%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO084^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:46:35 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO084^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.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 16:34:05 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (1263899)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (1263907)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3998263889:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.29 % (1263907) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1263899-1263907"...
% 0.21/0.29 % (1263907)...printing done.
% 0.21/0.29 % (1263907)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% 0.21/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.29 thf(func_def_0, type, cP: ($i > $i > $i > $o)).
% 0.21/0.29 thf(func_def_1, type, k: ($i > $i)).
% 0.21/0.29 thf(func_def_2, type, h: ($i > $i)).
% 0.21/0.29 thf(func_def_7, type, sK0: ($i > $i)).
% 0.21/0.29 thf(f1,conjecture,(
% 0.21/0.29 ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : (((cP @ a @ X1 @ (h @ X1)) | (cP @ X0 @ X1 @ (k @ X1))) => (cP @ X0 @ X1 @ X2))),
% 0.21/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM75)).
% 0.21/0.29 thf(f2,negated_conjecture,(
% 0.21/0.29 ~ ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : (((cP @ a @ X1 @ (h @ X1)) | (cP @ X0 @ X1 @ (k @ X1))) => (cP @ X0 @ X1 @ X2))),
% 0.21/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.29 thf(f3,plain,(
% 0.21/0.29 ~ ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : (((cP @ a @ X1 @ (h @ X1)) | (cP @ X0 @ X1 @ (k @ X1))) => (cP @ X0 @ X1 @ X2))),
% 0.21/0.29 inference(rectify,[],[f2])).
% 0.21/0.29 thf(f4,plain,(
% 0.21/0.29 ~ ? [X0 : $i] : ! [X1 : $i] : ? [X2 : $i] : (((((cP @ a @ X1 @ (h @ X1))) = $true) | (((cP @ X0 @ X1 @ (k @ X1))) = $true)) => (((cP @ X0 @ X1 @ X2)) = $true))),
% 0.21/0.29 inference(fool_elimination,[],[f3])).
% 0.21/0.29 thf(f5,plain,(
% 0.21/0.29 ! [X0 : $i] : ? [X1 : $i] : ! [X2 : $i] : (((((cP @ a @ X1 @ (h @ X1))) = $true) | (((cP @ X0 @ X1 @ (k @ X1))) = $true)) & (((cP @ X0 @ X1 @ X2)) != $true))),
% 0.21/0.29 inference(ennf_transformation,[],[f4])).
% 0.21/0.29 thf(f6,plain,(
% 0.21/0.29 ! [X0 : $i] : ! [X2 : $i] : (((((cP @ a @ (sK0 @ X0) @ (h @ (sK0 @ X0)))) = $true) | ($true = ((cP @ X0 @ (sK0 @ X0) @ (k @ (sK0 @ X0)))))) & ($true != ((cP @ X0 @ (sK0 @ X0) @ X2))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f5])).
% 0.21/0.29 thf(f7,plain,(
% 0.21/0.29 ( ! [X2 : $i,X0 : $i] : (($true != ((cP @ X0 @ (sK0 @ X0) @ X2)))) )),
% 0.21/0.29 inference(cnf_transformation,[],[f6])).
% 0.21/0.29 thf(f8,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true = ((cP @ X0 @ (sK0 @ X0) @ (k @ (sK0 @ X0))))) | (((cP @ a @ (sK0 @ X0) @ (h @ (sK0 @ X0)))) = $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f6])).
% 0.21/0.29 thf(f10,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != $true) | (((cP @ a @ (sK0 @ X0) @ (h @ (sK0 @ X0)))) = $true)) )),
% 0.21/0.29 inference(superposition,[],[f7,f8])).
% 0.21/0.29 thf(f11,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((cP @ a @ (sK0 @ X0) @ (h @ (sK0 @ X0)))) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f10])).
% 0.21/0.29 thf(f12,plain,(
% 0.21/0.29 ($true != $true)),
% 0.21/0.29 inference(superposition,[],[f7,f11])).
% 0.21/0.29 thf(f13,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f12])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (1263907)------------------------------
% 0.21/0.29 % (1263907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1263907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1263907)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1263907)Termination reason: Refutation
% 0.21/0.29 % (1263907)Time elapsed: 0.001 s
% 0.21/0.29 % (1263907)Peak memory usage: 12 MB
% 0.21/0.29 % (1263907)Instructions burned: 2 (million)
% 0.21/0.29 % (1263899)Success in time 0.036 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------