%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP015^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 08:07:47 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% 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.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n001.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 19:35:49 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.31 % (1704639)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (1704647)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1923869960:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.31 % (1704650)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (1704650)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.31 % (1704644)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1583279911:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (1704645)lrs+10_16_si=on:nwc=1.5:random_seed=3133719316:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (1704646)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3685663868:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (1704650)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3374563459:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (1704648)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3527761364:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (1704649)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4270589710:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (1704646)Instruction limit reached!
% 0.22/0.31 % (1704646)------------------------------
% 0.22/0.31 % (1704646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1704646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1704646)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1704646)Termination reason: Instruction limit
% 0.22/0.31 % (1704646)Termination phase: Clausification
% 0.22/0.31 % (1704646)Time elapsed: 0.002 s
% 0.22/0.31 % (1704646)Peak memory usage: 10 MB
% 0.22/0.31 % (1704646)Instructions burned: 3 (million)
% 0.22/0.31 % (1704647) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1704639-1704647"...
% 0.22/0.31 % (1704647)...printing done.
% 0.22/0.31 % (1704647)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% 0.22/0.31 thf(type_def_5, type, tyop_2Ebool_2Eitself: $tType > $tType).
% 0.22/0.31 thf(type_def_6, type, tyop_2Efcp_2Ecart: ($tType * $tType) > $tType).
% 0.22/0.31 thf(type_def_7, type, tyop_2Einteger_2Eint: $tType).
% 0.22/0.31 thf(type_def_8, type, tyop_2Emin_2Ebool: $tType).
% 0.22/0.31 thf(type_def_9, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 0.22/0.31 thf(type_def_10, type, tyop_2Enum_2Enum: $tType).
% 0.22/0.31 thf(type_def_11, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.31 thf(type_def_12, type, sK2: $tType).
% 0.22/0.31 thf(func_def_0, type, c_2Ebool_2E_21: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.31 thf(func_def_1, type, c_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 0.22/0.31 thf(func_def_2, type, c_2Enum_2E0: tyop_2Enum_2Enum).
% 0.22/0.31 thf(func_def_3, type, c_2Eprim__rec_2E_3C: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o)).
% 0.22/0.31 thf(func_def_4, type, c_2Emin_2E_3D: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.31 thf(func_def_5, type, c_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 0.22/0.31 thf(func_def_6, type, c_2Ebool_2E_3F: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.31 thf(func_def_7, type, c_2Ebool_2ECOND: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.22/0.31 thf(func_def_8, type, c_2Ebool_2EF: $o).
% 0.22/0.31 thf(func_def_9, type, c_2Earithmetic_2EMOD: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum)).
% 0.22/0.31 thf(func_def_10, type, c_2Einteger_2ENum: (tyop_2Einteger_2Eint > tyop_2Enum_2Enum)).
% 0.22/0.31 thf(func_def_11, type, c_2Ebool_2ET: $o).
% 0.22/0.31 thf(func_def_12, type, c_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 0.22/0.31 thf(func_def_13, type, c_2Ewords_2Edimword: !>[X0: $tType]:((tyop_2Ebool_2Eitself @ X0 > tyop_2Enum_2Enum))).
% 0.22/0.31 thf(func_def_14, type, c_2Einteger__word_2Ei2w: !>[X0: $tType]:((tyop_2Einteger_2Eint > tyop_2Efcp_2Ecart @ $o @ X0))).
% 0.22/0.31 thf(func_def_15, type, c_2Einteger_2Eint__lt: (tyop_2Einteger_2Eint > tyop_2Einteger_2Eint > $o)).
% 0.22/0.31 thf(func_def_16, type, c_2Einteger_2Eint__neg: (tyop_2Einteger_2Eint > tyop_2Einteger_2Eint)).
% 0.22/0.31 thf(func_def_17, type, c_2Einteger_2Eint__of__num: (tyop_2Enum_2Enum > tyop_2Einteger_2Eint)).
% 0.22/0.31 thf(func_def_18, type, c_2Ewords_2En2w: !>[X0: $tType]:((tyop_2Enum_2Enum > tyop_2Efcp_2Ecart @ $o @ X0))).
% 0.22/0.31 thf(func_def_19, type, c_2Ebool_2Ethe__value: !>[X0: $tType]:(tyop_2Ebool_2Eitself @ X0)).
% 0.22/0.31 thf(func_def_20, type, c_2Ewords_2Eword__2comp: !>[X0: $tType]:((tyop_2Efcp_2Ecart @ $o @ X0 > tyop_2Efcp_2Ecart @ $o @ X0))).
% 0.22/0.31 thf(func_def_21, type, c_2Ebool_2E_7E: ($o > $o)).
% 0.22/0.31 thf(func_def_23, type, vNOT: ($o > $o)).
% 0.22/0.31 thf(func_def_26, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.31 thf(func_def_27, type, sK0: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.31 thf(func_def_28, type, sK1: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.31 thf(f8,axiom,(
% 0.22/0.31 c_2Ebool_2ET),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2ETRUTH)).
% 0.22/0.31 thf(f10,axiom,(
% 0.22/0.31 ! [X0 : $o] : (c_2Ebool_2EF => X0)),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EFALSITY)).
% 0.22/0.31 thf(f15,axiom,(
% 0.22/0.31 ! [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))),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm)).
% 0.22/0.31 thf(f16,axiom,(
% 0.22/0.31 (((c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))) = ((c_2Einteger_2Eint__of__num @ c_2Enum_2E0)))),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__NEG__0)).
% 0.22/0.31 thf(f17,axiom,(
% 0.22/0.31 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((((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__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__of__num @ X0) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1)))) = c_2Ebool_2EF) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Eprim__rec_2E_3C @ X0 @ X1))))),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2EINT__LT__CALCULATE)).
% 0.22/0.31 thf(f18,axiom,(
% 0.22/0.31 ! [X0 : tyop_2Enum_2Enum] : (((c_2Einteger_2ENum @ (c_2Einteger_2Eint__of__num @ X0))) = X0)),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger_2ENUM__OF__INT)).
% 0.22/0.31 thf(f19,axiom,(
% 0.22/0.31 ! [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)))))),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__def)).
% 0.22/0.31 thf(f20,axiom,(
% 0.22/0.31 ! [X0 : tyop_2Enum_2Enum] : (~ (c_2Eprim__rec_2E_3C @ X0 @ c_2Enum_2E0))),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eprim__rec_2ENOT__LESS__0)).
% 0.22/0.31 thf(f22,axiom,(
% 0.22/0.31 ! [X0 : $tType] : (((c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ c_2Enum_2E0))) = ((c_2Ewords_2En2w @ X0 @ c_2Enum_2E0)))),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__NEG__0)).
% 0.22/0.31 thf(f23,conjecture,(
% 0.22/0.31 ! [X0 : $tType] : (((c_2Einteger__word_2Ei2w @ X0 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))) = ((c_2Ewords_2En2w @ X0 @ c_2Enum_2E0)))),
% 0.22/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Einteger__word_2Ei2w__0)).
% 0.22/0.31 thf(f24,negated_conjecture,(
% 0.22/0.31 ~ ! [X0 : $tType] : (((c_2Einteger__word_2Ei2w @ X0 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))) = ((c_2Ewords_2En2w @ X0 @ c_2Enum_2E0)))),
% 0.22/0.31 inference(negated_conjecture,[status(cth)],[f23])).
% 0.22/0.31 thf(f29,plain,(
% 0.22/0.31 ! [X0 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((((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__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__of__num @ X0) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1)))) = c_2Ebool_2EF) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Eprim__rec_2E_3C @ X0 @ X1))))),
% 0.22/0.31 inference(rectify,[],[f17])).
% 0.22/0.31 thf(f30,plain,(
% 0.22/0.31 ! [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)))) = $true) <=> (c_2Ebool_2EF = $true)) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Eprim__rec_2E_3C @ X0 @ X1))) & ((((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__of__num @ X1))) = $true) <=> ((((~ (c_2Enum_2E0 = X0))) = $true) | (((~ (c_2Enum_2E0 = 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))))),
% 0.22/0.31 inference(fool_elimination,[],[f29])).
% 0.22/0.31 thf(f33,plain,(
% 0.22/0.31 ! [X0 : tyop_2Enum_2Enum] : (~ (c_2Eprim__rec_2E_3C @ X0 @ c_2Enum_2E0))),
% 0.22/0.31 inference(rectify,[],[f20])).
% 0.22/0.31 thf(f34,plain,(
% 0.22/0.31 ! [X0 : tyop_2Enum_2Enum] : (((~ (c_2Eprim__rec_2E_3C @ X0 @ c_2Enum_2E0))) = $true)),
% 0.22/0.31 inference(fool_elimination,[],[f33])).
% 0.22/0.31 thf(f37,plain,(
% 0.22/0.31 c_2Ebool_2ET),
% 0.22/0.31 inference(rectify,[],[f8])).
% 0.22/0.31 thf(f38,plain,(
% 0.22/0.31 (c_2Ebool_2ET = $true)),
% 0.22/0.31 inference(fool_elimination,[],[f37])).
% 0.22/0.31 thf(f45,plain,(
% 0.22/0.31 ! [X0 : $o] : (c_2Ebool_2EF => X0)),
% 0.22/0.31 inference(rectify,[],[f10])).
% 0.22/0.31 thf(f46,plain,(
% 0.22/0.31 ! [X0 : $o] : ((c_2Ebool_2EF = $true) => ($true = X0))),
% 0.22/0.31 inference(fool_elimination,[],[f45])).
% 0.22/0.31 thf(f55,plain,(
% 0.22/0.31 ! [X0 : $tType] : (! [X3 : X0,X4 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2ET @ X3 @ X4)) = X3) & ! [X2 : X0,X1 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2EF @ X1 @ X2)) = X2))),
% 0.22/0.31 inference(rectify,[],[f15])).
% 0.22/0.31 thf(f60,plain,(
% 0.22/0.31 ! [X0 : $o] : (($true = X0) | (c_2Ebool_2EF != $true))),
% 0.22/0.31 inference(ennf_transformation,[],[f46])).
% 0.22/0.31 thf(f62,plain,(
% 0.22/0.31 ? [X0 : $tType] : (((c_2Ewords_2En2w @ X0 @ c_2Enum_2E0)) != ((c_2Einteger__word_2Ei2w @ X0 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))))),
% 0.22/0.31 inference(ennf_transformation,[],[f24])).
% 0.22/0.31 thf(f74,plain,(
% 0.22/0.31 ! [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)))) = $true) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1)))) != $true))) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Eprim__rec_2E_3C @ X0 @ X1))) & (((((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__of__num @ X1))) = $true) | ((((~ (c_2Enum_2E0 = X0))) != $true) & (((~ (c_2Enum_2E0 = X1))) != $true))) & (((((~ (c_2Enum_2E0 = X0))) = $true) | (((~ (c_2Enum_2E0 = X1))) = $true)) | (((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))))),
% 0.22/0.31 inference(nnf_transformation,[],[f30])).
% 0.22/0.31 thf(f75,plain,(
% 0.22/0.31 ! [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)))) = $true) | (c_2Ebool_2EF != $true)) & ((c_2Ebool_2EF = $true) | (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X1)))) != $true)) & (((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ X0) @ (c_2Einteger_2Eint__of__num @ X1))) = ((c_2Eprim__rec_2E_3C @ X0 @ X1))) & ((((c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ X0)) @ (c_2Einteger_2Eint__of__num @ X1))) = $true) | ((((~ (c_2Enum_2E0 = X0))) != $true) & (((~ (c_2Enum_2E0 = X1))) != $true))) & ((((~ (c_2Enum_2E0 = X0))) = $true) | (((~ (c_2Enum_2E0 = X1))) = $true) | (((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))))),
% 0.22/0.31 inference(flattening,[],[f74])).
% 0.22/0.31 thf(f85,plain,(
% 0.22/0.31 (((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)) != ((c_2Einteger__word_2Ei2w @ sK2 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))))),
% 0.22/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f62])).
% 0.22/0.31 thf(f87,plain,(
% 0.22/0.31 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2ET @ X1 @ X2)) = X1) & ! [X3 : X0,X4 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2EF @ X4 @ X3)) = X3))),
% 0.22/0.31 inference(rectify,[],[f55])).
% 0.22/0.31 thf(f102,plain,(
% 0.22/0.31 ( ! [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)))))) )),
% 0.22/0.31 inference(cnf_transformation,[],[f19])).
% 0.22/0.31 thf(f103,plain,(
% 0.22/0.31 ( ! [X0 : tyop_2Enum_2Enum] : ((((~ (c_2Eprim__rec_2E_3C @ X0 @ c_2Enum_2E0))) = $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f34])).
% 0.22/0.31 thf(f110,plain,(
% 0.22/0.31 ( ! [X0 : tyop_2Enum_2Enum] : ((((c_2Einteger_2ENum @ (c_2Einteger_2Eint__of__num @ X0))) = X0)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f18])).
% 0.22/0.31 thf(f111,plain,(
% 0.22/0.31 (((c_2Einteger_2Eint__of__num @ c_2Enum_2E0)) = ((c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))))),
% 0.22/0.31 inference(cnf_transformation,[],[f16])).
% 0.22/0.31 thf(f116,plain,(
% 0.22/0.31 ( ! [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)))) )),
% 0.22/0.31 inference(cnf_transformation,[],[f75])).
% 0.22/0.31 thf(f126,plain,(
% 0.22/0.31 ( ! [X0 : $o] : (($true = X0) | (c_2Ebool_2EF != $true)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f60])).
% 0.22/0.31 thf(f131,plain,(
% 0.22/0.31 (c_2Ebool_2ET = $true)),
% 0.22/0.31 inference(cnf_transformation,[],[f38])).
% 0.22/0.31 thf(f132,plain,(
% 0.22/0.31 (((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)) != ((c_2Einteger__word_2Ei2w @ sK2 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))))),
% 0.22/0.31 inference(cnf_transformation,[],[f85])).
% 0.22/0.31 thf(f135,plain,(
% 0.22/0.31 ( ! [X0 : $tType,X3 : X0,X4 : X0] : ((((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2EF @ X4 @ X3)) = X3)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f87])).
% 0.22/0.31 thf(f136,plain,(
% 0.22/0.31 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2ET @ X1 @ X2)) = X1)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f87])).
% 0.22/0.31 thf(f145,plain,(
% 0.22/0.31 ( ! [X0 : $tType] : ((((c_2Ewords_2En2w @ X0 @ c_2Enum_2E0)) = ((c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ c_2Enum_2E0))))) )),
% 0.22/0.31 inference(cnf_transformation,[],[f22])).
% 0.22/0.31 thf(f199,plain,(
% 0.22/0.31 ( ! [X0 : tyop_2Enum_2Enum] : ((((c_2Eprim__rec_2E_3C @ X0 @ c_2Enum_2E0)) = $false)) )),
% 0.22/0.31 inference(not_proxy_clausification,[],[f103])).
% 0.22/0.31 thf(f201,plain,(
% 0.22/0.31 ( ! [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)) )),
% 0.22/0.31 inference(iff_proxy_clausification,[],[f116])).
% 0.22/0.31 thf(f207,definition,(
% 0.22/0.31 spl3_1 <=> (((c_2Einteger_2Eint__of__num @ c_2Enum_2E0)) = ((c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition])).
% 0.22/0.31 thf(f209,plain,(
% 0.22/0.31 (((c_2Einteger_2Eint__of__num @ c_2Enum_2E0)) = ((c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)))) | ~spl3_1),
% 0.22/0.31 inference(avatar_component_clause,[],[f207])).
% 0.22/0.31 thf(f210,plain,(
% 0.22/0.31 spl3_1),
% 0.22/0.31 inference(avatar_split_clause,[],[f111,f207])).
% 0.22/0.31 thf(f212,definition,(
% 0.22/0.31 spl3_2 <=> ! [X0 : $o] : ($true = X0)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition])).
% 0.22/0.31 thf(f213,plain,(
% 0.22/0.31 ( ! [X0 : $o] : (($true = X0)) ) | ~spl3_2),
% 0.22/0.31 inference(avatar_component_clause,[],[f212])).
% 0.22/0.31 thf(f215,definition,(
% 0.22/0.31 spl3_3 <=> (c_2Ebool_2EF = $true)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 0.22/0.31 thf(f217,plain,(
% 0.22/0.31 (c_2Ebool_2EF != $true) | spl3_3),
% 0.22/0.31 inference(avatar_component_clause,[],[f215])).
% 0.22/0.31 thf(f218,plain,(
% 0.22/0.31 spl3_2 | ~spl3_3),
% 0.22/0.31 inference(avatar_split_clause,[],[f126,f215,f212])).
% 0.22/0.31 thf(f220,definition,(
% 0.22/0.31 spl3_4 <=> (c_2Ebool_2ET = $true)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 0.22/0.31 thf(f222,plain,(
% 0.22/0.31 (c_2Ebool_2ET = $true) | ~spl3_4),
% 0.22/0.31 inference(avatar_component_clause,[],[f220])).
% 0.22/0.31 thf(f223,plain,(
% 0.22/0.31 spl3_4),
% 0.22/0.31 inference(avatar_split_clause,[],[f131,f220])).
% 0.22/0.31 thf(f225,definition,(
% 0.22/0.31 spl3_5 <=> (((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)) = ((c_2Einteger__word_2Ei2w @ sK2 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition])).
% 0.22/0.31 thf(f227,plain,(
% 0.22/0.31 (((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)) != ((c_2Einteger__word_2Ei2w @ sK2 @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)))) | spl3_5),
% 0.22/0.31 inference(avatar_component_clause,[],[f225])).
% 0.22/0.31 thf(f228,plain,(
% 0.22/0.31 ~spl3_5),
% 0.22/0.31 inference(avatar_split_clause,[],[f132,f225])).
% 0.22/0.31 thf(f243,plain,(
% 0.22/0.31 (c_2Ebool_2EF = $false) | ($true != $true) | spl3_3),
% 0.22/0.31 inference(fool_paramodulation,[],[f217])).
% 0.22/0.31 thf(f244,plain,(
% 0.22/0.31 (c_2Ebool_2EF = $false) | spl3_3),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f243])).
% 0.22/0.31 thf(f246,definition,(
% 0.22/0.31 spl3_9 <=> (c_2Ebool_2EF = $false)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl3_9])],[avatar_definition])).
% 0.22/0.31 thf(f248,plain,(
% 0.22/0.31 (c_2Ebool_2EF = $false) | ~spl3_9),
% 0.22/0.31 inference(avatar_component_clause,[],[f246])).
% 0.22/0.31 thf(f249,plain,(
% 0.22/0.31 spl3_9 | spl3_3),
% 0.22/0.31 inference(avatar_split_clause,[],[f244,f215,f246])).
% 0.22/0.31 thf(f256,plain,(
% 0.22/0.31 ( ! [X0 : $tType,X3 : X0,X4 : X0] : ((((c_2Ebool_2ECOND @ X0 @ $false @ X4 @ X3)) = X3)) ) | ~spl3_9),
% 0.22/0.31 inference(forward_demodulation,[],[f135,f248])).
% 0.22/0.31 thf(f257,plain,(
% 0.22/0.31 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((c_2Ebool_2ECOND @ X0 @ $true @ X1 @ X2)) = X1)) ) | ~spl3_4),
% 0.22/0.31 inference(forward_demodulation,[],[f136,f222])).
% 0.22/0.31 thf(f321,plain,(
% 0.22/0.31 (((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)) != ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ sK2 @ (c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0) @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)) @ (c_2Ewords_2Eword__2comp @ sK2 @ (c_2Ewords_2En2w @ sK2 @ (c_2Einteger_2ENum @ (c_2Einteger_2Eint__neg @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))))) @ (c_2Ewords_2En2w @ sK2 @ (c_2Einteger_2ENum @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)))))) | spl3_5),
% 0.22/0.31 inference(superposition,[],[f227,f102])).
% 0.22/0.31 thf(f328,plain,(
% 0.22/0.31 (((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ sK2 @ (c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0) @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)) @ (c_2Ewords_2Eword__2comp @ sK2 @ (c_2Ewords_2En2w @ sK2 @ (c_2Einteger_2ENum @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)))) @ (c_2Ewords_2En2w @ sK2 @ (c_2Einteger_2ENum @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0))))) != ((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0))) | (~spl3_1 | spl3_5)),
% 0.22/0.31 inference(forward_demodulation,[],[f321,f209])).
% 0.22/0.31 thf(f329,plain,(
% 0.22/0.31 (((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)) != ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ sK2 @ (c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0) @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)) @ (c_2Ewords_2Eword__2comp @ sK2 @ (c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)) @ (c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)))) | (~spl3_1 | spl3_5)),
% 0.22/0.31 inference(forward_demodulation,[],[f328,f110])).
% 0.22/0.31 thf(f330,plain,(
% 0.22/0.31 (((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ sK2 @ (c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0) @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)) @ (c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0) @ (c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0))) != ((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0))) | (~spl3_1 | spl3_5)),
% 0.22/0.31 inference(forward_demodulation,[],[f329,f145])).
% 0.22/0.31 thf(f332,definition,(
% 0.22/0.31 spl3_10 <=> (((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ sK2 @ (c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0) @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)) @ (c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0) @ (c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0))) = ((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl3_10])],[avatar_definition])).
% 0.22/0.31 thf(f334,plain,(
% 0.22/0.31 (((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ sK2 @ (c_2Einteger_2Eint__lt @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0) @ (c_2Einteger_2Eint__of__num @ c_2Enum_2E0)) @ (c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0) @ (c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0))) != ((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0))) | spl3_10),
% 0.22/0.31 inference(avatar_component_clause,[],[f332])).
% 0.22/0.31 thf(f335,plain,(
% 0.22/0.31 ~spl3_10 | ~spl3_1 | spl3_5),
% 0.22/0.31 inference(avatar_split_clause,[],[f330,f225,f207,f332])).
% 0.22/0.31 thf(f351,plain,(
% 0.22/0.31 (((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ sK2 @ $false @ (c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0) @ (c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0))) != ((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0))) | (((c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0)) = $true) | spl3_10),
% 0.22/0.31 inference(superposition,[],[f334,f201])).
% 0.22/0.31 thf(f376,plain,(
% 0.22/0.31 (((c_2Eprim__rec_2E_3C @ c_2Enum_2E0 @ c_2Enum_2E0)) = $true) | (~spl3_9 | spl3_10)),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f351,f256])).
% 0.22/0.31 thf(f378,plain,(
% 0.22/0.31 ($false = $true) | (~spl3_9 | spl3_10)),
% 0.22/0.31 inference(forward_demodulation,[],[f376,f199])).
% 0.22/0.31 thf(f379,plain,(
% 0.22/0.31 $false | (~spl3_9 | spl3_10)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f378])).
% 0.22/0.31 thf(f380,plain,(
% 0.22/0.31 ~spl3_9 | spl3_10),
% 0.22/0.31 inference(avatar_contradiction_clause,[],[f379])).
% 0.22/0.31 thf(f399,plain,(
% 0.22/0.31 ( ! [X1 : $tType,X2 : X1,X3 : X1,X0 : $o] : ((((c_2Ebool_2ECOND @ X1 @ X0 @ X2 @ X3)) = X2)) ) | (~spl3_2 | ~spl3_4)),
% 0.22/0.31 inference(superposition,[],[f257,f213])).
% 0.22/0.31 thf(f488,plain,(
% 0.22/0.31 (((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0)) != ((c_2Ewords_2En2w @ sK2 @ c_2Enum_2E0))) | (~spl3_2 | ~spl3_4 | spl3_10)),
% 0.22/0.31 inference(superposition,[],[f334,f399])).
% 0.22/0.31 thf(f489,plain,(
% 0.22/0.31 $false | (~spl3_2 | ~spl3_4 | spl3_10)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f488])).
% 0.22/0.31 thf(f490,plain,(
% 0.22/0.31 ~spl3_2 | ~spl3_4 | spl3_10),
% 0.22/0.31 inference(avatar_contradiction_clause,[],[f489])).
% 0.22/0.31 cnf(s1, plain, spl3_1, inference(sat_conversion,[],[f210])).
% 0.22/0.31 cnf(s2, plain, spl3_2 | ~spl3_3, inference(sat_conversion,[],[f218])).
% 0.22/0.31 cnf(s3, plain, spl3_4, inference(sat_conversion,[],[f223])).
% 0.22/0.31 cnf(s4, plain, ~spl3_5, inference(sat_conversion,[],[f228])).
% 0.22/0.31 cnf(s9, plain, spl3_3 | spl3_9, inference(sat_conversion,[],[f249])).
% 0.22/0.31 cnf(s10, plain, ~spl3_1 | spl3_5 | ~spl3_10, inference(sat_conversion,[],[f335])).
% 0.22/0.31 cnf(s16, plain, ~spl3_9 | spl3_10, inference(sat_conversion,[],[f380])).
% 0.22/0.31 cnf(s20, plain, ~spl3_2 | ~spl3_4 | spl3_10, inference(sat_conversion,[],[f490])).
% 0.22/0.31 cnf(s21, plain, ~spl3_10, inference(rat,[],[s10,s4,s1])).
% 0.22/0.31 cnf(s23, plain, ~spl3_9, inference(rat,[],[s16,s21])).
% 0.22/0.31 cnf(s25, plain, ~spl3_2, inference(rat,[],[s20,s3,s21])).
% 0.22/0.31 cnf(s26, plain, spl3_3, inference(rat,[],[s9,s23])).
% 0.22/0.31 cnf(s27, plain, $false, inference(rat,[],[s2,s26,s25])).
% 0.22/0.31 thf(f491,plain,(
% 0.22/0.31 $false),
% 0.22/0.31 inference(avatar_sat_refutation,[],[s27])).
% 0.22/0.31 % SZS output end Proof for theBenchmark
% 0.22/0.31 % (1704647)------------------------------
% 0.22/0.31 % (1704647)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1704647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1704647)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1704647)Termination reason: Refutation
% 0.22/0.31 % (1704647)Time elapsed: 0.012 s
% 0.22/0.31 % (1704647)Peak memory usage: 13 MB
% 0.22/0.31 % (1704647)Instructions burned: 34 (million)
% 0.22/0.31 % (1704639)Success in time 0.045 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------