%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN382^5 : 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 : 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 08:41:52 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN382^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n015.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:18:48 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.08/0.26 % (3723807)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (3723817)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1727764756:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.26 % (3723817) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3723807-3723817"...
% 0.08/0.26 % (3723817)...printing done.
% 0.08/0.26 % (3723817)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% 0.08/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.26 thf(func_def_0, type, cQ: ($i > $i > $o)).
% 0.08/0.26 thf(func_def_1, type, cP: ($i > $i > $o)).
% 0.08/0.26 thf(func_def_6, type, sK1: ($i > $i)).
% 0.08/0.26 thf(f1,conjecture,(
% 0.08/0.26 ! [X0 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X0) | ! [X2 : $i] : (cP @ X1 @ X2)) => ! [X2 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X2) | (cP @ X1 @ X2))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2134)).
% 0.08/0.26 thf(f2,negated_conjecture,(
% 0.08/0.26 ~(! [X0 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X0) | ! [X2 : $i] : (cP @ X1 @ X2)) => ! [X2 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X2) | (cP @ X1 @ X2)))),
% 0.08/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.08/0.26 thf(f3,plain,(
% 0.08/0.26 ~(! [X0 : $i] : ? [X1 : $i] : ((cQ @ X1 @ X0) | ! [X2 : $i] : (cP @ X1 @ X2)) => ! [X3 : $i] : ? [X4 : $i] : ((cQ @ X4 @ X3) | (cP @ X4 @ X3)))),
% 0.08/0.26 inference(rectify,[],[f2])).
% 0.08/0.26 thf(f4,plain,(
% 0.08/0.26 ~(! [X0 : $i] : ? [X1 : $i] : ((((cQ @ X1 @ X0)) = $true) | ! [X2 : $i] : (((cP @ X1 @ X2)) = $true)) => ! [X3 : $i] : ? [X4 : $i] : ((((cQ @ X4 @ X3)) = $true) | (((cP @ X4 @ X3)) = $true)))),
% 0.08/0.26 inference(fool_elimination,[],[f3])).
% 0.08/0.26 thf(f5,plain,(
% 0.08/0.26 ? [X3 : $i] : ! [X4 : $i] : ((((cQ @ X4 @ X3)) != $true) & (((cP @ X4 @ X3)) != $true)) & ! [X0 : $i] : ? [X1 : $i] : ((((cQ @ X1 @ X0)) = $true) | ! [X2 : $i] : (((cP @ X1 @ X2)) = $true))),
% 0.08/0.26 inference(ennf_transformation,[],[f4])).
% 0.08/0.26 thf(f6,plain,(
% 0.08/0.26 ? [X0 : $i] : ! [X1 : $i] : ((((cQ @ X1 @ X0)) != $true) & ($true != ((cP @ X1 @ X0)))) & ! [X2 : $i] : ? [X3 : $i] : (($true = ((cQ @ X3 @ X2))) | ! [X4 : $i] : ($true = ((cP @ X3 @ X4))))),
% 0.08/0.26 inference(rectify,[],[f5])).
% 0.08/0.26 thf(f7,plain,(
% 0.08/0.26 ! [X1 : $i] : (($true != ((cQ @ X1 @ sK0))) & ($true != ((cP @ X1 @ sK0)))) & ! [X2 : $i] : (($true = ((cQ @ (sK1 @ X2) @ X2))) | ! [X4 : $i] : ($true = ((cP @ (sK1 @ X2) @ X4))))),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X0,sK0),skolemize(X3,sK1 @ X2)],[f6])).
% 0.08/0.26 thf(f8,plain,(
% 0.08/0.26 ( ! [X2 : $i,X4 : $i] : (($true = ((cP @ (sK1 @ X2) @ X4))) | ($true = ((cQ @ (sK1 @ X2) @ X2)))) )),
% 0.08/0.26 inference(cnf_transformation,[],[f7])).
% 0.08/0.26 thf(f9,plain,(
% 0.08/0.26 ( ! [X1 : $i] : (($true != ((cP @ X1 @ sK0)))) )),
% 0.08/0.26 inference(cnf_transformation,[],[f7])).
% 0.08/0.26 thf(f10,plain,(
% 0.08/0.26 ( ! [X1 : $i] : (($true != ((cQ @ X1 @ sK0)))) )),
% 0.08/0.26 inference(cnf_transformation,[],[f7])).
% 0.08/0.26 thf(f13,plain,(
% 0.08/0.26 ( ! [X0 : $i] : (($true != $true) | ($true = ((cQ @ (sK1 @ X0) @ X0)))) )),
% 0.08/0.26 inference(constrained_superposition,[],[f9,f8])).
% 0.08/0.26 thf(f14,plain,(
% 0.08/0.26 ( ! [X0 : $i] : (($true = ((cQ @ (sK1 @ X0) @ X0)))) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f13])).
% 0.08/0.26 thf(f15,plain,(
% 0.08/0.26 ($true != $true)),
% 0.08/0.26 inference(constrained_superposition,[],[f10,f14])).
% 0.08/0.26 thf(f16,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f15])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (3723817)------------------------------
% 0.08/0.26 % (3723817)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (3723817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (3723817)CaDiCaL version: 2.1.3
% 0.08/0.26 % (3723817)Termination reason: Refutation
% 0.08/0.26 % (3723817)Time elapsed: 0.001 s
% 0.08/0.26 % (3723817)Peak memory usage: 12 MB
% 0.08/0.26 % (3723817)Instructions burned: 1 (million)
% 0.08/0.26 % (3723807)Success in time 0.028 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------