%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU567^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:30:06 AM UTC 2026
% Result : Theorem 0.08s 0.16s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU567^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 13:50:19 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 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
% 0.08/0.16 % (136161)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.16 % (136172)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.16 % (136172)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.08/0.16 % (136167)lrs+10_16_si=on:nwc=1.5:random_seed=1303222670:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.16 % (136166)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3524495115:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.16 % (136172)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1945228246:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.16 % (136168)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3248683517:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.16 % (136169)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=414517764: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)
% 0.08/0.16 % (136170)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2301948407:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.16 % (136171)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1199435251:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.16 % (136168)Refutation not found, incomplete strategy
% 0.08/0.16 % (136168)------------------------------
% 0.08/0.16 % (136168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.16 % (136168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.16 % (136168)CaDiCaL version: 2.1.3
% 0.08/0.16 % (136168)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.16 % (136168)Time elapsed: 0.0000 s
% 0.08/0.16 % (136168)Peak memory usage: 12 MB
% 0.08/0.16 % (136168)Instructions burned: 1 (million)
% 0.08/0.16 % (136166) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-136161-136166"...
% 0.08/0.16 % (136167) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-136161-136167"...
% 0.08/0.16 % (136170) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-136161-136170"...
% 0.08/0.16 % (136168)------------------------------
% 0.08/0.16 % (136168)------------------------------
% 0.08/0.16 % (136171) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-136161-136171"...
% 0.08/0.16 % (136169) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-136161-136169"...
% 0.08/0.16 % (136172) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-136161-136172"...
% 0.08/0.16 % (136166)...printing done.
% 0.08/0.16 % (136167)...printing done.
% 0.08/0.16 % (136170)...printing done.
% 0.08/0.16 % (136171)...printing done.
% 0.08/0.16 % (136166)Refutation found. Thanks to Tanya!
% 0.08/0.16 % SZS status Theorem for theBenchmark
% 0.08/0.16 % SZS output start Proof for theBenchmark
% 0.08/0.16 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.16 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.08/0.16 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.08/0.16 thf(func_def_2, type, subsetI1: $o).
% 0.08/0.16 thf(func_def_8, type, sK2: ($i > $i > $i)).
% 0.08/0.16 thf(func_def_11, type, vNOT: ($o > $o)).
% 0.08/0.16 thf(f1,axiom,(
% 0.08/0.16 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.08/0.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1)).
% 0.08/0.16 thf(f2,conjecture,(
% 0.08/0.16 subsetI1 => ! [X1 : $i,X0 : $i] : (~(subset @ X0 @ X1) => (X0 != X1))),
% 0.08/0.16 file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1)).
% 0.08/0.16 thf(f3,negated_conjecture,(
% 0.08/0.16 ~(subsetI1 => ! [X1 : $i,X0 : $i] : (~(subset @ X0 @ X1) => (X0 != X1)))),
% 0.08/0.16 inference(negated_conjecture,[status(cth)],[f2])).
% 0.08/0.16 thf(f4,plain,(
% 0.08/0.16 ~(subsetI1 => ! [X0 : $i,X1 : $i] : (~(subset @ X1 @ X0) => (X0 != X1)))),
% 0.08/0.16 inference(rectify,[],[f3])).
% 0.08/0.16 thf(f5,plain,(
% 0.08/0.16 ~((subsetI1 = $true) => ! [X0 : $i,X1 : $i] : (~ (((subset @ X1 @ X0)) = $true) => (X0 != X1)))),
% 0.08/0.16 inference(fool_elimination,[],[f4])).
% 0.08/0.16 thf(f6,plain,(
% 0.08/0.16 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
% 0.08/0.16 inference(rectify,[],[f1])).
% 0.08/0.16 thf(f7,plain,(
% 0.08/0.16 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true)) <=> (subsetI1 = $true)),
% 0.08/0.16 inference(fool_elimination,[],[f6])).
% 0.08/0.16 thf(f8,plain,(
% 0.08/0.16 ~((subsetI1 = $true) => ! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) => (X0 != X1)))),
% 0.08/0.16 inference(flattening,[],[f5])).
% 0.08/0.16 thf(f9,plain,(
% 0.08/0.16 ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) <=> (subsetI1 = $true)),
% 0.08/0.16 inference(ennf_transformation,[],[f7])).
% 0.08/0.16 thf(f10,plain,(
% 0.08/0.16 (subsetI1 = $true) & ? [X1 : $i,X0 : $i] : ((X0 = X1) & (((subset @ X1 @ X0)) != $true))),
% 0.08/0.16 inference(ennf_transformation,[],[f8])).
% 0.08/0.16 thf(f11,plain,(
% 0.08/0.16 (subsetI1 = $true) & ? [X0 : $i,X1 : $i] : ((X0 = X1) & (((subset @ X0 @ X1)) != $true))),
% 0.08/0.16 inference(rectify,[],[f10])).
% 0.08/0.16 thf(f12,plain,(
% 0.08/0.16 (subsetI1 = $true) & ((sK1 = sK0) & (((subset @ sK0 @ sK1)) != $true))),
% 0.08/0.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11])).
% 0.08/0.16 thf(f13,plain,(
% 0.08/0.16 (! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true))))),
% 0.08/0.16 inference(nnf_transformation,[],[f9])).
% 0.08/0.16 thf(f14,plain,(
% 0.08/0.16 (! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : ((((subset @ X4 @ X3)) != $true) & ! [X5 : $i] : ((((in @ X5 @ X4)) != $true) | ($true = ((in @ X5 @ X3))))))),
% 0.08/0.16 inference(rectify,[],[f13])).
% 0.08/0.16 thf(f15,plain,(
% 0.08/0.16 (! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | (($true = ((in @ (sK2 @ X1 @ X0) @ X1))) & (((in @ (sK2 @ X1 @ X0) @ X0)) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ((((subset @ sK4 @ sK3)) != $true) & ! [X5 : $i] : ((((in @ X5 @ sK4)) != $true) | (((in @ X5 @ sK3)) = $true))))),
% 0.08/0.16 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK3,sK4]),skolemize(X2,sK2 @ X1 @ X0),skolemize(X3,sK3),skolemize(X4,sK4)],[f14])).
% 0.08/0.16 thf(f16,plain,(
% 0.08/0.16 (((subset @ sK0 @ sK1)) != $true)),
% 0.08/0.16 inference(cnf_transformation,[],[f12])).
% 0.08/0.16 thf(f17,plain,(
% 0.08/0.16 (sK1 = sK0)),
% 0.08/0.16 inference(cnf_transformation,[],[f12])).
% 0.08/0.16 thf(f18,plain,(
% 0.08/0.16 (subsetI1 = $true)),
% 0.08/0.16 inference(cnf_transformation,[],[f12])).
% 0.08/0.16 thf(f21,plain,(
% 0.08/0.16 ( ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | (((in @ (sK2 @ X1 @ X0) @ X0)) != $true) | (subsetI1 != $true)) )),
% 0.08/0.16 inference(cnf_transformation,[],[f15])).
% 0.08/0.16 thf(f22,plain,(
% 0.08/0.16 ( ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | ($true = ((in @ (sK2 @ X1 @ X0) @ X1))) | (subsetI1 != $true)) )),
% 0.08/0.17 inference(cnf_transformation,[],[f15])).
% 0.08/0.17 thf(f25,plain,(
% 0.08/0.17 (((subset @ sK0 @ sK0)) != $true)),
% 0.08/0.17 inference(definition_unfolding,[],[f16,f17])).
% 0.08/0.17 thf(f26,plain,(
% 0.08/0.17 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK2 @ X1 @ X0) @ X1))) | ($true != $true) | (((subset @ X1 @ X0)) = $true)) )),
% 0.08/0.17 inference(definition_unfolding,[],[f22,f18])).
% 0.08/0.17 thf(f27,plain,(
% 0.08/0.17 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((subset @ X1 @ X0)) = $true) | (((in @ (sK2 @ X1 @ X0) @ X0)) != $true)) )),
% 0.08/0.17 inference(definition_unfolding,[],[f21,f18])).
% 0.08/0.17 thf(f30,plain,(
% 0.08/0.17 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK2 @ X1 @ X0) @ X0)) != $true) | (((subset @ X1 @ X0)) = $true)) )),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f27])).
% 0.08/0.17 thf(f31,plain,(
% 0.08/0.17 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK2 @ X1 @ X0) @ X1))) | (((subset @ X1 @ X0)) = $true)) )),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f26])).
% 0.08/0.17 thf(f32,plain,(
% 0.08/0.17 ( ! [X0 : $i] : (($true != $true) | (((subset @ X0 @ X0)) = $true) | (((subset @ X0 @ X0)) = $true)) )),
% 0.08/0.17 inference(constrained_superposition,[],[f30,f31])).
% 0.08/0.17 thf(f33,plain,(
% 0.08/0.17 ( ! [X0 : $i] : ((((subset @ X0 @ X0)) = $true) | ($true != $true)) )),
% 0.08/0.17 inference(duplicate_literal_removal,[],[f32])).
% 0.08/0.17 thf(f34,plain,(
% 0.08/0.17 ( ! [X0 : $i] : ((((subset @ X0 @ X0)) = $true)) )),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f33])).
% 0.08/0.17 thf(f35,plain,(
% 0.08/0.17 ($true != $true)),
% 0.08/0.17 inference(constrained_superposition,[],[f25,f34])).
% 0.08/0.17 thf(f36,plain,(
% 0.08/0.17 $false),
% 0.08/0.17 inference(trivial_inequality_removal,[],[f35])).
% 0.08/0.17 % SZS output end Proof for theBenchmark
% 0.08/0.17 % (136166)------------------------------
% 0.08/0.17 % (136166)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.17 % (136166)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.17 % (136166)CaDiCaL version: 2.1.3
% 0.08/0.17 % (136166)Termination reason: Refutation
% 0.08/0.17 % (136166)Time elapsed: 0.001 s
% 0.08/0.17 % (136166)Peak memory usage: 12 MB
% 0.08/0.17 % (136166)Instructions burned: 2 (million)
% 0.08/0.17 % (136161)Success in time 0.028 s
% 0.08/0.17 % Vampire exiting
%------------------------------------------------------------------------------