%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO255^5 : 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 : 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 08:47:17 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO255^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n018.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 16:43:56 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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
% 0.21/0.28 % (321794)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (321803)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2149552345:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (321803) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-321794-321803"...
% 0.21/0.28 % (321803)...printing done.
% 0.21/0.28 % (321803)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, cP: ($i > $o)).
% 0.21/0.28 thf(func_def_5, type, sK0: (($i > $o) > $i)).
% 0.21/0.28 thf(func_def_6, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.21/0.28 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(f1,conjecture,(
% 0.21/0.28 (cP @ a) => ? [X0 : ($i > $o)] : (! [X1 : $i] : ((X0 @ X1) => (cP @ X1)) & ? [X2 : $i] : (X0 @ X2))),
% 0.21/0.28 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE3)).
% 0.21/0.28 thf(f2,negated_conjecture,(
% 0.21/0.28 ~((cP @ a) => ? [X0 : ($i > $o)] : (! [X1 : $i] : ((X0 @ X1) => (cP @ X1)) & ? [X2 : $i] : (X0 @ X2)))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f1])).
% 0.21/0.28 thf(f3,plain,(
% 0.21/0.28 ~((cP @ a) => ? [X0 : ($i > $o)] : (! [X1 : $i] : ((X0 @ X1) => (cP @ X1)) & ? [X2 : $i] : (X0 @ X2)))),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f4,plain,(
% 0.21/0.28 ~((((cP @ a)) = $true) => ? [X0 : ($i > $o)] : (? [X2 : $i] : (((X0 @ X2)) = $true) & ! [X1 : $i] : ((((X0 @ X1)) = $true) => (((cP @ X1)) = $true))))),
% 0.21/0.28 inference(fool_elimination,[],[f3])).
% 0.21/0.28 thf(f5,plain,(
% 0.21/0.28 ! [X0 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) != $true) | ? [X1 : $i] : ((((X0 @ X1)) = $true) & (((cP @ X1)) != $true))) & (((cP @ a)) = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f4])).
% 0.21/0.28 thf(f6,plain,(
% 0.21/0.28 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) != $true) | ? [X2 : $i] : ((((X0 @ X2)) = $true) & ($true != ((cP @ X2))))) & (((cP @ a)) = $true)),
% 0.21/0.28 inference(rectify,[],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) != $true) | (($true = ((X0 @ (sK0 @ X0)))) & (((cP @ (sK0 @ X0))) != $true))) & (((cP @ a)) = $true)),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK0 @ X0)],[f6])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 (((cP @ a)) = $true)),
% 0.21/0.28 inference(cnf_transformation,[],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 ( ! [X0 : ($i > $o),X1 : $i] : ((((cP @ (sK0 @ X0))) != $true) | (((X0 @ X1)) != $true)) )),
% 0.21/0.28 inference(cnf_transformation,[],[f7])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 ( ! [X0 : ($i > $o),X1 : $i] : ((((X0 @ X1)) != $true) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 0.21/0.28 inference(cnf_transformation,[],[f7])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 ($true != $true) | ($true = ((cP @ (sK0 @ cP))))),
% 0.21/0.28 inference(superposition,[],[f10,f8])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 ($true = ((cP @ (sK0 @ cP))))),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f17])).
% 0.21/0.28 thf(f25,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($true != ((cP @ X0))) | ($true != $true)) )),
% 0.21/0.28 inference(superposition,[],[f9,f23])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 ( ! [X0 : $i] : (($true != ((cP @ X0)))) )),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f25])).
% 0.21/0.28 thf(f28,plain,(
% 0.21/0.28 ($true != $true)),
% 0.21/0.28 inference(superposition,[],[f26,f23])).
% 0.21/0.28 thf(f29,plain,(
% 0.21/0.28 $false),
% 0.21/0.28 inference(trivial_inequality_removal,[],[f28])).
% 0.21/0.28 % SZS output end Proof for theBenchmark
% 0.21/0.28 % (321803)------------------------------
% 0.21/0.28 % (321803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (321803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (321803)CaDiCaL version: 2.1.3
% 0.21/0.28 % (321803)Termination reason: Refutation
% 0.21/0.28 % (321803)Time elapsed: 0.001 s
% 0.21/0.28 % (321803)Peak memory usage: 12 MB
% 0.21/0.28 % (321803)Instructions burned: 1 (million)
% 0.21/0.28 % (321794)Success in time 0.032 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------