%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV382^5 : 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 : n008.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 08:39:25 AM UTC 2026
% Result : Theorem 1.09s 0.37s
% Output : Refutation 1.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV382^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n008.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 15:44:25 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.20 Running first-order model finding
% 0.07/0.20 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
% 1.09/0.37 % (3319801)Will run a generic schedule for satisfiability detection.
% 1.09/0.37 % (3319810)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=900638419:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.09/0.37 % (3319810)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.09/0.37 % (3319807)% WARNING: option uhcvi not known.
% 1.09/0.37 % (3319806)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=232086_2999 on theBenchmark for (2999ds/0Mi)
% 1.09/0.37 % (3319807)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=671505021:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.09/0.37 % (3319808)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=314703951:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.09/0.37 % (3319811)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3313672216:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.09/0.37 % (3319807)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.09/0.37 % Exception at run slice level
% 1.09/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.09/0.37 % (3319812)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3222618041:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.09/0.37 % (3319807)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.09/0.37 % (3319809)dis+10_1_sil=32000:sp=arity:random_seed=1830338987:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.09/0.37 % (3319819)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1326134130:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.09/0.37 % Exception at run slice level
% 1.09/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.09/0.37 % (3319810)Instruction limit reached!
% 1.09/0.37 % (3319810)------------------------------
% 1.09/0.37 % (3319810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.37 % (3319810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.37 % (3319810)CaDiCaL version: 2.1.3
% 1.09/0.37 % (3319810)Termination reason: Instruction limit
% 1.09/0.37 % (3319810)Termination phase: Saturation
% 1.09/0.37 % (3319810)Time elapsed: 0.033 s
% 1.09/0.37 % (3319810)Peak memory usage: 12 MB
% 1.09/0.37 % (3319810)Instructions burned: 119 (million)
% 1.09/0.37 % (3319823)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=374404999:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.09/0.37 % (3319823)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.09/0.37 % (3319823)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.09/0.37 % (3319822)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3522438045:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.09/0.37 % (3319809)Instruction limit reached!
% 1.09/0.37 % (3319809)------------------------------
% 1.09/0.37 % (3319809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.37 % (3319809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.37 % (3319809)CaDiCaL version: 2.1.3
% 1.09/0.37 % (3319809)Termination reason: Instruction limit
% 1.09/0.37 % (3319809)Termination phase: Saturation
% 1.09/0.37 % (3319809)Time elapsed: 0.057 s
% 1.09/0.37 % (3319809)Peak memory usage: 12 MB
% 1.09/0.37 % (3319809)Instructions burned: 105 (million)
% 1.09/0.37 % (3319811)Instruction limit reached!
% 1.09/0.37 % (3319811)------------------------------
% 1.09/0.37 % (3319811)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.37 % (3319811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.37 % (3319811)CaDiCaL version: 2.1.3
% 1.09/0.37 % (3319811)Termination reason: Instruction limit
% 1.09/0.37 % (3319811)Termination phase: Saturation
% 1.09/0.37 % (3319811)Time elapsed: 0.069 s
% 1.09/0.37 % (3319811)Peak memory usage: 12 MB
% 1.09/0.37 % (3319811)Instructions burned: 132 (million)
% 1.09/0.37 % (3319812)Instruction limit reached!
% 1.09/0.37 % (3319812)------------------------------
% 1.09/0.37 % (3319812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.37 % (3319812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.37 % (3319812)CaDiCaL version: 2.1.3
% 1.09/0.37 % (3319812)Termination reason: Instruction limit
% 1.09/0.37 % (3319812)Termination phase: Saturation
% 1.09/0.37 % (3319812)Time elapsed: 0.083 s
% 1.09/0.37 % (3319812)Peak memory usage: 13 MB
% 1.09/0.37 % (3319812)Instructions burned: 161 (million)
% 1.09/0.37 % (3319826)ott-21_1_sil=16000:fs=off:random_seed=1858687420:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 1.09/0.37 % (3319827)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=583337681:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.09/0.37 % (3319828)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3942095455:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.09/0.37 % Exception at run slice level
% 1.09/0.37 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.09/0.37 % (3319822)Instruction limit reached!
% 1.09/0.37 % (3319822)------------------------------
% 1.09/0.37 % (3319822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.37 % (3319822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.37 % (3319822)CaDiCaL version: 2.1.3
% 1.09/0.37 % (3319822)Termination reason: Instruction limit
% 1.09/0.37 % (3319822)Termination phase: Saturation
% 1.09/0.37 % (3319822)Time elapsed: 0.071 s
% 1.09/0.37 % (3319822)Peak memory usage: 12 MB
% 1.09/0.37 % (3319822)Instructions burned: 131 (million)
% 1.09/0.37 % (3319823) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3319801-3319823"...
% 1.09/0.37 % (3319823)...printing done.
% 1.09/0.37 % (3319823)Refutation found. Thanks to Tanya!
% 1.09/0.37 % SZS status Theorem for theBenchmark
% 1.09/0.37 % SZS output start Proof for theBenchmark
% 1.09/0.37 thf(type_def_5, type, a: $tType).
% 1.09/0.37 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 1.09/0.37 thf(func_def_3, type, sK0: (a > a > $o)).
% 1.09/0.37 thf(func_def_4, type, sK1: (a > $o)).
% 1.09/0.37 thf(func_def_5, type, sK2: a).
% 1.09/0.37 thf(func_def_6, type, sK3: (a > a)).
% 1.09/0.37 thf(func_def_7, type, sK4: ((a > $o) > a)).
% 1.09/0.37 thf(func_def_8, type, vNOT: ($o > $o)).
% 1.09/0.37 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.09/0.37 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 1.09/0.37 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.09/0.37 thf(f1,conjecture,(
% 1.09/0.37 ! [X0 : (a > a > $o),X1 : (a > $o)] : ((! [X6 : a] : (! [X4 : a] : ((X0 @ X4 @ X6) => (X1 @ X4)) => (X1 @ X6)) & ! [X2 : (a > $o)] : (? [X3 : a] : (X2 @ X3) => ? [X4 : a] : (! [X5 : a] : ((X0 @ X5 @ X4) => ~(X2 @ X5)) & (X2 @ X4)))) => ! [X6 : a] : (X1 @ X6))),
% 1.09/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTRANS_IND)).
% 1.09/0.37 thf(f2,negated_conjecture,(
% 1.09/0.37 ~ ! [X0 : (a > a > $o),X1 : (a > $o)] : ((! [X6 : a] : (! [X4 : a] : ((X0 @ X4 @ X6) => (X1 @ X4)) => (X1 @ X6)) & ! [X2 : (a > $o)] : (? [X3 : a] : (X2 @ X3) => ? [X4 : a] : (! [X5 : a] : ((X0 @ X5 @ X4) => ~(X2 @ X5)) & (X2 @ X4)))) => ! [X6 : a] : (X1 @ X6))),
% 1.09/0.37 inference(negated_conjecture,[status(cth)],[f1])).
% 1.09/0.37 thf(f3,plain,(
% 1.09/0.37 ~ ! [X0 : (a > a > $o),X1 : (a > $o)] : ((! [X2 : a] : (! [X3 : a] : ((X0 @ X3 @ X2) => (X1 @ X3)) => (X1 @ X2)) & ! [X4 : (a > $o)] : (? [X5 : a] : (X4 @ X5) => ? [X6 : a] : (! [X7 : a] : ((X0 @ X7 @ X6) => ~(X4 @ X7)) & (X4 @ X6)))) => ! [X8 : a] : (X1 @ X8))),
% 1.09/0.37 inference(rectify,[],[f2])).
% 1.09/0.37 thf(f4,plain,(
% 1.09/0.37 ~ ! [X0 : (a > a > $o),X1 : (a > $o)] : ((! [X2 : a] : (! [X3 : a] : ((((X0 @ X3 @ X2)) = $true) => (((X1 @ X3)) = $true)) => (((X1 @ X2)) = $true)) & ! [X4 : (a > $o)] : (? [X5 : a] : (((X4 @ X5)) = $true) => ? [X6 : a] : (! [X7 : a] : ((((X0 @ X7 @ X6)) = $true) => ~ (((X4 @ X7)) = $true)) & (((X4 @ X6)) = $true)))) => ! [X8 : a] : (((X1 @ X8)) = $true))),
% 1.09/0.37 inference(fool_elimination,[],[f3])).
% 1.09/0.37 thf(f5,plain,(
% 1.09/0.37 ~ ! [X0 : (a > a > $o),X1 : (a > $o)] : ((! [X2 : a] : (! [X3 : a] : ((((X0 @ X3 @ X2)) = $true) => (((X1 @ X3)) = $true)) => (((X1 @ X2)) = $true)) & ! [X4 : (a > $o)] : (? [X5 : a] : (((X4 @ X5)) = $true) => ? [X6 : a] : (! [X7 : a] : ((((X0 @ X7 @ X6)) = $true) => (((X4 @ X7)) != $true)) & (((X4 @ X6)) = $true)))) => ! [X8 : a] : (((X1 @ X8)) = $true))),
% 1.09/0.37 inference(flattening,[],[f4])).
% 1.09/0.37 thf(f6,plain,(
% 1.09/0.37 ? [X0 : (a > a > $o),X1 : (a > $o)] : (? [X8 : a] : (((X1 @ X8)) != $true) & (! [X2 : a] : ((((X1 @ X2)) = $true) | ? [X3 : a] : ((((X1 @ X3)) != $true) & (((X0 @ X3 @ X2)) = $true))) & ! [X4 : (a > $o)] : (? [X6 : a] : (! [X7 : a] : ((((X4 @ X7)) != $true) | (((X0 @ X7 @ X6)) != $true)) & (((X4 @ X6)) = $true)) | ! [X5 : a] : (((X4 @ X5)) != $true))))),
% 1.09/0.37 inference(ennf_transformation,[],[f5])).
% 1.09/0.37 thf(f7,plain,(
% 1.09/0.37 ? [X0 : (a > a > $o),X1 : (a > $o)] : (? [X8 : a] : (((X1 @ X8)) != $true) & ! [X2 : a] : ((((X1 @ X2)) = $true) | ? [X3 : a] : ((((X1 @ X3)) != $true) & (((X0 @ X3 @ X2)) = $true))) & ! [X4 : (a > $o)] : (? [X6 : a] : (! [X7 : a] : ((((X4 @ X7)) != $true) | (((X0 @ X7 @ X6)) != $true)) & (((X4 @ X6)) = $true)) | ! [X5 : a] : (((X4 @ X5)) != $true)))),
% 1.09/0.37 inference(flattening,[],[f6])).
% 1.09/0.37 thf(f8,plain,(
% 1.09/0.37 ? [X0 : (a > a > $o),X1 : (a > $o)] : (? [X2 : a] : (((X1 @ X2)) != $true) & ! [X3 : a] : ((((X1 @ X3)) = $true) | ? [X4 : a] : ((((X1 @ X4)) != $true) & ($true = ((X0 @ X4 @ X3))))) & ! [X5 : (a > $o)] : (? [X6 : a] : (! [X7 : a] : (($true != ((X5 @ X7))) | (((X0 @ X7 @ X6)) != $true)) & ($true = ((X5 @ X6)))) | ! [X8 : a] : ($true != ((X5 @ X8)))))),
% 1.09/0.37 inference(rectify,[],[f7])).
% 1.09/0.37 thf(f9,plain,(
% 1.09/0.37 ($true != ((sK1 @ sK2))) & ! [X3 : a] : (($true = ((sK1 @ X3))) | (($true != ((sK1 @ (sK3 @ X3)))) & ($true = ((sK0 @ (sK3 @ X3) @ X3))))) & ! [X5 : (a > $o)] : ((! [X7 : a] : (($true != ((X5 @ X7))) | ($true != ((sK0 @ X7 @ (sK4 @ X5))))) & ($true = ((X5 @ (sK4 @ X5))))) | ! [X8 : a] : ($true != ((X5 @ X8))))),
% 1.09/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X6,sK4 @ X5),skolemize(X6,sK4 @ X5)],[f8])).
% 1.09/0.37 thf(f10,plain,(
% 1.09/0.37 ( ! [X8 : a,X5 : (a > $o)] : (($true != ((X5 @ X8))) | ($true = ((X5 @ (sK4 @ X5))))) )),
% 1.09/0.37 inference(cnf_transformation,[],[f9])).
% 1.09/0.37 thf(f11,plain,(
% 1.09/0.37 ( ! [X8 : a,X7 : a,X5 : (a > $o)] : (($true != ((sK0 @ X7 @ (sK4 @ X5)))) | ($true != ((X5 @ X7))) | ($true != ((X5 @ X8)))) )),
% 1.09/0.37 inference(cnf_transformation,[],[f9])).
% 1.09/0.37 thf(f12,plain,(
% 1.09/0.37 ( ! [X3 : a] : (($true = ((sK0 @ (sK3 @ X3) @ X3))) | ($true = ((sK1 @ X3)))) )),
% 1.09/0.37 inference(cnf_transformation,[],[f9])).
% 1.09/0.37 thf(f13,plain,(
% 1.09/0.37 ( ! [X3 : a] : (($true != ((sK1 @ (sK3 @ X3)))) | ($true = ((sK1 @ X3)))) )),
% 1.09/0.37 inference(cnf_transformation,[],[f9])).
% 1.09/0.37 thf(f14,plain,(
% 1.09/0.37 ($true != ((sK1 @ sK2)))),
% 1.09/0.37 inference(cnf_transformation,[],[f9])).
% 1.09/0.37 thf(f16,definition,(
% 1.09/0.37 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.09/0.37 introduced(theory,[fool_exhaustiveness_axiom])).
% 1.09/0.37 thf(f20,plain,(
% 1.09/0.37 ( ! [X8 : a,X9 : (a > $o)] : (($true != (((^[Y0 : a]: (~ (X9 @ Y0))) @ X8))) | ($true = (((^[Y0 : a]: (~ (X9 @ Y0))) @ (sK4 @ (^[Y0 : a]: (~ (X9 @ Y0)))))))) )),
% 1.09/0.37 inference(primitive_instantiation,[],[f10])).
% 1.09/0.37 thf(f23,plain,(
% 1.09/0.37 ( ! [X8 : a,X9 : (a > $o)] : (($true != ((~ (X9 @ X8)))) | ($true = ((~ (X9 @ (sK4 @ (^[Y0 : a]: (~ (X9 @ Y0))))))))) )),
% 1.09/0.37 inference(beta-eta_normalization,[],[f20])).
% 1.09/0.37 thf(f24,plain,(
% 1.09/0.37 ( ! [X8 : a,X9 : (a > $o)] : (($true = ((X9 @ X8))) | ($true = ((~ (X9 @ (sK4 @ (^[Y0 : a]: (~ (X9 @ Y0))))))))) )),
% 1.09/0.37 inference(not_proxy_clausification,[],[f23])).
% 1.09/0.37 thf(f25,plain,(
% 1.09/0.37 ( ! [X8 : a,X9 : (a > $o)] : (($true = ((X9 @ X8))) | ($false = ((X9 @ (sK4 @ (^[Y0 : a]: (~ (X9 @ Y0)))))))) )),
% 1.09/0.37 inference(not_proxy_clausification,[],[f24])).
% 1.09/0.37 thf(f131,definition,(
% 1.09/0.37 spl5_6 <=> ! [X0 : a] : (sK2 != X0)),
% 1.09/0.37 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 1.09/0.37 thf(f132,plain,(
% 1.09/0.37 ( ! [X0 : a] : ((sK2 != X0)) ) | ~spl5_6),
% 1.09/0.37 inference(avatar_component_clause,[],[f131])).
% 1.09/0.37 thf(f134,definition,(
% 1.09/0.37 spl5_7 <=> ($false = ((sK1 @ (sK4 @ (^[Y0 : a]: (~ (sK1 @ Y0)))))))),
% 1.09/0.37 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 1.09/0.37 thf(f136,plain,(
% 1.09/0.37 ($false = ((sK1 @ (sK4 @ (^[Y0 : a]: (~ (sK1 @ Y0))))))) | ~spl5_7),
% 1.09/0.37 inference(avatar_component_clause,[],[f134])).
% 1.09/0.37 thf(f151,plain,(
% 1.09/0.37 ($true != $true) | (((sK1 @ sK2)) = $false)),
% 1.09/0.37 inference(constrained_superposition,[],[f14,f16])).
% 1.09/0.37 thf(f159,plain,(
% 1.09/0.37 (((sK1 @ sK2)) = $false)),
% 1.09/0.37 inference(trivial_inequality_removal,[],[f151])).
% 1.09/0.37 thf(f476,plain,(
% 1.09/0.37 ( ! [X2 : a,X0 : a,X1 : (a > $o)] : (($true != $true) | ($true != ((X1 @ X0))) | (((X1 @ X2)) != $true) | ($false = ((sK0 @ X0 @ (sK4 @ X1))))) )),
% 1.09/0.37 inference(constrained_superposition,[],[f11,f16])).
% 1.09/0.37 thf(f477,plain,(
% 1.09/0.37 ( ! [X2 : a,X0 : a,X1 : (a > $o)] : (($true != ((X1 @ X0))) | (((X1 @ X2)) != $true) | ($false = ((sK0 @ X0 @ (sK4 @ X1))))) )),
% 1.09/0.37 inference(trivial_inequality_removal,[],[f476])).
% 1.09/0.37 thf(f541,plain,(
% 1.09/0.37 ( ! [X2 : a,X3 : (a > $o),X0 : a] : (($true != (((^[Y0 : a]: (~ (X3 @ Y0))) @ X0))) | ($true != (((^[Y0 : a]: (~ (X3 @ Y0))) @ X2))) | ($false = ((sK0 @ X0 @ (sK4 @ (^[Y0 : a]: (~ (X3 @ Y0)))))))) )),
% 1.09/0.37 inference(primitive_instantiation,[],[f477])).
% 1.09/0.37 thf(f586,plain,(
% 1.09/0.37 ( ! [X2 : a,X3 : (a > $o),X0 : a] : (($true != ((~ (X3 @ X0)))) | ($true != ((~ (X3 @ X2)))) | ($false = ((sK0 @ X0 @ (sK4 @ (^[Y0 : a]: (~ (X3 @ Y0)))))))) )),
% 1.09/0.37 inference(beta-eta_normalization,[],[f541])).
% 1.09/0.37 thf(f587,plain,(
% 1.09/0.37 ( ! [X2 : a,X3 : (a > $o),X0 : a] : (($true = ((X3 @ X0))) | ($true != ((~ (X3 @ X2)))) | ($false = ((sK0 @ X0 @ (sK4 @ (^[Y0 : a]: (~ (X3 @ Y0)))))))) )),
% 1.09/0.37 inference(not_proxy_clausification,[],[f586])).
% 1.09/0.37 thf(f588,plain,(
% 1.09/0.37 ( ! [X2 : a,X3 : (a > $o),X0 : a] : (($false = ((sK0 @ X0 @ (sK4 @ (^[Y0 : a]: (~ (X3 @ Y0))))))) | ($true = ((X3 @ X2))) | ($true = ((X3 @ X0)))) )),
% 1.09/0.37 inference(not_proxy_clausification,[],[f587])).
% 1.09/0.37 thf(f1021,plain,(
% 1.09/0.37 ( ! [X0 : a] : (($true = $false) | ($false = (((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK4 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK1 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0))))))) | (sK2 != X0)) )),
% 1.09/0.37 inference(constrained_superposition,[],[f25,f159])).
% 1.09/0.37 thf(f1173,plain,(
% 1.09/0.37 ( ! [X0 : a] : (($false = (((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK4 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK1 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0))))))) | (sK2 != X0)) )),
% 1.09/0.37 inference(trivial_inequality_removal,[],[f1021])).
% 1.09/0.37 thf(f1174,plain,(
% 1.09/0.37 ( ! [X0 : a] : (($false = ((sK1 @ (sK4 @ (^[Y0 : a]: (~ (sK1 @ Y0))))))) | (sK2 != X0)) )),
% 1.09/0.37 inference(beta-eta_normalization,[],[f1173])).
% 1.09/0.37 thf(f1202,plain,(
% 1.09/0.37 spl5_6 | spl5_7),
% 1.09/0.37 inference(avatar_split_clause,[],[f1174,f134,f131])).
% 1.09/0.37 thf(f3891,plain,(
% 1.09/0.37 ( ! [X0 : a,X1 : a] : (($true = $false) | ($false = ((sK0 @ X1 @ (sK4 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK1 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X1))) | (sK2 != X0)) )),
% 1.09/0.37 inference(constrained_superposition,[],[f588,f159])).
% 1.09/0.37 thf(f4119,plain,(
% 1.09/0.37 ( ! [X0 : a,X1 : a] : (($false = ((sK0 @ X1 @ (sK4 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK1 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0))))))) | ($true = (((^[Y0 : a]: (sK1 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X1))) | (sK2 != X0)) )),
% 1.09/0.37 inference(trivial_inequality_removal,[],[f3891])).
% 1.09/0.37 thf(f4120,plain,(
% 1.09/0.37 ( ! [X0 : a,X1 : a] : (($false = ((sK0 @ X1 @ (sK4 @ (^[Y0 : a]: (~ (sK1 @ Y0))))))) | ($true = ((sK1 @ X1))) | (sK2 != X0)) )),
% 1.09/0.37 inference(beta-eta_normalization,[],[f4119])).
% 1.09/0.37 thf(f4184,definition,(
% 1.09/0.37 spl5_27 <=> ! [X1 : a] : (($false = ((sK0 @ X1 @ (sK4 @ (^[Y0 : a]: (~ (sK1 @ Y0))))))) | ($true = ((sK1 @ X1))))),
% 1.09/0.37 introduced(definition,[new_symbols(definition,[spl5_27])],[avatar_definition])).
% 1.09/0.37 thf(f4185,plain,(
% 1.09/0.37 ( ! [X1 : a] : (($false = ((sK0 @ X1 @ (sK4 @ (^[Y0 : a]: (~ (sK1 @ Y0))))))) | ($true = ((sK1 @ X1)))) ) | ~spl5_27),
% 1.09/0.37 inference(avatar_component_clause,[],[f4184])).
% 1.09/0.37 thf(f4193,plain,(
% 1.09/0.37 spl5_6 | spl5_27),
% 1.09/0.37 inference(avatar_split_clause,[],[f4120,f4184,f131])).
% 1.09/0.37 thf(f4330,plain,(
% 1.09/0.37 ($true = $false) | ($true = ((sK1 @ (sK3 @ (sK4 @ (^[Y0 : a]: (~ (sK1 @ Y0)))))))) | ($true = ((sK1 @ (sK4 @ (^[Y0 : a]: (~ (sK1 @ Y0))))))) | ~spl5_27),
% 1.09/0.37 inference(constrained_superposition,[],[f4185,f12])).
% 1.09/0.37 thf(f4396,plain,(
% 1.09/0.37 ($true = ((sK1 @ (sK3 @ (sK4 @ (^[Y0 : a]: (~ (sK1 @ Y0)))))))) | ($true = ((sK1 @ (sK4 @ (^[Y0 : a]: (~ (sK1 @ Y0))))))) | ~spl5_27),
% 1.09/0.37 inference(trivial_inequality_removal,[],[f4330])).
% 1.09/0.37 thf(f4398,plain,(
% 1.09/0.37 ($true = ((sK1 @ (sK4 @ (^[Y0 : a]: (~ (sK1 @ Y0))))))) | ~spl5_27),
% 1.09/0.37 inference(forward_subsumption_resolution,[],[f4396,f13])).
% 1.09/0.37 thf(f4402,plain,(
% 1.09/0.37 ($true = $false) | (~spl5_7 | ~spl5_27)),
% 1.09/0.37 inference(forward_demodulation,[],[f4398,f136])).
% 1.09/0.37 thf(f4403,plain,(
% 1.09/0.37 $false | (~spl5_7 | ~spl5_27)),
% 1.09/0.37 inference(trivial_inequality_removal,[],[f4402])).
% 1.09/0.37 thf(f4404,plain,(
% 1.09/0.37 ~spl5_7 | ~spl5_27),
% 1.09/0.37 inference(avatar_contradiction_clause,[],[f4403])).
% 1.09/0.37 thf(f4405,plain,(
% 1.09/0.37 $false | ~spl5_6),
% 1.09/0.37 inference(equality_resolution,[],[f132])).
% 1.09/0.37 thf(f4406,plain,(
% 1.09/0.37 ~spl5_6),
% 1.09/0.37 inference(avatar_contradiction_clause,[],[f4405])).
% 1.09/0.37 cnf(s25, plain, spl5_6 | spl5_7, inference(sat_conversion,[],[f1202])).
% 1.09/0.37 cnf(s60, plain, spl5_6 | spl5_27, inference(sat_conversion,[],[f4193])).
% 1.09/0.37 cnf(s63, plain, ~spl5_7 | ~spl5_27, inference(sat_conversion,[],[f4404])).
% 1.09/0.37 cnf(s64, plain, ~spl5_6, inference(sat_conversion,[],[f4406])).
% 1.09/0.37 cnf(s65, plain, spl5_27, inference(rat,[],[s60,s64])).
% 1.09/0.37 cnf(s66, plain, ~spl5_7, inference(rat,[],[s63,s65])).
% 1.09/0.37 cnf(s72, plain, $false, inference(rat,[],[s25,s66,s64])).
% 1.09/0.37 thf(f4407,plain,(
% 1.09/0.37 $false),
% 1.09/0.37 inference(avatar_sat_refutation,[],[s72])).
% 1.09/0.37 % SZS output end Proof for theBenchmark
% 1.09/0.37 % (3319823)------------------------------
% 1.09/0.37 % (3319823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.09/0.37 % (3319823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.09/0.37 % (3319823)CaDiCaL version: 2.1.3
% 1.09/0.37 % (3319823)Termination reason: Refutation
% 1.09/0.37 % (3319823)Time elapsed: 0.086 s
% 1.09/0.37 % (3319823)Peak memory usage: 14 MB
% 1.09/0.37 % (3319823)Instructions burned: 327 (million)
% 1.09/0.37 % (3319801)Success in time 0.159 s
% 1.09/0.37 % Vampire exiting
%------------------------------------------------------------------------------