%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU610^2 : 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 : n004.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 0.20s 0.26s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU610^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n004.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:57:37 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 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
% 0.20/0.26 % (1329319)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.26 % (1329326)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=117894989:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.26 % (1329326)Refutation not found, incomplete strategy
% 0.20/0.26 % (1329326)------------------------------
% 0.20/0.26 % (1329326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (1329326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (1329326)CaDiCaL version: 2.1.3
% 0.20/0.26 % (1329326)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.26 % (1329326)Time elapsed: 0.001 s
% 0.20/0.26 % (1329326)Peak memory usage: 12 MB
% 0.20/0.26 % (1329326)Instructions burned: 3 (million)
% 0.20/0.26 % (1329326)------------------------------
% 0.20/0.26 % (1329326)------------------------------
% 0.20/0.26 % (1329325)lrs+10_16_si=on:nwc=1.5:random_seed=921550950:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.26 % (1329324)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3781491389:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.26 % (1329328)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1590209146:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.26 % (1329327)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=860214881: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)
% 0.20/0.26 % (1329324) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1329319-1329324"...
% 0.20/0.26 % (1329332)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2213136918:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.26 % (1329329)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=899674840:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.26 % (1329327) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1329319-1329327"...
% 0.20/0.26 % (1329328) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1329319-1329328"...
% 0.20/0.26 % (1329332)Instruction limit reached!
% 0.20/0.26 % (1329332)------------------------------
% 0.20/0.26 % (1329332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (1329332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (1329332)CaDiCaL version: 2.1.3
% 0.20/0.26 % (1329332)Termination reason: Instruction limit
% 0.20/0.26 % (1329332)Termination phase: Saturation
% 0.20/0.26 % (1329332)Time elapsed: 0.001 s
% 0.20/0.26 % (1329332)Peak memory usage: 12 MB
% 0.20/0.26 % (1329332)Instructions burned: 4 (million)
% 0.20/0.26 % (1329324)...printing done.
% 0.20/0.26 % (1329324)Refutation found. Thanks to Tanya!
% 0.20/0.26 % SZS status Theorem for theBenchmark
% 0.20/0.26 % SZS output start Proof for theBenchmark
% 0.20/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.26 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.26 thf(func_def_2, type, emptysetE: $o).
% 0.20/0.26 thf(func_def_4, type, in__Cong: $o).
% 0.20/0.26 thf(func_def_5, type, subset: ($i > $i > $o)).
% 0.20/0.26 thf(func_def_6, type, subsetI2: $o).
% 0.20/0.26 thf(func_def_7, type, setminus: ($i > $i > $i)).
% 0.20/0.26 thf(func_def_8, type, setminusI: $o).
% 0.20/0.26 thf(func_def_18, type, sK7: ($i > $i > $i)).
% 0.20/0.26 thf(func_def_24, type, sK13: $o).
% 0.20/0.26 thf(func_def_25, type, vNOT: ($o > $o)).
% 0.20/0.26 thf(f1,axiom,(
% 0.20/0.26 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE)).
% 0.20/0.26 thf(f3,axiom,(
% 0.20/0.26 (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 0.20/0.26 thf(f4,axiom,(
% 0.20/0.26 (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))) = setminusI)),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI)).
% 0.20/0.26 thf(f5,conjecture,(
% 0.20/0.26 emptysetE => (in__Cong => (subsetI2 => (setminusI => ! [X0 : $i,X1 : $i] : ((((setminus @ X0 @ X1)) = emptyset) => (subset @ X0 @ X1)))))),
% 0.20/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1)).
% 0.20/0.26 thf(f6,negated_conjecture,(
% 0.20/0.26 ~(emptysetE => (in__Cong => (subsetI2 => (setminusI => ! [X0 : $i,X1 : $i] : ((((setminus @ X0 @ X1)) = emptyset) => (subset @ X0 @ X1))))))),
% 0.20/0.26 inference(negated_conjecture,[status(cth)],[f5])).
% 0.20/0.26 thf(f7,plain,(
% 0.20/0.26 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI2)),
% 0.20/0.26 inference(rectify,[],[f3])).
% 0.20/0.26 thf(f8,plain,(
% 0.20/0.26 ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => ($true = ((subset @ X1 @ X0)))) <=> (subsetI2 = $true)),
% 0.20/0.26 inference(fool_elimination,[],[f7])).
% 0.20/0.26 thf(f9,plain,(
% 0.20/0.26 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => (~(in @ X1 @ X0) => (in @ X1 @ (setminus @ X2 @ X0)))) = setminusI)),
% 0.20/0.26 inference(rectify,[],[f4])).
% 0.20/0.26 thf(f10,plain,(
% 0.20/0.26 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X1 @ X2))) => (~ ($true = ((in @ X1 @ X0))) => ($true = ((in @ X1 @ (setminus @ X2 @ X0)))))) <=> (setminusI = $true)),
% 0.20/0.26 inference(fool_elimination,[],[f9])).
% 0.20/0.26 thf(f11,plain,(
% 0.20/0.26 (! [X0 : $i] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1) = emptysetE)),
% 0.20/0.26 inference(rectify,[],[f1])).
% 0.20/0.26 thf(f12,plain,(
% 0.20/0.26 ! [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) => ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 0.20/0.26 inference(fool_elimination,[],[f11])).
% 0.20/0.26 thf(f15,plain,(
% 0.20/0.26 ~(emptysetE => (in__Cong => (subsetI2 => (setminusI => ! [X0 : $i,X1 : $i] : ((((setminus @ X0 @ X1)) = emptyset) => (subset @ X0 @ X1))))))),
% 0.20/0.26 inference(rectify,[],[f6])).
% 0.20/0.26 thf(f16,plain,(
% 0.20/0.26 ~((emptysetE = $true) => ((in__Cong = $true) => ((subsetI2 = $true) => ((setminusI = $true) => ! [X0 : $i,X1 : $i] : ((emptyset = ((setminus @ X0 @ X1))) => (((subset @ X0 @ X1)) = $true))))))),
% 0.20/0.26 inference(fool_elimination,[],[f15])).
% 0.20/0.26 thf(f17,plain,(
% 0.20/0.26 (setminusI = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (($true = ((in @ X1 @ X2))) => (($true != ((in @ X1 @ X0))) => ($true = ((in @ X1 @ (setminus @ X2 @ X0))))))),
% 0.20/0.26 inference(flattening,[],[f10])).
% 0.20/0.26 thf(f18,plain,(
% 0.20/0.26 (((? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & (emptyset = ((setminus @ X0 @ X1)))) & (setminusI = $true)) & (subsetI2 = $true)) & (in__Cong = $true)) & (emptysetE = $true)),
% 0.20/0.26 inference(ennf_transformation,[],[f16])).
% 0.20/0.26 thf(f19,plain,(
% 0.20/0.26 (emptysetE = $true) & (setminusI = $true) & ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & (emptyset = ((setminus @ X0 @ X1)))) & (in__Cong = $true) & (subsetI2 = $true)),
% 0.20/0.26 inference(flattening,[],[f18])).
% 0.20/0.26 thf(f20,plain,(
% 0.20/0.26 (subsetI2 = $true) <=> ! [X1 : $i,X0 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)))),
% 0.20/0.26 inference(ennf_transformation,[],[f8])).
% 0.20/0.26 thf(f21,plain,(
% 0.20/0.26 (emptysetE = $true) <=> ! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1))),
% 0.20/0.26 inference(ennf_transformation,[],[f12])).
% 0.20/0.26 thf(f22,plain,(
% 0.20/0.26 (setminusI = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : ((($true = ((in @ X1 @ (setminus @ X2 @ X0)))) | ($true = ((in @ X1 @ X0)))) | ($true != ((in @ X1 @ X2))))),
% 0.20/0.26 inference(ennf_transformation,[],[f17])).
% 0.20/0.26 thf(f23,plain,(
% 0.20/0.26 ! [X1 : $i,X2 : $i,X0 : $i] : (($true = ((in @ X1 @ (setminus @ X2 @ X0)))) | ($true = ((in @ X1 @ X0))) | ($true != ((in @ X1 @ X2)))) <=> (setminusI = $true)),
% 0.20/0.26 inference(flattening,[],[f22])).
% 0.20/0.26 thf(f25,plain,(
% 0.20/0.26 (! [X1 : $i,X2 : $i,X0 : $i] : (($true = ((in @ X1 @ (setminus @ X2 @ X0)))) | ($true = ((in @ X1 @ X0))) | ($true != ((in @ X1 @ X2)))) | (setminusI != $true)) & ((setminusI = $true) | ? [X1 : $i,X2 : $i,X0 : $i] : (($true != ((in @ X1 @ (setminus @ X2 @ X0)))) & ($true != ((in @ X1 @ X0))) & ($true = ((in @ X1 @ X2)))))),
% 0.20/0.26 inference(nnf_transformation,[],[f23])).
% 0.20/0.26 thf(f26,plain,(
% 0.20/0.26 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ (setminus @ X1 @ X2)))) | ($true = ((in @ X0 @ X2))) | ($true != ((in @ X0 @ X1)))) | (setminusI != $true)) & ((setminusI = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ (setminus @ X4 @ X5))) != $true) & ($true != ((in @ X3 @ X5))) & ($true = ((in @ X3 @ X4)))))),
% 0.20/0.26 inference(rectify,[],[f25])).
% 0.20/0.26 thf(f27,plain,(
% 0.20/0.26 (! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X0 @ (setminus @ X1 @ X2)))) | ($true = ((in @ X0 @ X2))) | ($true != ((in @ X0 @ X1)))) | (setminusI != $true)) & ((setminusI = $true) | (($true != ((in @ sK0 @ (setminus @ sK1 @ sK2)))) & ($true != ((in @ sK0 @ sK2))) & ($true = ((in @ sK0 @ sK1)))))),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0),skolemize(X4,sK1),skolemize(X5,sK2)],[f26])).
% 0.20/0.26 thf(f28,plain,(
% 0.20/0.26 (emptysetE = $true) & (setminusI = $true) & (($true != ((subset @ sK3 @ sK4))) & (emptyset = ((setminus @ sK3 @ sK4)))) & (in__Cong = $true) & (subsetI2 = $true)),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f19])).
% 0.20/0.26 thf(f29,plain,(
% 0.20/0.26 ((subsetI2 = $true) | ? [X1 : $i,X0 : $i] : (($true != ((subset @ X1 @ X0))) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)))) & (! [X1 : $i,X0 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (subsetI2 != $true))),
% 0.20/0.26 inference(nnf_transformation,[],[f20])).
% 0.20/0.26 thf(f30,plain,(
% 0.20/0.26 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true)))) & (! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | ? [X5 : $i] : (($true = ((in @ X5 @ X3))) & ($true != ((in @ X5 @ X4))))) | (subsetI2 != $true))),
% 0.20/0.26 inference(rectify,[],[f29])).
% 0.20/0.26 thf(f31,plain,(
% 0.20/0.26 ((subsetI2 = $true) | (($true != ((subset @ sK5 @ sK6))) & ! [X2 : $i] : ((((in @ X2 @ sK5)) != $true) | ($true = ((in @ X2 @ sK6)))))) & (! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | (($true = ((in @ (sK7 @ X4 @ X3) @ X3))) & ($true != ((in @ (sK7 @ X4 @ X3) @ X4))))) | (subsetI2 != $true))),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,vAPP]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X5,sK7 @ X4 @ X3)],[f30])).
% 0.20/0.26 thf(f35,plain,(
% 0.20/0.26 ((emptysetE = $true) | ? [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) & ? [X1 : $o] : ($true != X1))) & (! [X0 : $i] : ((((in @ X0 @ emptyset)) != $true) | ! [X1 : $o] : ($true = X1)) | (emptysetE != $true))),
% 0.20/0.26 inference(nnf_transformation,[],[f21])).
% 0.20/0.26 thf(f36,plain,(
% 0.20/0.26 ((emptysetE = $true) | ? [X0 : $i] : ((((in @ X0 @ emptyset)) = $true) & ? [X1 : $o] : ($true != X1))) & (! [X2 : $i] : ((((in @ X2 @ emptyset)) != $true) | ! [X3 : $o] : ($true = X3)) | (emptysetE != $true))),
% 0.20/0.26 inference(rectify,[],[f35])).
% 0.20/0.26 thf(f37,plain,(
% 0.20/0.26 ((emptysetE = $true) | (($true = ((in @ sK12 @ emptyset))) & ($true != sK13))) & (! [X2 : $i] : ((((in @ X2 @ emptyset)) != $true) | ! [X3 : $o] : ($true = X3)) | (emptysetE != $true))),
% 0.20/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f36])).
% 0.20/0.26 thf(f41,plain,(
% 0.20/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (setminus @ X1 @ X2)))) | ($true = ((in @ X0 @ X2))) | ($true != ((in @ X0 @ X1))) | (setminusI != $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f27])).
% 0.20/0.26 thf(f42,plain,(
% 0.20/0.26 (subsetI2 = $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f28])).
% 0.20/0.26 thf(f44,plain,(
% 0.20/0.26 (emptyset = ((setminus @ sK3 @ sK4)))),
% 0.20/0.26 inference(cnf_transformation,[],[f28])).
% 0.20/0.26 thf(f45,plain,(
% 0.20/0.26 ($true != ((subset @ sK3 @ sK4)))),
% 0.20/0.26 inference(cnf_transformation,[],[f28])).
% 0.20/0.26 thf(f46,plain,(
% 0.20/0.26 (setminusI = $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f28])).
% 0.20/0.26 thf(f47,plain,(
% 0.20/0.26 (emptysetE = $true)),
% 0.20/0.26 inference(cnf_transformation,[],[f28])).
% 0.20/0.26 thf(f48,plain,(
% 0.20/0.26 ( ! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | ($true != ((in @ (sK7 @ X4 @ X3) @ X4))) | (subsetI2 != $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f31])).
% 0.20/0.26 thf(f49,plain,(
% 0.20/0.26 ( ! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | ($true = ((in @ (sK7 @ X4 @ X3) @ X3))) | (subsetI2 != $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f31])).
% 0.20/0.26 thf(f56,plain,(
% 0.20/0.26 ( ! [X2 : $i,X3 : $o] : ((((in @ X2 @ emptyset)) != $true) | ($true = X3) | (emptysetE != $true)) )),
% 0.20/0.26 inference(cnf_transformation,[],[f37])).
% 0.20/0.26 thf(f61,plain,(
% 0.20/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((in @ X0 @ (setminus @ X1 @ X2)))) | ($true != ((in @ X0 @ X1))) | ($true = ((in @ X0 @ X2)))) )),
% 0.20/0.26 inference(definition_unfolding,[],[f41,f46])).
% 0.20/0.26 thf(f67,plain,(
% 0.20/0.26 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ($true = ((in @ (sK7 @ X4 @ X3) @ X3))) | (((subset @ X3 @ X4)) = $true)) )),
% 0.20/0.26 inference(definition_unfolding,[],[f49,f42])).
% 0.20/0.26 thf(f68,plain,(
% 0.20/0.26 ( ! [X3 : $i,X4 : $i] : (($true != $true) | (((subset @ X3 @ X4)) = $true) | ($true != ((in @ (sK7 @ X4 @ X3) @ X4)))) )),
% 0.20/0.26 inference(definition_unfolding,[],[f48,f42])).
% 0.20/0.26 thf(f75,plain,(
% 0.20/0.26 ( ! [X2 : $i,X3 : $o] : (($true = X3) | (((in @ X2 @ emptyset)) != $true) | ($true != $true)) )),
% 0.20/0.26 inference(definition_unfolding,[],[f56,f47])).
% 0.20/0.26 thf(f78,plain,(
% 0.20/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ X1))) | ($true = ((in @ X0 @ X2))) | ($true = ((in @ X0 @ (setminus @ X1 @ X2))))) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f61])).
% 0.20/0.26 thf(f81,plain,(
% 0.20/0.26 ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK7 @ X4 @ X3) @ X3))) | (((subset @ X3 @ X4)) = $true)) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f67])).
% 0.20/0.26 thf(f82,plain,(
% 0.20/0.26 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (sK7 @ X4 @ X3) @ X4))) | (((subset @ X3 @ X4)) = $true)) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f68])).
% 0.20/0.26 thf(f85,plain,(
% 0.20/0.26 ( ! [X2 : $i,X3 : $o] : ((((in @ X2 @ emptyset)) != $true) | ($true = X3)) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f75])).
% 0.20/0.26 thf(f87,definition,(
% 0.20/0.26 spl14_1 <=> ! [X2 : $i] : (((in @ X2 @ emptyset)) != $true)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition])).
% 0.20/0.26 thf(f88,plain,(
% 0.20/0.26 ( ! [X2 : $i] : ((((in @ X2 @ emptyset)) != $true)) ) | ~spl14_1),
% 0.20/0.26 inference(avatar_component_clause,[],[f87])).
% 0.20/0.26 thf(f90,definition,(
% 0.20/0.26 spl14_2 <=> ! [X3 : $o] : ($true = X3)),
% 0.20/0.26 introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition])).
% 0.20/0.26 thf(f91,plain,(
% 0.20/0.26 ( ! [X3 : $o] : (($true = X3)) ) | ~spl14_2),
% 0.20/0.26 inference(avatar_component_clause,[],[f90])).
% 0.20/0.26 thf(f92,plain,(
% 0.20/0.26 spl14_1 | spl14_2),
% 0.20/0.26 inference(avatar_split_clause,[],[f85,f90,f87])).
% 0.20/0.26 thf(f96,plain,(
% 0.20/0.26 ($true != $true) | ~spl14_2),
% 0.20/0.26 inference(constrained_superposition,[],[f45,f91])).
% 0.20/0.26 thf(f97,plain,(
% 0.20/0.26 $false | ~spl14_2),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f96])).
% 0.20/0.26 thf(f98,plain,(
% 0.20/0.26 ~spl14_2),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f97])).
% 0.20/0.26 thf(f104,plain,(
% 0.20/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((subset @ X1 @ X0))) | ($true = ((in @ (sK7 @ X0 @ X1) @ X2))) | ($true != $true) | ($true = ((in @ (sK7 @ X0 @ X1) @ (setminus @ X1 @ X2))))) )),
% 0.20/0.26 inference(constrained_superposition,[],[f78,f81])).
% 0.20/0.26 thf(f105,plain,(
% 0.20/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK7 @ X0 @ X1) @ (setminus @ X1 @ X2)))) | ($true = ((in @ (sK7 @ X0 @ X1) @ X2))) | ($true = ((subset @ X1 @ X0)))) )),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f104])).
% 0.20/0.26 thf(f106,plain,(
% 0.20/0.26 ( ! [X0 : $i] : (($true = ((subset @ sK3 @ X0))) | ($true = ((in @ (sK7 @ X0 @ sK3) @ emptyset))) | ($true = ((in @ (sK7 @ X0 @ sK3) @ sK4)))) )),
% 0.20/0.26 inference(constrained_superposition,[],[f105,f44])).
% 0.20/0.26 thf(f112,plain,(
% 0.20/0.26 ( ! [X0 : $i] : (($true = ((in @ (sK7 @ X0 @ sK3) @ sK4))) | ($true = ((subset @ sK3 @ X0)))) ) | ~spl14_1),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f106,f88])).
% 0.20/0.26 thf(f114,plain,(
% 0.20/0.26 ($true != $true) | ($true = ((subset @ sK3 @ sK4))) | ($true = ((subset @ sK3 @ sK4))) | ~spl14_1),
% 0.20/0.26 inference(constrained_superposition,[],[f82,f112])).
% 0.20/0.26 thf(f115,plain,(
% 0.20/0.26 ($true != $true) | ($true = ((subset @ sK3 @ sK4))) | ~spl14_1),
% 0.20/0.26 inference(duplicate_literal_removal,[],[f114])).
% 0.20/0.26 thf(f116,plain,(
% 0.20/0.26 ($true = ((subset @ sK3 @ sK4))) | ~spl14_1),
% 0.20/0.26 inference(trivial_inequality_removal,[],[f115])).
% 0.20/0.26 thf(f118,plain,(
% 0.20/0.26 $false | ~spl14_1),
% 0.20/0.26 inference(forward_subsumption_resolution,[],[f116,f45])).
% 0.20/0.26 thf(f119,plain,(
% 0.20/0.26 ~spl14_1),
% 0.20/0.26 inference(avatar_contradiction_clause,[],[f118])).
% 0.20/0.26 cnf(s1, plain, spl14_1 | spl14_2, inference(sat_conversion,[],[f92])).
% 0.20/0.26 cnf(s2, plain, ~spl14_2, inference(sat_conversion,[],[f98])).
% 0.20/0.26 cnf(s3, plain, ~spl14_1, inference(sat_conversion,[],[f119])).
% 0.20/0.26 cnf(s4, plain, $false, inference(rat,[],[s1,s2,s3])).
% 0.20/0.26 thf(f120,plain,(
% 0.20/0.26 $false),
% 0.20/0.26 inference(avatar_sat_refutation,[],[s4])).
% 0.20/0.26 % SZS output end Proof for theBenchmark
% 0.20/0.26 % (1329324)------------------------------
% 0.20/0.26 % (1329324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.26 % (1329324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.26 % (1329324)CaDiCaL version: 2.1.3
% 0.20/0.26 % (1329324)Termination reason: Refutation
% 0.20/0.26 % (1329324)Time elapsed: 0.006 s
% 0.20/0.26 % (1329324)Peak memory usage: 13 MB
% 0.20/0.26 % (1329324)Instructions burned: 8 (million)
% 0.20/0.26 % (1329319)Success in time 0.035 s
% 0.20/0.26 % Vampire exiting
%------------------------------------------------------------------------------