%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO296^5 : 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 : n017.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 08:47:23 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO296^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n017.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 16:39:41 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 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
% 0.19/0.26 % (577225)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.26 % (577234)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=56901659:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.26 % (577234) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-577225-577234"...
% 0.19/0.26 % (577234)...printing done.
% 0.19/0.26 % (577234)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% 0.19/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.26 thf(func_def_0, type, q: ($i > $o)).
% 0.19/0.26 thf(func_def_1, type, p: ($i > $o)).
% 0.19/0.26 thf(func_def_5, type, sK0: (($i > $o) > $i)).
% 0.19/0.26 thf(func_def_6, type, sK1: (($i > $o) > $i)).
% 0.19/0.26 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.19/0.26 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.26 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.26 thf(f1,conjecture,(
% 0.19/0.26 ? [X0 : ($i > $o)] : ! [X2 : $i,X1 : $i] : (((X0 @ X2) | (X0 @ X1)) => ((p @ X1) & (q @ X2)))),
% 0.19/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBLEDSOE5D)).
% 0.19/0.26 thf(f2,negated_conjecture,(
% 0.19/0.26 ~ ? [X0 : ($i > $o)] : ! [X2 : $i,X1 : $i] : (((X0 @ X2) | (X0 @ X1)) => ((p @ X1) & (q @ X2)))),
% 0.19/0.26 inference(negated_conjecture,[status(cth)],[f1])).
% 0.19/0.26 thf(f3,plain,(
% 0.19/0.26 ~ ? [X0 : ($i > $o)] : ! [X1 : $i,X2 : $i] : (((X0 @ X1) | (X0 @ X2)) => ((p @ X2) & (q @ X1)))),
% 0.19/0.26 inference(rectify,[],[f2])).
% 0.19/0.26 thf(f4,plain,(
% 0.19/0.26 ~ ? [X0 : ($i > $o)] : ! [X2 : $i,X1 : $i] : (((((X0 @ X1)) = $true) | (((X0 @ X2)) = $true)) => (($true = ((q @ X1))) & ($true = ((p @ X2)))))),
% 0.19/0.26 inference(fool_elimination,[],[f3])).
% 0.19/0.26 thf(f5,plain,(
% 0.19/0.26 ! [X0 : ($i > $o)] : ? [X2 : $i,X1 : $i] : (((((X0 @ X1)) = $true) | (((X0 @ X2)) = $true)) & (($true != ((q @ X1))) | ($true != ((p @ X2)))))),
% 0.19/0.26 inference(ennf_transformation,[],[f4])).
% 0.19/0.26 thf(f6,plain,(
% 0.19/0.26 ! [X0 : ($i > $o)] : ? [X1 : $i,X2 : $i] : (((((X0 @ X2)) = $true) | (((X0 @ X1)) = $true)) & ((((q @ X2)) != $true) | (((p @ X1)) != $true)))),
% 0.19/0.26 inference(rectify,[],[f5])).
% 0.19/0.26 thf(f7,plain,(
% 0.19/0.26 ! [X0 : ($i > $o)] : ((($true = ((X0 @ (sK1 @ X0)))) | ($true = ((X0 @ (sK0 @ X0))))) & (($true != ((q @ (sK1 @ X0)))) | ($true != ((p @ (sK0 @ X0))))))),
% 0.19/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X2,sK1 @ X0),skolemize(X2,sK1 @ X0)],[f6])).
% 0.19/0.26 thf(f9,plain,(
% 0.19/0.26 ( ! [X0 : ($i > $o)] : (($true = ((X0 @ (sK1 @ X0)))) | ($true = ((X0 @ (sK0 @ X0))))) )),
% 0.19/0.26 inference(cnf_transformation,[],[f7])).
% 0.19/0.26 thf(f12,plain,(
% 0.19/0.26 ($true = (((^[Y0 : $i]: ($false)) @ (sK0 @ (^[Y0 : $i]: ($false)))))) | ($true = (((^[Y0 : $i]: ($false)) @ (sK1 @ (^[Y0 : $i]: ($false))))))),
% 0.19/0.26 inference(primitive_instantiation,[],[f9])).
% 0.19/0.26 thf(f18,plain,(
% 0.19/0.26 ($false = $true) | ($false = $true)),
% 0.19/0.26 inference(beta-eta_normalization,[],[f12])).
% 0.19/0.26 thf(f19,plain,(
% 0.19/0.26 ($false = $true)),
% 0.19/0.26 inference(duplicate_literal_removal,[],[f18])).
% 0.19/0.26 thf(f20,plain,(
% 0.19/0.26 $false),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f19])).
% 0.19/0.26 % SZS output end Proof for theBenchmark
% 0.19/0.26 % (577234)------------------------------
% 0.19/0.26 % (577234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (577234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (577234)CaDiCaL version: 2.1.3
% 0.19/0.26 % (577234)Termination reason: Refutation
% 0.19/0.26 % (577234)Time elapsed: 0.001 s
% 0.19/0.26 % (577234)Peak memory usage: 12 MB
% 0.19/0.26 % (577234)Instructions burned: 1 (million)
% 0.19/0.26 % (577225)Success in time 0.034 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------