)),
inference(symmetry,[status(thm)],[322]) ).
tff(324,plain,
rselect_head(rstore_seq(q23,earray_112)) = rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))),
inference(monotonicity,[status(thm)],[323]) ).
tff(325,plain,
rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = rselect_head(rstore_seq(q23,earray_112)),
inference(symmetry,[status(thm)],[324]) ).
tff(326,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = rselect_head(rstore_tail(queue_107,index_108)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(327,plain,
rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = rselect_head(rstore_tail(queue_107,index_108)),
inference(unit_resolution,[status(thm)],[326,128]) ).
tff(328,plain,
rselect_head(rstore_tail(queue_107,index_108)) = rselect_head(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))),
inference(symmetry,[status(thm)],[327]) ).
tff(329,plain,
( ( index_108 = s(index_105) )
<=> ( index_108 = s(index_105) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(330,axiom,
index_108 = s(index_105),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp65) ).
tff(331,plain,
index_108 = s(index_105),
inference(modus_ponens,[status(thm)],[330,329]) ).
tff(332,plain,
s(index_105) = index_108,
inference(symmetry,[status(thm)],[331]) ).
tff(333,plain,
( ( queue_107 = rstore_seq(q22,earray_106) )
<=> ( queue_107 = rstore_seq(q22,earray_106) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(334,axiom,
queue_107 = rstore_seq(q22,earray_106),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp147) ).
tff(335,plain,
queue_107 = rstore_seq(q22,earray_106),
inference(modus_ponens,[status(thm)],[334,333]) ).
tff(336,plain,
rstore_seq(q22,earray_106) = queue_107,
inference(symmetry,[status(thm)],[335]) ).
tff(337,plain,
rstore_tail(rstore_seq(q22,earray_106),s(index_105)) = rstore_tail(queue_107,index_108),
inference(monotonicity,[status(thm)],[336,332]) ).
tff(338,plain,
rstore_tail(queue_107,index_108) = rstore_tail(rstore_seq(q22,earray_106),s(index_105)),
inference(symmetry,[status(thm)],[337]) ).
tff(339,plain,
rselect_head(rstore_tail(queue_107,index_108)) = rselect_head(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(monotonicity,[status(thm)],[338]) ).
tff(340,plain,
rselect_head(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_head(rstore_tail(queue_107,index_108)),
inference(symmetry,[status(thm)],[339]) ).
tff(341,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_head(rstore_seq(q22,earray_106)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(342,plain,
rselect_head(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_head(rstore_seq(q22,earray_106)),
inference(unit_resolution,[status(thm)],[341,153]) ).
tff(343,plain,
rselect_head(rstore_seq(q22,earray_106)) = rselect_head(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(symmetry,[status(thm)],[342]) ).
tff(344,plain,
( ( earray_106 = store(earray_104,index_105,e22) )
<=> ( earray_106 = store(earray_104,index_105,e22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(345,axiom,
earray_106 = store(earray_104,index_105,e22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp3) ).
tff(346,plain,
earray_106 = store(earray_104,index_105,e22),
inference(modus_ponens,[status(thm)],[345,344]) ).
tff(347,plain,
store(earray_104,index_105,e22) = earray_106,
inference(symmetry,[status(thm)],[346]) ).
tff(348,plain,
( ( q22 = queue_103 )
<=> ( q22 = queue_103 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(349,axiom,
q22 = queue_103,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp230) ).
tff(350,plain,
q22 = queue_103,
inference(modus_ponens,[status(thm)],[349,348]) ).
tff(351,plain,
queue_103 = q22,
inference(symmetry,[status(thm)],[350]) ).
tff(352,plain,
( ( queue_103 = rstore_tail(queue_101,index_102) )
<=> ( queue_103 = rstore_tail(queue_101,index_102) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(353,axiom,
queue_103 = rstore_tail(queue_101,index_102),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp146) ).
tff(354,plain,
queue_103 = rstore_tail(queue_101,index_102),
inference(modus_ponens,[status(thm)],[353,352]) ).
tff(355,plain,
rstore_tail(queue_101,index_102) = queue_103,
inference(symmetry,[status(thm)],[354]) ).
tff(356,plain,
rstore_tail(queue_101,index_102) = q22,
inference(transitivity,[status(thm)],[355,351]) ).
tff(357,plain,
rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22)) = rstore_seq(q22,earray_106),
inference(monotonicity,[status(thm)],[356,347]) ).
tff(358,plain,
rstore_seq(q22,earray_106) = rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22)),
inference(symmetry,[status(thm)],[357]) ).
tff(359,plain,
rselect_head(rstore_seq(q22,earray_106)) = rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))),
inference(monotonicity,[status(thm)],[358]) ).
tff(360,plain,
rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = rselect_head(rstore_seq(q22,earray_106)),
inference(symmetry,[status(thm)],[359]) ).
tff(361,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = rselect_head(rstore_tail(queue_101,index_102)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(362,plain,
rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = rselect_head(rstore_tail(queue_101,index_102)),
inference(unit_resolution,[status(thm)],[361,128]) ).
tff(363,plain,
rselect_head(rstore_tail(queue_101,index_102)) = rselect_head(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))),
inference(symmetry,[status(thm)],[362]) ).
tff(364,plain,
( ( index_102 = s(index_99) )
<=> ( index_102 = s(index_99) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(365,axiom,
index_102 = s(index_99),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp63) ).
tff(366,plain,
index_102 = s(index_99),
inference(modus_ponens,[status(thm)],[365,364]) ).
tff(367,plain,
s(index_99) = index_102,
inference(symmetry,[status(thm)],[366]) ).
tff(368,plain,
( ( queue_101 = rstore_seq(q21,earray_100) )
<=> ( queue_101 = rstore_seq(q21,earray_100) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(369,axiom,
queue_101 = rstore_seq(q21,earray_100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp145) ).
tff(370,plain,
queue_101 = rstore_seq(q21,earray_100),
inference(modus_ponens,[status(thm)],[369,368]) ).
tff(371,plain,
rstore_seq(q21,earray_100) = queue_101,
inference(symmetry,[status(thm)],[370]) ).
tff(372,plain,
rstore_tail(rstore_seq(q21,earray_100),s(index_99)) = rstore_tail(queue_101,index_102),
inference(monotonicity,[status(thm)],[371,367]) ).
tff(373,plain,
rstore_tail(queue_101,index_102) = rstore_tail(rstore_seq(q21,earray_100),s(index_99)),
inference(symmetry,[status(thm)],[372]) ).
tff(374,plain,
rselect_head(rstore_tail(queue_101,index_102)) = rselect_head(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(monotonicity,[status(thm)],[373]) ).
tff(375,plain,
rselect_head(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_head(rstore_tail(queue_101,index_102)),
inference(symmetry,[status(thm)],[374]) ).
tff(376,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_head(rstore_seq(q21,earray_100)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(377,plain,
rselect_head(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_head(rstore_seq(q21,earray_100)),
inference(unit_resolution,[status(thm)],[376,153]) ).
tff(378,plain,
rselect_head(rstore_seq(q21,earray_100)) = rselect_head(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(symmetry,[status(thm)],[377]) ).
tff(379,plain,
( ( earray_100 = store(earray_98,index_99,e21) )
<=> ( earray_100 = store(earray_98,index_99,e21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(380,axiom,
earray_100 = store(earray_98,index_99,e21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp1) ).
tff(381,plain,
earray_100 = store(earray_98,index_99,e21),
inference(modus_ponens,[status(thm)],[380,379]) ).
tff(382,plain,
store(earray_98,index_99,e21) = earray_100,
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
( ( q21 = queue_97 )
<=> ( q21 = queue_97 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(384,axiom,
q21 = queue_97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp229) ).
tff(385,plain,
q21 = queue_97,
inference(modus_ponens,[status(thm)],[384,383]) ).
tff(386,plain,
queue_97 = q21,
inference(symmetry,[status(thm)],[385]) ).
tff(387,plain,
( ( queue_97 = rstore_head(queue_94,index_96) )
<=> ( queue_97 = rstore_head(queue_94,index_96) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(388,axiom,
queue_97 = rstore_head(queue_94,index_96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp214) ).
tff(389,plain,
queue_97 = rstore_head(queue_94,index_96),
inference(modus_ponens,[status(thm)],[388,387]) ).
tff(390,plain,
rstore_head(queue_94,index_96) = queue_97,
inference(symmetry,[status(thm)],[389]) ).
tff(391,plain,
rstore_head(queue_94,index_96) = q21,
inference(transitivity,[status(thm)],[390,386]) ).
tff(392,plain,
rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21)) = rstore_seq(q21,earray_100),
inference(monotonicity,[status(thm)],[391,382]) ).
tff(393,plain,
rselect_head(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = rselect_head(rstore_seq(q21,earray_100)),
inference(monotonicity,[status(thm)],[392]) ).
tff(394,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = rselect_head(rstore_head(queue_94,index_96)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(395,plain,
rselect_head(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = rselect_head(rstore_head(queue_94,index_96)),
inference(unit_resolution,[status(thm)],[394,128]) ).
tff(396,plain,
rselect_head(rstore_head(queue_94,index_96)) = rselect_head(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))),
inference(symmetry,[status(thm)],[395]) ).
tff(397,plain,
( ( index_96 = s(index_95) )
<=> ( index_96 = s(index_95) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(398,axiom,
index_96 = s(index_95),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp142) ).
tff(399,plain,
index_96 = s(index_95),
inference(modus_ponens,[status(thm)],[398,397]) ).
tff(400,plain,
s(index_95) = index_96,
inference(symmetry,[status(thm)],[399]) ).
tff(401,plain,
( ( queue_94 = rstore_tail(queue_92,index_93) )
<=> ( queue_94 = rstore_tail(queue_92,index_93) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(402,axiom,
queue_94 = rstore_tail(queue_92,index_93),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp213) ).
tff(403,plain,
queue_94 = rstore_tail(queue_92,index_93),
inference(modus_ponens,[status(thm)],[402,401]) ).
tff(404,plain,
rstore_tail(queue_92,index_93) = queue_94,
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
rstore_head(rstore_tail(queue_92,index_93),s(index_95)) = rstore_head(queue_94,index_96),
inference(monotonicity,[status(thm)],[404,400]) ).
tff(406,plain,
rselect_head(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_head(rstore_head(queue_94,index_96)),
inference(monotonicity,[status(thm)],[405]) ).
tff(407,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = s(index_95) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(408,plain,
rselect_head(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = s(index_95),
inference(unit_resolution,[status(thm)],[407,99]) ).
tff(409,plain,
s(index_95) = rselect_head(rstore_head(rstore_tail(queue_92,index_93),s(index_95))),
inference(symmetry,[status(thm)],[408]) ).
tff(410,plain,
( ( index_95 = rselect_head(queue_94) )
<=> ( index_95 = rselect_head(queue_94) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(411,axiom,
index_95 = rselect_head(queue_94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp141) ).
tff(412,plain,
index_95 = rselect_head(queue_94),
inference(modus_ponens,[status(thm)],[411,410]) ).
tff(413,plain,
rselect_head(queue_94) = index_95,
inference(symmetry,[status(thm)],[412]) ).
tff(414,plain,
s(rselect_head(queue_94)) = s(index_95),
inference(monotonicity,[status(thm)],[413]) ).
tff(415,plain,
s(rselect_head(queue_94)) = index_116,
inference(transitivity,[status(thm)],[414,409,406,396,393,378,375,363,360,343,340,328,325,308,305,287]) ).
tff(416,plain,
s(s(rselect_head(queue_94))) = s(index_116),
inference(monotonicity,[status(thm)],[415]) ).
tff(417,plain,
s(index_95) = s(rselect_head(queue_94)),
inference(symmetry,[status(thm)],[414]) ).
tff(418,plain,
( ( index_93 = s(index_90) )
<=> ( index_93 = s(index_90) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(419,axiom,
index_93 = s(index_90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp140) ).
tff(420,plain,
index_93 = s(index_90),
inference(modus_ponens,[status(thm)],[419,418]) ).
tff(421,plain,
s(index_90) = index_93,
inference(symmetry,[status(thm)],[420]) ).
tff(422,plain,
( ( queue_92 = rstore_seq(q20,earray_91) )
<=> ( queue_92 = rstore_seq(q20,earray_91) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(423,axiom,
queue_92 = rstore_seq(q20,earray_91),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp212) ).
tff(424,plain,
queue_92 = rstore_seq(q20,earray_91),
inference(modus_ponens,[status(thm)],[423,422]) ).
tff(425,plain,
rstore_seq(q20,earray_91) = queue_92,
inference(symmetry,[status(thm)],[424]) ).
tff(426,plain,
rstore_tail(rstore_seq(q20,earray_91),s(index_90)) = rstore_tail(queue_92,index_93),
inference(monotonicity,[status(thm)],[425,421]) ).
tff(427,plain,
rstore_tail(queue_92,index_93) = rstore_tail(rstore_seq(q20,earray_91),s(index_90)),
inference(symmetry,[status(thm)],[426]) ).
tff(428,plain,
queue_94 = rstore_tail(rstore_seq(q20,earray_91),s(index_90)),
inference(transitivity,[status(thm)],[403,427]) ).
tff(429,plain,
rselect_head(queue_94) = rselect_head(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(monotonicity,[status(thm)],[428]) ).
tff(430,plain,
rselect_head(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_head(queue_94),
inference(symmetry,[status(thm)],[429]) ).
tff(431,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_head(rstore_seq(q20,earray_91)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(432,plain,
rselect_head(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_head(rstore_seq(q20,earray_91)),
inference(unit_resolution,[status(thm)],[431,153]) ).
tff(433,plain,
rselect_head(rstore_seq(q20,earray_91)) = rselect_head(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(symmetry,[status(thm)],[432]) ).
tff(434,plain,
( ( earray_91 = store(earray_89,index_90,e20) )
<=> ( earray_91 = store(earray_89,index_90,e20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(435,axiom,
earray_91 = store(earray_89,index_90,e20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp59) ).
tff(436,plain,
earray_91 = store(earray_89,index_90,e20),
inference(modus_ponens,[status(thm)],[435,434]) ).
tff(437,plain,
store(earray_89,index_90,e20) = earray_91,
inference(symmetry,[status(thm)],[436]) ).
tff(438,plain,
( ( q20 = queue_88 )
<=> ( q20 = queue_88 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(439,axiom,
q20 = queue_88,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp228) ).
tff(440,plain,
q20 = queue_88,
inference(modus_ponens,[status(thm)],[439,438]) ).
tff(441,plain,
queue_88 = q20,
inference(symmetry,[status(thm)],[440]) ).
tff(442,plain,
( ( queue_88 = rstore_tail(queue_86,index_87) )
<=> ( queue_88 = rstore_tail(queue_86,index_87) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(443,axiom,
queue_88 = rstore_tail(queue_86,index_87),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp211) ).
tff(444,plain,
queue_88 = rstore_tail(queue_86,index_87),
inference(modus_ponens,[status(thm)],[443,442]) ).
tff(445,plain,
rstore_tail(queue_86,index_87) = queue_88,
inference(symmetry,[status(thm)],[444]) ).
tff(446,plain,
rstore_tail(queue_86,index_87) = q20,
inference(transitivity,[status(thm)],[445,441]) ).
tff(447,plain,
rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20)) = rstore_seq(q20,earray_91),
inference(monotonicity,[status(thm)],[446,437]) ).
tff(448,plain,
rstore_seq(q20,earray_91) = rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20)),
inference(symmetry,[status(thm)],[447]) ).
tff(449,plain,
rselect_head(rstore_seq(q20,earray_91)) = rselect_head(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))),
inference(monotonicity,[status(thm)],[448]) ).
tff(450,plain,
rselect_head(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = rselect_head(rstore_seq(q20,earray_91)),
inference(symmetry,[status(thm)],[449]) ).
tff(451,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = rselect_head(rstore_tail(queue_86,index_87)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(452,plain,
rselect_head(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = rselect_head(rstore_tail(queue_86,index_87)),
inference(unit_resolution,[status(thm)],[451,128]) ).
tff(453,plain,
rselect_head(rstore_tail(queue_86,index_87)) = rselect_head(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))),
inference(symmetry,[status(thm)],[452]) ).
tff(454,plain,
( ( index_87 = s(index_84) )
<=> ( index_87 = s(index_84) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(455,axiom,
index_87 = s(index_84),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp137) ).
tff(456,plain,
index_87 = s(index_84),
inference(modus_ponens,[status(thm)],[455,454]) ).
tff(457,plain,
s(index_84) = index_87,
inference(symmetry,[status(thm)],[456]) ).
tff(458,plain,
( ( queue_86 = rstore_seq(q19,earray_85) )
<=> ( queue_86 = rstore_seq(q19,earray_85) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(459,axiom,
queue_86 = rstore_seq(q19,earray_85),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp210) ).
tff(460,plain,
queue_86 = rstore_seq(q19,earray_85),
inference(modus_ponens,[status(thm)],[459,458]) ).
tff(461,plain,
rstore_seq(q19,earray_85) = queue_86,
inference(symmetry,[status(thm)],[460]) ).
tff(462,plain,
rstore_tail(rstore_seq(q19,earray_85),s(index_84)) = rstore_tail(queue_86,index_87),
inference(monotonicity,[status(thm)],[461,457]) ).
tff(463,plain,
rstore_tail(queue_86,index_87) = rstore_tail(rstore_seq(q19,earray_85),s(index_84)),
inference(symmetry,[status(thm)],[462]) ).
tff(464,plain,
rselect_head(rstore_tail(queue_86,index_87)) = rselect_head(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(monotonicity,[status(thm)],[463]) ).
tff(465,plain,
rselect_head(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_head(rstore_tail(queue_86,index_87)),
inference(symmetry,[status(thm)],[464]) ).
tff(466,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_head(rstore_seq(q19,earray_85)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(467,plain,
rselect_head(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_head(rstore_seq(q19,earray_85)),
inference(unit_resolution,[status(thm)],[466,153]) ).
tff(468,plain,
rselect_head(rstore_seq(q19,earray_85)) = rselect_head(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(symmetry,[status(thm)],[467]) ).
tff(469,plain,
( ( earray_85 = store(earray_83,index_84,e19) )
<=> ( earray_85 = store(earray_83,index_84,e19) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(470,axiom,
earray_85 = store(earray_83,index_84,e19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp57) ).
tff(471,plain,
earray_85 = store(earray_83,index_84,e19),
inference(modus_ponens,[status(thm)],[470,469]) ).
tff(472,plain,
store(earray_83,index_84,e19) = earray_85,
inference(symmetry,[status(thm)],[471]) ).
tff(473,plain,
( ( q19 = queue_76 )
<=> ( q19 = queue_76 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(474,axiom,
q19 = queue_76,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp226) ).
tff(475,plain,
q19 = queue_76,
inference(modus_ponens,[status(thm)],[474,473]) ).
tff(476,plain,
queue_76 = q19,
inference(symmetry,[status(thm)],[475]) ).
tff(477,plain,
( ( queue_76 = rstore_tail(queue_74,index_75) )
<=> ( queue_76 = rstore_tail(queue_74,index_75) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(478,axiom,
queue_76 = rstore_tail(queue_74,index_75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp207) ).
tff(479,plain,
queue_76 = rstore_tail(queue_74,index_75),
inference(modus_ponens,[status(thm)],[478,477]) ).
tff(480,plain,
rstore_tail(queue_74,index_75) = queue_76,
inference(symmetry,[status(thm)],[479]) ).
tff(481,plain,
rstore_tail(queue_74,index_75) = q19,
inference(transitivity,[status(thm)],[480,476]) ).
tff(482,plain,
rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19)) = rstore_seq(q19,earray_85),
inference(monotonicity,[status(thm)],[481,472]) ).
tff(483,plain,
rstore_seq(q19,earray_85) = rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19)),
inference(symmetry,[status(thm)],[482]) ).
tff(484,plain,
rselect_head(rstore_seq(q19,earray_85)) = rselect_head(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))),
inference(monotonicity,[status(thm)],[483]) ).
tff(485,plain,
rselect_head(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = rselect_head(rstore_seq(q19,earray_85)),
inference(symmetry,[status(thm)],[484]) ).
tff(486,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = rselect_head(rstore_tail(queue_74,index_75)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(487,plain,
rselect_head(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = rselect_head(rstore_tail(queue_74,index_75)),
inference(unit_resolution,[status(thm)],[486,128]) ).
tff(488,plain,
rselect_head(rstore_tail(queue_74,index_75)) = rselect_head(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))),
inference(symmetry,[status(thm)],[487]) ).
tff(489,plain,
( ( index_75 = s(index_72) )
<=> ( index_75 = s(index_72) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(490,axiom,
index_75 = s(index_72),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp133) ).
tff(491,plain,
index_75 = s(index_72),
inference(modus_ponens,[status(thm)],[490,489]) ).
tff(492,plain,
s(index_72) = index_75,
inference(symmetry,[status(thm)],[491]) ).
tff(493,plain,
( ( queue_74 = rstore_seq(q18,earray_73) )
<=> ( queue_74 = rstore_seq(q18,earray_73) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(494,axiom,
queue_74 = rstore_seq(q18,earray_73),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp206) ).
tff(495,plain,
queue_74 = rstore_seq(q18,earray_73),
inference(modus_ponens,[status(thm)],[494,493]) ).
tff(496,plain,
rstore_seq(q18,earray_73) = queue_74,
inference(symmetry,[status(thm)],[495]) ).
tff(497,plain,
rstore_tail(rstore_seq(q18,earray_73),s(index_72)) = rstore_tail(queue_74,index_75),
inference(monotonicity,[status(thm)],[496,492]) ).
tff(498,plain,
rstore_tail(queue_74,index_75) = rstore_tail(rstore_seq(q18,earray_73),s(index_72)),
inference(symmetry,[status(thm)],[497]) ).
tff(499,plain,
rselect_head(rstore_tail(queue_74,index_75)) = rselect_head(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(monotonicity,[status(thm)],[498]) ).
tff(500,plain,
rselect_head(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_head(rstore_tail(queue_74,index_75)),
inference(symmetry,[status(thm)],[499]) ).
tff(501,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_head(rstore_seq(q18,earray_73)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(502,plain,
rselect_head(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_head(rstore_seq(q18,earray_73)),
inference(unit_resolution,[status(thm)],[501,153]) ).
tff(503,plain,
rselect_head(rstore_seq(q18,earray_73)) = rselect_head(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(symmetry,[status(thm)],[502]) ).
tff(504,plain,
( ( earray_73 = store(earray_71,index_72,e18) )
<=> ( earray_73 = store(earray_71,index_72,e18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(505,axiom,
earray_73 = store(earray_71,index_72,e18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp52) ).
tff(506,plain,
earray_73 = store(earray_71,index_72,e18),
inference(modus_ponens,[status(thm)],[505,504]) ).
tff(507,plain,
store(earray_71,index_72,e18) = earray_73,
inference(symmetry,[status(thm)],[506]) ).
tff(508,plain,
( ( q18 = queue_70 )
<=> ( q18 = queue_70 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(509,axiom,
q18 = queue_70,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp225) ).
tff(510,plain,
q18 = queue_70,
inference(modus_ponens,[status(thm)],[509,508]) ).
tff(511,plain,
queue_70 = q18,
inference(symmetry,[status(thm)],[510]) ).
tff(512,plain,
( ( queue_70 = rstore_head(queue_67,index_69) )
<=> ( queue_70 = rstore_head(queue_67,index_69) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(513,axiom,
queue_70 = rstore_head(queue_67,index_69),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp205) ).
tff(514,plain,
queue_70 = rstore_head(queue_67,index_69),
inference(modus_ponens,[status(thm)],[513,512]) ).
tff(515,plain,
rstore_head(queue_67,index_69) = queue_70,
inference(symmetry,[status(thm)],[514]) ).
tff(516,plain,
rstore_head(queue_67,index_69) = q18,
inference(transitivity,[status(thm)],[515,511]) ).
tff(517,plain,
rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18)) = rstore_seq(q18,earray_73),
inference(monotonicity,[status(thm)],[516,507]) ).
tff(518,plain,
rselect_head(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = rselect_head(rstore_seq(q18,earray_73)),
inference(monotonicity,[status(thm)],[517]) ).
tff(519,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = rselect_head(rstore_head(queue_67,index_69)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(520,plain,
rselect_head(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = rselect_head(rstore_head(queue_67,index_69)),
inference(unit_resolution,[status(thm)],[519,128]) ).
tff(521,plain,
rselect_head(rstore_head(queue_67,index_69)) = rselect_head(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))),
inference(symmetry,[status(thm)],[520]) ).
tff(522,plain,
( ( index_69 = s(index_68) )
<=> ( index_69 = s(index_68) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(523,axiom,
index_69 = s(index_68),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp131) ).
tff(524,plain,
index_69 = s(index_68),
inference(modus_ponens,[status(thm)],[523,522]) ).
tff(525,plain,
s(index_68) = index_69,
inference(symmetry,[status(thm)],[524]) ).
tff(526,plain,
( ( queue_67 = rstore_tail(queue_65,index_66) )
<=> ( queue_67 = rstore_tail(queue_65,index_66) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(527,axiom,
queue_67 = rstore_tail(queue_65,index_66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp203) ).
tff(528,plain,
queue_67 = rstore_tail(queue_65,index_66),
inference(modus_ponens,[status(thm)],[527,526]) ).
tff(529,plain,
rstore_tail(queue_65,index_66) = queue_67,
inference(symmetry,[status(thm)],[528]) ).
tff(530,plain,
rstore_head(rstore_tail(queue_65,index_66),s(index_68)) = rstore_head(queue_67,index_69),
inference(monotonicity,[status(thm)],[529,525]) ).
tff(531,plain,
rselect_head(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_head(rstore_head(queue_67,index_69)),
inference(monotonicity,[status(thm)],[530]) ).
tff(532,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = s(index_68) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(533,plain,
rselect_head(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = s(index_68),
inference(unit_resolution,[status(thm)],[532,99]) ).
tff(534,plain,
s(index_68) = rselect_head(rstore_head(rstore_tail(queue_65,index_66),s(index_68))),
inference(symmetry,[status(thm)],[533]) ).
tff(535,plain,
( ( index_68 = rselect_head(queue_67) )
<=> ( index_68 = rselect_head(queue_67) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(536,axiom,
index_68 = rselect_head(queue_67),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp130) ).
tff(537,plain,
index_68 = rselect_head(queue_67),
inference(modus_ponens,[status(thm)],[536,535]) ).
tff(538,plain,
rselect_head(queue_67) = index_68,
inference(symmetry,[status(thm)],[537]) ).
tff(539,plain,
s(rselect_head(queue_67)) = s(index_68),
inference(monotonicity,[status(thm)],[538]) ).
tff(540,plain,
s(rselect_head(queue_67)) = index_95,
inference(transitivity,[status(thm)],[539,534,531,521,518,503,500,488,485,468,465,453,450,433,430,413]) ).
tff(541,plain,
s(s(rselect_head(queue_67))) = s(index_95),
inference(monotonicity,[status(thm)],[540]) ).
tff(542,plain,
s(index_68) = s(rselect_head(queue_67)),
inference(symmetry,[status(thm)],[539]) ).
tff(543,plain,
( ( index_66 = s(index_63) )
<=> ( index_66 = s(index_63) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(544,axiom,
index_66 = s(index_63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp129) ).
tff(545,plain,
index_66 = s(index_63),
inference(modus_ponens,[status(thm)],[544,543]) ).
tff(546,plain,
s(index_63) = index_66,
inference(symmetry,[status(thm)],[545]) ).
tff(547,plain,
( ( queue_65 = rstore_seq(q17,earray_64) )
<=> ( queue_65 = rstore_seq(q17,earray_64) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(548,axiom,
queue_65 = rstore_seq(q17,earray_64),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp202) ).
tff(549,plain,
queue_65 = rstore_seq(q17,earray_64),
inference(modus_ponens,[status(thm)],[548,547]) ).
tff(550,plain,
rstore_seq(q17,earray_64) = queue_65,
inference(symmetry,[status(thm)],[549]) ).
tff(551,plain,
rstore_tail(rstore_seq(q17,earray_64),s(index_63)) = rstore_tail(queue_65,index_66),
inference(monotonicity,[status(thm)],[550,546]) ).
tff(552,plain,
rstore_tail(queue_65,index_66) = rstore_tail(rstore_seq(q17,earray_64),s(index_63)),
inference(symmetry,[status(thm)],[551]) ).
tff(553,plain,
queue_67 = rstore_tail(rstore_seq(q17,earray_64),s(index_63)),
inference(transitivity,[status(thm)],[528,552]) ).
tff(554,plain,
rselect_head(queue_67) = rselect_head(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(monotonicity,[status(thm)],[553]) ).
tff(555,plain,
rselect_head(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_head(queue_67),
inference(symmetry,[status(thm)],[554]) ).
tff(556,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_head(rstore_seq(q17,earray_64)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(557,plain,
rselect_head(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_head(rstore_seq(q17,earray_64)),
inference(unit_resolution,[status(thm)],[556,153]) ).
tff(558,plain,
rselect_head(rstore_seq(q17,earray_64)) = rselect_head(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(symmetry,[status(thm)],[557]) ).
tff(559,plain,
( ( earray_64 = store(earray_62,index_63,e17) )
<=> ( earray_64 = store(earray_62,index_63,e17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(560,axiom,
earray_64 = store(earray_62,index_63,e17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp50) ).
tff(561,plain,
earray_64 = store(earray_62,index_63,e17),
inference(modus_ponens,[status(thm)],[560,559]) ).
tff(562,plain,
store(earray_62,index_63,e17) = earray_64,
inference(symmetry,[status(thm)],[561]) ).
tff(563,plain,
( ( q17 = queue_61 )
<=> ( q17 = queue_61 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(564,axiom,
q17 = queue_61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp224) ).
tff(565,plain,
q17 = queue_61,
inference(modus_ponens,[status(thm)],[564,563]) ).
tff(566,plain,
queue_61 = q17,
inference(symmetry,[status(thm)],[565]) ).
tff(567,plain,
( ( queue_61 = rstore_tail(queue_59,index_60) )
<=> ( queue_61 = rstore_tail(queue_59,index_60) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(568,axiom,
queue_61 = rstore_tail(queue_59,index_60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp201) ).
tff(569,plain,
queue_61 = rstore_tail(queue_59,index_60),
inference(modus_ponens,[status(thm)],[568,567]) ).
tff(570,plain,
rstore_tail(queue_59,index_60) = queue_61,
inference(symmetry,[status(thm)],[569]) ).
tff(571,plain,
rstore_tail(queue_59,index_60) = q17,
inference(transitivity,[status(thm)],[570,566]) ).
tff(572,plain,
rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17)) = rstore_seq(q17,earray_64),
inference(monotonicity,[status(thm)],[571,562]) ).
tff(573,plain,
rstore_seq(q17,earray_64) = rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17)),
inference(symmetry,[status(thm)],[572]) ).
tff(574,plain,
rselect_head(rstore_seq(q17,earray_64)) = rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))),
inference(monotonicity,[status(thm)],[573]) ).
tff(575,plain,
rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = rselect_head(rstore_seq(q17,earray_64)),
inference(symmetry,[status(thm)],[574]) ).
tff(576,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = rselect_head(rstore_tail(queue_59,index_60)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(577,plain,
rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = rselect_head(rstore_tail(queue_59,index_60)),
inference(unit_resolution,[status(thm)],[576,128]) ).
tff(578,plain,
rselect_head(rstore_tail(queue_59,index_60)) = rselect_head(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))),
inference(symmetry,[status(thm)],[577]) ).
tff(579,plain,
( ( index_60 = s(index_57) )
<=> ( index_60 = s(index_57) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(580,axiom,
index_60 = s(index_57),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp127) ).
tff(581,plain,
index_60 = s(index_57),
inference(modus_ponens,[status(thm)],[580,579]) ).
tff(582,plain,
s(index_57) = index_60,
inference(symmetry,[status(thm)],[581]) ).
tff(583,plain,
( ( queue_59 = rstore_seq(q16,earray_58) )
<=> ( queue_59 = rstore_seq(q16,earray_58) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(584,axiom,
queue_59 = rstore_seq(q16,earray_58),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp200) ).
tff(585,plain,
queue_59 = rstore_seq(q16,earray_58),
inference(modus_ponens,[status(thm)],[584,583]) ).
tff(586,plain,
rstore_seq(q16,earray_58) = queue_59,
inference(symmetry,[status(thm)],[585]) ).
tff(587,plain,
rstore_tail(rstore_seq(q16,earray_58),s(index_57)) = rstore_tail(queue_59,index_60),
inference(monotonicity,[status(thm)],[586,582]) ).
tff(588,plain,
rstore_tail(queue_59,index_60) = rstore_tail(rstore_seq(q16,earray_58),s(index_57)),
inference(symmetry,[status(thm)],[587]) ).
tff(589,plain,
rselect_head(rstore_tail(queue_59,index_60)) = rselect_head(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(monotonicity,[status(thm)],[588]) ).
tff(590,plain,
rselect_head(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_head(rstore_tail(queue_59,index_60)),
inference(symmetry,[status(thm)],[589]) ).
tff(591,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_head(rstore_seq(q16,earray_58)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(592,plain,
rselect_head(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_head(rstore_seq(q16,earray_58)),
inference(unit_resolution,[status(thm)],[591,153]) ).
tff(593,plain,
rselect_head(rstore_seq(q16,earray_58)) = rselect_head(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(symmetry,[status(thm)],[592]) ).
tff(594,plain,
( ( earray_58 = store(earray_56,index_57,e16) )
<=> ( earray_58 = store(earray_56,index_57,e16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(595,axiom,
earray_58 = store(earray_56,index_57,e16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp48) ).
tff(596,plain,
earray_58 = store(earray_56,index_57,e16),
inference(modus_ponens,[status(thm)],[595,594]) ).
tff(597,plain,
store(earray_56,index_57,e16) = earray_58,
inference(symmetry,[status(thm)],[596]) ).
tff(598,plain,
( ( q16 = queue_55 )
<=> ( q16 = queue_55 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(599,axiom,
q16 = queue_55,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp223) ).
tff(600,plain,
q16 = queue_55,
inference(modus_ponens,[status(thm)],[599,598]) ).
tff(601,plain,
queue_55 = q16,
inference(symmetry,[status(thm)],[600]) ).
tff(602,plain,
( ( queue_55 = rstore_tail(queue_53,index_54) )
<=> ( queue_55 = rstore_tail(queue_53,index_54) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(603,axiom,
queue_55 = rstore_tail(queue_53,index_54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp199) ).
tff(604,plain,
queue_55 = rstore_tail(queue_53,index_54),
inference(modus_ponens,[status(thm)],[603,602]) ).
tff(605,plain,
rstore_tail(queue_53,index_54) = queue_55,
inference(symmetry,[status(thm)],[604]) ).
tff(606,plain,
rstore_tail(queue_53,index_54) = q16,
inference(transitivity,[status(thm)],[605,601]) ).
tff(607,plain,
rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16)) = rstore_seq(q16,earray_58),
inference(monotonicity,[status(thm)],[606,597]) ).
tff(608,plain,
rstore_seq(q16,earray_58) = rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16)),
inference(symmetry,[status(thm)],[607]) ).
tff(609,plain,
rselect_head(rstore_seq(q16,earray_58)) = rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))),
inference(monotonicity,[status(thm)],[608]) ).
tff(610,plain,
rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = rselect_head(rstore_seq(q16,earray_58)),
inference(symmetry,[status(thm)],[609]) ).
tff(611,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = rselect_head(rstore_tail(queue_53,index_54)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(612,plain,
rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = rselect_head(rstore_tail(queue_53,index_54)),
inference(unit_resolution,[status(thm)],[611,128]) ).
tff(613,plain,
rselect_head(rstore_tail(queue_53,index_54)) = rselect_head(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))),
inference(symmetry,[status(thm)],[612]) ).
tff(614,plain,
( ( index_54 = s(index_51) )
<=> ( index_54 = s(index_51) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(615,axiom,
index_54 = s(index_51),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp124) ).
tff(616,plain,
index_54 = s(index_51),
inference(modus_ponens,[status(thm)],[615,614]) ).
tff(617,plain,
s(index_51) = index_54,
inference(symmetry,[status(thm)],[616]) ).
tff(618,plain,
( ( queue_53 = rstore_seq(q15,earray_52) )
<=> ( queue_53 = rstore_seq(q15,earray_52) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(619,axiom,
queue_53 = rstore_seq(q15,earray_52),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp198) ).
tff(620,plain,
queue_53 = rstore_seq(q15,earray_52),
inference(modus_ponens,[status(thm)],[619,618]) ).
tff(621,plain,
rstore_seq(q15,earray_52) = queue_53,
inference(symmetry,[status(thm)],[620]) ).
tff(622,plain,
rstore_tail(rstore_seq(q15,earray_52),s(index_51)) = rstore_tail(queue_53,index_54),
inference(monotonicity,[status(thm)],[621,617]) ).
tff(623,plain,
rstore_tail(queue_53,index_54) = rstore_tail(rstore_seq(q15,earray_52),s(index_51)),
inference(symmetry,[status(thm)],[622]) ).
tff(624,plain,
rselect_head(rstore_tail(queue_53,index_54)) = rselect_head(rstore_tail(rstore_seq(q15,earray_52),s(index_51))),
inference(monotonicity,[status(thm)],[623]) ).
tff(625,plain,
rselect_head(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = rselect_head(rstore_tail(queue_53,index_54)),
inference(symmetry,[status(thm)],[624]) ).
tff(626,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = rselect_head(rstore_seq(q15,earray_52)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(627,plain,
rselect_head(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = rselect_head(rstore_seq(q15,earray_52)),
inference(unit_resolution,[status(thm)],[626,153]) ).
tff(628,plain,
rselect_head(rstore_seq(q15,earray_52)) = rselect_head(rstore_tail(rstore_seq(q15,earray_52),s(index_51))),
inference(symmetry,[status(thm)],[627]) ).
tff(629,plain,
( ( earray_52 = store(earray_50,index_51,e15) )
<=> ( earray_52 = store(earray_50,index_51,e15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(630,axiom,
earray_52 = store(earray_50,index_51,e15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp46) ).
tff(631,plain,
earray_52 = store(earray_50,index_51,e15),
inference(modus_ponens,[status(thm)],[630,629]) ).
tff(632,plain,
store(earray_50,index_51,e15) = earray_52,
inference(symmetry,[status(thm)],[631]) ).
tff(633,plain,
( ( q15 = queue_49 )
<=> ( q15 = queue_49 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(634,axiom,
q15 = queue_49,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp222) ).
tff(635,plain,
q15 = queue_49,
inference(modus_ponens,[status(thm)],[634,633]) ).
tff(636,plain,
queue_49 = q15,
inference(symmetry,[status(thm)],[635]) ).
tff(637,plain,
( ( queue_49 = rstore_head(queue_46,index_48) )
<=> ( queue_49 = rstore_head(queue_46,index_48) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(638,axiom,
queue_49 = rstore_head(queue_46,index_48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp196) ).
tff(639,plain,
queue_49 = rstore_head(queue_46,index_48),
inference(modus_ponens,[status(thm)],[638,637]) ).
tff(640,plain,
rstore_head(queue_46,index_48) = queue_49,
inference(symmetry,[status(thm)],[639]) ).
tff(641,plain,
rstore_head(queue_46,index_48) = q15,
inference(transitivity,[status(thm)],[640,636]) ).
tff(642,plain,
rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15)) = rstore_seq(q15,earray_52),
inference(monotonicity,[status(thm)],[641,632]) ).
tff(643,plain,
rselect_head(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))) = rselect_head(rstore_seq(q15,earray_52)),
inference(monotonicity,[status(thm)],[642]) ).
tff(644,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))) = rselect_head(rstore_head(queue_46,index_48)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(645,plain,
rselect_head(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))) = rselect_head(rstore_head(queue_46,index_48)),
inference(unit_resolution,[status(thm)],[644,128]) ).
tff(646,plain,
rselect_head(rstore_head(queue_46,index_48)) = rselect_head(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))),
inference(symmetry,[status(thm)],[645]) ).
tff(647,plain,
( ( index_48 = s(index_47) )
<=> ( index_48 = s(index_47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(648,axiom,
index_48 = s(index_47),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp122) ).
tff(649,plain,
index_48 = s(index_47),
inference(modus_ponens,[status(thm)],[648,647]) ).
tff(650,plain,
s(index_47) = index_48,
inference(symmetry,[status(thm)],[649]) ).
tff(651,plain,
( ( queue_46 = rstore_tail(queue_44,index_45) )
<=> ( queue_46 = rstore_tail(queue_44,index_45) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(652,axiom,
queue_46 = rstore_tail(queue_44,index_45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp195) ).
tff(653,plain,
queue_46 = rstore_tail(queue_44,index_45),
inference(modus_ponens,[status(thm)],[652,651]) ).
tff(654,plain,
rstore_tail(queue_44,index_45) = queue_46,
inference(symmetry,[status(thm)],[653]) ).
tff(655,plain,
rstore_head(rstore_tail(queue_44,index_45),s(index_47)) = rstore_head(queue_46,index_48),
inference(monotonicity,[status(thm)],[654,650]) ).
tff(656,plain,
rselect_head(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = rselect_head(rstore_head(queue_46,index_48)),
inference(monotonicity,[status(thm)],[655]) ).
tff(657,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = s(index_47) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(658,plain,
rselect_head(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = s(index_47),
inference(unit_resolution,[status(thm)],[657,99]) ).
tff(659,plain,
s(index_47) = rselect_head(rstore_head(rstore_tail(queue_44,index_45),s(index_47))),
inference(symmetry,[status(thm)],[658]) ).
tff(660,plain,
( ( index_47 = rselect_head(queue_46) )
<=> ( index_47 = rselect_head(queue_46) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(661,axiom,
index_47 = rselect_head(queue_46),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp121) ).
tff(662,plain,
index_47 = rselect_head(queue_46),
inference(modus_ponens,[status(thm)],[661,660]) ).
tff(663,plain,
rselect_head(queue_46) = index_47,
inference(symmetry,[status(thm)],[662]) ).
tff(664,plain,
s(rselect_head(queue_46)) = s(index_47),
inference(monotonicity,[status(thm)],[663]) ).
tff(665,plain,
s(rselect_head(queue_46)) = index_68,
inference(transitivity,[status(thm)],[664,659,656,646,643,628,625,613,610,593,590,578,575,558,555,538]) ).
tff(666,plain,
s(s(rselect_head(queue_46))) = s(index_68),
inference(monotonicity,[status(thm)],[665]) ).
tff(667,plain,
s(index_47) = s(rselect_head(queue_46)),
inference(symmetry,[status(thm)],[664]) ).
tff(668,plain,
( ( index_45 = s(index_42) )
<=> ( index_45 = s(index_42) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(669,axiom,
index_45 = s(index_42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp120) ).
tff(670,plain,
index_45 = s(index_42),
inference(modus_ponens,[status(thm)],[669,668]) ).
tff(671,plain,
s(index_42) = index_45,
inference(symmetry,[status(thm)],[670]) ).
tff(672,plain,
( ( queue_44 = rstore_seq(q14,earray_43) )
<=> ( queue_44 = rstore_seq(q14,earray_43) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(673,axiom,
queue_44 = rstore_seq(q14,earray_43),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp194) ).
tff(674,plain,
queue_44 = rstore_seq(q14,earray_43),
inference(modus_ponens,[status(thm)],[673,672]) ).
tff(675,plain,
rstore_seq(q14,earray_43) = queue_44,
inference(symmetry,[status(thm)],[674]) ).
tff(676,plain,
rstore_tail(rstore_seq(q14,earray_43),s(index_42)) = rstore_tail(queue_44,index_45),
inference(monotonicity,[status(thm)],[675,671]) ).
tff(677,plain,
rstore_tail(queue_44,index_45) = rstore_tail(rstore_seq(q14,earray_43),s(index_42)),
inference(symmetry,[status(thm)],[676]) ).
tff(678,plain,
queue_46 = rstore_tail(rstore_seq(q14,earray_43),s(index_42)),
inference(transitivity,[status(thm)],[653,677]) ).
tff(679,plain,
rselect_head(queue_46) = rselect_head(rstore_tail(rstore_seq(q14,earray_43),s(index_42))),
inference(monotonicity,[status(thm)],[678]) ).
tff(680,plain,
rselect_head(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = rselect_head(queue_46),
inference(symmetry,[status(thm)],[679]) ).
tff(681,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = rselect_head(rstore_seq(q14,earray_43)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(682,plain,
rselect_head(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = rselect_head(rstore_seq(q14,earray_43)),
inference(unit_resolution,[status(thm)],[681,153]) ).
tff(683,plain,
rselect_head(rstore_seq(q14,earray_43)) = rselect_head(rstore_tail(rstore_seq(q14,earray_43),s(index_42))),
inference(symmetry,[status(thm)],[682]) ).
tff(684,plain,
( ( earray_43 = store(earray_41,index_42,e14) )
<=> ( earray_43 = store(earray_41,index_42,e14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(685,axiom,
earray_43 = store(earray_41,index_42,e14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp44) ).
tff(686,plain,
earray_43 = store(earray_41,index_42,e14),
inference(modus_ponens,[status(thm)],[685,684]) ).
tff(687,plain,
store(earray_41,index_42,e14) = earray_43,
inference(symmetry,[status(thm)],[686]) ).
tff(688,plain,
( ( q14 = queue_40 )
<=> ( q14 = queue_40 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(689,axiom,
q14 = queue_40,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp221) ).
tff(690,plain,
q14 = queue_40,
inference(modus_ponens,[status(thm)],[689,688]) ).
tff(691,plain,
queue_40 = q14,
inference(symmetry,[status(thm)],[690]) ).
tff(692,plain,
( ( queue_40 = rstore_tail(queue_38,index_39) )
<=> ( queue_40 = rstore_tail(queue_38,index_39) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(693,axiom,
queue_40 = rstore_tail(queue_38,index_39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp193) ).
tff(694,plain,
queue_40 = rstore_tail(queue_38,index_39),
inference(modus_ponens,[status(thm)],[693,692]) ).
tff(695,plain,
rstore_tail(queue_38,index_39) = queue_40,
inference(symmetry,[status(thm)],[694]) ).
tff(696,plain,
rstore_tail(queue_38,index_39) = q14,
inference(transitivity,[status(thm)],[695,691]) ).
tff(697,plain,
rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14)) = rstore_seq(q14,earray_43),
inference(monotonicity,[status(thm)],[696,687]) ).
tff(698,plain,
rstore_seq(q14,earray_43) = rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14)),
inference(symmetry,[status(thm)],[697]) ).
tff(699,plain,
rselect_head(rstore_seq(q14,earray_43)) = rselect_head(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))),
inference(monotonicity,[status(thm)],[698]) ).
tff(700,plain,
rselect_head(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))) = rselect_head(rstore_seq(q14,earray_43)),
inference(symmetry,[status(thm)],[699]) ).
tff(701,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))) = rselect_head(rstore_tail(queue_38,index_39)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(702,plain,
rselect_head(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))) = rselect_head(rstore_tail(queue_38,index_39)),
inference(unit_resolution,[status(thm)],[701,128]) ).
tff(703,plain,
rselect_head(rstore_tail(queue_38,index_39)) = rselect_head(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))),
inference(symmetry,[status(thm)],[702]) ).
tff(704,plain,
( ( index_39 = s(index_36) )
<=> ( index_39 = s(index_36) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(705,axiom,
index_39 = s(index_36),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp118) ).
tff(706,plain,
index_39 = s(index_36),
inference(modus_ponens,[status(thm)],[705,704]) ).
tff(707,plain,
s(index_36) = index_39,
inference(symmetry,[status(thm)],[706]) ).
tff(708,plain,
( ( queue_38 = rstore_seq(q13,earray_37) )
<=> ( queue_38 = rstore_seq(q13,earray_37) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(709,axiom,
queue_38 = rstore_seq(q13,earray_37),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp192) ).
tff(710,plain,
queue_38 = rstore_seq(q13,earray_37),
inference(modus_ponens,[status(thm)],[709,708]) ).
tff(711,plain,
rstore_seq(q13,earray_37) = queue_38,
inference(symmetry,[status(thm)],[710]) ).
tff(712,plain,
rstore_tail(rstore_seq(q13,earray_37),s(index_36)) = rstore_tail(queue_38,index_39),
inference(monotonicity,[status(thm)],[711,707]) ).
tff(713,plain,
rstore_tail(queue_38,index_39) = rstore_tail(rstore_seq(q13,earray_37),s(index_36)),
inference(symmetry,[status(thm)],[712]) ).
tff(714,plain,
rselect_head(rstore_tail(queue_38,index_39)) = rselect_head(rstore_tail(rstore_seq(q13,earray_37),s(index_36))),
inference(monotonicity,[status(thm)],[713]) ).
tff(715,plain,
rselect_head(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = rselect_head(rstore_tail(queue_38,index_39)),
inference(symmetry,[status(thm)],[714]) ).
tff(716,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = rselect_head(rstore_seq(q13,earray_37)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(717,plain,
rselect_head(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = rselect_head(rstore_seq(q13,earray_37)),
inference(unit_resolution,[status(thm)],[716,153]) ).
tff(718,plain,
rselect_head(rstore_seq(q13,earray_37)) = rselect_head(rstore_tail(rstore_seq(q13,earray_37),s(index_36))),
inference(symmetry,[status(thm)],[717]) ).
tff(719,plain,
( ( earray_37 = store(earray_35,index_36,e13) )
<=> ( earray_37 = store(earray_35,index_36,e13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(720,axiom,
earray_37 = store(earray_35,index_36,e13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp41) ).
tff(721,plain,
earray_37 = store(earray_35,index_36,e13),
inference(modus_ponens,[status(thm)],[720,719]) ).
tff(722,plain,
store(earray_35,index_36,e13) = earray_37,
inference(symmetry,[status(thm)],[721]) ).
tff(723,plain,
( ( q13 = queue_34 )
<=> ( q13 = queue_34 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(724,axiom,
q13 = queue_34,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp220) ).
tff(725,plain,
q13 = queue_34,
inference(modus_ponens,[status(thm)],[724,723]) ).
tff(726,plain,
queue_34 = q13,
inference(symmetry,[status(thm)],[725]) ).
tff(727,plain,
( ( queue_34 = rstore_tail(queue_32,index_33) )
<=> ( queue_34 = rstore_tail(queue_32,index_33) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(728,axiom,
queue_34 = rstore_tail(queue_32,index_33),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp191) ).
tff(729,plain,
queue_34 = rstore_tail(queue_32,index_33),
inference(modus_ponens,[status(thm)],[728,727]) ).
tff(730,plain,
rstore_tail(queue_32,index_33) = queue_34,
inference(symmetry,[status(thm)],[729]) ).
tff(731,plain,
rstore_tail(queue_32,index_33) = q13,
inference(transitivity,[status(thm)],[730,726]) ).
tff(732,plain,
rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13)) = rstore_seq(q13,earray_37),
inference(monotonicity,[status(thm)],[731,722]) ).
tff(733,plain,
rstore_seq(q13,earray_37) = rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13)),
inference(symmetry,[status(thm)],[732]) ).
tff(734,plain,
rselect_head(rstore_seq(q13,earray_37)) = rselect_head(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))),
inference(monotonicity,[status(thm)],[733]) ).
tff(735,plain,
rselect_head(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))) = rselect_head(rstore_seq(q13,earray_37)),
inference(symmetry,[status(thm)],[734]) ).
tff(736,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))) = rselect_head(rstore_tail(queue_32,index_33)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(737,plain,
rselect_head(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))) = rselect_head(rstore_tail(queue_32,index_33)),
inference(unit_resolution,[status(thm)],[736,128]) ).
tff(738,plain,
rselect_head(rstore_tail(queue_32,index_33)) = rselect_head(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))),
inference(symmetry,[status(thm)],[737]) ).
tff(739,plain,
( ( index_33 = s(index_30) )
<=> ( index_33 = s(index_30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(740,axiom,
index_33 = s(index_30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp116) ).
tff(741,plain,
index_33 = s(index_30),
inference(modus_ponens,[status(thm)],[740,739]) ).
tff(742,plain,
s(index_30) = index_33,
inference(symmetry,[status(thm)],[741]) ).
tff(743,plain,
( ( queue_32 = rstore_seq(q12,earray_31) )
<=> ( queue_32 = rstore_seq(q12,earray_31) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(744,axiom,
queue_32 = rstore_seq(q12,earray_31),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp190) ).
tff(745,plain,
queue_32 = rstore_seq(q12,earray_31),
inference(modus_ponens,[status(thm)],[744,743]) ).
tff(746,plain,
rstore_seq(q12,earray_31) = queue_32,
inference(symmetry,[status(thm)],[745]) ).
tff(747,plain,
rstore_tail(rstore_seq(q12,earray_31),s(index_30)) = rstore_tail(queue_32,index_33),
inference(monotonicity,[status(thm)],[746,742]) ).
tff(748,plain,
rstore_tail(queue_32,index_33) = rstore_tail(rstore_seq(q12,earray_31),s(index_30)),
inference(symmetry,[status(thm)],[747]) ).
tff(749,plain,
rselect_head(rstore_tail(queue_32,index_33)) = rselect_head(rstore_tail(rstore_seq(q12,earray_31),s(index_30))),
inference(monotonicity,[status(thm)],[748]) ).
tff(750,plain,
rselect_head(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = rselect_head(rstore_tail(queue_32,index_33)),
inference(symmetry,[status(thm)],[749]) ).
tff(751,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = rselect_head(rstore_seq(q12,earray_31)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(752,plain,
rselect_head(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = rselect_head(rstore_seq(q12,earray_31)),
inference(unit_resolution,[status(thm)],[751,153]) ).
tff(753,plain,
rselect_head(rstore_seq(q12,earray_31)) = rselect_head(rstore_tail(rstore_seq(q12,earray_31),s(index_30))),
inference(symmetry,[status(thm)],[752]) ).
tff(754,plain,
( ( earray_31 = store(earray_29,index_30,e12) )
<=> ( earray_31 = store(earray_29,index_30,e12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(755,axiom,
earray_31 = store(earray_29,index_30,e12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp39) ).
tff(756,plain,
earray_31 = store(earray_29,index_30,e12),
inference(modus_ponens,[status(thm)],[755,754]) ).
tff(757,plain,
store(earray_29,index_30,e12) = earray_31,
inference(symmetry,[status(thm)],[756]) ).
tff(758,plain,
( ( q12 = queue_28 )
<=> ( q12 = queue_28 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(759,axiom,
q12 = queue_28,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp219) ).
tff(760,plain,
q12 = queue_28,
inference(modus_ponens,[status(thm)],[759,758]) ).
tff(761,plain,
queue_28 = q12,
inference(symmetry,[status(thm)],[760]) ).
tff(762,plain,
( ( queue_28 = rstore_head(queue_25,index_27) )
<=> ( queue_28 = rstore_head(queue_25,index_27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(763,axiom,
queue_28 = rstore_head(queue_25,index_27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp189) ).
tff(764,plain,
queue_28 = rstore_head(queue_25,index_27),
inference(modus_ponens,[status(thm)],[763,762]) ).
tff(765,plain,
rstore_head(queue_25,index_27) = queue_28,
inference(symmetry,[status(thm)],[764]) ).
tff(766,plain,
rstore_head(queue_25,index_27) = q12,
inference(transitivity,[status(thm)],[765,761]) ).
tff(767,plain,
rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12)) = rstore_seq(q12,earray_31),
inference(monotonicity,[status(thm)],[766,757]) ).
tff(768,plain,
rselect_head(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))) = rselect_head(rstore_seq(q12,earray_31)),
inference(monotonicity,[status(thm)],[767]) ).
tff(769,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))) = rselect_head(rstore_head(queue_25,index_27)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(770,plain,
rselect_head(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))) = rselect_head(rstore_head(queue_25,index_27)),
inference(unit_resolution,[status(thm)],[769,128]) ).
tff(771,plain,
rselect_head(rstore_head(queue_25,index_27)) = rselect_head(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))),
inference(symmetry,[status(thm)],[770]) ).
tff(772,plain,
( ( index_27 = s(index_26) )
<=> ( index_27 = s(index_26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(773,axiom,
index_27 = s(index_26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp113) ).
tff(774,plain,
index_27 = s(index_26),
inference(modus_ponens,[status(thm)],[773,772]) ).
tff(775,plain,
s(index_26) = index_27,
inference(symmetry,[status(thm)],[774]) ).
tff(776,plain,
( ( queue_25 = rstore_tail(queue_23,index_24) )
<=> ( queue_25 = rstore_tail(queue_23,index_24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(777,axiom,
queue_25 = rstore_tail(queue_23,index_24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp188) ).
tff(778,plain,
queue_25 = rstore_tail(queue_23,index_24),
inference(modus_ponens,[status(thm)],[777,776]) ).
tff(779,plain,
rstore_tail(queue_23,index_24) = queue_25,
inference(symmetry,[status(thm)],[778]) ).
tff(780,plain,
rstore_head(rstore_tail(queue_23,index_24),s(index_26)) = rstore_head(queue_25,index_27),
inference(monotonicity,[status(thm)],[779,775]) ).
tff(781,plain,
rselect_head(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = rselect_head(rstore_head(queue_25,index_27)),
inference(monotonicity,[status(thm)],[780]) ).
tff(782,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = s(index_26) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(783,plain,
rselect_head(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = s(index_26),
inference(unit_resolution,[status(thm)],[782,99]) ).
tff(784,plain,
s(index_26) = rselect_head(rstore_head(rstore_tail(queue_23,index_24),s(index_26))),
inference(symmetry,[status(thm)],[783]) ).
tff(785,plain,
( ( index_26 = rselect_head(queue_25) )
<=> ( index_26 = rselect_head(queue_25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(786,axiom,
index_26 = rselect_head(queue_25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp112) ).
tff(787,plain,
index_26 = rselect_head(queue_25),
inference(modus_ponens,[status(thm)],[786,785]) ).
tff(788,plain,
rselect_head(queue_25) = index_26,
inference(symmetry,[status(thm)],[787]) ).
tff(789,plain,
s(rselect_head(queue_25)) = s(index_26),
inference(monotonicity,[status(thm)],[788]) ).
tff(790,plain,
s(rselect_head(queue_25)) = index_47,
inference(transitivity,[status(thm)],[789,784,781,771,768,753,750,738,735,718,715,703,700,683,680,663]) ).
tff(791,plain,
s(s(rselect_head(queue_25))) = s(index_47),
inference(monotonicity,[status(thm)],[790]) ).
tff(792,plain,
s(index_26) = s(rselect_head(queue_25)),
inference(symmetry,[status(thm)],[789]) ).
tff(793,plain,
( ( index_24 = s(index_21) )
<=> ( index_24 = s(index_21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(794,axiom,
index_24 = s(index_21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp111) ).
tff(795,plain,
index_24 = s(index_21),
inference(modus_ponens,[status(thm)],[794,793]) ).
tff(796,plain,
s(index_21) = index_24,
inference(symmetry,[status(thm)],[795]) ).
tff(797,plain,
( ( queue_23 = rstore_seq(q11,earray_22) )
<=> ( queue_23 = rstore_seq(q11,earray_22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(798,axiom,
queue_23 = rstore_seq(q11,earray_22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp187) ).
tff(799,plain,
queue_23 = rstore_seq(q11,earray_22),
inference(modus_ponens,[status(thm)],[798,797]) ).
tff(800,plain,
rstore_seq(q11,earray_22) = queue_23,
inference(symmetry,[status(thm)],[799]) ).
tff(801,plain,
rstore_tail(rstore_seq(q11,earray_22),s(index_21)) = rstore_tail(queue_23,index_24),
inference(monotonicity,[status(thm)],[800,796]) ).
tff(802,plain,
rstore_tail(queue_23,index_24) = rstore_tail(rstore_seq(q11,earray_22),s(index_21)),
inference(symmetry,[status(thm)],[801]) ).
tff(803,plain,
queue_25 = rstore_tail(rstore_seq(q11,earray_22),s(index_21)),
inference(transitivity,[status(thm)],[778,802]) ).
tff(804,plain,
rselect_head(queue_25) = rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(monotonicity,[status(thm)],[803]) ).
tff(805,plain,
rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_head(queue_25),
inference(symmetry,[status(thm)],[804]) ).
tff(806,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_head(rstore_seq(q11,earray_22)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(807,plain,
rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_head(rstore_seq(q11,earray_22)),
inference(unit_resolution,[status(thm)],[806,153]) ).
tff(808,plain,
rselect_head(rstore_seq(q11,earray_22)) = rselect_head(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(symmetry,[status(thm)],[807]) ).
tff(809,plain,
( ( earray_22 = store(earray_20,index_21,e11) )
<=> ( earray_22 = store(earray_20,index_21,e11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(810,axiom,
earray_22 = store(earray_20,index_21,e11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp37) ).
tff(811,plain,
earray_22 = store(earray_20,index_21,e11),
inference(modus_ponens,[status(thm)],[810,809]) ).
tff(812,plain,
store(earray_20,index_21,e11) = earray_22,
inference(symmetry,[status(thm)],[811]) ).
tff(813,plain,
rstore_tail(queue_17,index_18) = q11,
inference(transitivity,[status(thm)],[23,19]) ).
tff(814,plain,
rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11)) = rstore_seq(q11,earray_22),
inference(monotonicity,[status(thm)],[813,812]) ).
tff(815,plain,
rstore_seq(q11,earray_22) = rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11)),
inference(symmetry,[status(thm)],[814]) ).
tff(816,plain,
rselect_head(rstore_seq(q11,earray_22)) = rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))),
inference(monotonicity,[status(thm)],[815]) ).
tff(817,plain,
rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))) = rselect_head(rstore_seq(q11,earray_22)),
inference(symmetry,[status(thm)],[816]) ).
tff(818,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))) = rselect_head(rstore_tail(queue_17,index_18)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(819,plain,
rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))) = rselect_head(rstore_tail(queue_17,index_18)),
inference(unit_resolution,[status(thm)],[818,128]) ).
tff(820,plain,
rselect_head(rstore_tail(queue_17,index_18)) = rselect_head(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))),
inference(symmetry,[status(thm)],[819]) ).
tff(821,plain,
rstore_tail(queue_17,index_18) = rstore_tail(rstore_seq(q10,earray_16),s(index_15)),
inference(symmetry,[status(thm)],[32]) ).
tff(822,plain,
rselect_head(rstore_tail(queue_17,index_18)) = rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))),
inference(monotonicity,[status(thm)],[821]) ).
tff(823,plain,
rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_head(rstore_tail(queue_17,index_18)),
inference(symmetry,[status(thm)],[822]) ).
tff(824,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_head(rstore_seq(q10,earray_16)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(825,plain,
rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_head(rstore_seq(q10,earray_16)),
inference(unit_resolution,[status(thm)],[824,153]) ).
tff(826,plain,
rselect_head(rstore_seq(q10,earray_16)) = rselect_head(rstore_tail(rstore_seq(q10,earray_16),s(index_15))),
inference(symmetry,[status(thm)],[825]) ).
tff(827,plain,
( ( earray_16 = store(earray_14,index_15,e10) )
<=> ( earray_16 = store(earray_14,index_15,e10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(828,axiom,
earray_16 = store(earray_14,index_15,e10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp19) ).
tff(829,plain,
earray_16 = store(earray_14,index_15,e10),
inference(modus_ponens,[status(thm)],[828,827]) ).
tff(830,plain,
store(earray_14,index_15,e10) = earray_16,
inference(symmetry,[status(thm)],[829]) ).
tff(831,plain,
( ( q10 = queue_13 )
<=> ( q10 = queue_13 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(832,axiom,
q10 = queue_13,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp217) ).
tff(833,plain,
q10 = queue_13,
inference(modus_ponens,[status(thm)],[832,831]) ).
tff(834,plain,
queue_13 = q10,
inference(symmetry,[status(thm)],[833]) ).
tff(835,plain,
( ( queue_13 = rstore_tail(queue_11,index_12) )
<=> ( queue_13 = rstore_tail(queue_11,index_12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(836,axiom,
queue_13 = rstore_tail(queue_11,index_12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp156) ).
tff(837,plain,
queue_13 = rstore_tail(queue_11,index_12),
inference(modus_ponens,[status(thm)],[836,835]) ).
tff(838,plain,
rstore_tail(queue_11,index_12) = queue_13,
inference(symmetry,[status(thm)],[837]) ).
tff(839,plain,
rstore_tail(queue_11,index_12) = q10,
inference(transitivity,[status(thm)],[838,834]) ).
tff(840,plain,
rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10)) = rstore_seq(q10,earray_16),
inference(monotonicity,[status(thm)],[839,830]) ).
tff(841,plain,
rstore_seq(q10,earray_16) = rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10)),
inference(symmetry,[status(thm)],[840]) ).
tff(842,plain,
rselect_head(rstore_seq(q10,earray_16)) = rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))),
inference(monotonicity,[status(thm)],[841]) ).
tff(843,plain,
rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))) = rselect_head(rstore_seq(q10,earray_16)),
inference(symmetry,[status(thm)],[842]) ).
tff(844,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))) = rselect_head(rstore_tail(queue_11,index_12)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(845,plain,
rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))) = rselect_head(rstore_tail(queue_11,index_12)),
inference(unit_resolution,[status(thm)],[844,128]) ).
tff(846,plain,
rselect_head(rstore_tail(queue_11,index_12)) = rselect_head(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))),
inference(symmetry,[status(thm)],[845]) ).
tff(847,plain,
( ( index_12 = s(index_9) )
<=> ( index_12 = s(index_9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(848,axiom,
index_12 = s(index_9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp70) ).
tff(849,plain,
index_12 = s(index_9),
inference(modus_ponens,[status(thm)],[848,847]) ).
tff(850,plain,
s(index_9) = index_12,
inference(symmetry,[status(thm)],[849]) ).
tff(851,plain,
( ( queue_11 = rstore_seq(q9,earray_10) )
<=> ( queue_11 = rstore_seq(q9,earray_10) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(852,axiom,
queue_11 = rstore_seq(q9,earray_10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp149) ).
tff(853,plain,
queue_11 = rstore_seq(q9,earray_10),
inference(modus_ponens,[status(thm)],[852,851]) ).
tff(854,plain,
rstore_seq(q9,earray_10) = queue_11,
inference(symmetry,[status(thm)],[853]) ).
tff(855,plain,
rstore_tail(rstore_seq(q9,earray_10),s(index_9)) = rstore_tail(queue_11,index_12),
inference(monotonicity,[status(thm)],[854,850]) ).
tff(856,plain,
rstore_tail(queue_11,index_12) = rstore_tail(rstore_seq(q9,earray_10),s(index_9)),
inference(symmetry,[status(thm)],[855]) ).
tff(857,plain,
rselect_head(rstore_tail(queue_11,index_12)) = rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))),
inference(monotonicity,[status(thm)],[856]) ).
tff(858,plain,
rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = rselect_head(rstore_tail(queue_11,index_12)),
inference(symmetry,[status(thm)],[857]) ).
tff(859,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = rselect_head(rstore_seq(q9,earray_10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(860,plain,
rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = rselect_head(rstore_seq(q9,earray_10)),
inference(unit_resolution,[status(thm)],[859,153]) ).
tff(861,plain,
rselect_head(rstore_seq(q9,earray_10)) = rselect_head(rstore_tail(rstore_seq(q9,earray_10),s(index_9))),
inference(symmetry,[status(thm)],[860]) ).
tff(862,plain,
( ( earray_10 = store(earray_8,index_9,e9) )
<=> ( earray_10 = store(earray_8,index_9,e9) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(863,axiom,
earray_10 = store(earray_8,index_9,e9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp0) ).
tff(864,plain,
earray_10 = store(earray_8,index_9,e9),
inference(modus_ponens,[status(thm)],[863,862]) ).
tff(865,plain,
store(earray_8,index_9,e9) = earray_10,
inference(symmetry,[status(thm)],[864]) ).
tff(866,plain,
queue_211 = q9,
inference(symmetry,[status(thm)],[255]) ).
tff(867,plain,
rstore_head(queue_208,index_210) = queue_211,
inference(symmetry,[status(thm)],[252]) ).
tff(868,plain,
rstore_head(queue_208,index_210) = q9,
inference(transitivity,[status(thm)],[867,866]) ).
tff(869,plain,
rstore_seq(rstore_head(queue_208,index_210),store(earray_8,index_9,e9)) = rstore_seq(q9,earray_10),
inference(monotonicity,[status(thm)],[868,865]) ).
tff(870,plain,
rselect_head(rstore_seq(rstore_head(queue_208,index_210),store(earray_8,index_9,e9))) = rselect_head(rstore_seq(q9,earray_10)),
inference(monotonicity,[status(thm)],[869]) ).
tff(871,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_208,index_210),store(earray_8,index_9,e9))) = rselect_head(rstore_head(queue_208,index_210)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(872,plain,
rselect_head(rstore_seq(rstore_head(queue_208,index_210),store(earray_8,index_9,e9))) = rselect_head(rstore_head(queue_208,index_210)),
inference(unit_resolution,[status(thm)],[871,128]) ).
tff(873,plain,
rselect_head(rstore_head(queue_208,index_210)) = rselect_head(rstore_seq(rstore_head(queue_208,index_210),store(earray_8,index_9,e9))),
inference(symmetry,[status(thm)],[872]) ).
tff(874,plain,
rselect_head(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = rselect_head(rstore_head(queue_208,index_210)),
inference(monotonicity,[status(thm)],[248]) ).
tff(875,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = s(index_209) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(876,plain,
rselect_head(rstore_head(rstore_tail(queue_206,index_207),s(index_209))) = s(index_209),
inference(unit_resolution,[status(thm)],[875,99]) ).
tff(877,plain,
s(index_209) = rselect_head(rstore_head(rstore_tail(queue_206,index_207),s(index_209))),
inference(symmetry,[status(thm)],[876]) ).
tff(878,plain,
( ( index_209 = rselect_head(queue_208) )
<=> ( index_209 = rselect_head(queue_208) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(879,axiom,
index_209 = rselect_head(queue_208),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp107) ).
tff(880,plain,
index_209 = rselect_head(queue_208),
inference(modus_ponens,[status(thm)],[879,878]) ).
tff(881,plain,
rselect_head(queue_208) = index_209,
inference(symmetry,[status(thm)],[880]) ).
tff(882,plain,
s(rselect_head(queue_208)) = s(index_209),
inference(monotonicity,[status(thm)],[881]) ).
tff(883,plain,
s(rselect_head(queue_208)) = index_26,
inference(transitivity,[status(thm)],[882,877,874,873,870,861,858,846,843,826,823,820,817,808,805,788]) ).
tff(884,plain,
s(s(rselect_head(queue_208))) = s(index_26),
inference(monotonicity,[status(thm)],[883]) ).
tff(885,plain,
s(index_209) = s(rselect_head(queue_208)),
inference(symmetry,[status(thm)],[882]) ).
tff(886,plain,
queue_208 = rstore_tail(rstore_seq(q8,earray_205),s(index_204)),
inference(transitivity,[status(thm)],[246,278]) ).
tff(887,plain,
rselect_head(queue_208) = rselect_head(rstore_tail(rstore_seq(q8,earray_205),s(index_204))),
inference(monotonicity,[status(thm)],[886]) ).
tff(888,plain,
rselect_head(rstore_tail(rstore_seq(q8,earray_205),s(index_204))) = rselect_head(queue_208),
inference(symmetry,[status(thm)],[887]) ).
tff(889,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q8,earray_205),s(index_204))) = rselect_head(rstore_seq(q8,earray_205)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(890,plain,
rselect_head(rstore_tail(rstore_seq(q8,earray_205),s(index_204))) = rselect_head(rstore_seq(q8,earray_205)),
inference(unit_resolution,[status(thm)],[889,153]) ).
tff(891,plain,
rselect_head(rstore_seq(q8,earray_205)) = rselect_head(rstore_tail(rstore_seq(q8,earray_205),s(index_204))),
inference(symmetry,[status(thm)],[890]) ).
tff(892,plain,
( ( earray_205 = store(earray_203,index_204,e8) )
<=> ( earray_205 = store(earray_203,index_204,e8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(893,axiom,
earray_205 = store(earray_203,index_204,e8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp35) ).
tff(894,plain,
earray_205 = store(earray_203,index_204,e8),
inference(modus_ponens,[status(thm)],[893,892]) ).
tff(895,plain,
store(earray_203,index_204,e8) = earray_205,
inference(symmetry,[status(thm)],[894]) ).
tff(896,plain,
( ( q8 = queue_202 )
<=> ( q8 = queue_202 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(897,axiom,
q8 = queue_202,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp244) ).
tff(898,plain,
q8 = queue_202,
inference(modus_ponens,[status(thm)],[897,896]) ).
tff(899,plain,
queue_202 = q8,
inference(symmetry,[status(thm)],[898]) ).
tff(900,plain,
( ( queue_202 = rstore_tail(queue_200,index_201) )
<=> ( queue_202 = rstore_tail(queue_200,index_201) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(901,axiom,
queue_202 = rstore_tail(queue_200,index_201),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp183) ).
tff(902,plain,
queue_202 = rstore_tail(queue_200,index_201),
inference(modus_ponens,[status(thm)],[901,900]) ).
tff(903,plain,
rstore_tail(queue_200,index_201) = queue_202,
inference(symmetry,[status(thm)],[902]) ).
tff(904,plain,
rstore_tail(queue_200,index_201) = q8,
inference(transitivity,[status(thm)],[903,899]) ).
tff(905,plain,
rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e8)) = rstore_seq(q8,earray_205),
inference(monotonicity,[status(thm)],[904,895]) ).
tff(906,plain,
rstore_seq(q8,earray_205) = rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e8)),
inference(symmetry,[status(thm)],[905]) ).
tff(907,plain,
rselect_head(rstore_seq(q8,earray_205)) = rselect_head(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e8))),
inference(monotonicity,[status(thm)],[906]) ).
tff(908,plain,
rselect_head(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e8))) = rselect_head(rstore_seq(q8,earray_205)),
inference(symmetry,[status(thm)],[907]) ).
tff(909,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e8))) = rselect_head(rstore_tail(queue_200,index_201)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(910,plain,
rselect_head(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e8))) = rselect_head(rstore_tail(queue_200,index_201)),
inference(unit_resolution,[status(thm)],[909,128]) ).
tff(911,plain,
rselect_head(rstore_tail(queue_200,index_201)) = rselect_head(rstore_seq(rstore_tail(queue_200,index_201),store(earray_203,index_204,e8))),
inference(symmetry,[status(thm)],[910]) ).
tff(912,plain,
( ( index_201 = s(index_198) )
<=> ( index_201 = s(index_198) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(913,axiom,
index_201 = s(index_198),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp104) ).
tff(914,plain,
index_201 = s(index_198),
inference(modus_ponens,[status(thm)],[913,912]) ).
tff(915,plain,
s(index_198) = index_201,
inference(symmetry,[status(thm)],[914]) ).
tff(916,plain,
( ( queue_200 = rstore_seq(q7,earray_199) )
<=> ( queue_200 = rstore_seq(q7,earray_199) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(917,axiom,
queue_200 = rstore_seq(q7,earray_199),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp182) ).
tff(918,plain,
queue_200 = rstore_seq(q7,earray_199),
inference(modus_ponens,[status(thm)],[917,916]) ).
tff(919,plain,
rstore_seq(q7,earray_199) = queue_200,
inference(symmetry,[status(thm)],[918]) ).
tff(920,plain,
rstore_tail(rstore_seq(q7,earray_199),s(index_198)) = rstore_tail(queue_200,index_201),
inference(monotonicity,[status(thm)],[919,915]) ).
tff(921,plain,
rstore_tail(queue_200,index_201) = rstore_tail(rstore_seq(q7,earray_199),s(index_198)),
inference(symmetry,[status(thm)],[920]) ).
tff(922,plain,
rselect_head(rstore_tail(queue_200,index_201)) = rselect_head(rstore_tail(rstore_seq(q7,earray_199),s(index_198))),
inference(monotonicity,[status(thm)],[921]) ).
tff(923,plain,
rselect_head(rstore_tail(rstore_seq(q7,earray_199),s(index_198))) = rselect_head(rstore_tail(queue_200,index_201)),
inference(symmetry,[status(thm)],[922]) ).
tff(924,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q7,earray_199),s(index_198))) = rselect_head(rstore_seq(q7,earray_199)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(925,plain,
rselect_head(rstore_tail(rstore_seq(q7,earray_199),s(index_198))) = rselect_head(rstore_seq(q7,earray_199)),
inference(unit_resolution,[status(thm)],[924,153]) ).
tff(926,plain,
rselect_head(rstore_seq(q7,earray_199)) = rselect_head(rstore_tail(rstore_seq(q7,earray_199),s(index_198))),
inference(symmetry,[status(thm)],[925]) ).
tff(927,plain,
( ( earray_199 = store(earray_197,index_198,e7) )
<=> ( earray_199 = store(earray_197,index_198,e7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(928,axiom,
earray_199 = store(earray_197,index_198,e7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp31) ).
tff(929,plain,
earray_199 = store(earray_197,index_198,e7),
inference(modus_ponens,[status(thm)],[928,927]) ).
tff(930,plain,
store(earray_197,index_198,e7) = earray_199,
inference(symmetry,[status(thm)],[929]) ).
tff(931,plain,
( ( q7 = queue_196 )
<=> ( q7 = queue_196 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(932,axiom,
q7 = queue_196,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp243) ).
tff(933,plain,
q7 = queue_196,
inference(modus_ponens,[status(thm)],[932,931]) ).
tff(934,plain,
queue_196 = q7,
inference(symmetry,[status(thm)],[933]) ).
tff(935,plain,
( ( queue_196 = rstore_tail(queue_194,index_195) )
<=> ( queue_196 = rstore_tail(queue_194,index_195) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(936,axiom,
queue_196 = rstore_tail(queue_194,index_195),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp181) ).
tff(937,plain,
queue_196 = rstore_tail(queue_194,index_195),
inference(modus_ponens,[status(thm)],[936,935]) ).
tff(938,plain,
rstore_tail(queue_194,index_195) = queue_196,
inference(symmetry,[status(thm)],[937]) ).
tff(939,plain,
rstore_tail(queue_194,index_195) = q7,
inference(transitivity,[status(thm)],[938,934]) ).
tff(940,plain,
rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e7)) = rstore_seq(q7,earray_199),
inference(monotonicity,[status(thm)],[939,930]) ).
tff(941,plain,
rstore_seq(q7,earray_199) = rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e7)),
inference(symmetry,[status(thm)],[940]) ).
tff(942,plain,
rselect_head(rstore_seq(q7,earray_199)) = rselect_head(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e7))),
inference(monotonicity,[status(thm)],[941]) ).
tff(943,plain,
rselect_head(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e7))) = rselect_head(rstore_seq(q7,earray_199)),
inference(symmetry,[status(thm)],[942]) ).
tff(944,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e7))) = rselect_head(rstore_tail(queue_194,index_195)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(945,plain,
rselect_head(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e7))) = rselect_head(rstore_tail(queue_194,index_195)),
inference(unit_resolution,[status(thm)],[944,128]) ).
tff(946,plain,
rselect_head(rstore_tail(queue_194,index_195)) = rselect_head(rstore_seq(rstore_tail(queue_194,index_195),store(earray_197,index_198,e7))),
inference(symmetry,[status(thm)],[945]) ).
tff(947,plain,
( ( index_195 = s(index_192) )
<=> ( index_195 = s(index_192) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(948,axiom,
index_195 = s(index_192),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp102) ).
tff(949,plain,
index_195 = s(index_192),
inference(modus_ponens,[status(thm)],[948,947]) ).
tff(950,plain,
s(index_192) = index_195,
inference(symmetry,[status(thm)],[949]) ).
tff(951,plain,
( ( queue_194 = rstore_seq(q6,earray_193) )
<=> ( queue_194 = rstore_seq(q6,earray_193) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(952,axiom,
queue_194 = rstore_seq(q6,earray_193),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp180) ).
tff(953,plain,
queue_194 = rstore_seq(q6,earray_193),
inference(modus_ponens,[status(thm)],[952,951]) ).
tff(954,plain,
rstore_seq(q6,earray_193) = queue_194,
inference(symmetry,[status(thm)],[953]) ).
tff(955,plain,
rstore_tail(rstore_seq(q6,earray_193),s(index_192)) = rstore_tail(queue_194,index_195),
inference(monotonicity,[status(thm)],[954,950]) ).
tff(956,plain,
rstore_tail(queue_194,index_195) = rstore_tail(rstore_seq(q6,earray_193),s(index_192)),
inference(symmetry,[status(thm)],[955]) ).
tff(957,plain,
rselect_head(rstore_tail(queue_194,index_195)) = rselect_head(rstore_tail(rstore_seq(q6,earray_193),s(index_192))),
inference(monotonicity,[status(thm)],[956]) ).
tff(958,plain,
rselect_head(rstore_tail(rstore_seq(q6,earray_193),s(index_192))) = rselect_head(rstore_tail(queue_194,index_195)),
inference(symmetry,[status(thm)],[957]) ).
tff(959,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q6,earray_193),s(index_192))) = rselect_head(rstore_seq(q6,earray_193)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(960,plain,
rselect_head(rstore_tail(rstore_seq(q6,earray_193),s(index_192))) = rselect_head(rstore_seq(q6,earray_193)),
inference(unit_resolution,[status(thm)],[959,153]) ).
tff(961,plain,
rselect_head(rstore_seq(q6,earray_193)) = rselect_head(rstore_tail(rstore_seq(q6,earray_193),s(index_192))),
inference(symmetry,[status(thm)],[960]) ).
tff(962,plain,
( ( earray_193 = store(earray_191,index_192,e6) )
<=> ( earray_193 = store(earray_191,index_192,e6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(963,axiom,
earray_193 = store(earray_191,index_192,e6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp29) ).
tff(964,plain,
earray_193 = store(earray_191,index_192,e6),
inference(modus_ponens,[status(thm)],[963,962]) ).
tff(965,plain,
store(earray_191,index_192,e6) = earray_193,
inference(symmetry,[status(thm)],[964]) ).
tff(966,plain,
( ( q6 = queue_190 )
<=> ( q6 = queue_190 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(967,axiom,
q6 = queue_190,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp242) ).
tff(968,plain,
q6 = queue_190,
inference(modus_ponens,[status(thm)],[967,966]) ).
tff(969,plain,
queue_190 = q6,
inference(symmetry,[status(thm)],[968]) ).
tff(970,plain,
( ( queue_190 = rstore_head(queue_187,index_189) )
<=> ( queue_190 = rstore_head(queue_187,index_189) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(971,axiom,
queue_190 = rstore_head(queue_187,index_189),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp179) ).
tff(972,plain,
queue_190 = rstore_head(queue_187,index_189),
inference(modus_ponens,[status(thm)],[971,970]) ).
tff(973,plain,
rstore_head(queue_187,index_189) = queue_190,
inference(symmetry,[status(thm)],[972]) ).
tff(974,plain,
rstore_head(queue_187,index_189) = q6,
inference(transitivity,[status(thm)],[973,969]) ).
tff(975,plain,
rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e6)) = rstore_seq(q6,earray_193),
inference(monotonicity,[status(thm)],[974,965]) ).
tff(976,plain,
rselect_head(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e6))) = rselect_head(rstore_seq(q6,earray_193)),
inference(monotonicity,[status(thm)],[975]) ).
tff(977,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e6))) = rselect_head(rstore_head(queue_187,index_189)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(978,plain,
rselect_head(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e6))) = rselect_head(rstore_head(queue_187,index_189)),
inference(unit_resolution,[status(thm)],[977,128]) ).
tff(979,plain,
rselect_head(rstore_head(queue_187,index_189)) = rselect_head(rstore_seq(rstore_head(queue_187,index_189),store(earray_191,index_192,e6))),
inference(symmetry,[status(thm)],[978]) ).
tff(980,plain,
( ( index_189 = s(index_188) )
<=> ( index_189 = s(index_188) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(981,axiom,
index_189 = s(index_188),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp100) ).
tff(982,plain,
index_189 = s(index_188),
inference(modus_ponens,[status(thm)],[981,980]) ).
tff(983,plain,
s(index_188) = index_189,
inference(symmetry,[status(thm)],[982]) ).
tff(984,plain,
( ( queue_187 = rstore_tail(queue_185,index_186) )
<=> ( queue_187 = rstore_tail(queue_185,index_186) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(985,axiom,
queue_187 = rstore_tail(queue_185,index_186),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp177) ).
tff(986,plain,
queue_187 = rstore_tail(queue_185,index_186),
inference(modus_ponens,[status(thm)],[985,984]) ).
tff(987,plain,
rstore_tail(queue_185,index_186) = queue_187,
inference(symmetry,[status(thm)],[986]) ).
tff(988,plain,
rstore_head(rstore_tail(queue_185,index_186),s(index_188)) = rstore_head(queue_187,index_189),
inference(monotonicity,[status(thm)],[987,983]) ).
tff(989,plain,
rselect_head(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = rselect_head(rstore_head(queue_187,index_189)),
inference(monotonicity,[status(thm)],[988]) ).
tff(990,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = s(index_188) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(991,plain,
rselect_head(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = s(index_188),
inference(unit_resolution,[status(thm)],[990,99]) ).
tff(992,plain,
s(index_188) = rselect_head(rstore_head(rstore_tail(queue_185,index_186),s(index_188))),
inference(symmetry,[status(thm)],[991]) ).
tff(993,plain,
( ( index_188 = rselect_head(queue_187) )
<=> ( index_188 = rselect_head(queue_187) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(994,axiom,
index_188 = rselect_head(queue_187),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp99) ).
tff(995,plain,
index_188 = rselect_head(queue_187),
inference(modus_ponens,[status(thm)],[994,993]) ).
tff(996,plain,
rselect_head(queue_187) = index_188,
inference(symmetry,[status(thm)],[995]) ).
tff(997,plain,
s(rselect_head(queue_187)) = s(index_188),
inference(monotonicity,[status(thm)],[996]) ).
tff(998,plain,
s(rselect_head(queue_187)) = index_209,
inference(transitivity,[status(thm)],[997,992,989,979,976,961,958,946,943,926,923,911,908,891,888,881]) ).
tff(999,plain,
s(s(rselect_head(queue_187))) = s(index_209),
inference(monotonicity,[status(thm)],[998]) ).
tff(1000,plain,
s(index_188) = s(rselect_head(queue_187)),
inference(symmetry,[status(thm)],[997]) ).
tff(1001,plain,
( ( index_186 = s(index_183) )
<=> ( index_186 = s(index_183) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1002,axiom,
index_186 = s(index_183),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp98) ).
tff(1003,plain,
index_186 = s(index_183),
inference(modus_ponens,[status(thm)],[1002,1001]) ).
tff(1004,plain,
s(index_183) = index_186,
inference(symmetry,[status(thm)],[1003]) ).
tff(1005,plain,
( ( queue_185 = rstore_seq(q5,earray_184) )
<=> ( queue_185 = rstore_seq(q5,earray_184) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1006,axiom,
queue_185 = rstore_seq(q5,earray_184),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp176) ).
tff(1007,plain,
queue_185 = rstore_seq(q5,earray_184),
inference(modus_ponens,[status(thm)],[1006,1005]) ).
tff(1008,plain,
rstore_seq(q5,earray_184) = queue_185,
inference(symmetry,[status(thm)],[1007]) ).
tff(1009,plain,
rstore_tail(rstore_seq(q5,earray_184),s(index_183)) = rstore_tail(queue_185,index_186),
inference(monotonicity,[status(thm)],[1008,1004]) ).
tff(1010,plain,
rstore_tail(queue_185,index_186) = rstore_tail(rstore_seq(q5,earray_184),s(index_183)),
inference(symmetry,[status(thm)],[1009]) ).
tff(1011,plain,
queue_187 = rstore_tail(rstore_seq(q5,earray_184),s(index_183)),
inference(transitivity,[status(thm)],[986,1010]) ).
tff(1012,plain,
rselect_head(queue_187) = rselect_head(rstore_tail(rstore_seq(q5,earray_184),s(index_183))),
inference(monotonicity,[status(thm)],[1011]) ).
tff(1013,plain,
rselect_head(rstore_tail(rstore_seq(q5,earray_184),s(index_183))) = rselect_head(queue_187),
inference(symmetry,[status(thm)],[1012]) ).
tff(1014,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q5,earray_184),s(index_183))) = rselect_head(rstore_seq(q5,earray_184)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1015,plain,
rselect_head(rstore_tail(rstore_seq(q5,earray_184),s(index_183))) = rselect_head(rstore_seq(q5,earray_184)),
inference(unit_resolution,[status(thm)],[1014,153]) ).
tff(1016,plain,
rselect_head(rstore_seq(q5,earray_184)) = rselect_head(rstore_tail(rstore_seq(q5,earray_184),s(index_183))),
inference(symmetry,[status(thm)],[1015]) ).
tff(1017,plain,
( ( earray_184 = store(earray_182,index_183,e5) )
<=> ( earray_184 = store(earray_182,index_183,e5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1018,axiom,
earray_184 = store(earray_182,index_183,e5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp27) ).
tff(1019,plain,
earray_184 = store(earray_182,index_183,e5),
inference(modus_ponens,[status(thm)],[1018,1017]) ).
tff(1020,plain,
store(earray_182,index_183,e5) = earray_184,
inference(symmetry,[status(thm)],[1019]) ).
tff(1021,plain,
( ( q5 = queue_181 )
<=> ( q5 = queue_181 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1022,axiom,
q5 = queue_181,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp241) ).
tff(1023,plain,
q5 = queue_181,
inference(modus_ponens,[status(thm)],[1022,1021]) ).
tff(1024,plain,
queue_181 = q5,
inference(symmetry,[status(thm)],[1023]) ).
tff(1025,plain,
( ( queue_181 = rstore_tail(queue_179,index_180) )
<=> ( queue_181 = rstore_tail(queue_179,index_180) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1026,axiom,
queue_181 = rstore_tail(queue_179,index_180),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp175) ).
tff(1027,plain,
queue_181 = rstore_tail(queue_179,index_180),
inference(modus_ponens,[status(thm)],[1026,1025]) ).
tff(1028,plain,
rstore_tail(queue_179,index_180) = queue_181,
inference(symmetry,[status(thm)],[1027]) ).
tff(1029,plain,
rstore_tail(queue_179,index_180) = q5,
inference(transitivity,[status(thm)],[1028,1024]) ).
tff(1030,plain,
rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e5)) = rstore_seq(q5,earray_184),
inference(monotonicity,[status(thm)],[1029,1020]) ).
tff(1031,plain,
rstore_seq(q5,earray_184) = rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e5)),
inference(symmetry,[status(thm)],[1030]) ).
tff(1032,plain,
rselect_head(rstore_seq(q5,earray_184)) = rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e5))),
inference(monotonicity,[status(thm)],[1031]) ).
tff(1033,plain,
rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e5))) = rselect_head(rstore_seq(q5,earray_184)),
inference(symmetry,[status(thm)],[1032]) ).
tff(1034,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e5))) = rselect_head(rstore_tail(queue_179,index_180)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1035,plain,
rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e5))) = rselect_head(rstore_tail(queue_179,index_180)),
inference(unit_resolution,[status(thm)],[1034,128]) ).
tff(1036,plain,
rselect_head(rstore_tail(queue_179,index_180)) = rselect_head(rstore_seq(rstore_tail(queue_179,index_180),store(earray_182,index_183,e5))),
inference(symmetry,[status(thm)],[1035]) ).
tff(1037,plain,
( ( index_180 = s(index_177) )
<=> ( index_180 = s(index_177) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1038,axiom,
index_180 = s(index_177),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp96) ).
tff(1039,plain,
index_180 = s(index_177),
inference(modus_ponens,[status(thm)],[1038,1037]) ).
tff(1040,plain,
s(index_177) = index_180,
inference(symmetry,[status(thm)],[1039]) ).
tff(1041,plain,
( ( queue_179 = rstore_seq(q4,earray_178) )
<=> ( queue_179 = rstore_seq(q4,earray_178) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1042,axiom,
queue_179 = rstore_seq(q4,earray_178),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp174) ).
tff(1043,plain,
queue_179 = rstore_seq(q4,earray_178),
inference(modus_ponens,[status(thm)],[1042,1041]) ).
tff(1044,plain,
rstore_seq(q4,earray_178) = queue_179,
inference(symmetry,[status(thm)],[1043]) ).
tff(1045,plain,
rstore_tail(rstore_seq(q4,earray_178),s(index_177)) = rstore_tail(queue_179,index_180),
inference(monotonicity,[status(thm)],[1044,1040]) ).
tff(1046,plain,
rstore_tail(queue_179,index_180) = rstore_tail(rstore_seq(q4,earray_178),s(index_177)),
inference(symmetry,[status(thm)],[1045]) ).
tff(1047,plain,
rselect_head(rstore_tail(queue_179,index_180)) = rselect_head(rstore_tail(rstore_seq(q4,earray_178),s(index_177))),
inference(monotonicity,[status(thm)],[1046]) ).
tff(1048,plain,
rselect_head(rstore_tail(rstore_seq(q4,earray_178),s(index_177))) = rselect_head(rstore_tail(queue_179,index_180)),
inference(symmetry,[status(thm)],[1047]) ).
tff(1049,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q4,earray_178),s(index_177))) = rselect_head(rstore_seq(q4,earray_178)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1050,plain,
rselect_head(rstore_tail(rstore_seq(q4,earray_178),s(index_177))) = rselect_head(rstore_seq(q4,earray_178)),
inference(unit_resolution,[status(thm)],[1049,153]) ).
tff(1051,plain,
rselect_head(rstore_seq(q4,earray_178)) = rselect_head(rstore_tail(rstore_seq(q4,earray_178),s(index_177))),
inference(symmetry,[status(thm)],[1050]) ).
tff(1052,plain,
( ( earray_178 = store(earray_176,index_177,e4) )
<=> ( earray_178 = store(earray_176,index_177,e4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1053,axiom,
earray_178 = store(earray_176,index_177,e4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp25) ).
tff(1054,plain,
earray_178 = store(earray_176,index_177,e4),
inference(modus_ponens,[status(thm)],[1053,1052]) ).
tff(1055,plain,
store(earray_176,index_177,e4) = earray_178,
inference(symmetry,[status(thm)],[1054]) ).
tff(1056,plain,
( ( q4 = queue_175 )
<=> ( q4 = queue_175 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1057,axiom,
q4 = queue_175,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp240) ).
tff(1058,plain,
q4 = queue_175,
inference(modus_ponens,[status(thm)],[1057,1056]) ).
tff(1059,plain,
queue_175 = q4,
inference(symmetry,[status(thm)],[1058]) ).
tff(1060,plain,
( ( queue_175 = rstore_tail(queue_173,index_174) )
<=> ( queue_175 = rstore_tail(queue_173,index_174) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1061,axiom,
queue_175 = rstore_tail(queue_173,index_174),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp173) ).
tff(1062,plain,
queue_175 = rstore_tail(queue_173,index_174),
inference(modus_ponens,[status(thm)],[1061,1060]) ).
tff(1063,plain,
rstore_tail(queue_173,index_174) = queue_175,
inference(symmetry,[status(thm)],[1062]) ).
tff(1064,plain,
rstore_tail(queue_173,index_174) = q4,
inference(transitivity,[status(thm)],[1063,1059]) ).
tff(1065,plain,
rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e4)) = rstore_seq(q4,earray_178),
inference(monotonicity,[status(thm)],[1064,1055]) ).
tff(1066,plain,
rstore_seq(q4,earray_178) = rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e4)),
inference(symmetry,[status(thm)],[1065]) ).
tff(1067,plain,
rselect_head(rstore_seq(q4,earray_178)) = rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e4))),
inference(monotonicity,[status(thm)],[1066]) ).
tff(1068,plain,
rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e4))) = rselect_head(rstore_seq(q4,earray_178)),
inference(symmetry,[status(thm)],[1067]) ).
tff(1069,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e4))) = rselect_head(rstore_tail(queue_173,index_174)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1070,plain,
rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e4))) = rselect_head(rstore_tail(queue_173,index_174)),
inference(unit_resolution,[status(thm)],[1069,128]) ).
tff(1071,plain,
rselect_head(rstore_tail(queue_173,index_174)) = rselect_head(rstore_seq(rstore_tail(queue_173,index_174),store(earray_176,index_177,e4))),
inference(symmetry,[status(thm)],[1070]) ).
tff(1072,plain,
( ( index_174 = s(index_171) )
<=> ( index_174 = s(index_171) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1073,axiom,
index_174 = s(index_171),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp93) ).
tff(1074,plain,
index_174 = s(index_171),
inference(modus_ponens,[status(thm)],[1073,1072]) ).
tff(1075,plain,
s(index_171) = index_174,
inference(symmetry,[status(thm)],[1074]) ).
tff(1076,plain,
( ( queue_173 = rstore_seq(q3,earray_172) )
<=> ( queue_173 = rstore_seq(q3,earray_172) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1077,axiom,
queue_173 = rstore_seq(q3,earray_172),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp172) ).
tff(1078,plain,
queue_173 = rstore_seq(q3,earray_172),
inference(modus_ponens,[status(thm)],[1077,1076]) ).
tff(1079,plain,
rstore_seq(q3,earray_172) = queue_173,
inference(symmetry,[status(thm)],[1078]) ).
tff(1080,plain,
rstore_tail(rstore_seq(q3,earray_172),s(index_171)) = rstore_tail(queue_173,index_174),
inference(monotonicity,[status(thm)],[1079,1075]) ).
tff(1081,plain,
rstore_tail(queue_173,index_174) = rstore_tail(rstore_seq(q3,earray_172),s(index_171)),
inference(symmetry,[status(thm)],[1080]) ).
tff(1082,plain,
rselect_head(rstore_tail(queue_173,index_174)) = rselect_head(rstore_tail(rstore_seq(q3,earray_172),s(index_171))),
inference(monotonicity,[status(thm)],[1081]) ).
tff(1083,plain,
rselect_head(rstore_tail(rstore_seq(q3,earray_172),s(index_171))) = rselect_head(rstore_tail(queue_173,index_174)),
inference(symmetry,[status(thm)],[1082]) ).
tff(1084,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q3,earray_172),s(index_171))) = rselect_head(rstore_seq(q3,earray_172)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1085,plain,
rselect_head(rstore_tail(rstore_seq(q3,earray_172),s(index_171))) = rselect_head(rstore_seq(q3,earray_172)),
inference(unit_resolution,[status(thm)],[1084,153]) ).
tff(1086,plain,
rselect_head(rstore_seq(q3,earray_172)) = rselect_head(rstore_tail(rstore_seq(q3,earray_172),s(index_171))),
inference(symmetry,[status(thm)],[1085]) ).
tff(1087,plain,
( ( earray_172 = store(earray_170,index_171,e3) )
<=> ( earray_172 = store(earray_170,index_171,e3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1088,axiom,
earray_172 = store(earray_170,index_171,e3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp23) ).
tff(1089,plain,
earray_172 = store(earray_170,index_171,e3),
inference(modus_ponens,[status(thm)],[1088,1087]) ).
tff(1090,plain,
store(earray_170,index_171,e3) = earray_172,
inference(symmetry,[status(thm)],[1089]) ).
tff(1091,plain,
( ( q3 = queue_160 )
<=> ( q3 = queue_160 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1092,axiom,
q3 = queue_160,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp238) ).
tff(1093,plain,
q3 = queue_160,
inference(modus_ponens,[status(thm)],[1092,1091]) ).
tff(1094,plain,
queue_160 = q3,
inference(symmetry,[status(thm)],[1093]) ).
tff(1095,plain,
( ( queue_160 = rstore_head(queue_157,index_159) )
<=> ( queue_160 = rstore_head(queue_157,index_159) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1096,axiom,
queue_160 = rstore_head(queue_157,index_159),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp167) ).
tff(1097,plain,
queue_160 = rstore_head(queue_157,index_159),
inference(modus_ponens,[status(thm)],[1096,1095]) ).
tff(1098,plain,
rstore_head(queue_157,index_159) = queue_160,
inference(symmetry,[status(thm)],[1097]) ).
tff(1099,plain,
rstore_head(queue_157,index_159) = q3,
inference(transitivity,[status(thm)],[1098,1094]) ).
tff(1100,plain,
rstore_seq(rstore_head(queue_157,index_159),store(earray_170,index_171,e3)) = rstore_seq(q3,earray_172),
inference(monotonicity,[status(thm)],[1099,1090]) ).
tff(1101,plain,
rselect_head(rstore_seq(rstore_head(queue_157,index_159),store(earray_170,index_171,e3))) = rselect_head(rstore_seq(q3,earray_172)),
inference(monotonicity,[status(thm)],[1100]) ).
tff(1102,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_157,index_159),store(earray_170,index_171,e3))) = rselect_head(rstore_head(queue_157,index_159)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1103,plain,
rselect_head(rstore_seq(rstore_head(queue_157,index_159),store(earray_170,index_171,e3))) = rselect_head(rstore_head(queue_157,index_159)),
inference(unit_resolution,[status(thm)],[1102,128]) ).
tff(1104,plain,
rselect_head(rstore_head(queue_157,index_159)) = rselect_head(rstore_seq(rstore_head(queue_157,index_159),store(earray_170,index_171,e3))),
inference(symmetry,[status(thm)],[1103]) ).
tff(1105,plain,
( ( index_159 = s(index_158) )
<=> ( index_159 = s(index_158) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1106,axiom,
index_159 = s(index_158),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp87) ).
tff(1107,plain,
index_159 = s(index_158),
inference(modus_ponens,[status(thm)],[1106,1105]) ).
tff(1108,plain,
s(index_158) = index_159,
inference(symmetry,[status(thm)],[1107]) ).
tff(1109,plain,
( ( queue_157 = rstore_tail(queue_155,index_156) )
<=> ( queue_157 = rstore_tail(queue_155,index_156) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1110,axiom,
queue_157 = rstore_tail(queue_155,index_156),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp166) ).
tff(1111,plain,
queue_157 = rstore_tail(queue_155,index_156),
inference(modus_ponens,[status(thm)],[1110,1109]) ).
tff(1112,plain,
rstore_tail(queue_155,index_156) = queue_157,
inference(symmetry,[status(thm)],[1111]) ).
tff(1113,plain,
rstore_head(rstore_tail(queue_155,index_156),s(index_158)) = rstore_head(queue_157,index_159),
inference(monotonicity,[status(thm)],[1112,1108]) ).
tff(1114,plain,
rselect_head(rstore_head(rstore_tail(queue_155,index_156),s(index_158))) = rselect_head(rstore_head(queue_157,index_159)),
inference(monotonicity,[status(thm)],[1113]) ).
tff(1115,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_155,index_156),s(index_158))) = s(index_158) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1116,plain,
rselect_head(rstore_head(rstore_tail(queue_155,index_156),s(index_158))) = s(index_158),
inference(unit_resolution,[status(thm)],[1115,99]) ).
tff(1117,plain,
s(index_158) = rselect_head(rstore_head(rstore_tail(queue_155,index_156),s(index_158))),
inference(symmetry,[status(thm)],[1116]) ).
tff(1118,plain,
( ( index_158 = rselect_head(queue_157) )
<=> ( index_158 = rselect_head(queue_157) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1119,axiom,
index_158 = rselect_head(queue_157),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp86) ).
tff(1120,plain,
index_158 = rselect_head(queue_157),
inference(modus_ponens,[status(thm)],[1119,1118]) ).
tff(1121,plain,
rselect_head(queue_157) = index_158,
inference(symmetry,[status(thm)],[1120]) ).
tff(1122,plain,
s(rselect_head(queue_157)) = s(index_158),
inference(monotonicity,[status(thm)],[1121]) ).
tff(1123,plain,
s(rselect_head(queue_157)) = index_188,
inference(transitivity,[status(thm)],[1122,1117,1114,1104,1101,1086,1083,1071,1068,1051,1048,1036,1033,1016,1013,996]) ).
tff(1124,plain,
s(s(rselect_head(queue_157))) = s(index_188),
inference(monotonicity,[status(thm)],[1123]) ).
tff(1125,plain,
s(index_158) = s(rselect_head(queue_157)),
inference(symmetry,[status(thm)],[1122]) ).
tff(1126,plain,
( ( index_156 = s(index_153) )
<=> ( index_156 = s(index_153) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1127,axiom,
index_156 = s(index_153),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp85) ).
tff(1128,plain,
index_156 = s(index_153),
inference(modus_ponens,[status(thm)],[1127,1126]) ).
tff(1129,plain,
s(index_153) = index_156,
inference(symmetry,[status(thm)],[1128]) ).
tff(1130,plain,
( ( queue_155 = rstore_seq(q2,earray_154) )
<=> ( queue_155 = rstore_seq(q2,earray_154) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1131,axiom,
queue_155 = rstore_seq(q2,earray_154),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp165) ).
tff(1132,plain,
queue_155 = rstore_seq(q2,earray_154),
inference(modus_ponens,[status(thm)],[1131,1130]) ).
tff(1133,plain,
rstore_seq(q2,earray_154) = queue_155,
inference(symmetry,[status(thm)],[1132]) ).
tff(1134,plain,
rstore_tail(rstore_seq(q2,earray_154),s(index_153)) = rstore_tail(queue_155,index_156),
inference(monotonicity,[status(thm)],[1133,1129]) ).
tff(1135,plain,
rstore_tail(queue_155,index_156) = rstore_tail(rstore_seq(q2,earray_154),s(index_153)),
inference(symmetry,[status(thm)],[1134]) ).
tff(1136,plain,
queue_157 = rstore_tail(rstore_seq(q2,earray_154),s(index_153)),
inference(transitivity,[status(thm)],[1111,1135]) ).
tff(1137,plain,
rselect_head(queue_157) = rselect_head(rstore_tail(rstore_seq(q2,earray_154),s(index_153))),
inference(monotonicity,[status(thm)],[1136]) ).
tff(1138,plain,
rselect_head(rstore_tail(rstore_seq(q2,earray_154),s(index_153))) = rselect_head(queue_157),
inference(symmetry,[status(thm)],[1137]) ).
tff(1139,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q2,earray_154),s(index_153))) = rselect_head(rstore_seq(q2,earray_154)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1140,plain,
rselect_head(rstore_tail(rstore_seq(q2,earray_154),s(index_153))) = rselect_head(rstore_seq(q2,earray_154)),
inference(unit_resolution,[status(thm)],[1139,153]) ).
tff(1141,plain,
rselect_head(rstore_seq(q2,earray_154)) = rselect_head(rstore_tail(rstore_seq(q2,earray_154),s(index_153))),
inference(symmetry,[status(thm)],[1140]) ).
tff(1142,plain,
( ( earray_154 = store(earray_152,index_153,e2) )
<=> ( earray_154 = store(earray_152,index_153,e2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1143,axiom,
earray_154 = store(earray_152,index_153,e2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp18) ).
tff(1144,plain,
earray_154 = store(earray_152,index_153,e2),
inference(modus_ponens,[status(thm)],[1143,1142]) ).
tff(1145,plain,
store(earray_152,index_153,e2) = earray_154,
inference(symmetry,[status(thm)],[1144]) ).
tff(1146,plain,
( ( q2 = queue_82 )
<=> ( q2 = queue_82 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1147,axiom,
q2 = queue_82,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp227) ).
tff(1148,plain,
q2 = queue_82,
inference(modus_ponens,[status(thm)],[1147,1146]) ).
tff(1149,plain,
queue_82 = q2,
inference(symmetry,[status(thm)],[1148]) ).
tff(1150,plain,
( ( queue_82 = rstore_tail(queue_80,index_81) )
<=> ( queue_82 = rstore_tail(queue_80,index_81) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1151,axiom,
queue_82 = rstore_tail(queue_80,index_81),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp209) ).
tff(1152,plain,
queue_82 = rstore_tail(queue_80,index_81),
inference(modus_ponens,[status(thm)],[1151,1150]) ).
tff(1153,plain,
rstore_tail(queue_80,index_81) = queue_82,
inference(symmetry,[status(thm)],[1152]) ).
tff(1154,plain,
rstore_tail(queue_80,index_81) = q2,
inference(transitivity,[status(thm)],[1153,1149]) ).
tff(1155,plain,
rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2)) = rstore_seq(q2,earray_154),
inference(monotonicity,[status(thm)],[1154,1145]) ).
tff(1156,plain,
rstore_seq(q2,earray_154) = rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2)),
inference(symmetry,[status(thm)],[1155]) ).
tff(1157,plain,
rselect_head(rstore_seq(q2,earray_154)) = rselect_head(rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2))),
inference(monotonicity,[status(thm)],[1156]) ).
tff(1158,plain,
rselect_head(rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2))) = rselect_head(rstore_seq(q2,earray_154)),
inference(symmetry,[status(thm)],[1157]) ).
tff(1159,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2))) = rselect_head(rstore_tail(queue_80,index_81)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1160,plain,
rselect_head(rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2))) = rselect_head(rstore_tail(queue_80,index_81)),
inference(unit_resolution,[status(thm)],[1159,128]) ).
tff(1161,plain,
rselect_head(rstore_tail(queue_80,index_81)) = rselect_head(rstore_seq(rstore_tail(queue_80,index_81),store(earray_152,index_153,e2))),
inference(symmetry,[status(thm)],[1160]) ).
tff(1162,plain,
( ( index_81 = s(index_78) )
<=> ( index_81 = s(index_78) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1163,axiom,
index_81 = s(index_78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp135) ).
tff(1164,plain,
index_81 = s(index_78),
inference(modus_ponens,[status(thm)],[1163,1162]) ).
tff(1165,plain,
s(index_78) = index_81,
inference(symmetry,[status(thm)],[1164]) ).
tff(1166,plain,
( ( queue_80 = rstore_seq(q1,earray_79) )
<=> ( queue_80 = rstore_seq(q1,earray_79) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1167,axiom,
queue_80 = rstore_seq(q1,earray_79),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp208) ).
tff(1168,plain,
queue_80 = rstore_seq(q1,earray_79),
inference(modus_ponens,[status(thm)],[1167,1166]) ).
tff(1169,plain,
rstore_seq(q1,earray_79) = queue_80,
inference(symmetry,[status(thm)],[1168]) ).
tff(1170,plain,
rstore_tail(rstore_seq(q1,earray_79),s(index_78)) = rstore_tail(queue_80,index_81),
inference(monotonicity,[status(thm)],[1169,1165]) ).
tff(1171,plain,
rstore_tail(queue_80,index_81) = rstore_tail(rstore_seq(q1,earray_79),s(index_78)),
inference(symmetry,[status(thm)],[1170]) ).
tff(1172,plain,
rselect_head(rstore_tail(queue_80,index_81)) = rselect_head(rstore_tail(rstore_seq(q1,earray_79),s(index_78))),
inference(monotonicity,[status(thm)],[1171]) ).
tff(1173,plain,
rselect_head(rstore_tail(rstore_seq(q1,earray_79),s(index_78))) = rselect_head(rstore_tail(queue_80,index_81)),
inference(symmetry,[status(thm)],[1172]) ).
tff(1174,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q1,earray_79),s(index_78))) = rselect_head(rstore_seq(q1,earray_79)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1175,plain,
rselect_head(rstore_tail(rstore_seq(q1,earray_79),s(index_78))) = rselect_head(rstore_seq(q1,earray_79)),
inference(unit_resolution,[status(thm)],[1174,153]) ).
tff(1176,plain,
rselect_head(rstore_seq(q1,earray_79)) = rselect_head(rstore_tail(rstore_seq(q1,earray_79),s(index_78))),
inference(symmetry,[status(thm)],[1175]) ).
tff(1177,plain,
( ( earray_79 = store(earray_77,index_78,e1) )
<=> ( earray_79 = store(earray_77,index_78,e1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1178,axiom,
earray_79 = store(earray_77,index_78,e1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp54) ).
tff(1179,plain,
earray_79 = store(earray_77,index_78,e1),
inference(modus_ponens,[status(thm)],[1178,1177]) ).
tff(1180,plain,
store(earray_77,index_78,e1) = earray_79,
inference(symmetry,[status(thm)],[1179]) ).
tff(1181,plain,
( ( q1 = queue_7 )
<=> ( q1 = queue_7 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1182,axiom,
q1 = queue_7,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp216) ).
tff(1183,plain,
q1 = queue_7,
inference(modus_ponens,[status(thm)],[1182,1181]) ).
tff(1184,plain,
queue_7 = q1,
inference(symmetry,[status(thm)],[1183]) ).
tff(1185,plain,
( ( queue_7 = rstore_tail(queue_5,index_6) )
<=> ( queue_7 = rstore_tail(queue_5,index_6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1186,axiom,
queue_7 = rstore_tail(queue_5,index_6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp204) ).
tff(1187,plain,
queue_7 = rstore_tail(queue_5,index_6),
inference(modus_ponens,[status(thm)],[1186,1185]) ).
tff(1188,plain,
rstore_tail(queue_5,index_6) = queue_7,
inference(symmetry,[status(thm)],[1187]) ).
tff(1189,plain,
rstore_tail(queue_5,index_6) = q1,
inference(transitivity,[status(thm)],[1188,1184]) ).
tff(1190,plain,
rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1)) = rstore_seq(q1,earray_79),
inference(monotonicity,[status(thm)],[1189,1180]) ).
tff(1191,plain,
rstore_seq(q1,earray_79) = rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1)),
inference(symmetry,[status(thm)],[1190]) ).
tff(1192,plain,
rselect_head(rstore_seq(q1,earray_79)) = rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1))),
inference(monotonicity,[status(thm)],[1191]) ).
tff(1193,plain,
rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1))) = rselect_head(rstore_seq(q1,earray_79)),
inference(symmetry,[status(thm)],[1192]) ).
tff(1194,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1))) = rselect_head(rstore_tail(queue_5,index_6)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1195,plain,
rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1))) = rselect_head(rstore_tail(queue_5,index_6)),
inference(unit_resolution,[status(thm)],[1194,128]) ).
tff(1196,plain,
rselect_head(rstore_tail(queue_5,index_6)) = rselect_head(rstore_seq(rstore_tail(queue_5,index_6),store(earray_77,index_78,e1))),
inference(symmetry,[status(thm)],[1195]) ).
tff(1197,plain,
( ( index_6 = s(index_3) )
<=> ( index_6 = s(index_3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1198,axiom,
index_6 = s(index_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp126) ).
tff(1199,plain,
index_6 = s(index_3),
inference(modus_ponens,[status(thm)],[1198,1197]) ).
tff(1200,plain,
s(index_3) = index_6,
inference(symmetry,[status(thm)],[1199]) ).
tff(1201,plain,
( ( queue_5 = rstore_seq(q0,earray_4) )
<=> ( queue_5 = rstore_seq(q0,earray_4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1202,axiom,
queue_5 = rstore_seq(q0,earray_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp197) ).
tff(1203,plain,
queue_5 = rstore_seq(q0,earray_4),
inference(modus_ponens,[status(thm)],[1202,1201]) ).
tff(1204,plain,
rstore_seq(q0,earray_4) = queue_5,
inference(symmetry,[status(thm)],[1203]) ).
tff(1205,plain,
rstore_tail(rstore_seq(q0,earray_4),s(index_3)) = rstore_tail(queue_5,index_6),
inference(monotonicity,[status(thm)],[1204,1200]) ).
tff(1206,plain,
rstore_tail(queue_5,index_6) = rstore_tail(rstore_seq(q0,earray_4),s(index_3)),
inference(symmetry,[status(thm)],[1205]) ).
tff(1207,plain,
rselect_head(rstore_tail(queue_5,index_6)) = rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))),
inference(monotonicity,[status(thm)],[1206]) ).
tff(1208,plain,
rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = rselect_head(rstore_tail(queue_5,index_6)),
inference(symmetry,[status(thm)],[1207]) ).
tff(1209,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = rselect_head(rstore_seq(q0,earray_4)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1210,plain,
rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = rselect_head(rstore_seq(q0,earray_4)),
inference(unit_resolution,[status(thm)],[1209,153]) ).
tff(1211,plain,
rselect_head(rstore_seq(q0,earray_4)) = rselect_head(rstore_tail(rstore_seq(q0,earray_4),s(index_3))),
inference(symmetry,[status(thm)],[1210]) ).
tff(1212,plain,
( ( earray_4 = store(earray_2,index_3,e0) )
<=> ( earray_4 = store(earray_2,index_3,e0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1213,axiom,
earray_4 = store(earray_2,index_3,e0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp42) ).
tff(1214,plain,
earray_4 = store(earray_2,index_3,e0),
inference(modus_ponens,[status(thm)],[1213,1212]) ).
tff(1215,plain,
store(earray_2,index_3,e0) = earray_4,
inference(symmetry,[status(thm)],[1214]) ).
tff(1216,plain,
( ( q0 = queue_1 )
<=> ( q0 = queue_1 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1217,axiom,
q0 = queue_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp215) ).
tff(1218,plain,
q0 = queue_1,
inference(modus_ponens,[status(thm)],[1217,1216]) ).
tff(1219,plain,
queue_1 = q0,
inference(symmetry,[status(thm)],[1218]) ).
tff(1220,plain,
( ( queue_1 = rstore_head(q,index_0) )
<=> ( queue_1 = rstore_head(q,index_0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1221,axiom,
queue_1 = rstore_head(q,index_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp144) ).
tff(1222,plain,
queue_1 = rstore_head(q,index_0),
inference(modus_ponens,[status(thm)],[1221,1220]) ).
tff(1223,plain,
rstore_head(q,index_0) = queue_1,
inference(symmetry,[status(thm)],[1222]) ).
tff(1224,plain,
rstore_head(q,index_0) = q0,
inference(transitivity,[status(thm)],[1223,1219]) ).
tff(1225,plain,
rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0)) = rstore_seq(q0,earray_4),
inference(monotonicity,[status(thm)],[1224,1215]) ).
tff(1226,plain,
rstore_seq(q0,earray_4) = rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0)),
inference(symmetry,[status(thm)],[1225]) ).
tff(1227,plain,
rselect_head(rstore_seq(q0,earray_4)) = rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))),
inference(monotonicity,[status(thm)],[1226]) ).
tff(1228,plain,
rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))) = rselect_head(rstore_seq(q0,earray_4)),
inference(symmetry,[status(thm)],[1227]) ).
tff(1229,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))) = rselect_head(rstore_head(q,index_0)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1230,plain,
rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))) = rselect_head(rstore_head(q,index_0)),
inference(unit_resolution,[status(thm)],[1229,128]) ).
tff(1231,plain,
rselect_head(rstore_head(q,index_0)) = rselect_head(rstore_seq(rstore_head(q,index_0),store(earray_2,index_3,e0))),
inference(symmetry,[status(thm)],[1230]) ).
tff(1232,plain,
( ( index_0 = rselect_tail(q) )
<=> ( index_0 = rselect_tail(q) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1233,axiom,
index_0 = rselect_tail(q),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp62) ).
tff(1234,plain,
index_0 = rselect_tail(q),
inference(modus_ponens,[status(thm)],[1233,1232]) ).
tff(1235,plain,
rselect_tail(q) = index_0,
inference(symmetry,[status(thm)],[1234]) ).
tff(1236,plain,
rstore_head(q,rselect_tail(q)) = rstore_head(q,index_0),
inference(monotonicity,[status(thm)],[1235]) ).
tff(1237,plain,
rstore_head(q,index_0) = rstore_head(q,rselect_tail(q)),
inference(symmetry,[status(thm)],[1236]) ).
tff(1238,plain,
rselect_head(rstore_head(q,index_0)) = rselect_head(rstore_head(q,rselect_tail(q))),
inference(monotonicity,[status(thm)],[1237]) ).
tff(1239,plain,
rselect_head(rstore_head(q,rselect_tail(q))) = rselect_head(rstore_head(q,index_0)),
inference(symmetry,[status(thm)],[1238]) ).
tff(1240,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(q,rselect_tail(q))) = rselect_tail(q) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1241,plain,
rselect_head(rstore_head(q,rselect_tail(q))) = rselect_tail(q),
inference(unit_resolution,[status(thm)],[1240,99]) ).
tff(1242,plain,
rselect_tail(q) = rselect_head(rstore_head(q,rselect_tail(q))),
inference(symmetry,[status(thm)],[1241]) ).
tff(1243,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(q,rselect_tail(q))) = rselect_tail(q) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1244,plain,
rselect_tail(rstore_head(q,rselect_tail(q))) = rselect_tail(q),
inference(unit_resolution,[status(thm)],[1243,265]) ).
tff(1245,plain,
rstore_head(q,rselect_tail(q)) = q0,
inference(transitivity,[status(thm)],[1236,1223,1219]) ).
tff(1246,plain,
rselect_tail(rstore_head(q,rselect_tail(q))) = rselect_tail(q0),
inference(monotonicity,[status(thm)],[1245]) ).
tff(1247,plain,
rselect_tail(q0) = rselect_tail(rstore_head(q,rselect_tail(q))),
inference(symmetry,[status(thm)],[1246]) ).
tff(1248,plain,
( ( index_3 = rselect_tail(q0) )
<=> ( index_3 = rselect_tail(q0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1249,axiom,
index_3 = rselect_tail(q0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp114) ).
tff(1250,plain,
index_3 = rselect_tail(q0),
inference(modus_ponens,[status(thm)],[1249,1248]) ).
tff(1251,plain,
index_3 = index_158,
inference(transitivity,[status(thm)],[1250,1247,1244,1242,1239,1231,1228,1211,1208,1196,1193,1176,1173,1161,1158,1141,1138,1121]) ).
tff(1252,plain,
s(index_3) = s(index_158),
inference(monotonicity,[status(thm)],[1251]) ).
tff(1253,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = s(index_3) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1254,plain,
rselect_tail(rstore_tail(rstore_seq(q0,earray_4),s(index_3))) = s(index_3),
inference(unit_resolution,[status(thm)],[1253,13]) ).
tff(1255,plain,
q1 = rstore_tail(rstore_seq(q0,earray_4),s(index_3)),
inference(transitivity,[status(thm)],[1183,1187,1206]) ).
tff(1256,plain,
rselect_tail(q1) = rselect_tail(rstore_tail(rstore_seq(q0,earray_4),s(index_3))),
inference(monotonicity,[status(thm)],[1255]) ).
tff(1257,plain,
( ( index_78 = rselect_tail(q1) )
<=> ( index_78 = rselect_tail(q1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1258,axiom,
index_78 = rselect_tail(q1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp134) ).
tff(1259,plain,
index_78 = rselect_tail(q1),
inference(modus_ponens,[status(thm)],[1258,1257]) ).
tff(1260,plain,
index_78 = s(rselect_head(queue_157)),
inference(transitivity,[status(thm)],[1259,1256,1254,1252,1125]) ).
tff(1261,plain,
s(index_78) = s(s(rselect_head(queue_157))),
inference(monotonicity,[status(thm)],[1260]) ).
tff(1262,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q1,earray_79),s(index_78))) = s(index_78) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1263,plain,
rselect_tail(rstore_tail(rstore_seq(q1,earray_79),s(index_78))) = s(index_78),
inference(unit_resolution,[status(thm)],[1262,13]) ).
tff(1264,plain,
q2 = rstore_tail(rstore_seq(q1,earray_79),s(index_78)),
inference(transitivity,[status(thm)],[1148,1152,1171]) ).
tff(1265,plain,
rselect_tail(q2) = rselect_tail(rstore_tail(rstore_seq(q1,earray_79),s(index_78))),
inference(monotonicity,[status(thm)],[1264]) ).
tff(1266,plain,
( ( index_153 = rselect_tail(q2) )
<=> ( index_153 = rselect_tail(q2) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1267,axiom,
index_153 = rselect_tail(q2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp84) ).
tff(1268,plain,
index_153 = rselect_tail(q2),
inference(modus_ponens,[status(thm)],[1267,1266]) ).
tff(1269,plain,
index_153 = s(rselect_head(queue_187)),
inference(transitivity,[status(thm)],[1268,1265,1263,1261,1124,1000]) ).
tff(1270,plain,
s(index_153) = s(s(rselect_head(queue_187))),
inference(monotonicity,[status(thm)],[1269]) ).
tff(1271,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q2,earray_154),s(index_153))) = s(index_153) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1272,plain,
rselect_tail(rstore_tail(rstore_seq(q2,earray_154),s(index_153))) = s(index_153),
inference(unit_resolution,[status(thm)],[1271,13]) ).
tff(1273,plain,
rselect_tail(rstore_tail(queue_155,index_156)) = rselect_tail(rstore_tail(rstore_seq(q2,earray_154),s(index_153))),
inference(monotonicity,[status(thm)],[1135]) ).
tff(1274,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_155,index_156),s(index_158))) = rselect_tail(rstore_tail(queue_155,index_156)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1275,plain,
rselect_tail(rstore_head(rstore_tail(queue_155,index_156),s(index_158))) = rselect_tail(rstore_tail(queue_155,index_156)),
inference(unit_resolution,[status(thm)],[1274,265]) ).
tff(1276,plain,
rstore_head(queue_157,index_159) = rstore_head(rstore_tail(queue_155,index_156),s(index_158)),
inference(symmetry,[status(thm)],[1113]) ).
tff(1277,plain,
q3 = rstore_head(rstore_tail(queue_155,index_156),s(index_158)),
inference(transitivity,[status(thm)],[1093,1097,1276]) ).
tff(1278,plain,
rselect_tail(q3) = rselect_tail(rstore_head(rstore_tail(queue_155,index_156),s(index_158))),
inference(monotonicity,[status(thm)],[1277]) ).
tff(1279,plain,
( ( index_171 = rselect_tail(q3) )
<=> ( index_171 = rselect_tail(q3) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1280,axiom,
index_171 = rselect_tail(q3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp92) ).
tff(1281,plain,
index_171 = rselect_tail(q3),
inference(modus_ponens,[status(thm)],[1280,1279]) ).
tff(1282,plain,
index_171 = s(rselect_head(queue_208)),
inference(transitivity,[status(thm)],[1281,1278,1275,1273,1272,1270,999,885]) ).
tff(1283,plain,
s(index_171) = s(s(rselect_head(queue_208))),
inference(monotonicity,[status(thm)],[1282]) ).
tff(1284,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q3,earray_172),s(index_171))) = s(index_171) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1285,plain,
rselect_tail(rstore_tail(rstore_seq(q3,earray_172),s(index_171))) = s(index_171),
inference(unit_resolution,[status(thm)],[1284,13]) ).
tff(1286,plain,
q4 = rstore_tail(rstore_seq(q3,earray_172),s(index_171)),
inference(transitivity,[status(thm)],[1058,1062,1081]) ).
tff(1287,plain,
rselect_tail(q4) = rselect_tail(rstore_tail(rstore_seq(q3,earray_172),s(index_171))),
inference(monotonicity,[status(thm)],[1286]) ).
tff(1288,plain,
( ( index_177 = rselect_tail(q4) )
<=> ( index_177 = rselect_tail(q4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1289,axiom,
index_177 = rselect_tail(q4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp94) ).
tff(1290,plain,
index_177 = rselect_tail(q4),
inference(modus_ponens,[status(thm)],[1289,1288]) ).
tff(1291,plain,
index_177 = s(rselect_head(queue_25)),
inference(transitivity,[status(thm)],[1290,1287,1285,1283,884,792]) ).
tff(1292,plain,
s(index_177) = s(s(rselect_head(queue_25))),
inference(monotonicity,[status(thm)],[1291]) ).
tff(1293,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q4,earray_178),s(index_177))) = s(index_177) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1294,plain,
rselect_tail(rstore_tail(rstore_seq(q4,earray_178),s(index_177))) = s(index_177),
inference(unit_resolution,[status(thm)],[1293,13]) ).
tff(1295,plain,
q5 = rstore_tail(rstore_seq(q4,earray_178),s(index_177)),
inference(transitivity,[status(thm)],[1023,1027,1046]) ).
tff(1296,plain,
rselect_tail(q5) = rselect_tail(rstore_tail(rstore_seq(q4,earray_178),s(index_177))),
inference(monotonicity,[status(thm)],[1295]) ).
tff(1297,plain,
( ( index_183 = rselect_tail(q5) )
<=> ( index_183 = rselect_tail(q5) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1298,axiom,
index_183 = rselect_tail(q5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp97) ).
tff(1299,plain,
index_183 = rselect_tail(q5),
inference(modus_ponens,[status(thm)],[1298,1297]) ).
tff(1300,plain,
index_183 = s(rselect_head(queue_46)),
inference(transitivity,[status(thm)],[1299,1296,1294,1292,791,667]) ).
tff(1301,plain,
s(index_183) = s(s(rselect_head(queue_46))),
inference(monotonicity,[status(thm)],[1300]) ).
tff(1302,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q5,earray_184),s(index_183))) = s(index_183) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1303,plain,
rselect_tail(rstore_tail(rstore_seq(q5,earray_184),s(index_183))) = s(index_183),
inference(unit_resolution,[status(thm)],[1302,13]) ).
tff(1304,plain,
rselect_tail(rstore_tail(queue_185,index_186)) = rselect_tail(rstore_tail(rstore_seq(q5,earray_184),s(index_183))),
inference(monotonicity,[status(thm)],[1010]) ).
tff(1305,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = rselect_tail(rstore_tail(queue_185,index_186)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1306,plain,
rselect_tail(rstore_head(rstore_tail(queue_185,index_186),s(index_188))) = rselect_tail(rstore_tail(queue_185,index_186)),
inference(unit_resolution,[status(thm)],[1305,265]) ).
tff(1307,plain,
rstore_head(queue_187,index_189) = rstore_head(rstore_tail(queue_185,index_186),s(index_188)),
inference(symmetry,[status(thm)],[988]) ).
tff(1308,plain,
q6 = rstore_head(rstore_tail(queue_185,index_186),s(index_188)),
inference(transitivity,[status(thm)],[968,972,1307]) ).
tff(1309,plain,
rselect_tail(q6) = rselect_tail(rstore_head(rstore_tail(queue_185,index_186),s(index_188))),
inference(monotonicity,[status(thm)],[1308]) ).
tff(1310,plain,
( ( index_192 = rselect_tail(q6) )
<=> ( index_192 = rselect_tail(q6) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1311,axiom,
index_192 = rselect_tail(q6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp101) ).
tff(1312,plain,
index_192 = rselect_tail(q6),
inference(modus_ponens,[status(thm)],[1311,1310]) ).
tff(1313,plain,
index_192 = s(rselect_head(queue_67)),
inference(transitivity,[status(thm)],[1312,1309,1306,1304,1303,1301,666,542]) ).
tff(1314,plain,
s(index_192) = s(s(rselect_head(queue_67))),
inference(monotonicity,[status(thm)],[1313]) ).
tff(1315,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q6,earray_193),s(index_192))) = s(index_192) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1316,plain,
rselect_tail(rstore_tail(rstore_seq(q6,earray_193),s(index_192))) = s(index_192),
inference(unit_resolution,[status(thm)],[1315,13]) ).
tff(1317,plain,
q7 = rstore_tail(rstore_seq(q6,earray_193),s(index_192)),
inference(transitivity,[status(thm)],[933,937,956]) ).
tff(1318,plain,
rselect_tail(q7) = rselect_tail(rstore_tail(rstore_seq(q6,earray_193),s(index_192))),
inference(monotonicity,[status(thm)],[1317]) ).
tff(1319,plain,
( ( index_198 = rselect_tail(q7) )
<=> ( index_198 = rselect_tail(q7) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1320,axiom,
index_198 = rselect_tail(q7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp103) ).
tff(1321,plain,
index_198 = rselect_tail(q7),
inference(modus_ponens,[status(thm)],[1320,1319]) ).
tff(1322,plain,
index_198 = s(rselect_head(queue_94)),
inference(transitivity,[status(thm)],[1321,1318,1316,1314,541,417]) ).
tff(1323,plain,
s(index_198) = s(s(rselect_head(queue_94))),
inference(monotonicity,[status(thm)],[1322]) ).
tff(1324,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q7,earray_199),s(index_198))) = s(index_198) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1325,plain,
rselect_tail(rstore_tail(rstore_seq(q7,earray_199),s(index_198))) = s(index_198),
inference(unit_resolution,[status(thm)],[1324,13]) ).
tff(1326,plain,
q8 = rstore_tail(rstore_seq(q7,earray_199),s(index_198)),
inference(transitivity,[status(thm)],[898,902,921]) ).
tff(1327,plain,
rselect_tail(q8) = rselect_tail(rstore_tail(rstore_seq(q7,earray_199),s(index_198))),
inference(monotonicity,[status(thm)],[1326]) ).
tff(1328,plain,
( ( index_204 = rselect_tail(q8) )
<=> ( index_204 = rselect_tail(q8) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1329,axiom,
index_204 = rselect_tail(q8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp105) ).
tff(1330,plain,
index_204 = rselect_tail(q8),
inference(modus_ponens,[status(thm)],[1329,1328]) ).
tff(1331,plain,
index_204 = s(rselect_head(queue_115)),
inference(transitivity,[status(thm)],[1330,1327,1325,1323,416,289]) ).
tff(1332,plain,
s(index_204) = s(s(rselect_head(queue_115))),
inference(monotonicity,[status(thm)],[1331]) ).
tff(1333,plain,
s(s(rselect_head(queue_115))) = s(index_204),
inference(symmetry,[status(thm)],[1332]) ).
tff(1334,plain,
( ( index_135 = s(index_132) )
<=> ( index_135 = s(index_132) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1335,axiom,
index_135 = s(index_132),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp76) ).
tff(1336,plain,
index_135 = s(index_132),
inference(modus_ponens,[status(thm)],[1335,1334]) ).
tff(1337,plain,
s(index_132) = index_135,
inference(symmetry,[status(thm)],[1336]) ).
tff(1338,plain,
( ( queue_134 = rstore_seq(q26,earray_133) )
<=> ( queue_134 = rstore_seq(q26,earray_133) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1339,axiom,
queue_134 = rstore_seq(q26,earray_133),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp158) ).
tff(1340,plain,
queue_134 = rstore_seq(q26,earray_133),
inference(modus_ponens,[status(thm)],[1339,1338]) ).
tff(1341,plain,
rstore_seq(q26,earray_133) = queue_134,
inference(symmetry,[status(thm)],[1340]) ).
tff(1342,plain,
rstore_tail(rstore_seq(q26,earray_133),s(index_132)) = rstore_tail(queue_134,index_135),
inference(monotonicity,[status(thm)],[1341,1337]) ).
tff(1343,plain,
rstore_tail(queue_134,index_135) = rstore_tail(rstore_seq(q26,earray_133),s(index_132)),
inference(symmetry,[status(thm)],[1342]) ).
tff(1344,plain,
queue_136 = rstore_tail(rstore_seq(q26,earray_133),s(index_132)),
inference(transitivity,[status(thm)],[117,1343]) ).
tff(1345,plain,
rselect_head(queue_136) = rselect_head(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(monotonicity,[status(thm)],[1344]) ).
tff(1346,plain,
rselect_head(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_head(queue_136),
inference(symmetry,[status(thm)],[1345]) ).
tff(1347,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_head(rstore_seq(q26,earray_133)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1348,plain,
rselect_head(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_head(rstore_seq(q26,earray_133)),
inference(unit_resolution,[status(thm)],[1347,153]) ).
tff(1349,plain,
rselect_head(rstore_seq(q26,earray_133)) = rselect_head(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(symmetry,[status(thm)],[1348]) ).
tff(1350,plain,
( ( earray_133 = store(earray_131,index_132,e26) )
<=> ( earray_133 = store(earray_131,index_132,e26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1351,axiom,
earray_133 = store(earray_131,index_132,e26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp11) ).
tff(1352,plain,
earray_133 = store(earray_131,index_132,e26),
inference(modus_ponens,[status(thm)],[1351,1350]) ).
tff(1353,plain,
store(earray_131,index_132,e26) = earray_133,
inference(symmetry,[status(thm)],[1352]) ).
tff(1354,plain,
( ( q26 = queue_130 )
<=> ( q26 = queue_130 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1355,axiom,
q26 = queue_130,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp234) ).
tff(1356,plain,
q26 = queue_130,
inference(modus_ponens,[status(thm)],[1355,1354]) ).
tff(1357,plain,
queue_130 = q26,
inference(symmetry,[status(thm)],[1356]) ).
tff(1358,plain,
( ( queue_130 = rstore_tail(queue_128,index_129) )
<=> ( queue_130 = rstore_tail(queue_128,index_129) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1359,axiom,
queue_130 = rstore_tail(queue_128,index_129),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp157) ).
tff(1360,plain,
queue_130 = rstore_tail(queue_128,index_129),
inference(modus_ponens,[status(thm)],[1359,1358]) ).
tff(1361,plain,
rstore_tail(queue_128,index_129) = queue_130,
inference(symmetry,[status(thm)],[1360]) ).
tff(1362,plain,
rstore_tail(queue_128,index_129) = q26,
inference(transitivity,[status(thm)],[1361,1357]) ).
tff(1363,plain,
rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26)) = rstore_seq(q26,earray_133),
inference(monotonicity,[status(thm)],[1362,1353]) ).
tff(1364,plain,
rstore_seq(q26,earray_133) = rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26)),
inference(symmetry,[status(thm)],[1363]) ).
tff(1365,plain,
rselect_head(rstore_seq(q26,earray_133)) = rselect_head(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))),
inference(monotonicity,[status(thm)],[1364]) ).
tff(1366,plain,
rselect_head(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = rselect_head(rstore_seq(q26,earray_133)),
inference(symmetry,[status(thm)],[1365]) ).
tff(1367,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = rselect_head(rstore_tail(queue_128,index_129)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1368,plain,
rselect_head(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = rselect_head(rstore_tail(queue_128,index_129)),
inference(unit_resolution,[status(thm)],[1367,128]) ).
tff(1369,plain,
rselect_head(rstore_tail(queue_128,index_129)) = rselect_head(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))),
inference(symmetry,[status(thm)],[1368]) ).
tff(1370,plain,
( ( index_129 = s(index_126) )
<=> ( index_129 = s(index_126) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1371,axiom,
index_129 = s(index_126),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp74) ).
tff(1372,plain,
index_129 = s(index_126),
inference(modus_ponens,[status(thm)],[1371,1370]) ).
tff(1373,plain,
s(index_126) = index_129,
inference(symmetry,[status(thm)],[1372]) ).
tff(1374,plain,
( ( queue_128 = rstore_seq(q25,earray_127) )
<=> ( queue_128 = rstore_seq(q25,earray_127) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1375,axiom,
queue_128 = rstore_seq(q25,earray_127),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp155) ).
tff(1376,plain,
queue_128 = rstore_seq(q25,earray_127),
inference(modus_ponens,[status(thm)],[1375,1374]) ).
tff(1377,plain,
rstore_seq(q25,earray_127) = queue_128,
inference(symmetry,[status(thm)],[1376]) ).
tff(1378,plain,
rstore_tail(rstore_seq(q25,earray_127),s(index_126)) = rstore_tail(queue_128,index_129),
inference(monotonicity,[status(thm)],[1377,1373]) ).
tff(1379,plain,
rstore_tail(queue_128,index_129) = rstore_tail(rstore_seq(q25,earray_127),s(index_126)),
inference(symmetry,[status(thm)],[1378]) ).
tff(1380,plain,
rselect_head(rstore_tail(queue_128,index_129)) = rselect_head(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(monotonicity,[status(thm)],[1379]) ).
tff(1381,plain,
rselect_head(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_head(rstore_tail(queue_128,index_129)),
inference(symmetry,[status(thm)],[1380]) ).
tff(1382,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_head(rstore_seq(q25,earray_127)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1383,plain,
rselect_head(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_head(rstore_seq(q25,earray_127)),
inference(unit_resolution,[status(thm)],[1382,153]) ).
tff(1384,plain,
rselect_head(rstore_seq(q25,earray_127)) = rselect_head(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(symmetry,[status(thm)],[1383]) ).
tff(1385,plain,
( ( earray_127 = store(earray_125,index_126,e25) )
<=> ( earray_127 = store(earray_125,index_126,e25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1386,axiom,
earray_127 = store(earray_125,index_126,e25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp9) ).
tff(1387,plain,
earray_127 = store(earray_125,index_126,e25),
inference(modus_ponens,[status(thm)],[1386,1385]) ).
tff(1388,plain,
store(earray_125,index_126,e25) = earray_127,
inference(symmetry,[status(thm)],[1387]) ).
tff(1389,plain,
( ( q25 = queue_124 )
<=> ( q25 = queue_124 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1390,axiom,
q25 = queue_124,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp233) ).
tff(1391,plain,
q25 = queue_124,
inference(modus_ponens,[status(thm)],[1390,1389]) ).
tff(1392,plain,
queue_124 = q25,
inference(symmetry,[status(thm)],[1391]) ).
tff(1393,plain,
( ( queue_124 = rstore_tail(queue_122,index_123) )
<=> ( queue_124 = rstore_tail(queue_122,index_123) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1394,axiom,
queue_124 = rstore_tail(queue_122,index_123),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp154) ).
tff(1395,plain,
queue_124 = rstore_tail(queue_122,index_123),
inference(modus_ponens,[status(thm)],[1394,1393]) ).
tff(1396,plain,
rstore_tail(queue_122,index_123) = queue_124,
inference(symmetry,[status(thm)],[1395]) ).
tff(1397,plain,
rstore_tail(queue_122,index_123) = q25,
inference(transitivity,[status(thm)],[1396,1392]) ).
tff(1398,plain,
rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25)) = rstore_seq(q25,earray_127),
inference(monotonicity,[status(thm)],[1397,1388]) ).
tff(1399,plain,
rstore_seq(q25,earray_127) = rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25)),
inference(symmetry,[status(thm)],[1398]) ).
tff(1400,plain,
rselect_head(rstore_seq(q25,earray_127)) = rselect_head(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))),
inference(monotonicity,[status(thm)],[1399]) ).
tff(1401,plain,
rselect_head(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = rselect_head(rstore_seq(q25,earray_127)),
inference(symmetry,[status(thm)],[1400]) ).
tff(1402,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = rselect_head(rstore_tail(queue_122,index_123)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1403,plain,
rselect_head(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = rselect_head(rstore_tail(queue_122,index_123)),
inference(unit_resolution,[status(thm)],[1402,128]) ).
tff(1404,plain,
rselect_head(rstore_tail(queue_122,index_123)) = rselect_head(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))),
inference(symmetry,[status(thm)],[1403]) ).
tff(1405,plain,
( ( index_123 = s(index_120) )
<=> ( index_123 = s(index_120) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1406,axiom,
index_123 = s(index_120),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp72) ).
tff(1407,plain,
index_123 = s(index_120),
inference(modus_ponens,[status(thm)],[1406,1405]) ).
tff(1408,plain,
s(index_120) = index_123,
inference(symmetry,[status(thm)],[1407]) ).
tff(1409,plain,
( ( queue_122 = rstore_seq(q24,earray_121) )
<=> ( queue_122 = rstore_seq(q24,earray_121) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1410,axiom,
queue_122 = rstore_seq(q24,earray_121),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp153) ).
tff(1411,plain,
queue_122 = rstore_seq(q24,earray_121),
inference(modus_ponens,[status(thm)],[1410,1409]) ).
tff(1412,plain,
rstore_seq(q24,earray_121) = queue_122,
inference(symmetry,[status(thm)],[1411]) ).
tff(1413,plain,
rstore_tail(rstore_seq(q24,earray_121),s(index_120)) = rstore_tail(queue_122,index_123),
inference(monotonicity,[status(thm)],[1412,1408]) ).
tff(1414,plain,
rstore_tail(queue_122,index_123) = rstore_tail(rstore_seq(q24,earray_121),s(index_120)),
inference(symmetry,[status(thm)],[1413]) ).
tff(1415,plain,
rselect_head(rstore_tail(queue_122,index_123)) = rselect_head(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(monotonicity,[status(thm)],[1414]) ).
tff(1416,plain,
rselect_head(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_head(rstore_tail(queue_122,index_123)),
inference(symmetry,[status(thm)],[1415]) ).
tff(1417,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_tail(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_head(rstore_seq(q24,earray_121)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1418,plain,
rselect_head(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_head(rstore_seq(q24,earray_121)),
inference(unit_resolution,[status(thm)],[1417,153]) ).
tff(1419,plain,
rselect_head(rstore_seq(q24,earray_121)) = rselect_head(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(symmetry,[status(thm)],[1418]) ).
tff(1420,plain,
( ( earray_121 = store(earray_119,index_120,e24) )
<=> ( earray_121 = store(earray_119,index_120,e24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1421,axiom,
earray_121 = store(earray_119,index_120,e24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp7) ).
tff(1422,plain,
earray_121 = store(earray_119,index_120,e24),
inference(modus_ponens,[status(thm)],[1421,1420]) ).
tff(1423,plain,
store(earray_119,index_120,e24) = earray_121,
inference(symmetry,[status(thm)],[1422]) ).
tff(1424,plain,
( ( q24 = queue_118 )
<=> ( q24 = queue_118 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1425,axiom,
q24 = queue_118,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp232) ).
tff(1426,plain,
q24 = queue_118,
inference(modus_ponens,[status(thm)],[1425,1424]) ).
tff(1427,plain,
queue_118 = q24,
inference(symmetry,[status(thm)],[1426]) ).
tff(1428,plain,
( ( queue_118 = rstore_head(queue_115,index_117) )
<=> ( queue_118 = rstore_head(queue_115,index_117) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1429,axiom,
queue_118 = rstore_head(queue_115,index_117),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp152) ).
tff(1430,plain,
queue_118 = rstore_head(queue_115,index_117),
inference(modus_ponens,[status(thm)],[1429,1428]) ).
tff(1431,plain,
rstore_head(queue_115,index_117) = queue_118,
inference(symmetry,[status(thm)],[1430]) ).
tff(1432,plain,
rstore_head(queue_115,index_117) = q24,
inference(transitivity,[status(thm)],[1431,1427]) ).
tff(1433,plain,
rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24)) = rstore_seq(q24,earray_121),
inference(monotonicity,[status(thm)],[1432,1423]) ).
tff(1434,plain,
rselect_head(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = rselect_head(rstore_seq(q24,earray_121)),
inference(monotonicity,[status(thm)],[1433]) ).
tff(1435,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_seq(A,E)) = rselect_head(A) )
| ( rselect_head(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = rselect_head(rstore_head(queue_115,index_117)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1436,plain,
rselect_head(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = rselect_head(rstore_head(queue_115,index_117)),
inference(unit_resolution,[status(thm)],[1435,128]) ).
tff(1437,plain,
rselect_head(rstore_head(queue_115,index_117)) = rselect_head(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))),
inference(symmetry,[status(thm)],[1436]) ).
tff(1438,plain,
( ( index_117 = s(index_116) )
<=> ( index_117 = s(index_116) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1439,axiom,
index_117 = s(index_116),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp69) ).
tff(1440,plain,
index_117 = s(index_116),
inference(modus_ponens,[status(thm)],[1439,1438]) ).
tff(1441,plain,
s(index_116) = index_117,
inference(symmetry,[status(thm)],[1440]) ).
tff(1442,plain,
rstore_tail(queue_113,index_114) = queue_115,
inference(symmetry,[status(thm)],[302]) ).
tff(1443,plain,
rstore_head(rstore_tail(queue_113,index_114),s(index_116)) = rstore_head(queue_115,index_117),
inference(monotonicity,[status(thm)],[1442,1441]) ).
tff(1444,plain,
rselect_head(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_head(rstore_head(queue_115,index_117)),
inference(monotonicity,[status(thm)],[1443]) ).
tff(1445,plain,
( ~ ! [E: $i,A: $i] : ( rselect_head(rstore_head(A,E)) = E )
| ( rselect_head(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = s(index_116) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1446,plain,
rselect_head(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = s(index_116),
inference(unit_resolution,[status(thm)],[1445,99]) ).
tff(1447,plain,
s(index_116) = rselect_head(rstore_head(rstore_tail(queue_113,index_114),s(index_116))),
inference(symmetry,[status(thm)],[1446]) ).
tff(1448,plain,
s(rselect_head(queue_115)) = index_137,
inference(transitivity,[status(thm)],[288,1447,1444,1437,1434,1419,1416,1404,1401,1384,1381,1369,1366,1349,1346,106]) ).
tff(1449,plain,
s(s(rselect_head(queue_115))) = s(index_137),
inference(monotonicity,[status(thm)],[1448]) ).
tff(1450,plain,
s(index_137) = s(s(rselect_head(queue_115))),
inference(symmetry,[status(thm)],[1449]) ).
tff(1451,plain,
s(rselect_head(queue_136)) = index_9,
inference(transitivity,[status(thm)],[107,1450,1333,283,280,268,258,239]) ).
tff(1452,plain,
s(s(rselect_head(queue_136))) = s(index_9),
inference(monotonicity,[status(thm)],[1451]) ).
tff(1453,plain,
s(index_9) = s(s(rselect_head(queue_136))),
inference(symmetry,[status(thm)],[1452]) ).
tff(1454,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = s(index_9) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1455,plain,
rselect_tail(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = s(index_9),
inference(unit_resolution,[status(thm)],[1454,13]) ).
tff(1456,plain,
rstore_tail(rstore_seq(q9,earray_10),s(index_9)) = q10,
inference(transitivity,[status(thm)],[855,838,834]) ).
tff(1457,plain,
rselect_tail(rstore_tail(rstore_seq(q9,earray_10),s(index_9))) = rselect_tail(q10),
inference(monotonicity,[status(thm)],[1456]) ).
tff(1458,plain,
rselect_tail(q10) = rselect_tail(rstore_tail(rstore_seq(q9,earray_10),s(index_9))),
inference(symmetry,[status(thm)],[1457]) ).
tff(1459,plain,
rselect_tail(q10) = index_213,
inference(transitivity,[status(thm)],[1458,1455,1453,235,102,92,73]) ).
tff(1460,plain,
( ( earray_212 = rselect_seq(q30) )
<=> ( earray_212 = rselect_seq(q30) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1461,axiom,
earray_212 = rselect_seq(q30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp36) ).
tff(1462,plain,
earray_212 = rselect_seq(q30),
inference(modus_ponens,[status(thm)],[1461,1460]) ).
tff(1463,plain,
rselect_seq(q30) = earray_212,
inference(symmetry,[status(thm)],[1462]) ).
tff(1464,plain,
rselect_seq(q30) = rselect_seq(rstore_head(rstore_tail(queue_164,index_165),s(index_167))),
inference(monotonicity,[status(thm)],[90]) ).
tff(1465,plain,
rselect_seq(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = rselect_seq(q30),
inference(symmetry,[status(thm)],[1464]) ).
tff(1466,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
<=> ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ) )),
inference(bind,[status(th)],[]) ).
tff(1467,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ) ),
inference(quant_intro,[status(thm)],[1466]) ).
tff(1468,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1469,axiom,
! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_seq_head) ).
tff(1470,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ),
inference(modus_ponens,[status(thm)],[1469,1468]) ).
tff(1471,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ),
inference(skolemize,[status(sab)],[1470]) ).
tff(1472,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) ),
inference(modus_ponens,[status(thm)],[1471,1467]) ).
tff(1473,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = rselect_seq(rstore_tail(queue_164,index_165)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1474,plain,
rselect_seq(rstore_head(rstore_tail(queue_164,index_165),s(index_167))) = rselect_seq(rstore_tail(queue_164,index_165)),
inference(unit_resolution,[status(thm)],[1473,1472]) ).
tff(1475,plain,
rselect_seq(rstore_tail(queue_164,index_165)) = rselect_seq(rstore_head(rstore_tail(queue_164,index_165),s(index_167))),
inference(symmetry,[status(thm)],[1474]) ).
tff(1476,plain,
rselect_seq(rstore_tail(queue_164,index_165)) = rselect_seq(rstore_tail(rstore_seq(q29,earray_163),s(index_162))),
inference(monotonicity,[status(thm)],[227]) ).
tff(1477,plain,
rselect_seq(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_seq(rstore_tail(queue_164,index_165)),
inference(symmetry,[status(thm)],[1476]) ).
tff(1478,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
<=> ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ) )),
inference(bind,[status(th)],[]) ).
tff(1479,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ) ),
inference(quant_intro,[status(thm)],[1478]) ).
tff(1480,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1481,axiom,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_seq_tail) ).
tff(1482,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
inference(modus_ponens,[status(thm)],[1481,1480]) ).
tff(1483,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
inference(skolemize,[status(sab)],[1482]) ).
tff(1484,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) ),
inference(modus_ponens,[status(thm)],[1483,1479]) ).
tff(1485,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_seq(rstore_seq(q29,earray_163)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1486,plain,
rselect_seq(rstore_tail(rstore_seq(q29,earray_163),s(index_162))) = rselect_seq(rstore_seq(q29,earray_163)),
inference(unit_resolution,[status(thm)],[1485,1484]) ).
tff(1487,plain,
rselect_seq(rstore_seq(q29,earray_163)) = rselect_seq(rstore_tail(rstore_seq(q29,earray_163),s(index_162))),
inference(symmetry,[status(thm)],[1486]) ).
tff(1488,plain,
rselect_seq(rstore_seq(q29,earray_163)) = rselect_seq(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))),
inference(monotonicity,[status(thm)],[214]) ).
tff(1489,plain,
rselect_seq(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))) = rselect_seq(rstore_seq(q29,earray_163)),
inference(symmetry,[status(thm)],[1488]) ).
tff(1490,plain,
^ [E: $i,A: $i] :
refl(( ( rselect_seq(rstore_seq(A,E)) = E )
<=> ( rselect_seq(rstore_seq(A,E)) = E ) )),
inference(bind,[status(th)],[]) ).
tff(1491,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ) ),
inference(quant_intro,[status(thm)],[1490]) ).
tff(1492,plain,
( ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
<=> ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1493,axiom,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1_seq) ).
tff(1494,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
inference(modus_ponens,[status(thm)],[1493,1492]) ).
tff(1495,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
inference(skolemize,[status(sab)],[1494]) ).
tff(1496,plain,
! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E ),
inference(modus_ponens,[status(thm)],[1495,1491]) ).
tff(1497,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))) = store(earray_161,index_162,e29) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1498,plain,
rselect_seq(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))) = store(earray_161,index_162,e29),
inference(unit_resolution,[status(thm)],[1497,1496]) ).
tff(1499,plain,
store(earray_161,index_162,e29) = rselect_seq(rstore_seq(rstore_tail(queue_149,index_150),store(earray_161,index_162,e29))),
inference(symmetry,[status(thm)],[1498]) ).
tff(1500,plain,
( ( index_162 = rselect_tail(q29) )
<=> ( index_162 = rselect_tail(q29) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1501,axiom,
index_162 = rselect_tail(q29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp88) ).
tff(1502,plain,
index_162 = rselect_tail(q29),
inference(modus_ponens,[status(thm)],[1501,1500]) ).
tff(1503,plain,
rselect_tail(q29) = index_162,
inference(symmetry,[status(thm)],[1502]) ).
tff(1504,plain,
( ( earray_161 = rselect_seq(q29) )
<=> ( earray_161 = rselect_seq(q29) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1505,axiom,
earray_161 = rselect_seq(q29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp20) ).
tff(1506,plain,
earray_161 = rselect_seq(q29),
inference(modus_ponens,[status(thm)],[1505,1504]) ).
tff(1507,plain,
rselect_seq(q29) = earray_161,
inference(symmetry,[status(thm)],[1506]) ).
tff(1508,plain,
q29 = rstore_tail(rstore_seq(q28,earray_148),s(index_147)),
inference(transitivity,[status(thm)],[206,210,196]) ).
tff(1509,plain,
rselect_seq(q29) = rselect_seq(rstore_tail(rstore_seq(q28,earray_148),s(index_147))),
inference(monotonicity,[status(thm)],[1508]) ).
tff(1510,plain,
rselect_seq(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_seq(q29),
inference(symmetry,[status(thm)],[1509]) ).
tff(1511,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_seq(rstore_seq(q28,earray_148)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1512,plain,
rselect_seq(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_seq(rstore_seq(q28,earray_148)),
inference(unit_resolution,[status(thm)],[1511,1484]) ).
tff(1513,plain,
rselect_seq(rstore_seq(q28,earray_148)) = rselect_seq(rstore_tail(rstore_seq(q28,earray_148),s(index_147))),
inference(symmetry,[status(thm)],[1512]) ).
tff(1514,plain,
rselect_seq(rstore_seq(q28,earray_148)) = rselect_seq(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))),
inference(monotonicity,[status(thm)],[183]) ).
tff(1515,plain,
rselect_seq(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))) = rselect_seq(rstore_seq(q28,earray_148)),
inference(symmetry,[status(thm)],[1514]) ).
tff(1516,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))) = store(earray_146,index_147,e28) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1517,plain,
rselect_seq(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))) = store(earray_146,index_147,e28),
inference(unit_resolution,[status(thm)],[1516,1496]) ).
tff(1518,plain,
store(earray_146,index_147,e28) = rselect_seq(rstore_seq(rstore_tail(queue_143,index_144),store(earray_146,index_147,e28))),
inference(symmetry,[status(thm)],[1517]) ).
tff(1519,plain,
store(earray_146,index_147,e28) = earray_161,
inference(transitivity,[status(thm)],[1518,1515,1513,1510,1507]) ).
tff(1520,plain,
store(store(earray_146,index_147,e28),rselect_tail(q29),e29) = store(earray_161,index_162,e29),
inference(monotonicity,[status(thm)],[1519,1503]) ).
tff(1521,plain,
store(store(earray_146,index_147,e28),rselect_tail(q29),e29) = earray_212,
inference(transitivity,[status(thm)],[1520,1499,1489,1487,1477,1475,1465,1463]) ).
tff(1522,plain,
select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_tail(q10)) = select(earray_212,index_213),
inference(monotonicity,[status(thm)],[1521,1459]) ).
tff(1523,plain,
( ( index_147 = rselect_tail(q28) )
<=> ( index_147 = rselect_tail(q28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1524,axiom,
index_147 = rselect_tail(q28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp81) ).
tff(1525,plain,
index_147 = rselect_tail(q28),
inference(modus_ponens,[status(thm)],[1524,1523]) ).
tff(1526,plain,
rselect_tail(q28) = index_147,
inference(symmetry,[status(thm)],[1525]) ).
tff(1527,plain,
rstore_tail(rstore_seq(q27,earray_142),s(index_141)) = q28,
inference(transitivity,[status(thm)],[164,180,176]) ).
tff(1528,plain,
rselect_tail(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_tail(q28),
inference(monotonicity,[status(thm)],[1527]) ).
tff(1529,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = s(index_141) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1530,plain,
rselect_tail(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = s(index_141),
inference(unit_resolution,[status(thm)],[1529,13]) ).
tff(1531,plain,
s(index_141) = rselect_tail(rstore_tail(rstore_seq(q27,earray_142),s(index_141))),
inference(symmetry,[status(thm)],[1530]) ).
tff(1532,plain,
( ( index_141 = rselect_tail(q27) )
<=> ( index_141 = rselect_tail(q27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1533,axiom,
index_141 = rselect_tail(q27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp79) ).
tff(1534,plain,
index_141 = rselect_tail(q27),
inference(modus_ponens,[status(thm)],[1533,1532]) ).
tff(1535,plain,
rselect_tail(q27) = index_141,
inference(symmetry,[status(thm)],[1534]) ).
tff(1536,plain,
rstore_head(rstore_tail(queue_134,index_135),s(index_137)) = q27,
inference(transitivity,[status(thm)],[119,142,138]) ).
tff(1537,plain,
rselect_tail(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_tail(q27),
inference(monotonicity,[status(thm)],[1536]) ).
tff(1538,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_tail(rstore_tail(queue_134,index_135)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1539,plain,
rselect_tail(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_tail(rstore_tail(queue_134,index_135)),
inference(unit_resolution,[status(thm)],[1538,265]) ).
tff(1540,plain,
rselect_tail(rstore_tail(queue_134,index_135)) = rselect_tail(rstore_head(rstore_tail(queue_134,index_135),s(index_137))),
inference(symmetry,[status(thm)],[1539]) ).
tff(1541,plain,
rselect_tail(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_tail(rstore_tail(queue_134,index_135)),
inference(monotonicity,[status(thm)],[1342]) ).
tff(1542,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = s(index_132) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1543,plain,
rselect_tail(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = s(index_132),
inference(unit_resolution,[status(thm)],[1542,13]) ).
tff(1544,plain,
s(index_132) = rselect_tail(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(symmetry,[status(thm)],[1543]) ).
tff(1545,plain,
( ( index_132 = rselect_tail(q26) )
<=> ( index_132 = rselect_tail(q26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1546,axiom,
index_132 = rselect_tail(q26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp75) ).
tff(1547,plain,
index_132 = rselect_tail(q26),
inference(modus_ponens,[status(thm)],[1546,1545]) ).
tff(1548,plain,
rselect_tail(q26) = index_132,
inference(symmetry,[status(thm)],[1547]) ).
tff(1549,plain,
rstore_tail(rstore_seq(q25,earray_127),s(index_126)) = q26,
inference(transitivity,[status(thm)],[1378,1361,1357]) ).
tff(1550,plain,
rselect_tail(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_tail(q26),
inference(monotonicity,[status(thm)],[1549]) ).
tff(1551,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = s(index_126) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1552,plain,
rselect_tail(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = s(index_126),
inference(unit_resolution,[status(thm)],[1551,13]) ).
tff(1553,plain,
s(index_126) = rselect_tail(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(symmetry,[status(thm)],[1552]) ).
tff(1554,plain,
( ( index_126 = rselect_tail(q25) )
<=> ( index_126 = rselect_tail(q25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1555,axiom,
index_126 = rselect_tail(q25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp73) ).
tff(1556,plain,
index_126 = rselect_tail(q25),
inference(modus_ponens,[status(thm)],[1555,1554]) ).
tff(1557,plain,
rselect_tail(q25) = index_126,
inference(symmetry,[status(thm)],[1556]) ).
tff(1558,plain,
rstore_tail(rstore_seq(q24,earray_121),s(index_120)) = q25,
inference(transitivity,[status(thm)],[1413,1396,1392]) ).
tff(1559,plain,
rselect_tail(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_tail(q25),
inference(monotonicity,[status(thm)],[1558]) ).
tff(1560,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = s(index_120) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1561,plain,
rselect_tail(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = s(index_120),
inference(unit_resolution,[status(thm)],[1560,13]) ).
tff(1562,plain,
s(index_120) = rselect_tail(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(symmetry,[status(thm)],[1561]) ).
tff(1563,plain,
( ( index_120 = rselect_tail(q24) )
<=> ( index_120 = rselect_tail(q24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1564,axiom,
index_120 = rselect_tail(q24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp71) ).
tff(1565,plain,
index_120 = rselect_tail(q24),
inference(modus_ponens,[status(thm)],[1564,1563]) ).
tff(1566,plain,
rselect_tail(q24) = index_120,
inference(symmetry,[status(thm)],[1565]) ).
tff(1567,plain,
rstore_head(rstore_tail(queue_113,index_114),s(index_116)) = q24,
inference(transitivity,[status(thm)],[1443,1431,1427]) ).
tff(1568,plain,
rselect_tail(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_tail(q24),
inference(monotonicity,[status(thm)],[1567]) ).
tff(1569,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_tail(rstore_tail(queue_113,index_114)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1570,plain,
rselect_tail(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_tail(rstore_tail(queue_113,index_114)),
inference(unit_resolution,[status(thm)],[1569,265]) ).
tff(1571,plain,
rselect_tail(rstore_tail(queue_113,index_114)) = rselect_tail(rstore_head(rstore_tail(queue_113,index_114),s(index_116))),
inference(symmetry,[status(thm)],[1570]) ).
tff(1572,plain,
rselect_tail(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_tail(rstore_tail(queue_113,index_114)),
inference(monotonicity,[status(thm)],[298]) ).
tff(1573,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = s(index_111) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1574,plain,
rselect_tail(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = s(index_111),
inference(unit_resolution,[status(thm)],[1573,13]) ).
tff(1575,plain,
s(index_111) = rselect_tail(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(symmetry,[status(thm)],[1574]) ).
tff(1576,plain,
( ( index_111 = rselect_tail(q23) )
<=> ( index_111 = rselect_tail(q23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1577,axiom,
index_111 = rselect_tail(q23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp66) ).
tff(1578,plain,
index_111 = rselect_tail(q23),
inference(modus_ponens,[status(thm)],[1577,1576]) ).
tff(1579,plain,
rselect_tail(q23) = index_111,
inference(symmetry,[status(thm)],[1578]) ).
tff(1580,plain,
rstore_tail(rstore_seq(q22,earray_106),s(index_105)) = q23,
inference(transitivity,[status(thm)],[337,320,316]) ).
tff(1581,plain,
rselect_tail(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_tail(q23),
inference(monotonicity,[status(thm)],[1580]) ).
tff(1582,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = s(index_105) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1583,plain,
rselect_tail(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = s(index_105),
inference(unit_resolution,[status(thm)],[1582,13]) ).
tff(1584,plain,
s(index_105) = rselect_tail(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(symmetry,[status(thm)],[1583]) ).
tff(1585,plain,
( ( index_105 = rselect_tail(q22) )
<=> ( index_105 = rselect_tail(q22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1586,axiom,
index_105 = rselect_tail(q22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp64) ).
tff(1587,plain,
index_105 = rselect_tail(q22),
inference(modus_ponens,[status(thm)],[1586,1585]) ).
tff(1588,plain,
rselect_tail(q22) = index_105,
inference(symmetry,[status(thm)],[1587]) ).
tff(1589,plain,
rstore_tail(rstore_seq(q21,earray_100),s(index_99)) = q22,
inference(transitivity,[status(thm)],[372,355,351]) ).
tff(1590,plain,
rselect_tail(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_tail(q22),
inference(monotonicity,[status(thm)],[1589]) ).
tff(1591,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = s(index_99) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1592,plain,
rselect_tail(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = s(index_99),
inference(unit_resolution,[status(thm)],[1591,13]) ).
tff(1593,plain,
s(index_99) = rselect_tail(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(symmetry,[status(thm)],[1592]) ).
tff(1594,plain,
( ( index_99 = rselect_tail(q21) )
<=> ( index_99 = rselect_tail(q21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1595,axiom,
index_99 = rselect_tail(q21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp143) ).
tff(1596,plain,
index_99 = rselect_tail(q21),
inference(modus_ponens,[status(thm)],[1595,1594]) ).
tff(1597,plain,
rselect_tail(q21) = index_99,
inference(symmetry,[status(thm)],[1596]) ).
tff(1598,plain,
rstore_head(rstore_tail(queue_92,index_93),s(index_95)) = q21,
inference(transitivity,[status(thm)],[405,390,386]) ).
tff(1599,plain,
rselect_tail(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_tail(q21),
inference(monotonicity,[status(thm)],[1598]) ).
tff(1600,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_tail(rstore_tail(queue_92,index_93)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1601,plain,
rselect_tail(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_tail(rstore_tail(queue_92,index_93)),
inference(unit_resolution,[status(thm)],[1600,265]) ).
tff(1602,plain,
rselect_tail(rstore_tail(queue_92,index_93)) = rselect_tail(rstore_head(rstore_tail(queue_92,index_93),s(index_95))),
inference(symmetry,[status(thm)],[1601]) ).
tff(1603,plain,
rselect_tail(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_tail(rstore_tail(queue_92,index_93)),
inference(monotonicity,[status(thm)],[426]) ).
tff(1604,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = s(index_90) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1605,plain,
rselect_tail(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = s(index_90),
inference(unit_resolution,[status(thm)],[1604,13]) ).
tff(1606,plain,
s(index_90) = rselect_tail(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(symmetry,[status(thm)],[1605]) ).
tff(1607,plain,
( ( index_90 = rselect_tail(q20) )
<=> ( index_90 = rselect_tail(q20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1608,axiom,
index_90 = rselect_tail(q20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp139) ).
tff(1609,plain,
index_90 = rselect_tail(q20),
inference(modus_ponens,[status(thm)],[1608,1607]) ).
tff(1610,plain,
rselect_tail(q20) = index_90,
inference(symmetry,[status(thm)],[1609]) ).
tff(1611,plain,
rstore_tail(rstore_seq(q19,earray_85),s(index_84)) = q20,
inference(transitivity,[status(thm)],[462,445,441]) ).
tff(1612,plain,
rselect_tail(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_tail(q20),
inference(monotonicity,[status(thm)],[1611]) ).
tff(1613,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = s(index_84) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1614,plain,
rselect_tail(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = s(index_84),
inference(unit_resolution,[status(thm)],[1613,13]) ).
tff(1615,plain,
s(index_84) = rselect_tail(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(symmetry,[status(thm)],[1614]) ).
tff(1616,plain,
( ( index_84 = rselect_tail(q19) )
<=> ( index_84 = rselect_tail(q19) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1617,axiom,
index_84 = rselect_tail(q19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp136) ).
tff(1618,plain,
index_84 = rselect_tail(q19),
inference(modus_ponens,[status(thm)],[1617,1616]) ).
tff(1619,plain,
rselect_tail(q19) = index_84,
inference(symmetry,[status(thm)],[1618]) ).
tff(1620,plain,
rstore_tail(rstore_seq(q18,earray_73),s(index_72)) = q19,
inference(transitivity,[status(thm)],[497,480,476]) ).
tff(1621,plain,
rselect_tail(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_tail(q19),
inference(monotonicity,[status(thm)],[1620]) ).
tff(1622,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = s(index_72) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1623,plain,
rselect_tail(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = s(index_72),
inference(unit_resolution,[status(thm)],[1622,13]) ).
tff(1624,plain,
s(index_72) = rselect_tail(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(symmetry,[status(thm)],[1623]) ).
tff(1625,plain,
( ( index_72 = rselect_tail(q18) )
<=> ( index_72 = rselect_tail(q18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1626,axiom,
index_72 = rselect_tail(q18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp132) ).
tff(1627,plain,
index_72 = rselect_tail(q18),
inference(modus_ponens,[status(thm)],[1626,1625]) ).
tff(1628,plain,
rselect_tail(q18) = index_72,
inference(symmetry,[status(thm)],[1627]) ).
tff(1629,plain,
rstore_head(rstore_tail(queue_65,index_66),s(index_68)) = q18,
inference(transitivity,[status(thm)],[530,515,511]) ).
tff(1630,plain,
rselect_tail(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_tail(q18),
inference(monotonicity,[status(thm)],[1629]) ).
tff(1631,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_tail(rstore_tail(queue_65,index_66)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1632,plain,
rselect_tail(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_tail(rstore_tail(queue_65,index_66)),
inference(unit_resolution,[status(thm)],[1631,265]) ).
tff(1633,plain,
rselect_tail(rstore_tail(queue_65,index_66)) = rselect_tail(rstore_head(rstore_tail(queue_65,index_66),s(index_68))),
inference(symmetry,[status(thm)],[1632]) ).
tff(1634,plain,
rselect_tail(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_tail(rstore_tail(queue_65,index_66)),
inference(monotonicity,[status(thm)],[551]) ).
tff(1635,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = s(index_63) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1636,plain,
rselect_tail(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = s(index_63),
inference(unit_resolution,[status(thm)],[1635,13]) ).
tff(1637,plain,
s(index_63) = rselect_tail(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(symmetry,[status(thm)],[1636]) ).
tff(1638,plain,
( ( index_63 = rselect_tail(q17) )
<=> ( index_63 = rselect_tail(q17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1639,axiom,
index_63 = rselect_tail(q17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp128) ).
tff(1640,plain,
index_63 = rselect_tail(q17),
inference(modus_ponens,[status(thm)],[1639,1638]) ).
tff(1641,plain,
rselect_tail(q17) = index_63,
inference(symmetry,[status(thm)],[1640]) ).
tff(1642,plain,
rstore_tail(rstore_seq(q16,earray_58),s(index_57)) = q17,
inference(transitivity,[status(thm)],[587,570,566]) ).
tff(1643,plain,
rselect_tail(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_tail(q17),
inference(monotonicity,[status(thm)],[1642]) ).
tff(1644,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = s(index_57) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1645,plain,
rselect_tail(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = s(index_57),
inference(unit_resolution,[status(thm)],[1644,13]) ).
tff(1646,plain,
s(index_57) = rselect_tail(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(symmetry,[status(thm)],[1645]) ).
tff(1647,plain,
( ( index_57 = rselect_tail(q16) )
<=> ( index_57 = rselect_tail(q16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1648,axiom,
index_57 = rselect_tail(q16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp125) ).
tff(1649,plain,
index_57 = rselect_tail(q16),
inference(modus_ponens,[status(thm)],[1648,1647]) ).
tff(1650,plain,
rselect_tail(q16) = index_57,
inference(symmetry,[status(thm)],[1649]) ).
tff(1651,plain,
rstore_tail(rstore_seq(q15,earray_52),s(index_51)) = q16,
inference(transitivity,[status(thm)],[622,605,601]) ).
tff(1652,plain,
rselect_tail(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = rselect_tail(q16),
inference(monotonicity,[status(thm)],[1651]) ).
tff(1653,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = s(index_51) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1654,plain,
rselect_tail(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = s(index_51),
inference(unit_resolution,[status(thm)],[1653,13]) ).
tff(1655,plain,
s(index_51) = rselect_tail(rstore_tail(rstore_seq(q15,earray_52),s(index_51))),
inference(symmetry,[status(thm)],[1654]) ).
tff(1656,plain,
( ( index_51 = rselect_tail(q15) )
<=> ( index_51 = rselect_tail(q15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1657,axiom,
index_51 = rselect_tail(q15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp123) ).
tff(1658,plain,
index_51 = rselect_tail(q15),
inference(modus_ponens,[status(thm)],[1657,1656]) ).
tff(1659,plain,
rselect_tail(q15) = index_51,
inference(symmetry,[status(thm)],[1658]) ).
tff(1660,plain,
rstore_head(rstore_tail(queue_44,index_45),s(index_47)) = q15,
inference(transitivity,[status(thm)],[655,640,636]) ).
tff(1661,plain,
rselect_tail(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = rselect_tail(q15),
inference(monotonicity,[status(thm)],[1660]) ).
tff(1662,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = rselect_tail(rstore_tail(queue_44,index_45)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1663,plain,
rselect_tail(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = rselect_tail(rstore_tail(queue_44,index_45)),
inference(unit_resolution,[status(thm)],[1662,265]) ).
tff(1664,plain,
rselect_tail(rstore_tail(queue_44,index_45)) = rselect_tail(rstore_head(rstore_tail(queue_44,index_45),s(index_47))),
inference(symmetry,[status(thm)],[1663]) ).
tff(1665,plain,
rselect_tail(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = rselect_tail(rstore_tail(queue_44,index_45)),
inference(monotonicity,[status(thm)],[676]) ).
tff(1666,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = s(index_42) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1667,plain,
rselect_tail(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = s(index_42),
inference(unit_resolution,[status(thm)],[1666,13]) ).
tff(1668,plain,
s(index_42) = rselect_tail(rstore_tail(rstore_seq(q14,earray_43),s(index_42))),
inference(symmetry,[status(thm)],[1667]) ).
tff(1669,plain,
( ( index_42 = rselect_tail(q14) )
<=> ( index_42 = rselect_tail(q14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1670,axiom,
index_42 = rselect_tail(q14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp119) ).
tff(1671,plain,
index_42 = rselect_tail(q14),
inference(modus_ponens,[status(thm)],[1670,1669]) ).
tff(1672,plain,
rselect_tail(q14) = index_42,
inference(symmetry,[status(thm)],[1671]) ).
tff(1673,plain,
rstore_tail(rstore_seq(q13,earray_37),s(index_36)) = q14,
inference(transitivity,[status(thm)],[712,695,691]) ).
tff(1674,plain,
rselect_tail(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = rselect_tail(q14),
inference(monotonicity,[status(thm)],[1673]) ).
tff(1675,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = s(index_36) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1676,plain,
rselect_tail(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = s(index_36),
inference(unit_resolution,[status(thm)],[1675,13]) ).
tff(1677,plain,
s(index_36) = rselect_tail(rstore_tail(rstore_seq(q13,earray_37),s(index_36))),
inference(symmetry,[status(thm)],[1676]) ).
tff(1678,plain,
( ( index_36 = rselect_tail(q13) )
<=> ( index_36 = rselect_tail(q13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1679,axiom,
index_36 = rselect_tail(q13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp117) ).
tff(1680,plain,
index_36 = rselect_tail(q13),
inference(modus_ponens,[status(thm)],[1679,1678]) ).
tff(1681,plain,
rselect_tail(q13) = index_36,
inference(symmetry,[status(thm)],[1680]) ).
tff(1682,plain,
rstore_tail(rstore_seq(q12,earray_31),s(index_30)) = q13,
inference(transitivity,[status(thm)],[747,730,726]) ).
tff(1683,plain,
rselect_tail(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = rselect_tail(q13),
inference(monotonicity,[status(thm)],[1682]) ).
tff(1684,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = s(index_30) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1685,plain,
rselect_tail(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = s(index_30),
inference(unit_resolution,[status(thm)],[1684,13]) ).
tff(1686,plain,
s(index_30) = rselect_tail(rstore_tail(rstore_seq(q12,earray_31),s(index_30))),
inference(symmetry,[status(thm)],[1685]) ).
tff(1687,plain,
( ( index_30 = rselect_tail(q12) )
<=> ( index_30 = rselect_tail(q12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1688,axiom,
index_30 = rselect_tail(q12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp115) ).
tff(1689,plain,
index_30 = rselect_tail(q12),
inference(modus_ponens,[status(thm)],[1688,1687]) ).
tff(1690,plain,
rselect_tail(q12) = index_30,
inference(symmetry,[status(thm)],[1689]) ).
tff(1691,plain,
rstore_head(rstore_tail(queue_23,index_24),s(index_26)) = q12,
inference(transitivity,[status(thm)],[780,765,761]) ).
tff(1692,plain,
rselect_tail(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = rselect_tail(q12),
inference(monotonicity,[status(thm)],[1691]) ).
tff(1693,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_head(A,E)) = rselect_tail(A) )
| ( rselect_tail(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = rselect_tail(rstore_tail(queue_23,index_24)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1694,plain,
rselect_tail(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = rselect_tail(rstore_tail(queue_23,index_24)),
inference(unit_resolution,[status(thm)],[1693,265]) ).
tff(1695,plain,
rselect_tail(rstore_tail(queue_23,index_24)) = rselect_tail(rstore_head(rstore_tail(queue_23,index_24),s(index_26))),
inference(symmetry,[status(thm)],[1694]) ).
tff(1696,plain,
rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_tail(rstore_tail(queue_23,index_24)),
inference(monotonicity,[status(thm)],[801]) ).
tff(1697,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = s(index_21) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1698,plain,
rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = s(index_21),
inference(unit_resolution,[status(thm)],[1697,13]) ).
tff(1699,plain,
s(index_21) = rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(symmetry,[status(thm)],[1698]) ).
tff(1700,plain,
( ( index_21 = rselect_tail(q11) )
<=> ( index_21 = rselect_tail(q11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1701,axiom,
index_21 = rselect_tail(q11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp108) ).
tff(1702,plain,
index_21 = rselect_tail(q11),
inference(modus_ponens,[status(thm)],[1701,1700]) ).
tff(1703,plain,
rselect_tail(q11) = index_21,
inference(symmetry,[status(thm)],[1702]) ).
tff(1704,plain,
s(index_15) = rselect_tail(rstore_tail(rstore_seq(q10,earray_16),s(index_15))),
inference(symmetry,[status(thm)],[15]) ).
tff(1705,plain,
s(rselect_tail(q10)) = index_21,
inference(transitivity,[status(thm)],[5,1704,34,1703]) ).
tff(1706,plain,
s(s(rselect_tail(q10))) = s(index_21),
inference(monotonicity,[status(thm)],[1705]) ).
tff(1707,plain,
s(s(rselect_tail(q10))) = index_30,
inference(transitivity,[status(thm)],[1706,1699,1696,1695,1692,1690]) ).
tff(1708,plain,
s(s(s(rselect_tail(q10)))) = s(index_30),
inference(monotonicity,[status(thm)],[1707]) ).
tff(1709,plain,
s(s(s(rselect_tail(q10)))) = index_36,
inference(transitivity,[status(thm)],[1708,1686,1683,1681]) ).
tff(1710,plain,
s(s(s(s(rselect_tail(q10))))) = s(index_36),
inference(monotonicity,[status(thm)],[1709]) ).
tff(1711,plain,
s(s(s(s(rselect_tail(q10))))) = index_42,
inference(transitivity,[status(thm)],[1710,1677,1674,1672]) ).
tff(1712,plain,
s(s(s(s(s(rselect_tail(q10)))))) = s(index_42),
inference(monotonicity,[status(thm)],[1711]) ).
tff(1713,plain,
s(s(s(s(s(rselect_tail(q10)))))) = index_51,
inference(transitivity,[status(thm)],[1712,1668,1665,1664,1661,1659]) ).
tff(1714,plain,
s(s(s(s(s(s(rselect_tail(q10))))))) = s(index_51),
inference(monotonicity,[status(thm)],[1713]) ).
tff(1715,plain,
s(s(s(s(s(s(rselect_tail(q10))))))) = index_57,
inference(transitivity,[status(thm)],[1714,1655,1652,1650]) ).
tff(1716,plain,
s(s(s(s(s(s(s(rselect_tail(q10)))))))) = s(index_57),
inference(monotonicity,[status(thm)],[1715]) ).
tff(1717,plain,
s(s(s(s(s(s(s(rselect_tail(q10)))))))) = index_63,
inference(transitivity,[status(thm)],[1716,1646,1643,1641]) ).
tff(1718,plain,
s(s(s(s(s(s(s(s(rselect_tail(q10))))))))) = s(index_63),
inference(monotonicity,[status(thm)],[1717]) ).
tff(1719,plain,
s(s(s(s(s(s(s(s(rselect_tail(q10))))))))) = index_72,
inference(transitivity,[status(thm)],[1718,1637,1634,1633,1630,1628]) ).
tff(1720,plain,
s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))) = s(index_72),
inference(monotonicity,[status(thm)],[1719]) ).
tff(1721,plain,
s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))) = index_84,
inference(transitivity,[status(thm)],[1720,1624,1621,1619]) ).
tff(1722,plain,
s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))) = s(index_84),
inference(monotonicity,[status(thm)],[1721]) ).
tff(1723,plain,
s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))) = index_90,
inference(transitivity,[status(thm)],[1722,1615,1612,1610]) ).
tff(1724,plain,
s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))) = s(index_90),
inference(monotonicity,[status(thm)],[1723]) ).
tff(1725,plain,
s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))) = index_99,
inference(transitivity,[status(thm)],[1724,1606,1603,1602,1599,1597]) ).
tff(1726,plain,
s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))) = s(index_99),
inference(monotonicity,[status(thm)],[1725]) ).
tff(1727,plain,
s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))) = index_105,
inference(transitivity,[status(thm)],[1726,1593,1590,1588]) ).
tff(1728,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))) = s(index_105),
inference(monotonicity,[status(thm)],[1727]) ).
tff(1729,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))) = index_111,
inference(transitivity,[status(thm)],[1728,1584,1581,1579]) ).
tff(1730,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))) = s(index_111),
inference(monotonicity,[status(thm)],[1729]) ).
tff(1731,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))) = index_120,
inference(transitivity,[status(thm)],[1730,1575,1572,1571,1568,1566]) ).
tff(1732,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))) = s(index_120),
inference(monotonicity,[status(thm)],[1731]) ).
tff(1733,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))) = index_126,
inference(transitivity,[status(thm)],[1732,1562,1559,1557]) ).
tff(1734,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))) = s(index_126),
inference(monotonicity,[status(thm)],[1733]) ).
tff(1735,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))) = index_132,
inference(transitivity,[status(thm)],[1734,1553,1550,1548]) ).
tff(1736,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))) = s(index_132),
inference(monotonicity,[status(thm)],[1735]) ).
tff(1737,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))) = index_141,
inference(transitivity,[status(thm)],[1736,1544,1541,1540,1537,1535]) ).
tff(1738,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))))) = s(index_141),
inference(monotonicity,[status(thm)],[1737]) ).
tff(1739,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))))) = index_147,
inference(transitivity,[status(thm)],[1738,1531,1528,1526]) ).
tff(1740,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))))) = s(index_147),
inference(monotonicity,[status(thm)],[1739]) ).
tff(1741,plain,
s(index_147) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))))),
inference(symmetry,[status(thm)],[1740]) ).
tff(1742,plain,
( ~ ! [E: $i,A: $i] : ( rselect_tail(rstore_tail(A,E)) = E )
| ( rselect_tail(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = s(index_147) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1743,plain,
rselect_tail(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = s(index_147),
inference(unit_resolution,[status(thm)],[1742,13]) ).
tff(1744,plain,
rstore_tail(rstore_seq(q28,earray_148),s(index_147)) = q29,
inference(transitivity,[status(thm)],[195,211,207]) ).
tff(1745,plain,
rselect_tail(rstore_tail(rstore_seq(q28,earray_148),s(index_147))) = rselect_tail(q29),
inference(monotonicity,[status(thm)],[1744]) ).
tff(1746,plain,
rselect_tail(q29) = rselect_tail(rstore_tail(rstore_seq(q28,earray_148),s(index_147))),
inference(symmetry,[status(thm)],[1745]) ).
tff(1747,plain,
rselect_tail(q29) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))))),
inference(transitivity,[status(thm)],[1746,1743,1741]) ).
tff(1748,plain,
( ( rselect_tail(q29) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1747]) ).
tff(1749,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q29) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[1748]) ).
tff(1750,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q29) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1749]) ).
tff(1751,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(1752,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[1751]) ).
tff(1753,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1754,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as19) ).
tff(1755,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1754,1753]) ).
tff(1756,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[1755]) ).
tff(1757,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1756,1752]) ).
tff(1758,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1759,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[1758,1757]) ).
tff(1760,plain,
rselect_tail(q29) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[1759,1750]) ).
tff(1761,plain,
( ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
<=> ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1762,plain,
( ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
<=> ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1763,axiom,
! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
tff(1764,plain,
! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ),
inference(modus_ponens,[status(thm)],[1763,1762]) ).
tff(1765,plain,
! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ),
inference(skolemize,[status(sab)],[1764]) ).
tff(1766,plain,
! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) ),
inference(modus_ponens,[status(thm)],[1765,1761]) ).
tff(1767,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q29) = rselect_tail(q10) )
| ( select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_tail(q10)) = select(store(earray_146,index_147,e28),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q29) = rselect_tail(q10) )
| ( select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_tail(q10)) = select(store(earray_146,index_147,e28),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1768,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q29) = rselect_tail(q10) )
| ( select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_tail(q10)) = select(store(earray_146,index_147,e28),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1769,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q29) = rselect_tail(q10) )
| ( select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_tail(q10)) = select(store(earray_146,index_147,e28),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[1768,1767]) ).
tff(1770,plain,
( ( rselect_tail(q29) = rselect_tail(q10) )
| ( select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_tail(q10)) = select(store(earray_146,index_147,e28),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[1769,1766]) ).
tff(1771,plain,
select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_tail(q10)) = select(store(earray_146,index_147,e28),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[1770,1760]) ).
tff(1772,plain,
select(store(earray_146,index_147,e28),rselect_tail(q10)) = select(store(store(earray_146,index_147,e28),rselect_tail(q29),e29),rselect_tail(q10)),
inference(symmetry,[status(thm)],[1771]) ).
tff(1773,plain,
( ( earray_146 = rselect_seq(q28) )
<=> ( earray_146 = rselect_seq(q28) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1774,axiom,
earray_146 = rselect_seq(q28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp15) ).
tff(1775,plain,
earray_146 = rselect_seq(q28),
inference(modus_ponens,[status(thm)],[1774,1773]) ).
tff(1776,plain,
rselect_seq(q28) = earray_146,
inference(symmetry,[status(thm)],[1775]) ).
tff(1777,plain,
q28 = rstore_tail(rstore_seq(q27,earray_142),s(index_141)),
inference(transitivity,[status(thm)],[175,179,165]) ).
tff(1778,plain,
rselect_seq(q28) = rselect_seq(rstore_tail(rstore_seq(q27,earray_142),s(index_141))),
inference(monotonicity,[status(thm)],[1777]) ).
tff(1779,plain,
rselect_seq(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_seq(q28),
inference(symmetry,[status(thm)],[1778]) ).
tff(1780,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_seq(rstore_seq(q27,earray_142)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1781,plain,
rselect_seq(rstore_tail(rstore_seq(q27,earray_142),s(index_141))) = rselect_seq(rstore_seq(q27,earray_142)),
inference(unit_resolution,[status(thm)],[1780,1484]) ).
tff(1782,plain,
rselect_seq(rstore_seq(q27,earray_142)) = rselect_seq(rstore_tail(rstore_seq(q27,earray_142),s(index_141))),
inference(symmetry,[status(thm)],[1781]) ).
tff(1783,plain,
rstore_seq(q27,earray_142) = rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27)),
inference(symmetry,[status(thm)],[144]) ).
tff(1784,plain,
rselect_seq(rstore_seq(q27,earray_142)) = rselect_seq(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))),
inference(monotonicity,[status(thm)],[1783]) ).
tff(1785,plain,
rselect_seq(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = rselect_seq(rstore_seq(q27,earray_142)),
inference(symmetry,[status(thm)],[1784]) ).
tff(1786,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = store(earray_140,index_141,e27) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1787,plain,
rselect_seq(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))) = store(earray_140,index_141,e27),
inference(unit_resolution,[status(thm)],[1786,1496]) ).
tff(1788,plain,
store(earray_140,index_141,e27) = rselect_seq(rstore_seq(rstore_head(queue_136,index_138),store(earray_140,index_141,e27))),
inference(symmetry,[status(thm)],[1787]) ).
tff(1789,plain,
store(earray_140,index_141,e27) = earray_146,
inference(transitivity,[status(thm)],[1788,1785,1782,1779,1776]) ).
tff(1790,plain,
store(store(earray_140,index_141,e27),rselect_tail(q28),e28) = store(earray_146,index_147,e28),
inference(monotonicity,[status(thm)],[1789,1526]) ).
tff(1791,plain,
select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_tail(q10)) = select(store(earray_146,index_147,e28),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[1790]) ).
tff(1792,plain,
s(index_141) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))))),
inference(symmetry,[status(thm)],[1738]) ).
tff(1793,plain,
rselect_tail(q28) = rselect_tail(rstore_tail(rstore_seq(q27,earray_142),s(index_141))),
inference(symmetry,[status(thm)],[1528]) ).
tff(1794,plain,
rselect_tail(q28) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))))),
inference(transitivity,[status(thm)],[1793,1530,1792]) ).
tff(1795,plain,
( ( rselect_tail(q28) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1794]) ).
tff(1796,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q28) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[1795]) ).
tff(1797,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q28) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1796]) ).
tff(1798,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(1799,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[1798]) ).
tff(1800,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1801,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as18) ).
tff(1802,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1801,1800]) ).
tff(1803,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[1802]) ).
tff(1804,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1803,1799]) ).
tff(1805,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1806,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[1805,1804]) ).
tff(1807,plain,
rselect_tail(q28) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[1806,1797]) ).
tff(1808,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q28) = rselect_tail(q10) )
| ( select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_tail(q10)) = select(store(earray_140,index_141,e27),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q28) = rselect_tail(q10) )
| ( select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_tail(q10)) = select(store(earray_140,index_141,e27),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1809,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q28) = rselect_tail(q10) )
| ( select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_tail(q10)) = select(store(earray_140,index_141,e27),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1810,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q28) = rselect_tail(q10) )
| ( select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_tail(q10)) = select(store(earray_140,index_141,e27),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[1809,1808]) ).
tff(1811,plain,
( ( rselect_tail(q28) = rselect_tail(q10) )
| ( select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_tail(q10)) = select(store(earray_140,index_141,e27),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[1810,1766]) ).
tff(1812,plain,
select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_tail(q10)) = select(store(earray_140,index_141,e27),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[1811,1807]) ).
tff(1813,plain,
select(store(earray_140,index_141,e27),rselect_tail(q10)) = select(store(store(earray_140,index_141,e27),rselect_tail(q28),e28),rselect_tail(q10)),
inference(symmetry,[status(thm)],[1812]) ).
tff(1814,plain,
( ( earray_140 = rselect_seq(q27) )
<=> ( earray_140 = rselect_seq(q27) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1815,axiom,
earray_140 = rselect_seq(q27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp13) ).
tff(1816,plain,
earray_140 = rselect_seq(q27),
inference(modus_ponens,[status(thm)],[1815,1814]) ).
tff(1817,plain,
rselect_seq(q27) = earray_140,
inference(symmetry,[status(thm)],[1816]) ).
tff(1818,plain,
rstore_head(queue_136,index_138) = rstore_head(rstore_tail(queue_134,index_135),s(index_137)),
inference(symmetry,[status(thm)],[119]) ).
tff(1819,plain,
q27 = rstore_head(rstore_tail(queue_134,index_135),s(index_137)),
inference(transitivity,[status(thm)],[137,141,1818]) ).
tff(1820,plain,
rselect_seq(q27) = rselect_seq(rstore_head(rstore_tail(queue_134,index_135),s(index_137))),
inference(monotonicity,[status(thm)],[1819]) ).
tff(1821,plain,
rselect_seq(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_seq(q27),
inference(symmetry,[status(thm)],[1820]) ).
tff(1822,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_seq(rstore_tail(queue_134,index_135)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1823,plain,
rselect_seq(rstore_head(rstore_tail(queue_134,index_135),s(index_137))) = rselect_seq(rstore_tail(queue_134,index_135)),
inference(unit_resolution,[status(thm)],[1822,1472]) ).
tff(1824,plain,
rselect_seq(rstore_tail(queue_134,index_135)) = rselect_seq(rstore_head(rstore_tail(queue_134,index_135),s(index_137))),
inference(symmetry,[status(thm)],[1823]) ).
tff(1825,plain,
rselect_seq(rstore_tail(queue_134,index_135)) = rselect_seq(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(monotonicity,[status(thm)],[1343]) ).
tff(1826,plain,
rselect_seq(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_seq(rstore_tail(queue_134,index_135)),
inference(symmetry,[status(thm)],[1825]) ).
tff(1827,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_seq(rstore_seq(q26,earray_133)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1828,plain,
rselect_seq(rstore_tail(rstore_seq(q26,earray_133),s(index_132))) = rselect_seq(rstore_seq(q26,earray_133)),
inference(unit_resolution,[status(thm)],[1827,1484]) ).
tff(1829,plain,
rselect_seq(rstore_seq(q26,earray_133)) = rselect_seq(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(symmetry,[status(thm)],[1828]) ).
tff(1830,plain,
rselect_seq(rstore_seq(q26,earray_133)) = rselect_seq(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))),
inference(monotonicity,[status(thm)],[1364]) ).
tff(1831,plain,
rselect_seq(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = rselect_seq(rstore_seq(q26,earray_133)),
inference(symmetry,[status(thm)],[1830]) ).
tff(1832,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = store(earray_131,index_132,e26) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1833,plain,
rselect_seq(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))) = store(earray_131,index_132,e26),
inference(unit_resolution,[status(thm)],[1832,1496]) ).
tff(1834,plain,
store(earray_131,index_132,e26) = rselect_seq(rstore_seq(rstore_tail(queue_128,index_129),store(earray_131,index_132,e26))),
inference(symmetry,[status(thm)],[1833]) ).
tff(1835,plain,
store(earray_131,index_132,e26) = earray_140,
inference(transitivity,[status(thm)],[1834,1831,1829,1826,1824,1821,1817]) ).
tff(1836,plain,
store(store(earray_131,index_132,e26),rselect_tail(q27),e27) = store(earray_140,index_141,e27),
inference(monotonicity,[status(thm)],[1835,1535]) ).
tff(1837,plain,
select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_tail(q10)) = select(store(earray_140,index_141,e27),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[1836]) ).
tff(1838,plain,
s(index_132) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))),
inference(symmetry,[status(thm)],[1736]) ).
tff(1839,plain,
rselect_tail(rstore_tail(queue_134,index_135)) = rselect_tail(rstore_tail(rstore_seq(q26,earray_133),s(index_132))),
inference(symmetry,[status(thm)],[1541]) ).
tff(1840,plain,
rselect_tail(q27) = rselect_tail(rstore_head(rstore_tail(queue_134,index_135),s(index_137))),
inference(symmetry,[status(thm)],[1537]) ).
tff(1841,plain,
rselect_tail(q27) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))),
inference(transitivity,[status(thm)],[1840,1539,1839,1543,1838]) ).
tff(1842,plain,
( ( rselect_tail(q27) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1841]) ).
tff(1843,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q27) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[1842]) ).
tff(1844,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q27) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1843]) ).
tff(1845,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(1846,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[1845]) ).
tff(1847,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1848,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as17) ).
tff(1849,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1848,1847]) ).
tff(1850,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ),
inference(skolemize,[status(sab)],[1849]) ).
tff(1851,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1850,1846]) ).
tff(1852,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1853,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[1852,1851]) ).
tff(1854,plain,
rselect_tail(q27) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[1853,1844]) ).
tff(1855,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q27) = rselect_tail(q10) )
| ( select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_tail(q10)) = select(store(earray_131,index_132,e26),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q27) = rselect_tail(q10) )
| ( select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_tail(q10)) = select(store(earray_131,index_132,e26),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1856,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q27) = rselect_tail(q10) )
| ( select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_tail(q10)) = select(store(earray_131,index_132,e26),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1857,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q27) = rselect_tail(q10) )
| ( select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_tail(q10)) = select(store(earray_131,index_132,e26),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[1856,1855]) ).
tff(1858,plain,
( ( rselect_tail(q27) = rselect_tail(q10) )
| ( select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_tail(q10)) = select(store(earray_131,index_132,e26),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[1857,1766]) ).
tff(1859,plain,
select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_tail(q10)) = select(store(earray_131,index_132,e26),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[1858,1854]) ).
tff(1860,plain,
select(store(earray_131,index_132,e26),rselect_tail(q10)) = select(store(store(earray_131,index_132,e26),rselect_tail(q27),e27),rselect_tail(q10)),
inference(symmetry,[status(thm)],[1859]) ).
tff(1861,plain,
( ( earray_131 = rselect_seq(q26) )
<=> ( earray_131 = rselect_seq(q26) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1862,axiom,
earray_131 = rselect_seq(q26),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp10) ).
tff(1863,plain,
earray_131 = rselect_seq(q26),
inference(modus_ponens,[status(thm)],[1862,1861]) ).
tff(1864,plain,
rselect_seq(q26) = earray_131,
inference(symmetry,[status(thm)],[1863]) ).
tff(1865,plain,
q26 = rstore_tail(rstore_seq(q25,earray_127),s(index_126)),
inference(transitivity,[status(thm)],[1356,1360,1379]) ).
tff(1866,plain,
rselect_seq(q26) = rselect_seq(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(monotonicity,[status(thm)],[1865]) ).
tff(1867,plain,
rselect_seq(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_seq(q26),
inference(symmetry,[status(thm)],[1866]) ).
tff(1868,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_seq(rstore_seq(q25,earray_127)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1869,plain,
rselect_seq(rstore_tail(rstore_seq(q25,earray_127),s(index_126))) = rselect_seq(rstore_seq(q25,earray_127)),
inference(unit_resolution,[status(thm)],[1868,1484]) ).
tff(1870,plain,
rselect_seq(rstore_seq(q25,earray_127)) = rselect_seq(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(symmetry,[status(thm)],[1869]) ).
tff(1871,plain,
rselect_seq(rstore_seq(q25,earray_127)) = rselect_seq(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))),
inference(monotonicity,[status(thm)],[1399]) ).
tff(1872,plain,
rselect_seq(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = rselect_seq(rstore_seq(q25,earray_127)),
inference(symmetry,[status(thm)],[1871]) ).
tff(1873,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = store(earray_125,index_126,e25) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1874,plain,
rselect_seq(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))) = store(earray_125,index_126,e25),
inference(unit_resolution,[status(thm)],[1873,1496]) ).
tff(1875,plain,
store(earray_125,index_126,e25) = rselect_seq(rstore_seq(rstore_tail(queue_122,index_123),store(earray_125,index_126,e25))),
inference(symmetry,[status(thm)],[1874]) ).
tff(1876,plain,
store(earray_125,index_126,e25) = earray_131,
inference(transitivity,[status(thm)],[1875,1872,1870,1867,1864]) ).
tff(1877,plain,
store(store(earray_125,index_126,e25),rselect_tail(q26),e26) = store(earray_131,index_132,e26),
inference(monotonicity,[status(thm)],[1876,1548]) ).
tff(1878,plain,
select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_tail(q10)) = select(store(earray_131,index_132,e26),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[1877]) ).
tff(1879,plain,
s(index_126) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))),
inference(symmetry,[status(thm)],[1734]) ).
tff(1880,plain,
rselect_tail(q26) = rselect_tail(rstore_tail(rstore_seq(q25,earray_127),s(index_126))),
inference(symmetry,[status(thm)],[1550]) ).
tff(1881,plain,
rselect_tail(q26) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))),
inference(transitivity,[status(thm)],[1880,1552,1879]) ).
tff(1882,plain,
( ( rselect_tail(q26) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1881]) ).
tff(1883,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q26) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[1882]) ).
tff(1884,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q26) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1883]) ).
tff(1885,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(1886,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[1885]) ).
tff(1887,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1888,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as16) ).
tff(1889,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1888,1887]) ).
tff(1890,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ),
inference(skolemize,[status(sab)],[1889]) ).
tff(1891,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1890,1886]) ).
tff(1892,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1893,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[1892,1891]) ).
tff(1894,plain,
rselect_tail(q26) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[1893,1884]) ).
tff(1895,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q26) = rselect_tail(q10) )
| ( select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_tail(q10)) = select(store(earray_125,index_126,e25),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q26) = rselect_tail(q10) )
| ( select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_tail(q10)) = select(store(earray_125,index_126,e25),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1896,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q26) = rselect_tail(q10) )
| ( select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_tail(q10)) = select(store(earray_125,index_126,e25),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1897,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q26) = rselect_tail(q10) )
| ( select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_tail(q10)) = select(store(earray_125,index_126,e25),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[1896,1895]) ).
tff(1898,plain,
( ( rselect_tail(q26) = rselect_tail(q10) )
| ( select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_tail(q10)) = select(store(earray_125,index_126,e25),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[1897,1766]) ).
tff(1899,plain,
select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_tail(q10)) = select(store(earray_125,index_126,e25),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[1898,1894]) ).
tff(1900,plain,
select(store(earray_125,index_126,e25),rselect_tail(q10)) = select(store(store(earray_125,index_126,e25),rselect_tail(q26),e26),rselect_tail(q10)),
inference(symmetry,[status(thm)],[1899]) ).
tff(1901,plain,
( ( earray_125 = rselect_seq(q25) )
<=> ( earray_125 = rselect_seq(q25) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1902,axiom,
earray_125 = rselect_seq(q25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp8) ).
tff(1903,plain,
earray_125 = rselect_seq(q25),
inference(modus_ponens,[status(thm)],[1902,1901]) ).
tff(1904,plain,
rselect_seq(q25) = earray_125,
inference(symmetry,[status(thm)],[1903]) ).
tff(1905,plain,
q25 = rstore_tail(rstore_seq(q24,earray_121),s(index_120)),
inference(transitivity,[status(thm)],[1391,1395,1414]) ).
tff(1906,plain,
rselect_seq(q25) = rselect_seq(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(monotonicity,[status(thm)],[1905]) ).
tff(1907,plain,
rselect_seq(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_seq(q25),
inference(symmetry,[status(thm)],[1906]) ).
tff(1908,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_seq(rstore_seq(q24,earray_121)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1909,plain,
rselect_seq(rstore_tail(rstore_seq(q24,earray_121),s(index_120))) = rselect_seq(rstore_seq(q24,earray_121)),
inference(unit_resolution,[status(thm)],[1908,1484]) ).
tff(1910,plain,
rselect_seq(rstore_seq(q24,earray_121)) = rselect_seq(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(symmetry,[status(thm)],[1909]) ).
tff(1911,plain,
rstore_seq(q24,earray_121) = rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24)),
inference(symmetry,[status(thm)],[1433]) ).
tff(1912,plain,
rselect_seq(rstore_seq(q24,earray_121)) = rselect_seq(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))),
inference(monotonicity,[status(thm)],[1911]) ).
tff(1913,plain,
rselect_seq(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = rselect_seq(rstore_seq(q24,earray_121)),
inference(symmetry,[status(thm)],[1912]) ).
tff(1914,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = store(earray_119,index_120,e24) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1915,plain,
rselect_seq(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))) = store(earray_119,index_120,e24),
inference(unit_resolution,[status(thm)],[1914,1496]) ).
tff(1916,plain,
store(earray_119,index_120,e24) = rselect_seq(rstore_seq(rstore_head(queue_115,index_117),store(earray_119,index_120,e24))),
inference(symmetry,[status(thm)],[1915]) ).
tff(1917,plain,
store(earray_119,index_120,e24) = earray_125,
inference(transitivity,[status(thm)],[1916,1913,1910,1907,1904]) ).
tff(1918,plain,
store(store(earray_119,index_120,e24),rselect_tail(q25),e25) = store(earray_125,index_126,e25),
inference(monotonicity,[status(thm)],[1917,1557]) ).
tff(1919,plain,
select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_tail(q10)) = select(store(earray_125,index_126,e25),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[1918]) ).
tff(1920,plain,
s(index_120) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))),
inference(symmetry,[status(thm)],[1732]) ).
tff(1921,plain,
rselect_tail(q25) = rselect_tail(rstore_tail(rstore_seq(q24,earray_121),s(index_120))),
inference(symmetry,[status(thm)],[1559]) ).
tff(1922,plain,
rselect_tail(q25) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))),
inference(transitivity,[status(thm)],[1921,1561,1920]) ).
tff(1923,plain,
( ( rselect_tail(q25) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1922]) ).
tff(1924,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q25) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[1923]) ).
tff(1925,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q25) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1924]) ).
tff(1926,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(1927,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[1926]) ).
tff(1928,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1929,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as15) ).
tff(1930,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1929,1928]) ).
tff(1931,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ),
inference(skolemize,[status(sab)],[1930]) ).
tff(1932,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1931,1927]) ).
tff(1933,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1934,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[1933,1932]) ).
tff(1935,plain,
rselect_tail(q25) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[1934,1925]) ).
tff(1936,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q25) = rselect_tail(q10) )
| ( select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_tail(q10)) = select(store(earray_119,index_120,e24),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q25) = rselect_tail(q10) )
| ( select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_tail(q10)) = select(store(earray_119,index_120,e24),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1937,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q25) = rselect_tail(q10) )
| ( select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_tail(q10)) = select(store(earray_119,index_120,e24),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1938,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q25) = rselect_tail(q10) )
| ( select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_tail(q10)) = select(store(earray_119,index_120,e24),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[1937,1936]) ).
tff(1939,plain,
( ( rselect_tail(q25) = rselect_tail(q10) )
| ( select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_tail(q10)) = select(store(earray_119,index_120,e24),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[1938,1766]) ).
tff(1940,plain,
select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_tail(q10)) = select(store(earray_119,index_120,e24),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[1939,1935]) ).
tff(1941,plain,
select(store(earray_119,index_120,e24),rselect_tail(q10)) = select(store(store(earray_119,index_120,e24),rselect_tail(q25),e25),rselect_tail(q10)),
inference(symmetry,[status(thm)],[1940]) ).
tff(1942,plain,
( ( earray_119 = rselect_seq(q24) )
<=> ( earray_119 = rselect_seq(q24) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1943,axiom,
earray_119 = rselect_seq(q24),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp6) ).
tff(1944,plain,
earray_119 = rselect_seq(q24),
inference(modus_ponens,[status(thm)],[1943,1942]) ).
tff(1945,plain,
rselect_seq(q24) = earray_119,
inference(symmetry,[status(thm)],[1944]) ).
tff(1946,plain,
rstore_head(queue_115,index_117) = rstore_head(rstore_tail(queue_113,index_114),s(index_116)),
inference(symmetry,[status(thm)],[1443]) ).
tff(1947,plain,
q24 = rstore_head(rstore_tail(queue_113,index_114),s(index_116)),
inference(transitivity,[status(thm)],[1426,1430,1946]) ).
tff(1948,plain,
rselect_seq(q24) = rselect_seq(rstore_head(rstore_tail(queue_113,index_114),s(index_116))),
inference(monotonicity,[status(thm)],[1947]) ).
tff(1949,plain,
rselect_seq(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_seq(q24),
inference(symmetry,[status(thm)],[1948]) ).
tff(1950,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_seq(rstore_tail(queue_113,index_114)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1951,plain,
rselect_seq(rstore_head(rstore_tail(queue_113,index_114),s(index_116))) = rselect_seq(rstore_tail(queue_113,index_114)),
inference(unit_resolution,[status(thm)],[1950,1472]) ).
tff(1952,plain,
rselect_seq(rstore_tail(queue_113,index_114)) = rselect_seq(rstore_head(rstore_tail(queue_113,index_114),s(index_116))),
inference(symmetry,[status(thm)],[1951]) ).
tff(1953,plain,
rselect_seq(rstore_tail(queue_113,index_114)) = rselect_seq(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(monotonicity,[status(thm)],[299]) ).
tff(1954,plain,
rselect_seq(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_seq(rstore_tail(queue_113,index_114)),
inference(symmetry,[status(thm)],[1953]) ).
tff(1955,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_seq(rstore_seq(q23,earray_112)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1956,plain,
rselect_seq(rstore_tail(rstore_seq(q23,earray_112),s(index_111))) = rselect_seq(rstore_seq(q23,earray_112)),
inference(unit_resolution,[status(thm)],[1955,1484]) ).
tff(1957,plain,
rselect_seq(rstore_seq(q23,earray_112)) = rselect_seq(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(symmetry,[status(thm)],[1956]) ).
tff(1958,plain,
rselect_seq(rstore_seq(q23,earray_112)) = rselect_seq(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))),
inference(monotonicity,[status(thm)],[323]) ).
tff(1959,plain,
rselect_seq(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = rselect_seq(rstore_seq(q23,earray_112)),
inference(symmetry,[status(thm)],[1958]) ).
tff(1960,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = store(earray_110,index_111,e23) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1961,plain,
rselect_seq(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))) = store(earray_110,index_111,e23),
inference(unit_resolution,[status(thm)],[1960,1496]) ).
tff(1962,plain,
store(earray_110,index_111,e23) = rselect_seq(rstore_seq(rstore_tail(queue_107,index_108),store(earray_110,index_111,e23))),
inference(symmetry,[status(thm)],[1961]) ).
tff(1963,plain,
store(earray_110,index_111,e23) = earray_119,
inference(transitivity,[status(thm)],[1962,1959,1957,1954,1952,1949,1945]) ).
tff(1964,plain,
store(store(earray_110,index_111,e23),rselect_tail(q24),e24) = store(earray_119,index_120,e24),
inference(monotonicity,[status(thm)],[1963,1566]) ).
tff(1965,plain,
select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_tail(q10)) = select(store(earray_119,index_120,e24),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[1964]) ).
tff(1966,plain,
s(index_111) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))),
inference(symmetry,[status(thm)],[1730]) ).
tff(1967,plain,
rselect_tail(rstore_tail(queue_113,index_114)) = rselect_tail(rstore_tail(rstore_seq(q23,earray_112),s(index_111))),
inference(symmetry,[status(thm)],[1572]) ).
tff(1968,plain,
rselect_tail(q24) = rselect_tail(rstore_head(rstore_tail(queue_113,index_114),s(index_116))),
inference(symmetry,[status(thm)],[1568]) ).
tff(1969,plain,
rselect_tail(q24) = s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))),
inference(transitivity,[status(thm)],[1968,1570,1967,1574,1966]) ).
tff(1970,plain,
( ( rselect_tail(q24) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1969]) ).
tff(1971,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q24) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[1970]) ).
tff(1972,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q24) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[1971]) ).
tff(1973,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(1974,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[1973]) ).
tff(1975,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1976,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as14) ).
tff(1977,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1976,1975]) ).
tff(1978,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(skolemize,[status(sab)],[1977]) ).
tff(1979,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[1978,1974]) ).
tff(1980,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1981,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[1980,1979]) ).
tff(1982,plain,
rselect_tail(q24) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[1981,1972]) ).
tff(1983,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q24) = rselect_tail(q10) )
| ( select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_tail(q10)) = select(store(earray_110,index_111,e23),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q24) = rselect_tail(q10) )
| ( select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_tail(q10)) = select(store(earray_110,index_111,e23),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1984,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q24) = rselect_tail(q10) )
| ( select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_tail(q10)) = select(store(earray_110,index_111,e23),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1985,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q24) = rselect_tail(q10) )
| ( select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_tail(q10)) = select(store(earray_110,index_111,e23),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[1984,1983]) ).
tff(1986,plain,
( ( rselect_tail(q24) = rselect_tail(q10) )
| ( select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_tail(q10)) = select(store(earray_110,index_111,e23),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[1985,1766]) ).
tff(1987,plain,
select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_tail(q10)) = select(store(earray_110,index_111,e23),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[1986,1982]) ).
tff(1988,plain,
select(store(earray_110,index_111,e23),rselect_tail(q10)) = select(store(store(earray_110,index_111,e23),rselect_tail(q24),e24),rselect_tail(q10)),
inference(symmetry,[status(thm)],[1987]) ).
tff(1989,plain,
( ( earray_110 = rselect_seq(q23) )
<=> ( earray_110 = rselect_seq(q23) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(1990,axiom,
earray_110 = rselect_seq(q23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp4) ).
tff(1991,plain,
earray_110 = rselect_seq(q23),
inference(modus_ponens,[status(thm)],[1990,1989]) ).
tff(1992,plain,
rselect_seq(q23) = earray_110,
inference(symmetry,[status(thm)],[1991]) ).
tff(1993,plain,
q23 = rstore_tail(rstore_seq(q22,earray_106),s(index_105)),
inference(transitivity,[status(thm)],[315,319,338]) ).
tff(1994,plain,
rselect_seq(q23) = rselect_seq(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(monotonicity,[status(thm)],[1993]) ).
tff(1995,plain,
rselect_seq(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_seq(q23),
inference(symmetry,[status(thm)],[1994]) ).
tff(1996,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_seq(rstore_seq(q22,earray_106)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(1997,plain,
rselect_seq(rstore_tail(rstore_seq(q22,earray_106),s(index_105))) = rselect_seq(rstore_seq(q22,earray_106)),
inference(unit_resolution,[status(thm)],[1996,1484]) ).
tff(1998,plain,
rselect_seq(rstore_seq(q22,earray_106)) = rselect_seq(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(symmetry,[status(thm)],[1997]) ).
tff(1999,plain,
rselect_seq(rstore_seq(q22,earray_106)) = rselect_seq(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))),
inference(monotonicity,[status(thm)],[358]) ).
tff(2000,plain,
rselect_seq(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = rselect_seq(rstore_seq(q22,earray_106)),
inference(symmetry,[status(thm)],[1999]) ).
tff(2001,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = store(earray_104,index_105,e22) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2002,plain,
rselect_seq(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))) = store(earray_104,index_105,e22),
inference(unit_resolution,[status(thm)],[2001,1496]) ).
tff(2003,plain,
store(earray_104,index_105,e22) = rselect_seq(rstore_seq(rstore_tail(queue_101,index_102),store(earray_104,index_105,e22))),
inference(symmetry,[status(thm)],[2002]) ).
tff(2004,plain,
store(earray_104,index_105,e22) = earray_110,
inference(transitivity,[status(thm)],[2003,2000,1998,1995,1992]) ).
tff(2005,plain,
store(store(earray_104,index_105,e22),rselect_tail(q23),e23) = store(earray_110,index_111,e23),
inference(monotonicity,[status(thm)],[2004,1579]) ).
tff(2006,plain,
select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_tail(q10)) = select(store(earray_110,index_111,e23),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2005]) ).
tff(2007,plain,
s(index_105) = s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))),
inference(symmetry,[status(thm)],[1728]) ).
tff(2008,plain,
rselect_tail(q23) = rselect_tail(rstore_tail(rstore_seq(q22,earray_106),s(index_105))),
inference(symmetry,[status(thm)],[1581]) ).
tff(2009,plain,
rselect_tail(q23) = s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))),
inference(transitivity,[status(thm)],[2008,1583,2007]) ).
tff(2010,plain,
( ( rselect_tail(q23) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2009]) ).
tff(2011,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q23) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2010]) ).
tff(2012,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q23) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2011]) ).
tff(2013,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2014,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[2013]) ).
tff(2015,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2016,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as13) ).
tff(2017,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[2016,2015]) ).
tff(2018,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(skolemize,[status(sab)],[2017]) ).
tff(2019,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X ),
inference(modus_ponens,[status(thm)],[2018,2014]) ).
tff(2020,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(s(X))))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2021,plain,
s(s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2020,2019]) ).
tff(2022,plain,
rselect_tail(q23) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2021,2012]) ).
tff(2023,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q23) = rselect_tail(q10) )
| ( select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_tail(q10)) = select(store(earray_104,index_105,e22),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q23) = rselect_tail(q10) )
| ( select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_tail(q10)) = select(store(earray_104,index_105,e22),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2024,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q23) = rselect_tail(q10) )
| ( select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_tail(q10)) = select(store(earray_104,index_105,e22),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2025,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q23) = rselect_tail(q10) )
| ( select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_tail(q10)) = select(store(earray_104,index_105,e22),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2024,2023]) ).
tff(2026,plain,
( ( rselect_tail(q23) = rselect_tail(q10) )
| ( select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_tail(q10)) = select(store(earray_104,index_105,e22),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2025,1766]) ).
tff(2027,plain,
select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_tail(q10)) = select(store(earray_104,index_105,e22),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2026,2022]) ).
tff(2028,plain,
select(store(earray_104,index_105,e22),rselect_tail(q10)) = select(store(store(earray_104,index_105,e22),rselect_tail(q23),e23),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2027]) ).
tff(2029,plain,
( ( earray_104 = rselect_seq(q22) )
<=> ( earray_104 = rselect_seq(q22) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2030,axiom,
earray_104 = rselect_seq(q22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp2) ).
tff(2031,plain,
earray_104 = rselect_seq(q22),
inference(modus_ponens,[status(thm)],[2030,2029]) ).
tff(2032,plain,
rselect_seq(q22) = earray_104,
inference(symmetry,[status(thm)],[2031]) ).
tff(2033,plain,
q22 = rstore_tail(rstore_seq(q21,earray_100),s(index_99)),
inference(transitivity,[status(thm)],[350,354,373]) ).
tff(2034,plain,
rselect_seq(q22) = rselect_seq(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(monotonicity,[status(thm)],[2033]) ).
tff(2035,plain,
rselect_seq(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_seq(q22),
inference(symmetry,[status(thm)],[2034]) ).
tff(2036,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_seq(rstore_seq(q21,earray_100)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2037,plain,
rselect_seq(rstore_tail(rstore_seq(q21,earray_100),s(index_99))) = rselect_seq(rstore_seq(q21,earray_100)),
inference(unit_resolution,[status(thm)],[2036,1484]) ).
tff(2038,plain,
rselect_seq(rstore_seq(q21,earray_100)) = rselect_seq(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(symmetry,[status(thm)],[2037]) ).
tff(2039,plain,
rstore_seq(q21,earray_100) = rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21)),
inference(symmetry,[status(thm)],[392]) ).
tff(2040,plain,
rselect_seq(rstore_seq(q21,earray_100)) = rselect_seq(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))),
inference(monotonicity,[status(thm)],[2039]) ).
tff(2041,plain,
rselect_seq(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = rselect_seq(rstore_seq(q21,earray_100)),
inference(symmetry,[status(thm)],[2040]) ).
tff(2042,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = store(earray_98,index_99,e21) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2043,plain,
rselect_seq(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))) = store(earray_98,index_99,e21),
inference(unit_resolution,[status(thm)],[2042,1496]) ).
tff(2044,plain,
store(earray_98,index_99,e21) = rselect_seq(rstore_seq(rstore_head(queue_94,index_96),store(earray_98,index_99,e21))),
inference(symmetry,[status(thm)],[2043]) ).
tff(2045,plain,
store(earray_98,index_99,e21) = earray_104,
inference(transitivity,[status(thm)],[2044,2041,2038,2035,2032]) ).
tff(2046,plain,
store(store(earray_98,index_99,e21),rselect_tail(q22),e22) = store(earray_104,index_105,e22),
inference(monotonicity,[status(thm)],[2045,1588]) ).
tff(2047,plain,
select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_tail(q10)) = select(store(earray_104,index_105,e22),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2046]) ).
tff(2048,plain,
s(index_99) = s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))),
inference(symmetry,[status(thm)],[1726]) ).
tff(2049,plain,
rselect_tail(q22) = rselect_tail(rstore_tail(rstore_seq(q21,earray_100),s(index_99))),
inference(symmetry,[status(thm)],[1590]) ).
tff(2050,plain,
rselect_tail(q22) = s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))),
inference(transitivity,[status(thm)],[2049,1592,2048]) ).
tff(2051,plain,
( ( rselect_tail(q22) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2050]) ).
tff(2052,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q22) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2051]) ).
tff(2053,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q22) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2052]) ).
tff(2054,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2055,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[2054]) ).
tff(2056,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2057,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as12) ).
tff(2058,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(modus_ponens,[status(thm)],[2057,2056]) ).
tff(2059,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(skolemize,[status(sab)],[2058]) ).
tff(2060,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X ),
inference(modus_ponens,[status(thm)],[2059,2055]) ).
tff(2061,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(s(X)))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2062,plain,
s(s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2061,2060]) ).
tff(2063,plain,
rselect_tail(q22) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2062,2053]) ).
tff(2064,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q22) = rselect_tail(q10) )
| ( select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_tail(q10)) = select(store(earray_98,index_99,e21),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q22) = rselect_tail(q10) )
| ( select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_tail(q10)) = select(store(earray_98,index_99,e21),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2065,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q22) = rselect_tail(q10) )
| ( select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_tail(q10)) = select(store(earray_98,index_99,e21),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2066,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q22) = rselect_tail(q10) )
| ( select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_tail(q10)) = select(store(earray_98,index_99,e21),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2065,2064]) ).
tff(2067,plain,
( ( rselect_tail(q22) = rselect_tail(q10) )
| ( select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_tail(q10)) = select(store(earray_98,index_99,e21),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2066,1766]) ).
tff(2068,plain,
select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_tail(q10)) = select(store(earray_98,index_99,e21),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2067,2063]) ).
tff(2069,plain,
select(store(earray_98,index_99,e21),rselect_tail(q10)) = select(store(store(earray_98,index_99,e21),rselect_tail(q22),e22),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2068]) ).
tff(2070,plain,
( ( earray_98 = rselect_seq(q21) )
<=> ( earray_98 = rselect_seq(q21) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2071,axiom,
earray_98 = rselect_seq(q21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp60) ).
tff(2072,plain,
earray_98 = rselect_seq(q21),
inference(modus_ponens,[status(thm)],[2071,2070]) ).
tff(2073,plain,
rselect_seq(q21) = earray_98,
inference(symmetry,[status(thm)],[2072]) ).
tff(2074,plain,
rstore_head(queue_94,index_96) = rstore_head(rstore_tail(queue_92,index_93),s(index_95)),
inference(symmetry,[status(thm)],[405]) ).
tff(2075,plain,
q21 = rstore_head(rstore_tail(queue_92,index_93),s(index_95)),
inference(transitivity,[status(thm)],[385,389,2074]) ).
tff(2076,plain,
rselect_seq(q21) = rselect_seq(rstore_head(rstore_tail(queue_92,index_93),s(index_95))),
inference(monotonicity,[status(thm)],[2075]) ).
tff(2077,plain,
rselect_seq(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_seq(q21),
inference(symmetry,[status(thm)],[2076]) ).
tff(2078,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_seq(rstore_tail(queue_92,index_93)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2079,plain,
rselect_seq(rstore_head(rstore_tail(queue_92,index_93),s(index_95))) = rselect_seq(rstore_tail(queue_92,index_93)),
inference(unit_resolution,[status(thm)],[2078,1472]) ).
tff(2080,plain,
rselect_seq(rstore_tail(queue_92,index_93)) = rselect_seq(rstore_head(rstore_tail(queue_92,index_93),s(index_95))),
inference(symmetry,[status(thm)],[2079]) ).
tff(2081,plain,
rselect_seq(rstore_tail(queue_92,index_93)) = rselect_seq(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(monotonicity,[status(thm)],[427]) ).
tff(2082,plain,
rselect_seq(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_seq(rstore_tail(queue_92,index_93)),
inference(symmetry,[status(thm)],[2081]) ).
tff(2083,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_seq(rstore_seq(q20,earray_91)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2084,plain,
rselect_seq(rstore_tail(rstore_seq(q20,earray_91),s(index_90))) = rselect_seq(rstore_seq(q20,earray_91)),
inference(unit_resolution,[status(thm)],[2083,1484]) ).
tff(2085,plain,
rselect_seq(rstore_seq(q20,earray_91)) = rselect_seq(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(symmetry,[status(thm)],[2084]) ).
tff(2086,plain,
rselect_seq(rstore_seq(q20,earray_91)) = rselect_seq(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))),
inference(monotonicity,[status(thm)],[448]) ).
tff(2087,plain,
rselect_seq(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = rselect_seq(rstore_seq(q20,earray_91)),
inference(symmetry,[status(thm)],[2086]) ).
tff(2088,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = store(earray_89,index_90,e20) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2089,plain,
rselect_seq(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))) = store(earray_89,index_90,e20),
inference(unit_resolution,[status(thm)],[2088,1496]) ).
tff(2090,plain,
store(earray_89,index_90,e20) = rselect_seq(rstore_seq(rstore_tail(queue_86,index_87),store(earray_89,index_90,e20))),
inference(symmetry,[status(thm)],[2089]) ).
tff(2091,plain,
store(earray_89,index_90,e20) = earray_98,
inference(transitivity,[status(thm)],[2090,2087,2085,2082,2080,2077,2073]) ).
tff(2092,plain,
store(store(earray_89,index_90,e20),rselect_tail(q21),e21) = store(earray_98,index_99,e21),
inference(monotonicity,[status(thm)],[2091,1597]) ).
tff(2093,plain,
select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_tail(q10)) = select(store(earray_98,index_99,e21),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2092]) ).
tff(2094,plain,
s(index_90) = s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))),
inference(symmetry,[status(thm)],[1724]) ).
tff(2095,plain,
rselect_tail(rstore_tail(queue_92,index_93)) = rselect_tail(rstore_tail(rstore_seq(q20,earray_91),s(index_90))),
inference(symmetry,[status(thm)],[1603]) ).
tff(2096,plain,
rselect_tail(q21) = rselect_tail(rstore_head(rstore_tail(queue_92,index_93),s(index_95))),
inference(symmetry,[status(thm)],[1599]) ).
tff(2097,plain,
rselect_tail(q21) = s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))),
inference(transitivity,[status(thm)],[2096,1601,2095,1605,2094]) ).
tff(2098,plain,
( ( rselect_tail(q21) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2097]) ).
tff(2099,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q21) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2098]) ).
tff(2100,plain,
( ( s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q21) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2099]) ).
tff(2101,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2102,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ) ),
inference(quant_intro,[status(thm)],[2101]) ).
tff(2103,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2104,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as11) ).
tff(2105,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ),
inference(modus_ponens,[status(thm)],[2104,2103]) ).
tff(2106,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ),
inference(skolemize,[status(sab)],[2105]) ).
tff(2107,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X ),
inference(modus_ponens,[status(thm)],[2106,2102]) ).
tff(2108,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(s(X))))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2109,plain,
s(s(s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2108,2107]) ).
tff(2110,plain,
rselect_tail(q21) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2109,2100]) ).
tff(2111,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q21) = rselect_tail(q10) )
| ( select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_tail(q10)) = select(store(earray_89,index_90,e20),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q21) = rselect_tail(q10) )
| ( select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_tail(q10)) = select(store(earray_89,index_90,e20),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2112,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q21) = rselect_tail(q10) )
| ( select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_tail(q10)) = select(store(earray_89,index_90,e20),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2113,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q21) = rselect_tail(q10) )
| ( select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_tail(q10)) = select(store(earray_89,index_90,e20),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2112,2111]) ).
tff(2114,plain,
( ( rselect_tail(q21) = rselect_tail(q10) )
| ( select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_tail(q10)) = select(store(earray_89,index_90,e20),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2113,1766]) ).
tff(2115,plain,
select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_tail(q10)) = select(store(earray_89,index_90,e20),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2114,2110]) ).
tff(2116,plain,
select(store(earray_89,index_90,e20),rselect_tail(q10)) = select(store(store(earray_89,index_90,e20),rselect_tail(q21),e21),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2115]) ).
tff(2117,plain,
( ( earray_89 = rselect_seq(q20) )
<=> ( earray_89 = rselect_seq(q20) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2118,axiom,
earray_89 = rselect_seq(q20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp58) ).
tff(2119,plain,
earray_89 = rselect_seq(q20),
inference(modus_ponens,[status(thm)],[2118,2117]) ).
tff(2120,plain,
rselect_seq(q20) = earray_89,
inference(symmetry,[status(thm)],[2119]) ).
tff(2121,plain,
q20 = rstore_tail(rstore_seq(q19,earray_85),s(index_84)),
inference(transitivity,[status(thm)],[440,444,463]) ).
tff(2122,plain,
rselect_seq(q20) = rselect_seq(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(monotonicity,[status(thm)],[2121]) ).
tff(2123,plain,
rselect_seq(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_seq(q20),
inference(symmetry,[status(thm)],[2122]) ).
tff(2124,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_seq(rstore_seq(q19,earray_85)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2125,plain,
rselect_seq(rstore_tail(rstore_seq(q19,earray_85),s(index_84))) = rselect_seq(rstore_seq(q19,earray_85)),
inference(unit_resolution,[status(thm)],[2124,1484]) ).
tff(2126,plain,
rselect_seq(rstore_seq(q19,earray_85)) = rselect_seq(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(symmetry,[status(thm)],[2125]) ).
tff(2127,plain,
rselect_seq(rstore_seq(q19,earray_85)) = rselect_seq(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))),
inference(monotonicity,[status(thm)],[483]) ).
tff(2128,plain,
rselect_seq(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = rselect_seq(rstore_seq(q19,earray_85)),
inference(symmetry,[status(thm)],[2127]) ).
tff(2129,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = store(earray_83,index_84,e19) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2130,plain,
rselect_seq(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))) = store(earray_83,index_84,e19),
inference(unit_resolution,[status(thm)],[2129,1496]) ).
tff(2131,plain,
store(earray_83,index_84,e19) = rselect_seq(rstore_seq(rstore_tail(queue_74,index_75),store(earray_83,index_84,e19))),
inference(symmetry,[status(thm)],[2130]) ).
tff(2132,plain,
store(earray_83,index_84,e19) = earray_89,
inference(transitivity,[status(thm)],[2131,2128,2126,2123,2120]) ).
tff(2133,plain,
store(store(earray_83,index_84,e19),rselect_tail(q20),e20) = store(earray_89,index_90,e20),
inference(monotonicity,[status(thm)],[2132,1610]) ).
tff(2134,plain,
select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_tail(q10)) = select(store(earray_89,index_90,e20),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2133]) ).
tff(2135,plain,
s(index_84) = s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))),
inference(symmetry,[status(thm)],[1722]) ).
tff(2136,plain,
rselect_tail(q20) = rselect_tail(rstore_tail(rstore_seq(q19,earray_85),s(index_84))),
inference(symmetry,[status(thm)],[1612]) ).
tff(2137,plain,
rselect_tail(q20) = s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))),
inference(transitivity,[status(thm)],[2136,1614,2135]) ).
tff(2138,plain,
( ( rselect_tail(q20) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2137]) ).
tff(2139,plain,
( ( s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q20) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2138]) ).
tff(2140,plain,
( ( s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q20) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2139]) ).
tff(2141,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2142,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ) ),
inference(quant_intro,[status(thm)],[2141]) ).
tff(2143,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2144,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as10) ).
tff(2145,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(modus_ponens,[status(thm)],[2144,2143]) ).
tff(2146,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(skolemize,[status(sab)],[2145]) ).
tff(2147,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X ),
inference(modus_ponens,[status(thm)],[2146,2142]) ).
tff(2148,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(s(X)))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2149,plain,
s(s(s(s(s(s(s(s(s(s(rselect_tail(q10))))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2148,2147]) ).
tff(2150,plain,
rselect_tail(q20) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2149,2140]) ).
tff(2151,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q20) = rselect_tail(q10) )
| ( select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_tail(q10)) = select(store(earray_83,index_84,e19),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q20) = rselect_tail(q10) )
| ( select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_tail(q10)) = select(store(earray_83,index_84,e19),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2152,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q20) = rselect_tail(q10) )
| ( select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_tail(q10)) = select(store(earray_83,index_84,e19),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2153,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q20) = rselect_tail(q10) )
| ( select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_tail(q10)) = select(store(earray_83,index_84,e19),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2152,2151]) ).
tff(2154,plain,
( ( rselect_tail(q20) = rselect_tail(q10) )
| ( select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_tail(q10)) = select(store(earray_83,index_84,e19),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2153,1766]) ).
tff(2155,plain,
select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_tail(q10)) = select(store(earray_83,index_84,e19),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2154,2150]) ).
tff(2156,plain,
select(store(earray_83,index_84,e19),rselect_tail(q10)) = select(store(store(earray_83,index_84,e19),rselect_tail(q20),e20),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2155]) ).
tff(2157,plain,
( ( earray_83 = rselect_seq(q19) )
<=> ( earray_83 = rselect_seq(q19) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2158,axiom,
earray_83 = rselect_seq(q19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp56) ).
tff(2159,plain,
earray_83 = rselect_seq(q19),
inference(modus_ponens,[status(thm)],[2158,2157]) ).
tff(2160,plain,
rselect_seq(q19) = earray_83,
inference(symmetry,[status(thm)],[2159]) ).
tff(2161,plain,
q19 = rstore_tail(rstore_seq(q18,earray_73),s(index_72)),
inference(transitivity,[status(thm)],[475,479,498]) ).
tff(2162,plain,
rselect_seq(q19) = rselect_seq(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(monotonicity,[status(thm)],[2161]) ).
tff(2163,plain,
rselect_seq(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_seq(q19),
inference(symmetry,[status(thm)],[2162]) ).
tff(2164,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_seq(rstore_seq(q18,earray_73)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2165,plain,
rselect_seq(rstore_tail(rstore_seq(q18,earray_73),s(index_72))) = rselect_seq(rstore_seq(q18,earray_73)),
inference(unit_resolution,[status(thm)],[2164,1484]) ).
tff(2166,plain,
rselect_seq(rstore_seq(q18,earray_73)) = rselect_seq(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(symmetry,[status(thm)],[2165]) ).
tff(2167,plain,
rstore_seq(q18,earray_73) = rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18)),
inference(symmetry,[status(thm)],[517]) ).
tff(2168,plain,
rselect_seq(rstore_seq(q18,earray_73)) = rselect_seq(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))),
inference(monotonicity,[status(thm)],[2167]) ).
tff(2169,plain,
rselect_seq(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = rselect_seq(rstore_seq(q18,earray_73)),
inference(symmetry,[status(thm)],[2168]) ).
tff(2170,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = store(earray_71,index_72,e18) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2171,plain,
rselect_seq(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))) = store(earray_71,index_72,e18),
inference(unit_resolution,[status(thm)],[2170,1496]) ).
tff(2172,plain,
store(earray_71,index_72,e18) = rselect_seq(rstore_seq(rstore_head(queue_67,index_69),store(earray_71,index_72,e18))),
inference(symmetry,[status(thm)],[2171]) ).
tff(2173,plain,
store(earray_71,index_72,e18) = earray_83,
inference(transitivity,[status(thm)],[2172,2169,2166,2163,2160]) ).
tff(2174,plain,
store(store(earray_71,index_72,e18),rselect_tail(q19),e19) = store(earray_83,index_84,e19),
inference(monotonicity,[status(thm)],[2173,1619]) ).
tff(2175,plain,
select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_tail(q10)) = select(store(earray_83,index_84,e19),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2174]) ).
tff(2176,plain,
s(index_72) = s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))),
inference(symmetry,[status(thm)],[1720]) ).
tff(2177,plain,
rselect_tail(q19) = rselect_tail(rstore_tail(rstore_seq(q18,earray_73),s(index_72))),
inference(symmetry,[status(thm)],[1621]) ).
tff(2178,plain,
rselect_tail(q19) = s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))),
inference(transitivity,[status(thm)],[2177,1623,2176]) ).
tff(2179,plain,
( ( rselect_tail(q19) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2178]) ).
tff(2180,plain,
( ( s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q19) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2179]) ).
tff(2181,plain,
( ( s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q19) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2180]) ).
tff(2182,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(s(X))))))))) != X )
<=> ( s(s(s(s(s(s(s(s(s(X))))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2183,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ) ),
inference(quant_intro,[status(thm)],[2182]) ).
tff(2184,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2185,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as9) ).
tff(2186,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(modus_ponens,[status(thm)],[2185,2184]) ).
tff(2187,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(skolemize,[status(sab)],[2186]) ).
tff(2188,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X ),
inference(modus_ponens,[status(thm)],[2187,2183]) ).
tff(2189,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(s(X))))))))) != X )
| ( s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2190,plain,
s(s(s(s(s(s(s(s(s(rselect_tail(q10)))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2189,2188]) ).
tff(2191,plain,
rselect_tail(q19) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2190,2181]) ).
tff(2192,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q19) = rselect_tail(q10) )
| ( select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_tail(q10)) = select(store(earray_71,index_72,e18),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q19) = rselect_tail(q10) )
| ( select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_tail(q10)) = select(store(earray_71,index_72,e18),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2193,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q19) = rselect_tail(q10) )
| ( select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_tail(q10)) = select(store(earray_71,index_72,e18),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2194,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q19) = rselect_tail(q10) )
| ( select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_tail(q10)) = select(store(earray_71,index_72,e18),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2193,2192]) ).
tff(2195,plain,
( ( rselect_tail(q19) = rselect_tail(q10) )
| ( select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_tail(q10)) = select(store(earray_71,index_72,e18),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2194,1766]) ).
tff(2196,plain,
select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_tail(q10)) = select(store(earray_71,index_72,e18),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2195,2191]) ).
tff(2197,plain,
select(store(earray_71,index_72,e18),rselect_tail(q10)) = select(store(store(earray_71,index_72,e18),rselect_tail(q19),e19),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2196]) ).
tff(2198,plain,
( ( earray_71 = rselect_seq(q18) )
<=> ( earray_71 = rselect_seq(q18) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2199,axiom,
earray_71 = rselect_seq(q18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp51) ).
tff(2200,plain,
earray_71 = rselect_seq(q18),
inference(modus_ponens,[status(thm)],[2199,2198]) ).
tff(2201,plain,
rselect_seq(q18) = earray_71,
inference(symmetry,[status(thm)],[2200]) ).
tff(2202,plain,
rstore_head(queue_67,index_69) = rstore_head(rstore_tail(queue_65,index_66),s(index_68)),
inference(symmetry,[status(thm)],[530]) ).
tff(2203,plain,
q18 = rstore_head(rstore_tail(queue_65,index_66),s(index_68)),
inference(transitivity,[status(thm)],[510,514,2202]) ).
tff(2204,plain,
rselect_seq(q18) = rselect_seq(rstore_head(rstore_tail(queue_65,index_66),s(index_68))),
inference(monotonicity,[status(thm)],[2203]) ).
tff(2205,plain,
rselect_seq(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_seq(q18),
inference(symmetry,[status(thm)],[2204]) ).
tff(2206,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_seq(rstore_tail(queue_65,index_66)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2207,plain,
rselect_seq(rstore_head(rstore_tail(queue_65,index_66),s(index_68))) = rselect_seq(rstore_tail(queue_65,index_66)),
inference(unit_resolution,[status(thm)],[2206,1472]) ).
tff(2208,plain,
rselect_seq(rstore_tail(queue_65,index_66)) = rselect_seq(rstore_head(rstore_tail(queue_65,index_66),s(index_68))),
inference(symmetry,[status(thm)],[2207]) ).
tff(2209,plain,
rselect_seq(rstore_tail(queue_65,index_66)) = rselect_seq(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(monotonicity,[status(thm)],[552]) ).
tff(2210,plain,
rselect_seq(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_seq(rstore_tail(queue_65,index_66)),
inference(symmetry,[status(thm)],[2209]) ).
tff(2211,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_seq(rstore_seq(q17,earray_64)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2212,plain,
rselect_seq(rstore_tail(rstore_seq(q17,earray_64),s(index_63))) = rselect_seq(rstore_seq(q17,earray_64)),
inference(unit_resolution,[status(thm)],[2211,1484]) ).
tff(2213,plain,
rselect_seq(rstore_seq(q17,earray_64)) = rselect_seq(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(symmetry,[status(thm)],[2212]) ).
tff(2214,plain,
rselect_seq(rstore_seq(q17,earray_64)) = rselect_seq(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))),
inference(monotonicity,[status(thm)],[573]) ).
tff(2215,plain,
rselect_seq(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = rselect_seq(rstore_seq(q17,earray_64)),
inference(symmetry,[status(thm)],[2214]) ).
tff(2216,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = store(earray_62,index_63,e17) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2217,plain,
rselect_seq(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))) = store(earray_62,index_63,e17),
inference(unit_resolution,[status(thm)],[2216,1496]) ).
tff(2218,plain,
store(earray_62,index_63,e17) = rselect_seq(rstore_seq(rstore_tail(queue_59,index_60),store(earray_62,index_63,e17))),
inference(symmetry,[status(thm)],[2217]) ).
tff(2219,plain,
store(earray_62,index_63,e17) = earray_71,
inference(transitivity,[status(thm)],[2218,2215,2213,2210,2208,2205,2201]) ).
tff(2220,plain,
store(store(earray_62,index_63,e17),rselect_tail(q18),e18) = store(earray_71,index_72,e18),
inference(monotonicity,[status(thm)],[2219,1628]) ).
tff(2221,plain,
select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_tail(q10)) = select(store(earray_71,index_72,e18),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2220]) ).
tff(2222,plain,
s(index_63) = s(s(s(s(s(s(s(s(rselect_tail(q10))))))))),
inference(symmetry,[status(thm)],[1718]) ).
tff(2223,plain,
rselect_tail(rstore_tail(queue_65,index_66)) = rselect_tail(rstore_tail(rstore_seq(q17,earray_64),s(index_63))),
inference(symmetry,[status(thm)],[1634]) ).
tff(2224,plain,
rselect_tail(q18) = rselect_tail(rstore_head(rstore_tail(queue_65,index_66),s(index_68))),
inference(symmetry,[status(thm)],[1630]) ).
tff(2225,plain,
rselect_tail(q18) = s(s(s(s(s(s(s(s(rselect_tail(q10))))))))),
inference(transitivity,[status(thm)],[2224,1632,2223,1636,2222]) ).
tff(2226,plain,
( ( rselect_tail(q18) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(s(rselect_tail(q10))))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2225]) ).
tff(2227,plain,
( ( s(s(s(s(s(s(s(s(rselect_tail(q10))))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q18) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2226]) ).
tff(2228,plain,
( ( s(s(s(s(s(s(s(s(rselect_tail(q10))))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q18) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2227]) ).
tff(2229,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(s(X)))))))) != X )
<=> ( s(s(s(s(s(s(s(s(X)))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2230,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ) ),
inference(quant_intro,[status(thm)],[2229]) ).
tff(2231,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2232,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as8) ).
tff(2233,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(modus_ponens,[status(thm)],[2232,2231]) ).
tff(2234,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(skolemize,[status(sab)],[2233]) ).
tff(2235,plain,
! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X ),
inference(modus_ponens,[status(thm)],[2234,2230]) ).
tff(2236,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(s(X)))))))) != X )
| ( s(s(s(s(s(s(s(s(rselect_tail(q10))))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2237,plain,
s(s(s(s(s(s(s(s(rselect_tail(q10))))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2236,2235]) ).
tff(2238,plain,
rselect_tail(q18) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2237,2228]) ).
tff(2239,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q18) = rselect_tail(q10) )
| ( select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_tail(q10)) = select(store(earray_62,index_63,e17),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q18) = rselect_tail(q10) )
| ( select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_tail(q10)) = select(store(earray_62,index_63,e17),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2240,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q18) = rselect_tail(q10) )
| ( select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_tail(q10)) = select(store(earray_62,index_63,e17),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2241,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q18) = rselect_tail(q10) )
| ( select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_tail(q10)) = select(store(earray_62,index_63,e17),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2240,2239]) ).
tff(2242,plain,
( ( rselect_tail(q18) = rselect_tail(q10) )
| ( select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_tail(q10)) = select(store(earray_62,index_63,e17),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2241,1766]) ).
tff(2243,plain,
select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_tail(q10)) = select(store(earray_62,index_63,e17),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2242,2238]) ).
tff(2244,plain,
select(store(earray_62,index_63,e17),rselect_tail(q10)) = select(store(store(earray_62,index_63,e17),rselect_tail(q18),e18),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2243]) ).
tff(2245,plain,
( ( earray_62 = rselect_seq(q17) )
<=> ( earray_62 = rselect_seq(q17) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2246,axiom,
earray_62 = rselect_seq(q17),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp49) ).
tff(2247,plain,
earray_62 = rselect_seq(q17),
inference(modus_ponens,[status(thm)],[2246,2245]) ).
tff(2248,plain,
rselect_seq(q17) = earray_62,
inference(symmetry,[status(thm)],[2247]) ).
tff(2249,plain,
q17 = rstore_tail(rstore_seq(q16,earray_58),s(index_57)),
inference(transitivity,[status(thm)],[565,569,588]) ).
tff(2250,plain,
rselect_seq(q17) = rselect_seq(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(monotonicity,[status(thm)],[2249]) ).
tff(2251,plain,
rselect_seq(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_seq(q17),
inference(symmetry,[status(thm)],[2250]) ).
tff(2252,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_seq(rstore_seq(q16,earray_58)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2253,plain,
rselect_seq(rstore_tail(rstore_seq(q16,earray_58),s(index_57))) = rselect_seq(rstore_seq(q16,earray_58)),
inference(unit_resolution,[status(thm)],[2252,1484]) ).
tff(2254,plain,
rselect_seq(rstore_seq(q16,earray_58)) = rselect_seq(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(symmetry,[status(thm)],[2253]) ).
tff(2255,plain,
rselect_seq(rstore_seq(q16,earray_58)) = rselect_seq(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))),
inference(monotonicity,[status(thm)],[608]) ).
tff(2256,plain,
rselect_seq(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = rselect_seq(rstore_seq(q16,earray_58)),
inference(symmetry,[status(thm)],[2255]) ).
tff(2257,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = store(earray_56,index_57,e16) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2258,plain,
rselect_seq(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))) = store(earray_56,index_57,e16),
inference(unit_resolution,[status(thm)],[2257,1496]) ).
tff(2259,plain,
store(earray_56,index_57,e16) = rselect_seq(rstore_seq(rstore_tail(queue_53,index_54),store(earray_56,index_57,e16))),
inference(symmetry,[status(thm)],[2258]) ).
tff(2260,plain,
store(earray_56,index_57,e16) = earray_62,
inference(transitivity,[status(thm)],[2259,2256,2254,2251,2248]) ).
tff(2261,plain,
store(store(earray_56,index_57,e16),rselect_tail(q17),e17) = store(earray_62,index_63,e17),
inference(monotonicity,[status(thm)],[2260,1641]) ).
tff(2262,plain,
select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_tail(q10)) = select(store(earray_62,index_63,e17),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2261]) ).
tff(2263,plain,
s(index_57) = s(s(s(s(s(s(s(rselect_tail(q10)))))))),
inference(symmetry,[status(thm)],[1716]) ).
tff(2264,plain,
rselect_tail(q17) = rselect_tail(rstore_tail(rstore_seq(q16,earray_58),s(index_57))),
inference(symmetry,[status(thm)],[1643]) ).
tff(2265,plain,
rselect_tail(q17) = s(s(s(s(s(s(s(rselect_tail(q10)))))))),
inference(transitivity,[status(thm)],[2264,1645,2263]) ).
tff(2266,plain,
( ( rselect_tail(q17) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(s(rselect_tail(q10)))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2265]) ).
tff(2267,plain,
( ( s(s(s(s(s(s(s(rselect_tail(q10)))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q17) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2266]) ).
tff(2268,plain,
( ( s(s(s(s(s(s(s(rselect_tail(q10)))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q17) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2267]) ).
tff(2269,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(s(X))))))) != X )
<=> ( s(s(s(s(s(s(s(X))))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2270,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ) ),
inference(quant_intro,[status(thm)],[2269]) ).
tff(2271,plain,
( ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2272,axiom,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as7) ).
tff(2273,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(modus_ponens,[status(thm)],[2272,2271]) ).
tff(2274,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(skolemize,[status(sab)],[2273]) ).
tff(2275,plain,
! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X ),
inference(modus_ponens,[status(thm)],[2274,2270]) ).
tff(2276,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(s(X))))))) != X )
| ( s(s(s(s(s(s(s(rselect_tail(q10)))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2277,plain,
s(s(s(s(s(s(s(rselect_tail(q10)))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2276,2275]) ).
tff(2278,plain,
rselect_tail(q17) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2277,2268]) ).
tff(2279,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q17) = rselect_tail(q10) )
| ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_tail(q10)) = select(store(earray_56,index_57,e16),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q17) = rselect_tail(q10) )
| ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_tail(q10)) = select(store(earray_56,index_57,e16),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2280,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q17) = rselect_tail(q10) )
| ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_tail(q10)) = select(store(earray_56,index_57,e16),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2281,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q17) = rselect_tail(q10) )
| ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_tail(q10)) = select(store(earray_56,index_57,e16),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2280,2279]) ).
tff(2282,plain,
( ( rselect_tail(q17) = rselect_tail(q10) )
| ( select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_tail(q10)) = select(store(earray_56,index_57,e16),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2281,1766]) ).
tff(2283,plain,
select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_tail(q10)) = select(store(earray_56,index_57,e16),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2282,2278]) ).
tff(2284,plain,
select(store(earray_56,index_57,e16),rselect_tail(q10)) = select(store(store(earray_56,index_57,e16),rselect_tail(q17),e17),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2283]) ).
tff(2285,plain,
( ( earray_56 = rselect_seq(q16) )
<=> ( earray_56 = rselect_seq(q16) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2286,axiom,
earray_56 = rselect_seq(q16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp47) ).
tff(2287,plain,
earray_56 = rselect_seq(q16),
inference(modus_ponens,[status(thm)],[2286,2285]) ).
tff(2288,plain,
rselect_seq(q16) = earray_56,
inference(symmetry,[status(thm)],[2287]) ).
tff(2289,plain,
q16 = rstore_tail(rstore_seq(q15,earray_52),s(index_51)),
inference(transitivity,[status(thm)],[600,604,623]) ).
tff(2290,plain,
rselect_seq(q16) = rselect_seq(rstore_tail(rstore_seq(q15,earray_52),s(index_51))),
inference(monotonicity,[status(thm)],[2289]) ).
tff(2291,plain,
rselect_seq(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = rselect_seq(q16),
inference(symmetry,[status(thm)],[2290]) ).
tff(2292,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = rselect_seq(rstore_seq(q15,earray_52)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2293,plain,
rselect_seq(rstore_tail(rstore_seq(q15,earray_52),s(index_51))) = rselect_seq(rstore_seq(q15,earray_52)),
inference(unit_resolution,[status(thm)],[2292,1484]) ).
tff(2294,plain,
rselect_seq(rstore_seq(q15,earray_52)) = rselect_seq(rstore_tail(rstore_seq(q15,earray_52),s(index_51))),
inference(symmetry,[status(thm)],[2293]) ).
tff(2295,plain,
rstore_seq(q15,earray_52) = rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15)),
inference(symmetry,[status(thm)],[642]) ).
tff(2296,plain,
rselect_seq(rstore_seq(q15,earray_52)) = rselect_seq(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))),
inference(monotonicity,[status(thm)],[2295]) ).
tff(2297,plain,
rselect_seq(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))) = rselect_seq(rstore_seq(q15,earray_52)),
inference(symmetry,[status(thm)],[2296]) ).
tff(2298,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))) = store(earray_50,index_51,e15) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2299,plain,
rselect_seq(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))) = store(earray_50,index_51,e15),
inference(unit_resolution,[status(thm)],[2298,1496]) ).
tff(2300,plain,
store(earray_50,index_51,e15) = rselect_seq(rstore_seq(rstore_head(queue_46,index_48),store(earray_50,index_51,e15))),
inference(symmetry,[status(thm)],[2299]) ).
tff(2301,plain,
store(earray_50,index_51,e15) = earray_56,
inference(transitivity,[status(thm)],[2300,2297,2294,2291,2288]) ).
tff(2302,plain,
store(store(earray_50,index_51,e15),rselect_tail(q16),e16) = store(earray_56,index_57,e16),
inference(monotonicity,[status(thm)],[2301,1650]) ).
tff(2303,plain,
select(store(store(earray_50,index_51,e15),rselect_tail(q16),e16),rselect_tail(q10)) = select(store(earray_56,index_57,e16),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2302]) ).
tff(2304,plain,
s(index_51) = s(s(s(s(s(s(rselect_tail(q10))))))),
inference(symmetry,[status(thm)],[1714]) ).
tff(2305,plain,
rselect_tail(q16) = rselect_tail(rstore_tail(rstore_seq(q15,earray_52),s(index_51))),
inference(symmetry,[status(thm)],[1652]) ).
tff(2306,plain,
rselect_tail(q16) = s(s(s(s(s(s(rselect_tail(q10))))))),
inference(transitivity,[status(thm)],[2305,1654,2304]) ).
tff(2307,plain,
( ( rselect_tail(q16) = rselect_tail(q10) )
<=> ( s(s(s(s(s(s(rselect_tail(q10))))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2306]) ).
tff(2308,plain,
( ( s(s(s(s(s(s(rselect_tail(q10))))))) = rselect_tail(q10) )
<=> ( rselect_tail(q16) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2307]) ).
tff(2309,plain,
( ( s(s(s(s(s(s(rselect_tail(q10))))))) != rselect_tail(q10) )
<=> ( rselect_tail(q16) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2308]) ).
tff(2310,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(s(X)))))) != X )
<=> ( s(s(s(s(s(s(X)))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2311,plain,
( ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ) ),
inference(quant_intro,[status(thm)],[2310]) ).
tff(2312,plain,
( ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2313,axiom,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as6) ).
tff(2314,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(modus_ponens,[status(thm)],[2313,2312]) ).
tff(2315,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(skolemize,[status(sab)],[2314]) ).
tff(2316,plain,
! [X: $i] : ( s(s(s(s(s(s(X)))))) != X ),
inference(modus_ponens,[status(thm)],[2315,2311]) ).
tff(2317,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(s(X)))))) != X )
| ( s(s(s(s(s(s(rselect_tail(q10))))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2318,plain,
s(s(s(s(s(s(rselect_tail(q10))))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2317,2316]) ).
tff(2319,plain,
rselect_tail(q16) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2318,2309]) ).
tff(2320,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q16) = rselect_tail(q10) )
| ( select(store(store(earray_50,index_51,e15),rselect_tail(q16),e16),rselect_tail(q10)) = select(store(earray_50,index_51,e15),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q16) = rselect_tail(q10) )
| ( select(store(store(earray_50,index_51,e15),rselect_tail(q16),e16),rselect_tail(q10)) = select(store(earray_50,index_51,e15),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2321,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q16) = rselect_tail(q10) )
| ( select(store(store(earray_50,index_51,e15),rselect_tail(q16),e16),rselect_tail(q10)) = select(store(earray_50,index_51,e15),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2322,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q16) = rselect_tail(q10) )
| ( select(store(store(earray_50,index_51,e15),rselect_tail(q16),e16),rselect_tail(q10)) = select(store(earray_50,index_51,e15),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2321,2320]) ).
tff(2323,plain,
( ( rselect_tail(q16) = rselect_tail(q10) )
| ( select(store(store(earray_50,index_51,e15),rselect_tail(q16),e16),rselect_tail(q10)) = select(store(earray_50,index_51,e15),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2322,1766]) ).
tff(2324,plain,
select(store(store(earray_50,index_51,e15),rselect_tail(q16),e16),rselect_tail(q10)) = select(store(earray_50,index_51,e15),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2323,2319]) ).
tff(2325,plain,
select(store(earray_50,index_51,e15),rselect_tail(q10)) = select(store(store(earray_50,index_51,e15),rselect_tail(q16),e16),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2324]) ).
tff(2326,plain,
( ( earray_50 = rselect_seq(q15) )
<=> ( earray_50 = rselect_seq(q15) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2327,axiom,
earray_50 = rselect_seq(q15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp45) ).
tff(2328,plain,
earray_50 = rselect_seq(q15),
inference(modus_ponens,[status(thm)],[2327,2326]) ).
tff(2329,plain,
rselect_seq(q15) = earray_50,
inference(symmetry,[status(thm)],[2328]) ).
tff(2330,plain,
rstore_head(queue_46,index_48) = rstore_head(rstore_tail(queue_44,index_45),s(index_47)),
inference(symmetry,[status(thm)],[655]) ).
tff(2331,plain,
q15 = rstore_head(rstore_tail(queue_44,index_45),s(index_47)),
inference(transitivity,[status(thm)],[635,639,2330]) ).
tff(2332,plain,
rselect_seq(q15) = rselect_seq(rstore_head(rstore_tail(queue_44,index_45),s(index_47))),
inference(monotonicity,[status(thm)],[2331]) ).
tff(2333,plain,
rselect_seq(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = rselect_seq(q15),
inference(symmetry,[status(thm)],[2332]) ).
tff(2334,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = rselect_seq(rstore_tail(queue_44,index_45)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2335,plain,
rselect_seq(rstore_head(rstore_tail(queue_44,index_45),s(index_47))) = rselect_seq(rstore_tail(queue_44,index_45)),
inference(unit_resolution,[status(thm)],[2334,1472]) ).
tff(2336,plain,
rselect_seq(rstore_tail(queue_44,index_45)) = rselect_seq(rstore_head(rstore_tail(queue_44,index_45),s(index_47))),
inference(symmetry,[status(thm)],[2335]) ).
tff(2337,plain,
rselect_seq(rstore_tail(queue_44,index_45)) = rselect_seq(rstore_tail(rstore_seq(q14,earray_43),s(index_42))),
inference(monotonicity,[status(thm)],[677]) ).
tff(2338,plain,
rselect_seq(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = rselect_seq(rstore_tail(queue_44,index_45)),
inference(symmetry,[status(thm)],[2337]) ).
tff(2339,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = rselect_seq(rstore_seq(q14,earray_43)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2340,plain,
rselect_seq(rstore_tail(rstore_seq(q14,earray_43),s(index_42))) = rselect_seq(rstore_seq(q14,earray_43)),
inference(unit_resolution,[status(thm)],[2339,1484]) ).
tff(2341,plain,
rselect_seq(rstore_seq(q14,earray_43)) = rselect_seq(rstore_tail(rstore_seq(q14,earray_43),s(index_42))),
inference(symmetry,[status(thm)],[2340]) ).
tff(2342,plain,
rselect_seq(rstore_seq(q14,earray_43)) = rselect_seq(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))),
inference(monotonicity,[status(thm)],[698]) ).
tff(2343,plain,
rselect_seq(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))) = rselect_seq(rstore_seq(q14,earray_43)),
inference(symmetry,[status(thm)],[2342]) ).
tff(2344,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))) = store(earray_41,index_42,e14) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2345,plain,
rselect_seq(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))) = store(earray_41,index_42,e14),
inference(unit_resolution,[status(thm)],[2344,1496]) ).
tff(2346,plain,
store(earray_41,index_42,e14) = rselect_seq(rstore_seq(rstore_tail(queue_38,index_39),store(earray_41,index_42,e14))),
inference(symmetry,[status(thm)],[2345]) ).
tff(2347,plain,
store(earray_41,index_42,e14) = earray_50,
inference(transitivity,[status(thm)],[2346,2343,2341,2338,2336,2333,2329]) ).
tff(2348,plain,
store(store(earray_41,index_42,e14),rselect_tail(q15),e15) = store(earray_50,index_51,e15),
inference(monotonicity,[status(thm)],[2347,1659]) ).
tff(2349,plain,
select(store(store(earray_41,index_42,e14),rselect_tail(q15),e15),rselect_tail(q10)) = select(store(earray_50,index_51,e15),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2348]) ).
tff(2350,plain,
s(index_42) = s(s(s(s(s(rselect_tail(q10)))))),
inference(symmetry,[status(thm)],[1712]) ).
tff(2351,plain,
rselect_tail(rstore_tail(queue_44,index_45)) = rselect_tail(rstore_tail(rstore_seq(q14,earray_43),s(index_42))),
inference(symmetry,[status(thm)],[1665]) ).
tff(2352,plain,
rselect_tail(q15) = rselect_tail(rstore_head(rstore_tail(queue_44,index_45),s(index_47))),
inference(symmetry,[status(thm)],[1661]) ).
tff(2353,plain,
rselect_tail(q15) = s(s(s(s(s(rselect_tail(q10)))))),
inference(transitivity,[status(thm)],[2352,1663,2351,1667,2350]) ).
tff(2354,plain,
( ( rselect_tail(q15) = rselect_tail(q10) )
<=> ( s(s(s(s(s(rselect_tail(q10)))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2353]) ).
tff(2355,plain,
( ( s(s(s(s(s(rselect_tail(q10)))))) = rselect_tail(q10) )
<=> ( rselect_tail(q15) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2354]) ).
tff(2356,plain,
( ( s(s(s(s(s(rselect_tail(q10)))))) != rselect_tail(q10) )
<=> ( rselect_tail(q15) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2355]) ).
tff(2357,plain,
^ [X: $i] :
refl(( ( s(s(s(s(s(X))))) != X )
<=> ( s(s(s(s(s(X))))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2358,plain,
( ! [X: $i] : ( s(s(s(s(s(X))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(X))))) != X ) ),
inference(quant_intro,[status(thm)],[2357]) ).
tff(2359,plain,
( ! [X: $i] : ( s(s(s(s(s(X))))) != X )
<=> ! [X: $i] : ( s(s(s(s(s(X))))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2360,axiom,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as5) ).
tff(2361,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(modus_ponens,[status(thm)],[2360,2359]) ).
tff(2362,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(skolemize,[status(sab)],[2361]) ).
tff(2363,plain,
! [X: $i] : ( s(s(s(s(s(X))))) != X ),
inference(modus_ponens,[status(thm)],[2362,2358]) ).
tff(2364,plain,
( ~ ! [X: $i] : ( s(s(s(s(s(X))))) != X )
| ( s(s(s(s(s(rselect_tail(q10)))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2365,plain,
s(s(s(s(s(rselect_tail(q10)))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2364,2363]) ).
tff(2366,plain,
rselect_tail(q15) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2365,2356]) ).
tff(2367,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q15) = rselect_tail(q10) )
| ( select(store(store(earray_41,index_42,e14),rselect_tail(q15),e15),rselect_tail(q10)) = select(store(earray_41,index_42,e14),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q15) = rselect_tail(q10) )
| ( select(store(store(earray_41,index_42,e14),rselect_tail(q15),e15),rselect_tail(q10)) = select(store(earray_41,index_42,e14),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2368,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q15) = rselect_tail(q10) )
| ( select(store(store(earray_41,index_42,e14),rselect_tail(q15),e15),rselect_tail(q10)) = select(store(earray_41,index_42,e14),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2369,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q15) = rselect_tail(q10) )
| ( select(store(store(earray_41,index_42,e14),rselect_tail(q15),e15),rselect_tail(q10)) = select(store(earray_41,index_42,e14),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2368,2367]) ).
tff(2370,plain,
( ( rselect_tail(q15) = rselect_tail(q10) )
| ( select(store(store(earray_41,index_42,e14),rselect_tail(q15),e15),rselect_tail(q10)) = select(store(earray_41,index_42,e14),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2369,1766]) ).
tff(2371,plain,
select(store(store(earray_41,index_42,e14),rselect_tail(q15),e15),rselect_tail(q10)) = select(store(earray_41,index_42,e14),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2370,2366]) ).
tff(2372,plain,
select(store(earray_41,index_42,e14),rselect_tail(q10)) = select(store(store(earray_41,index_42,e14),rselect_tail(q15),e15),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2371]) ).
tff(2373,plain,
( ( earray_41 = rselect_seq(q14) )
<=> ( earray_41 = rselect_seq(q14) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2374,axiom,
earray_41 = rselect_seq(q14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp43) ).
tff(2375,plain,
earray_41 = rselect_seq(q14),
inference(modus_ponens,[status(thm)],[2374,2373]) ).
tff(2376,plain,
rselect_seq(q14) = earray_41,
inference(symmetry,[status(thm)],[2375]) ).
tff(2377,plain,
q14 = rstore_tail(rstore_seq(q13,earray_37),s(index_36)),
inference(transitivity,[status(thm)],[690,694,713]) ).
tff(2378,plain,
rselect_seq(q14) = rselect_seq(rstore_tail(rstore_seq(q13,earray_37),s(index_36))),
inference(monotonicity,[status(thm)],[2377]) ).
tff(2379,plain,
rselect_seq(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = rselect_seq(q14),
inference(symmetry,[status(thm)],[2378]) ).
tff(2380,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = rselect_seq(rstore_seq(q13,earray_37)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2381,plain,
rselect_seq(rstore_tail(rstore_seq(q13,earray_37),s(index_36))) = rselect_seq(rstore_seq(q13,earray_37)),
inference(unit_resolution,[status(thm)],[2380,1484]) ).
tff(2382,plain,
rselect_seq(rstore_seq(q13,earray_37)) = rselect_seq(rstore_tail(rstore_seq(q13,earray_37),s(index_36))),
inference(symmetry,[status(thm)],[2381]) ).
tff(2383,plain,
rselect_seq(rstore_seq(q13,earray_37)) = rselect_seq(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))),
inference(monotonicity,[status(thm)],[733]) ).
tff(2384,plain,
rselect_seq(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))) = rselect_seq(rstore_seq(q13,earray_37)),
inference(symmetry,[status(thm)],[2383]) ).
tff(2385,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))) = store(earray_35,index_36,e13) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2386,plain,
rselect_seq(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))) = store(earray_35,index_36,e13),
inference(unit_resolution,[status(thm)],[2385,1496]) ).
tff(2387,plain,
store(earray_35,index_36,e13) = rselect_seq(rstore_seq(rstore_tail(queue_32,index_33),store(earray_35,index_36,e13))),
inference(symmetry,[status(thm)],[2386]) ).
tff(2388,plain,
store(earray_35,index_36,e13) = earray_41,
inference(transitivity,[status(thm)],[2387,2384,2382,2379,2376]) ).
tff(2389,plain,
store(store(earray_35,index_36,e13),rselect_tail(q14),e14) = store(earray_41,index_42,e14),
inference(monotonicity,[status(thm)],[2388,1672]) ).
tff(2390,plain,
select(store(store(earray_35,index_36,e13),rselect_tail(q14),e14),rselect_tail(q10)) = select(store(earray_41,index_42,e14),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2389]) ).
tff(2391,plain,
s(index_36) = s(s(s(s(rselect_tail(q10))))),
inference(symmetry,[status(thm)],[1710]) ).
tff(2392,plain,
rselect_tail(q14) = rselect_tail(rstore_tail(rstore_seq(q13,earray_37),s(index_36))),
inference(symmetry,[status(thm)],[1674]) ).
tff(2393,plain,
rselect_tail(q14) = s(s(s(s(rselect_tail(q10))))),
inference(transitivity,[status(thm)],[2392,1676,2391]) ).
tff(2394,plain,
( ( rselect_tail(q14) = rselect_tail(q10) )
<=> ( s(s(s(s(rselect_tail(q10))))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2393]) ).
tff(2395,plain,
( ( s(s(s(s(rselect_tail(q10))))) = rselect_tail(q10) )
<=> ( rselect_tail(q14) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2394]) ).
tff(2396,plain,
( ( s(s(s(s(rselect_tail(q10))))) != rselect_tail(q10) )
<=> ( rselect_tail(q14) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2395]) ).
tff(2397,plain,
^ [X: $i] :
refl(( ( s(s(s(s(X)))) != X )
<=> ( s(s(s(s(X)))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2398,plain,
( ! [X: $i] : ( s(s(s(s(X)))) != X )
<=> ! [X: $i] : ( s(s(s(s(X)))) != X ) ),
inference(quant_intro,[status(thm)],[2397]) ).
tff(2399,plain,
( ! [X: $i] : ( s(s(s(s(X)))) != X )
<=> ! [X: $i] : ( s(s(s(s(X)))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2400,axiom,
! [X: $i] : ( s(s(s(s(X)))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as4) ).
tff(2401,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(modus_ponens,[status(thm)],[2400,2399]) ).
tff(2402,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(skolemize,[status(sab)],[2401]) ).
tff(2403,plain,
! [X: $i] : ( s(s(s(s(X)))) != X ),
inference(modus_ponens,[status(thm)],[2402,2398]) ).
tff(2404,plain,
( ~ ! [X: $i] : ( s(s(s(s(X)))) != X )
| ( s(s(s(s(rselect_tail(q10))))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2405,plain,
s(s(s(s(rselect_tail(q10))))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2404,2403]) ).
tff(2406,plain,
rselect_tail(q14) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2405,2396]) ).
tff(2407,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q14) = rselect_tail(q10) )
| ( select(store(store(earray_35,index_36,e13),rselect_tail(q14),e14),rselect_tail(q10)) = select(store(earray_35,index_36,e13),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q14) = rselect_tail(q10) )
| ( select(store(store(earray_35,index_36,e13),rselect_tail(q14),e14),rselect_tail(q10)) = select(store(earray_35,index_36,e13),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2408,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q14) = rselect_tail(q10) )
| ( select(store(store(earray_35,index_36,e13),rselect_tail(q14),e14),rselect_tail(q10)) = select(store(earray_35,index_36,e13),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2409,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q14) = rselect_tail(q10) )
| ( select(store(store(earray_35,index_36,e13),rselect_tail(q14),e14),rselect_tail(q10)) = select(store(earray_35,index_36,e13),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2408,2407]) ).
tff(2410,plain,
( ( rselect_tail(q14) = rselect_tail(q10) )
| ( select(store(store(earray_35,index_36,e13),rselect_tail(q14),e14),rselect_tail(q10)) = select(store(earray_35,index_36,e13),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2409,1766]) ).
tff(2411,plain,
select(store(store(earray_35,index_36,e13),rselect_tail(q14),e14),rselect_tail(q10)) = select(store(earray_35,index_36,e13),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2410,2406]) ).
tff(2412,plain,
select(store(earray_35,index_36,e13),rselect_tail(q10)) = select(store(store(earray_35,index_36,e13),rselect_tail(q14),e14),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2411]) ).
tff(2413,plain,
( ( earray_35 = rselect_seq(q13) )
<=> ( earray_35 = rselect_seq(q13) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2414,axiom,
earray_35 = rselect_seq(q13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp40) ).
tff(2415,plain,
earray_35 = rselect_seq(q13),
inference(modus_ponens,[status(thm)],[2414,2413]) ).
tff(2416,plain,
rselect_seq(q13) = earray_35,
inference(symmetry,[status(thm)],[2415]) ).
tff(2417,plain,
q13 = rstore_tail(rstore_seq(q12,earray_31),s(index_30)),
inference(transitivity,[status(thm)],[725,729,748]) ).
tff(2418,plain,
rselect_seq(q13) = rselect_seq(rstore_tail(rstore_seq(q12,earray_31),s(index_30))),
inference(monotonicity,[status(thm)],[2417]) ).
tff(2419,plain,
rselect_seq(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = rselect_seq(q13),
inference(symmetry,[status(thm)],[2418]) ).
tff(2420,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = rselect_seq(rstore_seq(q12,earray_31)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2421,plain,
rselect_seq(rstore_tail(rstore_seq(q12,earray_31),s(index_30))) = rselect_seq(rstore_seq(q12,earray_31)),
inference(unit_resolution,[status(thm)],[2420,1484]) ).
tff(2422,plain,
rselect_seq(rstore_seq(q12,earray_31)) = rselect_seq(rstore_tail(rstore_seq(q12,earray_31),s(index_30))),
inference(symmetry,[status(thm)],[2421]) ).
tff(2423,plain,
rstore_seq(q12,earray_31) = rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12)),
inference(symmetry,[status(thm)],[767]) ).
tff(2424,plain,
rselect_seq(rstore_seq(q12,earray_31)) = rselect_seq(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))),
inference(monotonicity,[status(thm)],[2423]) ).
tff(2425,plain,
rselect_seq(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))) = rselect_seq(rstore_seq(q12,earray_31)),
inference(symmetry,[status(thm)],[2424]) ).
tff(2426,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))) = store(earray_29,index_30,e12) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2427,plain,
rselect_seq(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))) = store(earray_29,index_30,e12),
inference(unit_resolution,[status(thm)],[2426,1496]) ).
tff(2428,plain,
store(earray_29,index_30,e12) = rselect_seq(rstore_seq(rstore_head(queue_25,index_27),store(earray_29,index_30,e12))),
inference(symmetry,[status(thm)],[2427]) ).
tff(2429,plain,
store(earray_29,index_30,e12) = earray_35,
inference(transitivity,[status(thm)],[2428,2425,2422,2419,2416]) ).
tff(2430,plain,
store(store(earray_29,index_30,e12),rselect_tail(q13),e13) = store(earray_35,index_36,e13),
inference(monotonicity,[status(thm)],[2429,1681]) ).
tff(2431,plain,
select(store(store(earray_29,index_30,e12),rselect_tail(q13),e13),rselect_tail(q10)) = select(store(earray_35,index_36,e13),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2430]) ).
tff(2432,plain,
s(index_30) = s(s(s(rselect_tail(q10)))),
inference(symmetry,[status(thm)],[1708]) ).
tff(2433,plain,
rselect_tail(q13) = rselect_tail(rstore_tail(rstore_seq(q12,earray_31),s(index_30))),
inference(symmetry,[status(thm)],[1683]) ).
tff(2434,plain,
rselect_tail(q13) = s(s(s(rselect_tail(q10)))),
inference(transitivity,[status(thm)],[2433,1685,2432]) ).
tff(2435,plain,
( ( rselect_tail(q13) = rselect_tail(q10) )
<=> ( s(s(s(rselect_tail(q10)))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2434]) ).
tff(2436,plain,
( ( s(s(s(rselect_tail(q10)))) = rselect_tail(q10) )
<=> ( rselect_tail(q13) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2435]) ).
tff(2437,plain,
( ( s(s(s(rselect_tail(q10)))) != rselect_tail(q10) )
<=> ( rselect_tail(q13) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2436]) ).
tff(2438,plain,
^ [X: $i] :
refl(( ( s(s(s(X))) != X )
<=> ( s(s(s(X))) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2439,plain,
( ! [X: $i] : ( s(s(s(X))) != X )
<=> ! [X: $i] : ( s(s(s(X))) != X ) ),
inference(quant_intro,[status(thm)],[2438]) ).
tff(2440,plain,
( ! [X: $i] : ( s(s(s(X))) != X )
<=> ! [X: $i] : ( s(s(s(X))) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2441,axiom,
! [X: $i] : ( s(s(s(X))) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as3) ).
tff(2442,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(modus_ponens,[status(thm)],[2441,2440]) ).
tff(2443,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(skolemize,[status(sab)],[2442]) ).
tff(2444,plain,
! [X: $i] : ( s(s(s(X))) != X ),
inference(modus_ponens,[status(thm)],[2443,2439]) ).
tff(2445,plain,
( ~ ! [X: $i] : ( s(s(s(X))) != X )
| ( s(s(s(rselect_tail(q10)))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2446,plain,
s(s(s(rselect_tail(q10)))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2445,2444]) ).
tff(2447,plain,
rselect_tail(q13) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2446,2437]) ).
tff(2448,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q13) = rselect_tail(q10) )
| ( select(store(store(earray_29,index_30,e12),rselect_tail(q13),e13),rselect_tail(q10)) = select(store(earray_29,index_30,e12),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q13) = rselect_tail(q10) )
| ( select(store(store(earray_29,index_30,e12),rselect_tail(q13),e13),rselect_tail(q10)) = select(store(earray_29,index_30,e12),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2449,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q13) = rselect_tail(q10) )
| ( select(store(store(earray_29,index_30,e12),rselect_tail(q13),e13),rselect_tail(q10)) = select(store(earray_29,index_30,e12),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2450,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q13) = rselect_tail(q10) )
| ( select(store(store(earray_29,index_30,e12),rselect_tail(q13),e13),rselect_tail(q10)) = select(store(earray_29,index_30,e12),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2449,2448]) ).
tff(2451,plain,
( ( rselect_tail(q13) = rselect_tail(q10) )
| ( select(store(store(earray_29,index_30,e12),rselect_tail(q13),e13),rselect_tail(q10)) = select(store(earray_29,index_30,e12),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2450,1766]) ).
tff(2452,plain,
select(store(store(earray_29,index_30,e12),rselect_tail(q13),e13),rselect_tail(q10)) = select(store(earray_29,index_30,e12),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2451,2447]) ).
tff(2453,plain,
select(store(earray_29,index_30,e12),rselect_tail(q10)) = select(store(store(earray_29,index_30,e12),rselect_tail(q13),e13),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2452]) ).
tff(2454,plain,
( ( earray_29 = rselect_seq(q12) )
<=> ( earray_29 = rselect_seq(q12) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2455,axiom,
earray_29 = rselect_seq(q12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp38) ).
tff(2456,plain,
earray_29 = rselect_seq(q12),
inference(modus_ponens,[status(thm)],[2455,2454]) ).
tff(2457,plain,
rselect_seq(q12) = earray_29,
inference(symmetry,[status(thm)],[2456]) ).
tff(2458,plain,
rstore_head(queue_25,index_27) = rstore_head(rstore_tail(queue_23,index_24),s(index_26)),
inference(symmetry,[status(thm)],[780]) ).
tff(2459,plain,
q12 = rstore_head(rstore_tail(queue_23,index_24),s(index_26)),
inference(transitivity,[status(thm)],[760,764,2458]) ).
tff(2460,plain,
rselect_seq(q12) = rselect_seq(rstore_head(rstore_tail(queue_23,index_24),s(index_26))),
inference(monotonicity,[status(thm)],[2459]) ).
tff(2461,plain,
rselect_seq(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = rselect_seq(q12),
inference(symmetry,[status(thm)],[2460]) ).
tff(2462,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_head(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = rselect_seq(rstore_tail(queue_23,index_24)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2463,plain,
rselect_seq(rstore_head(rstore_tail(queue_23,index_24),s(index_26))) = rselect_seq(rstore_tail(queue_23,index_24)),
inference(unit_resolution,[status(thm)],[2462,1472]) ).
tff(2464,plain,
rselect_seq(rstore_tail(queue_23,index_24)) = rselect_seq(rstore_head(rstore_tail(queue_23,index_24),s(index_26))),
inference(symmetry,[status(thm)],[2463]) ).
tff(2465,plain,
rselect_seq(rstore_tail(queue_23,index_24)) = rselect_seq(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(monotonicity,[status(thm)],[802]) ).
tff(2466,plain,
rselect_seq(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_seq(rstore_tail(queue_23,index_24)),
inference(symmetry,[status(thm)],[2465]) ).
tff(2467,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_seq(rstore_seq(q11,earray_22)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2468,plain,
rselect_seq(rstore_tail(rstore_seq(q11,earray_22),s(index_21))) = rselect_seq(rstore_seq(q11,earray_22)),
inference(unit_resolution,[status(thm)],[2467,1484]) ).
tff(2469,plain,
rselect_seq(rstore_seq(q11,earray_22)) = rselect_seq(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(symmetry,[status(thm)],[2468]) ).
tff(2470,plain,
rselect_seq(rstore_seq(q11,earray_22)) = rselect_seq(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))),
inference(monotonicity,[status(thm)],[815]) ).
tff(2471,plain,
rselect_seq(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))) = rselect_seq(rstore_seq(q11,earray_22)),
inference(symmetry,[status(thm)],[2470]) ).
tff(2472,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))) = store(earray_20,index_21,e11) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2473,plain,
rselect_seq(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))) = store(earray_20,index_21,e11),
inference(unit_resolution,[status(thm)],[2472,1496]) ).
tff(2474,plain,
store(earray_20,index_21,e11) = rselect_seq(rstore_seq(rstore_tail(queue_17,index_18),store(earray_20,index_21,e11))),
inference(symmetry,[status(thm)],[2473]) ).
tff(2475,plain,
store(earray_20,index_21,e11) = earray_29,
inference(transitivity,[status(thm)],[2474,2471,2469,2466,2464,2461,2457]) ).
tff(2476,plain,
store(store(earray_20,index_21,e11),rselect_tail(q12),e12) = store(earray_29,index_30,e12),
inference(monotonicity,[status(thm)],[2475,1690]) ).
tff(2477,plain,
select(store(store(earray_20,index_21,e11),rselect_tail(q12),e12),rselect_tail(q10)) = select(store(earray_29,index_30,e12),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2476]) ).
tff(2478,plain,
s(index_21) = s(s(rselect_tail(q10))),
inference(symmetry,[status(thm)],[1706]) ).
tff(2479,plain,
rselect_tail(rstore_tail(queue_23,index_24)) = rselect_tail(rstore_tail(rstore_seq(q11,earray_22),s(index_21))),
inference(symmetry,[status(thm)],[1696]) ).
tff(2480,plain,
rselect_tail(q12) = rselect_tail(rstore_head(rstore_tail(queue_23,index_24),s(index_26))),
inference(symmetry,[status(thm)],[1692]) ).
tff(2481,plain,
rselect_tail(q12) = s(s(rselect_tail(q10))),
inference(transitivity,[status(thm)],[2480,1694,2479,1698,2478]) ).
tff(2482,plain,
( ( rselect_tail(q12) = rselect_tail(q10) )
<=> ( s(s(rselect_tail(q10))) = rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2481]) ).
tff(2483,plain,
( ( s(s(rselect_tail(q10))) = rselect_tail(q10) )
<=> ( rselect_tail(q12) = rselect_tail(q10) ) ),
inference(symmetry,[status(thm)],[2482]) ).
tff(2484,plain,
( ( s(s(rselect_tail(q10))) != rselect_tail(q10) )
<=> ( rselect_tail(q12) != rselect_tail(q10) ) ),
inference(monotonicity,[status(thm)],[2483]) ).
tff(2485,plain,
^ [X: $i] :
refl(( ( s(s(X)) != X )
<=> ( s(s(X)) != X ) )),
inference(bind,[status(th)],[]) ).
tff(2486,plain,
( ! [X: $i] : ( s(s(X)) != X )
<=> ! [X: $i] : ( s(s(X)) != X ) ),
inference(quant_intro,[status(thm)],[2485]) ).
tff(2487,plain,
( ! [X: $i] : ( s(s(X)) != X )
<=> ! [X: $i] : ( s(s(X)) != X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2488,axiom,
! [X: $i] : ( s(s(X)) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',as2) ).
tff(2489,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(modus_ponens,[status(thm)],[2488,2487]) ).
tff(2490,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(skolemize,[status(sab)],[2489]) ).
tff(2491,plain,
! [X: $i] : ( s(s(X)) != X ),
inference(modus_ponens,[status(thm)],[2490,2486]) ).
tff(2492,plain,
( ~ ! [X: $i] : ( s(s(X)) != X )
| ( s(s(rselect_tail(q10))) != rselect_tail(q10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2493,plain,
s(s(rselect_tail(q10))) != rselect_tail(q10),
inference(unit_resolution,[status(thm)],[2492,2491]) ).
tff(2494,plain,
rselect_tail(q12) != rselect_tail(q10),
inference(modus_ponens,[status(thm)],[2493,2484]) ).
tff(2495,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q12) = rselect_tail(q10) )
| ( select(store(store(earray_20,index_21,e11),rselect_tail(q12),e12),rselect_tail(q10)) = select(store(earray_20,index_21,e11),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q12) = rselect_tail(q10) )
| ( select(store(store(earray_20,index_21,e11),rselect_tail(q12),e12),rselect_tail(q10)) = select(store(earray_20,index_21,e11),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2496,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q12) = rselect_tail(q10) )
| ( select(store(store(earray_20,index_21,e11),rselect_tail(q12),e12),rselect_tail(q10)) = select(store(earray_20,index_21,e11),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2497,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q12) = rselect_tail(q10) )
| ( select(store(store(earray_20,index_21,e11),rselect_tail(q12),e12),rselect_tail(q10)) = select(store(earray_20,index_21,e11),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2496,2495]) ).
tff(2498,plain,
( ( rselect_tail(q12) = rselect_tail(q10) )
| ( select(store(store(earray_20,index_21,e11),rselect_tail(q12),e12),rselect_tail(q10)) = select(store(earray_20,index_21,e11),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2497,1766]) ).
tff(2499,plain,
select(store(store(earray_20,index_21,e11),rselect_tail(q12),e12),rselect_tail(q10)) = select(store(earray_20,index_21,e11),rselect_tail(q10)),
inference(unit_resolution,[status(thm)],[2498,2494]) ).
tff(2500,plain,
select(store(earray_20,index_21,e11),rselect_tail(q10)) = select(store(store(earray_20,index_21,e11),rselect_tail(q12),e12),rselect_tail(q10)),
inference(symmetry,[status(thm)],[2499]) ).
tff(2501,plain,
( ( earray_20 = rselect_seq(q11) )
<=> ( earray_20 = rselect_seq(q11) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2502,axiom,
earray_20 = rselect_seq(q11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hyp33) ).
tff(2503,plain,
earray_20 = rselect_seq(q11),
inference(modus_ponens,[status(thm)],[2502,2501]) ).
tff(2504,plain,
rselect_seq(q11) = earray_20,
inference(symmetry,[status(thm)],[2503]) ).
tff(2505,plain,
q11 = rstore_tail(rstore_seq(q10,earray_16),s(index_15)),
inference(transitivity,[status(thm)],[18,22,821]) ).
tff(2506,plain,
rselect_seq(q11) = rselect_seq(rstore_tail(rstore_seq(q10,earray_16),s(index_15))),
inference(monotonicity,[status(thm)],[2505]) ).
tff(2507,plain,
rselect_seq(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_seq(q11),
inference(symmetry,[status(thm)],[2506]) ).
tff(2508,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_tail(A,E)) = rselect_seq(A) )
| ( rselect_seq(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_seq(rstore_seq(q10,earray_16)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2509,plain,
rselect_seq(rstore_tail(rstore_seq(q10,earray_16),s(index_15))) = rselect_seq(rstore_seq(q10,earray_16)),
inference(unit_resolution,[status(thm)],[2508,1484]) ).
tff(2510,plain,
rselect_seq(rstore_seq(q10,earray_16)) = rselect_seq(rstore_tail(rstore_seq(q10,earray_16),s(index_15))),
inference(symmetry,[status(thm)],[2509]) ).
tff(2511,plain,
rselect_seq(rstore_seq(q10,earray_16)) = rselect_seq(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))),
inference(monotonicity,[status(thm)],[841]) ).
tff(2512,plain,
rselect_seq(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))) = rselect_seq(rstore_seq(q10,earray_16)),
inference(symmetry,[status(thm)],[2511]) ).
tff(2513,plain,
( ~ ! [E: $i,A: $i] : ( rselect_seq(rstore_seq(A,E)) = E )
| ( rselect_seq(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))) = store(earray_14,index_15,e10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2514,plain,
rselect_seq(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))) = store(earray_14,index_15,e10),
inference(unit_resolution,[status(thm)],[2513,1496]) ).
tff(2515,plain,
store(earray_14,index_15,e10) = rselect_seq(rstore_seq(rstore_tail(queue_11,index_12),store(earray_14,index_15,e10))),
inference(symmetry,[status(thm)],[2514]) ).
tff(2516,plain,
store(earray_14,index_15,e10) = earray_20,
inference(transitivity,[status(thm)],[2515,2512,2510,2507,2504]) ).
tff(2517,plain,
store(store(earray_14,index_15,e10),rselect_tail(q11),e11) = store(earray_20,index_21,e11),
inference(monotonicity,[status(thm)],[2516,1703]) ).
tff(2518,plain,
select(store(store(earray_14,index_15,e10),rselect_tail(q11),e11),rselect_tail(q10)) = select(store(earray_20,index_21,e11),rselect_tail(q10)),
inference(monotonicity,[status(thm)],[2517]) ).
tff(2519,plain,
select(store(store(earray_14,index_15,e10),rselect_tail(q11),e11),rselect_tail(q10)) = elem_214,
inference(transitivity,[status(thm)],[2518,2500,2477,2453,2431,2412,2390,2372,2349,2325,2303,2284,2262,2244,2221,2197,2175,2156,2134,2116,2093,2069,2047,2028,2006,1988,1965,1941,1919,1900,1878,1860,1837,1813,1791,1772,1522,69]) ).
tff(2520,plain,
( ( select(store(store(earray_14,index_15,e10),rselect_tail(q11),e11),rselect_tail(q10)) = select(store(earray_14,index_15,e10),rselect_tail(q10)) )
<=> ( elem_214 = e10 ) ),
inference(monotonicity,[status(thm)],[2519,65]) ).
tff(2521,plain,
( ( elem_214 = e10 )
<=> ( select(store(store(earray_14,index_15,e10),rselect_tail(q11),e11),rselect_tail(q10)) = select(store(earray_14,index_15,e10),rselect_tail(q10)) ) ),
inference(symmetry,[status(thm)],[2520]) ).
tff(2522,plain,
( ( elem_214 != e10 )
<=> ( select(store(store(earray_14,index_15,e10),rselect_tail(q11),e11),rselect_tail(q10)) != select(store(earray_14,index_15,e10),rselect_tail(q10)) ) ),
inference(monotonicity,[status(thm)],[2521]) ).
tff(2523,plain,
( ( elem_214 != e10 )
<=> ( elem_214 != e10 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2524,axiom,
elem_214 != e10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(2525,plain,
elem_214 != e10,
inference(modus_ponens,[status(thm)],[2524,2523]) ).
tff(2526,plain,
select(store(store(earray_14,index_15,e10),rselect_tail(q11),e11),rselect_tail(q10)) != select(store(earray_14,index_15,e10),rselect_tail(q10)),
inference(modus_ponens,[status(thm)],[2525,2522]) ).
tff(2527,plain,
( ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q11) = rselect_tail(q10) )
| ( select(store(store(earray_14,index_15,e10),rselect_tail(q11),e11),rselect_tail(q10)) = select(store(earray_14,index_15,e10),rselect_tail(q10)) ) )
<=> ( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q11) = rselect_tail(q10) )
| ( select(store(store(earray_14,index_15,e10),rselect_tail(q11),e11),rselect_tail(q10)) = select(store(earray_14,index_15,e10),rselect_tail(q10)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2528,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q11) = rselect_tail(q10) )
| ( select(store(store(earray_14,index_15,e10),rselect_tail(q11),e11),rselect_tail(q10)) = select(store(earray_14,index_15,e10),rselect_tail(q10)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(2529,plain,
( ~ ! [I: $i,E: $i,A: $i,J: $i] :
( ( I = J )
| ( select(store(A,I,E),J) = select(A,J) ) )
| ( rselect_tail(q11) = rselect_tail(q10) )
| ( select(store(store(earray_14,index_15,e10),rselect_tail(q11),e11),rselect_tail(q10)) = select(store(earray_14,index_15,e10),rselect_tail(q10)) ) ),
inference(modus_ponens,[status(thm)],[2528,2527]) ).
tff(2530,plain,
( ( rselect_tail(q11) = rselect_tail(q10) )
| ( select(store(store(earray_14,index_15,e10),rselect_tail(q11),e11),rselect_tail(q10)) = select(store(earray_14,index_15,e10),rselect_tail(q10)) ) ),
inference(unit_resolution,[status(thm)],[2529,1766]) ).
tff(2531,plain,
$false,
inference(unit_resolution,[status(thm)],[2530,2526,49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV568-1.030 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n012.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Jun 20 10:22:40 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.59/0.78 % SZS status Unsatisfiable
% 0.59/0.78 % SZS output start Proof
% See solution above
% 0.71/0.91 % E exiting
%------------------------------------------------------------------------------