%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN381^5 : 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 : 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 08:41:52 AM UTC 2026
% Result : Theorem 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN381^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:16:09 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.26 % (3356115)Will run a generic schedule for satisfiability detection.
% 0.20/0.26 % (3356126)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2260776775:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.26 % (3356126) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3356115-3356126"...
% 0.20/0.26 % (3356126)...printing done.
% 0.20/0.26 % (3356121)% WARNING: option uhcvi not known.
% 0.20/0.26 % (3356126)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% 0.20/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.26 thf(func_def_0, type, cP: ($i > $o)).
% 0.20/0.26 thf(func_def_1, type, cQ: ($i > $i > $o)).
% 0.20/0.26 thf(func_def_6, type, sK1: ($i > $i)).
% 0.20/0.26 thf(f1,conjecture,(
% 0.20/0.26 (! [X4 : $i,X5 : $i] : ((cQ @ X4 @ X5) => ((cQ @ X5 @ X5) | (cQ @ X5 @ X4))) & ! [X2 : $i] : ? [X3 : $i] : (cQ @ X3 @ X2) & ! [X0 : $i] : (? [X1 : $i] : (cQ @ X0 @ X1) => (cP @ X0))) => ! [X5 : $i] : (cP @ X5)),
% 0.20/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2133)).
% 0.20/0.26 thf(f2,negated_conjecture,(
% 0.20/0.26 ~((! [X4 : $i,X5 : $i] : ((cQ @ X4 @ X5) => ((cQ @ X5 @ X5) | (cQ @ X5 @ X4))) & ! [X2 : $i] : ? [X3 : $i] : (cQ @ X3 @ X2) & ! [X0 : $i] : (? [X1 : $i] : (cQ @ X0 @ X1) => (cP @ X0))) => ! [X5 : $i] : (cP @ X5))),
% 0.20/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.20/0.26 thf(f3,plain,(
% 0.20/0.26 ~((! [X0 : $i,X1 : $i] : ((cQ @ X0 @ X1) => ((cQ @ X1 @ X1) | (cQ @ X1 @ X0))) & ! [X2 : $i] : ? [X3 : $i] : (cQ @ X3 @ X2) & ! [X4 : $i] : (? [X5 : $i] : (cQ @ X4 @ X5) => (cP @ X4))) => ! [X6 : $i] : (cP @ X6))),
% 0.20/0.26 inference(rectify,[],[f2])).
% 0.20/0.26 thf(f4,plain,(
% 0.20/0.26 ~((! [X0 : $i,X1 : $i] : ((((cQ @ X0 @ X1)) = $true) => ((((cQ @ X1 @ X1)) = $true) | (((cQ @ X1 @ X0)) = $true))) & ! [X2 : $i] : ? [X3 : $i] : (((cQ @ X3 @ X2)) = $true) & ! [X4 : $i] : (? [X5 : $i] : (((cQ @ X4 @ X5)) = $true) => (((cP @ X4)) = $true))) => ! [X6 : $i] : (((cP @ X6)) = $true))),
% 0.20/0.26 inference(fool_elimination,[],[f3])).
% 0.20/0.26 thf(f5,plain,(
% 0.20/0.26 ? [X6 : $i] : (((cP @ X6)) != $true) & (! [X0 : $i,X1 : $i] : (((((cQ @ X1 @ X1)) = $true) | (((cQ @ X1 @ X0)) = $true)) | (((cQ @ X0 @ X1)) != $true)) & ! [X2 : $i] : ? [X3 : $i] : (((cQ @ X3 @ X2)) = $true) & ! [X4 : $i] : ((((cP @ X4)) = $true) | ! [X5 : $i] : (((cQ @ X4 @ X5)) != $true)))),
% 0.20/0.26 inference(ennf_transformation,[],[f4])).
% 0.20/0.26 thf(f6,plain,(
% 0.20/0.26 ? [X6 : $i] : (((cP @ X6)) != $true) & ! [X0 : $i,X1 : $i] : ((((cQ @ X1 @ X1)) = $true) | (((cQ @ X1 @ X0)) = $true) | (((cQ @ X0 @ X1)) != $true)) & ! [X2 : $i] : ? [X3 : $i] : (((cQ @ X3 @ X2)) = $true) & ! [X4 : $i] : ((((cP @ X4)) = $true) | ! [X5 : $i] : (((cQ @ X4 @ X5)) != $true))),
% 0.20/0.26 inference(flattening,[],[f5])).
% 0.20/0.26 thf(f7,plain,(
% 0.20/0.26 ? [X0 : $i] : (((cP @ X0)) != $true) & ! [X1 : $i,X2 : $i] : (($true = ((cQ @ X2 @ X2))) | ($true = ((cQ @ X2 @ X1))) | ($true != ((cQ @ X1 @ X2)))) & ! [X3 : $i] : ? [X4 : $i] : ($true = ((cQ @ X4 @ X3))) & ! [X5 : $i] : ((((cP @ X5)) = $true) | ! [X6 : $i] : ($true != ((cQ @ X5 @ X6))))),
% 0.20/0.26 inference(rectify,[],[f6])).
% 0.20/0.26 thf(f8,plain,(
% 0.20/0.26 ($true != ((cP @ sK0))) & ! [X1 : $i,X2 : $i] : (($true = ((cQ @ X2 @ X2))) | ($true = ((cQ @ X2 @ X1))) | ($true != ((cQ @ X1 @ X2)))) & ! [X3 : $i] : ($true = ((cQ @ (sK1 @ X3) @ X3))) & ! [X5 : $i] : ((((cP @ X5)) = $true) | ! [X6 : $i] : ($true != ((cQ @ X5 @ X6))))),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X4,sK1 @ X3)],[f7])).
% 0.20/0.26 thf(f9,plain,(
% 0.20/0.26 ( ! [X6 : $i,X5 : $i] : (($true != ((cQ @ X5 @ X6))) | (((cP @ X5)) = $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f8])).
% 0.20/0.26 thf(f10,plain,(
% 0.20/0.26 ( ! [X3 : $i] : (($true = ((cQ @ (sK1 @ X3) @ X3)))) )),
% 0.20/0.26 inference(cnf_transformation,[],[f8])).
% 0.20/0.26 thf(f11,plain,(
% 0.20/0.26 ( ! [X2 : $i,X1 : $i] : (($true != ((cQ @ X1 @ X2))) | ($true = ((cQ @ X2 @ X1))) | ($true = ((cQ @ X2 @ X2)))) )),
% 0.20/0.26 inference(cnf_transformation,[],[f8])).
% 0.20/0.26 thf(f12,plain,(
% 0.20/0.26 ($true != ((cP @ sK0)))),
% 0.20/0.26 inference(cnf_transformation,[],[f8])).
% 0.20/0.26 thf(f17,plain,(
% 0.20/0.26 ( ! [X0 : $i] : (($true != $true) | ($true = ((cQ @ X0 @ (sK1 @ X0)))) | ($true = ((cQ @ X0 @ X0)))) )),
% 0.20/0.26 inference(constrained_superposition,[],[f11,f10])).
% 0.20/0.26 thf(f18,plain,(
% 0.20/0.26 ( ! [X0 : $i] : (($true = ((cQ @ X0 @ (sK1 @ X0)))) | ($true = ((cQ @ X0 @ X0)))) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f17])).
% 0.20/0.27 thf(f20,plain,(
% 0.20/0.27 ( ! [X0 : $i] : (($true != $true) | (((cP @ X0)) = $true) | ($true = ((cQ @ X0 @ X0)))) )),
% 0.20/0.27 inference(constrained_superposition,[],[f9,f18])).
% 0.20/0.27 thf(f21,plain,(
% 0.20/0.27 ( ! [X0 : $i] : (($true = ((cQ @ X0 @ X0))) | (((cP @ X0)) = $true)) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f20])).
% 0.20/0.27 thf(f23,plain,(
% 0.20/0.27 ( ! [X0 : $i] : (($true != $true) | (((cP @ X0)) = $true) | (((cP @ X0)) = $true)) )),
% 0.20/0.27 inference(constrained_superposition,[],[f9,f21])).
% 0.20/0.27 thf(f24,plain,(
% 0.20/0.27 ( ! [X0 : $i] : (($true != $true) | (((cP @ X0)) = $true)) )),
% 0.20/0.27 inference(duplicate_literal_removal,[],[f23])).
% 0.20/0.27 thf(f25,plain,(
% 0.20/0.27 ( ! [X0 : $i] : ((((cP @ X0)) = $true)) )),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f24])).
% 0.20/0.27 thf(f26,plain,(
% 0.20/0.27 ($true != $true)),
% 0.20/0.27 inference(constrained_superposition,[],[f12,f25])).
% 0.20/0.27 thf(f27,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f26])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (3356126)------------------------------
% 0.20/0.27 % (3356126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (3356126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (3356126)CaDiCaL version: 2.1.3
% 0.20/0.27 % (3356126)Termination reason: Refutation
% 0.20/0.27 % (3356126)Time elapsed: 0.002 s
% 0.20/0.27 % (3356126)Peak memory usage: 12 MB
% 0.20/0.27 % (3356126)Instructions burned: 3 (million)
% 0.20/0.27 % (3356115)Success in time 0.029 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------