%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU713^2 : 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 : n018.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 08:30:55 AM UTC 2026
% Result : Theorem 0.32s 0.38s
% Output : Refutation 0.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU713^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n018.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Tue Sep 29 14:15:56 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.32 Running higher-order theorem proving
% 0.26/0.33 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
% 0.32/0.38 % (141495)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.32/0.38 % (141503)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=3730100187: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)
% 0.32/0.38 % (141506)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.32/0.38 % (141506)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
% 0.32/0.38 % (141503) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-141495-141503"...
% 0.32/0.38 % (141503)...printing done.
% 0.32/0.38 % (141501)lrs+10_16_si=on:nwc=1.5:random_seed=2081637858:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.32/0.38 % (141502)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=575381103:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.32/0.38 % (141500)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2306975904:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.32/0.38 % (141503)Refutation found. Thanks to Tanya!
% 0.32/0.38 % SZS status Theorem for theBenchmark
% 0.32/0.38 % SZS output start Proof for theBenchmark
% 0.32/0.38 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.32/0.38 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.32/0.38 thf(func_def_1, type, powerset: ($i > $i)).
% 0.32/0.38 thf(func_def_2, type, powersetI: $o).
% 0.32/0.38 thf(func_def_4, type, powersetE: $o).
% 0.32/0.38 thf(func_def_5, type, setminus: ($i > $i > $i)).
% 0.32/0.38 thf(func_def_6, type, setminusEL: $o).
% 0.32/0.38 thf(func_def_9, type, sK0: ($i > $i > $i)).
% 0.32/0.38 thf(f1,axiom,(
% 0.32/0.38 (powersetI = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.32/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI)).
% 0.32/0.38 thf(f2,axiom,(
% 0.32/0.38 (powersetE = ! [X2 : $i,X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))))),
% 0.32/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE)).
% 0.32/0.38 thf(f3,axiom,(
% 0.32/0.38 (! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X0)) = setminusEL)),
% 0.32/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL)).
% 0.32/0.38 thf(f4,conjecture,(
% 0.32/0.38 powersetI => (powersetE => (setminusEL => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X1 @ X2) @ (powerset @ X0))))))),
% 0.32/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusT_lem)).
% 0.32/0.38 thf(f5,negated_conjecture,(
% 0.32/0.38 ~(powersetI => (powersetE => (setminusEL => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X1 @ X2) @ (powerset @ X0)))))))),
% 0.32/0.38 inference(negated_conjecture,[status(cth)],[f4])).
% 0.32/0.38 thf(f6,plain,(
% 0.32/0.38 ~(powersetI => (powersetE => (setminusEL => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X1 @ X2) @ (powerset @ X0)))))))),
% 0.32/0.38 inference(rectify,[],[f5])).
% 0.32/0.38 thf(f7,plain,(
% 0.32/0.38 ~((powersetI = $true) => ((powersetE = $true) => ((setminusEL = $true) => ! [X1 : $i,X0 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => (((in @ (setminus @ X1 @ X2) @ (powerset @ X0))) = $true))))))),
% 0.32/0.38 inference(fool_elimination,[],[f6])).
% 0.32/0.38 thf(f8,plain,(
% 0.32/0.38 (powersetI = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))))),
% 0.32/0.38 inference(rectify,[],[f1])).
% 0.32/0.38 thf(f9,plain,(
% 0.32/0.38 (powersetI = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((in @ X0 @ (powerset @ X1))) = $true))),
% 0.32/0.38 inference(fool_elimination,[],[f8])).
% 0.32/0.38 thf(f10,plain,(
% 0.32/0.38 (powersetE = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ((in @ X0 @ X2) => (in @ X0 @ X1))))),
% 0.32/0.38 inference(rectify,[],[f2])).
% 0.32/0.38 thf(f11,plain,(
% 0.32/0.38 (powersetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => ((((in @ X0 @ X2)) = $true) => (((in @ X0 @ X1)) = $true)))),
% 0.32/0.38 inference(fool_elimination,[],[f10])).
% 0.32/0.38 thf(f12,plain,(
% 0.32/0.38 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setminus @ X2 @ X1)) => (in @ X0 @ X2)) = setminusEL)),
% 0.32/0.38 inference(rectify,[],[f3])).
% 0.32/0.38 thf(f13,plain,(
% 0.32/0.38 ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (setminus @ X2 @ X1))) = $true) => (((in @ X0 @ X2)) = $true)) <=> (setminusEL = $true)),
% 0.32/0.38 inference(fool_elimination,[],[f12])).
% 0.32/0.38 thf(f14,plain,(
% 0.32/0.38 ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X2)) = $true) | (((in @ X0 @ (setminus @ X2 @ X1))) != $true)) <=> (setminusEL = $true)),
% 0.32/0.38 inference(ennf_transformation,[],[f13])).
% 0.32/0.38 thf(f15,plain,(
% 0.32/0.38 ! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((in @ X0 @ (powerset @ X1))) = $true)) <=> (powersetI = $true)),
% 0.32/0.38 inference(ennf_transformation,[],[f9])).
% 0.32/0.38 thf(f16,plain,(
% 0.32/0.38 (powersetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((((in @ X0 @ X1)) = $true) | (((in @ X0 @ X2)) != $true)) | (((in @ X2 @ (powerset @ X1))) != $true))),
% 0.32/0.38 inference(ennf_transformation,[],[f11])).
% 0.32/0.38 thf(f17,plain,(
% 0.32/0.38 ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X0 @ X1)) = $true) | (((in @ X0 @ X2)) != $true) | (((in @ X2 @ (powerset @ X1))) != $true)) <=> (powersetE = $true)),
% 0.32/0.38 inference(flattening,[],[f16])).
% 0.32/0.38 thf(f18,plain,(
% 0.32/0.38 ((? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) & (((in @ (setminus @ X1 @ X2) @ (powerset @ X0))) != $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (setminusEL = $true)) & (powersetE = $true)) & (powersetI = $true)),
% 0.32/0.38 inference(ennf_transformation,[],[f7])).
% 0.32/0.38 thf(f19,plain,(
% 0.32/0.38 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) & (((in @ (setminus @ X1 @ X2) @ (powerset @ X0))) != $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (setminusEL = $true) & (powersetE = $true) & (powersetI = $true)),
% 0.32/0.38 inference(flattening,[],[f18])).
% 0.32/0.38 thf(f20,plain,(
% 0.32/0.38 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((in @ X0 @ (powerset @ X1))) = $true)) | (powersetI != $true)) & ((powersetI = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((in @ X0 @ (powerset @ X1))) != $true)))),
% 0.32/0.38 inference(nnf_transformation,[],[f15])).
% 0.32/0.38 thf(f21,plain,(
% 0.32/0.38 (! [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((in @ X0 @ (powerset @ X1))) = $true)) | (powersetI != $true)) & ((powersetI = $true) | ? [X3 : $i,X4 : $i] : (! [X5 : $i] : ((((in @ X5 @ X4)) = $true) | (((in @ X5 @ X3)) != $true)) & (((in @ X3 @ (powerset @ X4))) != $true)))),
% 0.32/0.38 inference(rectify,[],[f20])).
% 0.32/0.38 thf(f22,plain,(
% 0.32/0.38 (! [X0 : $i,X1 : $i] : (((((in @ (sK0 @ X1 @ X0) @ X1)) != $true) & (((in @ (sK0 @ X1 @ X0) @ X0)) = $true)) | (((in @ X0 @ (powerset @ X1))) = $true)) | (powersetI != $true)) & ((powersetI = $true) | (! [X5 : $i] : ((((in @ X5 @ sK2)) = $true) | (((in @ X5 @ sK1)) != $true)) & (((in @ sK1 @ (powerset @ sK2))) != $true)))),
% 0.32/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK1,sK2]),skolemize(X2,sK0 @ X1 @ X0),skolemize(X3,sK1),skolemize(X4,sK2)],[f21])).
% 0.32/0.38 thf(f23,plain,(
% 0.32/0.38 (! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X2)) = $true) | (((in @ X0 @ (setminus @ X2 @ X1))) != $true)) | (setminusEL != $true)) & ((setminusEL = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X2)) != $true) & (((in @ X0 @ (setminus @ X2 @ X1))) = $true)))),
% 0.32/0.38 inference(nnf_transformation,[],[f14])).
% 0.32/0.38 thf(f24,plain,(
% 0.32/0.38 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) | (((in @ X1 @ (setminus @ X0 @ X2))) != $true)) | (setminusEL != $true)) & ((setminusEL = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) != $true) & (((in @ X4 @ (setminus @ X3 @ X5))) = $true)))),
% 0.32/0.38 inference(rectify,[],[f23])).
% 0.32/0.38 thf(f25,plain,(
% 0.32/0.38 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) | (((in @ X1 @ (setminus @ X0 @ X2))) != $true)) | (setminusEL != $true)) & ((setminusEL = $true) | ((((in @ sK4 @ sK3)) != $true) & (((in @ sK4 @ (setminus @ sK3 @ sK5))) = $true)))),
% 0.32/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f24])).
% 0.32/0.38 thf(f26,plain,(
% 0.32/0.38 (! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X0 @ X1)) = $true) | (((in @ X0 @ X2)) != $true) | (((in @ X2 @ (powerset @ X1))) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X0 @ X1)) != $true) & (((in @ X0 @ X2)) = $true) & (((in @ X2 @ (powerset @ X1))) = $true)))),
% 0.32/0.38 inference(nnf_transformation,[],[f17])).
% 0.32/0.38 thf(f27,plain,(
% 0.32/0.38 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) | (((in @ X1 @ X2)) != $true) | (((in @ X2 @ (powerset @ X0))) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) != $true) & (((in @ X4 @ X5)) = $true) & (((in @ X5 @ (powerset @ X3))) = $true)))),
% 0.32/0.38 inference(rectify,[],[f26])).
% 0.32/0.38 thf(f28,plain,(
% 0.32/0.38 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) = $true) | (((in @ X1 @ X2)) != $true) | (((in @ X2 @ (powerset @ X0))) != $true)) | (powersetE != $true)) & ((powersetE = $true) | ((((in @ sK7 @ sK6)) != $true) & (((in @ sK7 @ sK8)) = $true) & (((in @ sK8 @ (powerset @ sK6))) = $true)))),
% 0.32/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X3,sK6),skolemize(X4,sK7),skolemize(X5,sK8)],[f27])).
% 0.32/0.38 thf(f29,plain,(
% 0.32/0.38 (((((in @ sK11 @ (powerset @ sK9))) = $true) & ($true != ((in @ (setminus @ sK10 @ sK11) @ (powerset @ sK9))))) & (((in @ sK10 @ (powerset @ sK9))) = $true)) & (setminusEL = $true) & (powersetE = $true) & (powersetI = $true)),
% 0.32/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f19])).
% 0.32/0.38 thf(f32,plain,(
% 0.32/0.38 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) | (powersetI != $true) | (((in @ (sK0 @ X1 @ X0) @ X0)) = $true)) )),
% 0.32/0.38 inference(cnf_transformation,[],[f22])).
% 0.32/0.38 thf(f33,plain,(
% 0.32/0.38 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X1)) != $true) | (powersetI != $true) | (((in @ X0 @ (powerset @ X1))) = $true)) )),
% 0.32/0.38 inference(cnf_transformation,[],[f22])).
% 0.32/0.38 thf(f36,plain,(
% 0.32/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (setminus @ X0 @ X2))) != $true) | (setminusEL != $true) | (((in @ X1 @ X0)) = $true)) )),
% 0.32/0.38 inference(cnf_transformation,[],[f25])).
% 0.32/0.38 thf(f40,plain,(
% 0.32/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((powersetE != $true) | (((in @ X1 @ X0)) = $true) | (((in @ X1 @ X2)) != $true) | (((in @ X2 @ (powerset @ X0))) != $true)) )),
% 0.32/0.38 inference(cnf_transformation,[],[f28])).
% 0.32/0.38 thf(f41,plain,(
% 0.32/0.38 (powersetI = $true)),
% 0.32/0.38 inference(cnf_transformation,[],[f29])).
% 0.32/0.38 thf(f42,plain,(
% 0.32/0.38 (powersetE = $true)),
% 0.32/0.38 inference(cnf_transformation,[],[f29])).
% 0.32/0.38 thf(f43,plain,(
% 0.32/0.38 (setminusEL = $true)),
% 0.32/0.38 inference(cnf_transformation,[],[f29])).
% 0.32/0.38 thf(f44,plain,(
% 0.32/0.38 (((in @ sK10 @ (powerset @ sK9))) = $true)),
% 0.32/0.38 inference(cnf_transformation,[],[f29])).
% 0.32/0.38 thf(f45,plain,(
% 0.32/0.38 ($true != ((in @ (setminus @ sK10 @ sK11) @ (powerset @ sK9))))),
% 0.32/0.38 inference(cnf_transformation,[],[f29])).
% 0.32/0.38 thf(f49,definition,(
% 0.32/0.38 spl12_1 <=> (powersetE = $true)),
% 0.32/0.38 introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition])).
% 0.32/0.38 thf(f52,plain,(
% 0.32/0.38 spl12_1),
% 0.32/0.38 inference(avatar_split_clause,[],[f42,f49])).
% 0.32/0.38 thf(f59,definition,(
% 0.32/0.38 spl12_3 <=> (((in @ sK10 @ (powerset @ sK9))) = $true)),
% 0.32/0.38 introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition])).
% 0.32/0.38 thf(f61,plain,(
% 0.32/0.38 (((in @ sK10 @ (powerset @ sK9))) = $true) | ~spl12_3),
% 0.32/0.38 inference(avatar_component_clause,[],[f59])).
% 0.32/0.38 thf(f62,plain,(
% 0.32/0.38 spl12_3),
% 0.32/0.38 inference(avatar_split_clause,[],[f44,f59])).
% 0.32/0.38 thf(f68,definition,(
% 0.32/0.38 spl12_5 <=> (setminusEL = $true)),
% 0.32/0.38 introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition])).
% 0.32/0.38 thf(f81,definition,(
% 0.32/0.38 spl12_8 <=> (powersetI = $true)),
% 0.32/0.38 introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition])).
% 0.32/0.38 thf(f85,plain,(
% 0.32/0.38 spl12_8),
% 0.32/0.38 inference(avatar_split_clause,[],[f41,f81])).
% 0.32/0.38 thf(f92,definition,(
% 0.32/0.38 spl12_10 <=> ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (powerset @ X1))) = $true) | (((in @ (sK0 @ X1 @ X0) @ X0)) = $true))),
% 0.32/0.38 introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition])).
% 0.32/0.38 thf(f93,plain,(
% 0.32/0.38 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X0)) = $true) | (((in @ X0 @ (powerset @ X1))) = $true)) ) | ~spl12_10),
% 0.32/0.38 inference(avatar_component_clause,[],[f92])).
% 0.32/0.38 thf(f94,plain,(
% 0.32/0.38 ~spl12_8 | spl12_10),
% 0.32/0.38 inference(avatar_split_clause,[],[f32,f92,f81])).
% 0.32/0.38 thf(f96,definition,(
% 0.32/0.38 spl12_11 <=> ($true = ((in @ (setminus @ sK10 @ sK11) @ (powerset @ sK9))))),
% 0.32/0.38 introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition])).
% 0.32/0.38 thf(f98,plain,(
% 0.32/0.38 ($true != ((in @ (setminus @ sK10 @ sK11) @ (powerset @ sK9)))) | spl12_11),
% 0.32/0.38 inference(avatar_component_clause,[],[f96])).
% 0.32/0.38 thf(f99,plain,(
% 0.32/0.38 ~spl12_11),
% 0.32/0.38 inference(avatar_split_clause,[],[f45,f96])).
% 0.32/0.38 thf(f101,definition,(
% 0.32/0.38 spl12_12 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) = $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X1 @ X2)) != $true))),
% 0.32/0.38 introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition])).
% 0.32/0.38 thf(f102,plain,(
% 0.32/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X1 @ X2)) != $true) | (((in @ X1 @ X0)) = $true)) ) | ~spl12_12),
% 0.32/0.38 inference(avatar_component_clause,[],[f101])).
% 0.32/0.38 thf(f103,plain,(
% 0.32/0.38 ~spl12_1 | spl12_12),
% 0.32/0.38 inference(avatar_split_clause,[],[f40,f101,f49])).
% 0.32/0.38 thf(f104,plain,(
% 0.32/0.38 spl12_5),
% 0.32/0.38 inference(avatar_split_clause,[],[f43,f68])).
% 0.32/0.38 thf(f111,definition,(
% 0.32/0.38 spl12_14 <=> ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X1)) != $true) | (((in @ X0 @ (powerset @ X1))) = $true))),
% 0.32/0.38 introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition])).
% 0.32/0.38 thf(f112,plain,(
% 0.32/0.38 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK0 @ X1 @ X0) @ X1)) != $true) | (((in @ X0 @ (powerset @ X1))) = $true)) ) | ~spl12_14),
% 0.32/0.38 inference(avatar_component_clause,[],[f111])).
% 0.32/0.38 thf(f113,plain,(
% 0.32/0.38 ~spl12_8 | spl12_14),
% 0.32/0.38 inference(avatar_split_clause,[],[f33,f111,f81])).
% 0.32/0.38 thf(f125,definition,(
% 0.32/0.38 spl12_17 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (setminus @ X0 @ X2))) != $true) | (((in @ X1 @ X0)) = $true))),
% 0.32/0.38 introduced(definition,[new_symbols(definition,[spl12_17])],[avatar_definition])).
% 0.32/0.38 thf(f126,plain,(
% 0.32/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (setminus @ X0 @ X2))) != $true) | (((in @ X1 @ X0)) = $true)) ) | ~spl12_17),
% 0.32/0.38 inference(avatar_component_clause,[],[f125])).
% 0.32/0.38 thf(f127,plain,(
% 0.32/0.38 spl12_17 | ~spl12_5),
% 0.32/0.38 inference(avatar_split_clause,[],[f36,f68,f125])).
% 0.32/0.38 thf(f131,plain,(
% 0.32/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((in @ (setminus @ X1 @ X2) @ (powerset @ X0))) = $true) | (((in @ (sK0 @ X0 @ (setminus @ X1 @ X2)) @ X1)) = $true)) ) | (~spl12_10 | ~spl12_17)),
% 0.32/0.38 inference(superposition,[],[f126,f93])).
% 0.32/0.38 thf(f132,plain,(
% 0.32/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK0 @ X0 @ (setminus @ X1 @ X2)) @ X1)) = $true) | (((in @ (setminus @ X1 @ X2) @ (powerset @ X0))) = $true)) ) | (~spl12_10 | ~spl12_17)),
% 0.32/0.38 inference(trivial_inequality_removal,[],[f131])).
% 0.32/0.38 thf(f136,plain,(
% 0.32/0.38 ( ! [X0 : $i] : ((((in @ X0 @ sK10)) != $true) | (((in @ X0 @ sK9)) = $true) | ($true != $true)) ) | (~spl12_3 | ~spl12_12)),
% 0.32/0.38 inference(superposition,[],[f102,f61])).
% 0.32/0.38 thf(f141,plain,(
% 0.32/0.38 ( ! [X0 : $i] : ((((in @ X0 @ sK9)) = $true) | (((in @ X0 @ sK10)) != $true)) ) | (~spl12_3 | ~spl12_12)),
% 0.32/0.38 inference(trivial_inequality_removal,[],[f136])).
% 0.32/0.38 thf(f143,plain,(
% 0.32/0.38 ( ! [X0 : $i] : ((((in @ (sK0 @ sK9 @ X0) @ sK10)) != $true) | (((in @ X0 @ (powerset @ sK9))) = $true) | ($true != $true)) ) | (~spl12_3 | ~spl12_12 | ~spl12_14)),
% 0.32/0.38 inference(superposition,[],[f112,f141])).
% 0.32/0.38 thf(f144,plain,(
% 0.32/0.38 ( ! [X0 : $i] : ((((in @ (sK0 @ sK9 @ X0) @ sK10)) != $true) | (((in @ X0 @ (powerset @ sK9))) = $true)) ) | (~spl12_3 | ~spl12_12 | ~spl12_14)),
% 0.32/0.38 inference(trivial_inequality_removal,[],[f143])).
% 0.32/0.38 thf(f159,plain,(
% 0.32/0.38 ( ! [X0 : $i] : (($true != $true) | (((in @ (setminus @ sK10 @ X0) @ (powerset @ sK9))) = $true) | (((in @ (setminus @ sK10 @ X0) @ (powerset @ sK9))) = $true)) ) | (~spl12_3 | ~spl12_10 | ~spl12_12 | ~spl12_14 | ~spl12_17)),
% 0.32/0.38 inference(superposition,[],[f144,f132])).
% 0.32/0.38 thf(f162,plain,(
% 0.32/0.38 ( ! [X0 : $i] : ((((in @ (setminus @ sK10 @ X0) @ (powerset @ sK9))) = $true) | ($true != $true)) ) | (~spl12_3 | ~spl12_10 | ~spl12_12 | ~spl12_14 | ~spl12_17)),
% 0.32/0.38 inference(duplicate_literal_removal,[],[f159])).
% 0.32/0.38 thf(f163,plain,(
% 0.32/0.38 ( ! [X0 : $i] : ((((in @ (setminus @ sK10 @ X0) @ (powerset @ sK9))) = $true)) ) | (~spl12_3 | ~spl12_10 | ~spl12_12 | ~spl12_14 | ~spl12_17)),
% 0.32/0.38 inference(trivial_inequality_removal,[],[f162])).
% 0.32/0.38 thf(f227,plain,(
% 0.32/0.38 ($true != $true) | (~spl12_3 | ~spl12_10 | spl12_11 | ~spl12_12 | ~spl12_14 | ~spl12_17)),
% 0.32/0.38 inference(superposition,[],[f98,f163])).
% 0.32/0.38 thf(f229,plain,(
% 0.32/0.38 $false | (~spl12_3 | ~spl12_10 | spl12_11 | ~spl12_12 | ~spl12_14 | ~spl12_17)),
% 0.32/0.38 inference(trivial_inequality_removal,[],[f227])).
% 0.32/0.38 thf(f230,plain,(
% 0.32/0.38 ~spl12_3 | ~spl12_10 | spl12_11 | ~spl12_12 | ~spl12_14 | ~spl12_17),
% 0.32/0.38 inference(avatar_contradiction_clause,[],[f229])).
% 0.32/0.38 cnf(s1, plain, spl12_1, inference(sat_conversion,[],[f52])).
% 0.32/0.38 cnf(s3, plain, spl12_3, inference(sat_conversion,[],[f62])).
% 0.32/0.38 cnf(s7, plain, spl12_8, inference(sat_conversion,[],[f85])).
% 0.32/0.38 cnf(s9, plain, ~spl12_8 | spl12_10, inference(sat_conversion,[],[f94])).
% 0.32/0.38 cnf(s10, plain, ~spl12_11, inference(sat_conversion,[],[f99])).
% 0.32/0.38 cnf(s11, plain, ~spl12_1 | spl12_12, inference(sat_conversion,[],[f103])).
% 0.32/0.38 cnf(s12, plain, spl12_5, inference(sat_conversion,[],[f104])).
% 0.32/0.38 cnf(s14, plain, ~spl12_8 | spl12_14, inference(sat_conversion,[],[f113])).
% 0.32/0.38 cnf(s17, plain, ~spl12_5 | spl12_17, inference(sat_conversion,[],[f127])).
% 0.32/0.38 cnf(s18, plain, ~spl12_3 | ~spl12_10 | spl12_11 | ~spl12_12 | ~spl12_14 | ~spl12_17, inference(sat_conversion,[],[f230])).
% 0.32/0.38 cnf(s19, plain, spl12_17, inference(rat,[],[s17,s12])).
% 0.32/0.38 cnf(s20, plain, spl12_14, inference(rat,[],[s14,s7])).
% 0.32/0.38 cnf(s21, plain, spl12_10, inference(rat,[],[s9,s7])).
% 0.32/0.38 cnf(s22, plain, ~spl12_12, inference(rat,[],[s18,s19,s20,s21,s10,s3])).
% 0.32/0.38 cnf(s23, plain, ~spl12_1, inference(rat,[],[s11,s22])).
% 0.32/0.38 cnf(s27, plain, $false, inference(rat,[],[s1,s23])).
% 0.32/0.38 thf(f232,plain,(
% 0.32/0.38 $false),
% 0.32/0.38 inference(avatar_sat_refutation,[],[s27])).
% 0.32/0.38 % SZS output end Proof for theBenchmark
% 0.32/0.38 % (141503)------------------------------
% 0.32/0.38 % (141503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.38 % (141503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.38 % (141503)CaDiCaL version: 2.1.3
% 0.32/0.38 % (141503)Termination reason: Refutation
% 0.32/0.38 % (141503)Time elapsed: 0.011 s
% 0.32/0.38 % (141503)Peak memory usage: 13 MB
% 0.32/0.38 % (141503)Instructions burned: 20 (million)
% 0.32/0.38 % (141495)Success in time 0.034 s
% 0.32/0.38 % Vampire exiting
%------------------------------------------------------------------------------