%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU592^2 : 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 : n007.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 08:30:13 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU592^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n007.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:51:41 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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
% 0.20/0.29 % (3400934)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (3400939)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2397945038:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (3400945)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (3400945)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
% 0.20/0.29 % (3400940)lrs+10_16_si=on:nwc=1.5:random_seed=3800585758:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (3400941)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2692287599:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (3400945)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=3683870454:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (3400943)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3658081942:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (3400942)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=192017882: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)
% 0.20/0.29 % (3400944)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4144524698:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (3400941)Refutation not found, incomplete strategy
% 0.20/0.29 % (3400941)------------------------------
% 0.20/0.29 % (3400941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3400941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3400941)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3400941)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (3400941)Time elapsed: 0.002 s
% 0.20/0.29 % (3400941)Peak memory usage: 12 MB
% 0.20/0.29 % (3400941)Instructions burned: 2 (million)
% 0.20/0.29 % (3400941)------------------------------
% 0.20/0.29 % (3400941)------------------------------
% 0.20/0.29 % (3400942) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3400934-3400942"...
% 0.20/0.29 % (3400943) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3400934-3400943"...
% 0.20/0.29 % (3400944) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3400934-3400944"...
% 0.20/0.29 % (3400940) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3400934-3400940"...
% 0.20/0.29 % (3400943)...printing done.
% 0.20/0.29 % (3400942)...printing done.
% 0.20/0.29 % (3400944)...printing done.
% 0.20/0.29 % (3400943)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% 0.20/0.29 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.29 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.29 thf(func_def_1, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.20/0.29 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.20/0.29 thf(func_def_3, type, subsetI2: $o).
% 0.20/0.29 thf(func_def_5, type, binintersect: ($i > $i > $i)).
% 0.20/0.29 thf(func_def_6, type, binintersectEL: $o).
% 0.20/0.29 thf(func_def_9, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.29 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.29 thf(func_def_19, type, sK7: ($i > $i > $i)).
% 0.20/0.29 thf(f1,axiom,(
% 0.20/0.29 (subsetI2 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 0.20/0.29 thf(f3,axiom,(
% 0.20/0.29 (binintersectEL = ! [X1 : $i,X0 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL)).
% 0.20/0.29 thf(f4,conjecture,(
% 0.20/0.29 subsetI2 => (binintersectEL => ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0))),
% 0.20/0.29 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub)).
% 0.20/0.29 thf(f5,negated_conjecture,(
% 0.20/0.29 ~(subsetI2 => (binintersectEL => ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0)))),
% 0.20/0.29 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.29 thf(f6,plain,(
% 0.20/0.29 ~(subsetI2 => (binintersectEL => ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0)))),
% 0.20/0.29 inference(rectify,[],[f5])).
% 0.20/0.29 thf(f7,plain,(
% 0.20/0.29 ~((subsetI2 = $true) => ((binintersectEL = $true) => ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X0)) = $true)))),
% 0.20/0.29 inference(fool_elimination,[],[f6])).
% 0.20/0.29 thf(f8,plain,(
% 0.20/0.29 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 0.20/0.29 inference(rectify,[],[f1])).
% 0.20/0.29 thf(f9,plain,(
% 0.20/0.29 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f8])).
% 0.20/0.29 thf(f10,plain,(
% 0.20/0.29 (binintersectEL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X1 @ X0)) => (in @ X2 @ X1)))),
% 0.20/0.29 inference(rectify,[],[f3])).
% 0.20/0.29 thf(f11,plain,(
% 0.20/0.29 (binintersectEL = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X2 @ (binintersect @ X1 @ X0)))) => (((in @ X2 @ X1)) = $true))),
% 0.20/0.29 inference(fool_elimination,[],[f10])).
% 0.20/0.29 thf(f14,plain,(
% 0.20/0.29 (? [X1 : $i,X0 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X0)) != $true) & (binintersectEL = $true)) & (subsetI2 = $true)),
% 0.20/0.29 inference(ennf_transformation,[],[f7])).
% 0.20/0.29 thf(f15,plain,(
% 0.20/0.29 (subsetI2 = $true) & ? [X1 : $i,X0 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X0)) != $true) & (binintersectEL = $true)),
% 0.20/0.29 inference(flattening,[],[f14])).
% 0.20/0.29 thf(f16,plain,(
% 0.20/0.29 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true))),
% 0.20/0.29 inference(ennf_transformation,[],[f9])).
% 0.20/0.29 thf(f17,plain,(
% 0.20/0.29 ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) = $true) | ($true != ((in @ X2 @ (binintersect @ X1 @ X0))))) <=> (binintersectEL = $true)),
% 0.20/0.29 inference(ennf_transformation,[],[f11])).
% 0.20/0.29 thf(f18,plain,(
% 0.20/0.29 (subsetI2 = $true) & ? [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X0) @ X1)) != $true) & (binintersectEL = $true)),
% 0.20/0.29 inference(rectify,[],[f15])).
% 0.20/0.29 thf(f19,plain,(
% 0.20/0.29 (subsetI2 = $true) & (((subset @ (binintersect @ sK1 @ sK0) @ sK1)) != $true) & (binintersectEL = $true)),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f18])).
% 0.20/0.29 thf(f20,plain,(
% 0.20/0.29 (! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) = $true) | ($true != ((in @ X2 @ (binintersect @ X1 @ X0))))) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) != $true) & ($true = ((in @ X2 @ (binintersect @ X1 @ X0))))))),
% 0.20/0.29 inference(nnf_transformation,[],[f17])).
% 0.20/0.29 thf(f21,plain,(
% 0.20/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X2)) = $true) | (((in @ X0 @ (binintersect @ X2 @ X1))) != $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X3 @ X5))) & (((in @ X3 @ (binintersect @ X5 @ X4))) = $true)))),
% 0.20/0.29 inference(rectify,[],[f20])).
% 0.20/0.29 thf(f22,plain,(
% 0.20/0.29 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X2)) = $true) | (((in @ X0 @ (binintersect @ X2 @ X1))) != $true)) | (binintersectEL != $true)) & ((binintersectEL = $true) | ((((in @ sK2 @ sK4)) != $true) & (((in @ sK2 @ (binintersect @ sK4 @ sK3))) = $true)))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2),skolemize(X4,sK3),skolemize(X5,sK4)],[f21])).
% 0.20/0.29 thf(f23,plain,(
% 0.20/0.29 ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) & (((subset @ X1 @ X0)) != $true))) & (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)) | (((subset @ X1 @ X0)) = $true)) | (subsetI2 != $true))),
% 0.20/0.29 inference(nnf_transformation,[],[f16])).
% 0.20/0.29 thf(f24,plain,(
% 0.20/0.29 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((subset @ X0 @ X1)) != $true))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true != ((in @ X5 @ X4))) & ($true = ((in @ X5 @ X3)))) | (((subset @ X3 @ X4)) = $true)) | (subsetI2 != $true))),
% 0.20/0.29 inference(rectify,[],[f23])).
% 0.20/0.29 thf(f25,plain,(
% 0.20/0.29 ((subsetI2 = $true) | (! [X2 : $i] : (($true = ((in @ X2 @ sK6))) | (((in @ X2 @ sK5)) != $true)) & ($true != ((subset @ sK5 @ sK6))))) & (! [X3 : $i,X4 : $i] : (((((in @ (sK7 @ X4 @ X3) @ X4)) != $true) & (((in @ (sK7 @ X4 @ X3) @ X3)) = $true)) | (((subset @ X3 @ X4)) = $true)) | (subsetI2 != $true))),
% 0.20/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,vAPP]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X5,sK7 @ X4 @ X3)],[f24])).
% 0.20/0.29 thf(f26,plain,(
% 0.20/0.29 (binintersectEL = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f19])).
% 0.20/0.29 thf(f27,plain,(
% 0.20/0.29 (((subset @ (binintersect @ sK1 @ sK0) @ sK1)) != $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f19])).
% 0.20/0.29 thf(f28,plain,(
% 0.20/0.29 (subsetI2 = $true)),
% 0.20/0.29 inference(cnf_transformation,[],[f19])).
% 0.20/0.29 thf(f31,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((binintersectEL != $true) | (((in @ X0 @ X2)) = $true) | (((in @ X0 @ (binintersect @ X2 @ X1))) != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f22])).
% 0.20/0.29 thf(f32,plain,(
% 0.20/0.29 ( ! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | (((in @ (sK7 @ X4 @ X3) @ X3)) = $true) | (subsetI2 != $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f25])).
% 0.20/0.29 thf(f33,plain,(
% 0.20/0.29 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK7 @ X4 @ X3) @ X4)) != $true) | (subsetI2 != $true) | (((subset @ X3 @ X4)) = $true)) )),
% 0.20/0.29 inference(cnf_transformation,[],[f25])).
% 0.20/0.29 thf(f40,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (binintersect @ X2 @ X1))) != $true) | (((in @ X0 @ X2)) = $true)) )),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f31,f26])).
% 0.20/0.29 thf(f41,plain,(
% 0.20/0.29 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK7 @ X4 @ X3) @ X3)) = $true) | (((subset @ X3 @ X4)) = $true)) )),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f32,f28])).
% 0.20/0.29 thf(f42,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ (binintersect @ X1 @ X2) @ X0)) = $true) | (((in @ (sK7 @ X0 @ (binintersect @ X1 @ X2)) @ X1)) = $true) | ($true != $true)) )),
% 0.20/0.29 inference(superposition,[],[f40,f41])).
% 0.20/0.29 thf(f43,plain,(
% 0.20/0.29 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK7 @ X0 @ (binintersect @ X1 @ X2)) @ X1)) = $true) | (((subset @ (binintersect @ X1 @ X2) @ X0)) = $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f42])).
% 0.20/0.29 thf(f52,plain,(
% 0.20/0.29 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK7 @ X4 @ X3) @ X4)) != $true) | (((subset @ X3 @ X4)) = $true)) )),
% 0.20/0.29 inference(forward_subsumption_resolution,[],[f33,f28])).
% 0.20/0.29 thf(f54,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((subset @ (binintersect @ X0 @ X1) @ X0)) = $true) | (((subset @ (binintersect @ X0 @ X1) @ X0)) = $true)) )),
% 0.20/0.29 inference(superposition,[],[f52,f43])).
% 0.20/0.29 thf(f64,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : ((((subset @ (binintersect @ X0 @ X1) @ X0)) = $true) | ($true != $true)) )),
% 0.20/0.29 inference(duplicate_literal_removal,[],[f54])).
% 0.20/0.29 thf(f65,plain,(
% 0.20/0.29 ( ! [X0 : $i,X1 : $i] : ((((subset @ (binintersect @ X0 @ X1) @ X0)) = $true)) )),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f64])).
% 0.20/0.29 thf(f68,plain,(
% 0.20/0.29 ($true != $true)),
% 0.20/0.29 inference(superposition,[],[f27,f65])).
% 0.20/0.29 thf(f69,plain,(
% 0.20/0.29 $false),
% 0.20/0.29 inference(trivial_inequality_removal,[],[f68])).
% 0.20/0.29 % SZS output end Proof for theBenchmark
% 0.20/0.29 % (3400943)------------------------------
% 0.20/0.29 % (3400943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3400943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3400943)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3400943)Termination reason: Refutation
% 0.20/0.29 % (3400943)Time elapsed: 0.005 s
% 0.20/0.29 % (3400943)Peak memory usage: 12 MB
% 0.20/0.29 % (3400943)Instructions burned: 7 (million)
% 0.20/0.29 % (3400934)Success in time 0.048 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------