%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO306^5 : 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 : n011.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 08:47:24 AM UTC 2026
% Result : Theorem 0.26s 0.33s
% Output : Refutation 0.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO306^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n011.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 16:44:46 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.28 Running higher-order theorem proving
% 0.09/0.29 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
% 0.26/0.33 % (330666)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.33 % (330672)lrs+10_16_si=on:nwc=1.5:random_seed=3195607597:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.26/0.33 % (330672) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-330666-330672"...
% 0.26/0.33 % (330671)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=387901324:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.26/0.33 % (330672)...printing done.
% 0.26/0.33 % (330672)Refutation found. Thanks to Tanya!
% 0.26/0.33 % SZS status Theorem for theBenchmark
% 0.26/0.33 % SZS output start Proof for theBenchmark
% 0.26/0.33 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.26/0.33 thf(func_def_0, type, cT: ($i > $o)).
% 0.26/0.33 thf(func_def_1, type, cS: ($i > $o)).
% 0.26/0.33 thf(func_def_6, type, sK1: (($i > $o) > $i)).
% 0.26/0.33 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.26/0.33 thf(f1,conjecture,(
% 0.26/0.33 ! [X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1) => ! [X1 : $i] : (X0 @ X1)) => (! [X1 : $i] : ((cS @ X1) & (cT @ X1)) => ! [X1 : $i] : ((cS @ X1) & (cT @ X1)))),
% 0.26/0.33 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cDUP_BUG_2)).
% 0.26/0.33 thf(f2,negated_conjecture,(
% 0.26/0.33 ~(! [X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1) => ! [X1 : $i] : (X0 @ X1)) => (! [X1 : $i] : ((cS @ X1) & (cT @ X1)) => ! [X1 : $i] : ((cS @ X1) & (cT @ X1))))),
% 0.26/0.33 inference(negated_conjecture,[status(cth)],[f1])).
% 0.26/0.33 thf(f3,plain,(
% 0.26/0.33 ~(! [X0 : ($i > $o)] : (! [X1 : $i] : (X0 @ X1) => ! [X2 : $i] : (X0 @ X2)) => (! [X3 : $i] : ((cS @ X3) & (cT @ X3)) => ! [X4 : $i] : ((cS @ X4) & (cT @ X4))))),
% 0.26/0.33 inference(rectify,[],[f2])).
% 0.26/0.33 thf(f4,plain,(
% 0.26/0.33 ~(! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) => ! [X2 : $i] : ($true = ((X0 @ X2)))) => (! [X3 : $i] : ((((cT @ X3)) = $true) & ($true = ((cS @ X3)))) => ! [X4 : $i] : ((((cS @ X4)) = $true) & (((cT @ X4)) = $true))))),
% 0.26/0.33 inference(fool_elimination,[],[f3])).
% 0.26/0.33 thf(f5,plain,(
% 0.26/0.33 (? [X4 : $i] : ((((cT @ X4)) != $true) | (((cS @ X4)) != $true)) & ! [X3 : $i] : ((((cT @ X3)) = $true) & ($true = ((cS @ X3))))) & ! [X0 : ($i > $o)] : (? [X1 : $i] : (((X0 @ X1)) != $true) | ! [X2 : $i] : ($true = ((X0 @ X2))))),
% 0.26/0.33 inference(ennf_transformation,[],[f4])).
% 0.26/0.33 thf(f6,plain,(
% 0.26/0.33 ! [X3 : $i] : ((((cT @ X3)) = $true) & ($true = ((cS @ X3)))) & ? [X4 : $i] : ((((cT @ X4)) != $true) | (((cS @ X4)) != $true)) & ! [X0 : ($i > $o)] : (? [X1 : $i] : (((X0 @ X1)) != $true) | ! [X2 : $i] : ($true = ((X0 @ X2))))),
% 0.26/0.33 inference(flattening,[],[f5])).
% 0.26/0.33 thf(f7,plain,(
% 0.26/0.33 ! [X0 : $i] : ((((cT @ X0)) = $true) & (((cS @ X0)) = $true)) & ? [X1 : $i] : ((((cT @ X1)) != $true) | (((cS @ X1)) != $true)) & ! [X2 : ($i > $o)] : (? [X3 : $i] : ($true != ((X2 @ X3))) | ! [X4 : $i] : (((X2 @ X4)) = $true))),
% 0.26/0.33 inference(rectify,[],[f6])).
% 0.26/0.33 thf(f8,plain,(
% 0.26/0.33 ! [X0 : $i] : ((((cT @ X0)) = $true) & (((cS @ X0)) = $true)) & (($true != ((cT @ sK0))) | (((cS @ sK0)) != $true)) & ! [X2 : ($i > $o)] : ((((X2 @ (sK1 @ X2))) != $true) | ! [X4 : $i] : (((X2 @ X4)) = $true))),
% 0.26/0.33 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,vAPP]),skolemize(X1,sK0),skolemize(X3,sK1 @ X2)],[f7])).
% 0.26/0.33 thf(f10,plain,(
% 0.26/0.33 (((cS @ sK0)) != $true) | ($true != ((cT @ sK0)))),
% 0.26/0.33 inference(cnf_transformation,[],[f8])).
% 0.26/0.33 thf(f11,plain,(
% 0.26/0.33 ( ! [X0 : $i] : ((((cS @ X0)) = $true)) )),
% 0.26/0.33 inference(cnf_transformation,[],[f8])).
% 0.26/0.33 thf(f12,plain,(
% 0.26/0.33 ( ! [X0 : $i] : ((((cT @ X0)) = $true)) )),
% 0.26/0.33 inference(cnf_transformation,[],[f8])).
% 0.26/0.33 thf(f15,plain,(
% 0.26/0.33 (((cS @ sK0)) != $true)),
% 0.26/0.33 inference(forward_subsumption_resolution,[],[f10,f12])).
% 0.26/0.33 thf(f16,plain,(
% 0.26/0.33 $false),
% 0.26/0.33 inference(forward_subsumption_resolution,[],[f15,f11])).
% 0.26/0.33 % SZS output end Proof for theBenchmark
% 0.26/0.33 % (330672)------------------------------
% 0.26/0.33 % (330672)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.33 % (330672)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.33 % (330672)CaDiCaL version: 2.1.3
% 0.26/0.33 % (330672)Termination reason: Refutation
% 0.26/0.33 % (330672)Time elapsed: 0.001 s
% 0.26/0.33 % (330672)Peak memory usage: 12 MB
% 0.26/0.33 % (330672)Instructions burned: 1 (million)
% 0.26/0.33 % (330666)Success in time 0.024 s
% 0.26/0.33 % Vampire exiting
%------------------------------------------------------------------------------