%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU588^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:30:12 AM UTC 2026
% Result : Theorem 0.09s 0.16s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU588^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 13:52:33 UTC 2026
% 0.00/0.10 % CPUTime :
% 0.00/0.10 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.12 Running higher-order theorem proving
% 0.09/0.13 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
% 0.09/0.16 % (141023)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.16 % (141034)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.16 % (141034)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
% 0.09/0.16 % (141031)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=1208298553: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)
% 0.09/0.16 % (141029)lrs+10_16_si=on:nwc=1.5:random_seed=1922842554:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.09/0.16 % (141030)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1486874275:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.09/0.16 % (141028)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1547720820:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.16 % (141032)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4056872880:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.09/0.16 % (141033)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1451061986:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.09/0.16 % (141034)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=1435131575:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.09/0.16 % (141030)Refutation not found, incomplete strategy
% 0.09/0.16 % (141030)------------------------------
% 0.09/0.16 % (141030)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.16 % (141030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.16 % (141030)CaDiCaL version: 2.1.3
% 0.09/0.16 % (141030)Termination reason: Refutation not found, incomplete strategy
% 0.09/0.16 % (141030)Time elapsed: 0.001 s
% 0.09/0.16 % (141030)Peak memory usage: 12 MB
% 0.09/0.16 % (141030)Instructions burned: 1 (million)
% 0.09/0.16 % (141028) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-141023-141028"...
% 0.09/0.16 % (141032) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-141023-141032"...
% 0.09/0.16 % (141030)------------------------------
% 0.09/0.16 % (141030)------------------------------
% 0.09/0.16 % (141033) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-141023-141033"...
% 0.09/0.16 % (141029) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-141023-141029"...
% 0.09/0.16 % (141031) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-141023-141031"...
% 0.09/0.16 % (141032)...printing done.
% 0.09/0.16 % (141028)...printing done.
% 0.09/0.16 % (141033)...printing done.
% 0.09/0.16 % (141029)...printing done.
% 0.09/0.16 % (141034) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-141023-141034"...
% 0.09/0.16 % (141032)Refutation found. Thanks to Tanya!
% 0.09/0.16 % SZS status Theorem for theBenchmark
% 0.09/0.16 % SZS output start Proof for theBenchmark
% 0.09/0.16 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.09/0.16 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.09/0.16 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.09/0.16 thf(func_def_2, type, subsetI2: $o).
% 0.09/0.16 thf(func_def_4, type, binunion: ($i > $i > $i)).
% 0.09/0.16 thf(func_def_5, type, binunionIR: $o).
% 0.09/0.16 thf(func_def_10, type, sK2: ($i > $i > $i)).
% 0.09/0.16 thf(f1,axiom,(
% 0.09/0.16 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.09/0.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 0.09/0.16 thf(f2,axiom,(
% 0.09/0.16 (binunionIR = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X0 @ X1))))),
% 0.09/0.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR)).
% 0.09/0.16 thf(f3,conjecture,(
% 0.09/0.16 subsetI2 => (binunionIR => ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1)))),
% 0.09/0.16 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub)).
% 0.09/0.16 thf(f4,negated_conjecture,(
% 0.09/0.16 ~(subsetI2 => (binunionIR => ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1))))),
% 0.09/0.16 inference(negated_conjecture,[status(cth)],[f3])).
% 0.09/0.16 thf(f5,plain,(
% 0.09/0.16 (binunionIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X2) => (in @ X0 @ (binunion @ X1 @ X2))))),
% 0.09/0.16 inference(rectify,[],[f2])).
% 0.09/0.16 thf(f6,plain,(
% 0.09/0.16 ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ X2))) => (((in @ X0 @ (binunion @ X1 @ X2))) = $true)) <=> (binunionIR = $true)),
% 0.09/0.16 inference(fool_elimination,[],[f5])).
% 0.09/0.16 thf(f7,plain,(
% 0.09/0.16 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.09/0.16 inference(rectify,[],[f1])).
% 0.09/0.16 thf(f8,plain,(
% 0.09/0.16 (subsetI2 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true))),
% 0.09/0.16 inference(fool_elimination,[],[f7])).
% 0.09/0.16 thf(f9,plain,(
% 0.09/0.16 ~(subsetI2 => (binunionIR => ! [X0 : $i,X1 : $i] : (subset @ X1 @ (binunion @ X0 @ X1))))),
% 0.09/0.16 inference(rectify,[],[f4])).
% 0.09/0.16 thf(f10,plain,(
% 0.09/0.16 ~((subsetI2 = $true) => ((binunionIR = $true) => ! [X0 : $i,X1 : $i] : (((subset @ X1 @ (binunion @ X0 @ X1))) = $true)))),
% 0.09/0.16 inference(fool_elimination,[],[f9])).
% 0.09/0.16 thf(f11,plain,(
% 0.09/0.16 (binunionIR = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (binunion @ X1 @ X2))) = $true) | ($true != ((in @ X0 @ X2))))),
% 0.09/0.16 inference(ennf_transformation,[],[f6])).
% 0.09/0.16 thf(f12,plain,(
% 0.09/0.16 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)) | (((subset @ X0 @ X1)) = $true))),
% 0.09/0.16 inference(ennf_transformation,[],[f8])).
% 0.09/0.16 thf(f13,plain,(
% 0.09/0.16 (? [X0 : $i,X1 : $i] : (((subset @ X1 @ (binunion @ X0 @ X1))) != $true) & (binunionIR = $true)) & (subsetI2 = $true)),
% 0.09/0.16 inference(ennf_transformation,[],[f10])).
% 0.09/0.16 thf(f14,plain,(
% 0.09/0.16 ? [X0 : $i,X1 : $i] : (((subset @ X1 @ (binunion @ X0 @ X1))) != $true) & (binunionIR = $true) & (subsetI2 = $true)),
% 0.09/0.16 inference(flattening,[],[f13])).
% 0.09/0.16 thf(f15,plain,(
% 0.09/0.16 ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true)) & (((subset @ X0 @ X1)) != $true))) & (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI2 != $true))),
% 0.09/0.16 inference(nnf_transformation,[],[f12])).
% 0.09/0.16 thf(f16,plain,(
% 0.09/0.16 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) & ($true != ((subset @ X1 @ X0))))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : ((((in @ X5 @ X4)) = $true) & (((in @ X5 @ X3)) != $true)) | (((subset @ X4 @ X3)) = $true)) | (subsetI2 != $true))),
% 0.09/0.16 inference(rectify,[],[f15])).
% 0.09/0.16 thf(f17,plain,(
% 0.09/0.16 ((subsetI2 = $true) | (! [X2 : $i] : (($true != ((in @ X2 @ sK1))) | ($true = ((in @ X2 @ sK0)))) & ($true != ((subset @ sK1 @ sK0))))) & (! [X3 : $i,X4 : $i] : ((($true = ((in @ (sK2 @ X4 @ X3) @ X4))) & ($true != ((in @ (sK2 @ X4 @ X3) @ X3)))) | (((subset @ X4 @ X3)) = $true)) | (subsetI2 != $true))),
% 0.09/0.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X5,sK2 @ X4 @ X3)],[f16])).
% 0.09/0.16 thf(f18,plain,(
% 0.09/0.16 (((subset @ sK4 @ (binunion @ sK3 @ sK4))) != $true) & (binunionIR = $true) & (subsetI2 = $true)),
% 0.09/0.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f14])).
% 0.09/0.16 thf(f19,plain,(
% 0.09/0.16 ((binunionIR = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (binunion @ X1 @ X2))) != $true) & ($true = ((in @ X0 @ X2))))) & (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (binunion @ X1 @ X2))) = $true) | ($true != ((in @ X0 @ X2)))) | (binunionIR != $true))),
% 0.09/0.16 inference(nnf_transformation,[],[f11])).
% 0.09/0.16 thf(f20,plain,(
% 0.09/0.16 ((binunionIR = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (binunion @ X1 @ X2))) != $true) & ($true = ((in @ X0 @ X2))))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ (binunion @ X4 @ X5))) = $true) | (((in @ X3 @ X5)) != $true)) | (binunionIR != $true))),
% 0.09/0.16 inference(rectify,[],[f19])).
% 0.09/0.16 thf(f21,plain,(
% 0.09/0.16 ((binunionIR = $true) | ((((in @ sK5 @ (binunion @ sK6 @ sK7))) != $true) & (((in @ sK5 @ sK7)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ (binunion @ X4 @ X5))) = $true) | (((in @ X3 @ X5)) != $true)) | (binunionIR != $true))),
% 0.09/0.16 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7)],[f20])).
% 0.09/0.16 thf(f22,plain,(
% 0.09/0.16 ( ! [X3 : $i,X4 : $i] : ((subsetI2 != $true) | (((subset @ X4 @ X3)) = $true) | ($true != ((in @ (sK2 @ X4 @ X3) @ X3)))) )),
% 0.09/0.16 inference(cnf_transformation,[],[f17])).
% 0.09/0.16 thf(f23,plain,(
% 0.09/0.16 ( ! [X3 : $i,X4 : $i] : ((subsetI2 != $true) | ($true = ((in @ (sK2 @ X4 @ X3) @ X4))) | (((subset @ X4 @ X3)) = $true)) )),
% 0.09/0.16 inference(cnf_transformation,[],[f17])).
% 0.09/0.16 thf(f26,plain,(
% 0.09/0.16 (subsetI2 = $true)),
% 0.09/0.16 inference(cnf_transformation,[],[f18])).
% 0.09/0.16 thf(f27,plain,(
% 0.09/0.16 (binunionIR = $true)),
% 0.09/0.16 inference(cnf_transformation,[],[f18])).
% 0.09/0.16 thf(f28,plain,(
% 0.09/0.16 (((subset @ sK4 @ (binunion @ sK3 @ sK4))) != $true)),
% 0.09/0.16 inference(cnf_transformation,[],[f18])).
% 0.09/0.16 thf(f29,plain,(
% 0.09/0.16 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((binunionIR != $true) | (((in @ X3 @ X5)) != $true) | (((in @ X3 @ (binunion @ X4 @ X5))) = $true)) )),
% 0.09/0.16 inference(cnf_transformation,[],[f21])).
% 0.09/0.16 thf(f35,plain,(
% 0.09/0.16 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (sK2 @ X4 @ X3) @ X3))) | (((subset @ X4 @ X3)) = $true)) )),
% 0.09/0.16 inference(forward_subsumption_resolution,[],[f22,f26])).
% 0.09/0.16 thf(f36,plain,(
% 0.09/0.16 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK2 @ X4 @ X3) @ X4))) | (((subset @ X4 @ X3)) = $true)) )),
% 0.09/0.16 inference(forward_subsumption_resolution,[],[f23,f26])).
% 0.09/0.16 thf(f40,plain,(
% 0.09/0.16 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ (binunion @ X4 @ X5))) = $true) | (((in @ X3 @ X5)) != $true)) )),
% 0.09/0.16 inference(forward_subsumption_resolution,[],[f29,f27])).
% 0.09/0.16 thf(f41,plain,(
% 0.09/0.16 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((subset @ X0 @ (binunion @ X1 @ X2)))) | ($true != ((in @ (sK2 @ X0 @ (binunion @ X1 @ X2)) @ X2)))) )),
% 0.09/0.16 inference(superposition,[],[f35,f40])).
% 0.09/0.16 thf(f42,plain,(
% 0.09/0.16 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK2 @ X0 @ (binunion @ X1 @ X2)) @ X2))) | ($true = ((subset @ X0 @ (binunion @ X1 @ X2))))) )),
% 0.09/0.16 inference(trivial_inequality_removal,[],[f41])).
% 0.09/0.16 thf(f43,plain,(
% 0.09/0.16 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ (binunion @ X1 @ X0))) = $true) | ($true != $true) | (((subset @ X0 @ (binunion @ X1 @ X0))) = $true)) )),
% 0.09/0.16 inference(superposition,[],[f42,f36])).
% 0.09/0.16 thf(f45,plain,(
% 0.09/0.16 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ (binunion @ X1 @ X0))) = $true) | ($true != $true)) )),
% 0.09/0.16 inference(duplicate_literal_removal,[],[f43])).
% 0.09/0.16 thf(f46,plain,(
% 0.09/0.16 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ (binunion @ X1 @ X0))) = $true)) )),
% 0.09/0.16 inference(trivial_inequality_removal,[],[f45])).
% 0.09/0.16 thf(f48,plain,(
% 0.09/0.16 ($true != $true)),
% 0.09/0.16 inference(superposition,[],[f28,f46])).
% 0.09/0.16 thf(f49,plain,(
% 0.09/0.16 $false),
% 0.09/0.16 inference(trivial_inequality_removal,[],[f48])).
% 0.09/0.16 % SZS output end Proof for theBenchmark
% 0.09/0.16 % (141032)------------------------------
% 0.09/0.16 % (141032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.16 % (141032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.16 % (141032)CaDiCaL version: 2.1.3
% 0.09/0.16 % (141032)Termination reason: Refutation
% 0.09/0.16 % (141032)Time elapsed: 0.002 s
% 0.09/0.16 % (141032)Peak memory usage: 12 MB
% 0.09/0.16 % (141032)Instructions burned: 5 (million)
% 0.09/0.16 % (141023)Success in time 0.03 s
% 0.09/0.16 % Vampire exiting
%------------------------------------------------------------------------------