%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV384^5 : 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 : n015.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 08:39:26 AM UTC 2026
% Result : Theorem 1.03s 0.47s
% Output : Refutation 1.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV384^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n015.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 15:46:33 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 1.03/0.47 % (3690069)Will run a generic schedule for satisfiability detection.
% 1.03/0.47 % (3690077)dis+10_1_sil=32000:sp=arity:random_seed=3875578277:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.03/0.47 % (3690075)% WARNING: option uhcvi not known.
% 1.03/0.47 % (3690074)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2282905371_2999 on theBenchmark for (2999ds/0Mi)
% 1.03/0.47 % (3690078)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2544642308:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.03/0.47 % (3690075)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2775384198:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.03/0.47 % (3690076)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=961884107:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.03/0.47 % (3690075)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.03/0.47 % (3690078)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.03/0.47 % Exception at run slice level
% 1.03/0.47 % (3690075)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.03/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.03/0.47 % (3690079)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2634681129:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.03/0.47 % (3690080)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1382658504:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.03/0.47 % (3690086)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=976395434:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.03/0.47 % Exception at run slice level
% 1.03/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.03/0.47 % (3690077)Instruction limit reached!
% 1.03/0.47 % (3690077)------------------------------
% 1.03/0.47 % (3690077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.47 % (3690077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.47 % (3690077)CaDiCaL version: 2.1.3
% 1.03/0.47 % (3690077)Termination reason: Instruction limit
% 1.03/0.47 % (3690077)Termination phase: Saturation
% 1.03/0.47 % (3690077)Time elapsed: 0.030 s
% 1.03/0.47 % (3690077)Peak memory usage: 12 MB
% 1.03/0.47 % (3690077)Instructions burned: 106 (million)
% 1.03/0.47 % (3690091)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=3723004907:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.03/0.47 % (3690091)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.03/0.47 % (3690091)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.03/0.47 % (3690090)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2908065334:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.03/0.47 % (3690078)Instruction limit reached!
% 1.03/0.47 % (3690078)------------------------------
% 1.03/0.47 % (3690078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.47 % (3690078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.47 % (3690078)CaDiCaL version: 2.1.3
% 1.03/0.47 % (3690078)Termination reason: Instruction limit
% 1.03/0.47 % (3690078)Termination phase: Saturation
% 1.03/0.47 % (3690078)Time elapsed: 0.094 s
% 1.03/0.47 % (3690078)Peak memory usage: 12 MB
% 1.03/0.47 % (3690078)Instructions burned: 116 (million)
% 1.03/0.47 % (3690080)Instruction limit reached!
% 1.03/0.47 % (3690080)------------------------------
% 1.03/0.47 % (3690080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.47 % (3690080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.47 % (3690080)CaDiCaL version: 2.1.3
% 1.03/0.47 % (3690080)Termination reason: Instruction limit
% 1.03/0.47 % (3690080)Termination phase: Saturation
% 1.03/0.47 % (3690080)Time elapsed: 0.084 s
% 1.03/0.47 % (3690080)Peak memory usage: 13 MB
% 1.03/0.47 % (3690080)Instructions burned: 160 (million)
% 1.03/0.47 % (3690079)Instruction limit reached!
% 1.03/0.47 % (3690079)------------------------------
% 1.03/0.47 % (3690079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.47 % (3690079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.47 % (3690079)CaDiCaL version: 2.1.3
% 1.03/0.47 % (3690079)Termination reason: Instruction limit
% 1.03/0.47 % (3690079)Termination phase: Saturation
% 1.03/0.47 % (3690079)Time elapsed: 0.088 s
% 1.03/0.47 % (3690079)Peak memory usage: 12 MB
% 1.03/0.47 % (3690079)Instructions burned: 131 (million)
% 1.03/0.47 % (3690090)Instruction limit reached!
% 1.03/0.47 % (3690090)------------------------------
% 1.03/0.47 % (3690090)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.47 % (3690090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.47 % (3690090)CaDiCaL version: 2.1.3
% 1.03/0.47 % (3690090)Termination reason: Instruction limit
% 1.03/0.47 % (3690090)Termination phase: Saturation
% 1.03/0.47 % (3690090)Time elapsed: 0.071 s
% 1.03/0.47 % (3690090)Peak memory usage: 12 MB
% 1.03/0.47 % (3690090)Instructions burned: 131 (million)
% 1.03/0.47 % (3690095)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2189784498:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.03/0.47 % (3690096)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2283177636:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.03/0.47 % Exception at run slice level
% 1.03/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.03/0.47 % (3690094)ott-21_1_sil=16000:fs=off:random_seed=3948354537:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.03/0.47 % (3690097)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=1358807846:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.03/0.47 % (3690100)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=593728688:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 1.03/0.47 % Exception at run slice level
% 1.03/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.03/0.47 % (3690104)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=1912283183:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 1.03/0.47 % (3690104)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.03/0.47 % (3690091) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3690069-3690091"...
% 1.03/0.47 % (3690091)...printing done.
% 1.03/0.47 % (3690091)Refutation found. Thanks to Tanya!
% 1.03/0.47 % SZS status Theorem for theBenchmark
% 1.03/0.47 % SZS output start Proof for theBenchmark
% 1.03/0.47 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 1.03/0.47 thf(func_def_0, type, cP: ($i > $o)).
% 1.03/0.47 thf(func_def_1, type, s: ($i > $o)).
% 1.03/0.47 thf(func_def_2, type, cR: ($i > $i > $o)).
% 1.03/0.47 thf(func_def_7, type, sK1: ($i > $i)).
% 1.03/0.47 thf(func_def_8, type, sK2: (($i > $o) > $i)).
% 1.03/0.47 thf(func_def_9, type, vNOT: ($o > $o)).
% 1.03/0.47 thf(func_def_10, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.03/0.47 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 1.03/0.47 thf(func_def_12, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.03/0.47 thf(func_def_14, type, db1: !>[X0: $tType]:(X0)).
% 1.03/0.47 thf(f1,conjecture,(
% 1.03/0.47 (! [X4 : $i] : (! [X5 : $i] : (((cR @ X4 @ X5) & (s @ X5)) => (cP @ X5)) => (cP @ X4)) & ! [X0 : ($i > $o),X1 : $i] : ((X0 @ X1) => ? [X2 : $i] : (! [X3 : $i] : ((cR @ X2 @ X3) => ~(X0 @ X3)) & (X0 @ X2)))) => ! [X6 : $i] : ((s @ X6) => (cP @ X6))),
% 1.03/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM117B)).
% 1.03/0.47 thf(f2,negated_conjecture,(
% 1.03/0.47 ~((! [X4 : $i] : (! [X5 : $i] : (((cR @ X4 @ X5) & (s @ X5)) => (cP @ X5)) => (cP @ X4)) & ! [X0 : ($i > $o),X1 : $i] : ((X0 @ X1) => ? [X2 : $i] : (! [X3 : $i] : ((cR @ X2 @ X3) => ~(X0 @ X3)) & (X0 @ X2)))) => ! [X6 : $i] : ((s @ X6) => (cP @ X6)))),
% 1.03/0.47 inference(negated_conjecture,[status(cth)],[f1])).
% 1.03/0.47 thf(f3,plain,(
% 1.03/0.47 ~((! [X0 : $i] : (! [X1 : $i] : (((cR @ X0 @ X1) & (s @ X1)) => (cP @ X1)) => (cP @ X0)) & ! [X2 : ($i > $o),X3 : $i] : ((X2 @ X3) => ? [X4 : $i] : (! [X5 : $i] : ((cR @ X4 @ X5) => ~(X2 @ X5)) & (X2 @ X4)))) => ! [X6 : $i] : ((s @ X6) => (cP @ X6)))),
% 1.03/0.47 inference(rectify,[],[f2])).
% 1.03/0.47 thf(f4,plain,(
% 1.03/0.47 ~((! [X0 : $i] : (! [X1 : $i] : (((((cR @ X0 @ X1)) = $true) & (((s @ X1)) = $true)) => (((cP @ X1)) = $true)) => (((cP @ X0)) = $true)) & ! [X2 : ($i > $o),X3 : $i] : ((((X2 @ X3)) = $true) => ? [X4 : $i] : (! [X5 : $i] : ((((cR @ X4 @ X5)) = $true) => ~ (((X2 @ X5)) = $true)) & (((X2 @ X4)) = $true)))) => ! [X6 : $i] : ((((s @ X6)) = $true) => (((cP @ X6)) = $true)))),
% 1.03/0.47 inference(fool_elimination,[],[f3])).
% 1.03/0.47 thf(f5,plain,(
% 1.03/0.47 ~((! [X0 : $i] : (! [X1 : $i] : (((((cR @ X0 @ X1)) = $true) & (((s @ X1)) = $true)) => (((cP @ X1)) = $true)) => (((cP @ X0)) = $true)) & ! [X2 : ($i > $o),X3 : $i] : ((((X2 @ X3)) = $true) => ? [X4 : $i] : (! [X5 : $i] : ((((cR @ X4 @ X5)) = $true) => (((X2 @ X5)) != $true)) & (((X2 @ X4)) = $true)))) => ! [X6 : $i] : ((((s @ X6)) = $true) => (((cP @ X6)) = $true)))),
% 1.03/0.47 inference(flattening,[],[f4])).
% 1.03/0.47 thf(f6,plain,(
% 1.03/0.47 ? [X6 : $i] : ((((cP @ X6)) != $true) & (((s @ X6)) = $true)) & (! [X0 : $i] : ((((cP @ X0)) = $true) | ? [X1 : $i] : ((((cP @ X1)) != $true) & ((((cR @ X0 @ X1)) = $true) & (((s @ X1)) = $true)))) & ! [X2 : ($i > $o),X3 : $i] : (? [X4 : $i] : (! [X5 : $i] : ((((X2 @ X5)) != $true) | (((cR @ X4 @ X5)) != $true)) & (((X2 @ X4)) = $true)) | (((X2 @ X3)) != $true)))),
% 1.03/0.47 inference(ennf_transformation,[],[f5])).
% 1.03/0.47 thf(f7,plain,(
% 1.03/0.47 ? [X6 : $i] : ((((cP @ X6)) != $true) & (((s @ X6)) = $true)) & ! [X0 : $i] : ((((cP @ X0)) = $true) | ? [X1 : $i] : ((((cP @ X1)) != $true) & (((cR @ X0 @ X1)) = $true) & (((s @ X1)) = $true))) & ! [X2 : ($i > $o),X3 : $i] : (? [X4 : $i] : (! [X5 : $i] : ((((X2 @ X5)) != $true) | (((cR @ X4 @ X5)) != $true)) & (((X2 @ X4)) = $true)) | (((X2 @ X3)) != $true))),
% 1.03/0.47 inference(flattening,[],[f6])).
% 1.03/0.47 thf(f8,plain,(
% 1.03/0.47 ? [X0 : $i] : ((((cP @ X0)) != $true) & ($true = ((s @ X0)))) & ! [X1 : $i] : ((((cP @ X1)) = $true) | ? [X2 : $i] : (($true != ((cP @ X2))) & ($true = ((cR @ X1 @ X2))) & ($true = ((s @ X2))))) & ! [X3 : ($i > $o),X4 : $i] : (? [X5 : $i] : (! [X6 : $i] : (($true != ((X3 @ X6))) | ($true != ((cR @ X5 @ X6)))) & ($true = ((X3 @ X5)))) | ($true != ((X3 @ X4))))),
% 1.03/0.47 inference(rectify,[],[f7])).
% 1.03/0.47 thf(f9,plain,(
% 1.03/0.47 (($true != ((cP @ sK0))) & ($true = ((s @ sK0)))) & ! [X1 : $i] : ((((cP @ X1)) = $true) | (($true != ((cP @ (sK1 @ X1)))) & ($true = ((cR @ X1 @ (sK1 @ X1)))) & ($true = ((s @ (sK1 @ X1)))))) & ! [X3 : ($i > $o),X4 : $i] : ((! [X6 : $i] : (($true != ((X3 @ X6))) | ($true != ((cR @ (sK2 @ X3) @ X6)))) & ($true = ((X3 @ (sK2 @ X3))))) | ($true != ((X3 @ X4))))),
% 1.03/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X5,sK2 @ X3),skolemize(X5,sK2 @ X3)],[f8])).
% 1.03/0.47 thf(f10,plain,(
% 1.03/0.47 ( ! [X3 : ($i > $o),X4 : $i] : (($true != ((X3 @ X4))) | ($true = ((X3 @ (sK2 @ X3))))) )),
% 1.03/0.47 inference(cnf_transformation,[],[f9])).
% 1.03/0.47 thf(f11,plain,(
% 1.03/0.47 ( ! [X3 : ($i > $o),X6 : $i,X4 : $i] : (($true != ((cR @ (sK2 @ X3) @ X6))) | ($true != ((X3 @ X6))) | ($true != ((X3 @ X4)))) )),
% 1.03/0.47 inference(cnf_transformation,[],[f9])).
% 1.03/0.47 thf(f13,plain,(
% 1.03/0.47 ( ! [X1 : $i] : (($true = ((cR @ X1 @ (sK1 @ X1)))) | (((cP @ X1)) = $true)) )),
% 1.03/0.47 inference(cnf_transformation,[],[f9])).
% 1.03/0.47 thf(f14,plain,(
% 1.03/0.47 ( ! [X1 : $i] : (($true != ((cP @ (sK1 @ X1)))) | (((cP @ X1)) = $true)) )),
% 1.03/0.47 inference(cnf_transformation,[],[f9])).
% 1.03/0.47 thf(f16,plain,(
% 1.03/0.47 ($true != ((cP @ sK0)))),
% 1.03/0.47 inference(cnf_transformation,[],[f9])).
% 1.03/0.47 thf(f18,definition,(
% 1.03/0.47 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 1.03/0.47 introduced(theory,[fool_exhaustiveness_axiom])).
% 1.03/0.47 thf(f22,plain,(
% 1.03/0.47 ( ! [X4 : $i,X5 : ($i > $o)] : (($true != (((^[Y0 : $i]: (~ (X5 @ Y0))) @ X4))) | ($true = (((^[Y0 : $i]: (~ (X5 @ Y0))) @ (sK2 @ (^[Y0 : $i]: (~ (X5 @ Y0)))))))) )),
% 1.03/0.47 inference(primitive_instantiation,[],[f10])).
% 1.03/0.47 thf(f37,plain,(
% 1.03/0.47 ( ! [X4 : $i,X5 : ($i > $o)] : (($true != ((~ (X5 @ X4)))) | ($true = ((~ (X5 @ (sK2 @ (^[Y0 : $i]: (~ (X5 @ Y0))))))))) )),
% 1.03/0.47 inference(beta-eta_normalization,[],[f22])).
% 1.03/0.47 thf(f38,plain,(
% 1.03/0.47 ( ! [X4 : $i,X5 : ($i > $o)] : (($true = ((X5 @ X4))) | ($true = ((~ (X5 @ (sK2 @ (^[Y0 : $i]: (~ (X5 @ Y0))))))))) )),
% 1.03/0.47 inference(not_proxy_clausification,[],[f37])).
% 1.03/0.47 thf(f39,plain,(
% 1.03/0.47 ( ! [X4 : $i,X5 : ($i > $o)] : (($true = ((X5 @ X4))) | ($false = ((X5 @ (sK2 @ (^[Y0 : $i]: (~ (X5 @ Y0)))))))) )),
% 1.03/0.47 inference(not_proxy_clausification,[],[f38])).
% 1.03/0.47 thf(f51,definition,(
% 1.03/0.47 spl3_3 <=> ! [X0 : $i] : (sK0 != X0)),
% 1.03/0.47 introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition])).
% 1.03/0.47 thf(f52,plain,(
% 1.03/0.47 ( ! [X0 : $i] : ((sK0 != X0)) ) | ~spl3_3),
% 1.03/0.47 inference(avatar_component_clause,[],[f51])).
% 1.03/0.47 thf(f63,plain,(
% 1.03/0.47 ($true != $true) | (((cP @ sK0)) = $false)),
% 1.03/0.47 inference(constrained_superposition,[],[f16,f18])).
% 1.03/0.47 thf(f69,plain,(
% 1.03/0.47 (((cP @ sK0)) = $false)),
% 1.03/0.47 inference(trivial_inequality_removal,[],[f63])).
% 1.03/0.47 thf(f438,definition,(
% 1.03/0.47 spl3_4 <=> ($false = ((cP @ (sK2 @ (^[Y0 : $i]: (~ (cP @ Y0)))))))),
% 1.03/0.47 introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition])).
% 1.03/0.47 thf(f440,plain,(
% 1.03/0.47 ($false = ((cP @ (sK2 @ (^[Y0 : $i]: (~ (cP @ Y0))))))) | ~spl3_4),
% 1.03/0.47 inference(avatar_component_clause,[],[f438])).
% 1.03/0.47 thf(f445,plain,(
% 1.03/0.47 $false | ~spl3_3),
% 1.03/0.47 inference(equality_resolution,[],[f52])).
% 1.03/0.47 thf(f446,plain,(
% 1.03/0.47 ~spl3_3),
% 1.03/0.47 inference(avatar_contradiction_clause,[],[f445])).
% 1.03/0.47 thf(f622,plain,(
% 1.03/0.47 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : (($true != $true) | (((X0 @ X1)) != $true) | (((X0 @ X2)) != $true) | ($false = ((cR @ (sK2 @ X0) @ X1)))) )),
% 1.03/0.47 inference(constrained_superposition,[],[f11,f18])).
% 1.03/0.47 thf(f623,plain,(
% 1.03/0.47 ( ! [X2 : $i,X0 : ($i > $o),X1 : $i] : ((((X0 @ X2)) != $true) | (((X0 @ X1)) != $true) | ($false = ((cR @ (sK2 @ X0) @ X1)))) )),
% 1.03/0.47 inference(trivial_inequality_removal,[],[f622])).
% 1.03/0.47 thf(f689,plain,(
% 1.03/0.47 ( ! [X2 : $i,X3 : ($i > $o),X1 : $i] : (($true != (((^[Y0 : $i]: (~ (X3 @ Y0))) @ X2))) | ($true != (((^[Y0 : $i]: (~ (X3 @ Y0))) @ X1))) | ($false = ((cR @ (sK2 @ (^[Y0 : $i]: (~ (X3 @ Y0)))) @ X1)))) )),
% 1.03/0.47 inference(primitive_instantiation,[],[f623])).
% 1.03/0.47 thf(f752,plain,(
% 1.03/0.47 ( ! [X2 : $i,X3 : ($i > $o),X1 : $i] : (($true != ((~ (X3 @ X2)))) | ($true != ((~ (X3 @ X1)))) | ($false = ((cR @ (sK2 @ (^[Y0 : $i]: (~ (X3 @ Y0)))) @ X1)))) )),
% 1.03/0.47 inference(beta-eta_normalization,[],[f689])).
% 1.03/0.47 thf(f753,plain,(
% 1.03/0.47 ( ! [X2 : $i,X3 : ($i > $o),X1 : $i] : (($true = ((X3 @ X2))) | ($true != ((~ (X3 @ X1)))) | ($false = ((cR @ (sK2 @ (^[Y0 : $i]: (~ (X3 @ Y0)))) @ X1)))) )),
% 1.03/0.47 inference(not_proxy_clausification,[],[f752])).
% 1.03/0.47 thf(f754,plain,(
% 1.03/0.47 ( ! [X2 : $i,X3 : ($i > $o),X1 : $i] : (($false = ((cR @ (sK2 @ (^[Y0 : $i]: (~ (X3 @ Y0)))) @ X1))) | ($true = ((X3 @ X2))) | ($true = ((X3 @ X1)))) )),
% 1.03/0.47 inference(not_proxy_clausification,[],[f753])).
% 1.03/0.47 thf(f3024,plain,(
% 1.03/0.47 ( ! [X0 : $i] : (($true = $false) | ($false = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK2 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (cP @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | (sK0 != X0)) )),
% 1.03/0.47 inference(constrained_superposition,[],[f69,f39])).
% 1.03/0.47 thf(f3066,plain,(
% 1.03/0.47 ( ! [X0 : $i] : (($false = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ (sK2 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (cP @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0))))))) | (sK0 != X0)) )),
% 1.03/0.47 inference(trivial_inequality_removal,[],[f3024])).
% 1.03/0.47 thf(f3067,plain,(
% 1.03/0.47 ( ! [X0 : $i] : (($false = ((cP @ (sK2 @ (^[Y0 : $i]: (~ (cP @ Y0))))))) | (sK0 != X0)) )),
% 1.03/0.47 inference(beta-eta_normalization,[],[f3066])).
% 1.03/0.47 thf(f3072,plain,(
% 1.03/0.47 spl3_3 | spl3_4),
% 1.03/0.47 inference(avatar_split_clause,[],[f3067,f438,f51])).
% 1.03/0.47 thf(f6037,plain,(
% 1.03/0.47 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((cR @ (sK2 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (cP @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0)))) @ X1))) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1))) | (sK0 != X0)) )),
% 1.03/0.47 inference(constrained_superposition,[],[f754,f69])).
% 1.03/0.47 thf(f6437,plain,(
% 1.03/0.47 ( ! [X0 : $i,X1 : $i] : (($false = ((cR @ (sK2 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (cP @ ((^[Y2 : $i]: (Y2)) @ Y1))) @ Y0)))) @ X1))) | ($true = (((^[Y0 : $i]: (cP @ ((^[Y1 : $i]: (Y1)) @ Y0))) @ X1))) | (sK0 != X0)) )),
% 1.03/0.47 inference(trivial_inequality_removal,[],[f6037])).
% 1.03/0.47 thf(f6438,plain,(
% 1.03/0.47 ( ! [X0 : $i,X1 : $i] : (($false = ((cR @ (sK2 @ (^[Y0 : $i]: (~ (cP @ Y0)))) @ X1))) | (((cP @ X1)) = $true) | (sK0 != X0)) )),
% 1.03/0.47 inference(beta-eta_normalization,[],[f6437])).
% 1.03/0.47 thf(f6493,definition,(
% 1.03/0.47 spl3_53 <=> ! [X1 : $i] : (($false = ((cR @ (sK2 @ (^[Y0 : $i]: (~ (cP @ Y0)))) @ X1))) | (((cP @ X1)) = $true))),
% 1.03/0.47 introduced(definition,[new_symbols(definition,[spl3_53])],[avatar_definition])).
% 1.03/0.47 thf(f6494,plain,(
% 1.03/0.47 ( ! [X1 : $i] : (($false = ((cR @ (sK2 @ (^[Y0 : $i]: (~ (cP @ Y0)))) @ X1))) | (((cP @ X1)) = $true)) ) | ~spl3_53),
% 1.03/0.47 inference(avatar_component_clause,[],[f6493])).
% 1.03/0.47 thf(f6519,plain,(
% 1.03/0.47 spl3_3 | spl3_53),
% 1.03/0.47 inference(avatar_split_clause,[],[f6438,f6493,f51])).
% 1.03/0.47 thf(f6769,plain,(
% 1.03/0.47 ($true = $false) | ($true = ((cP @ (sK2 @ (^[Y0 : $i]: (~ (cP @ Y0))))))) | ($true = ((cP @ (sK1 @ (sK2 @ (^[Y0 : $i]: (~ (cP @ Y0)))))))) | ~spl3_53),
% 1.03/0.47 inference(constrained_superposition,[],[f13,f6494])).
% 1.03/0.47 thf(f6778,plain,(
% 1.03/0.47 ($true = ((cP @ (sK2 @ (^[Y0 : $i]: (~ (cP @ Y0))))))) | ($true = ((cP @ (sK1 @ (sK2 @ (^[Y0 : $i]: (~ (cP @ Y0)))))))) | ~spl3_53),
% 1.03/0.47 inference(trivial_inequality_removal,[],[f6769])).
% 1.03/0.47 thf(f6822,plain,(
% 1.03/0.47 ($true = ((cP @ (sK2 @ (^[Y0 : $i]: (~ (cP @ Y0))))))) | ~spl3_53),
% 1.03/0.47 inference(forward_subsumption_resolution,[],[f6778,f14])).
% 1.03/0.47 thf(f6824,plain,(
% 1.03/0.47 ($true = $false) | (~spl3_4 | ~spl3_53)),
% 1.03/0.47 inference(forward_demodulation,[],[f6822,f440])).
% 1.03/0.47 thf(f6825,plain,(
% 1.03/0.47 $false | (~spl3_4 | ~spl3_53)),
% 1.03/0.47 inference(trivial_inequality_removal,[],[f6824])).
% 1.03/0.47 thf(f6826,plain,(
% 1.03/0.47 ~spl3_4 | ~spl3_53),
% 1.03/0.47 inference(avatar_contradiction_clause,[],[f6825])).
% 1.03/0.47 cnf(s6, plain, ~spl3_3, inference(sat_conversion,[],[f446])).
% 1.03/0.47 cnf(s75, plain, spl3_3 | spl3_4, inference(sat_conversion,[],[f3072])).
% 1.03/0.47 cnf(s114, plain, spl3_3 | spl3_53, inference(sat_conversion,[],[f6519])).
% 1.03/0.47 cnf(s117, plain, ~spl3_4 | ~spl3_53, inference(sat_conversion,[],[f6826])).
% 1.03/0.47 cnf(s143, plain, spl3_53, inference(rat,[],[s114,s6])).
% 1.03/0.47 cnf(s144, plain, spl3_4, inference(rat,[],[s75,s6])).
% 1.03/0.47 cnf(s146, plain, $false, inference(rat,[],[s117,s143,s144])).
% 1.03/0.47 thf(f6830,plain,(
% 1.03/0.47 $false),
% 1.03/0.47 inference(avatar_sat_refutation,[],[s146])).
% 1.03/0.47 % SZS output end Proof for theBenchmark
% 1.03/0.47 % (3690091)------------------------------
% 1.03/0.47 % (3690091)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.03/0.47 % (3690091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.03/0.47 % (3690091)CaDiCaL version: 2.1.3
% 1.03/0.47 % (3690091)Termination reason: Refutation
% 1.03/0.47 % (3690091)Time elapsed: 0.157 s
% 1.03/0.47 % (3690091)Peak memory usage: 14 MB
% 1.03/0.47 % (3690091)Instructions burned: 585 (million)
% 1.03/0.47 % (3690069)Success in time 0.238 s
% 1.03/0.47 % Vampire exiting
%------------------------------------------------------------------------------