%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP105^2 : 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 : n020.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 5.22s 1.07s
% Output : Refutation 5.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ITP105^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.24 % Computer : n020.cluster.edu
% 0.11/0.24 % Model : x86_64 x86_64
% 0.11/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.24 % Memory : 8046.5625MB
% 0.11/0.24 % OS : Linux 6.8.0-71-generic
% 0.11/0.24 % CPULimit : 300
% 0.11/0.24 % WCLimit : 300
% 0.11/0.24 % DateTime : Tue Sep 29 19:55:05 UTC 2026
% 0.11/0.25 % CPUTime :
% 0.11/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.23/0.29 Running first-order model finding
% 0.23/0.29 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
% 5.22/1.07 % (1512774)Will run a generic schedule for satisfiability detection.
% 5.22/1.07 % (1512780)% WARNING: option uhcvi not known.
% 5.22/1.07 % (1512780)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2479082421:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 5.22/1.07 % (1512779)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3945439016_2999 on theBenchmark for (2999ds/0Mi)
% 5.22/1.07 % (1512780)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.22/1.07 % (1512784)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=171312594:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 5.22/1.07 % (1512782)dis+10_1_sil=32000:sp=arity:random_seed=598983228:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 5.22/1.07 % (1512783)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=385173203:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 5.22/1.07 % (1512781)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3009292312:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 5.22/1.07 % (1512785)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=599954357:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 5.22/1.07 % (1512780)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.22/1.07 % (1512783)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.22/1.07 % Exception at run slice level
% 5.22/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.22/1.07 % (1512793)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=952927103:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 5.22/1.07 % (1512782)Instruction limit reached!
% 5.22/1.07 % (1512782)------------------------------
% 5.22/1.07 % (1512782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.07 % (1512782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.07 % (1512782)CaDiCaL version: 2.1.3
% 5.22/1.07 % (1512782)Termination reason: Instruction limit
% 5.22/1.07 % (1512782)Termination phase: Saturation
% 5.22/1.07 % (1512782)Time elapsed: 0.090 s
% 5.22/1.07 % (1512782)Peak memory usage: 13 MB
% 5.22/1.07 % (1512782)Instructions burned: 103 (million)
% 5.22/1.07 % (1512783)Instruction limit reached!
% 5.22/1.07 % (1512783)------------------------------
% 5.22/1.07 % (1512783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.07 % (1512783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.07 % (1512783)CaDiCaL version: 2.1.3
% 5.22/1.07 % (1512783)Termination reason: Instruction limit
% 5.22/1.07 % (1512783)Termination phase: Saturation
% 5.22/1.07 % (1512783)Time elapsed: 0.098 s
% 5.22/1.07 % (1512783)Peak memory usage: 13 MB
% 5.22/1.07 % (1512783)Instructions burned: 116 (million)
% 5.22/1.07 % (1512784)Instruction limit reached!
% 5.22/1.07 % (1512784)------------------------------
% 5.22/1.07 % (1512784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.07 % (1512784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.07 % (1512784)CaDiCaL version: 2.1.3
% 5.22/1.07 % (1512784)Termination reason: Instruction limit
% 5.22/1.07 % (1512784)Termination phase: Saturation
% 5.22/1.07 % (1512784)Time elapsed: 0.114 s
% 5.22/1.07 % (1512784)Peak memory usage: 13 MB
% 5.22/1.07 % (1512784)Instructions burned: 131 (million)
% 5.22/1.07 % Exception at run slice level
% 5.22/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.22/1.07 % (1512795)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3666274635:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 5.22/1.07 % (1512796)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=2389129917:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 5.22/1.07 % (1512785)Instruction limit reached!
% 5.22/1.07 % (1512785)------------------------------
% 5.22/1.07 % (1512785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.07 % (1512785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.07 % (1512785)CaDiCaL version: 2.1.3
% 5.22/1.07 % (1512785)Termination reason: Instruction limit
% 5.22/1.07 % (1512785)Termination phase: Saturation
% 5.22/1.07 % (1512785)Time elapsed: 0.145 s
% 5.22/1.07 % (1512785)Peak memory usage: 13 MB
% 5.22/1.07 % (1512785)Instructions burned: 159 (million)
% 5.22/1.07 % (1512798)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=605874674:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 5.22/1.07 % (1512797)ott-21_1_sil=16000:fs=off:random_seed=1768933793:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 5.22/1.07 % (1512796)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.22/1.07 % (1512802)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=4200033376:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 5.22/1.07 % (1512796)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 5.22/1.07 % Exception at run slice level
% 5.22/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.22/1.07 % (1512795)Instruction limit reached!
% 5.22/1.07 % (1512795)------------------------------
% 5.22/1.07 % (1512795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.07 % (1512795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.07 % (1512795)CaDiCaL version: 2.1.3
% 5.22/1.07 % (1512795)Termination reason: Instruction limit
% 5.22/1.07 % (1512795)Termination phase: Saturation
% 5.22/1.07 % (1512795)Time elapsed: 0.113 s
% 5.22/1.07 % (1512795)Peak memory usage: 13 MB
% 5.22/1.07 % (1512795)Instructions burned: 132 (million)
% 5.22/1.07 % (1512807)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=286301245:i=1179_2996 on theBenchmark for (2996ds/1179Mi)
% 5.22/1.07 % (1512808)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=18733796:i=889:ins=1_2996 on theBenchmark for (2996ds/889Mi)
% 5.22/1.07 % (1512797)Instruction limit reached!
% 5.22/1.07 % (1512797)------------------------------
% 5.22/1.07 % (1512797)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.07 % (1512797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.07 % (1512797)CaDiCaL version: 2.1.3
% 5.22/1.07 % (1512797)Termination reason: Instruction limit
% 5.22/1.07 % (1512797)Termination phase: Saturation
% 5.22/1.07 % (1512797)Time elapsed: 0.151 s
% 5.22/1.07 % (1512797)Peak memory usage: 13 MB
% 5.22/1.07 % (1512797)Instructions burned: 180 (million)
% 5.22/1.07 % (1512813)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=2149965695:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2996 on theBenchmark for (2996ds/692Mi)
% 5.22/1.07 % Exception at run slice level
% 5.22/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.22/1.07 % (1512813)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.22/1.07 % (1512815)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=445161234:i=879:kws=inv_precedence:fsr=off_2995 on theBenchmark for (2995ds/879Mi)
% 5.22/1.07 % (1512815)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 5.22/1.07 % (1512798)Instruction limit reached!
% 5.22/1.07 % (1512798)------------------------------
% 5.22/1.07 % (1512798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.07 % (1512798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.07 % (1512798)CaDiCaL version: 2.1.3
% 5.22/1.07 % (1512798)Termination reason: Instruction limit
% 5.22/1.07 % (1512798)Termination phase: Saturation
% 5.22/1.07 % (1512798)Time elapsed: 0.459 s
% 5.22/1.07 % (1512798)Peak memory usage: 14 MB
% 5.22/1.07 % (1512798)Instructions burned: 478 (million)
% 5.22/1.07 % (1512821)fmb+10_1_sil=64000:random_seed=357588840:i=22061:nm=2:gsp=on_2993 on theBenchmark for (2993ds/22061Mi)
% 5.22/1.07 % (1512821)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.22/1.07 % Exception at run slice level
% 5.22/1.07 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 5.22/1.07 % (1512780) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1512774-1512780"...
% 5.22/1.07 % (1512780)...printing done.
% 5.22/1.07 % (1512780)Refutation found. Thanks to Tanya!
% 5.22/1.07 % SZS status Theorem for theBenchmark
% 5.22/1.07 % SZS output start Proof for theBenchmark
% 5.22/1.07 thf(type_def_5, type, option: $tType > $tType).
% 5.22/1.07 thf(type_def_6, type, real: $tType).
% 5.22/1.07 thf(type_def_7, type, list: $tType > $tType).
% 5.22/1.07 thf(type_def_8, type, set: $tType > $tType).
% 5.22/1.07 thf(type_def_9, type, nat: $tType).
% 5.22/1.07 thf(type_def_10, type, int: $tType).
% 5.22/1.07 thf(type_def_11, type, a: $tType).
% 5.22/1.07 thf(type_def_12, type, sTfun: ($tType * $tType) > $tType).
% 5.22/1.07 thf(func_def_0, type, type: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_1, type, size: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_2, type, zero: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_3, type, field: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_4, type, order: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_5, type, semiring_1: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_6, type, linorder: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_7, type, semiring_char_0: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_8, type, wellorder: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_9, type, division_ring: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_10, type, semiring_bits: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_11, type, semidom_divide: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_12, type, linordered_idom: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_13, type, linordered_field: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_14, type, linordered_semidom: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_15, type, linord1659791738miring: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_16, type, semiri134348788visors: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_17, type, archim1804426504_field: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_18, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_19, type, unique1598680935umeral: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_20, type, euclid1852923125th_nat: !>[X0: $tType]:($o)).
% 5.22/1.07 thf(func_def_21, type, inverse_inverse: !>[X0: $tType]:((X0 > X0))).
% 5.22/1.07 thf(func_def_22, type, zero_zero: !>[X0: $tType]:(X0)).
% 5.22/1.07 thf(func_def_23, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 5.22/1.07 thf(func_def_24, type, listSl1903280966_slice: !>[X0: $tType]:((list @ X0 > nat > list @ list @ X0))).
% 5.22/1.07 thf(func_def_25, type, listSl1123830174ce_aux: !>[X0: $tType]:((list @ X0 > nat > nat > list @ list @ X0))).
% 5.22/1.07 thf(func_def_26, type, bind: !>[X0: $tType, X1: $tType]:((list @ X0 > (X0 > list @ X1) > list @ X1))).
% 5.22/1.07 thf(func_def_27, type, concat: !>[X0: $tType]:((list @ list @ X0 > list @ X0))).
% 5.22/1.07 thf(func_def_28, type, count_list: !>[X0: $tType]:((list @ X0 > X0 > nat))).
% 5.22/1.07 thf(func_def_29, type, gen_length: !>[X0: $tType]:((nat > list @ X0 > nat))).
% 5.22/1.07 thf(func_def_30, type, nil: !>[X0: $tType]:(list @ X0)).
% 5.22/1.07 thf(func_def_31, type, list_ex1: !>[X0: $tType]:(((X0 > $o) > list @ X0 > $o))).
% 5.22/1.07 thf(func_def_32, type, map_filter: !>[X0: $tType, X1: $tType]:(((X0 > option @ X1) > list @ X0 > list @ X1))).
% 5.22/1.07 thf(func_def_33, type, maps: !>[X0: $tType, X1: $tType]:(((X0 > list @ X1) > list @ X0 > list @ X1))).
% 5.22/1.07 thf(func_def_34, type, member: !>[X0: $tType]:((list @ X0 > X0 > $o))).
% 5.22/1.07 thf(func_def_35, type, null: !>[X0: $tType]:((list @ X0 > $o))).
% 5.22/1.07 thf(func_def_36, type, semiring_1_of_nat: !>[X0: $tType]:((nat > X0))).
% 5.22/1.07 thf(func_def_37, type, size_size: !>[X0: $tType]:((X0 > nat))).
% 5.22/1.07 thf(func_def_38, type, ord_less: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.22/1.07 thf(func_def_39, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.22/1.07 thf(func_def_40, type, power_power: !>[X0: $tType]:((X0 > nat > X0))).
% 5.22/1.07 thf(func_def_41, type, divide_divide: !>[X0: $tType]:((X0 > X0 > X0))).
% 5.22/1.07 thf(func_def_42, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 5.22/1.07 thf(func_def_43, type, member2: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 5.22/1.07 thf(func_def_44, type, k: nat).
% 5.22/1.07 thf(func_def_48, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 5.22/1.07 thf(func_def_49, type, vNOT: ($o > $o)).
% 5.22/1.07 thf(func_def_50, type, vOR: ($o > $o > $o)).
% 5.22/1.07 thf(func_def_51, type, db0: !>[X0: $tType]:(X0)).
% 5.22/1.07 thf(func_def_52, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 5.22/1.07 thf(func_def_53, type, db1: !>[X0: $tType]:(X0)).
% 5.22/1.07 thf(func_def_54, type, vAND: ($o > $o > $o)).
% 5.22/1.07 thf(func_def_55, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.22/1.07 thf(func_def_56, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 5.22/1.07 thf(func_def_57, type, vIMP: ($o > $o > $o)).
% 5.22/1.07 thf(func_def_58, type, db2: !>[X0: $tType]:(X0)).
% 5.22/1.07 thf(func_def_59, type, sK0: !>[X0: $tType]:(((list @ X0 > $o) > list @ X0))).
% 5.22/1.07 thf(func_def_60, type, sK1: !>[X0: $tType]:((nat > list @ X0))).
% 5.22/1.07 thf(func_def_61, type, sK2: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 5.22/1.07 thf(func_def_62, type, sK3: !>[X0: $tType, X1: $tType]:(((X1 > $o) > (X1 > X0) > X1))).
% 5.22/1.07 thf(func_def_63, type, sK4: !>[X0: $tType]:(((X0 > nat) > (X0 > $o) > X0))).
% 5.22/1.07 thf(func_def_64, type, sK5: ((nat > $o) > nat)).
% 5.22/1.07 thf(func_def_65, type, sK6: ((nat > $o) > nat)).
% 5.22/1.07 thf(func_def_66, type, sK7: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 5.22/1.07 thf(func_def_67, type, sK8: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 5.22/1.07 thf(func_def_68, type, sK9: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 5.22/1.07 thf(func_def_69, type, sK10: !>[X0: $tType]:(((X0 > $o) > (X0 > nat) > X0))).
% 5.22/1.07 thf(func_def_70, type, sK11: ((nat > $o) > nat)).
% 5.22/1.07 thf(func_def_71, type, sK12: !>[X0: $tType]:((X0 > X0 > X0))).
% 5.22/1.07 thf(func_def_72, type, sK13: ((nat > $o) > set @ nat > nat)).
% 5.22/1.07 thf(func_def_73, type, sK14: ((nat > $o) > set @ nat > nat)).
% 5.22/1.07 thf(func_def_74, type, sK15: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 5.22/1.07 thf(func_def_75, type, sK16: !>[X0: $tType]:(((X0 > $o) > set @ X0 > X0))).
% 5.22/1.07 thf(func_def_76, type, sK17: (int > nat)).
% 5.22/1.07 thf(func_def_77, type, sK18: (int > nat)).
% 5.22/1.07 thf(func_def_78, type, sK19: !>[X0: $tType]:((X0 > nat))).
% 5.22/1.07 thf(func_def_79, type, sK20: !>[X0: $tType]:((X0 > nat))).
% 5.22/1.07 thf(func_def_80, type, sK21: (int > nat)).
% 5.22/1.07 thf(func_def_81, type, sK22: (int > nat)).
% 5.22/1.07 thf(func_def_82, type, sK23: !>[X0: $tType]:((X0 > nat))).
% 5.22/1.07 thf(func_def_83, type, sK24: ((real > $o) > nat)).
% 5.22/1.07 thf(func_def_84, type, sK25: ((real > $o) > real)).
% 5.22/1.07 thf(func_def_85, type, sK26: ((real > $o) > real)).
% 5.22/1.07 thf(func_def_86, type, sK27: ((nat > nat) > nat)).
% 5.22/1.07 thf(func_def_87, type, sK28: ((nat > nat) > nat)).
% 5.22/1.07 thf(func_def_88, type, sK29: (nat > (nat > $o) > nat)).
% 5.22/1.07 thf(func_def_89, type, sK30: ((nat > $o) > nat)).
% 5.22/1.07 thf(func_def_90, type, sK31: (nat > (nat > $o) > nat)).
% 5.22/1.07 thf(func_def_91, type, sK32: !>[X0: $tType]:((X0 > X0))).
% 5.22/1.07 thf(func_def_92, type, sK33: !>[X0: $tType]:((X0 > X0))).
% 5.22/1.07 thf(func_def_93, type, sK34: (set @ real > real)).
% 5.22/1.07 thf(func_def_94, type, sK35: (real > set @ real > real)).
% 5.22/1.07 thf(func_def_95, type, sK36: (real > set @ real > real)).
% 5.22/1.07 thf(func_def_96, type, sK37: (real > nat > real)).
% 5.22/1.07 thf(func_def_97, type, sK38: (real > nat > real)).
% 5.22/1.07 thf(func_def_98, type, sK39: (real > nat)).
% 5.22/1.07 thf(func_def_100, type, db4: !>[X0: $tType]:(X0)).
% 5.22/1.07 thf(func_def_101, type, db3: !>[X0: $tType]:(X0)).
% 5.22/1.07 thf(f14,axiom,(
% 5.22/1.07 ! [X0 : $tType] : (((size_size @ list @ X0 @ nil @ X0)) = zero_zero @ nat)),
% 5.22/1.07 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_list_Osize_I3_J)).
% 5.22/1.07 thf(f56,axiom,(
% 5.22/1.07 ! [X0 : $tType,X1 : list @ X0,X2 : nat] : (((listSl1123830174ce_aux @ X0 @ X1 @ X2 @ zero_zero @ nat)) = nil @ list @ X0)),
% 5.22/1.07 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_list__slice__aux_Osimps_I1_J)).
% 5.22/1.07 thf(f76,axiom,(
% 5.22/1.07 ! [X0 : $tType] : (listSl1903280966_slice @ X0 = (^[X1 : list @ X0, X2 : nat] : ((listSl1123830174ce_aux @ X0 @ X1 @ X2 @ (divide_divide @ nat @ (size_size @ list @ X0 @ X1) @ X2)))))),
% 5.22/1.07 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_list__slice__def)).
% 5.22/1.07 thf(f217,axiom,(
% 5.22/1.07 ! [X0 : $tType] : (semiring_bits @ X0 => ! [X1 : X0] : (((divide_divide @ X0 @ zero_zero @ X0 @ X1)) = zero_zero @ X0))),
% 5.22/1.07 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_bits__div__0)).
% 5.22/1.07 thf(f275,axiom,(
% 5.22/1.07 semiring_bits @ nat),
% 5.22/1.07 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Parity_Osemiring__bits_8)).
% 5.22/1.07 thf(f304,conjecture,(
% 5.22/1.07 (((listSl1903280966_slice @ a @ nil @ a @ k)) = nil @ list @ a)),
% 5.22/1.07 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 5.22/1.07 thf(f305,negated_conjecture,(
% 5.22/1.07 ~ (((listSl1903280966_slice @ a @ nil @ a @ k)) = nil @ list @ a)),
% 5.22/1.07 inference(negated_conjecture,[status(cth)],[f304])).
% 5.22/1.07 thf(f417,plain,(
% 5.22/1.07 ! [X0 : $tType] : (listSl1903280966_slice @ X0 = (^[Y0 : list @ X0]: ((^[Y1 : nat]: (listSl1123830174ce_aux @ X0 @ Y0 @ Y1 @ (divide_divide @ nat @ (size_size @ list @ X0 @ Y0) @ Y1))))))),
% 5.22/1.07 inference(fool_elimination,[],[f76])).
% 5.22/1.07 thf(f689,plain,(
% 5.22/1.07 ! [X0 : $tType] : (semiring_bits @ X0 => ! [X1 : X0] : (((divide_divide @ X0 @ zero_zero @ X0 @ X1)) = zero_zero @ X0))),
% 5.22/1.07 inference(rectify,[],[f217])).
% 5.22/1.07 thf(f690,plain,(
% 5.22/1.07 ! [X0 : $tType] : ((semiring_bits @ X0 = $true) => ! [X1 : X0] : (zero_zero @ X0 = ((divide_divide @ X0 @ zero_zero @ X0 @ X1))))),
% 5.22/1.07 inference(fool_elimination,[],[f689])).
% 5.22/1.07 thf(f798,plain,(
% 5.22/1.07 semiring_bits @ nat),
% 5.22/1.07 inference(rectify,[],[f275])).
% 5.22/1.07 thf(f799,plain,(
% 5.22/1.07 (semiring_bits @ nat = $true)),
% 5.22/1.07 inference(fool_elimination,[],[f798])).
% 5.22/1.07 thf(f881,plain,(
% 5.22/1.07 (((listSl1903280966_slice @ a @ nil @ a @ k)) != nil @ list @ a)),
% 5.22/1.07 inference(flattening,[],[f305])).
% 5.22/1.07 thf(f1102,plain,(
% 5.22/1.07 ! [X0 : $tType] : (! [X1 : X0] : (zero_zero @ X0 = ((divide_divide @ X0 @ zero_zero @ X0 @ X1))) | (semiring_bits @ X0 != $true))),
% 5.22/1.07 inference(ennf_transformation,[],[f690])).
% 5.22/1.07 thf(f1195,plain,(
% 5.22/1.07 ( ! [X0 : $tType] : ((zero_zero @ nat = ((size_size @ list @ X0 @ nil @ X0)))) )),
% 5.22/1.07 inference(cnf_transformation,[],[f14])).
% 5.22/1.07 thf(f1252,plain,(
% 5.22/1.07 ( ! [X0 : $tType,X2 : nat,X1 : list @ X0] : ((nil @ list @ X0 = ((listSl1123830174ce_aux @ X0 @ X1 @ X2 @ zero_zero @ nat)))) )),
% 5.22/1.07 inference(cnf_transformation,[],[f56])).
% 5.22/1.07 thf(f1280,plain,(
% 5.22/1.07 ( ! [X0 : $tType] : ((listSl1903280966_slice @ X0 = (^[Y0 : list @ X0]: ((^[Y1 : nat]: (listSl1123830174ce_aux @ X0 @ Y0 @ Y1 @ (divide_divide @ nat @ (size_size @ list @ X0 @ Y0) @ Y1))))))) )),
% 5.22/1.07 inference(cnf_transformation,[],[f417])).
% 5.22/1.07 thf(f1434,plain,(
% 5.22/1.07 ( ! [X0 : $tType,X1 : X0] : ((semiring_bits @ X0 != $true) | (zero_zero @ X0 = ((divide_divide @ X0 @ zero_zero @ X0 @ X1)))) )),
% 5.22/1.07 inference(cnf_transformation,[],[f1102])).
% 5.22/1.07 thf(f1501,plain,(
% 5.22/1.07 (semiring_bits @ nat = $true)),
% 5.22/1.07 inference(cnf_transformation,[],[f799])).
% 5.22/1.07 thf(f1530,plain,(
% 5.22/1.07 (((listSl1903280966_slice @ a @ nil @ a @ k)) != nil @ list @ a)),
% 5.22/1.07 inference(cnf_transformation,[],[f881])).
% 5.22/1.07 thf(f1536,plain,(
% 5.22/1.07 (nil @ list @ a != (((^[Y0 : list @ a]: ((^[Y1 : nat]: (listSl1123830174ce_aux @ a @ Y0 @ Y1 @ (divide_divide @ nat @ (size_size @ list @ a @ Y0) @ Y1))))) @ nil @ a @ k)))),
% 5.22/1.07 inference(definition_unfolding,[],[f1530,f1280])).
% 5.22/1.07 thf(f1548,plain,(
% 5.22/1.07 (nil @ list @ a != ((listSl1123830174ce_aux @ a @ nil @ a @ k @ (divide_divide @ nat @ (size_size @ list @ a @ nil @ a) @ k))))),
% 5.22/1.07 inference(beta-eta_normalization,[],[f1536])).
% 5.22/1.07 thf(f1997,plain,(
% 5.22/1.07 (nil @ list @ a != ((listSl1123830174ce_aux @ a @ nil @ a @ k @ (divide_divide @ nat @ zero_zero @ nat @ k))))),
% 5.22/1.07 inference(constrained_superposition,[],[f1548,f1195])).
% 5.22/1.07 thf(f2639,plain,(
% 5.22/1.07 ( ! [X0 : nat] : (($true != $true) | (zero_zero @ nat = ((divide_divide @ nat @ zero_zero @ nat @ X0)))) )),
% 5.22/1.07 inference(constrained_superposition,[],[f1434,f1501])).
% 5.22/1.07 thf(f2640,plain,(
% 5.22/1.07 ( ! [X0 : nat] : ((zero_zero @ nat = ((divide_divide @ nat @ zero_zero @ nat @ X0)))) )),
% 5.22/1.07 inference(trivial_inequality_removal,[],[f2639])).
% 5.22/1.07 thf(f19577,plain,(
% 5.22/1.07 (nil @ list @ a != ((listSl1123830174ce_aux @ a @ nil @ a @ k @ zero_zero @ nat)))),
% 5.22/1.07 inference(constrained_superposition,[],[f1997,f2640])).
% 5.22/1.07 thf(f19600,plain,(
% 5.22/1.07 $false),
% 5.22/1.07 inference(forward_subsumption_resolution,[],[f19577,f1252])).
% 5.22/1.07 % SZS output end Proof for theBenchmark
% 5.22/1.07 % (1512780)------------------------------
% 5.22/1.07 % (1512780)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 5.22/1.07 % (1512780)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.22/1.07 % (1512780)CaDiCaL version: 2.1.3
% 5.22/1.07 % (1512780)Termination reason: Refutation
% 5.22/1.07 % (1512780)Time elapsed: 0.712 s
% 5.22/1.07 % (1512780)Peak memory usage: 21 MB
% 5.22/1.07 % (1512780)Instructions burned: 1532 (million)
% 5.22/1.07 % (1512774)Success in time 0.768 s
% 5.22/1.07 % Vampire exiting
%------------------------------------------------------------------------------