%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL727^5 : 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 : n004.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 08:14:34 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL727^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 09:58:52 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.23/0.30 % (1088902)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (1088908)lrs+10_16_si=on:nwc=1.5:random_seed=3876955989:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (1088907)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=536555760:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (1088909)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4133977207:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (1088911)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3891761262:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (1088910)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=330882759: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)
% 0.23/0.30 % (1088911) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1088902-1088911"...
% 0.23/0.30 % (1088907) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1088902-1088907"...
% 0.23/0.30 % (1088909) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1088902-1088909"...
% 0.23/0.30 % (1088910) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1088902-1088910"...
% 0.23/0.30 % (1088911)...printing done.
% 0.23/0.30 % (1088907)...printing done.
% 0.23/0.30 % (1088910)...printing done.
% 0.23/0.30 % (1088907)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% 0.23/0.30 thf(type_def_5, type, a: $tType).
% 0.23/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.23/0.30 thf(func_def_3, type, sK0: (((a > $o) > a > $o) > (a > $o) > a)).
% 0.23/0.30 thf(func_def_4, type, sK1: ((a > $o) > $o)).
% 0.23/0.30 thf(func_def_5, type, sK2: (((a > $o) > a) > a > $o)).
% 0.23/0.30 thf(func_def_6, type, sK3: ((a > $o) > a)).
% 0.23/0.30 thf(func_def_7, type, vNOT: ($o > $o)).
% 0.23/0.30 thf(f1,conjecture,(
% 0.23/0.30 ! [X0 : ((a > $o) > a > $o)] : ? [X1 : ((a > $o) > a)] : ! [X2 : (a > $o)] : (? [X3 : a] : (X0 @ X2 @ X3) => (X0 @ X2 @ (X1 @ X2))) => ! [X4 : ((a > $o) > $o)] : (! [X5 : (a > $o)] : ((X4 @ X5) => ? [X6 : a] : (X5 @ X6)) => ? [X7 : ((a > $o) > a)] : ! [X5 : (a > $o)] : ((X4 @ X5) => (X5 @ (X7 @ X5))))),
% 0.23/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM533)).
% 0.23/0.30 thf(f2,negated_conjecture,(
% 0.23/0.30 ~(! [X0 : ((a > $o) > a > $o)] : ? [X1 : ((a > $o) > a)] : ! [X2 : (a > $o)] : (? [X3 : a] : (X0 @ X2 @ X3) => (X0 @ X2 @ (X1 @ X2))) => ! [X4 : ((a > $o) > $o)] : (! [X5 : (a > $o)] : ((X4 @ X5) => ? [X6 : a] : (X5 @ X6)) => ? [X7 : ((a > $o) > a)] : ! [X5 : (a > $o)] : ((X4 @ X5) => (X5 @ (X7 @ X5)))))),
% 0.23/0.30 inference(negated_conjecture,[status(cth)],[f1])).
% 0.23/0.30 thf(f3,plain,(
% 0.23/0.30 ~(! [X0 : ((a > $o) > a > $o)] : ? [X1 : ((a > $o) > a)] : ! [X2 : (a > $o)] : (? [X3 : a] : (X0 @ X2 @ X3) => (X0 @ X2 @ (X1 @ X2))) => ! [X4 : ((a > $o) > $o)] : (! [X5 : (a > $o)] : ((X4 @ X5) => ? [X6 : a] : (X5 @ X6)) => ? [X7 : ((a > $o) > a)] : ! [X8 : (a > $o)] : ((X4 @ X8) => (X8 @ (X7 @ X8)))))),
% 0.23/0.30 inference(rectify,[],[f2])).
% 0.23/0.30 thf(f4,plain,(
% 0.23/0.30 ~(! [X0 : ((a > $o) > a > $o)] : ? [X1 : ((a > $o) > a)] : ! [X2 : (a > $o)] : (? [X3 : a] : (((X0 @ X2 @ X3)) = $true) => (((X0 @ X2 @ (X1 @ X2))) = $true)) => ! [X4 : ((a > $o) > $o)] : (! [X5 : (a > $o)] : ((((X4 @ X5)) = $true) => ? [X6 : a] : (((X5 @ X6)) = $true)) => ? [X7 : ((a > $o) > a)] : ! [X8 : (a > $o)] : (($true = ((X4 @ X8))) => ($true = ((X8 @ (X7 @ X8)))))))),
% 0.23/0.30 inference(fool_elimination,[],[f3])).
% 0.23/0.30 thf(f5,plain,(
% 0.23/0.30 ! [X0 : ((a > $o) > a > $o)] : ? [X1 : ((a > $o) > a)] : ! [X2 : (a > $o)] : (! [X3 : a] : (((X0 @ X2 @ X3)) != $true) | (((X0 @ X2 @ (X1 @ X2))) = $true)) & ? [X4 : ((a > $o) > $o)] : (! [X7 : ((a > $o) > a)] : ? [X8 : (a > $o)] : (($true != ((X8 @ (X7 @ X8)))) & ($true = ((X4 @ X8)))) & ! [X5 : (a > $o)] : (? [X6 : a] : (((X5 @ X6)) = $true) | (((X4 @ X5)) != $true)))),
% 0.23/0.30 inference(ennf_transformation,[],[f4])).
% 0.23/0.30 thf(f6,plain,(
% 0.23/0.30 ! [X0 : ((a > $o) > a > $o)] : ? [X1 : ((a > $o) > a)] : ! [X2 : (a > $o)] : (! [X3 : a] : (((X0 @ X2 @ X3)) != $true) | (((X0 @ X2 @ (X1 @ X2))) = $true)) & ? [X4 : ((a > $o) > $o)] : (! [X5 : ((a > $o) > a)] : ? [X6 : (a > $o)] : ((((X6 @ (X5 @ X6))) != $true) & (((X4 @ X6)) = $true)) & ! [X7 : (a > $o)] : (? [X8 : a] : (((X7 @ X8)) = $true) | ($true != ((X4 @ X7)))))),
% 0.23/0.30 inference(rectify,[],[f5])).
% 0.23/0.30 thf(f7,plain,(
% 0.23/0.30 ! [X0 : ((a > $o) > a > $o)] : ! [X2 : (a > $o)] : (! [X3 : a] : (((X0 @ X2 @ X3)) != $true) | (((X0 @ X2 @ (sK0 @ X0 @ X2))) = $true)) & (! [X5 : ((a > $o) > a)] : ((((sK2 @ X5 @ (X5 @ (sK2 @ X5)))) != $true) & (((sK1 @ (sK2 @ X5))) = $true)) & ! [X7 : (a > $o)] : ((((X7 @ (sK3 @ X7))) = $true) | (((sK1 @ X7)) != $true)))),
% 0.23/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,vAPP,vAPP]),skolemize(X8,sK3 @ X7),skolemize(X4,sK1),skolemize(X8,sK3 @ X7),skolemize(X8,sK3 @ X7)],[f6])).
% 0.23/0.30 thf(f8,plain,(
% 0.23/0.30 ( ! [X7 : (a > $o)] : ((((sK1 @ X7)) != $true) | (((X7 @ (sK3 @ X7))) = $true)) )),
% 0.23/0.30 inference(cnf_transformation,[],[f7])).
% 0.23/0.30 thf(f9,plain,(
% 0.23/0.30 ( ! [X5 : ((a > $o) > a)] : ((((sK1 @ (sK2 @ X5))) = $true)) )),
% 0.23/0.30 inference(cnf_transformation,[],[f7])).
% 0.23/0.30 thf(f10,plain,(
% 0.23/0.30 ( ! [X5 : ((a > $o) > a)] : ((((sK2 @ X5 @ (X5 @ (sK2 @ X5)))) != $true)) )),
% 0.23/0.30 inference(cnf_transformation,[],[f7])).
% 0.23/0.30 thf(f14,plain,(
% 0.23/0.30 ( ! [X0 : ((a > $o) > a)] : (($true != $true) | (((sK2 @ X0 @ (sK3 @ (sK2 @ X0)))) = $true)) )),
% 0.23/0.30 inference(constrained_superposition,[],[f8,f9])).
% 0.23/0.30 thf(f15,plain,(
% 0.23/0.30 ( ! [X0 : ((a > $o) > a)] : ((((sK2 @ X0 @ (sK3 @ (sK2 @ X0)))) = $true)) )),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f14])).
% 0.23/0.30 thf(f16,plain,(
% 0.23/0.30 ($true != $true)),
% 0.23/0.30 inference(constrained_superposition,[],[f10,f15])).
% 0.23/0.30 thf(f17,plain,(
% 0.23/0.30 $false),
% 0.23/0.30 inference(trivial_inequality_removal,[],[f16])).
% 0.23/0.30 % SZS output end Proof for theBenchmark
% 0.23/0.30 % (1088907)------------------------------
% 0.23/0.30 % (1088907)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1088907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1088907)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1088907)Termination reason: Refutation
% 0.23/0.30 % (1088907)Time elapsed: 0.002 s
% 0.23/0.30 % (1088907)Peak memory usage: 12 MB
% 0.23/0.30 % (1088907)Instructions burned: 2 (million)
% 0.23/0.30 % (1088902)Success in time 0.044 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------