%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU604^2 : 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 : 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 08:30:17 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU604^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:55:11 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.30 % (3402767)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (3402785)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=4207074177: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)
% 0.22/0.30 % (3402788)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (3402788)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
% 0.22/0.30 % (3402782)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2389767637:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (3402786)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1059187401:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (3402784)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2041612691:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (3402783)lrs+10_16_si=on:nwc=1.5:random_seed=1309330947:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (3402787)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3894281986:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (3402788)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=927006275:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (3402784)Instruction limit reached!
% 0.22/0.30 % (3402784)------------------------------
% 0.22/0.30 % (3402784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (3402784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (3402784)CaDiCaL version: 2.1.3
% 0.22/0.30 % (3402784)Termination reason: Instruction limit
% 0.22/0.30 % (3402784)Termination phase: Saturation
% 0.22/0.30 % (3402784)Time elapsed: 0.002 s
% 0.22/0.30 % (3402784)Peak memory usage: 12 MB
% 0.22/0.30 % (3402784)Instructions burned: 3 (million)
% 0.22/0.30 % (3402786) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3402767-3402786"...
% 0.22/0.30 % (3402782) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3402767-3402782"...
% 0.22/0.30 % (3402786)...printing done.
% 0.22/0.30 % (3402787) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3402767-3402787"...
% 0.22/0.30 % (3402786)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.30 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.22/0.30 thf(func_def_3, type, subsetI2: $o).
% 0.22/0.30 thf(func_def_5, type, subsetE: $o).
% 0.22/0.30 thf(func_def_6, type, subsetemptysetimpeq: $o).
% 0.22/0.30 thf(func_def_7, type, setminus: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_8, type, setminusEL: $o).
% 0.22/0.30 thf(func_def_9, type, setminusER: $o).
% 0.22/0.30 thf(func_def_14, type, sK2: ($i > $i > $i)).
% 0.22/0.30 thf(f1,axiom,(
% 0.22/0.30 (subsetI2 = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 0.22/0.30 thf(f2,axiom,(
% 0.22/0.30 (subsetE = ! [X0 : $i,X2 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
% 0.22/0.30 thf(f3,axiom,(
% 0.22/0.30 (subsetemptysetimpeq = ! [X0 : $i] : ((subset @ X0 @ emptyset) => (X0 = emptyset)))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq)).
% 0.22/0.30 thf(f4,axiom,(
% 0.22/0.30 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X0)) = setminusEL)),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL)).
% 0.22/0.30 thf(f5,axiom,(
% 0.22/0.30 (setminusER = ! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER)).
% 0.22/0.30 thf(f6,conjecture,(
% 0.22/0.30 subsetI2 => (subsetE => (subsetemptysetimpeq => (setminusEL => (setminusER => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (((setminus @ X0 @ X1)) = emptyset))))))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2)).
% 0.22/0.30 thf(f7,negated_conjecture,(
% 0.22/0.30 ~(subsetI2 => (subsetE => (subsetemptysetimpeq => (setminusEL => (setminusER => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => (((setminus @ X0 @ X1)) = emptyset)))))))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f6])).
% 0.22/0.30 thf(f8,plain,(
% 0.22/0.30 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setminus @ X2 @ X0)) => ~(in @ X1 @ X0)))),
% 0.22/0.30 inference(rectify,[],[f5])).
% 0.22/0.30 thf(f9,plain,(
% 0.22/0.30 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X1 @ (setminus @ X2 @ X0)))) => ~ ($true = ((in @ X1 @ X0))))),
% 0.22/0.30 inference(fool_elimination,[],[f8])).
% 0.22/0.30 thf(f10,plain,(
% 0.22/0.30 (subsetI2 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 0.22/0.30 inference(rectify,[],[f1])).
% 0.22/0.30 thf(f11,plain,(
% 0.22/0.30 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => ($true = ((subset @ X1 @ X0)))) <=> (subsetI2 = $true)),
% 0.22/0.30 inference(fool_elimination,[],[f10])).
% 0.22/0.30 thf(f12,plain,(
% 0.22/0.30 (subsetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ X2))))),
% 0.22/0.30 inference(rectify,[],[f2])).
% 0.22/0.30 thf(f13,plain,(
% 0.22/0.30 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X0 @ X2)) = $true) => (($true = ((in @ X1 @ X0))) => ($true = ((in @ X1 @ X2)))))),
% 0.22/0.30 inference(fool_elimination,[],[f12])).
% 0.22/0.30 thf(f14,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X2 @ X1)) => (in @ X0 @ X2)) = setminusEL)),
% 0.22/0.30 inference(rectify,[],[f4])).
% 0.22/0.30 thf(f15,plain,(
% 0.22/0.30 (setminusEL = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (setminus @ X2 @ X1)))) => ($true = ((in @ X0 @ X2))))),
% 0.22/0.30 inference(fool_elimination,[],[f14])).
% 0.22/0.30 thf(f16,plain,(
% 0.22/0.30 (subsetemptysetimpeq = ! [X0 : $i] : ((subset @ X0 @ emptyset) => (X0 = emptyset)))),
% 0.22/0.30 inference(rectify,[],[f3])).
% 0.22/0.30 thf(f17,plain,(
% 0.22/0.30 ! [X0 : $i] : ((((subset @ X0 @ emptyset)) = $true) => (emptyset = X0)) <=> (subsetemptysetimpeq = $true)),
% 0.22/0.30 inference(fool_elimination,[],[f16])).
% 0.22/0.30 thf(f18,plain,(
% 0.22/0.30 ~(subsetI2 => (subsetE => (subsetemptysetimpeq => (setminusEL => (setminusER => ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => (emptyset = ((setminus @ X1 @ X0)))))))))),
% 0.22/0.30 inference(rectify,[],[f7])).
% 0.22/0.30 thf(f19,plain,(
% 0.22/0.30 ~((subsetI2 = $true) => ((subsetE = $true) => ((subsetemptysetimpeq = $true) => ((setminusEL = $true) => ((setminusER = $true) => ! [X1 : $i,X0 : $i] : (($true = ((subset @ X1 @ X0))) => (emptyset = ((setminus @ X1 @ X0)))))))))),
% 0.22/0.30 inference(fool_elimination,[],[f18])).
% 0.22/0.30 thf(f20,plain,(
% 0.22/0.30 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X1 @ (setminus @ X2 @ X0)))) => ($true != ((in @ X1 @ X0))))),
% 0.22/0.30 inference(flattening,[],[f9])).
% 0.22/0.30 thf(f21,plain,(
% 0.22/0.30 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((($true = ((in @ X1 @ X2))) | ($true != ((in @ X1 @ X0)))) | (((subset @ X0 @ X2)) != $true))),
% 0.22/0.30 inference(ennf_transformation,[],[f13])).
% 0.22/0.30 thf(f22,plain,(
% 0.22/0.30 ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X1 @ X0))) | (((subset @ X0 @ X2)) != $true) | ($true = ((in @ X1 @ X2)))) <=> (subsetE = $true)),
% 0.22/0.30 inference(flattening,[],[f21])).
% 0.22/0.30 thf(f23,plain,(
% 0.22/0.30 (subsetemptysetimpeq = $true) <=> ! [X0 : $i] : ((emptyset = X0) | (((subset @ X0 @ emptyset)) != $true))),
% 0.22/0.30 inference(ennf_transformation,[],[f17])).
% 0.22/0.30 thf(f24,plain,(
% 0.22/0.30 (setminusEL = $true) <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ X2))) | ($true != ((in @ X0 @ (setminus @ X2 @ X1)))))),
% 0.22/0.30 inference(ennf_transformation,[],[f15])).
% 0.22/0.30 thf(f25,plain,(
% 0.22/0.30 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X1 @ X0))) | ($true != ((in @ X1 @ (setminus @ X2 @ X0)))))),
% 0.22/0.30 inference(ennf_transformation,[],[f20])).
% 0.22/0.30 thf(f26,plain,(
% 0.22/0.30 (subsetI2 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true)))),
% 0.22/0.30 inference(ennf_transformation,[],[f11])).
% 0.22/0.30 thf(f27,plain,(
% 0.22/0.30 ((((? [X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) & (emptyset != ((setminus @ X1 @ X0)))) & (setminusER = $true)) & (setminusEL = $true)) & (subsetemptysetimpeq = $true)) & (subsetE = $true)) & (subsetI2 = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f19])).
% 0.22/0.30 thf(f28,plain,(
% 0.22/0.30 (subsetemptysetimpeq = $true) & ? [X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) & (emptyset != ((setminus @ X1 @ X0)))) & (subsetE = $true) & (setminusER = $true) & (subsetI2 = $true) & (setminusEL = $true)),
% 0.22/0.30 inference(flattening,[],[f27])).
% 0.22/0.30 thf(f29,plain,(
% 0.22/0.30 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (($true != ((subset @ X1 @ X0))) & ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)))) & (! [X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) | (subsetI2 != $true))),
% 0.22/0.30 inference(nnf_transformation,[],[f26])).
% 0.22/0.30 thf(f30,plain,(
% 0.22/0.30 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : (($true != ((subset @ X1 @ X0))) & ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)))) & (! [X3 : $i,X4 : $i] : (($true = ((subset @ X4 @ X3))) | ? [X5 : $i] : (($true != ((in @ X5 @ X3))) & ($true = ((in @ X5 @ X4))))) | (subsetI2 != $true))),
% 0.22/0.30 inference(rectify,[],[f29])).
% 0.22/0.30 thf(f31,plain,(
% 0.22/0.30 ((subsetI2 = $true) | ((((subset @ sK1 @ sK0)) != $true) & ! [X2 : $i] : (($true = ((in @ X2 @ sK0))) | ($true != ((in @ X2 @ sK1)))))) & (! [X3 : $i,X4 : $i] : (($true = ((subset @ X4 @ X3))) | (($true != ((in @ (sK2 @ X4 @ X3) @ X3))) & ($true = ((in @ (sK2 @ X4 @ X3) @ X4))))) | (subsetI2 != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X5,sK2 @ X4 @ X3)],[f30])).
% 0.22/0.30 thf(f32,plain,(
% 0.22/0.30 ((subsetemptysetimpeq = $true) | ? [X0 : $i] : ((emptyset != X0) & (((subset @ X0 @ emptyset)) = $true))) & (! [X0 : $i] : ((emptyset = X0) | (((subset @ X0 @ emptyset)) != $true)) | (subsetemptysetimpeq != $true))),
% 0.22/0.30 inference(nnf_transformation,[],[f23])).
% 0.22/0.30 thf(f33,plain,(
% 0.22/0.30 ((subsetemptysetimpeq = $true) | ? [X0 : $i] : ((emptyset != X0) & (((subset @ X0 @ emptyset)) = $true))) & (! [X1 : $i] : ((emptyset = X1) | ($true != ((subset @ X1 @ emptyset)))) | (subsetemptysetimpeq != $true))),
% 0.22/0.30 inference(rectify,[],[f32])).
% 0.22/0.30 thf(f34,plain,(
% 0.22/0.30 ((subsetemptysetimpeq = $true) | ((emptyset != sK3) & (((subset @ sK3 @ emptyset)) = $true))) & (! [X1 : $i] : ((emptyset = X1) | ($true != ((subset @ X1 @ emptyset)))) | (subsetemptysetimpeq != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3)],[f33])).
% 0.22/0.30 thf(f35,plain,(
% 0.22/0.30 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X1 @ X0))) & ($true = ((in @ X1 @ (setminus @ X2 @ X0)))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X1 @ X0))) | ($true != ((in @ X1 @ (setminus @ X2 @ X0))))) | (setminusER != $true))),
% 0.22/0.30 inference(nnf_transformation,[],[f25])).
% 0.22/0.30 thf(f36,plain,(
% 0.22/0.30 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X1 @ X0))) & ($true = ((in @ X1 @ (setminus @ X2 @ X0)))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X3))) | ($true != ((in @ X4 @ (setminus @ X5 @ X3))))) | (setminusER != $true))),
% 0.22/0.30 inference(rectify,[],[f35])).
% 0.22/0.30 thf(f37,plain,(
% 0.22/0.30 ((setminusER = $true) | (($true = ((in @ sK5 @ sK4))) & ($true = ((in @ sK5 @ (setminus @ sK6 @ sK4)))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ X3))) | ($true != ((in @ X4 @ (setminus @ X5 @ X3))))) | (setminusER != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f36])).
% 0.22/0.30 thf(f38,plain,(
% 0.22/0.30 (! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X1 @ X0))) | (((subset @ X0 @ X2)) != $true) | ($true = ((in @ X1 @ X2)))) | (subsetE != $true)) & ((subsetE = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ X0))) & (((subset @ X0 @ X2)) = $true) & ($true != ((in @ X1 @ X2)))))),
% 0.22/0.30 inference(nnf_transformation,[],[f22])).
% 0.22/0.30 thf(f39,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) != $true) | ($true != ((subset @ X1 @ X0))) | (((in @ X2 @ X0)) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X5 @ X4))) & ($true = ((subset @ X4 @ X3))) & ($true != ((in @ X5 @ X3)))))),
% 0.22/0.30 inference(rectify,[],[f38])).
% 0.22/0.30 thf(f40,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) != $true) | ($true != ((subset @ X1 @ X0))) | (((in @ X2 @ X0)) = $true)) | (subsetE != $true)) & ((subsetE = $true) | (($true = ((in @ sK9 @ sK8))) & ($true = ((subset @ sK8 @ sK7))) & ($true != ((in @ sK9 @ sK7)))))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X3,sK7),skolemize(X4,sK8),skolemize(X5,sK9)],[f39])).
% 0.22/0.30 thf(f41,plain,(
% 0.22/0.30 (subsetemptysetimpeq = $true) & (($true = ((subset @ sK11 @ sK10))) & (emptyset != ((setminus @ sK11 @ sK10)))) & (subsetE = $true) & (setminusER = $true) & (subsetI2 = $true) & (setminusEL = $true)),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f28])).
% 0.22/0.30 thf(f42,plain,(
% 0.22/0.30 ((setminusEL = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ X2))) & ($true = ((in @ X0 @ (setminus @ X2 @ X1)))))) & (! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ X2))) | ($true != ((in @ X0 @ (setminus @ X2 @ X1))))) | (setminusEL != $true))),
% 0.22/0.30 inference(nnf_transformation,[],[f24])).
% 0.22/0.30 thf(f43,plain,(
% 0.22/0.30 ((setminusEL = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true != ((in @ X1 @ X0))) & (((in @ X1 @ (setminus @ X0 @ X2))) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X4 @ X3))) | ($true != ((in @ X4 @ (setminus @ X3 @ X5))))) | (setminusEL != $true))),
% 0.22/0.30 inference(rectify,[],[f42])).
% 0.22/0.30 thf(f44,plain,(
% 0.22/0.30 ((setminusEL = $true) | (($true != ((in @ sK13 @ sK12))) & ($true = ((in @ sK13 @ (setminus @ sK12 @ sK14)))))) & (! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X4 @ X3))) | ($true != ((in @ X4 @ (setminus @ X3 @ X5))))) | (setminusEL != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f43])).
% 0.22/0.30 thf(f45,plain,(
% 0.22/0.30 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK2 @ X4 @ X3) @ X4))) | (subsetI2 != $true) | ($true = ((subset @ X4 @ X3)))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f31])).
% 0.22/0.30 thf(f49,plain,(
% 0.22/0.30 ( ! [X1 : $i] : (($true != ((subset @ X1 @ emptyset))) | (subsetemptysetimpeq != $true) | (emptyset = X1)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f34])).
% 0.22/0.30 thf(f52,plain,(
% 0.22/0.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ (setminus @ X5 @ X3)))) | (setminusER != $true) | ($true != ((in @ X4 @ X3)))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f37])).
% 0.22/0.30 thf(f58,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((subsetE != $true) | ($true != ((subset @ X1 @ X0))) | (((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f40])).
% 0.22/0.30 thf(f59,plain,(
% 0.22/0.30 (setminusEL = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f41])).
% 0.22/0.30 thf(f60,plain,(
% 0.22/0.30 (subsetI2 = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f41])).
% 0.22/0.30 thf(f61,plain,(
% 0.22/0.30 (setminusER = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f41])).
% 0.22/0.30 thf(f62,plain,(
% 0.22/0.30 (subsetE = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f41])).
% 0.22/0.30 thf(f63,plain,(
% 0.22/0.30 (emptyset != ((setminus @ sK11 @ sK10)))),
% 0.22/0.30 inference(cnf_transformation,[],[f41])).
% 0.22/0.30 thf(f64,plain,(
% 0.22/0.30 ($true = ((subset @ sK11 @ sK10)))),
% 0.22/0.30 inference(cnf_transformation,[],[f41])).
% 0.22/0.30 thf(f65,plain,(
% 0.22/0.30 (subsetemptysetimpeq = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f41])).
% 0.22/0.30 thf(f66,plain,(
% 0.22/0.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = ((in @ X4 @ X3))) | (setminusEL != $true) | ($true != ((in @ X4 @ (setminus @ X3 @ X5))))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f44])).
% 0.22/0.30 thf(f75,plain,(
% 0.22/0.30 ( ! [X1 : $i] : (($true != ((subset @ X1 @ emptyset))) | (emptyset = X1)) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f49,f65])).
% 0.22/0.30 thf(f76,plain,(
% 0.22/0.30 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK2 @ X4 @ X3) @ X4))) | ($true = ((subset @ X4 @ X3)))) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f45,f60])).
% 0.22/0.30 thf(f81,plain,(
% 0.22/0.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ (setminus @ X5 @ X3)))) | ($true != ((in @ X4 @ X3)))) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f52,f61])).
% 0.22/0.30 thf(f82,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK2 @ (setminus @ X0 @ X1) @ X2) @ X1))) | ($true != $true) | ($true = ((subset @ (setminus @ X0 @ X1) @ X2)))) )),
% 0.22/0.30 inference(superposition,[],[f81,f76])).
% 0.22/0.30 thf(f83,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK2 @ (setminus @ X0 @ X1) @ X2) @ X1))) | ($true = ((subset @ (setminus @ X0 @ X1) @ X2)))) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f82])).
% 0.22/0.30 thf(f84,plain,(
% 0.22/0.30 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != ((in @ X4 @ (setminus @ X3 @ X5)))) | ($true = ((in @ X4 @ X3)))) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f66,f59])).
% 0.22/0.30 thf(f85,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((subset @ (setminus @ X0 @ X1) @ X2))) | ($true = ((in @ (sK2 @ (setminus @ X0 @ X1) @ X2) @ X0)))) )),
% 0.22/0.30 inference(superposition,[],[f84,f76])).
% 0.22/0.30 thf(f86,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK2 @ (setminus @ X0 @ X1) @ X2) @ X0))) | ($true = ((subset @ (setminus @ X0 @ X1) @ X2)))) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f85])).
% 0.22/0.30 thf(f87,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((subset @ X1 @ X0))) | (((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f58,f62])).
% 0.22/0.30 thf(f88,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != $true) | ($true != ((in @ X0 @ sK11))) | ($true = ((in @ X0 @ sK10)))) )),
% 0.22/0.30 inference(superposition,[],[f87,f64])).
% 0.22/0.30 thf(f90,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != ((in @ X0 @ sK11))) | ($true = ((in @ X0 @ sK10)))) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f88])).
% 0.22/0.30 thf(f100,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ (setminus @ sK11 @ X0) @ X1))) | ($true = ((in @ (sK2 @ (setminus @ sK11 @ X0) @ X1) @ sK10))) | ($true != $true)) )),
% 0.22/0.30 inference(superposition,[],[f90,f86])).
% 0.22/0.30 thf(f102,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK2 @ (setminus @ sK11 @ X0) @ X1) @ sK10))) | ($true = ((subset @ (setminus @ sK11 @ X0) @ X1)))) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f100])).
% 0.22/0.30 thf(f131,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true = ((subset @ (setminus @ sK11 @ sK10) @ X0))) | ($true = ((subset @ (setminus @ sK11 @ sK10) @ X0))) | ($true != $true)) )),
% 0.22/0.30 inference(superposition,[],[f83,f102])).
% 0.22/0.30 thf(f133,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != $true) | ($true = ((subset @ (setminus @ sK11 @ sK10) @ X0)))) )),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f131])).
% 0.22/0.30 thf(f134,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true = ((subset @ (setminus @ sK11 @ sK10) @ X0)))) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f133])).
% 0.22/0.30 thf(f137,plain,(
% 0.22/0.30 (emptyset = ((setminus @ sK11 @ sK10))) | ($true != $true)),
% 0.22/0.30 inference(superposition,[],[f75,f134])).
% 0.22/0.30 thf(f140,plain,(
% 0.22/0.30 (emptyset = ((setminus @ sK11 @ sK10)))),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f137])).
% 0.22/0.30 thf(f141,plain,(
% 0.22/0.30 $false),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f140,f63])).
% 0.22/0.30 % SZS output end Proof for theBenchmark
% 0.22/0.30 % (3402786)------------------------------
% 0.22/0.30 % (3402786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (3402786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (3402786)CaDiCaL version: 2.1.3
% 0.22/0.30 % (3402786)Termination reason: Refutation
% 0.22/0.30 % (3402786)Time elapsed: 0.008 s
% 0.22/0.30 % (3402786)Peak memory usage: 12 MB
% 0.22/0.30 % (3402786)Instructions burned: 13 (million)
% 0.22/0.30 % (3402767)Success in time 0.052 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------