%------------------------------------------------------------------------------
% File : Vampire---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 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 08:41:41 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% 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 THM
% 0.09/0.18 % Computer : n018.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:17:42 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.09/0.25 % (284140)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.25 % (284155)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1835506583:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.25 % (284155) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-284140-284155"...
% 0.09/0.25 % (284155)...printing done.
% 0.09/0.25 % (284155)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% 0.09/0.25 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.25 thf(func_def_0, type, cP: ($i > $o)).
% 0.09/0.25 thf(func_def_1, type, cQ: ($i > $i > $o)).
% 0.09/0.25 thf(func_def_5, type, sK0: ($i > $i)).
% 0.09/0.25 thf(f1,conjecture,(
% 0.09/0.25 (! [X5 : $i,X4 : $i] : ((cQ @ X4 @ X5) => ((cQ @ X5 @ X4) | (cQ @ X5 @ X5))) & ! [X2 : $i] : ? [X3 : $i] : (cQ @ X3 @ X2) & ! [X0 : $i] : (? [X1 : $i] : (cQ @ X0 @ X1) => (cP @ X0))) => ! [X5 : $i] : (cP @ X5)),
% 0.09/0.25 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cX2133)).
% 0.09/0.25 thf(f2,negated_conjecture,(
% 0.09/0.25 ~((! [X5 : $i,X4 : $i] : ((cQ @ X4 @ X5) => ((cQ @ X5 @ X4) | (cQ @ X5 @ X5))) & ! [X2 : $i] : ? [X3 : $i] : (cQ @ X3 @ X2) & ! [X0 : $i] : (? [X1 : $i] : (cQ @ X0 @ X1) => (cP @ X0))) => ! [X5 : $i] : (cP @ X5))),
% 0.09/0.25 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.25 thf(f3,plain,(
% 0.09/0.25 ~((! [X0 : $i,X1 : $i] : ((cQ @ X1 @ X0) => ((cQ @ X0 @ X1) | (cQ @ X0 @ X0))) & ! [X2 : $i] : ? [X3 : $i] : (cQ @ X3 @ X2) & ! [X4 : $i] : (? [X5 : $i] : (cQ @ X4 @ X5) => (cP @ X4))) => ! [X6 : $i] : (cP @ X6))),
% 0.09/0.25 inference(rectify,[],[f2])).
% 0.09/0.25 thf(f4,plain,(
% 0.09/0.25 ~((! [X4 : $i] : (? [X5 : $i] : (((cQ @ X4 @ X5)) = $true) => (((cP @ X4)) = $true)) & ! [X2 : $i] : ? [X3 : $i] : (((cQ @ X3 @ X2)) = $true) & ! [X1 : $i,X0 : $i] : ((((cQ @ X1 @ X0)) = $true) => ((((cQ @ X0 @ X0)) = $true) | (((cQ @ X0 @ X1)) = $true)))) => ! [X6 : $i] : (((cP @ X6)) = $true))),
% 0.09/0.25 inference(fool_elimination,[],[f3])).
% 0.09/0.25 thf(f5,plain,(
% 0.09/0.25 ? [X6 : $i] : (((cP @ X6)) != $true) & (! [X4 : $i] : (! [X5 : $i] : (((cQ @ X4 @ X5)) != $true) | (((cP @ X4)) = $true)) & ! [X2 : $i] : ? [X3 : $i] : (((cQ @ X3 @ X2)) = $true) & ! [X1 : $i,X0 : $i] : (((((cQ @ X0 @ X0)) = $true) | (((cQ @ X0 @ X1)) = $true)) | (((cQ @ X1 @ X0)) != $true)))),
% 0.09/0.25 inference(ennf_transformation,[],[f4])).
% 0.09/0.25 thf(f6,plain,(
% 0.09/0.25 ! [X0 : $i,X1 : $i] : ((((cQ @ X0 @ X0)) = $true) | (((cQ @ X1 @ X0)) != $true) | (((cQ @ X0 @ X1)) = $true)) & ! [X2 : $i] : ? [X3 : $i] : (((cQ @ X3 @ X2)) = $true) & ? [X6 : $i] : (((cP @ X6)) != $true) & ! [X4 : $i] : (! [X5 : $i] : (((cQ @ X4 @ X5)) != $true) | (((cP @ X4)) = $true))),
% 0.09/0.25 inference(flattening,[],[f5])).
% 0.09/0.25 thf(f7,plain,(
% 0.09/0.25 ! [X0 : $i,X1 : $i] : ((((cQ @ X0 @ X0)) = $true) | (((cQ @ X1 @ X0)) != $true) | (((cQ @ X0 @ X1)) = $true)) & ! [X2 : $i] : ? [X3 : $i] : (((cQ @ X3 @ X2)) = $true) & ? [X4 : $i] : (((cP @ X4)) != $true) & ! [X5 : $i] : (! [X6 : $i] : (((cQ @ X5 @ X6)) != $true) | (((cP @ X5)) = $true))),
% 0.09/0.25 inference(rectify,[],[f6])).
% 0.09/0.25 thf(f8,plain,(
% 0.09/0.25 ! [X0 : $i,X1 : $i] : ((((cQ @ X0 @ X0)) = $true) | (((cQ @ X1 @ X0)) != $true) | (((cQ @ X0 @ X1)) = $true)) & ! [X2 : $i] : ($true = ((cQ @ (sK0 @ X2) @ X2))) & (((cP @ sK1)) != $true) & ! [X5 : $i] : (! [X6 : $i] : (((cQ @ X5 @ X6)) != $true) | (((cP @ X5)) = $true))),
% 0.09/0.25 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1]),skolemize(X3,sK0 @ X2),skolemize(X4,sK1)],[f7])).
% 0.09/0.25 thf(f9,plain,(
% 0.09/0.25 ( ! [X6 : $i,X5 : $i] : ((((cQ @ X5 @ X6)) != $true) | (((cP @ X5)) = $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f10,plain,(
% 0.09/0.25 (((cP @ sK1)) != $true)),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f11,plain,(
% 0.09/0.25 ( ! [X2 : $i] : (($true = ((cQ @ (sK0 @ X2) @ X2)))) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f12,plain,(
% 0.09/0.25 ( ! [X0 : $i,X1 : $i] : ((((cQ @ X1 @ X0)) != $true) | (((cQ @ X0 @ X1)) = $true) | (((cQ @ X0 @ X0)) = $true)) )),
% 0.09/0.25 inference(cnf_transformation,[],[f8])).
% 0.09/0.25 thf(f17,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((cQ @ X0 @ X0)) = $true) | ($true = ((cQ @ X0 @ (sK0 @ X0)))) | ($true != $true)) )),
% 0.09/0.25 inference(constrained_superposition,[],[f12,f11])).
% 0.09/0.25 thf(f18,plain,(
% 0.09/0.25 ( ! [X0 : $i] : (($true = ((cQ @ X0 @ (sK0 @ X0)))) | (((cQ @ X0 @ X0)) = $true)) )),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f17])).
% 0.09/0.25 thf(f20,plain,(
% 0.09/0.25 ( ! [X0 : $i] : (($true != $true) | (((cP @ X0)) = $true) | (((cQ @ X0 @ X0)) = $true)) )),
% 0.09/0.25 inference(constrained_superposition,[],[f9,f18])).
% 0.09/0.25 thf(f22,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((cP @ X0)) = $true) | (((cQ @ X0 @ X0)) = $true)) )),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f20])).
% 0.09/0.25 thf(f23,plain,(
% 0.09/0.25 ( ! [X0 : $i] : ((((cP @ X0)) = $true)) )),
% 0.09/0.25 inference(forward_subsumption_resolution,[],[f22,f9])).
% 0.09/0.25 thf(f24,plain,(
% 0.09/0.25 ($true != $true)),
% 0.09/0.25 inference(backward_demodulation,[],[f10,f23])).
% 0.09/0.25 thf(f25,plain,(
% 0.09/0.25 $false),
% 0.09/0.25 inference(trivial_inequality_removal,[],[f24])).
% 0.09/0.25 % SZS output end Proof for theBenchmark
% 0.09/0.25 % (284155)------------------------------
% 0.09/0.25 % (284155)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (284155)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (284155)CaDiCaL version: 2.1.3
% 0.09/0.25 % (284155)Termination reason: Refutation
% 0.09/0.25 % (284155)Time elapsed: 0.001 s
% 0.09/0.25 % (284155)Peak memory usage: 12 MB
% 0.09/0.25 % (284155)Instructions burned: 2 (million)
% 0.09/0.25 % (284140)Success in time 0.017 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------