%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN360^5 : 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 : n014.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 08:41:40 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN360^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n014.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:14:45 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.29 % (2862579)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (2862588)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3920209946:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (2862588) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2862579-2862588"...
% 0.22/0.29 % (2862585)lrs+10_16_si=on:nwc=1.5:random_seed=4014921859:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (2862584)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1964034970:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (2862586)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4214732107:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (2862588)...printing done.
% 0.22/0.29 % (2862587)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=2356672367: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)
% 0.22/0.29 % (2862588)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% 0.22/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.29 thf(func_def_0, type, cQ: ($i > $i > $o)).
% 0.22/0.29 thf(func_def_1, type, c_less_: ($i > $i > $o)).
% 0.22/0.29 thf(func_def_5, type, sK0: ($i > $i)).
% 0.22/0.29 thf(f1,conjecture,(
% 0.22/0.29 (! [X0 : $i] : (? [X1 : $i] : (c_less_ @ X0 @ X1) => ! [X1 : $i] : (cQ @ X0 @ X1)) & ! [X2 : $i] : ? [X1 : $i] : (c_less_ @ X2 @ X1)) => ! [X1 : $i,X0 : $i] : (cQ @ X0 @ X1)),
% 0.22/0.29 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cX2111A_pme)).
% 0.22/0.29 thf(f2,negated_conjecture,(
% 0.22/0.29 ~((! [X0 : $i] : (? [X1 : $i] : (c_less_ @ X0 @ X1) => ! [X1 : $i] : (cQ @ X0 @ X1)) & ! [X2 : $i] : ? [X1 : $i] : (c_less_ @ X2 @ X1)) => ! [X1 : $i,X0 : $i] : (cQ @ X0 @ X1))),
% 0.22/0.29 inference(negated_conjecture,[status(cth)],[f1])).
% 0.22/0.29 thf(f3,plain,(
% 0.22/0.29 ~((! [X0 : $i] : (? [X1 : $i] : (c_less_ @ X0 @ X1) => ! [X2 : $i] : (cQ @ X0 @ X2)) & ! [X3 : $i] : ? [X4 : $i] : (c_less_ @ X3 @ X4)) => ! [X5 : $i,X6 : $i] : (cQ @ X6 @ X5))),
% 0.22/0.29 inference(rectify,[],[f2])).
% 0.22/0.29 thf(f4,plain,(
% 0.22/0.29 ~((! [X0 : $i] : (? [X1 : $i] : (((c_less_ @ X0 @ X1)) = $true) => ! [X2 : $i] : ($true = ((cQ @ X0 @ X2)))) & ! [X3 : $i] : ? [X4 : $i] : (((c_less_ @ X3 @ X4)) = $true)) => ! [X5 : $i,X6 : $i] : ($true = ((cQ @ X6 @ X5))))),
% 0.22/0.29 inference(fool_elimination,[],[f3])).
% 0.22/0.29 thf(f5,plain,(
% 0.22/0.29 ? [X6 : $i,X5 : $i] : ($true != ((cQ @ X6 @ X5))) & (! [X0 : $i] : (! [X2 : $i] : ($true = ((cQ @ X0 @ X2))) | ! [X1 : $i] : (((c_less_ @ X0 @ X1)) != $true)) & ! [X3 : $i] : ? [X4 : $i] : (((c_less_ @ X3 @ X4)) = $true))),
% 0.22/0.29 inference(ennf_transformation,[],[f4])).
% 0.22/0.29 thf(f6,plain,(
% 0.22/0.29 ! [X3 : $i] : ? [X4 : $i] : (((c_less_ @ X3 @ X4)) = $true) & ! [X0 : $i] : (! [X2 : $i] : ($true = ((cQ @ X0 @ X2))) | ! [X1 : $i] : (((c_less_ @ X0 @ X1)) != $true)) & ? [X6 : $i,X5 : $i] : ($true != ((cQ @ X6 @ X5)))),
% 0.22/0.29 inference(flattening,[],[f5])).
% 0.22/0.29 thf(f7,plain,(
% 0.22/0.29 ! [X0 : $i] : ? [X1 : $i] : (((c_less_ @ X0 @ X1)) = $true) & ! [X2 : $i] : (! [X3 : $i] : ($true = ((cQ @ X2 @ X3))) | ! [X4 : $i] : (((c_less_ @ X2 @ X4)) != $true)) & ? [X5 : $i,X6 : $i] : (((cQ @ X5 @ X6)) != $true)),
% 0.22/0.29 inference(rectify,[],[f6])).
% 0.22/0.29 thf(f8,plain,(
% 0.22/0.29 ! [X0 : $i] : (((c_less_ @ X0 @ (sK0 @ X0))) = $true) & ! [X2 : $i] : (! [X3 : $i] : ($true = ((cQ @ X2 @ X3))) | ! [X4 : $i] : (((c_less_ @ X2 @ X4)) != $true)) & (((cQ @ sK1 @ sK2)) != $true)),
% 0.22/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2]),skolemize(X1,sK0 @ X0),skolemize(X5,sK1),skolemize(X6,sK2)],[f7])).
% 0.22/0.29 thf(f9,plain,(
% 0.22/0.29 (((cQ @ sK1 @ sK2)) != $true)),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 thf(f10,plain,(
% 0.22/0.29 ( ! [X2 : $i,X3 : $i,X4 : $i] : ((((c_less_ @ X2 @ X4)) != $true) | ($true = ((cQ @ X2 @ X3)))) )),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 thf(f11,plain,(
% 0.22/0.29 ( ! [X0 : $i] : ((((c_less_ @ X0 @ (sK0 @ X0))) = $true)) )),
% 0.22/0.29 inference(cnf_transformation,[],[f8])).
% 0.22/0.29 thf(f13,plain,(
% 0.22/0.29 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((cQ @ X0 @ X1)) = $true)) )),
% 0.22/0.29 inference(superposition,[],[f10,f11])).
% 0.22/0.29 thf(f14,plain,(
% 0.22/0.29 ( ! [X0 : $i,X1 : $i] : ((((cQ @ X0 @ X1)) = $true)) )),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f13])).
% 0.22/0.29 thf(f15,plain,(
% 0.22/0.29 ($true != $true)),
% 0.22/0.29 inference(superposition,[],[f9,f14])).
% 0.22/0.29 thf(f16,plain,(
% 0.22/0.29 $false),
% 0.22/0.29 inference(trivial_inequality_removal,[],[f15])).
% 0.22/0.29 % SZS output end Proof for theBenchmark
% 0.22/0.29 % (2862588)------------------------------
% 0.22/0.29 % (2862588)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (2862588)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (2862588)CaDiCaL version: 2.1.3
% 0.22/0.29 % (2862588)Termination reason: Refutation
% 0.22/0.29 % (2862588)Time elapsed: 0.002 s
% 0.22/0.29 % (2862588)Peak memory usage: 12 MB
% 0.22/0.29 % (2862588)Instructions burned: 1 (million)
% 0.22/0.29 % (2862579)Success in time 0.035 s
% 0.22/0.29 % Vampire exiting
%------------------------------------------------------------------------------