%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU609^2 : 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 : n003.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 08:30:18 AM UTC 2026
% Result : Theorem 0.22s 0.27s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU609^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n003.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:59:29 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 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
% 0.22/0.27 % (2546452)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.27 % (2546469)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1388897914:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.27 % (2546469)Refutation not found, incomplete strategy
% 0.22/0.27 % (2546469)------------------------------
% 0.22/0.27 % (2546469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (2546469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (2546469)CaDiCaL version: 2.1.3
% 0.22/0.27 % (2546469)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.27 % (2546469)Time elapsed: 0.001 s
% 0.22/0.27 % (2546469)Peak memory usage: 12 MB
% 0.22/0.27 % (2546469)Instructions burned: 1 (million)
% 0.22/0.27 % (2546469)------------------------------
% 0.22/0.27 % (2546469)------------------------------
% 0.22/0.27 % (2546474)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.27 % (2546474)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
% 0.22/0.27 % (2546467)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1484990397:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.27 % (2546468)lrs+10_16_si=on:nwc=1.5:random_seed=840187370:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.27 % (2546471)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=1935818336: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)
% 0.22/0.27 % (2546472)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3461173310:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.27 % (2546474)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=2399525954:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.27 % (2546473)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=73333881:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.27 % (2546467) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2546452-2546467"...
% 0.22/0.27 % (2546472) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2546452-2546472"...
% 0.22/0.27 % (2546468) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2546452-2546468"...
% 0.22/0.27 % (2546471) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2546452-2546471"...
% 0.22/0.27 % (2546473) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2546452-2546473"...
% 0.22/0.27 % (2546467)...printing done.
% 0.22/0.27 % (2546472)...printing done.
% 0.22/0.27 % (2546478)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3642526221:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.27 % (2546474) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2546452-2546474"...
% 0.22/0.27 % (2546468)...printing done.
% 0.22/0.27 % (2546467)Refutation found. Thanks to Tanya!
% 0.22/0.27 % SZS status Theorem for theBenchmark
% 0.22/0.27 % SZS output start Proof for theBenchmark
% 0.22/0.27 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.27 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.27 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.22/0.27 thf(func_def_2, type, subsetI2: $o).
% 0.22/0.27 thf(func_def_4, type, setminus: ($i > $i > $i)).
% 0.22/0.27 thf(func_def_5, type, setminusEL: $o).
% 0.22/0.27 thf(func_def_13, type, sK5: ($i > $i > $i)).
% 0.22/0.27 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.22/0.27 thf(f1,axiom,(
% 0.22/0.27 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.22/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 0.22/0.27 thf(f2,axiom,(
% 0.22/0.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X0)) = setminusEL)),
% 0.22/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL)).
% 0.22/0.27 thf(f3,conjecture,(
% 0.22/0.27 subsetI2 => (setminusEL => ! [X0 : $i,X1 : $i] : (subset @ (setminus @ X0 @ X1) @ X0))),
% 0.22/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub)).
% 0.22/0.27 thf(f4,negated_conjecture,(
% 0.22/0.27 ~(subsetI2 => (setminusEL => ! [X0 : $i,X1 : $i] : (subset @ (setminus @ X0 @ X1) @ X0)))),
% 0.22/0.27 inference(negated_conjecture,[status(cth)],[f3])).
% 0.22/0.27 thf(f5,plain,(
% 0.22/0.27 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.22/0.27 inference(rectify,[],[f1])).
% 0.22/0.27 thf(f6,plain,(
% 0.22/0.27 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true)) <=> (subsetI2 = $true)),
% 0.22/0.27 inference(fool_elimination,[],[f5])).
% 0.22/0.27 thf(f7,plain,(
% 0.22/0.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X0)) = setminusEL)),
% 0.22/0.27 inference(rectify,[],[f2])).
% 0.22/0.27 thf(f8,plain,(
% 0.22/0.27 ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ (setminus @ X0 @ X1))) = $true) => (((in @ X2 @ X0)) = $true)) <=> (setminusEL = $true)),
% 0.22/0.27 inference(fool_elimination,[],[f7])).
% 0.22/0.27 thf(f9,plain,(
% 0.22/0.27 ~(subsetI2 => (setminusEL => ! [X0 : $i,X1 : $i] : (subset @ (setminus @ X0 @ X1) @ X0)))),
% 0.22/0.27 inference(rectify,[],[f4])).
% 0.22/0.27 thf(f10,plain,(
% 0.22/0.27 ~((subsetI2 = $true) => ((setminusEL = $true) => ! [X1 : $i,X0 : $i] : (((subset @ (setminus @ X0 @ X1) @ X0)) = $true)))),
% 0.22/0.27 inference(fool_elimination,[],[f9])).
% 0.22/0.27 thf(f11,plain,(
% 0.22/0.27 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) <=> (subsetI2 = $true)),
% 0.22/0.27 inference(ennf_transformation,[],[f6])).
% 0.22/0.27 thf(f12,plain,(
% 0.22/0.27 ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (setminus @ X0 @ X1))) != $true) | (((in @ X2 @ X0)) = $true)) <=> (setminusEL = $true)),
% 0.22/0.27 inference(ennf_transformation,[],[f8])).
% 0.22/0.27 thf(f13,plain,(
% 0.22/0.27 (? [X0 : $i,X1 : $i] : (((subset @ (setminus @ X0 @ X1) @ X0)) != $true) & (setminusEL = $true)) & (subsetI2 = $true)),
% 0.22/0.27 inference(ennf_transformation,[],[f10])).
% 0.22/0.27 thf(f14,plain,(
% 0.22/0.27 (setminusEL = $true) & ? [X0 : $i,X1 : $i] : (((subset @ (setminus @ X0 @ X1) @ X0)) != $true) & (subsetI2 = $true)),
% 0.22/0.27 inference(flattening,[],[f13])).
% 0.22/0.27 thf(f15,plain,(
% 0.22/0.27 (setminusEL = $true) & ($true != ((subset @ (setminus @ sK0 @ sK1) @ sK0))) & (subsetI2 = $true)),
% 0.22/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14])).
% 0.22/0.27 thf(f16,plain,(
% 0.22/0.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (setminus @ X0 @ X1))) != $true) | (((in @ X2 @ X0)) = $true)) | (setminusEL != $true)) & ((setminusEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (setminus @ X0 @ X1))) = $true) & (((in @ X2 @ X0)) != $true)))),
% 0.22/0.27 inference(nnf_transformation,[],[f12])).
% 0.22/0.27 thf(f17,plain,(
% 0.22/0.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (setminus @ X0 @ X1))) != $true) | (((in @ X2 @ X0)) = $true)) | (setminusEL != $true)) & ((setminusEL = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ (setminus @ X3 @ X4))) = $true) & ($true != ((in @ X5 @ X3)))))),
% 0.22/0.27 inference(rectify,[],[f16])).
% 0.22/0.27 thf(f18,plain,(
% 0.22/0.27 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (setminus @ X0 @ X1))) != $true) | (((in @ X2 @ X0)) = $true)) | (setminusEL != $true)) & ((setminusEL = $true) | (($true = ((in @ sK4 @ (setminus @ sK2 @ sK3)))) & ($true != ((in @ sK4 @ sK2)))))),
% 0.22/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,sK2),skolemize(X4,sK3),skolemize(X5,sK4)],[f17])).
% 0.22/0.27 thf(f19,plain,(
% 0.22/0.27 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((subset @ X0 @ X1)) != $true)))),
% 0.22/0.27 inference(nnf_transformation,[],[f11])).
% 0.22/0.27 thf(f20,plain,(
% 0.22/0.27 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : ((((in @ X5 @ X4)) = $true) | ($true != ((in @ X5 @ X3)))) & ($true != ((subset @ X3 @ X4)))))),
% 0.22/0.27 inference(rectify,[],[f19])).
% 0.22/0.27 thf(f21,plain,(
% 0.22/0.27 (! [X0 : $i,X1 : $i] : (((((in @ (sK5 @ X1 @ X0) @ X1)) != $true) & ($true = ((in @ (sK5 @ X1 @ X0) @ X0)))) | (((subset @ X0 @ X1)) = $true)) | (subsetI2 != $true)) & ((subsetI2 = $true) | (! [X5 : $i] : ((((in @ X5 @ sK7)) = $true) | ($true != ((in @ X5 @ sK6)))) & ($true != ((subset @ sK6 @ sK7)))))),
% 0.22/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK6,sK7]),skolemize(X2,sK5 @ X1 @ X0),skolemize(X3,sK6),skolemize(X4,sK7)],[f20])).
% 0.22/0.27 thf(f22,plain,(
% 0.22/0.27 (subsetI2 = $true)),
% 0.22/0.27 inference(cnf_transformation,[],[f15])).
% 0.22/0.27 thf(f23,plain,(
% 0.22/0.27 ($true != ((subset @ (setminus @ sK0 @ sK1) @ sK0)))),
% 0.22/0.27 inference(cnf_transformation,[],[f15])).
% 0.22/0.27 thf(f24,plain,(
% 0.22/0.27 (setminusEL = $true)),
% 0.22/0.27 inference(cnf_transformation,[],[f15])).
% 0.22/0.27 thf(f27,plain,(
% 0.22/0.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (setminus @ X0 @ X1))) != $true) | (((in @ X2 @ X0)) = $true) | (setminusEL != $true)) )),
% 0.22/0.27 inference(cnf_transformation,[],[f18])).
% 0.22/0.27 thf(f30,plain,(
% 0.22/0.27 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK5 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true) | (subsetI2 != $true)) )),
% 0.22/0.27 inference(cnf_transformation,[],[f21])).
% 0.22/0.27 thf(f31,plain,(
% 0.22/0.27 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK5 @ X1 @ X0) @ X1)) != $true) | (((subset @ X0 @ X1)) = $true) | (subsetI2 != $true)) )),
% 0.22/0.27 inference(cnf_transformation,[],[f21])).
% 0.22/0.27 thf(f34,plain,(
% 0.22/0.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (setminus @ X0 @ X1))) != $true) | ($true != $true) | (((in @ X2 @ X0)) = $true)) )),
% 0.22/0.27 inference(definition_unfolding,[],[f27,f24])).
% 0.22/0.27 thf(f37,plain,(
% 0.22/0.27 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK5 @ X1 @ X0) @ X1)) != $true) | ($true != $true) | (((subset @ X0 @ X1)) = $true)) )),
% 0.22/0.27 inference(definition_unfolding,[],[f31,f22])).
% 0.22/0.27 thf(f38,plain,(
% 0.22/0.27 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($true = ((in @ (sK5 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.22/0.27 inference(definition_unfolding,[],[f30,f22])).
% 0.22/0.27 thf(f41,plain,(
% 0.22/0.27 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK5 @ X1 @ X0) @ X0))) | (((subset @ X0 @ X1)) = $true)) )),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f38])).
% 0.22/0.27 thf(f42,plain,(
% 0.22/0.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (setminus @ X0 @ X1))) != $true) | (((in @ X2 @ X0)) = $true)) )),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f34])).
% 0.22/0.27 thf(f43,plain,(
% 0.22/0.27 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK5 @ X1 @ X0) @ X1)) != $true) | (((subset @ X0 @ X1)) = $true)) )),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f37])).
% 0.22/0.27 thf(f44,plain,(
% 0.22/0.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((subset @ (setminus @ X1 @ X2) @ X0))) | ($true = ((in @ (sK5 @ X0 @ (setminus @ X1 @ X2)) @ X1))) | ($true != $true)) )),
% 0.22/0.27 inference(constrained_superposition,[],[f42,f41])).
% 0.22/0.27 thf(f45,plain,(
% 0.22/0.27 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK5 @ X0 @ (setminus @ X1 @ X2)) @ X1))) | ($true = ((subset @ (setminus @ X1 @ X2) @ X0)))) )),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f44])).
% 0.22/0.27 thf(f49,plain,(
% 0.22/0.27 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((subset @ (setminus @ X0 @ X1) @ X0)) = $true) | (((subset @ (setminus @ X0 @ X1) @ X0)) = $true)) )),
% 0.22/0.27 inference(constrained_superposition,[],[f43,f45])).
% 0.22/0.27 thf(f52,plain,(
% 0.22/0.27 ( ! [X0 : $i,X1 : $i] : ((((subset @ (setminus @ X0 @ X1) @ X0)) = $true) | ($true != $true)) )),
% 0.22/0.27 inference(duplicate_literal_removal,[],[f49])).
% 0.22/0.27 thf(f53,plain,(
% 0.22/0.27 ( ! [X0 : $i,X1 : $i] : ((((subset @ (setminus @ X0 @ X1) @ X0)) = $true)) )),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f52])).
% 0.22/0.27 thf(f54,plain,(
% 0.22/0.27 ($true != $true)),
% 0.22/0.27 inference(constrained_superposition,[],[f23,f53])).
% 0.22/0.27 thf(f55,plain,(
% 0.22/0.27 $false),
% 0.22/0.27 inference(trivial_inequality_removal,[],[f54])).
% 0.22/0.27 % SZS output end Proof for theBenchmark
% 0.22/0.27 % (2546467)------------------------------
% 0.22/0.27 % (2546467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (2546467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (2546467)CaDiCaL version: 2.1.3
% 0.22/0.27 % (2546467)Termination reason: Refutation
% 0.22/0.27 % (2546467)Time elapsed: 0.004 s
% 0.22/0.27 % (2546467)Peak memory usage: 12 MB
% 0.22/0.27 % (2546467)Instructions burned: 5 (million)
% 0.22/0.27 % (2546452)Success in time 0.037 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------