%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP101^2 : 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 : n004.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 08:10:42 AM UTC 2026
% Result : Theorem 0.21s 0.35s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP101^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n004.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 19:53:38 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.21/0.35 % (1756417)Will run a generic schedule for satisfiability detection.
% 0.21/0.35 % (1756432)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=578642878:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.35 % (1756428)% WARNING: option uhcvi not known.
% 0.21/0.35 % (1756427)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=869936513_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.35 % (1756428)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=64723510:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.35 % (1756431)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2774342390:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.35 % (1756429)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3656984971:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.35 % (1756430)dis+10_1_sil=32000:sp=arity:random_seed=4195684791:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.35 % (1756433)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3308786195:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.35 % (1756431)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.35 % (1756428)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.21/0.35 % (1756432)Instruction limit reached!
% 0.21/0.35 % (1756432)------------------------------
% 0.21/0.35 % (1756432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (1756432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (1756432)CaDiCaL version: 2.1.3
% 0.21/0.35 % (1756432)Termination reason: Instruction limit
% 0.21/0.35 % (1756432)Termination phase: Saturation
% 0.21/0.35 % (1756432)Time elapsed: 0.030 s
% 0.21/0.35 % (1756432)Peak memory usage: 13 MB
% 0.21/0.35 % (1756432)Instructions burned: 133 (million)
% 0.21/0.35 % (1756458)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1138899187:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.21/0.35 % Exception at run slice level
% 0.21/0.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.35 % (1756428)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.21/0.35 % (1756430)Instruction limit reached!
% 0.21/0.35 % (1756430)------------------------------
% 0.21/0.35 % (1756430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (1756430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (1756430)CaDiCaL version: 2.1.3
% 0.21/0.35 % (1756430)Termination reason: Instruction limit
% 0.21/0.35 % (1756430)Termination phase: Saturation
% 0.21/0.35 % (1756430)Time elapsed: 0.044 s
% 0.21/0.35 % (1756430)Peak memory usage: 12 MB
% 0.21/0.35 % (1756430)Instructions burned: 105 (million)
% 0.21/0.35 % (1756431)Instruction limit reached!
% 0.21/0.35 % (1756431)------------------------------
% 0.21/0.35 % (1756431)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (1756431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (1756431)CaDiCaL version: 2.1.3
% 0.21/0.35 % (1756431)Termination reason: Instruction limit
% 0.21/0.35 % (1756431)Termination phase: Saturation
% 0.21/0.35 % (1756431)Time elapsed: 0.051 s
% 0.21/0.35 % (1756431)Peak memory usage: 13 MB
% 0.21/0.35 % (1756431)Instructions burned: 118 (million)
% 0.21/0.35 % Exception at run slice level
% 0.21/0.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.35 % (1756469)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3686511215:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.35 % (1756475)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=1145233818:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.21/0.35 % (1756482)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2426514626:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.21/0.35 % (1756429) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1756417-1756429"...
% 0.21/0.35 % (1756433)Instruction limit reached!
% 0.21/0.35 % (1756433)------------------------------
% 0.21/0.35 % (1756433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (1756433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (1756433)CaDiCaL version: 2.1.3
% 0.21/0.35 % (1756433)Termination reason: Instruction limit
% 0.21/0.35 % (1756433)Termination phase: Saturation
% 0.21/0.35 % (1756433)Time elapsed: 0.071 s
% 0.21/0.35 % (1756433)Peak memory usage: 13 MB
% 0.21/0.35 % (1756433)Instructions burned: 161 (million)
% 0.21/0.35 % (1756480)ott-21_1_sil=16000:fs=off:random_seed=1959956560:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.21/0.35 % (1756429)...printing done.
% 0.21/0.35 % (1756429)Refutation found. Thanks to Tanya!
% 0.21/0.35 % SZS status Theorem for theBenchmark
% 0.21/0.35 % SZS output start Proof for theBenchmark
% 0.21/0.35 thf(type_def_5, type, list: $tType > $tType).
% 0.21/0.35 thf(type_def_6, type, set: $tType > $tType).
% 0.21/0.35 thf(type_def_7, type, nat: $tType).
% 0.21/0.35 thf(type_def_8, type, a: $tType).
% 0.21/0.35 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.35 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_1, type, size: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_2, type, one: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_3, type, minus: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_4, type, ord: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_5, type, order: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_6, type, group_add: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_7, type, no_bot: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_8, type, no_top: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_10, type, preorder: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_11, type, wellorder: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_12, type, dense_order: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_13, type, dense_linorder: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_14, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_15, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_16, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 0.21/0.35 thf(func_def_17, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.21/0.35 thf(func_def_18, type, one_one: !>[X0: $tType]:(X0)).
% 0.21/0.35 thf(func_def_19, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.21/0.35 thf(func_def_20, type, list_asc: !>[X0: $tType]:((list @ X0 > $o))).
% 0.21/0.35 thf(func_def_21, type, list_desc: !>[X0: $tType]:((list @ X0 > $o))).
% 0.21/0.35 thf(func_def_22, type, list_strict_asc: !>[X0: $tType]:((list @ X0 > $o))).
% 0.21/0.35 thf(func_def_23, type, list_strict_desc: !>[X0: $tType]:((list @ X0 > $o))).
% 0.21/0.35 thf(func_def_24, type, listIn521021761append: !>[X0: $tType]:((list @ X0 > (nat > X0) > nat > X0))).
% 0.21/0.35 thf(func_def_25, type, append: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0))).
% 0.21/0.35 thf(func_def_26, type, butlast: !>[X0: $tType]:((list @ X0 > list @ X0))).
% 0.21/0.35 thf(func_def_27, type, set2: !>[X0: $tType]:((list @ X0 > set @ X0))).
% 0.21/0.35 thf(func_def_28, type, list_ex: !>[X0: $tType]:(((X0 > $o) > list @ X0 > $o))).
% 0.21/0.35 thf(func_def_29, type, list_update: !>[X0: $tType]:((list @ X0 > nat > X0 > list @ X0))).
% 0.21/0.35 thf(func_def_30, type, nth: !>[X0: $tType]:((list @ X0 > nat > X0))).
% 0.21/0.35 thf(func_def_31, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 0.21/0.35 thf(func_def_32, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.35 thf(func_def_33, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.35 thf(func_def_34, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.21/0.35 thf(func_def_35, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.21/0.35 thf(func_def_36, type, f: (nat > a)).
% 0.21/0.35 thf(func_def_37, type, g: (nat > a)).
% 0.21/0.35 thf(func_def_38, type, x: nat).
% 0.21/0.35 thf(func_def_39, type, xs: list @ a).
% 0.21/0.35 thf(func_def_40, type, ys: list @ a).
% 0.21/0.35 thf(func_def_44, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.35 thf(func_def_45, type, vIMP: ($o > $o > $o)).
% 0.21/0.35 thf(func_def_46, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.35 thf(func_def_47, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.21/0.35 thf(func_def_48, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.35 thf(func_def_49, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.35 thf(func_def_50, type, vAND: ($o > $o > $o)).
% 0.21/0.35 thf(func_def_51, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.35 thf(func_def_52, type, db2: !>[X0: $tType]:(X0)).
% 0.21/0.35 thf(func_def_53, type, vNOT: ($o > $o)).
% 0.21/0.35 thf(func_def_54, type, vOR: ($o > $o > $o)).
% 0.21/0.35 thf(func_def_55, type, sP0: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.21/0.35 thf(func_def_56, type, sP1: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.21/0.35 thf(func_def_57, type, sP2: !>[X0: $tType]:((X0 > X0 > X0 > $o))).
% 0.21/0.35 thf(func_def_58, type, sK3: !>[X0: $tType]:((list @ X0 > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_59, type, sK4: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_60, type, sK5: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_61, type, sK6: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_62, type, sK7: ((nat > $o) > nat)).
% 0.21/0.35 thf(func_def_63, type, sK8: ((nat > $o) > nat)).
% 0.21/0.35 thf(func_def_64, type, sK9: !>[X0: $tType]:((nat > list @ X0))).
% 0.21/0.35 thf(func_def_65, type, sK10: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 0.21/0.35 thf(func_def_66, type, sK11: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_67, type, sK12: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_68, type, sK13: ((nat > $o) > nat)).
% 0.21/0.35 thf(func_def_69, type, sK14: (nat > (nat > $o) > nat)).
% 0.21/0.35 thf(func_def_70, type, sK15: ((nat > nat) > nat)).
% 0.21/0.35 thf(func_def_71, type, sK16: ((nat > nat) > nat)).
% 0.21/0.35 thf(func_def_72, type, sK17: ((nat > $o) > nat > nat)).
% 0.21/0.35 thf(func_def_73, type, sK18: ((nat > $o) > nat > nat)).
% 0.21/0.35 thf(func_def_74, type, sK19: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_75, type, sK20: !>[X0: $tType]:((nat > (X0 > nat) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_76, type, sK21: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_77, type, sK22: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_78, type, sK23: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_79, type, sK24: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_80, type, sK25: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_81, type, sK26: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_82, type, sK27: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_83, type, sK28: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_84, type, sK29: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_85, type, sK30: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_86, type, sK31: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_87, type, sK32: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_88, type, sK33: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_89, type, sK34: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_90, type, sK35: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_91, type, sK36: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_92, type, sK37: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_93, type, sK38: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_94, type, sK39: !>[X0: $tType]:(((X0 > X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_95, type, sK40: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_96, type, sK41: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.21/0.35 thf(func_def_97, type, sK42: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_98, type, sK43: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_99, type, sK44: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_100, type, sK45: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_101, type, sK46: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_102, type, sK47: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_103, type, sK48: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_104, type, sK49: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_105, type, sK50: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_106, type, sK51: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_107, type, sK52: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_108, type, sK53: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_109, type, sK54: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_110, type, sK55: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_111, type, sK56: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_112, type, sK57: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_113, type, sK58: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_114, type, sK59: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_115, type, sK60: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_116, type, sK61: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_117, type, sK62: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.21/0.35 thf(func_def_118, type, sK63: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_119, type, sK64: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_120, type, sK65: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_121, type, sK66: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_122, type, sK67: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_123, type, sK68: !>[X0: $tType]:((X0 > (X0 > $o) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_124, type, sK69: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_125, type, sK70: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_126, type, sK71: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_127, type, sK72: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_128, type, sK73: !>[X0: $tType, X1: $tType]:((X1 > X0))).
% 0.21/0.35 thf(func_def_129, type, sK74: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_130, type, sK75: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.21/0.35 thf(func_def_131, type, sK76: !>[X0: $tType]:((X0 > X0 > X0 > X0))).
% 0.21/0.35 thf(func_def_132, type, sK77: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.21/0.35 thf(func_def_133, type, sK78: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.21/0.35 thf(func_def_134, type, sK79: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_135, type, sK80: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_136, type, sK81: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_137, type, sK82: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_138, type, sK83: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_139, type, sK84: !>[X0: $tType, X1: $tType]:(((X0 > X1) > X0))).
% 0.21/0.35 thf(func_def_140, type, sK85: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_141, type, sK86: !>[X0: $tType, X1: $tType]:(((X1 > X0) > X1))).
% 0.21/0.35 thf(func_def_142, type, sK87: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_143, type, sK88: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_144, type, sK89: !>[X0: $tType]:((X0 > X0))).
% 0.21/0.35 thf(func_def_145, type, sK90: !>[X0: $tType]:(((X0 > $o) > X0 > X0 > X0))).
% 0.21/0.35 thf(func_def_146, type, sK91: !>[X0: $tType]:((X0 > (X0 > $o) > X0 > X0))).
% 0.21/0.35 thf(func_def_147, type, sK92: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > list @ X0 > X0))).
% 0.21/0.35 thf(func_def_148, type, sK93: !>[X0: $tType]:(((X0 > $o) > list @ X0 > X0))).
% 0.21/0.35 thf(func_def_149, type, sK94: !>[X0: $tType]:(((X0 > $o) > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_150, type, sK95: !>[X0: $tType]:((list @ X0 > (X0 > $o) > X0))).
% 0.21/0.35 thf(func_def_151, type, sK96: !>[X0: $tType]:((list @ X0 > (X0 > $o) > nat))).
% 0.21/0.35 thf(func_def_152, type, sK97: !>[X0: $tType]:((X0 > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_153, type, sK98: !>[X0: $tType]:(((X0 > $o) > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_154, type, sK99: !>[X0: $tType]:(((X0 > $o) > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_155, type, sK100: !>[X0: $tType]:(((X0 > $o) > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_156, type, sK101: !>[X0: $tType]:(((X0 > $o) > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_157, type, sK102: !>[X0: $tType]:(((X0 > $o) > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_158, type, sK103: !>[X0: $tType]:(((X0 > $o) > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_159, type, sK104: !>[X0: $tType]:((list @ X0 > set @ X0 > X0))).
% 0.21/0.35 thf(func_def_160, type, sK105: !>[X0: $tType]:((list @ X0 > list @ X0 > list @ X0 > list @ X0 > list @ X0))).
% 0.21/0.35 thf(func_def_161, type, sK106: !>[X0: $tType]:(((X0 > $o) > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_162, type, sK107: !>[X0: $tType]:(((X0 > $o) > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_163, type, sK108: !>[X0: $tType]:(((X0 > $o) > list @ X0 > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_164, type, sK109: !>[X0: $tType]:(((X0 > $o) > list @ X0 > list @ X0 > nat))).
% 0.21/0.35 thf(func_def_165, type, sK110: !>[X0: $tType]:((nat > (nat > X0 > $o) > nat))).
% 0.21/0.35 thf(func_def_166, type, sK111: !>[X0: $tType]:((nat > (nat > X0 > $o) > list @ X0))).
% 0.21/0.35 thf(func_def_167, type, sK112: !>[X0: $tType]:((nat > list @ X0 > (nat > X0 > $o) > nat))).
% 0.21/0.35 thf(func_def_168, type, sK113: !>[X0: $tType]:(((nat > X0 > $o) > nat > X0))).
% 0.21/0.35 thf(f285,axiom,(
% 0.21/0.35 ! [X0 : nat] : ((~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => ((~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))) & ((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((nth @ a @ xs @ X0)) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))))) & ((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => ((~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((nth @ a @ ys @ X0)))) & ((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0)))))))),
% 0.21/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1)).
% 0.21/0.35 thf(f286,axiom,(
% 0.21/0.35 (ord_less @ nat @ x @ (size_size @ list @ a @ ys))),
% 0.21/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 0.21/0.35 thf(f287,conjecture,(
% 0.21/0.35 (((nth @ a @ xs @ x)) = ((nth @ a @ ys @ x)))),
% 0.21/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3)).
% 0.21/0.35 thf(f288,negated_conjecture,(
% 0.21/0.35 ~ (((nth @ a @ xs @ x)) = ((nth @ a @ ys @ x)))),
% 0.21/0.35 inference(negated_conjecture,[status(cth)],[f287])).
% 0.21/0.35 thf(f812,plain,(
% 0.21/0.35 ! [X0 : nat] : ((~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => ((~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))) & ((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((nth @ a @ xs @ X0)) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))))) & ((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => ((~(ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((nth @ a @ ys @ X0)))) & ((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys)) => (((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0)))))))),
% 0.21/0.35 inference(rectify,[],[f285])).
% 0.21/0.35 thf(f813,plain,(
% 0.21/0.35 ! [X0 : nat] : ((~ (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => ((~ (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))) & ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((nth @ a @ xs @ X0)) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))))) & ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => ((~ (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((nth @ a @ ys @ X0)) = ((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))))) & ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0)))))))),
% 0.21/0.35 inference(fool_elimination,[],[f812])).
% 0.21/0.35 thf(f814,plain,(
% 0.21/0.35 (ord_less @ nat @ x @ (size_size @ list @ a @ ys))),
% 0.21/0.35 inference(rectify,[],[f286])).
% 0.21/0.35 thf(f815,plain,(
% 0.21/0.35 (((ord_less @ nat @ x @ (size_size @ list @ a @ ys))) = $true)),
% 0.21/0.35 inference(fool_elimination,[],[f814])).
% 0.21/0.35 thf(f846,plain,(
% 0.21/0.35 ! [X0 : nat] : (((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true) => (((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true) => (((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))) & ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((nth @ a @ xs @ X0)) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys)))))))) & ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true) => (((nth @ a @ ys @ X0)) = ((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))))) & ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true) => (((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0)))))))),
% 0.21/0.35 inference(flattening,[],[f813])).
% 0.21/0.35 thf(f847,plain,(
% 0.21/0.35 (((nth @ a @ xs @ x)) != ((nth @ a @ ys @ x)))),
% 0.21/0.35 inference(flattening,[],[f288])).
% 0.21/0.35 thf(f1159,plain,(
% 0.21/0.35 ! [X0 : nat] : (((((((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs)))) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys))))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true)) & ((((nth @ a @ xs @ X0)) = ((g @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ ys))))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true)) & ((((((nth @ a @ ys @ X0)) = ((f @ (minus_minus @ nat @ X0 @ (size_size @ list @ a @ xs))))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) = $true)) & ((((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true)))),
% 0.21/0.35 inference(ennf_transformation,[],[f846])).
% 0.21/0.35 thf(f1609,plain,(
% 0.21/0.35 ( ! [X0 : nat] : ((((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0))) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true) | (((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true)) )),
% 0.21/0.35 inference(cnf_transformation,[],[f1159])).
% 0.21/0.35 thf(f1613,plain,(
% 0.21/0.35 (((ord_less @ nat @ x @ (size_size @ list @ a @ ys))) = $true)),
% 0.21/0.35 inference(cnf_transformation,[],[f815])).
% 0.21/0.35 thf(f1614,plain,(
% 0.21/0.35 (((nth @ a @ xs @ x)) != ((nth @ a @ ys @ x)))),
% 0.21/0.35 inference(cnf_transformation,[],[f847])).
% 0.21/0.35 thf(f1659,plain,(
% 0.21/0.35 ( ! [X0 : nat] : ((((ord_less @ nat @ X0 @ (size_size @ list @ a @ ys))) != $true) | (((nth @ a @ xs @ X0)) = ((nth @ a @ ys @ X0)))) )),
% 0.21/0.35 inference(duplicate_literal_removal,[],[f1609])).
% 0.21/0.35 thf(f2491,plain,(
% 0.21/0.35 ($true != $true) | (((nth @ a @ xs @ x)) = ((nth @ a @ ys @ x)))),
% 0.21/0.35 inference(constrained_superposition,[],[f1659,f1613])).
% 0.21/0.35 thf(f2493,plain,(
% 0.21/0.35 (((nth @ a @ xs @ x)) = ((nth @ a @ ys @ x)))),
% 0.21/0.35 inference(trivial_inequality_removal,[],[f2491])).
% 0.21/0.35 thf(f2494,plain,(
% 0.21/0.35 $false),
% 0.21/0.35 inference(forward_subsumption_resolution,[],[f2493,f1614])).
% 0.21/0.35 % SZS output end Proof for theBenchmark
% 0.21/0.35 % (1756429)------------------------------
% 0.21/0.35 % (1756429)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.35 % (1756429)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.35 % (1756429)CaDiCaL version: 2.1.3
% 0.21/0.35 % (1756429)Termination reason: Refutation
% 0.21/0.35 % (1756429)Time elapsed: 0.072 s
% 0.21/0.35 % (1756429)Peak memory usage: 14 MB
% 0.21/0.35 % (1756429)Instructions burned: 158 (million)
% 0.21/0.35 % (1756417)Success in time 0.11 s
% 0.21/0.35 % Vampire exiting
%------------------------------------------------------------------------------