%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN361^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 08:41:40 AM UTC 2026
% Result : Theorem 0.07s 0.25s
% Output : Refutation 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN361^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n018.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:17:27 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.25 % (283285)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.25 % (283294)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=352128544:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.07/0.25 % (283294) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-283285-283294"...
% 0.07/0.25 % (283294)...printing done.
% 0.07/0.25 % (283294)Refutation found. Thanks to Tanya!
% 0.07/0.25 % SZS status Theorem for theBenchmark
% 0.07/0.25 % SZS output start Proof for theBenchmark
% 0.07/0.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.07/0.25 thf(func_def_0, type, cS: ($i > $o)).
% 0.07/0.25 thf(func_def_1, type, cQ: ($i > $i > $o)).
% 0.07/0.25 thf(func_def_2, type, cP: ($i > $i > $o)).
% 0.07/0.25 thf(func_def_6, type, sK0: ($i > $i)).
% 0.07/0.25 thf(f1,conjecture,(
% 0.07/0.25 (! [X1 : $i,X2 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2)) & ! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0)) => ? [X3 : $i] : ~(cS @ X3)),
% 0.07/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2112)).
% 0.07/0.25 thf(f2,negated_conjecture,(
% 0.07/0.25 ~((! [X1 : $i,X2 : $i] : ((cP @ X1 @ X2) => ~(cQ @ X1 @ X2)) & ! [X1 : $i] : ((cS @ X1) => ? [X2 : $i] : (cQ @ X2 @ X1)) & ? [X0 : $i] : ! [X1 : $i] : (cP @ X1 @ X0)) => ? [X3 : $i] : ~(cS @ X3))),
% 0.07/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.07/0.25 thf(f3,plain,(
% 0.07/0.25 ~((! [X0 : $i,X1 : $i] : ((cP @ X0 @ X1) => ~(cQ @ X0 @ X1)) & ! [X2 : $i] : ((cS @ X2) => ? [X3 : $i] : (cQ @ X3 @ X2)) & ? [X4 : $i] : ! [X5 : $i] : (cP @ X5 @ X4)) => ? [X6 : $i] : ~(cS @ X6))),
% 0.07/0.25 inference(rectify,[],[f2])).
% 0.07/0.25 thf(f4,plain,(
% 0.07/0.25 ~((! [X0 : $i,X1 : $i] : ((((cP @ X0 @ X1)) = $true) => ~ ($true = ((cQ @ X0 @ X1)))) & ! [X2 : $i] : (($true = ((cS @ X2))) => ? [X3 : $i] : (((cQ @ X3 @ X2)) = $true)) & ? [X4 : $i] : ! [X5 : $i] : ($true = ((cP @ X5 @ X4)))) => ? [X6 : $i] : ~ ($true = ((cS @ X6))))),
% 0.07/0.25 inference(fool_elimination,[],[f3])).
% 0.07/0.25 thf(f5,plain,(
% 0.07/0.25 ~((! [X2 : $i] : (($true = ((cS @ X2))) => ? [X3 : $i] : (((cQ @ X3 @ X2)) = $true)) & ? [X4 : $i] : ! [X5 : $i] : ($true = ((cP @ X5 @ X4))) & ! [X0 : $i,X1 : $i] : ((((cP @ X0 @ X1)) = $true) => ($true != ((cQ @ X0 @ X1))))) => ? [X6 : $i] : ($true != ((cS @ X6))))),
% 0.07/0.25 inference(flattening,[],[f4])).
% 0.07/0.25 thf(f6,plain,(
% 0.07/0.25 ! [X6 : $i] : ($true = ((cS @ X6))) & (! [X2 : $i] : (? [X3 : $i] : (((cQ @ X3 @ X2)) = $true) | ($true != ((cS @ X2)))) & ? [X4 : $i] : ! [X5 : $i] : ($true = ((cP @ X5 @ X4))) & ! [X1 : $i,X0 : $i] : ((((cP @ X0 @ X1)) != $true) | ($true != ((cQ @ X0 @ X1)))))),
% 0.07/0.25 inference(ennf_transformation,[],[f5])).
% 0.07/0.25 thf(f7,plain,(
% 0.07/0.25 ! [X1 : $i,X0 : $i] : ((((cP @ X0 @ X1)) != $true) | ($true != ((cQ @ X0 @ X1)))) & ! [X6 : $i] : ($true = ((cS @ X6))) & ! [X2 : $i] : (? [X3 : $i] : (((cQ @ X3 @ X2)) = $true) | ($true != ((cS @ X2)))) & ? [X4 : $i] : ! [X5 : $i] : ($true = ((cP @ X5 @ X4)))),
% 0.07/0.25 inference(flattening,[],[f6])).
% 0.07/0.25 thf(f8,plain,(
% 0.07/0.25 ! [X0 : $i,X1 : $i] : ((((cP @ X1 @ X0)) != $true) | ($true != ((cQ @ X1 @ X0)))) & ! [X2 : $i] : ($true = ((cS @ X2))) & ! [X3 : $i] : (? [X4 : $i] : (((cQ @ X4 @ X3)) = $true) | (((cS @ X3)) != $true)) & ? [X5 : $i] : ! [X6 : $i] : ($true = ((cP @ X6 @ X5)))),
% 0.07/0.25 inference(rectify,[],[f7])).
% 0.07/0.25 thf(f9,plain,(
% 0.07/0.25 ! [X0 : $i,X1 : $i] : ((((cP @ X1 @ X0)) != $true) | ($true != ((cQ @ X1 @ X0)))) & ! [X2 : $i] : ($true = ((cS @ X2))) & ! [X3 : $i] : ((((cQ @ (sK0 @ X3) @ X3)) = $true) | (((cS @ X3)) != $true)) & ! [X6 : $i] : ($true = ((cP @ X6 @ sK1)))),
% 0.07/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1]),skolemize(X4,sK0 @ X3),skolemize(X5,sK1)],[f8])).
% 0.07/0.25 thf(f10,plain,(
% 0.07/0.25 ( ! [X6 : $i] : (($true = ((cP @ X6 @ sK1)))) )),
% 0.07/0.25 inference(cnf_transformation,[],[f9])).
% 0.07/0.25 thf(f11,plain,(
% 0.07/0.25 ( ! [X3 : $i] : ((((cQ @ (sK0 @ X3) @ X3)) = $true) | (((cS @ X3)) != $true)) )),
% 0.07/0.25 inference(cnf_transformation,[],[f9])).
% 0.07/0.25 thf(f12,plain,(
% 0.07/0.25 ( ! [X2 : $i] : (($true = ((cS @ X2)))) )),
% 0.07/0.25 inference(cnf_transformation,[],[f9])).
% 0.07/0.25 thf(f13,plain,(
% 0.07/0.25 ( ! [X0 : $i,X1 : $i] : (($true != ((cQ @ X1 @ X0))) | (((cP @ X1 @ X0)) != $true)) )),
% 0.07/0.25 inference(cnf_transformation,[],[f9])).
% 0.07/0.25 thf(f15,plain,(
% 0.07/0.25 ( ! [X3 : $i] : ((((cQ @ (sK0 @ X3) @ X3)) = $true)) )),
% 0.07/0.25 inference(forward_subsumption_resolution,[],[f11,f12])).
% 0.07/0.25 thf(f16,plain,(
% 0.07/0.25 ( ! [X0 : $i] : (($true != $true) | ($true != ((cP @ (sK0 @ X0) @ X0)))) )),
% 0.07/0.25 inference(superposition,[],[f13,f15])).
% 0.07/0.25 thf(f17,plain,(
% 0.07/0.25 ( ! [X0 : $i] : (($true != ((cP @ (sK0 @ X0) @ X0)))) )),
% 0.07/0.25 inference(trivial_inequality_removal,[],[f16])).
% 0.07/0.25 thf(f18,plain,(
% 0.07/0.25 ($true != $true)),
% 0.07/0.25 inference(superposition,[],[f17,f10])).
% 0.07/0.25 thf(f19,plain,(
% 0.07/0.25 $false),
% 0.07/0.25 inference(trivial_inequality_removal,[],[f18])).
% 0.07/0.25 % SZS output end Proof for theBenchmark
% 0.07/0.25 % (283294)------------------------------
% 0.07/0.25 % (283294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.25 % (283294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.25 % (283294)CaDiCaL version: 2.1.3
% 0.07/0.25 % (283294)Termination reason: Refutation
% 0.07/0.25 % (283294)Time elapsed: 0.001 s
% 0.07/0.25 % (283294)Peak memory usage: 12 MB
% 0.07/0.25 % (283294)Instructions burned: 2 (million)
% 0.07/0.25 % (283285)Success in time 0.016 s
% 0.07/0.25 % Vampire exiting
%------------------------------------------------------------------------------