%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO258^5 : 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 : 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 08:47:18 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO258^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n015.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 16:45:04 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 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
% 0.09/0.26 % (3774245)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.26 % (3774252)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3564728640:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.26 % (3774252) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3774245-3774252"...
% 0.09/0.26 % (3774252)...printing done.
% 0.09/0.26 % (3774252)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% 0.09/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.26 thf(func_def_1, type, cQ: ($i > ($i > $o) > $o)).
% 0.09/0.26 thf(func_def_2, type, cP: ($i > $i > $o)).
% 0.09/0.26 thf(func_def_7, type, sK0: (($i > $o) > $i)).
% 0.09/0.26 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.09/0.26 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.09/0.26 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.09/0.26 thf(f1,conjecture,(
% 0.09/0.26 (! [X0 : ($i > $o)] : (cQ @ b @ X0) & (cP @ a @ b)) => ? [X1 : ($i > $o)] : ! [X2 : $i] : ((X1 @ X2) => (? [X3 : $i] : ((cP @ X2 @ X3) & (cQ @ X3 @ X1)) & (X1 @ a)))),
% 0.09/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cBLEDSOE_FENG_6)).
% 0.09/0.26 thf(f2,negated_conjecture,(
% 0.09/0.26 ~((! [X0 : ($i > $o)] : (cQ @ b @ X0) & (cP @ a @ b)) => ? [X1 : ($i > $o)] : ! [X2 : $i] : ((X1 @ X2) => (? [X3 : $i] : ((cP @ X2 @ X3) & (cQ @ X3 @ X1)) & (X1 @ a))))),
% 0.09/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.26 thf(f3,plain,(
% 0.09/0.26 ~((! [X0 : ($i > $o)] : (cQ @ b @ X0) & (cP @ a @ b)) => ? [X1 : ($i > $o)] : ! [X2 : $i] : ((X1 @ X2) => (? [X3 : $i] : ((cP @ X2 @ X3) & (cQ @ X3 @ X1)) & (X1 @ a))))),
% 0.09/0.26 inference(rectify,[],[f2])).
% 0.09/0.26 thf(f4,plain,(
% 0.09/0.26 ~(((((cP @ a @ b)) = $true) & ! [X0 : ($i > $o)] : (((cQ @ b @ X0)) = $true)) => ? [X1 : ($i > $o)] : ! [X2 : $i] : ((((X1 @ X2)) = $true) => (? [X3 : $i] : ((((cP @ X2 @ X3)) = $true) & (((cQ @ X3 @ X1)) = $true)) & (((X1 @ a)) = $true))))),
% 0.09/0.26 inference(fool_elimination,[],[f3])).
% 0.09/0.26 thf(f5,plain,(
% 0.09/0.26 ! [X1 : ($i > $o)] : ? [X2 : $i] : ((! [X3 : $i] : ((((cQ @ X3 @ X1)) != $true) | (((cP @ X2 @ X3)) != $true)) | (((X1 @ a)) != $true)) & (((X1 @ X2)) = $true)) & ((((cP @ a @ b)) = $true) & ! [X0 : ($i > $o)] : (((cQ @ b @ X0)) = $true))),
% 0.09/0.26 inference(ennf_transformation,[],[f4])).
% 0.09/0.26 thf(f6,plain,(
% 0.09/0.26 (((cP @ a @ b)) = $true) & ! [X1 : ($i > $o)] : ? [X2 : $i] : ((! [X3 : $i] : ((((cQ @ X3 @ X1)) != $true) | (((cP @ X2 @ X3)) != $true)) | (((X1 @ a)) != $true)) & (((X1 @ X2)) = $true)) & ! [X0 : ($i > $o)] : (((cQ @ b @ X0)) = $true)),
% 0.09/0.26 inference(flattening,[],[f5])).
% 0.09/0.26 thf(f7,plain,(
% 0.09/0.26 (((cP @ a @ b)) = $true) & ! [X0 : ($i > $o)] : ? [X1 : $i] : ((! [X2 : $i] : (($true != ((cQ @ X2 @ X0))) | ($true != ((cP @ X1 @ X2)))) | ($true != ((X0 @ a)))) & ($true = ((X0 @ X1)))) & ! [X3 : ($i > $o)] : ($true = ((cQ @ b @ X3)))),
% 0.09/0.26 inference(rectify,[],[f6])).
% 0.09/0.26 thf(f8,plain,(
% 0.09/0.26 (((cP @ a @ b)) = $true) & ! [X0 : ($i > $o)] : ((! [X2 : $i] : (($true != ((cQ @ X2 @ X0))) | ($true != ((cP @ (sK0 @ X0) @ X2)))) | ($true != ((X0 @ a)))) & (((X0 @ (sK0 @ X0))) = $true)) & ! [X3 : ($i > $o)] : ($true = ((cQ @ b @ X3)))),
% 0.09/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f7])).
% 0.09/0.26 thf(f10,plain,(
% 0.09/0.26 ( ! [X0 : ($i > $o)] : ((((X0 @ (sK0 @ X0))) = $true)) )),
% 0.09/0.26 inference(cnf_transformation,[],[f8])).
% 0.09/0.26 thf(f16,plain,(
% 0.09/0.26 ($true = (((^[Y0 : $i]: ($false)) @ (sK0 @ (^[Y0 : $i]: ($false))))))),
% 0.09/0.26 inference(primitive_instantiation,[],[f10])).
% 0.09/0.26 thf(f19,plain,(
% 0.09/0.26 ($true = $false)),
% 0.09/0.26 inference(beta-eta_normalization,[],[f16])).
% 0.09/0.26 thf(f20,plain,(
% 0.09/0.26 $false),
% 0.09/0.26 inference(trivial_inequality_removal,[],[f19])).
% 0.09/0.26 % SZS output end Proof for theBenchmark
% 0.09/0.26 % (3774252)------------------------------
% 0.09/0.26 % (3774252)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3774252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3774252)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3774252)Termination reason: Refutation
% 0.09/0.26 % (3774252)Time elapsed: 0.001 s
% 0.09/0.26 % (3774252)Peak memory usage: 12 MB
% 0.09/0.26 % (3774252)Instructions burned: 1 (million)
% 0.09/0.26 % (3774245)Success in time 0.016 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------