%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP015^3 : TPTP v9.3.1. Bugfixed 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 08:10:20 AM UTC 2026
% Result : Theorem 0.33s 0.31s
% Output : Refutation 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP015^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n020.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 19:31:04 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.33/0.31 % (1477794)Will run a generic schedule for satisfiability detection.
% 0.33/0.31 % (1477810)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3085127824:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.33/0.31 % (1477806)% WARNING: option uhcvi not known.
% 0.33/0.31 % (1477804)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3068295616_2999 on theBenchmark for (2999ds/0Mi)
% 0.33/0.31 % (1477807)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=676678160:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.33/0.31 % (1477811)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2204344279:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.33/0.31 % (1477809)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2239666873:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.33/0.31 % (1477806)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=865920707:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.33/0.31 % (1477809)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.33/0.31 % Exception at run slice level
% 0.33/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.33/0.31 % (1477806)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.33/0.31 % (1477806)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.33/0.31 % (1477808)dis+10_1_sil=32000:sp=arity:random_seed=3781493823:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.33/0.31 % (1477819)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3690564029:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.33/0.31 % Exception at run slice level
% 0.33/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.33/0.31 % (1477810)Instruction limit reached!
% 0.33/0.31 % (1477810)------------------------------
% 0.33/0.31 % (1477810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.31 % (1477810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.31 % (1477810)CaDiCaL version: 2.1.3
% 0.33/0.31 % (1477810)Termination reason: Instruction limit
% 0.33/0.31 % (1477810)Termination phase: Saturation
% 0.33/0.31 % (1477810)Time elapsed: 0.037 s
% 0.33/0.31 % (1477810)Peak memory usage: 13 MB
% 0.33/0.31 % (1477810)Instructions burned: 131 (million)
% 0.33/0.31 % (1477830)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=2261662506:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.33/0.31 % (1477830)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.33/0.31 % (1477830)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.33/0.31 % (1477828)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2930519717:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.33/0.31 % (1477830) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1477794-1477830"...
% 0.33/0.31 % (1477809)Instruction limit reached!
% 0.33/0.31 % (1477809)------------------------------
% 0.33/0.31 % (1477809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.31 % (1477809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.31 % (1477809)CaDiCaL version: 2.1.3
% 0.33/0.31 % (1477809)Termination reason: Instruction limit
% 0.33/0.31 % (1477809)Termination phase: Saturation
% 0.33/0.31 % (1477809)Time elapsed: 0.060 s
% 0.33/0.31 % (1477809)Peak memory usage: 13 MB
% 0.33/0.31 % (1477809)Instructions burned: 118 (million)
% 0.33/0.31 % (1477830)...printing done.
% 0.33/0.31 % (1477830)Refutation found. Thanks to Tanya!
% 0.33/0.31 % SZS status Theorem for theBenchmark
% 0.33/0.31 % SZS output start Proof for theBenchmark
% 0.33/0.31 thf(type_def_5, type, tyop_2Ebool_2Eitself: $tType > $tType).
% 0.33/0.31 thf(type_def_6, type, tyop_2Efcp_2Ecart: ($tType * $tType) > $tType).
% 0.33/0.31 thf(type_def_7, type, tyop_2Einteger_2Eint: $tType).
% 0.33/0.31 thf(type_def_8, type, tyop_2Emin_2Ebool: $tType).
% 0.33/0.31 thf(type_def_9, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 0.33/0.31 thf(type_def_10, type, tyop_2Enum_2Enum: $tType).
% 0.33/0.31 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.33/0.31 thf(type_def_12, type, sK2: $tType).
% 0.33/0.31 thf(func_def_0, type, c_2Ebool_2E_21: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.31 thf(func_def_1, type, c_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 0.33/0.31 thf(func_def_2, type, c_2Enum_2E0: tyop_2Enum_2Enum).
% 0.33/0.31 thf(func_def_3, type, c_2Eprim__rec_2E_3C: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o)).
% 0.33/0.31 thf(func_def_4, type, c_2Emin_2E_3D: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.33/0.31 thf(func_def_5, type, c_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 0.33/0.31 thf(func_def_6, type, c_2Ebool_2E_3F: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.33/0.31 thf(func_def_7, type, c_2Ebool_2ECOND: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.33/0.31 thf(func_def_8, type, c_2Ebool_2EF: $o).
% 0.33/0.31 thf(func_def_9, type, c_2Earithmetic_2EMOD: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum)).
% 0.33/0.31 thf(func_def_10, type, c_2Einteger_2ENum: (tyop_2Einteger_2Eint > tyop_2Enum_2Enum)).
% 0.33/0.31 thf(func_def_11, type, c_2Ebool_2ET: $o).
% 0.33/0.31 thf(func_def_12, type, c_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 0.33/0.31 thf(func_def_13, type, c_2Ewords_2Edimword: !>[X0: $tType]:((tyop_2Ebool_2Eitself @ X0 > tyop_2Enum_2Enum))).
% 0.33/0.31 thf(func_def_14, type, c_2Einteger__word_2Ei2w: !>[X0: $tType]:((tyop_2Einteger_2Eint > tyop_2Efcp_2Ecart @ $o @ X0))).
% 0.33/0.31 thf(func_def_15, type, c_2Einteger_2Eint__lt: (tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o)).
% 0.33/0.31 thf(func_def_16, type, c_2Einteger_2Eint__neg: (tyop_2Einteger_2Eint > tyop_2Einteger_2Eint)).
% 0.33/0.31 thf(func_def_17, type, c_2Einteger_2Eint__of__num: (tyop_2Enum_2Enum > tyop_2Einteger_2Eint)).
% 0.33/0.31 thf(func_def_18, type, c_2Ewords_2En2w: !>[X0: $tType]:((tyop_2Enum_2Enum > tyop_2Efcp_2Ecart @ $o @ X0))).
% 0.33/0.31 thf(func_def_19, type, c_2Ebool_2Ethe__value: !>[X0: $tType]:(tyop_2Ebool_2Eitself @ X0)).
% 0.33/0.31 thf(func_def_20, type, c_2Ewords_2Eword__2comp: !>[X0: $tType]:((tyop_2Efcp_2Ecart @ $o @ X0 > tyop_2Efcp_2Ecart @ $o @ X0))).
% 0.33/0.31 thf(func_def_21, type, c_2Ebool_2E_7E: ($o > $o)).
% 0.33/0.31 thf(func_def_23, type, vNOT: ($o > $o)).
% 0.33/0.31 thf(func_def_26, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.33/0.31 thf(func_def_27, type, sK0: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.33/0.31 thf(func_def_28, type, sK1: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.33/0.31 thf(func_def_30, type, db0: !>[X0: $tType]:(X0)).
% 0.33/0.31 thf(func_def_31, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.33/0.31 thf(func_def_32, type, db1: !>[X0: $tType]:(X0)).
% 0.33/0.31 thf(f10,axiom,(
% 0.33/0.31 ! [X0 : $o] : (c_2Ebool_2EF => X0)),
% 0.33/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY)).
% 0.33/0.31 thf(f15,axiom,(
% 0.33/0.31 ! [X0 : $tType] : (! [X3 : X0,X4 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2EF @ X3 @ X4)) = X4) & ! [X1 : X0,X2 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2ET @ X1 @ X2)) = X1))),
% 0.33/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm)).
% 0.33/0.31 thf(f17,axiom,(
% 0.33/0.31 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1)))) = c_2Ebool_2EF) & ((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__of__num @ X1)) <=> ((~ (X1 = c_2Enum_2E0)) | (~ (X0 = c_2Enum_2E0)))) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1)))) = ((c_2Eprim__rec_2E_3C @ X1 @ X0))) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Eprim__rec_2E_3C @ X0 @ X1))))),
% 0.33/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE)).
% 0.33/0.31 thf(f18,axiom,(
% 0.33/0.31 ! [X0 : tyop_2Enum_2Enum] : (((c_2Einteger_2ENum @ (c_2Einteger_2Eint__of__num @ X0))) = X0)),
% 0.33/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT)).
% 0.33/0.31 thf(f19,axiom,(
% 0.33/0.31 ! [X0 : $tType,X1 : tyop_2Einteger_2Eint] : (((c_2Einteger__word_2Ei2w @ X0 @ X1)) = ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ X0 @ (c_2Einteger_2Eint__lt @ X1 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)) @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ (c_2Einteger_2ENum @ (c_2Einteger_2Eint__neg @ X1)))) @ (c_2Ewords_2En2w @ X0 @ (c_2Einteger_2ENum @ X1)))))),
% 0.33/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def)).
% 0.33/0.31 thf(f20,axiom,(
% 0.33/0.31 ! [X0 : tyop_2Enum_2Enum] : (~ (c_2Eprim__rec_2E_3C @ X0 @ c_2Enum_2E0))),
% 0.33/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__0)).
% 0.33/0.31 thf(f23,conjecture,(
% 0.33/0.31 ! [X0 : $tType] : (((c_2Einteger__word_2Ei2w @ X0 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))) = ((c_2Ewords_2En2w @ X0 @ c_2Enum_2E0)))),
% 0.33/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0)).
% 0.33/0.31 thf(f24,negated_conjecture,(
% 0.33/0.31 ~ ! [X0 : $tType] : (((c_2Einteger__word_2Ei2w @ X0 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))) = ((c_2Ewords_2En2w @ X0 @ c_2Enum_2E0)))),
% 0.33/0.31 inference(negated_conjecture,[status(cth)],[f23])).
% 0.33/0.31 thf(f43,plain,(
% 0.33/0.31 ! [X0 : $o] : (c_2Ebool_2EF => X0)),
% 0.33/0.31 inference(rectify,[],[f10])).
% 0.33/0.31 thf(f44,plain,(
% 0.33/0.31 ! [X0 : $o] : ((c_2Ebool_2EF = $true) => ($true = X0))),
% 0.33/0.31 inference(fool_elimination,[],[f43])).
% 0.33/0.31 thf(f51,plain,(
% 0.33/0.31 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1)))) = c_2Ebool_2EF) & ((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__of__num @ X1)) <=> ((~ (X1 = c_2Enum_2E0)) | (~ (X0 = c_2Enum_2E0)))) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1)))) = ((c_2Eprim__rec_2E_3C @ X1 @ X0))) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Eprim__rec_2E_3C @ X0 @ X1))))),
% 0.33/0.31 inference(rectify,[],[f17])).
% 0.33/0.31 thf(f52,plain,(
% 0.33/0.31 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Ebool_2EF = ((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1))))) & ((((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__of__num @ X1))) = $true) <=> (($true = ((~ (c_2Enum_2E0 = X1)))) | ($true = ((~ (c_2Enum_2E0 = X0)))))) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1)))) = ((c_2Eprim__rec_2E_3C @ X1 @ X0))) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Eprim__rec_2E_3C @ X0 @ X1))))),
% 0.33/0.31 inference(fool_elimination,[],[f51])).
% 0.33/0.31 thf(f53,plain,(
% 0.33/0.31 ! [X0 : tyop_2Enum_2Enum] : (~ (c_2Eprim__rec_2E_3C @ X0 @ c_2Enum_2E0))),
% 0.33/0.31 inference(rectify,[],[f20])).
% 0.33/0.31 thf(f54,plain,(
% 0.33/0.31 ! [X0 : tyop_2Enum_2Enum] : (((~ (c_2Eprim__rec_2E_3C @ X0 @ c_2Enum_2E0))) = $true)),
% 0.33/0.31 inference(fool_elimination,[],[f53])).
% 0.33/0.31 thf(f55,plain,(
% 0.33/0.31 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2EF @ X1 @ X2)) = X2) & ! [X3 : X0,X4 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2ET @ X3 @ X4)) = X3))),
% 0.33/0.31 inference(rectify,[],[f15])).
% 0.33/0.31 thf(f59,plain,(
% 0.33/0.31 ! [X0 : $o] : (($true = X0) | (c_2Ebool_2EF != $true))),
% 0.33/0.31 inference(ennf_transformation,[],[f44])).
% 0.33/0.31 thf(f64,plain,(
% 0.33/0.31 ? [X0 : $tType] : (((c_2Ewords_2En2w @ X0 @ c_2Enum_2E0)) != ((c_2Einteger__word_2Ei2w @ X0 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))))),
% 0.33/0.31 inference(ennf_transformation,[],[f24])).
% 0.33/0.31 thf(f82,plain,(
% 0.33/0.31 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Ebool_2EF = ((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1))))) & (((((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__of__num @ X1))) = $true) | (($true != ((~ (c_2Enum_2E0 = X1)))) & ($true != ((~ (c_2Enum_2E0 = X0)))))) & ((($true = ((~ (c_2Enum_2E0 = X1)))) | ($true = ((~ (c_2Enum_2E0 = X0))))) | (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__of__num @ X1))) != $true))) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1)))) = ((c_2Eprim__rec_2E_3C @ X1 @ X0))) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Eprim__rec_2E_3C @ X0 @ X1))))),
% 0.33/0.31 inference(nnf_transformation,[],[f52])).
% 0.33/0.31 thf(f83,plain,(
% 0.33/0.31 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Ebool_2EF = ((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1))))) & ((((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__of__num @ X1))) = $true) | (($true != ((~ (c_2Enum_2E0 = X1)))) & ($true != ((~ (c_2Enum_2E0 = X0)))))) & (($true = ((~ (c_2Enum_2E0 = X1)))) | ($true = ((~ (c_2Enum_2E0 = X0)))) | (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__of__num @ X1))) != $true)) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1)))) = ((c_2Eprim__rec_2E_3C @ X1 @ X0))) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Eprim__rec_2E_3C @ X0 @ X1))))),
% 0.33/0.31 inference(flattening,[],[f82])).
% 0.33/0.31 thf(f85,plain,(
% 0.33/0.31 (((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)) != ((c_2Einteger__word_2Ei2w @ sK2 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))))),
% 0.33/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f64])).
% 0.33/0.31 thf(f107,plain,(
% 0.33/0.31 ( ! [X0 : $o] : (($true = X0) | (c_2Ebool_2EF != $true)) )),
% 0.33/0.31 inference(cnf_transformation,[],[f59])).
% 0.33/0.31 thf(f123,plain,(
% 0.33/0.31 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2EF @ X1 @ X2)) = X2)) )),
% 0.33/0.31 inference(cnf_transformation,[],[f55])).
% 0.33/0.31 thf(f125,plain,(
% 0.33/0.31 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Eprim__rec_2E_3C @ X0 @ X1)))) )),
% 0.33/0.31 inference(cnf_transformation,[],[f83])).
% 0.33/0.31 thf(f131,plain,(
% 0.33/0.31 ( ! [X0 : tyop_2Enum_2Enum] : ((((c_2Einteger_2ENum @ (c_2Einteger_2Eint__of__num @ X0))) = X0)) )),
% 0.33/0.31 inference(cnf_transformation,[],[f18])).
% 0.33/0.31 thf(f132,plain,(
% 0.33/0.31 ( ! [X0 : $tType,X1 : tyop_2Einteger_2Eint] : ((((c_2Einteger__word_2Ei2w @ X0 @ X1)) = ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ X0 @ (c_2Einteger_2Eint__lt @ X1 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)) @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ (c_2Einteger_2ENum @ (c_2Einteger_2Eint__neg @ X1)))) @ (c_2Ewords_2En2w @ X0 @ (c_2Einteger_2ENum @ X1)))))) )),
% 0.33/0.31 inference(cnf_transformation,[],[f19])).
% 0.33/0.31 thf(f133,plain,(
% 0.33/0.31 ( ! [X0 : tyop_2Enum_2Enum] : ((((~ (c_2Eprim__rec_2E_3C @ X0 @ c_2Enum_2E0))) = $true)) )),
% 0.33/0.31 inference(cnf_transformation,[],[f54])).
% 0.33/0.31 thf(f137,plain,(
% 0.33/0.31 (((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)) != ((c_2Einteger__word_2Ei2w @ sK2 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))))),
% 0.33/0.31 inference(cnf_transformation,[],[f85])).
% 0.33/0.31 thf(f138,definition,(
% 0.33/0.31 ($true != $false)),
% 0.33/0.31 introduced(theory,[fool_distinctness_axiom])).
% 0.33/0.31 thf(f139,definition,(
% 0.33/0.31 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.33/0.31 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.33/0.31 thf(f178,plain,(
% 0.33/0.31 ( ! [X0 : tyop_2Enum_2Enum] : ((((c_2Eprim__rec_2E_3C @ X0 @ c_2Enum_2E0)) = $false)) )),
% 0.33/0.31 inference(not_proxy_clausification,[],[f133])).
% 0.33/0.31 thf(f180,plain,(
% 0.33/0.31 ( ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = $false) | (((c_2Eprim__rec_2E_3C @ X0 @ X1)) = $true)) )),
% 0.33/0.31 inference(iff_proxy_clausification,[],[f125])).
% 0.33/0.31 thf(f215,definition,(
% 0.33/0.31 spl3_4 <=> (c_2Ebool_2EF = $true)),
% 0.33/0.31 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.33/0.31 thf(f216,plain,(
% 0.33/0.31 (c_2Ebool_2EF != $true) | spl3_4),
% 0.33/0.31 inference(avatar_component_clause,[],[f215])).
% 0.33/0.31 thf(f220,definition,(
% 0.33/0.31 spl3_5 <=> ! [X0 : $o] : ($true = X0)),
% 0.33/0.31 introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition])).
% 0.33/0.31 thf(f221,plain,(
% 0.33/0.31 ( ! [X0 : $o] : (($true = X0)) ) | ~spl3_5),
% 0.33/0.31 inference(avatar_component_clause,[],[f220])).
% 0.33/0.31 thf(f222,plain,(
% 0.33/0.31 ~spl3_4 | spl3_5),
% 0.33/0.31 inference(avatar_split_clause,[],[f107,f220,f215])).
% 0.33/0.31 thf(f229,plain,(
% 0.33/0.31 ( ! [X0 : $o] : (($false != X0)) ) | ~spl3_5),
% 0.33/0.31 inference(constrained_superposition,[],[f138,f221])).
% 0.33/0.31 thf(f232,plain,(
% 0.33/0.31 $false | ~spl3_5),
% 0.33/0.31 inference(equality_resolution,[],[f229])).
% 0.33/0.31 thf(f233,plain,(
% 0.33/0.31 ~spl3_5),
% 0.33/0.31 inference(avatar_contradiction_clause,[],[f232])).
% 0.33/0.31 thf(f236,plain,(
% 0.33/0.31 ($true != $true) | (c_2Ebool_2EF = $false) | spl3_4),
% 0.33/0.31 inference(constrained_superposition,[],[f216,f139])).
% 0.33/0.31 thf(f238,plain,(
% 0.33/0.31 (c_2Ebool_2EF = $false) | spl3_4),
% 0.33/0.31 inference(trivial_inequality_removal,[],[f236])).
% 0.33/0.31 thf(f395,plain,(
% 0.33/0.31 ( ! [X0 : $tType,X1 : tyop_2Enum_2Enum] : ((((c_2Einteger__word_2Ei2w @ X0 @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ X0 @ $false @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ (c_2Einteger_2ENum @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1))))) @ (c_2Ewords_2En2w @ X0 @ (c_2Einteger_2ENum @ (c_2Einteger_2Eint__of__num @ X1)))))) | ($true = ((c_2Eprim__rec_2E_3C @ X1 @ c_2Enum_2E0)))) )),
% 0.33/0.31 inference(constrained_superposition,[],[f132,f180])).
% 0.33/0.31 thf(f400,plain,(
% 0.33/0.31 ( ! [X0 : $tType,X1 : tyop_2Enum_2Enum] : ((((c_2Einteger__word_2Ei2w @ X0 @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ X0 @ $false @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ (c_2Einteger_2ENum @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1))))) @ (c_2Ewords_2En2w @ X0 @ X1)))) | ($true = ((c_2Eprim__rec_2E_3C @ X1 @ c_2Enum_2E0)))) )),
% 0.33/0.31 inference(forward_demodulation,[],[f395,f131])).
% 0.33/0.31 thf(f404,plain,(
% 0.33/0.31 ( ! [X0 : $tType,X1 : tyop_2Enum_2Enum] : (($true = $false) | (((c_2Einteger__word_2Ei2w @ X0 @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ X0 @ $false @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ (c_2Einteger_2ENum @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1))))) @ (c_2Ewords_2En2w @ X0 @ X1))))) )),
% 0.33/0.31 inference(forward_demodulation,[],[f400,f178])).
% 0.33/0.31 thf(f405,plain,(
% 0.33/0.31 ( ! [X0 : $tType,X1 : tyop_2Enum_2Enum] : ((((c_2Einteger__word_2Ei2w @ X0 @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ X0 @ $false @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ (c_2Einteger_2ENum @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1))))) @ (c_2Ewords_2En2w @ X0 @ X1))))) )),
% 0.33/0.31 inference(trivial_inequality_removal,[],[f404])).
% 0.33/0.31 thf(f873,plain,(
% 0.33/0.31 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((c_2Ebool_2ECOND @ X0 @ $false @ X1 @ X2)) = X2)) ) | spl3_4),
% 0.33/0.31 inference(forward_demodulation,[],[f123,f238])).
% 0.33/0.31 thf(f877,plain,(
% 0.33/0.31 ( ! [X0 : $tType,X1 : tyop_2Enum_2Enum] : ((((c_2Ewords_2En2w @ X0 @ X1)) = ((c_2Einteger__word_2Ei2w @ X0 @ (c_2Einteger_2Eint__of__num @ X1))))) ) | spl3_4),
% 0.33/0.31 inference(constrained_superposition,[],[f873,f405])).
% 0.33/0.31 thf(f900,plain,(
% 0.33/0.31 (((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)) != ((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0))) | spl3_4),
% 0.33/0.31 inference(constrained_superposition,[],[f137,f877])).
% 0.33/0.31 thf(f901,plain,(
% 0.33/0.31 $false | spl3_4),
% 0.33/0.31 inference(trivial_inequality_removal,[],[f900])).
% 0.33/0.31 thf(f902,plain,(
% 0.33/0.31 spl3_4),
% 0.33/0.31 inference(avatar_contradiction_clause,[],[f901])).
% 0.33/0.31 cnf(s3, plain, ~spl3_4 | spl3_5, inference(sat_conversion,[],[f222])).
% 0.33/0.31 cnf(s6, plain, ~spl3_5, inference(sat_conversion,[],[f233])).
% 0.33/0.31 cnf(s41, plain, spl3_4, inference(sat_conversion,[],[f902])).
% 0.33/0.31 cnf(s62, plain, $false, inference(rat,[],[s3,s6,s41])).
% 0.33/0.31 thf(f903,plain,(
% 0.33/0.31 $false),
% 0.33/0.31 inference(avatar_sat_refutation,[],[s62])).
% 0.33/0.31 % SZS output end Proof for theBenchmark
% 0.33/0.31 % (1477830)------------------------------
% 0.33/0.31 % (1477830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.31 % (1477830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.31 % (1477830)CaDiCaL version: 2.1.3
% 0.33/0.31 % (1477830)Termination reason: Refutation
% 0.33/0.31 % (1477830)Time elapsed: 0.020 s
% 0.33/0.31 % (1477830)Peak memory usage: 13 MB
% 0.33/0.31 % (1477830)Instructions burned: 66 (million)
% 0.33/0.31 % (1477794)Success in time 0.097 s
% 0.33/0.31 % Vampire exiting
%------------------------------------------------------------------------------