%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV019^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 08:38:52 AM UTC 2026
% Result : Theorem 0.61s 0.44s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV019^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.24 % Computer : n006.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.25 % CPULimit : 300
% 0.10/0.25 % WCLimit : 300
% 0.10/0.25 % DateTime : Tue Sep 29 15:00:09 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.24/0.30 Running first-order model finding
% 0.24/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.44 % (834088)Will run a generic schedule for satisfiability detection.
% 0.61/0.44 % (834096)dis+10_1_sil=32000:sp=arity:random_seed=1865100814:i=103:fgj=on_3000 on theBenchmark for (3000ds/103Mi)
% 0.61/0.44 % (834094)% WARNING: option uhcvi not known.
% 0.61/0.44 % (834093)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1388997495_3000 on theBenchmark for (3000ds/0Mi)
% 0.61/0.44 % (834098)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=321553619:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.61/0.44 % (834094)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3249954466:i=135531:add=off:rawr=on_3000 on theBenchmark for (3000ds/135531Mi)
% 0.61/0.44 % (834095)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1074290801:i=88024:add=on:rawr=on_3000 on theBenchmark for (3000ds/88024Mi)
% 0.61/0.44 % (834097)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=167472283:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.61/0.44 % (834099)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1295808025:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_3000 on theBenchmark for (3000ds/159Mi)
% 0.61/0.44 % (834094)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.61/0.44 % (834097)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.61/0.44 % Exception at run slice level
% 0.61/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.61/0.44 % (834094)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.61/0.44 % (834096)Instruction limit reached!
% 0.61/0.44 % (834096)------------------------------
% 0.61/0.44 % (834096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (834096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (834096)CaDiCaL version: 2.1.3
% 0.61/0.44 % (834096)Termination reason: Instruction limit
% 0.61/0.44 % (834096)Termination phase: Saturation
% 0.61/0.44 % (834096)Time elapsed: 0.046 s
% 0.61/0.44 % (834096)Peak memory usage: 11 MB
% 0.61/0.44 % (834096)Instructions burned: 104 (million)
% 0.61/0.44 % (834107)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3644498747:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.61/0.44 % Exception at run slice level
% 0.61/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.61/0.44 % (834108)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2394479438:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.61/0.44 % (834110)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=1345232694:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.61/0.44 % (834110)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.61/0.44 % (834110)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.61/0.44 % (834110) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-834088-834110"...
% 0.61/0.44 % (834110)...printing done.
% 0.61/0.44 % (834110)Refutation found. Thanks to Tanya!
% 0.61/0.44 % SZS status Theorem for theBenchmark
% 0.61/0.44 % SZS output start Proof for theBenchmark
% 0.61/0.44 thf(type_def_5, type, a: $tType).
% 0.61/0.44 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.61/0.44 thf(func_def_0, type, cQ: (a > a > $o)).
% 0.61/0.44 thf(func_def_4, type, sK0: a).
% 0.61/0.44 thf(func_def_5, type, sK1: a).
% 0.61/0.44 thf(func_def_6, type, sK2: a).
% 0.61/0.44 thf(func_def_7, type, sK3: a).
% 0.61/0.44 thf(func_def_8, type, sK4: a).
% 0.61/0.44 thf(func_def_9, type, sK5: a).
% 0.61/0.44 thf(func_def_10, type, sK6: (a > a > $o)).
% 0.61/0.44 thf(func_def_11, type, sK7: (a > a)).
% 0.61/0.44 thf(f1,conjecture,(
% 0.61/0.44 ! [X0 : a] : ? [X1 : (a > $o)] : ((X1 @ X0) & ! [X3 : a] : ((X1 @ X3) => ! [X4 : a] : ((X1 @ X4) <=> (cQ @ X3 @ X4))) & ? [X2 : a] : (X1 @ X2)) => (! [X0 : a,X4 : a,X2 : a] : (((cQ @ X4 @ X2) & (cQ @ X0 @ X4)) => (cQ @ X0 @ X2)) & ! [X0 : a,X4 : a] : ((cQ @ X0 @ X4) => (cQ @ X4 @ X0)) & ! [X0 : a] : (cQ @ X0 @ X0))),
% 0.61/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM559_pme)).
% 0.61/0.44 thf(f2,negated_conjecture,(
% 0.61/0.44 ~(! [X0 : a] : ? [X1 : (a > $o)] : ((X1 @ X0) & ! [X3 : a] : ((X1 @ X3) => ! [X4 : a] : ((X1 @ X4) <=> (cQ @ X3 @ X4))) & ? [X2 : a] : (X1 @ X2)) => (! [X0 : a,X4 : a,X2 : a] : (((cQ @ X4 @ X2) & (cQ @ X0 @ X4)) => (cQ @ X0 @ X2)) & ! [X0 : a,X4 : a] : ((cQ @ X0 @ X4) => (cQ @ X4 @ X0)) & ! [X0 : a] : (cQ @ X0 @ X0)))),
% 0.61/0.44 inference(negated_conjecture,[status(cth)],[f1])).
% 0.61/0.44 thf(f3,plain,(
% 0.61/0.44 ~(! [X0 : a] : ? [X1 : (a > $o)] : ((X1 @ X0) & ! [X2 : a] : ((X1 @ X2) => ! [X3 : a] : ((X1 @ X3) <=> (cQ @ X2 @ X3))) & ? [X4 : a] : (X1 @ X4)) => (! [X5 : a,X6 : a,X7 : a] : (((cQ @ X6 @ X7) & (cQ @ X5 @ X6)) => (cQ @ X5 @ X7)) & ! [X8 : a,X9 : a] : ((cQ @ X8 @ X9) => (cQ @ X9 @ X8)) & ! [X10 : a] : (cQ @ X10 @ X10)))),
% 0.61/0.44 inference(rectify,[],[f2])).
% 0.61/0.44 thf(f4,plain,(
% 0.61/0.44 ~(! [X0 : a] : ? [X1 : (a > $o)] : ((((X1 @ X0)) = $true) & ! [X2 : a] : ((((X1 @ X2)) = $true) => ! [X3 : a] : (((X1 @ X3)) = ((cQ @ X2 @ X3)))) & ? [X4 : a] : (((X1 @ X4)) = $true)) => (! [X5 : a,X6 : a,X7 : a] : (((((cQ @ X6 @ X7)) = $true) & (((cQ @ X5 @ X6)) = $true)) => (((cQ @ X5 @ X7)) = $true)) & ! [X8 : a,X9 : a] : ((((cQ @ X8 @ X9)) = $true) => (((cQ @ X9 @ X8)) = $true)) & ! [X10 : a] : (((cQ @ X10 @ X10)) = $true)))),
% 0.61/0.44 inference(fool_elimination,[],[f3])).
% 0.61/0.44 thf(f5,plain,(
% 0.61/0.44 (? [X5 : a,X6 : a,X7 : a] : ((((cQ @ X5 @ X7)) != $true) & ((((cQ @ X6 @ X7)) = $true) & (((cQ @ X5 @ X6)) = $true))) | ? [X8 : a,X9 : a] : ((((cQ @ X9 @ X8)) != $true) & (((cQ @ X8 @ X9)) = $true)) | ? [X10 : a] : (((cQ @ X10 @ X10)) != $true)) & ! [X0 : a] : ? [X1 : (a > $o)] : ((((X1 @ X0)) = $true) & ! [X2 : a] : (! [X3 : a] : (((X1 @ X3)) = ((cQ @ X2 @ X3))) | (((X1 @ X2)) != $true)) & ? [X4 : a] : (((X1 @ X4)) = $true))),
% 0.61/0.44 inference(ennf_transformation,[],[f4])).
% 0.61/0.44 thf(f6,plain,(
% 0.61/0.44 (? [X5 : a,X6 : a,X7 : a] : ((((cQ @ X5 @ X7)) != $true) & (((cQ @ X6 @ X7)) = $true) & (((cQ @ X5 @ X6)) = $true)) | ? [X8 : a,X9 : a] : ((((cQ @ X9 @ X8)) != $true) & (((cQ @ X8 @ X9)) = $true)) | ? [X10 : a] : (((cQ @ X10 @ X10)) != $true)) & ! [X0 : a] : ? [X1 : (a > $o)] : ((((X1 @ X0)) = $true) & ! [X2 : a] : (! [X3 : a] : (((X1 @ X3)) = ((cQ @ X2 @ X3))) | (((X1 @ X2)) != $true)) & ? [X4 : a] : (((X1 @ X4)) = $true))),
% 0.61/0.44 inference(flattening,[],[f5])).
% 0.61/0.44 thf(f7,plain,(
% 0.61/0.44 (? [X0 : a,X1 : a,X2 : a] : ((((cQ @ X0 @ X2)) != $true) & ($true = ((cQ @ X1 @ X2))) & ($true = ((cQ @ X0 @ X1)))) | ? [X3 : a,X4 : a] : (($true != ((cQ @ X4 @ X3))) & (((cQ @ X3 @ X4)) = $true)) | ? [X5 : a] : ($true != ((cQ @ X5 @ X5)))) & ! [X6 : a] : ? [X7 : (a > $o)] : (($true = ((X7 @ X6))) & ! [X8 : a] : (! [X9 : a] : (((cQ @ X8 @ X9)) = ((X7 @ X9))) | ($true != ((X7 @ X8)))) & ? [X10 : a] : ($true = ((X7 @ X10))))),
% 0.61/0.44 inference(rectify,[],[f6])).
% 0.61/0.44 thf(f8,plain,(
% 0.61/0.44 ((($true != ((cQ @ sK0 @ sK2))) & ($true = ((cQ @ sK1 @ sK2))) & ($true = ((cQ @ sK0 @ sK1)))) | (($true != ((cQ @ sK4 @ sK3))) & ($true = ((cQ @ sK3 @ sK4)))) | ($true != ((cQ @ sK5 @ sK5)))) & ! [X6 : a] : (($true = ((sK6 @ X6 @ X6))) & ! [X8 : a] : (! [X9 : a] : (((cQ @ X8 @ X9)) = ((sK6 @ X6 @ X9))) | ($true != ((sK6 @ X6 @ X8)))) & ($true = ((sK6 @ X6 @ (sK7 @ X6)))))),
% 0.61/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X10,sK7 @ X6),skolemize(X10,sK7 @ X6)],[f7])).
% 0.61/0.44 thf(f10,plain,(
% 0.61/0.44 ( ! [X8 : a,X6 : a,X9 : a] : ((((cQ @ X8 @ X9)) = ((sK6 @ X6 @ X9))) | ($true != ((sK6 @ X6 @ X8)))) )),
% 0.61/0.44 inference(cnf_transformation,[],[f8])).
% 0.61/0.44 thf(f11,plain,(
% 0.61/0.44 ( ! [X6 : a] : (($true = ((sK6 @ X6 @ X6)))) )),
% 0.61/0.44 inference(cnf_transformation,[],[f8])).
% 0.61/0.44 thf(f12,plain,(
% 0.61/0.44 ($true = ((cQ @ sK0 @ sK1))) | ($true = ((cQ @ sK3 @ sK4))) | ($true != ((cQ @ sK5 @ sK5)))),
% 0.61/0.44 inference(cnf_transformation,[],[f8])).
% 0.61/0.44 thf(f13,plain,(
% 0.61/0.44 ($true = ((cQ @ sK0 @ sK1))) | ($true != ((cQ @ sK4 @ sK3))) | ($true != ((cQ @ sK5 @ sK5)))),
% 0.61/0.44 inference(cnf_transformation,[],[f8])).
% 0.61/0.44 thf(f14,plain,(
% 0.61/0.44 ($true = ((cQ @ sK1 @ sK2))) | ($true = ((cQ @ sK3 @ sK4))) | ($true != ((cQ @ sK5 @ sK5)))),
% 0.61/0.44 inference(cnf_transformation,[],[f8])).
% 0.61/0.44 thf(f15,plain,(
% 0.61/0.44 ($true = ((cQ @ sK1 @ sK2))) | ($true != ((cQ @ sK4 @ sK3))) | ($true != ((cQ @ sK5 @ sK5)))),
% 0.61/0.44 inference(cnf_transformation,[],[f8])).
% 0.61/0.44 thf(f16,plain,(
% 0.61/0.44 ($true != ((cQ @ sK0 @ sK2))) | ($true = ((cQ @ sK3 @ sK4))) | ($true != ((cQ @ sK5 @ sK5)))),
% 0.61/0.44 inference(cnf_transformation,[],[f8])).
% 0.61/0.44 thf(f17,plain,(
% 0.61/0.44 ($true != ((cQ @ sK0 @ sK2))) | ($true != ((cQ @ sK4 @ sK3))) | ($true != ((cQ @ sK5 @ sK5)))),
% 0.61/0.44 inference(cnf_transformation,[],[f8])).
% 0.61/0.44 thf(f19,definition,(
% 0.61/0.44 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.61/0.44 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.61/0.44 thf(f20,plain,(
% 0.61/0.44 ( ! [X8 : a,X6 : a,X9 : a] : (($true != ((sK6 @ X6 @ X8))) | (((cQ @ X8 @ X9)) = $true) | (((sK6 @ X6 @ X9)) = $false)) )),
% 0.61/0.44 inference(iff_proxy_clausification,[],[f10])).
% 0.61/0.44 thf(f21,plain,(
% 0.61/0.44 ( ! [X8 : a,X6 : a,X9 : a] : (($true != ((sK6 @ X6 @ X8))) | (((cQ @ X8 @ X9)) = $false) | ($true = ((sK6 @ X6 @ X9)))) )),
% 0.61/0.44 inference(iff_proxy_clausification,[],[f10])).
% 0.61/0.44 thf(f23,definition,(
% 0.61/0.44 spl8_1 <=> ($true = ((cQ @ sK5 @ sK5)))),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition])).
% 0.61/0.44 thf(f25,plain,(
% 0.61/0.44 ($true != ((cQ @ sK5 @ sK5))) | spl8_1),
% 0.61/0.44 inference(avatar_component_clause,[],[f23])).
% 0.61/0.44 thf(f27,definition,(
% 0.61/0.44 spl8_2 <=> ($true = ((cQ @ sK3 @ sK4)))),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition])).
% 0.61/0.44 thf(f29,plain,(
% 0.61/0.44 ($true = ((cQ @ sK3 @ sK4))) | ~spl8_2),
% 0.61/0.44 inference(avatar_component_clause,[],[f27])).
% 0.61/0.44 thf(f31,definition,(
% 0.61/0.44 spl8_3 <=> ($true = ((cQ @ sK0 @ sK1)))),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition])).
% 0.61/0.44 thf(f33,plain,(
% 0.61/0.44 ($true = ((cQ @ sK0 @ sK1))) | ~spl8_3),
% 0.61/0.44 inference(avatar_component_clause,[],[f31])).
% 0.61/0.44 thf(f34,plain,(
% 0.61/0.44 ~spl8_1 | spl8_2 | spl8_3),
% 0.61/0.44 inference(avatar_split_clause,[],[f12,f31,f27,f23])).
% 0.61/0.44 thf(f36,definition,(
% 0.61/0.44 spl8_4 <=> ($true = ((cQ @ sK4 @ sK3)))),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition])).
% 0.61/0.44 thf(f38,plain,(
% 0.61/0.44 ($true != ((cQ @ sK4 @ sK3))) | spl8_4),
% 0.61/0.44 inference(avatar_component_clause,[],[f36])).
% 0.61/0.44 thf(f39,plain,(
% 0.61/0.44 ~spl8_1 | ~spl8_4 | spl8_3),
% 0.61/0.44 inference(avatar_split_clause,[],[f13,f31,f36,f23])).
% 0.61/0.44 thf(f41,definition,(
% 0.61/0.44 spl8_5 <=> ($true = ((cQ @ sK1 @ sK2)))),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition])).
% 0.61/0.44 thf(f43,plain,(
% 0.61/0.44 ($true = ((cQ @ sK1 @ sK2))) | ~spl8_5),
% 0.61/0.44 inference(avatar_component_clause,[],[f41])).
% 0.61/0.44 thf(f44,plain,(
% 0.61/0.44 ~spl8_1 | spl8_2 | spl8_5),
% 0.61/0.44 inference(avatar_split_clause,[],[f14,f41,f27,f23])).
% 0.61/0.44 thf(f45,plain,(
% 0.61/0.44 ~spl8_1 | ~spl8_4 | spl8_5),
% 0.61/0.44 inference(avatar_split_clause,[],[f15,f41,f36,f23])).
% 0.61/0.44 thf(f47,definition,(
% 0.61/0.44 spl8_6 <=> ($true = ((cQ @ sK0 @ sK2)))),
% 0.61/0.44 introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition])).
% 0.61/0.44 thf(f49,plain,(
% 0.61/0.44 ($true != ((cQ @ sK0 @ sK2))) | spl8_6),
% 0.61/0.44 inference(avatar_component_clause,[],[f47])).
% 0.61/0.44 thf(f50,plain,(
% 0.61/0.44 ~spl8_1 | spl8_2 | ~spl8_6),
% 0.61/0.44 inference(avatar_split_clause,[],[f16,f47,f27,f23])).
% 0.61/0.44 thf(f51,plain,(
% 0.61/0.44 ~spl8_1 | ~spl8_4 | ~spl8_6),
% 0.61/0.44 inference(avatar_split_clause,[],[f17,f47,f36,f23])).
% 0.61/0.44 thf(f52,plain,(
% 0.61/0.44 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = ((cQ @ X0 @ X1))) | ($false = ((sK6 @ X0 @ X1)))) )),
% 0.61/0.44 inference(constrained_superposition,[],[f20,f11])).
% 0.61/0.44 thf(f55,plain,(
% 0.61/0.44 ( ! [X0 : a,X1 : a] : (($false = ((sK6 @ X0 @ X1))) | ($true = ((cQ @ X0 @ X1)))) )),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f52])).
% 0.61/0.44 thf(f58,plain,(
% 0.61/0.44 ( ! [X0 : a] : (($true = $false) | (((cQ @ X0 @ X0)) = $true)) )),
% 0.61/0.44 inference(constrained_superposition,[],[f11,f55])).
% 0.61/0.44 thf(f62,plain,(
% 0.61/0.44 ( ! [X0 : a] : ((((cQ @ X0 @ X0)) = $true)) )),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f58])).
% 0.61/0.44 thf(f65,plain,(
% 0.61/0.44 ($true != $true) | spl8_1),
% 0.61/0.44 inference(constrained_superposition,[],[f25,f62])).
% 0.61/0.44 thf(f66,plain,(
% 0.61/0.44 $false | spl8_1),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f65])).
% 0.61/0.44 thf(f67,plain,(
% 0.61/0.44 spl8_1),
% 0.61/0.44 inference(avatar_contradiction_clause,[],[f66])).
% 0.61/0.44 thf(f71,plain,(
% 0.61/0.44 ( ! [X2 : a,X0 : a,X1 : a] : (($true != $true) | ($true = ((cQ @ X1 @ X2))) | ($false = ((sK6 @ X0 @ X2))) | ($false = ((sK6 @ X0 @ X1)))) )),
% 0.61/0.44 inference(constrained_superposition,[],[f20,f19])).
% 0.61/0.44 thf(f73,plain,(
% 0.61/0.44 ( ! [X2 : a,X0 : a,X1 : a] : (($true = ((cQ @ X1 @ X2))) | ($false = ((sK6 @ X0 @ X2))) | ($false = ((sK6 @ X0 @ X1)))) )),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f71])).
% 0.61/0.44 thf(f84,plain,(
% 0.61/0.44 ( ! [X0 : a,X1 : a] : (($true != $true) | (((cQ @ X0 @ X1)) = $false) | ($true = ((sK6 @ X0 @ X1)))) )),
% 0.61/0.44 inference(constrained_superposition,[],[f21,f11])).
% 0.61/0.44 thf(f87,plain,(
% 0.61/0.44 ( ! [X2 : a,X0 : a,X1 : a] : (($true != $true) | (((cQ @ X1 @ X2)) = $false) | ($true = ((sK6 @ X0 @ X2))) | ($false = ((sK6 @ X0 @ X1)))) )),
% 0.61/0.44 inference(constrained_superposition,[],[f21,f19])).
% 0.61/0.44 thf(f88,plain,(
% 0.61/0.44 ( ! [X2 : a,X0 : a,X1 : a] : ((((cQ @ X1 @ X2)) = $false) | ($true = ((sK6 @ X0 @ X2))) | ($false = ((sK6 @ X0 @ X1)))) )),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f87])).
% 0.61/0.44 thf(f90,plain,(
% 0.61/0.44 ( ! [X0 : a,X1 : a] : (($true = ((sK6 @ X0 @ X1))) | (((cQ @ X0 @ X1)) = $false)) )),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f84])).
% 0.61/0.44 thf(f164,plain,(
% 0.61/0.44 ( ! [X0 : a,X1 : a] : (($true = $false) | ($true = ((cQ @ X1 @ X0))) | ($false = ((sK6 @ X0 @ X1)))) )),
% 0.61/0.44 inference(constrained_superposition,[],[f11,f73])).
% 0.61/0.44 thf(f195,plain,(
% 0.61/0.44 ( ! [X0 : a,X1 : a] : (($true = ((cQ @ X1 @ X0))) | ($false = ((sK6 @ X0 @ X1)))) )),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f164])).
% 0.61/0.44 thf(f226,plain,(
% 0.61/0.44 ($true != $true) | ($false = ((sK6 @ sK2 @ sK0))) | spl8_6),
% 0.61/0.44 inference(constrained_superposition,[],[f49,f195])).
% 0.61/0.44 thf(f234,plain,(
% 0.61/0.44 ( ! [X0 : a,X1 : a] : (($true = $false) | (((cQ @ X0 @ X1)) = $false) | ($true = ((cQ @ X1 @ X0)))) )),
% 0.61/0.44 inference(constrained_superposition,[],[f90,f195])).
% 0.61/0.44 thf(f235,plain,(
% 0.61/0.44 ( ! [X0 : a,X1 : a] : ((((cQ @ X0 @ X1)) = $false) | ($true = ((cQ @ X1 @ X0)))) )),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f234])).
% 0.61/0.44 thf(f241,plain,(
% 0.61/0.44 ($false = ((sK6 @ sK2 @ sK0))) | spl8_6),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f226])).
% 0.61/0.44 thf(f257,plain,(
% 0.61/0.44 ($true = $false) | ($false = ((cQ @ sK2 @ sK0))) | spl8_6),
% 0.61/0.44 inference(constrained_superposition,[],[f90,f241])).
% 0.61/0.44 thf(f258,plain,(
% 0.61/0.44 ($false = ((cQ @ sK2 @ sK0))) | spl8_6),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f257])).
% 0.61/0.44 thf(f264,plain,(
% 0.61/0.44 ($true = $false) | ($false = ((sK6 @ sK0 @ sK2))) | spl8_6),
% 0.61/0.44 inference(constrained_superposition,[],[f195,f258])).
% 0.61/0.44 thf(f267,plain,(
% 0.61/0.44 ($false = ((sK6 @ sK0 @ sK2))) | spl8_6),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f264])).
% 0.61/0.44 thf(f362,plain,(
% 0.61/0.44 ($true = $false) | ($true = ((cQ @ sK4 @ sK3))) | ~spl8_2),
% 0.61/0.44 inference(constrained_superposition,[],[f29,f235])).
% 0.61/0.44 thf(f373,plain,(
% 0.61/0.44 ($true = ((cQ @ sK4 @ sK3))) | ~spl8_2),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f362])).
% 0.61/0.44 thf(f464,plain,(
% 0.61/0.44 ( ! [X0 : a] : (($true = $false) | ($true = ((sK6 @ X0 @ sK2))) | ($false = ((sK6 @ X0 @ sK1)))) ) | ~spl8_5),
% 0.61/0.44 inference(constrained_superposition,[],[f43,f88])).
% 0.61/0.44 thf(f509,plain,(
% 0.61/0.44 ( ! [X0 : a] : (($true = ((sK6 @ X0 @ sK2))) | ($false = ((sK6 @ X0 @ sK1)))) ) | ~spl8_5),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f464])).
% 0.61/0.44 thf(f732,plain,(
% 0.61/0.44 ($true = $false) | ($false = ((sK6 @ sK0 @ sK1))) | (~spl8_5 | spl8_6)),
% 0.61/0.44 inference(constrained_superposition,[],[f267,f509])).
% 0.61/0.44 thf(f733,plain,(
% 0.61/0.44 ($false = ((sK6 @ sK0 @ sK1))) | (~spl8_5 | spl8_6)),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f732])).
% 0.61/0.44 thf(f755,plain,(
% 0.61/0.44 ($true = $false) | (((cQ @ sK0 @ sK1)) = $false) | (~spl8_5 | spl8_6)),
% 0.61/0.44 inference(constrained_superposition,[],[f90,f733])).
% 0.61/0.44 thf(f756,plain,(
% 0.61/0.44 (((cQ @ sK0 @ sK1)) = $false) | (~spl8_5 | spl8_6)),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f755])).
% 0.61/0.44 thf(f764,plain,(
% 0.61/0.44 ($true = $false) | (~spl8_3 | ~spl8_5 | spl8_6)),
% 0.61/0.44 inference(constrained_superposition,[],[f756,f33])).
% 0.61/0.44 thf(f776,plain,(
% 0.61/0.44 $false | (~spl8_3 | ~spl8_5 | spl8_6)),
% 0.61/0.44 inference(trivial_inequality_removal,[],[f764])).
% 0.61/0.44 thf(f777,plain,(
% 0.61/0.44 ~spl8_3 | ~spl8_5 | spl8_6),
% 0.61/0.44 inference(avatar_contradiction_clause,[],[f776])).
% 0.61/0.44 thf(f781,plain,(
% 0.61/0.44 $false | (~spl8_2 | spl8_4)),
% 0.61/0.44 inference(forward_subsumption_resolution,[],[f38,f373])).
% 0.61/0.44 thf(f782,plain,(
% 0.61/0.44 ~spl8_2 | spl8_4),
% 0.61/0.44 inference(avatar_contradiction_clause,[],[f781])).
% 0.61/0.44 cnf(s1, plain, ~spl8_1 | spl8_2 | spl8_3, inference(sat_conversion,[],[f34])).
% 0.61/0.44 cnf(s2, plain, ~spl8_1 | spl8_3 | ~spl8_4, inference(sat_conversion,[],[f39])).
% 0.61/0.44 cnf(s3, plain, ~spl8_1 | spl8_2 | spl8_5, inference(sat_conversion,[],[f44])).
% 0.61/0.44 cnf(s4, plain, ~spl8_1 | ~spl8_4 | spl8_5, inference(sat_conversion,[],[f45])).
% 0.61/0.44 cnf(s5, plain, ~spl8_1 | spl8_2 | ~spl8_6, inference(sat_conversion,[],[f50])).
% 0.61/0.44 cnf(s6, plain, ~spl8_1 | ~spl8_4 | ~spl8_6, inference(sat_conversion,[],[f51])).
% 0.61/0.44 cnf(s7, plain, spl8_1, inference(sat_conversion,[],[f67])).
% 0.61/0.44 cnf(s9, plain, ~spl8_3 | ~spl8_5 | spl8_6, inference(sat_conversion,[],[f777])).
% 0.61/0.44 cnf(s10, plain, ~spl8_2 | spl8_4, inference(sat_conversion,[],[f782])).
% 0.61/0.44 cnf(s11, plain, ~spl8_4 | ~spl8_6, inference(rat,[],[s6,s7])).
% 0.61/0.44 cnf(s12, plain, spl8_2 | ~spl8_6, inference(rat,[],[s5,s7])).
% 0.61/0.44 cnf(s13, plain, ~spl8_4 | spl8_5, inference(rat,[],[s4,s7])).
% 0.61/0.44 cnf(s14, plain, spl8_2 | spl8_5, inference(rat,[],[s3,s7])).
% 0.61/0.44 cnf(s15, plain, spl8_3 | ~spl8_4, inference(rat,[],[s2,s7])).
% 0.61/0.44 cnf(s16, plain, spl8_2 | spl8_3, inference(rat,[],[s1,s7])).
% 0.61/0.44 cnf(s17, plain, spl8_2, inference(rat,[],[s9,s16,s14,s12])).
% 0.61/0.44 cnf(s18, plain, spl8_4, inference(rat,[],[s10,s17])).
% 0.61/0.44 cnf(s19, plain, ~spl8_6, inference(rat,[],[s11,s18])).
% 0.61/0.44 cnf(s20, plain, spl8_5, inference(rat,[],[s13,s18])).
% 0.61/0.44 cnf(s21, plain, spl8_3, inference(rat,[],[s15,s18])).
% 0.61/0.44 cnf(s22, plain, $false, inference(rat,[],[s9,s19,s20,s21])).
% 0.61/0.44 thf(f783,plain,(
% 0.61/0.44 $false),
% 0.61/0.44 inference(avatar_sat_refutation,[],[s22])).
% 0.61/0.44 % SZS output end Proof for theBenchmark
% 0.61/0.44 % (834110)------------------------------
% 0.61/0.44 % (834110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.44 % (834110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.44 % (834110)CaDiCaL version: 2.1.3
% 0.61/0.44 % (834110)Termination reason: Refutation
% 0.61/0.44 % (834110)Time elapsed: 0.031 s
% 0.61/0.44 % (834110)Peak memory usage: 13 MB
% 0.61/0.44 % (834110)Instructions burned: 53 (million)
% 0.61/0.44 % (834088)Success in time 0.128 s
% 0.61/0.44 % Vampire exiting
%------------------------------------------------------------------------------