%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU898^5 : 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 : n018.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 08:34:22 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU898^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n018.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 14:46:56 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.26 % (178025)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (178031)% WARNING: option uhcvi not known.
% 0.09/0.26 % (178031)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=323464090:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.26 % (178031)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.26 % (178031)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.26 % (178031) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-178025-178031"...
% 0.09/0.26 % (178031)...printing done.
% 0.09/0.26 % (178030)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3414448956_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.26 % (178032)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2252873575:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.26 % (178033)dis+10_1_sil=32000:sp=arity:random_seed=1506912010:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.26 % Exception at run slice level
% 0.09/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.26 % (178032) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-178025-178032"...
% 0.09/0.26 % (178033) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-178025-178033"...
% 0.09/0.26 % (178031)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% 0.09/0.26 thf(type_def_5, type, a: $tType).
% 0.09/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.26 thf(func_def_3, type, sK0: (a > a)).
% 0.09/0.26 thf(func_def_4, type, sK1: (a > $o)).
% 0.09/0.26 thf(func_def_5, type, sK2: (a > a)).
% 0.09/0.26 thf(func_def_6, type, sK3: a).
% 0.09/0.26 thf(f1,conjecture,(
% 0.09/0.26 ! [X0 : (a > a),X1 : (a > $o),X2 : (a > a)] : ((! [X3 : a] : ((X1 @ X3) => (((X0 @ (X2 @ X3))) = ((X2 @ (X0 @ X3))))) & ! [X3 : a] : ((X1 @ X3) => (X1 @ (X0 @ X3))) & ! [X3 : a] : ((X1 @ X3) => (X1 @ (X2 @ X3))) & ! [X3 : a] : ((X1 @ X3) => (X1 @ (X2 @ X3)))) => ! [X3 : a] : ((X1 @ X3) => (((X0 @ (X0 @ (X2 @ X3)))) = ((X2 @ (X0 @ (X0 @ X3)))))))),
% 0.09/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM132_pme)).
% 0.09/0.26 thf(f2,negated_conjecture,(
% 0.09/0.26 ~ ! [X0 : (a > a),X1 : (a > $o),X2 : (a > a)] : ((! [X3 : a] : ((X1 @ X3) => (((X0 @ (X2 @ X3))) = ((X2 @ (X0 @ X3))))) & ! [X3 : a] : ((X1 @ X3) => (X1 @ (X0 @ X3))) & ! [X3 : a] : ((X1 @ X3) => (X1 @ (X2 @ X3))) & ! [X3 : a] : ((X1 @ X3) => (X1 @ (X2 @ X3)))) => ! [X3 : a] : ((X1 @ X3) => (((X0 @ (X0 @ (X2 @ X3)))) = ((X2 @ (X0 @ (X0 @ X3)))))))),
% 0.09/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.26 thf(f3,plain,(
% 0.09/0.26 ~ ! [X0 : (a > a),X1 : (a > $o),X2 : (a > a)] : ((! [X3 : a] : ((X1 @ X3) => (((X0 @ (X2 @ X3))) = ((X2 @ (X0 @ X3))))) & ! [X4 : a] : ((X1 @ X4) => (X1 @ (X0 @ X4))) & ! [X5 : a] : ((X1 @ X5) => (X1 @ (X2 @ X5))) & ! [X6 : a] : ((X1 @ X6) => (X1 @ (X2 @ X6)))) => ! [X7 : a] : ((X1 @ X7) => (((X0 @ (X0 @ (X2 @ X7)))) = ((X2 @ (X0 @ (X0 @ X7)))))))),
% 0.09/0.26 inference(rectify,[],[f2])).
% 0.09/0.26 thf(f4,plain,(
% 0.09/0.26 ~ ! [X0 : (a > a),X1 : (a > $o),X2 : (a > a)] : ((! [X3 : a] : ((((X1 @ X3)) = $true) => (((X0 @ (X2 @ X3))) = ((X2 @ (X0 @ X3))))) & ! [X4 : a] : ((((X1 @ X4)) = $true) => (((X1 @ (X0 @ X4))) = $true)) & ! [X5 : a] : ((((X1 @ X5)) = $true) => (((X1 @ (X2 @ X5))) = $true)) & ! [X6 : a] : ((((X1 @ X6)) = $true) => (((X1 @ (X2 @ X6))) = $true))) => ! [X7 : a] : ((((X1 @ X7)) = $true) => (((X0 @ (X0 @ (X2 @ X7)))) = ((X2 @ (X0 @ (X0 @ X7)))))))),
% 0.09/0.26 inference(fool_elimination,[],[f3])).
% 0.09/0.26 thf(f5,plain,(
% 0.09/0.26 ? [X0 : (a > a),X1 : (a > $o),X2 : (a > a)] : (? [X7 : a] : ((((X0 @ (X0 @ (X2 @ X7)))) != ((X2 @ (X0 @ (X0 @ X7))))) & (((X1 @ X7)) = $true)) & (! [X3 : a] : ((((X0 @ (X2 @ X3))) = ((X2 @ (X0 @ X3)))) | (((X1 @ X3)) != $true)) & ! [X4 : a] : ((((X1 @ (X0 @ X4))) = $true) | (((X1 @ X4)) != $true)) & ! [X5 : a] : ((((X1 @ (X2 @ X5))) = $true) | (((X1 @ X5)) != $true)) & ! [X6 : a] : ((((X1 @ (X2 @ X6))) = $true) | (((X1 @ X6)) != $true))))),
% 0.09/0.26 inference(ennf_transformation,[],[f4])).
% 0.09/0.26 thf(f6,plain,(
% 0.09/0.26 ? [X0 : (a > a),X1 : (a > $o),X2 : (a > a)] : (? [X7 : a] : ((((X0 @ (X0 @ (X2 @ X7)))) != ((X2 @ (X0 @ (X0 @ X7))))) & (((X1 @ X7)) = $true)) & ! [X3 : a] : ((((X0 @ (X2 @ X3))) = ((X2 @ (X0 @ X3)))) | (((X1 @ X3)) != $true)) & ! [X4 : a] : ((((X1 @ (X0 @ X4))) = $true) | (((X1 @ X4)) != $true)) & ! [X5 : a] : ((((X1 @ (X2 @ X5))) = $true) | (((X1 @ X5)) != $true)) & ! [X6 : a] : ((((X1 @ (X2 @ X6))) = $true) | (((X1 @ X6)) != $true)))),
% 0.09/0.26 inference(flattening,[],[f5])).
% 0.09/0.26 thf(f7,plain,(
% 0.09/0.26 ? [X0 : (a > a),X1 : (a > $o),X2 : (a > a)] : (? [X3 : a] : ((((X0 @ (X0 @ (X2 @ X3)))) != ((X2 @ (X0 @ (X0 @ X3))))) & (((X1 @ X3)) = $true)) & ! [X4 : a] : ((((X0 @ (X2 @ X4))) = ((X2 @ (X0 @ X4)))) | (((X1 @ X4)) != $true)) & ! [X5 : a] : (($true = ((X1 @ (X0 @ X5)))) | (((X1 @ X5)) != $true)) & ! [X6 : a] : ((((X1 @ (X2 @ X6))) = $true) | (((X1 @ X6)) != $true)) & ! [X7 : a] : (($true = ((X1 @ (X2 @ X7)))) | (((X1 @ X7)) != $true)))),
% 0.09/0.26 inference(rectify,[],[f6])).
% 0.09/0.26 thf(f8,plain,(
% 0.09/0.26 ((((sK0 @ (sK0 @ (sK2 @ sK3)))) != ((sK2 @ (sK0 @ (sK0 @ sK3))))) & ($true = ((sK1 @ sK3)))) & ! [X4 : a] : ((((sK0 @ (sK2 @ X4))) = ((sK2 @ (sK0 @ X4)))) | ($true != ((sK1 @ X4)))) & ! [X5 : a] : (($true = ((sK1 @ (sK0 @ X5)))) | ($true != ((sK1 @ X5)))) & ! [X6 : a] : (($true = ((sK1 @ (sK2 @ X6)))) | ($true != ((sK1 @ X6)))) & ! [X7 : a] : (($true = ((sK1 @ (sK2 @ X7)))) | ($true != ((sK1 @ X7))))),
% 0.09/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f7])).
% 0.09/0.26 thf(f11,plain,(
% 0.09/0.26 ( ! [X5 : a] : (($true != ((sK1 @ X5))) | ($true = ((sK1 @ (sK0 @ X5))))) )),
% 0.09/0.26 inference(cnf_transformation,[],[f8])).
% 0.09/0.26 thf(f12,plain,(
% 0.09/0.26 ( ! [X4 : a] : (($true != ((sK1 @ X4))) | (((sK0 @ (sK2 @ X4))) = ((sK2 @ (sK0 @ X4))))) )),
% 0.09/0.26 inference(cnf_transformation,[],[f8])).
% 0.09/0.26 thf(f13,plain,(
% 0.09/0.26 ($true = ((sK1 @ sK3)))),
% 0.09/0.26 inference(cnf_transformation,[],[f8])).
% 0.09/0.26 thf(f14,plain,(
% 0.09/0.26 (((sK0 @ (sK0 @ (sK2 @ sK3)))) != ((sK2 @ (sK0 @ (sK0 @ sK3)))))),
% 0.09/0.26 inference(cnf_transformation,[],[f8])).
% 0.09/0.26 thf(f16,definition,(
% 0.09/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.09/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.09/0.26 thf(f19,plain,(
% 0.09/0.26 ($true != $true) | ($true = ((sK1 @ (sK0 @ sK3))))),
% 0.09/0.26 inference(constrained_superposition,[],[f11,f13])).
% 0.09/0.26 thf(f20,plain,(
% 0.09/0.26 ($true = ((sK1 @ (sK0 @ sK3))))),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f19])).
% 0.09/0.26 thf(f21,plain,(
% 0.09/0.26 ($true != $true) | (((sK0 @ (sK2 @ sK3))) = ((sK2 @ (sK0 @ sK3))))),
% 0.09/0.26 inference(constrained_superposition,[],[f12,f13])).
% 0.09/0.26 thf(f22,plain,(
% 0.09/0.26 (((sK0 @ (sK2 @ sK3))) = ((sK2 @ (sK0 @ sK3))))),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f21])).
% 0.09/0.26 thf(f31,plain,(
% 0.09/0.26 ( ! [X0 : a] : (($true != $true) | (((sK0 @ (sK2 @ X0))) = ((sK2 @ (sK0 @ X0)))) | ($false = ((sK1 @ X0)))) )),
% 0.09/0.26 inference(constrained_superposition,[],[f12,f16])).
% 0.09/0.26 thf(f37,plain,(
% 0.09/0.26 ( ! [X0 : a] : ((((sK0 @ (sK2 @ X0))) = ((sK2 @ (sK0 @ X0)))) | ($false = ((sK1 @ X0)))) )),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f31])).
% 0.09/0.26 thf(f92,plain,(
% 0.09/0.26 (((sK0 @ (sK0 @ (sK2 @ sK3)))) != ((sK0 @ (sK2 @ (sK0 @ sK3))))) | ($false = ((sK1 @ (sK0 @ sK3))))),
% 0.09/0.26 inference(constrained_superposition,[],[f14,f37])).
% 0.09/0.26 thf(f95,plain,(
% 0.09/0.26 (((sK0 @ (sK0 @ (sK2 @ sK3)))) != ((sK0 @ (sK0 @ (sK2 @ sK3))))) | ($false = ((sK1 @ (sK0 @ sK3))))),
% 0.09/0.26 inference(forward_demodulation,[],[f92,f22])).
% 0.09/0.26 thf(f96,plain,(
% 0.09/0.26 ($false = ((sK1 @ (sK0 @ sK3))))),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f95])).
% 0.09/0.26 thf(f103,plain,(
% 0.09/0.26 ($true = $false)),
% 0.09/0.26 inference(constrained_superposition,[],[f20,f96])).
% 0.09/0.26 thf(f106,plain,(
% 0.09/0.26 $false),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f103])).
% 0.09/0.26 % SZS output end Proof for theBenchmark
% 0.09/0.26 % (178031)------------------------------
% 0.09/0.26 % (178031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (178031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (178031)CaDiCaL version: 2.1.3
% 0.09/0.26 % (178031)Termination reason: Refutation
% 0.09/0.26 % (178031)Time elapsed: 0.003 s
% 0.09/0.26 % (178031)Peak memory usage: 12 MB
% 0.09/0.26 % (178031)Instructions burned: 9 (million)
% 0.09/0.26 % (178025)Success in time 0.037 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------