%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU590^2 : 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 : n008.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 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU590^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n008.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
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:54:10 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.28 % (3192328)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (3192333)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1239879068:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (3192339)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (3192339)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
% 0.21/0.28 % (3192333) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3192328-3192333"...
% 0.21/0.28 % (3192333)...printing done.
% 0.21/0.28 % (3192335)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=436415584:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (3192333)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% 0.21/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.21/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_1, type, dsetconstr: ($i > ($i > $o) > $i)).
% 0.21/0.28 thf(func_def_2, type, subset: ($i > $i > $o)).
% 0.21/0.28 thf(func_def_3, type, subsetI1: $o).
% 0.21/0.28 thf(func_def_5, type, subsetE: $o).
% 0.21/0.28 thf(func_def_6, type, binintersect: ($i > $i > $i)).
% 0.21/0.28 thf(func_def_7, type, binintersectI: $o).
% 0.21/0.28 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_9, type, db0: !>[X0: $tType]:(X0)).
% 0.21/0.28 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.21/0.28 thf(func_def_19, type, sK6: ($i > $i > $i)).
% 0.21/0.28 thf(func_def_25, type, vNOT: ($o > $o)).
% 0.21/0.28 thf(f1,axiom,(
% 0.21/0.28 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
% 0.21/0.28 thf(f2,axiom,(
% 0.21/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE)).
% 0.21/0.28 thf(f3,axiom,(
% 0.21/0.28 (binintersect = (^[X0 : $i, X1 : $i] : ((dsetconstr @ X0 @ (^[X2 : $i] : ((in @ X2 @ X1)))))))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersect)).
% 0.21/0.28 thf(f4,axiom,(
% 0.21/0.28 (! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))) = binintersectI)),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI)).
% 0.21/0.28 thf(f5,conjecture,(
% 0.21/0.28 subsetI1 => (subsetE => (binintersectI => ! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X2 @ X0) => ((subset @ X2 @ X1) => (subset @ X2 @ (binintersect @ X0 @ X1))))))),
% 0.21/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5)).
% 0.21/0.28 thf(f6,negated_conjecture,(
% 0.21/0.28 ~(subsetI1 => (subsetE => (binintersectI => ! [X2 : $i,X0 : $i,X1 : $i] : ((subset @ X2 @ X0) => ((subset @ X2 @ X1) => (subset @ X2 @ (binintersect @ X0 @ X1)))))))),
% 0.21/0.28 inference(negated_conjecture,[status(cth)],[f5])).
% 0.21/0.28 thf(f7,plain,(
% 0.21/0.28 (binintersect = (^[X0 : $i, X1 : $i] : ((dsetconstr @ X0 @ (^[X2 : $i] : ((in @ X2 @ X1)))))))),
% 0.21/0.28 inference(rectify,[],[f3])).
% 0.21/0.28 thf(f8,plain,(
% 0.21/0.28 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 0.21/0.28 inference(fool_elimination,[],[f7])).
% 0.21/0.28 thf(f9,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
% 0.21/0.28 inference(rectify,[],[f1])).
% 0.21/0.28 thf(f10,plain,(
% 0.21/0.28 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (((subset @ X1 @ X0)) = $true))),
% 0.21/0.28 inference(fool_elimination,[],[f9])).
% 0.21/0.28 thf(f11,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ (binintersect @ X1 @ X2)))) = binintersectI)),
% 0.21/0.28 inference(rectify,[],[f4])).
% 0.21/0.28 thf(f12,plain,(
% 0.21/0.28 ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X0 @ X1)) = $true) => ((((in @ X0 @ X2)) = $true) => (((in @ X0 @ (binintersect @ X1 @ X2))) = $true))) <=> (binintersectI = $true)),
% 0.21/0.28 inference(fool_elimination,[],[f11])).
% 0.21/0.28 thf(f13,plain,(
% 0.21/0.28 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.21/0.28 inference(rectify,[],[f2])).
% 0.21/0.28 thf(f14,plain,(
% 0.21/0.28 ! [X2 : $i,X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) = $true) => ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true))) <=> (subsetE = $true)),
% 0.21/0.28 inference(fool_elimination,[],[f13])).
% 0.21/0.28 thf(f15,plain,(
% 0.21/0.28 ~(subsetI1 => (subsetE => (binintersectI => ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((subset @ X0 @ X2) => (subset @ X0 @ (binintersect @ X1 @ X2)))))))),
% 0.21/0.28 inference(rectify,[],[f6])).
% 0.21/0.28 thf(f16,plain,(
% 0.21/0.28 ~((subsetI1 = $true) => ((subsetE = $true) => ((binintersectI = $true) => ! [X2 : $i,X1 : $i,X0 : $i] : ((((subset @ X0 @ X1)) = $true) => ((((subset @ X0 @ X2)) = $true) => (((subset @ X0 @ (binintersect @ X1 @ X2))) = $true))))))),
% 0.21/0.28 inference(fool_elimination,[],[f15])).
% 0.21/0.28 thf(f17,plain,(
% 0.21/0.28 ! [X1 : $i,X2 : $i,X0 : $i] : (((((in @ X0 @ (binintersect @ X1 @ X2))) = $true) | (((in @ X0 @ X2)) != $true)) | (((in @ X0 @ X1)) != $true)) <=> (binintersectI = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f12])).
% 0.21/0.28 thf(f18,plain,(
% 0.21/0.28 (binintersectI = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X2)) != $true) | (((in @ X0 @ X1)) != $true) | (((in @ X0 @ (binintersect @ X1 @ X2))) = $true))),
% 0.21/0.28 inference(flattening,[],[f17])).
% 0.21/0.28 thf(f19,plain,(
% 0.21/0.28 ((? [X2 : $i,X1 : $i,X0 : $i] : (((((subset @ X0 @ (binintersect @ X1 @ X2))) != $true) & (((subset @ X0 @ X2)) = $true)) & (((subset @ X0 @ X1)) = $true)) & (binintersectI = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f16])).
% 0.21/0.28 thf(f20,plain,(
% 0.21/0.28 (subsetE = $true) & ? [X1 : $i,X2 : $i,X0 : $i] : ((((subset @ X0 @ X2)) = $true) & (((subset @ X0 @ X1)) = $true) & (((subset @ X0 @ (binintersect @ X1 @ X2))) != $true)) & (binintersectI = $true) & (subsetI1 = $true)),
% 0.21/0.28 inference(flattening,[],[f19])).
% 0.21/0.28 thf(f21,plain,(
% 0.21/0.28 ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) <=> (subsetI1 = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f10])).
% 0.21/0.28 thf(f22,plain,(
% 0.21/0.28 ! [X2 : $i,X1 : $i,X0 : $i] : (((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) | (((subset @ X0 @ X1)) != $true)) <=> (subsetE = $true)),
% 0.21/0.28 inference(ennf_transformation,[],[f14])).
% 0.21/0.28 thf(f23,plain,(
% 0.21/0.28 (subsetE = $true) <=> ! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X2 @ X1)) = $true) | (((subset @ X0 @ X1)) != $true) | (((in @ X2 @ X0)) != $true))),
% 0.21/0.28 inference(flattening,[],[f22])).
% 0.21/0.28 thf(f24,plain,(
% 0.21/0.28 (subsetE = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X2 @ X1)) = $true) & (((subset @ X2 @ X0)) = $true) & (((subset @ X2 @ (binintersect @ X0 @ X1))) != $true)) & (binintersectI = $true) & (subsetI1 = $true)),
% 0.21/0.28 inference(rectify,[],[f20])).
% 0.21/0.28 thf(f25,plain,(
% 0.21/0.28 (subsetE = $true) & ((((subset @ sK2 @ sK1)) = $true) & (((subset @ sK2 @ sK0)) = $true) & (((subset @ sK2 @ (binintersect @ sK0 @ sK1))) != $true)) & (binintersectI = $true) & (subsetI1 = $true)),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f24])).
% 0.21/0.28 thf(f26,plain,(
% 0.21/0.28 ((subsetE = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X2 @ X1)) != $true) & (((subset @ X0 @ X1)) = $true) & (((in @ X2 @ X0)) = $true))) & (! [X1 : $i,X2 : $i,X0 : $i] : ((((in @ X2 @ X1)) = $true) | (((subset @ X0 @ X1)) != $true) | (((in @ X2 @ X0)) != $true)) | (subsetE != $true))),
% 0.21/0.28 inference(nnf_transformation,[],[f23])).
% 0.21/0.28 thf(f27,plain,(
% 0.21/0.28 ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) & (((subset @ X2 @ X0)) = $true) & (((in @ X1 @ X2)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) = $true) | (((subset @ X5 @ X3)) != $true) | (((in @ X4 @ X5)) != $true)) | (subsetE != $true))),
% 0.21/0.28 inference(rectify,[],[f26])).
% 0.21/0.28 thf(f28,plain,(
% 0.21/0.28 ((subsetE = $true) | ((((in @ sK4 @ sK3)) != $true) & ($true = ((subset @ sK5 @ sK3))) & (((in @ sK4 @ sK5)) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) = $true) | (((subset @ X5 @ X3)) != $true) | (((in @ X4 @ X5)) != $true)) | (subsetE != $true))),
% 0.21/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f27])).
% 0.21/0.29 thf(f29,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true))))),
% 0.21/0.29 inference(nnf_transformation,[],[f21])).
% 0.21/0.29 thf(f30,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X0)) != $true) & (((in @ X2 @ X1)) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3 : $i,X4 : $i] : ((((subset @ X4 @ X3)) != $true) & ! [X5 : $i] : ((((in @ X5 @ X3)) = $true) | (((in @ X5 @ X4)) != $true))))),
% 0.21/0.29 inference(rectify,[],[f29])).
% 0.21/0.29 thf(f31,plain,(
% 0.21/0.29 (! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | ((((in @ (sK6 @ X1 @ X0) @ X0)) != $true) & (((in @ (sK6 @ X1 @ X0) @ X1)) = $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ((((subset @ sK8 @ sK7)) != $true) & ! [X5 : $i] : ((((in @ X5 @ sK7)) = $true) | (((in @ X5 @ sK8)) != $true))))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK7,sK8]),skolemize(X2,sK6 @ X1 @ X0),skolemize(X3,sK7),skolemize(X4,sK8)],[f30])).
% 0.21/0.29 thf(f32,plain,(
% 0.21/0.29 ((binintersectI = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X2)) = $true) & (((in @ X0 @ X1)) = $true) & (((in @ X0 @ (binintersect @ X1 @ X2))) != $true))) & (! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X2)) != $true) | (((in @ X0 @ X1)) != $true) | (((in @ X0 @ (binintersect @ X1 @ X2))) = $true)) | (binintersectI != $true))),
% 0.21/0.29 inference(nnf_transformation,[],[f18])).
% 0.21/0.29 thf(f33,plain,(
% 0.21/0.29 ((binintersectI = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) = $true) & ($true != ((in @ X2 @ (binintersect @ X1 @ X0)))))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X3)) != $true) | (((in @ X5 @ X4)) != $true) | (((in @ X5 @ (binintersect @ X4 @ X3))) = $true)) | (binintersectI != $true))),
% 0.21/0.29 inference(rectify,[],[f32])).
% 0.21/0.29 thf(f34,plain,(
% 0.21/0.29 ((binintersectI = $true) | ((((in @ sK11 @ sK9)) = $true) & (((in @ sK11 @ sK10)) = $true) & (((in @ sK11 @ (binintersect @ sK10 @ sK9))) != $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X3)) != $true) | (((in @ X5 @ X4)) != $true) | (((in @ X5 @ (binintersect @ X4 @ X3))) = $true)) | (binintersectI != $true))),
% 0.21/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f33])).
% 0.21/0.29 thf(f35,plain,(
% 0.21/0.29 (subsetI1 = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f36,plain,(
% 0.21/0.29 (binintersectI = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f37,plain,(
% 0.21/0.29 (((subset @ sK2 @ (binintersect @ sK0 @ sK1))) != $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f38,plain,(
% 0.21/0.29 (((subset @ sK2 @ sK0)) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f39,plain,(
% 0.21/0.29 (((subset @ sK2 @ sK1)) = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f40,plain,(
% 0.21/0.29 (subsetE = $true)),
% 0.21/0.29 inference(cnf_transformation,[],[f25])).
% 0.21/0.29 thf(f41,plain,(
% 0.21/0.29 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 0.21/0.29 inference(cnf_transformation,[],[f8])).
% 0.21/0.29 thf(f42,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) = $true) | (((subset @ X5 @ X3)) != $true) | (((in @ X4 @ X5)) != $true) | (subsetE != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f28])).
% 0.21/0.29 thf(f48,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | (((in @ (sK6 @ X1 @ X0) @ X1)) = $true) | (subsetI1 != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f31])).
% 0.21/0.29 thf(f49,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) | (((in @ (sK6 @ X1 @ X0) @ X0)) != $true) | (subsetI1 != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f31])).
% 0.21/0.29 thf(f50,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X3)) != $true) | (((in @ X5 @ X4)) != $true) | (((in @ X5 @ (binintersect @ X4 @ X3))) = $true) | (binintersectI != $true)) )),
% 0.21/0.29 inference(cnf_transformation,[],[f34])).
% 0.21/0.29 thf(f56,plain,(
% 0.21/0.29 (((subset @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ sK0 @ sK1))) != $true)),
% 0.21/0.29 inference(definition_unfolding,[],[f37,f41])).
% 0.21/0.29 thf(f60,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X5)) != $true) | ($true != $true) | (((in @ X4 @ X3)) = $true) | (((subset @ X5 @ X3)) != $true)) )),
% 0.21/0.29 inference(definition_unfolding,[],[f42,f40])).
% 0.21/0.29 thf(f61,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK6 @ X1 @ X0) @ X0)) != $true) | (((subset @ X1 @ X0)) = $true) | ($true != $true)) )),
% 0.21/0.29 inference(definition_unfolding,[],[f49,f35])).
% 0.21/0.29 thf(f62,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK6 @ X1 @ X0) @ X1)) = $true) | (((subset @ X1 @ X0)) = $true) | ($true != $true)) )),
% 0.21/0.29 inference(definition_unfolding,[],[f48,f35])).
% 0.21/0.29 thf(f68,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | (((in @ X5 @ X4)) != $true) | (((in @ X5 @ X3)) != $true) | (((in @ X5 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ X4 @ X3))) = $true)) )),
% 0.21/0.29 inference(definition_unfolding,[],[f50,f41,f36])).
% 0.21/0.29 thf(f69,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((subset @ X5 @ X3)) != $true) | (((in @ X4 @ X5)) != $true) | (((in @ X4 @ X3)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f60])).
% 0.21/0.29 thf(f70,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK6 @ X1 @ X0) @ X1)) = $true) | (((subset @ X1 @ X0)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f62])).
% 0.21/0.29 thf(f71,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) != $true) | (((in @ X5 @ X3)) != $true) | (((in @ X5 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ X4 @ X3))) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f68])).
% 0.21/0.29 thf(f72,plain,(
% 0.21/0.29 ( ! [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) != $true) | (((in @ X5 @ X3)) != $true) | (((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (in @ Y0 @ X3))))) = $true)) )),
% 0.21/0.29 inference(beta-eta_normalization,[],[f71])).
% 0.21/0.29 thf(f73,plain,(
% 0.21/0.29 (((subset @ sK2 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ sK1))))) != $true)),
% 0.21/0.29 inference(beta-eta_normalization,[],[f56])).
% 0.21/0.29 thf(f74,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK6 @ X1 @ X0) @ X0)) != $true) | (((subset @ X1 @ X0)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f61])).
% 0.21/0.29 thf(f78,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((in @ X0 @ sK2)) != $true) | ($true != $true) | (((in @ X0 @ sK0)) = $true)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f69,f38])).
% 0.21/0.29 thf(f79,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != $true) | (((in @ X0 @ sK2)) != $true) | (((in @ X0 @ sK1)) = $true)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f69,f39])).
% 0.21/0.29 thf(f81,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((in @ X0 @ sK2)) != $true) | (((in @ X0 @ sK1)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f79])).
% 0.21/0.29 thf(f82,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((in @ X0 @ sK2)) != $true) | (((in @ X0 @ sK0)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f78])).
% 0.21/0.29 thf(f83,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != $true) | (((subset @ sK2 @ X0)) = $true) | (((in @ (sK6 @ sK2 @ X0) @ sK1)) = $true)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f81,f70])).
% 0.21/0.29 thf(f84,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((in @ (sK6 @ sK2 @ X0) @ sK1)) = $true) | (((subset @ sK2 @ X0)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f83])).
% 0.21/0.29 thf(f85,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != $true) | (((in @ (sK6 @ sK2 @ X0) @ sK0)) = $true) | (((subset @ sK2 @ X0)) = $true)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f82,f70])).
% 0.21/0.29 thf(f86,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((in @ (sK6 @ sK2 @ X0) @ sK0)) = $true) | (((subset @ sK2 @ X0)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f85])).
% 0.21/0.29 thf(f95,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK6 @ sK2 @ X0) @ X1)) != $true) | (((subset @ sK2 @ X0)) = $true) | (((in @ (sK6 @ sK2 @ X0) @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ X1))))) = $true) | ($true != $true)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f72,f86])).
% 0.21/0.29 thf(f96,plain,(
% 0.21/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK6 @ sK2 @ X0) @ X1)) != $true) | (((subset @ sK2 @ X0)) = $true) | (((in @ (sK6 @ sK2 @ X0) @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ X1))))) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f95])).
% 0.21/0.29 thf(f189,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((subset @ sK2 @ X0)) = $true) | ($true != $true) | (((subset @ sK2 @ X0)) = $true) | (((in @ (sK6 @ sK2 @ X0) @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ sK1))))) = $true)) )),
% 0.21/0.29 inference(constrained_superposition,[],[f96,f84])).
% 0.21/0.29 thf(f200,plain,(
% 0.21/0.29 ( ! [X0 : $i] : (($true != $true) | (((subset @ sK2 @ X0)) = $true) | (((in @ (sK6 @ sK2 @ X0) @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ sK1))))) = $true)) )),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f189])).
% 0.21/0.29 thf(f201,plain,(
% 0.21/0.29 ( ! [X0 : $i] : ((((in @ (sK6 @ sK2 @ X0) @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ sK1))))) = $true) | (((subset @ sK2 @ X0)) = $true)) )),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f200])).
% 0.21/0.29 thf(f206,plain,(
% 0.21/0.29 ($true != $true) | (((subset @ sK2 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ sK1))))) = $true) | (((subset @ sK2 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ sK1))))) = $true)),
% 0.21/0.29 inference(constrained_superposition,[],[f74,f201])).
% 0.21/0.29 thf(f212,plain,(
% 0.21/0.29 ($true != $true) | (((subset @ sK2 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ sK1))))) = $true)),
% 0.21/0.29 inference(duplicate_literal_removal,[],[f206])).
% 0.21/0.29 thf(f213,plain,(
% 0.21/0.29 (((subset @ sK2 @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ Y0 @ sK1))))) = $true)),
% 0.21/0.29 inference(trivial_inequality_removal,[],[f212])).
% 0.21/0.29 thf(f219,plain,(
% 0.21/0.29 $false),
% 0.21/0.29 inference(forward_subsumption_resolution,[],[f213,f73])).
% 0.21/0.29 % SZS output end Proof for theBenchmark
% 0.21/0.29 % (3192333)------------------------------
% 0.21/0.29 % (3192333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (3192333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (3192333)CaDiCaL version: 2.1.3
% 0.21/0.29 % (3192333)Termination reason: Refutation
% 0.21/0.29 % (3192333)Time elapsed: 0.006 s
% 0.21/0.29 % (3192333)Peak memory usage: 12 MB
% 0.21/0.29 % (3192333)Instructions burned: 20 (million)
% 0.21/0.29 % (3192328)Success in time 0.03 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------