%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP138^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:10:51 AM UTC 2026
% Result : Theorem 0.77s 0.36s
% Output : Refutation 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP138^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 20:01:53 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.77/0.36 % (1777224)Will run a generic schedule for satisfiability detection.
% 0.77/0.36 % (1777248)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=34797939:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.77/0.36 % (1777245)% WARNING: option uhcvi not known.
% 0.77/0.36 % (1777244)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3496620341_2999 on theBenchmark for (2999ds/0Mi)
% 0.77/0.36 % (1777245)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3998607367:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.77/0.36 % (1777247)dis+10_1_sil=32000:sp=arity:random_seed=950650288:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.77/0.36 % (1777249)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4273519671:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.77/0.36 % (1777246)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2366927426:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.77/0.36 % (1777250)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2890305746:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.77/0.36 % (1777248)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.77/0.36 % (1777245)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.77/0.36 % (1777248)Instruction limit reached!
% 0.77/0.36 % (1777248)------------------------------
% 0.77/0.36 % (1777248)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.36 % (1777248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.36 % (1777248)CaDiCaL version: 2.1.3
% 0.77/0.36 % (1777248)Termination reason: Instruction limit
% 0.77/0.36 % (1777248)Termination phase: Saturation
% 0.77/0.36 % (1777248)Time elapsed: 0.029 s
% 0.77/0.36 % (1777248)Peak memory usage: 13 MB
% 0.77/0.36 % (1777248)Instructions burned: 117 (million)
% 0.77/0.36 % (1777269)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2003708972:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.77/0.36 % (1777245)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.77/0.36 % Exception at run slice level
% 0.77/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.77/0.36 % (1777247)Instruction limit reached!
% 0.77/0.36 % (1777247)------------------------------
% 0.77/0.36 % (1777247)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.36 % (1777247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.36 % (1777247)CaDiCaL version: 2.1.3
% 0.77/0.36 % (1777247)Termination reason: Instruction limit
% 0.77/0.36 % (1777247)Termination phase: Saturation
% 0.77/0.36 % (1777247)Time elapsed: 0.050 s
% 0.77/0.36 % (1777247)Peak memory usage: 13 MB
% 0.77/0.36 % (1777247)Instructions burned: 111 (million)
% 0.77/0.36 % Exception at run slice level
% 0.77/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.77/0.36 % (1777249)Instruction limit reached!
% 0.77/0.36 % (1777249)------------------------------
% 0.77/0.36 % (1777249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.36 % (1777249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.36 % (1777249)CaDiCaL version: 2.1.3
% 0.77/0.36 % (1777249)Termination reason: Instruction limit
% 0.77/0.36 % (1777249)Termination phase: Saturation
% 0.77/0.36 % (1777249)Time elapsed: 0.061 s
% 0.77/0.36 % (1777249)Peak memory usage: 13 MB
% 0.77/0.36 % (1777249)Instructions burned: 131 (million)
% 0.77/0.36 % (1777284)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3200852126:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.77/0.36 % (1777293)ott-21_1_sil=16000:fs=off:random_seed=2019447411:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.77/0.36 % (1777290)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2519105524:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.77/0.36 % (1777245) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1777224-1777245"...
% 0.77/0.36 % (1777245)...printing done.
% 0.77/0.36 % (1777245)Refutation found. Thanks to Tanya!
% 0.77/0.36 % SZS status Theorem for theBenchmark
% 0.77/0.36 % SZS output start Proof for theBenchmark
% 0.77/0.36 thf(type_def_5, type, paraco415392788lle_tv: $tType).
% 0.77/0.36 thf(type_def_6, type, paraco414474393lle_fm: $tType).
% 0.77/0.36 thf(type_def_7, type, product_prod: ($tType * $tType) > $tType).
% 0.77/0.36 thf(type_def_8, type, char: $tType).
% 0.77/0.36 thf(type_def_9, type, list: $tType > $tType).
% 0.77/0.36 thf(type_def_10, type, set: $tType > $tType).
% 0.77/0.36 thf(type_def_11, type, nat: $tType).
% 0.77/0.36 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 0.77/0.36 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_1, type, ord: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_2, type, top: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_3, type, order: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_4, type, no_bot: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_5, type, linorder: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_6, type, preorder: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_7, type, finite_lattice: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_8, type, order_top: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_9, type, complete_Sup: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_10, type, comple187826305attice: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_11, type, comple1035589618norder: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_12, type, condit378418413attice: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_13, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 0.77/0.36 thf(func_def_14, type, complete_Sup_Sup: !>[X0: $tType]:((set @ X0 > X0))).
% 0.77/0.36 thf(func_def_15, type, finite_Fpow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 0.77/0.36 thf(func_def_16, type, swap: !>[X0: $tType, X1: $tType]:((X0 > X0 > (X0 > X1) > X0 > X1))).
% 0.77/0.36 thf(func_def_17, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.77/0.36 thf(func_def_18, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.77/0.36 thf(func_def_19, type, order_Greatest: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_20, type, order_strict_mono: !>[X0: $tType, X1: $tType]:(((X0 > X1) > $o))).
% 0.77/0.36 thf(func_def_21, type, top_top: !>[X0: $tType]:(X0)).
% 0.77/0.36 thf(func_def_22, type, paraco506338565domain: (set @ nat > set @ paraco415392788lle_tv)).
% 0.77/0.36 thf(func_def_23, type, paraco876059933e_eval: ((list @ char > paraco415392788lle_tv) > paraco414474393lle_fm > paraco415392788lle_tv)).
% 0.77/0.36 thf(func_def_24, type, paraco2100061555le_Con: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_25, type, paraco2084319816le_Eql: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_26, type, paraco1628874225le_Eql: (paraco414474393lle_fm > paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_27, type, paraco329115265le_Neg: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_28, type, paraco27778325le_Pro: (list @ char > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_29, type, paraco251304083_Truth: paraco414474393lle_fm).
% 0.77/0.36 thf(func_def_30, type, paraco2040174112le_Det: ($o > paraco415392788lle_tv)).
% 0.77/0.36 thf(func_def_31, type, paraco152590079rec_tv: !>[X0: $tType]:((($o > X0) > (nat > X0) > paraco415392788lle_tv > X0))).
% 0.77/0.36 thf(func_def_32, type, paraco769098683_valid: (paraco414474393lle_fm > $o)).
% 0.77/0.36 thf(func_def_33, type, paraco2086025920lid_in: (set @ nat > paraco414474393lle_fm > $o)).
% 0.77/0.36 thf(func_def_34, type, product_Pair: !>[X0: $tType, X1: $tType]:((X0 > X1 > product_prod @ X0 @ X1))).
% 0.77/0.36 thf(func_def_35, type, powp: !>[X0: $tType]:(((X0 > $o) > set @ X0 > $o))).
% 0.77/0.36 thf(func_def_36, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.77/0.36 thf(func_def_37, type, pow: !>[X0: $tType]:((set @ X0 > set @ set @ X0))).
% 0.77/0.36 thf(func_def_38, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.77/0.36 thf(func_def_39, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.77/0.36 thf(func_def_40, type, p: paraco414474393lle_fm).
% 0.77/0.36 thf(func_def_44, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.77/0.36 thf(func_def_45, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.77/0.36 thf(func_def_46, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.77/0.36 thf(func_def_47, type, vIMP: ($o > $o > $o)).
% 0.77/0.36 thf(func_def_48, type, db0: !>[X0: $tType]:(X0)).
% 0.77/0.36 thf(func_def_49, type, db2: !>[X0: $tType]:(X0)).
% 0.77/0.36 thf(func_def_50, type, db1: !>[X0: $tType]:(X0)).
% 0.77/0.36 thf(func_def_51, type, vAND: ($o > $o > $o)).
% 0.77/0.36 thf(func_def_52, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.77/0.36 thf(func_def_53, type, vNOT: ($o > $o)).
% 0.77/0.36 thf(func_def_54, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.77/0.36 thf(func_def_55, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.77/0.36 thf(func_def_56, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.77/0.36 thf(func_def_57, type, sP3: ((paraco414474393lle_fm > $o) > $o)).
% 0.77/0.36 thf(func_def_58, type, sP4: ((paraco414474393lle_fm > $o) > $o)).
% 0.77/0.36 thf(func_def_59, type, sK5: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.77/0.36 thf(func_def_60, type, sK6: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X0 > X1))).
% 0.77/0.36 thf(func_def_61, type, sK7: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > (X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_62, type, sK8: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_63, type, sK9: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_64, type, sK10: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_65, type, sK11: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_66, type, sK12: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.77/0.36 thf(func_def_67, type, sK13: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.77/0.36 thf(func_def_68, type, sK14: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.77/0.36 thf(func_def_69, type, sK15: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.77/0.36 thf(func_def_70, type, sK16: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.77/0.36 thf(func_def_71, type, sK17: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.77/0.36 thf(func_def_72, type, sK18: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.77/0.36 thf(func_def_73, type, sK19: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.77/0.36 thf(func_def_74, type, sK20: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.77/0.36 thf(func_def_75, type, sK21: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X0))).
% 0.77/0.36 thf(func_def_76, type, sK22: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.77/0.36 thf(func_def_77, type, sK23: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_78, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.77/0.36 thf(func_def_79, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > $o) > set @ X1 > (X1 > X0) > X1))).
% 0.77/0.36 thf(func_def_80, type, sK26: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_81, type, sK27: !>[X0: $tType]:(X0)).
% 0.77/0.36 thf(func_def_82, type, sK28: !>[X0: $tType]:((set @ X0 > X0))).
% 0.77/0.36 thf(func_def_83, type, sK29: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > X0 > X1))).
% 0.77/0.36 thf(func_def_84, type, sK30: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > X0) > set @ X0 > set @ X1))).
% 0.77/0.36 thf(func_def_85, type, sK31: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > X1) > set @ X0 > X0))).
% 0.77/0.36 thf(func_def_86, type, sK32: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X1))).
% 0.77/0.36 thf(func_def_87, type, sK33: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.77/0.36 thf(func_def_88, type, sK34: !>[X0: $tType, X1: $tType]:((X0 > (X1 > X0) > X1))).
% 0.77/0.36 thf(func_def_89, type, sK35: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > set @ X0 > X0))).
% 0.77/0.36 thf(func_def_90, type, sK36: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_91, type, sK37: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.77/0.36 thf(func_def_92, type, sK38: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.77/0.36 thf(func_def_93, type, sK39: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_94, type, sK40: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_95, type, sK41: !>[X0: $tType]:((X0 > (X0 > $o) > X0))).
% 0.77/0.36 thf(func_def_96, type, sK42: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X0 > X1) > X0))).
% 0.77/0.36 thf(func_def_97, type, sK43: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_98, type, sK44: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_99, type, sK45: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_100, type, sK46: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_101, type, sK47: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_102, type, sK48: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_103, type, sK49: (paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.36 thf(func_def_104, type, sK50: (paraco414474393lle_fm > list @ char)).
% 0.77/0.37 thf(func_def_105, type, sK51: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_106, type, sK52: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_107, type, sK53: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_108, type, sK54: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_109, type, sK55: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_110, type, sK56: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_111, type, sK57: ((paraco414474393lle_fm > $o) > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_112, type, sK58: ((paraco414474393lle_fm > $o) > list @ char)).
% 0.77/0.37 thf(func_def_113, type, sK59: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.77/0.37 thf(func_def_114, type, sK60: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > set @ X1 > X1))).
% 0.77/0.37 thf(func_def_115, type, sK61: !>[X0: $tType]:((set @ X0 > set @ set @ X0 > set @ X0))).
% 0.77/0.37 thf(func_def_116, type, sK62: !>[X0: $tType]:((set @ set @ X0 > set @ set @ X0 > set @ X0))).
% 0.77/0.37 thf(func_def_117, type, sK63: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_118, type, sK64: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_119, type, sK65: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_120, type, sK66: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_121, type, sK67: !>[X0: $tType, X1: $tType]:((set @ X1 > (X1 > set @ X0) > X0 > X1))).
% 0.77/0.37 thf(func_def_122, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X0 > X1) > set @ X2 > set @ X0 > X2))).
% 0.77/0.37 thf(func_def_123, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X0 > X1) > set @ X2 > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_124, type, sK70: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > set @ X0 > X1))).
% 0.77/0.37 thf(func_def_125, type, sK71: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_126, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X0 > X1) > set @ X2 > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_127, type, sK73: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_128, type, sK74: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.77/0.37 thf(func_def_129, type, sK75: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > (X1 > set @ X0) > set @ X1 > X1))).
% 0.77/0.37 thf(func_def_130, type, sK76: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > set @ X1) > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_131, type, sK77: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_132, type, sK78: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_133, type, sK79: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_134, type, sK80: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_135, type, sK81: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_136, type, sK82: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_137, type, sK83: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_138, type, sK84: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_139, type, sK85: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_140, type, sK86: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_141, type, sK87: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > paraco414474393lle_fm)).
% 0.77/0.37 thf(func_def_142, type, sK88: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_143, type, sK89: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_144, type, sK90: (product_prod @ (list @ char > paraco415392788lle_tv) @ paraco414474393lle_fm > list @ char)).
% 0.77/0.37 thf(func_def_145, type, sK91: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.77/0.37 thf(func_def_146, type, sK92: !>[X0: $tType, X1: $tType]:((X1 > set @ X0 > (X0 > X1 > $o) > X0))).
% 0.77/0.37 thf(func_def_147, type, sK93: !>[X0: $tType]:((X0 > set @ (X0 > $o) > X0 > $o))).
% 0.77/0.37 thf(func_def_148, type, sK94: !>[X0: $tType]:((set @ set @ X0 > X0 > set @ X0))).
% 0.77/0.37 thf(func_def_149, type, sK95: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X1))).
% 0.77/0.37 thf(func_def_150, type, sK96: !>[X0: $tType, X1: $tType]:((set @ product_prod @ X1 @ X0 > set @ product_prod @ X1 @ X0 > X0))).
% 0.77/0.37 thf(func_def_151, type, sK97: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_152, type, sK98: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_153, type, sK99: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > set @ X1) > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_154, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X0 > set @ X1 > (X1 > X0 > X2 > $o) > X1))).
% 0.77/0.37 thf(func_def_155, type, sK101: !>[X0: $tType, X1: $tType]:((X1 > X0 > set @ (X0 > X1 > $o) > X0 > X1 > $o))).
% 0.77/0.37 thf(func_def_156, type, sK102: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 0.77/0.37 thf(func_def_157, type, sK103: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.77/0.37 thf(func_def_158, type, sK104: (list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_159, type, sK105: (list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_160, type, sK106: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 0.77/0.37 thf(func_def_161, type, sK107: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.77/0.37 thf(func_def_162, type, sK108: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_163, type, sK109: !>[X0: $tType]:((X0 > set @ X0 > X0))).
% 0.77/0.37 thf(func_def_164, type, sK110: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.77/0.37 thf(func_def_165, type, sK111: !>[X0: $tType]:((set @ X0 > X0))).
% 0.77/0.37 thf(func_def_166, type, sK112: !>[X0: $tType, X1: $tType]:((set @ X0 > X1 > (X0 > X1) > X0))).
% 0.77/0.37 thf(func_def_167, type, sK113: !>[X0: $tType, X1: $tType]:((set @ X0 > (X0 > X1) > X1))).
% 0.77/0.37 thf(func_def_168, type, sK114: !>[X0: $tType]:((X0 > set @ set @ X0 > set @ X0))).
% 0.77/0.37 thf(func_def_169, type, sK115: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 0.77/0.37 thf(func_def_170, type, sK116: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > set @ X0))).
% 0.77/0.37 thf(func_def_171, type, sK117: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 0.77/0.37 thf(func_def_172, type, sK118: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > set @ X0))).
% 0.77/0.37 thf(func_def_173, type, sK119: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 0.77/0.37 thf(func_def_174, type, sK120: !>[X0: $tType]:((set @ set @ X0 > (X0 > $o) > X0))).
% 0.77/0.37 thf(func_def_175, type, sK121: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > set @ X0) > X1))).
% 0.77/0.37 thf(func_def_176, type, sK122: !>[X0: $tType, X1: $tType]:((set @ X1 > X0 > (X1 > X0) > X1))).
% 0.77/0.37 thf(func_def_177, type, sK123: !>[X0: $tType]:((set @ X0 > X0 > X0))).
% 0.77/0.37 thf(func_def_178, type, sK124: !>[X0: $tType, X1: $tType]:(((X1 > set @ X0) > set @ X1 > X0 > X1))).
% 0.77/0.37 thf(func_def_179, type, sK125: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 0.77/0.37 thf(func_def_180, type, sK126: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 0.77/0.37 thf(func_def_181, type, sK127: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 0.77/0.37 thf(func_def_182, type, sK128: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 0.77/0.37 thf(func_def_183, type, sK129: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 0.77/0.37 thf(func_def_184, type, sK130: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 0.77/0.37 thf(func_def_185, type, sK131: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 0.77/0.37 thf(func_def_186, type, sK132: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 0.77/0.37 thf(func_def_187, type, sK133: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 0.77/0.37 thf(func_def_188, type, sK134: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X1))).
% 0.77/0.37 thf(func_def_189, type, sK135: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 0.77/0.37 thf(func_def_190, type, sK136: !>[X0: $tType, X1: $tType]:((set @ X1 > (X0 > $o) > (X1 > set @ X0) > X0))).
% 0.77/0.37 thf(func_def_191, type, sK137: (paraco414474393lle_fm > paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_192, type, sK138: (paraco414474393lle_fm > paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_193, type, sK139: (paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_194, type, sK140: (paraco414474393lle_fm > list @ char > paraco415392788lle_tv)).
% 0.77/0.37 thf(func_def_195, type, sK141: !>[X0: $tType]:((set @ X0 > (X0 > $o) > X0))).
% 0.77/0.37 thf(func_def_196, type, sK142: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X0))).
% 0.77/0.37 thf(func_def_197, type, sK143: !>[X0: $tType, X1: $tType]:((set @ X1 > (set @ X0 > $o) > (X1 > X0) > set @ X1))).
% 0.77/0.37 thf(func_def_198, type, sK144: !>[X0: $tType, X1: $tType]:((X1 > (X0 > X1) > X0))).
% 0.77/0.37 thf(func_def_199, type, sK145: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X1))).
% 0.77/0.37 thf(func_def_200, type, sK146: !>[X0: $tType, X1: $tType]:((set @ X1 > set @ X0 > (X1 > X0) > X1))).
% 0.77/0.37 thf(func_def_201, type, sK147: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > set @ X0 > set @ X1))).
% 0.77/0.37 thf(func_def_202, type, sK148: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.77/0.37 thf(func_def_203, type, sK149: !>[X0: $tType, X1: $tType]:(((X1 > X0) > set @ X1 > X0 > X1))).
% 0.77/0.37 thf(f1,axiom,(
% 0.77/0.37 (((paraco506338565domain @ (collect @ nat @ (^[X2 : nat] : ($true))))) = ((collect @ paraco415392788lle_tv @ (^[X3 : paraco415392788lle_tv] : ($true)))))),
% 0.77/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_universal__domain)).
% 0.77/0.37 thf(f73,axiom,(
% 0.77/0.37 ! [X0 : $tType] : (top_top @ set @ X0 = ((collect @ X0 @ (^[X1 : X0] : ($true)))))),
% 0.77/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_UNIV__def)).
% 0.77/0.37 thf(f84,axiom,(
% 0.77/0.37 ! [X0 : $tType,X1 : set @ X0] : (ord_less_eq @ set @ X0 @ X1 @ top_top @ set @ X0)),
% 0.77/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_subset__UNIV)).
% 0.77/0.37 thf(f289,conjecture,(
% 0.77/0.37 (! [X0 : (list @ char > paraco415392788lle_tv)] : (((paraco876059933e_eval @ X0 @ p)) = ((paraco2040174112le_Det @ $true))) != ~ ! [X0 : (list @ char > paraco415392788lle_tv)] : ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ X0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[X1 : nat] : ($true))))) => (((paraco876059933e_eval @ X0 @ p)) = ((paraco2040174112le_Det @ $true)))))),
% 0.77/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 0.77/0.37 thf(f290,negated_conjecture,(
% 0.77/0.37 ~ (! [X0 : (list @ char > paraco415392788lle_tv)] : (((paraco876059933e_eval @ X0 @ p)) = ((paraco2040174112le_Det @ $true))) != ~ ! [X0 : (list @ char > paraco415392788lle_tv)] : ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ X0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[X1 : nat] : ($true))))) => (((paraco876059933e_eval @ X0 @ p)) = ((paraco2040174112le_Det @ $true)))))),
% 0.77/0.37 inference(negated_conjecture,[status(cth)],[f289])).
% 0.77/0.37 thf(f291,plain,(
% 0.77/0.37 (((paraco506338565domain @ (collect @ nat @ (^[X0 : nat] : ($true))))) = ((collect @ paraco415392788lle_tv @ (^[X1 : paraco415392788lle_tv] : ($true)))))),
% 0.77/0.37 inference(rectify,[],[f1])).
% 0.77/0.37 thf(f292,plain,(
% 0.77/0.37 (((paraco506338565domain @ (collect @ nat @ (^[Y0 : nat]: ($true))))) = ((collect @ paraco415392788lle_tv @ (^[Y0 : paraco415392788lle_tv]: ($true)))))),
% 0.77/0.37 inference(fool_elimination,[],[f291])).
% 0.77/0.37 thf(f426,plain,(
% 0.77/0.37 ! [X0 : $tType] : (top_top @ set @ X0 = ((collect @ X0 @ (^[X1 : X0] : ($true)))))),
% 0.77/0.37 inference(rectify,[],[f73])).
% 0.77/0.37 thf(f427,plain,(
% 0.77/0.37 ! [X0 : $tType] : (top_top @ set @ X0 = ((collect @ X0 @ (^[Y0 : X0]: ($true)))))),
% 0.77/0.37 inference(fool_elimination,[],[f426])).
% 0.77/0.37 thf(f448,plain,(
% 0.77/0.37 ! [X0 : $tType,X1 : set @ X0] : (ord_less_eq @ set @ X0 @ X1 @ top_top @ set @ X0)),
% 0.77/0.37 inference(rectify,[],[f84])).
% 0.77/0.37 thf(f449,plain,(
% 0.77/0.37 ! [X0 : $tType,X1 : set @ X0] : (((ord_less_eq @ set @ X0 @ X1 @ top_top @ set @ X0)) = $true)),
% 0.77/0.37 inference(fool_elimination,[],[f448])).
% 0.77/0.37 thf(f774,plain,(
% 0.77/0.37 ~ (! [X0 : (list @ char > paraco415392788lle_tv)] : (((paraco876059933e_eval @ X0 @ p)) = ((paraco2040174112le_Det @ $true))) != ~ ! [X1 : (list @ char > paraco415392788lle_tv)] : ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ X1 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[X2 : nat] : ($true))))) => (((paraco876059933e_eval @ X1 @ p)) = ((paraco2040174112le_Det @ $true)))))),
% 0.77/0.37 inference(rectify,[],[f290])).
% 0.77/0.37 thf(f775,plain,(
% 0.77/0.37 ~ (((!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))))) != ((~ (!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ Y0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y1 : nat]: ($true))))) => ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))))))))),
% 0.77/0.37 inference(fool_elimination,[],[f774])).
% 0.77/0.37 thf(f788,plain,(
% 0.77/0.37 (((!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))))) = ((~ (!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ Y0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y1 : nat]: ($true))))) => ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))))))))),
% 0.77/0.37 inference(flattening,[],[f775])).
% 0.77/0.37 thf(f1094,plain,(
% 0.77/0.37 (((paraco506338565domain @ (collect @ nat @ (^[Y0 : nat]: ($true))))) = ((collect @ paraco415392788lle_tv @ (^[Y0 : paraco415392788lle_tv]: ($true)))))),
% 0.77/0.37 inference(cnf_transformation,[],[f292])).
% 0.77/0.37 thf(f1194,plain,(
% 0.77/0.37 ( ! [X0 : $tType] : ((top_top @ set @ X0 = ((collect @ X0 @ (^[Y0 : X0]: ($true)))))) )),
% 0.77/0.37 inference(cnf_transformation,[],[f427])).
% 0.77/0.37 thf(f1207,plain,(
% 0.77/0.37 ( ! [X0 : $tType,X1 : set @ X0] : ((((ord_less_eq @ set @ X0 @ X1 @ top_top @ set @ X0)) = $true)) )),
% 0.77/0.37 inference(cnf_transformation,[],[f449])).
% 0.77/0.37 thf(f1481,plain,(
% 0.77/0.37 (((!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))))) = ((~ (!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ Y0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y1 : nat]: ($true))))) => ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))))))))),
% 0.77/0.37 inference(cnf_transformation,[],[f788])).
% 0.77/0.37 thf(f1523,plain,(
% 0.77/0.37 ($true = ((!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true)))))) | ($false = ((~ (!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ Y0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y1 : nat]: ($true))))) => ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))))))))),
% 0.77/0.37 inference(iff_proxy_clausification,[],[f1481])).
% 0.77/0.37 thf(f1524,plain,(
% 0.77/0.37 ($false = ((!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true)))))) | ($true = ((~ (!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ Y0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y1 : nat]: ($true))))) => ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))))))))),
% 0.77/0.37 inference(iff_proxy_clausification,[],[f1481])).
% 0.77/0.37 thf(f1525,plain,(
% 0.77/0.37 ($false = (((^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))) @ sK104))) | ($true = ((~ (!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ Y0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y1 : nat]: ($true))))) => ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))))))))),
% 0.77/0.37 inference(sigma_proxy_clausification,[],[f1524])).
% 0.77/0.37 thf(f1526,plain,(
% 0.77/0.37 ($false = (((^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))) @ sK104))) | ($false = ((!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ Y0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y1 : nat]: ($true))))) => ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true)))))))),
% 0.77/0.37 inference(not_proxy_clausification,[],[f1525])).
% 0.77/0.37 thf(f1527,plain,(
% 0.77/0.37 ($false = (((^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))) @ sK104))) | ($false = (((^[Y0 : list @ char > paraco415392788lle_tv]: ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ Y0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y1 : nat]: ($true))))) => ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true)))) @ sK105)))),
% 0.77/0.37 inference(sigma_proxy_clausification,[],[f1526])).
% 0.77/0.37 thf(f1528,plain,(
% 0.77/0.37 ($false = (((paraco876059933e_eval @ sK104 @ p) = (paraco2040174112le_Det @ $true)))) | ($false = (((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ sK105 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y0 : nat]: ($true))))) => ((paraco876059933e_eval @ sK105 @ p) = (paraco2040174112le_Det @ $true)))))),
% 0.77/0.37 inference(beta-eta_normalization,[],[f1527])).
% 0.77/0.37 thf(f1529,plain,(
% 0.77/0.37 (((paraco2040174112le_Det @ $true)) != ((paraco876059933e_eval @ sK104 @ p))) | ($false = (((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ sK105 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y0 : nat]: ($true))))) => ((paraco876059933e_eval @ sK105 @ p) = (paraco2040174112le_Det @ $true)))))),
% 0.77/0.37 inference(equality_proxy_clausification,[],[f1528])).
% 0.77/0.37 thf(f1530,plain,(
% 0.77/0.37 (((paraco2040174112le_Det @ $true)) != ((paraco876059933e_eval @ sK104 @ p))) | ($false = (((paraco876059933e_eval @ sK105 @ p) = (paraco2040174112le_Det @ $true))))),
% 0.77/0.37 inference(imp_proxy_clausification,[],[f1529])).
% 0.77/0.37 thf(f1532,plain,(
% 0.77/0.37 (((paraco2040174112le_Det @ $true)) != ((paraco876059933e_eval @ sK104 @ p))) | (((paraco2040174112le_Det @ $true)) != ((paraco876059933e_eval @ sK105 @ p)))),
% 0.77/0.37 inference(equality_proxy_clausification,[],[f1530])).
% 0.77/0.37 thf(f1533,plain,(
% 0.77/0.37 ( ! [X1 : (list @ char > paraco415392788lle_tv)] : (($true = (((^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))) @ X1))) | ($false = ((~ (!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ Y0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y1 : nat]: ($true))))) => ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))))))))) )),
% 0.77/0.37 inference(pi_proxy_clausification,[],[f1523])).
% 0.77/0.37 thf(f1534,plain,(
% 0.77/0.37 ( ! [X1 : (list @ char > paraco415392788lle_tv)] : (($true = (((^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))) @ X1))) | ($true = ((!! @ (list @ char > paraco415392788lle_tv) @ (^[Y0 : list @ char > paraco415392788lle_tv]: ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ Y0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y1 : nat]: ($true))))) => ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true)))))))) )),
% 0.77/0.37 inference(not_proxy_clausification,[],[f1533])).
% 0.77/0.37 thf(f1535,plain,(
% 0.77/0.37 ( ! [X2 : (list @ char > paraco415392788lle_tv),X1 : (list @ char > paraco415392788lle_tv)] : (($true = (((^[Y0 : list @ char > paraco415392788lle_tv]: ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true))) @ X1))) | ($true = (((^[Y0 : list @ char > paraco415392788lle_tv]: ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ Y0 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y1 : nat]: ($true))))) => ((paraco876059933e_eval @ Y0 @ p) = (paraco2040174112le_Det @ $true)))) @ X2)))) )),
% 0.77/0.37 inference(pi_proxy_clausification,[],[f1534])).
% 0.77/0.37 thf(f1536,plain,(
% 0.77/0.37 ( ! [X2 : (list @ char > paraco415392788lle_tv),X1 : (list @ char > paraco415392788lle_tv)] : (($true = (((paraco876059933e_eval @ X1 @ p) = (paraco2040174112le_Det @ $true)))) | ($true = (((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ X2 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y0 : nat]: ($true))))) => ((paraco876059933e_eval @ X2 @ p) = (paraco2040174112le_Det @ $true)))))) )),
% 0.77/0.37 inference(beta-eta_normalization,[],[f1535])).
% 0.77/0.37 thf(f1537,plain,(
% 0.77/0.37 ( ! [X2 : (list @ char > paraco415392788lle_tv),X1 : (list @ char > paraco415392788lle_tv)] : ((((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ X1 @ p))) | ($true = (((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ X2 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y0 : nat]: ($true))))) => ((paraco876059933e_eval @ X2 @ p) = (paraco2040174112le_Det @ $true)))))) )),
% 0.77/0.37 inference(equality_proxy_clausification,[],[f1536])).
% 0.77/0.37 thf(f1538,plain,(
% 0.77/0.37 ( ! [X2 : (list @ char > paraco415392788lle_tv),X1 : (list @ char > paraco415392788lle_tv)] : ((((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ X1 @ p))) | ($false = ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ X2 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y0 : nat]: ($true))))))) | ($true = (((paraco876059933e_eval @ X2 @ p) = (paraco2040174112le_Det @ $true))))) )),
% 0.77/0.37 inference(imp_proxy_clausification,[],[f1537])).
% 0.77/0.37 thf(f1539,plain,(
% 0.77/0.37 ( ! [X2 : (list @ char > paraco415392788lle_tv),X1 : (list @ char > paraco415392788lle_tv)] : ((((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ X1 @ p))) | ($false = ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ X2 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y0 : nat]: ($true))))))) | (((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ X2 @ p)))) )),
% 0.77/0.37 inference(equality_proxy_clausification,[],[f1538])).
% 0.77/0.37 thf(f2046,definition,(
% 0.77/0.37 spl150_2 <=> (((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ sK104 @ p)))),
% 0.77/0.37 introduced(definition,[new_symbols(definition,[spl150_2])],[avatar_definition])).
% 0.77/0.37 thf(f2048,plain,(
% 0.77/0.37 (((paraco2040174112le_Det @ $true)) != ((paraco876059933e_eval @ sK104 @ p))) | spl150_2),
% 0.77/0.37 inference(avatar_component_clause,[],[f2046])).
% 0.77/0.37 thf(f2051,definition,(
% 0.77/0.37 spl150_3 <=> (((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ sK105 @ p)))),
% 0.77/0.37 introduced(definition,[new_symbols(definition,[spl150_3])],[avatar_definition])).
% 0.77/0.37 thf(f2053,plain,(
% 0.77/0.37 (((paraco2040174112le_Det @ $true)) != ((paraco876059933e_eval @ sK105 @ p))) | spl150_3),
% 0.77/0.37 inference(avatar_component_clause,[],[f2051])).
% 0.77/0.37 thf(f2054,plain,(
% 0.77/0.37 ~spl150_3 | ~spl150_2),
% 0.77/0.37 inference(avatar_split_clause,[],[f1532,f2046,f2051])).
% 0.77/0.37 thf(f2056,definition,(
% 0.77/0.37 spl150_4 <=> ! [X2 : (list @ char > paraco415392788lle_tv)] : (($false = ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ X2 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y0 : nat]: ($true))))))) | (((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ X2 @ p))))),
% 0.77/0.37 introduced(definition,[new_symbols(definition,[spl150_4])],[avatar_definition])).
% 0.77/0.37 thf(f2057,plain,(
% 0.77/0.37 ( ! [X2 : (list @ char > paraco415392788lle_tv)] : (($false = ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ X2 @ top_top @ set @ list @ char) @ (paraco506338565domain @ (collect @ nat @ (^[Y0 : nat]: ($true))))))) | (((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ X2 @ p)))) ) | ~spl150_4),
% 0.77/0.37 inference(avatar_component_clause,[],[f2056])).
% 0.77/0.37 thf(f2059,definition,(
% 0.77/0.37 spl150_5 <=> ! [X1 : (list @ char > paraco415392788lle_tv)] : (((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ X1 @ p)))),
% 0.77/0.37 introduced(definition,[new_symbols(definition,[spl150_5])],[avatar_definition])).
% 0.77/0.37 thf(f2060,plain,(
% 0.77/0.37 ( ! [X1 : (list @ char > paraco415392788lle_tv)] : ((((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ X1 @ p)))) ) | ~spl150_5),
% 0.77/0.37 inference(avatar_component_clause,[],[f2059])).
% 0.77/0.37 thf(f2061,plain,(
% 0.77/0.37 spl150_4 | spl150_5),
% 0.77/0.37 inference(avatar_split_clause,[],[f1539,f2059,f2056])).
% 0.77/0.37 thf(f2268,plain,(
% 0.77/0.37 ( ! [X2 : (list @ char > paraco415392788lle_tv)] : (($false = ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ X2 @ top_top @ set @ list @ char) @ (paraco506338565domain @ top_top @ set @ nat)))) | (((paraco2040174112le_Det @ $true)) = ((paraco876059933e_eval @ X2 @ p)))) ) | ~spl150_4),
% 0.77/0.37 inference(forward_demodulation,[],[f2057,f1194])).
% 0.77/0.37 thf(f2319,plain,(
% 0.77/0.37 (((paraco506338565domain @ (collect @ nat @ (^[Y0 : nat]: ($true))))) = top_top @ set @ paraco415392788lle_tv)),
% 0.77/0.37 inference(forward_demodulation,[],[f1094,f1194])).
% 0.77/0.37 thf(f2320,plain,(
% 0.77/0.37 (((paraco506338565domain @ top_top @ set @ nat)) = top_top @ set @ paraco415392788lle_tv)),
% 0.77/0.37 inference(forward_demodulation,[],[f2319,f1194])).
% 0.77/0.37 thf(f2321,plain,(
% 0.77/0.37 ( ! [X0 : (list @ char > paraco415392788lle_tv)] : (($false = ((ord_less_eq @ set @ paraco415392788lle_tv @ (image @ list @ char @ paraco415392788lle_tv @ X0 @ top_top @ set @ list @ char) @ top_top @ set @ paraco415392788lle_tv))) | (((paraco876059933e_eval @ X0 @ p)) = ((paraco2040174112le_Det @ $true)))) ) | ~spl150_4),
% 0.77/0.37 inference(constrained_superposition,[],[f2268,f2320])).
% 0.77/0.37 thf(f2330,plain,(
% 0.77/0.37 ( ! [X0 : (list @ char > paraco415392788lle_tv)] : (($true = $false) | (((paraco876059933e_eval @ X0 @ p)) = ((paraco2040174112le_Det @ $true)))) ) | ~spl150_4),
% 0.77/0.37 inference(constrained_superposition,[],[f1207,f2321])).
% 0.77/0.37 thf(f2331,plain,(
% 0.77/0.37 ( ! [X0 : (list @ char > paraco415392788lle_tv)] : ((((paraco876059933e_eval @ X0 @ p)) = ((paraco2040174112le_Det @ $true)))) ) | ~spl150_4),
% 0.77/0.37 inference(trivial_inequality_removal,[],[f2330])).
% 0.77/0.37 thf(f2334,plain,(
% 0.77/0.37 spl150_5 | ~spl150_4),
% 0.77/0.37 inference(avatar_split_clause,[],[f2331,f2056,f2059])).
% 0.77/0.37 thf(f2335,plain,(
% 0.77/0.37 $false | (spl150_2 | ~spl150_5)),
% 0.77/0.37 inference(backward_subsumption_resolution,[],[f2048,f2060])).
% 0.77/0.37 thf(f2336,plain,(
% 0.77/0.37 spl150_2 | ~spl150_5),
% 0.77/0.37 inference(avatar_contradiction_clause,[],[f2335])).
% 0.77/0.37 thf(f2338,plain,(
% 0.77/0.37 $false | (spl150_3 | ~spl150_5)),
% 0.77/0.37 inference(forward_subsumption_resolution,[],[f2053,f2060])).
% 0.77/0.37 thf(f2339,plain,(
% 0.77/0.37 spl150_3 | ~spl150_5),
% 0.77/0.37 inference(avatar_contradiction_clause,[],[f2338])).
% 0.77/0.37 cnf(s2, plain, ~spl150_2 | ~spl150_3, inference(sat_conversion,[],[f2054])).
% 0.77/0.37 cnf(s3, plain, spl150_4 | spl150_5, inference(sat_conversion,[],[f2061])).
% 0.77/0.37 cnf(s15, plain, ~spl150_4 | spl150_5, inference(sat_conversion,[],[f2334])).
% 0.77/0.37 cnf(s17, plain, spl150_2 | ~spl150_5, inference(sat_conversion,[],[f2336])).
% 0.77/0.37 cnf(s18, plain, spl150_3 | ~spl150_5, inference(sat_conversion,[],[f2339])).
% 0.77/0.37 cnf(s19, plain, spl150_5, inference(rat,[],[s3,s15])).
% 0.77/0.37 cnf(s20, plain, spl150_3, inference(rat,[],[s18,s19])).
% 0.77/0.37 cnf(s21, plain, spl150_2, inference(rat,[],[s17,s19])).
% 0.77/0.37 cnf(s22, plain, $false, inference(rat,[],[s2,s20,s21])).
% 0.77/0.37 thf(f2341,plain,(
% 0.77/0.37 $false),
% 0.77/0.37 inference(avatar_sat_refutation,[],[s22])).
% 0.77/0.37 % SZS output end Proof for theBenchmark
% 0.77/0.37 % (1777245)------------------------------
% 0.77/0.37 % (1777245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.77/0.37 % (1777245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.77/0.37 % (1777245)CaDiCaL version: 2.1.3
% 0.77/0.37 % (1777245)Termination reason: Refutation
% 0.77/0.37 % (1777245)Time elapsed: 0.077 s
% 0.77/0.37 % (1777245)Peak memory usage: 15 MB
% 0.77/0.37 % (1777245)Instructions burned: 154 (million)
% 0.77/0.37 % (1777224)Success in time 0.134 s
% 0.77/0.37 % Vampire exiting
%------------------------------------------------------------------------------