%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN732^5 : 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 : n004.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 08:42:04 AM UTC 2026
% Result : Theorem 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN732^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n004.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
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:19:11 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
% 0.18/0.26 % (1497403)Will run a generic schedule for satisfiability detection.
% 0.18/0.26 % (1497412)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=308490608:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.26 % (1497412)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.26 % (1497412) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1497403-1497412"...
% 0.18/0.26 % (1497412)...printing done.
% 0.18/0.26 % (1497412)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Theorem for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% 0.18/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.18/0.26 thf(func_def_0, type, cQ: ($i > $i > $o)).
% 0.18/0.26 thf(func_def_1, type, cP: ($i > $i > $o)).
% 0.18/0.26 thf(func_def_5, type, sK0: ($i > $i)).
% 0.18/0.26 thf(func_def_6, type, sK1: ($i > $i)).
% 0.18/0.26 thf(f1,conjecture,(
% 0.18/0.26 ! [X0 : $i] : (! [X1 : $i] : (cP @ X1 @ X0) => ! [X2 : $i] : (cQ @ X2 @ X0)) => ? [X3 : $i] : (? [X4 : $i] : (cP @ X4 @ X3) => ? [X5 : $i] : ((cQ @ X5 @ X3) | (cP @ X3 @ X5)))),
% 0.18/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX3411)).
% 0.18/0.26 thf(f2,negated_conjecture,(
% 0.18/0.26 ~(! [X0 : $i] : (! [X1 : $i] : (cP @ X1 @ X0) => ! [X2 : $i] : (cQ @ X2 @ X0)) => ? [X3 : $i] : (? [X4 : $i] : (cP @ X4 @ X3) => ? [X5 : $i] : ((cQ @ X5 @ X3) | (cP @ X3 @ X5))))),
% 0.18/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.18/0.26 thf(f3,plain,(
% 0.18/0.26 ~(! [X0 : $i] : (! [X1 : $i] : (cP @ X1 @ X0) => ! [X2 : $i] : (cQ @ X2 @ X0)) => ? [X3 : $i] : (? [X4 : $i] : (cP @ X4 @ X3) => ? [X5 : $i] : ((cQ @ X5 @ X3) | (cP @ X3 @ X5))))),
% 0.18/0.26 inference(rectify,[],[f2])).
% 0.18/0.26 thf(f4,plain,(
% 0.18/0.26 ~(! [X0 : $i] : (! [X1 : $i] : (((cP @ X1 @ X0)) = $true) => ! [X2 : $i] : (((cQ @ X2 @ X0)) = $true)) => ? [X3 : $i] : (? [X4 : $i] : (((cP @ X4 @ X3)) = $true) => ? [X5 : $i] : ((((cQ @ X5 @ X3)) = $true) | (((cP @ X3 @ X5)) = $true))))),
% 0.18/0.26 inference(fool_elimination,[],[f3])).
% 0.18/0.26 thf(f5,plain,(
% 0.18/0.26 ! [X3 : $i] : (! [X5 : $i] : ((((cQ @ X5 @ X3)) != $true) & (((cP @ X3 @ X5)) != $true)) & ? [X4 : $i] : (((cP @ X4 @ X3)) = $true)) & ! [X0 : $i] : (! [X2 : $i] : (((cQ @ X2 @ X0)) = $true) | ? [X1 : $i] : (((cP @ X1 @ X0)) != $true))),
% 0.18/0.26 inference(ennf_transformation,[],[f4])).
% 0.18/0.26 thf(f6,plain,(
% 0.18/0.26 ! [X0 : $i] : (! [X1 : $i] : (($true != ((cQ @ X1 @ X0))) & ($true != ((cP @ X0 @ X1)))) & ? [X2 : $i] : ($true = ((cP @ X2 @ X0)))) & ! [X3 : $i] : (! [X4 : $i] : ($true = ((cQ @ X4 @ X3))) | ? [X5 : $i] : ($true != ((cP @ X5 @ X3))))),
% 0.18/0.26 inference(rectify,[],[f5])).
% 0.18/0.26 thf(f7,plain,(
% 0.18/0.26 ! [X0 : $i] : (! [X1 : $i] : (($true != ((cQ @ X1 @ X0))) & ($true != ((cP @ X0 @ X1)))) & ($true = ((cP @ (sK0 @ X0) @ X0)))) & ! [X3 : $i] : (! [X4 : $i] : ($true = ((cQ @ X4 @ X3))) | ($true != ((cP @ (sK1 @ X3) @ X3))))),
% 0.18/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X5,sK1 @ X3),skolemize(X5,sK1 @ X3)],[f6])).
% 0.18/0.26 thf(f9,plain,(
% 0.18/0.26 ( ! [X0 : $i] : (($true = ((cP @ (sK0 @ X0) @ X0)))) )),
% 0.18/0.26 inference(cnf_transformation,[],[f7])).
% 0.18/0.26 thf(f10,plain,(
% 0.18/0.26 ( ! [X0 : $i,X1 : $i] : (($true != ((cP @ X0 @ X1)))) )),
% 0.18/0.26 inference(cnf_transformation,[],[f7])).
% 0.18/0.26 thf(f14,plain,(
% 0.18/0.26 ($true != $true)),
% 0.18/0.26 inference(constrained_superposition,[],[f10,f9])).
% 0.18/0.26 thf(f15,plain,(
% 0.18/0.26 $false),
% 0.18/0.26 inference(trivial_inequality_removal,[],[f14])).
% 0.18/0.26 % SZS output end Proof for theBenchmark
% 0.18/0.26 % (1497412)------------------------------
% 0.18/0.26 % (1497412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.26 % (1497412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.26 % (1497412)CaDiCaL version: 2.1.3
% 0.18/0.26 % (1497412)Termination reason: Refutation
% 0.18/0.26 % (1497412)Time elapsed: 0.001 s
% 0.18/0.26 % (1497412)Peak memory usage: 12 MB
% 0.18/0.26 % (1497412)Instructions burned: 1 (million)
% 0.18/0.26 % (1497403)Success in time 0.027 s
% 0.18/0.26 % Vampire exiting
%------------------------------------------------------------------------------