%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO274^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 08:49:38 AM UTC 2026
% Result : Theorem 1.12s 0.53s
% Output : Refutation 1.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYO274^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.30 % Computer : n017.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8046.5625MB
% 0.11/0.30 % OS : Linux 6.8.0-71-generic
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Sep 29 16:37:53 UTC 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.31/0.35 Running first-order model finding
% 0.31/0.35 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.12/0.53 % (573490)Will run a generic schedule for satisfiability detection.
% 1.12/0.53 % (573498)dis+10_1_sil=32000:sp=arity:random_seed=3411448503:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.12/0.53 % (573496)% WARNING: option uhcvi not known.
% 1.12/0.53 % (573495)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3362228301_2999 on theBenchmark for (2999ds/0Mi)
% 1.12/0.53 % (573496)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1525571093:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.12/0.53 % (573497)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3927787464:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.12/0.53 % (573500)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1913025862:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.12/0.53 % (573496)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.12/0.53 % (573496)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.12/0.53 % Exception at run slice level
% 1.12/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.12/0.53 % (573501)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2892570709:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.12/0.53 % (573499)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3696935705:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.12/0.53 % (573499)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.12/0.53 % (573498)Instruction limit reached!
% 1.12/0.53 % (573498)------------------------------
% 1.12/0.53 % (573498)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.53 % (573498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.53 % (573498)CaDiCaL version: 2.1.3
% 1.12/0.53 % (573498)Termination reason: Instruction limit
% 1.12/0.53 % (573498)Termination phase: Saturation
% 1.12/0.53 % (573498)Time elapsed: 0.047 s
% 1.12/0.53 % (573498)Peak memory usage: 12 MB
% 1.12/0.53 % (573498)Instructions burned: 103 (million)
% 1.12/0.53 % (573507)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3635570606:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.12/0.53 % Exception at run slice level
% 1.12/0.53 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.12/0.53 % (573510)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1314312495:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.12/0.53 % (573512)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=3353891121:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.12/0.53 % (573512)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.12/0.53 % (573512)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.12/0.53 % (573501) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-573490-573501"...
% 1.12/0.53 % (573501)...printing done.
% 1.12/0.53 % (573501)Refutation found. Thanks to Tanya!
% 1.12/0.53 % SZS status Theorem for theBenchmark
% 1.12/0.53 % SZS output start Proof for theBenchmark
% 1.12/0.53 thf(type_def_5, type, c: $tType).
% 1.12/0.53 thf(type_def_6, type, b: $tType).
% 1.12/0.53 thf(type_def_7, type, a: $tType).
% 1.12/0.53 thf(type_def_8, type, sTfun: ($tType * $tType) > $tType).
% 1.12/0.53 thf(func_def_0, type, cG: (c > b)).
% 1.12/0.53 thf(func_def_1, type, cF: (b > a)).
% 1.12/0.53 thf(func_def_5, type, sK0: c).
% 1.12/0.53 thf(func_def_6, type, sK1: c).
% 1.12/0.53 thf(func_def_7, type, sK2: (c > $o)).
% 1.12/0.53 thf(func_def_8, type, sK3: (c > c > b > $o)).
% 1.12/0.53 thf(func_def_9, type, sK4: (b > b > a > $o)).
% 1.12/0.53 thf(func_def_10, type, vNOT: ($o > $o)).
% 1.12/0.53 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.12/0.53 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 1.12/0.53 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.12/0.53 thf(f1,conjecture,(
% 1.12/0.53 (! [X0 : c,X1 : c] : (! [X2 : (b > $o)] : ((X2 @ (cG @ X0)) => (X2 @ (cG @ X1))) => ! [X2 : (c > $o)] : ((X2 @ X0) => (X2 @ X1))) & ! [X0 : b,X1 : b] : (! [X2 : (a > $o)] : ((X2 @ (cF @ X0)) => (X2 @ (cF @ X1))) => ! [X2 : (b > $o)] : ((X2 @ X0) => (X2 @ X1)))) => ! [X0 : c,X1 : c] : (! [X2 : (a > $o)] : ((X2 @ (cF @ (cG @ X0))) => (X2 @ (cF @ (cG @ X1)))) => ! [X2 : (c > $o)] : ((X2 @ X0) => (X2 @ X1)))),
% 1.12/0.53 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM48_EXPD)).
% 1.12/0.53 thf(f2,negated_conjecture,(
% 1.12/0.53 ~((! [X0 : c,X1 : c] : (! [X2 : (b > $o)] : ((X2 @ (cG @ X0)) => (X2 @ (cG @ X1))) => ! [X2 : (c > $o)] : ((X2 @ X0) => (X2 @ X1))) & ! [X0 : b,X1 : b] : (! [X2 : (a > $o)] : ((X2 @ (cF @ X0)) => (X2 @ (cF @ X1))) => ! [X2 : (b > $o)] : ((X2 @ X0) => (X2 @ X1)))) => ! [X0 : c,X1 : c] : (! [X2 : (a > $o)] : ((X2 @ (cF @ (cG @ X0))) => (X2 @ (cF @ (cG @ X1)))) => ! [X2 : (c > $o)] : ((X2 @ X0) => (X2 @ X1))))),
% 1.12/0.53 inference(negated_conjecture,[status(cth)],[f1])).
% 1.12/0.53 thf(f3,plain,(
% 1.12/0.53 ~((! [X0 : c,X1 : c] : (! [X2 : (b > $o)] : ((X2 @ (cG @ X0)) => (X2 @ (cG @ X1))) => ! [X3 : (c > $o)] : ((X3 @ X0) => (X3 @ X1))) & ! [X4 : b,X5 : b] : (! [X6 : (a > $o)] : ((X6 @ (cF @ X4)) => (X6 @ (cF @ X5))) => ! [X7 : (b > $o)] : ((X7 @ X4) => (X7 @ X5)))) => ! [X8 : c,X9 : c] : (! [X10 : (a > $o)] : ((X10 @ (cF @ (cG @ X8))) => (X10 @ (cF @ (cG @ X9)))) => ! [X11 : (c > $o)] : ((X11 @ X8) => (X11 @ X9))))),
% 1.12/0.53 inference(rectify,[],[f2])).
% 1.12/0.53 thf(f4,plain,(
% 1.12/0.53 ~((! [X0 : c,X1 : c] : (! [X2 : (b > $o)] : ((((X2 @ (cG @ X0))) = $true) => (((X2 @ (cG @ X1))) = $true)) => ! [X3 : (c > $o)] : ((((X3 @ X0)) = $true) => (((X3 @ X1)) = $true))) & ! [X4 : b,X5 : b] : (! [X6 : (a > $o)] : ((((X6 @ (cF @ X4))) = $true) => (((X6 @ (cF @ X5))) = $true)) => ! [X7 : (b > $o)] : ((((X7 @ X4)) = $true) => (((X7 @ X5)) = $true)))) => ! [X8 : c,X9 : c] : (! [X10 : (a > $o)] : ((((X10 @ (cF @ (cG @ X8)))) = $true) => (((X10 @ (cF @ (cG @ X9)))) = $true)) => ! [X11 : (c > $o)] : ((((X11 @ X8)) = $true) => (((X11 @ X9)) = $true))))),
% 1.12/0.53 inference(fool_elimination,[],[f3])).
% 1.12/0.53 thf(f5,plain,(
% 1.12/0.53 ? [X8 : c,X9 : c] : (? [X11 : (c > $o)] : ((((X11 @ X9)) != $true) & (((X11 @ X8)) = $true)) & ! [X10 : (a > $o)] : ((((X10 @ (cF @ (cG @ X9)))) = $true) | (((X10 @ (cF @ (cG @ X8)))) != $true))) & (! [X0 : c,X1 : c] : (! [X3 : (c > $o)] : ((((X3 @ X1)) = $true) | (((X3 @ X0)) != $true)) | ? [X2 : (b > $o)] : ((((X2 @ (cG @ X1))) != $true) & (((X2 @ (cG @ X0))) = $true))) & ! [X4 : b,X5 : b] : (! [X7 : (b > $o)] : ((((X7 @ X5)) = $true) | (((X7 @ X4)) != $true)) | ? [X6 : (a > $o)] : ((((X6 @ (cF @ X5))) != $true) & (((X6 @ (cF @ X4))) = $true))))),
% 1.12/0.53 inference(ennf_transformation,[],[f4])).
% 1.12/0.53 thf(f6,plain,(
% 1.12/0.53 ? [X8 : c,X9 : c] : (? [X11 : (c > $o)] : ((((X11 @ X9)) != $true) & (((X11 @ X8)) = $true)) & ! [X10 : (a > $o)] : ((((X10 @ (cF @ (cG @ X9)))) = $true) | (((X10 @ (cF @ (cG @ X8)))) != $true))) & ! [X0 : c,X1 : c] : (! [X3 : (c > $o)] : ((((X3 @ X1)) = $true) | (((X3 @ X0)) != $true)) | ? [X2 : (b > $o)] : ((((X2 @ (cG @ X1))) != $true) & (((X2 @ (cG @ X0))) = $true))) & ! [X4 : b,X5 : b] : (! [X7 : (b > $o)] : ((((X7 @ X5)) = $true) | (((X7 @ X4)) != $true)) | ? [X6 : (a > $o)] : ((((X6 @ (cF @ X5))) != $true) & (((X6 @ (cF @ X4))) = $true)))),
% 1.12/0.53 inference(flattening,[],[f5])).
% 1.12/0.53 thf(f7,plain,(
% 1.12/0.53 ? [X0 : c,X1 : c] : (? [X2 : (c > $o)] : ((((X2 @ X1)) != $true) & (((X2 @ X0)) = $true)) & ! [X3 : (a > $o)] : (($true = ((X3 @ (cF @ (cG @ X1))))) | ($true != ((X3 @ (cF @ (cG @ X0))))))) & ! [X4 : c,X5 : c] : (! [X6 : (c > $o)] : (($true = ((X6 @ X5))) | ($true != ((X6 @ X4)))) | ? [X7 : (b > $o)] : (($true != ((X7 @ (cG @ X5)))) & ($true = ((X7 @ (cG @ X4)))))) & ! [X8 : b,X9 : b] : (! [X10 : (b > $o)] : (($true = ((X10 @ X9))) | ($true != ((X10 @ X8)))) | ? [X11 : (a > $o)] : (($true != ((X11 @ (cF @ X9)))) & ($true = ((X11 @ (cF @ X8))))))),
% 1.12/0.53 inference(rectify,[],[f6])).
% 1.12/0.53 thf(f8,plain,(
% 1.12/0.53 ((($true != ((sK2 @ sK1))) & ($true = ((sK2 @ sK0)))) & ! [X3 : (a > $o)] : (($true = ((X3 @ (cF @ (cG @ sK1))))) | ($true != ((X3 @ (cF @ (cG @ sK0))))))) & ! [X4 : c,X5 : c] : (! [X6 : (c > $o)] : (($true = ((X6 @ X5))) | ($true != ((X6 @ X4)))) | (($true != ((sK3 @ X5 @ X4 @ (cG @ X5)))) & ($true = ((sK3 @ X5 @ X4 @ (cG @ X4)))))) & ! [X8 : b,X9 : b] : (! [X10 : (b > $o)] : (($true = ((X10 @ X9))) | ($true != ((X10 @ X8)))) | (($true != ((sK4 @ X9 @ X8 @ (cF @ X9)))) & ($true = ((sK4 @ X9 @ X8 @ (cF @ X8))))))),
% 1.12/0.53 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X11,sK4 @ X9 @ X8),skolemize(X11,sK4 @ X9 @ X8)],[f7])).
% 1.12/0.53 thf(f9,plain,(
% 1.12/0.53 ( ! [X10 : (b > $o),X8 : b,X9 : b] : (($true != ((X10 @ X8))) | ($true = ((X10 @ X9))) | ($true = ((sK4 @ X9 @ X8 @ (cF @ X8))))) )),
% 1.12/0.53 inference(cnf_transformation,[],[f8])).
% 1.12/0.53 thf(f10,plain,(
% 1.12/0.53 ( ! [X10 : (b > $o),X8 : b,X9 : b] : (($true != ((sK4 @ X9 @ X8 @ (cF @ X9)))) | ($true != ((X10 @ X8))) | ($true = ((X10 @ X9)))) )),
% 1.12/0.53 inference(cnf_transformation,[],[f8])).
% 1.12/0.53 thf(f11,plain,(
% 1.12/0.53 ( ! [X6 : (c > $o),X4 : c,X5 : c] : (($true != ((X6 @ X4))) | ($true = ((X6 @ X5))) | ($true = ((sK3 @ X5 @ X4 @ (cG @ X4))))) )),
% 1.12/0.53 inference(cnf_transformation,[],[f8])).
% 1.12/0.53 thf(f12,plain,(
% 1.12/0.53 ( ! [X6 : (c > $o),X4 : c,X5 : c] : (($true != ((sK3 @ X5 @ X4 @ (cG @ X5)))) | ($true != ((X6 @ X4))) | ($true = ((X6 @ X5)))) )),
% 1.12/0.53 inference(cnf_transformation,[],[f8])).
% 1.12/0.53 thf(f13,plain,(
% 1.12/0.53 ( ! [X3 : (a > $o)] : (($true != ((X3 @ (cF @ (cG @ sK0))))) | ($true = ((X3 @ (cF @ (cG @ sK1)))))) )),
% 1.12/0.53 inference(cnf_transformation,[],[f8])).
% 1.12/0.53 thf(f14,plain,(
% 1.12/0.53 ($true = ((sK2 @ sK0)))),
% 1.12/0.53 inference(cnf_transformation,[],[f8])).
% 1.12/0.53 thf(f15,plain,(
% 1.12/0.53 ($true != ((sK2 @ sK1)))),
% 1.12/0.53 inference(cnf_transformation,[],[f8])).
% 1.12/0.53 thf(f19,plain,(
% 1.12/0.53 (((cF @ (cG @ sK1))) = ((cF @ (cG @ sK0))))),
% 1.12/0.53 inference(leibniz_equality_elimination,[],[f13])).
% 1.12/0.53 thf(f22,plain,(
% 1.12/0.53 ( ! [X4 : (a > $o)] : (($true != (((^[Y0 : a]: (~ (X4 @ Y0))) @ (cF @ (cG @ sK0))))) | ($true = (((^[Y0 : a]: (~ (X4 @ Y0))) @ (cF @ (cG @ sK1)))))) )),
% 1.12/0.53 inference(primitive_instantiation,[],[f13])).
% 1.12/0.53 thf(f28,plain,(
% 1.12/0.53 ( ! [X4 : (a > $o)] : (($true != ((~ (X4 @ (cF @ (cG @ sK0)))))) | ($true = ((~ (X4 @ (cF @ (cG @ sK1))))))) )),
% 1.12/0.53 inference(beta-eta_normalization,[],[f22])).
% 1.12/0.53 thf(f29,plain,(
% 1.12/0.53 ( ! [X4 : (a > $o)] : (($true = ((X4 @ (cF @ (cG @ sK0))))) | ($true = ((~ (X4 @ (cF @ (cG @ sK1))))))) )),
% 1.12/0.53 inference(not_proxy_clausification,[],[f28])).
% 1.12/0.53 thf(f30,plain,(
% 1.12/0.53 ( ! [X4 : (a > $o)] : (($false = ((X4 @ (cF @ (cG @ sK1))))) | ($true = ((X4 @ (cF @ (cG @ sK0)))))) )),
% 1.12/0.53 inference(not_proxy_clausification,[],[f29])).
% 1.12/0.53 thf(f37,plain,(
% 1.12/0.53 ( ! [X5 : (a > $o)] : (($false = (((^[Y0 : a]: (~ (X5 @ Y0))) @ (cF @ (cG @ sK1))))) | ($true = (((^[Y0 : a]: (~ (X5 @ Y0))) @ (cF @ (cG @ sK0)))))) )),
% 1.12/0.53 inference(primitive_instantiation,[],[f30])).
% 1.12/0.53 thf(f58,plain,(
% 1.12/0.53 ( ! [X5 : (a > $o)] : (($false = ((~ (X5 @ (cF @ (cG @ sK1)))))) | ($true = ((~ (X5 @ (cF @ (cG @ sK0))))))) )),
% 1.12/0.53 inference(beta-eta_normalization,[],[f37])).
% 1.12/0.53 thf(f59,plain,(
% 1.12/0.53 ( ! [X5 : (a > $o)] : (($true = ((X5 @ (cF @ (cG @ sK1))))) | ($true = ((~ (X5 @ (cF @ (cG @ sK0))))))) )),
% 1.12/0.53 inference(not_proxy_clausification,[],[f58])).
% 1.12/0.53 thf(f60,plain,(
% 1.12/0.53 ( ! [X5 : (a > $o)] : (($true = ((X5 @ (cF @ (cG @ sK1))))) | ($false = ((X5 @ (cF @ (cG @ sK0)))))) )),
% 1.12/0.53 inference(not_proxy_clausification,[],[f59])).
% 1.12/0.53 thf(f70,plain,(
% 1.12/0.53 ($true != $true) | ($false = (((^[Y0 : a]: (sK2 @ ((^[Y1 : a]: (sK1)) @ Y0))) @ (cF @ (cG @ sK0)))))),
% 1.12/0.53 inference(constrained_superposition,[],[f15,f60])).
% 1.12/0.53 thf(f86,plain,(
% 1.12/0.53 ($false = (((^[Y0 : a]: (sK2 @ ((^[Y1 : a]: (sK1)) @ Y0))) @ (cF @ (cG @ sK0)))))),
% 1.12/0.53 inference(trivial_inequality_removal,[],[f70])).
% 1.12/0.53 thf(f87,plain,(
% 1.12/0.53 (((sK2 @ sK1)) = $false)),
% 1.12/0.53 inference(beta-eta_normalization,[],[f86])).
% 1.12/0.53 thf(f107,plain,(
% 1.12/0.53 ( ! [X0 : b,X1 : b] : (($true = ((sK4 @ X1 @ X0 @ (cF @ X0)))) | (X0 = X1)) )),
% 1.12/0.53 inference(leibniz_equality_elimination,[],[f9])).
% 1.12/0.53 thf(f138,plain,(
% 1.12/0.53 ( ! [X0 : b] : (($true = ((sK4 @ X0 @ (cG @ sK1) @ (cF @ (cG @ sK0))))) | (((cG @ sK1)) = X0)) )),
% 1.12/0.53 inference(constrained_superposition,[],[f107,f19])).
% 1.12/0.53 thf(f161,plain,(
% 1.12/0.53 ( ! [X0 : b,X1 : b] : (($true != ((sK4 @ X1 @ X0 @ (cF @ X1)))) | (X0 = X1)) )),
% 1.12/0.53 inference(leibniz_equality_elimination,[],[f10])).
% 1.12/0.53 thf(f188,plain,(
% 1.12/0.53 ( ! [X7 : (c > $o),X4 : c,X5 : c] : (($true != (((^[Y0 : c]: (~ (X7 @ Y0))) @ X4))) | ($true = (((^[Y0 : c]: (~ (X7 @ Y0))) @ X5))) | ($true = ((sK3 @ X5 @ X4 @ (cG @ X4))))) )),
% 1.12/0.53 inference(primitive_instantiation,[],[f11])).
% 1.12/0.53 thf(f212,plain,(
% 1.12/0.53 ( ! [X7 : (c > $o),X4 : c,X5 : c] : (($true != ((~ (X7 @ X4)))) | ($true = ((~ (X7 @ X5)))) | ($true = ((sK3 @ X5 @ X4 @ (cG @ X4))))) )),
% 1.12/0.53 inference(beta-eta_normalization,[],[f188])).
% 1.12/0.53 thf(f213,plain,(
% 1.12/0.53 ( ! [X7 : (c > $o),X4 : c,X5 : c] : (($true = ((X7 @ X4))) | ($true = ((~ (X7 @ X5)))) | ($true = ((sK3 @ X5 @ X4 @ (cG @ X4))))) )),
% 1.12/0.53 inference(not_proxy_clausification,[],[f212])).
% 1.12/0.53 thf(f214,plain,(
% 1.12/0.53 ( ! [X7 : (c > $o),X4 : c,X5 : c] : (($true = ((X7 @ X4))) | ($false = ((X7 @ X5))) | ($true = ((sK3 @ X5 @ X4 @ (cG @ X4))))) )),
% 1.12/0.53 inference(not_proxy_clausification,[],[f213])).
% 1.12/0.53 thf(f400,plain,(
% 1.12/0.53 ( ! [X0 : c,X1 : c] : (($true != ((sK3 @ X1 @ X0 @ (cG @ X1)))) | (X0 = X1)) )),
% 1.12/0.53 inference(leibniz_equality_elimination,[],[f12])).
% 1.12/0.53 thf(f668,plain,(
% 1.12/0.53 ( ! [X0 : c,X1 : c] : (($true = $false) | ($true = (((^[Y0 : c]: (sK2 @ ((^[Y1 : c]: (Y1)) @ Y0))) @ X1))) | ($true = ((sK3 @ X0 @ X1 @ (cG @ X1)))) | (sK0 != X0)) )),
% 1.12/0.53 inference(constrained_superposition,[],[f14,f214])).
% 1.12/0.53 thf(f772,plain,(
% 1.12/0.53 ( ! [X0 : c,X1 : c] : (($true = (((^[Y0 : c]: (sK2 @ ((^[Y1 : c]: (Y1)) @ Y0))) @ X1))) | ($true = ((sK3 @ X0 @ X1 @ (cG @ X1)))) | (sK0 != X0)) )),
% 1.12/0.53 inference(trivial_inequality_removal,[],[f668])).
% 1.12/0.53 thf(f773,plain,(
% 1.12/0.53 ( ! [X0 : c,X1 : c] : ((sK0 != X0) | ($true = ((sK3 @ X0 @ X1 @ (cG @ X1)))) | ($true = ((sK2 @ X1)))) )),
% 1.12/0.53 inference(beta-eta_normalization,[],[f772])).
% 1.12/0.53 thf(f870,plain,(
% 1.12/0.53 ( ! [X0 : c] : (($true = ((sK3 @ sK0 @ X0 @ (cG @ X0)))) | ($true = ((sK2 @ X0)))) )),
% 1.12/0.53 inference(equality_resolution,[],[f773])).
% 1.12/0.53 thf(f956,plain,(
% 1.12/0.53 ($true != $true) | (((cG @ sK1)) = ((cG @ sK0))) | (((cG @ sK1)) = ((cG @ sK0)))),
% 1.12/0.53 inference(constrained_superposition,[],[f161,f138])).
% 1.12/0.53 thf(f959,plain,(
% 1.12/0.53 ($true != $true) | (((cG @ sK1)) = ((cG @ sK0)))),
% 1.12/0.53 inference(duplicate_literal_removal,[],[f956])).
% 1.12/0.53 thf(f960,plain,(
% 1.12/0.53 (((cG @ sK1)) = ((cG @ sK0)))),
% 1.12/0.53 inference(trivial_inequality_removal,[],[f959])).
% 1.12/0.53 thf(f982,definition,(
% 1.12/0.53 spl5_4 <=> (((cG @ sK1)) = ((cG @ sK0)))),
% 1.12/0.53 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 1.12/0.53 thf(f984,plain,(
% 1.12/0.53 (((cG @ sK1)) = ((cG @ sK0))) | ~spl5_4),
% 1.12/0.53 inference(avatar_component_clause,[],[f982])).
% 1.12/0.53 thf(f989,plain,(
% 1.12/0.53 spl5_4),
% 1.12/0.53 inference(avatar_split_clause,[],[f960,f982])).
% 1.12/0.53 thf(f994,plain,(
% 1.12/0.53 ($true = ((sK3 @ sK0 @ sK1 @ (cG @ sK0)))) | ($true = ((sK2 @ sK1))) | ~spl5_4),
% 1.12/0.53 inference(constrained_superposition,[],[f870,f984])).
% 1.12/0.53 thf(f1000,definition,(
% 1.12/0.53 spl5_6 <=> ($true = ((sK2 @ sK1)))),
% 1.12/0.53 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 1.12/0.53 thf(f1002,plain,(
% 1.12/0.53 ($true = ((sK2 @ sK1))) | ~spl5_6),
% 1.12/0.53 inference(avatar_component_clause,[],[f1000])).
% 1.12/0.53 thf(f1004,definition,(
% 1.12/0.53 spl5_7 <=> ($true = ((sK3 @ sK0 @ sK1 @ (cG @ sK0))))),
% 1.12/0.53 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 1.12/0.53 thf(f1006,plain,(
% 1.12/0.53 ($true = ((sK3 @ sK0 @ sK1 @ (cG @ sK0)))) | ~spl5_7),
% 1.12/0.53 inference(avatar_component_clause,[],[f1004])).
% 1.12/0.53 thf(f1007,plain,(
% 1.12/0.53 spl5_6 | spl5_7 | ~spl5_4),
% 1.12/0.53 inference(avatar_split_clause,[],[f994,f982,f1004,f1000])).
% 1.12/0.53 thf(f1008,plain,(
% 1.12/0.53 ($true = $false) | ~spl5_6),
% 1.12/0.53 inference(constrained_superposition,[],[f1002,f87])).
% 1.12/0.53 thf(f1051,plain,(
% 1.12/0.53 $false | ~spl5_6),
% 1.12/0.53 inference(trivial_inequality_removal,[],[f1008])).
% 1.12/0.53 thf(f1052,plain,(
% 1.12/0.53 ~spl5_6),
% 1.12/0.53 inference(avatar_contradiction_clause,[],[f1051])).
% 1.12/0.53 thf(f1059,plain,(
% 1.12/0.53 ($true != $true) | (sK0 = sK1) | ~spl5_7),
% 1.12/0.53 inference(constrained_superposition,[],[f400,f1006])).
% 1.12/0.53 thf(f1080,plain,(
% 1.12/0.53 (sK0 = sK1) | ~spl5_7),
% 1.12/0.53 inference(trivial_inequality_removal,[],[f1059])).
% 1.12/0.53 thf(f1093,plain,(
% 1.12/0.53 ($true != ((sK2 @ sK0))) | ~spl5_7),
% 1.12/0.53 inference(constrained_superposition,[],[f15,f1080])).
% 1.12/0.53 thf(f1101,plain,(
% 1.12/0.53 ($true != $true) | ~spl5_7),
% 1.12/0.53 inference(constrained_superposition,[],[f1093,f14])).
% 1.12/0.53 thf(f1122,plain,(
% 1.12/0.53 $false | ~spl5_7),
% 1.12/0.53 inference(trivial_inequality_removal,[],[f1101])).
% 1.12/0.53 thf(f1123,plain,(
% 1.12/0.53 ~spl5_7),
% 1.12/0.53 inference(avatar_contradiction_clause,[],[f1122])).
% 1.12/0.53 cnf(s6, plain, spl5_4, inference(sat_conversion,[],[f989])).
% 1.12/0.53 cnf(s7, plain, ~spl5_4 | spl5_6 | spl5_7, inference(sat_conversion,[],[f1007])).
% 1.12/0.53 cnf(s10, plain, ~spl5_6, inference(sat_conversion,[],[f1052])).
% 1.12/0.53 cnf(s11, plain, ~spl5_7, inference(sat_conversion,[],[f1123])).
% 1.12/0.53 cnf(s12, plain, ~spl5_4, inference(rat,[],[s7,s11,s10])).
% 1.12/0.53 cnf(s13, plain, $false, inference(rat,[],[s6,s12])).
% 1.12/0.53 thf(f1124,plain,(
% 1.12/0.53 $false),
% 1.12/0.53 inference(avatar_sat_refutation,[],[s13])).
% 1.12/0.53 % SZS output end Proof for theBenchmark
% 1.12/0.53 % (573501)------------------------------
% 1.12/0.53 % (573501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.12/0.53 % (573501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.12/0.53 % (573501)CaDiCaL version: 2.1.3
% 1.12/0.53 % (573501)Termination reason: Refutation
% 1.12/0.53 % (573501)Time elapsed: 0.093 s
% 1.12/0.53 % (573501)Peak memory usage: 13 MB
% 1.12/0.53 % (573501)Instructions burned: 96 (million)
% 1.12/0.53 % (573490)Success in time 0.16 s
% 1.12/0.53 % Vampire exiting
%------------------------------------------------------------------------------