%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU634^2 : 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 : n013.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 08:30:26 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU634^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n013.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:59:51 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (2164601)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (2164607)lrs+10_16_si=on:nwc=1.5:random_seed=2207299141:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (2164607)Instruction limit reached!
% 0.20/0.28 % (2164607)------------------------------
% 0.20/0.28 % (2164607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2164607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2164607)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2164607)Termination reason: Instruction limit
% 0.20/0.28 % (2164607)Termination phase: Saturation
% 0.20/0.28 % (2164607)Time elapsed: 0.006 s
% 0.20/0.28 % (2164607)Peak memory usage: 12 MB
% 0.20/0.28 % (2164607)Instructions burned: 21 (million)
% 0.20/0.28 % (2164606)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1997028900:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (2164608)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3270150786:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (2164610)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1284230420:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (2164609)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=3162295540: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)
% 0.20/0.28 % (2164608)Refutation not found, incomplete strategy
% 0.20/0.28 % (2164608)------------------------------
% 0.20/0.28 % (2164608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2164608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2164608)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2164608)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.28 % (2164608)Time elapsed: 0.002 s
% 0.20/0.28 % (2164608)Peak memory usage: 12 MB
% 0.20/0.28 % (2164608)Instructions burned: 2 (million)
% 0.20/0.28 % (2164608)------------------------------
% 0.20/0.28 % (2164608)------------------------------
% 0.20/0.28 % (2164610) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2164601-2164610"...
% 0.20/0.28 % (2164612)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (2164612)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
% 0.20/0.28 % (2164606) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2164601-2164606"...
% 0.20/0.28 % (2164609) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2164601-2164609"...
% 0.20/0.28 % (2164610)...printing done.
% 0.20/0.28 % (2164611)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3273448787:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (2164606)...printing done.
% 0.20/0.28 % (2164610)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.28 thf(func_def_2, type, setadjoin: ($i > $i > $i)).
% 0.20/0.28 thf(func_def_3, type, setunion: ($i > $i)).
% 0.20/0.28 thf(func_def_4, type, uniqinunit: $o).
% 0.20/0.28 thf(func_def_6, type, subset: ($i > $i > $o)).
% 0.20/0.28 thf(func_def_7, type, subsetI2: $o).
% 0.20/0.28 thf(func_def_8, type, setunionE2: $o).
% 0.20/0.28 thf(func_def_13, type, sK2: ($i > $i > $i)).
% 0.20/0.28 thf(func_def_14, type, sK3: ($i > $i > $i)).
% 0.20/0.28 thf(f1,axiom,(
% 0.20/0.28 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 0.20/0.28 thf(f2,axiom,(
% 0.20/0.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 0.20/0.28 thf(f3,axiom,(
% 0.20/0.28 (setunionE2 = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (setunion @ X0)) => ? [X2 : $i] : ((in @ X2 @ X0) & (in @ X1 @ X2))))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2)).
% 0.20/0.28 thf(f4,conjecture,(
% 0.20/0.28 uniqinunit => (subsetI2 => (setunionE2 => ! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1)).
% 0.20/0.28 thf(f5,negated_conjecture,(
% 0.20/0.28 ~(uniqinunit => (subsetI2 => (setunionE2 => ! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 ~(uniqinunit => (subsetI2 => (setunionE2 => ! [X0 : $i] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))))),
% 0.20/0.28 inference(rectify,[],[f5])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 ~((uniqinunit = $true) => ((subsetI2 = $true) => ((setunionE2 = $true) => ! [X0 : $i] : (((subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) = $true))))),
% 0.20/0.28 inference(fool_elimination,[],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 (setunionE2 = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) => ? [X2 : $i] : ((in @ X2 @ X1) & (in @ X0 @ X2))))),
% 0.20/0.28 inference(rectify,[],[f3])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 (setunionE2 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (setunion @ X1)))) => ? [X2 : $i] : ((((in @ X0 @ X2)) = $true) & (((in @ X2 @ X1)) = $true)))),
% 0.20/0.28 inference(fool_elimination,[],[f8])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 thf(f11,plain,(
% 0.20/0.28 ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true)) <=> (subsetI2 = $true)),
% 0.20/0.28 inference(fool_elimination,[],[f10])).
% 0.20/0.28 thf(f12,plain,(
% 0.20/0.28 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.20/0.28 inference(rectify,[],[f1])).
% 0.20/0.28 thf(f13,plain,(
% 0.20/0.28 (uniqinunit = $true) <=> ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) => (X0 = X1))),
% 0.20/0.28 inference(fool_elimination,[],[f12])).
% 0.20/0.28 thf(f14,plain,(
% 0.20/0.28 ((? [X0 : $i] : (((subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) != $true) & (setunionE2 = $true)) & (subsetI2 = $true)) & (uniqinunit = $true)),
% 0.20/0.28 inference(ennf_transformation,[],[f7])).
% 0.20/0.28 thf(f15,plain,(
% 0.20/0.28 (uniqinunit = $true) & (subsetI2 = $true) & ? [X0 : $i] : (((subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) != $true) & (setunionE2 = $true)),
% 0.20/0.28 inference(flattening,[],[f14])).
% 0.20/0.28 thf(f16,plain,(
% 0.20/0.28 (subsetI2 = $true) <=> ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)))),
% 0.20/0.28 inference(ennf_transformation,[],[f11])).
% 0.20/0.28 thf(f17,plain,(
% 0.20/0.28 ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (setunion @ X1)))) | ? [X2 : $i] : ((((in @ X0 @ X2)) = $true) & (((in @ X2 @ X1)) = $true))) <=> (setunionE2 = $true)),
% 0.20/0.28 inference(ennf_transformation,[],[f9])).
% 0.20/0.28 thf(f18,plain,(
% 0.20/0.28 ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true) | (X0 = X1)) <=> (uniqinunit = $true)),
% 0.20/0.28 inference(ennf_transformation,[],[f13])).
% 0.20/0.28 thf(f19,plain,(
% 0.20/0.28 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)))) & (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) | ? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true))) | (subsetI2 != $true))),
% 0.20/0.28 inference(nnf_transformation,[],[f16])).
% 0.20/0.28 thf(f20,plain,(
% 0.20/0.28 ((subsetI2 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)))) & (! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | ? [X5 : $i] : ((((in @ X5 @ X4)) != $true) & (((in @ X5 @ X3)) = $true))) | (subsetI2 != $true))),
% 0.20/0.28 inference(rectify,[],[f19])).
% 0.20/0.28 thf(f21,plain,(
% 0.20/0.28 ((subsetI2 = $true) | (($true != ((subset @ sK0 @ sK1))) & ! [X2 : $i] : (($true = ((in @ X2 @ sK1))) | (((in @ X2 @ sK0)) != $true)))) & (! [X3 : $i,X4 : $i] : ((((subset @ X3 @ X4)) = $true) | ((((in @ (sK2 @ X4 @ X3) @ X4)) != $true) & (((in @ (sK2 @ X4 @ X3) @ X3)) = $true))) | (subsetI2 != $true))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X5,sK2 @ X4 @ X3)],[f20])).
% 0.20/0.28 thf(f22,plain,(
% 0.20/0.28 (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (setunion @ X1)))) | ? [X2 : $i] : ((((in @ X0 @ X2)) = $true) & (((in @ X2 @ X1)) = $true))) | (setunionE2 != $true)) & ((setunionE2 = $true) | ? [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (setunion @ X1)))) & ! [X2 : $i] : ((((in @ X0 @ X2)) != $true) | (((in @ X2 @ X1)) != $true))))),
% 0.20/0.28 inference(nnf_transformation,[],[f17])).
% 0.20/0.28 thf(f23,plain,(
% 0.20/0.28 (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (setunion @ X1)))) | ? [X2 : $i] : ((((in @ X0 @ X2)) = $true) & (((in @ X2 @ X1)) = $true))) | (setunionE2 != $true)) & ((setunionE2 = $true) | ? [X3 : $i,X4 : $i] : ((((in @ X3 @ (setunion @ X4))) = $true) & ! [X5 : $i] : ((((in @ X3 @ X5)) != $true) | (((in @ X5 @ X4)) != $true))))),
% 0.20/0.28 inference(rectify,[],[f22])).
% 0.20/0.28 thf(f24,plain,(
% 0.20/0.28 (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (setunion @ X1)))) | ((((in @ X0 @ (sK3 @ X1 @ X0))) = $true) & ($true = ((in @ (sK3 @ X1 @ X0) @ X1))))) | (setunionE2 != $true)) & ((setunionE2 = $true) | ((((in @ sK4 @ (setunion @ sK5))) = $true) & ! [X5 : $i] : ((((in @ sK4 @ X5)) != $true) | (((in @ X5 @ sK5)) != $true))))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK4,sK5]),skolemize(X5,sK2 @ X4 @ X3),skolemize(X3,sK4),skolemize(X4,sK5)],[f23])).
% 0.20/0.28 thf(f25,plain,(
% 0.20/0.28 (uniqinunit = $true) & (subsetI2 = $true) & ($true != ((subset @ (setunion @ (setadjoin @ sK6 @ emptyset)) @ sK6))) & (setunionE2 = $true)),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X0,sK6)],[f15])).
% 0.20/0.28 thf(f26,plain,(
% 0.20/0.28 (! [X1 : $i,X0 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X1 : $i,X0 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) & (X0 != X1)))),
% 0.20/0.28 inference(nnf_transformation,[],[f18])).
% 0.20/0.28 thf(f27,plain,(
% 0.20/0.28 (! [X0 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ emptyset))) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X2 : $i,X3 : $i] : ((((in @ X3 @ (setadjoin @ X2 @ emptyset))) = $true) & (X2 != X3)))),
% 0.20/0.28 inference(rectify,[],[f26])).
% 0.20/0.28 thf(f28,plain,(
% 0.20/0.28 (! [X0 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ emptyset))) != $true) | (X0 = X1)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ((((in @ sK8 @ (setadjoin @ sK7 @ emptyset))) = $true) & (sK7 != sK8)))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X2,sK7),skolemize(X3,sK8)],[f27])).
% 0.20/0.28 thf(f29,plain,(
% 0.20/0.28 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X3)) = $true) | (subsetI2 != $true) | (((subset @ X3 @ X4)) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f21])).
% 0.20/0.28 thf(f30,plain,(
% 0.20/0.28 ( ! [X3 : $i,X4 : $i] : ((subsetI2 != $true) | (((subset @ X3 @ X4)) = $true) | (((in @ (sK2 @ X4 @ X3) @ X4)) != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f21])).
% 0.20/0.28 thf(f35,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (setunion @ X1)))) | (setunionE2 != $true) | ($true = ((in @ (sK3 @ X1 @ X0) @ X1)))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f24])).
% 0.20/0.28 thf(f36,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (setunion @ X1)))) | (setunionE2 != $true) | (((in @ X0 @ (sK3 @ X1 @ X0))) = $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f24])).
% 0.20/0.28 thf(f37,plain,(
% 0.20/0.28 (setunionE2 = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f25])).
% 0.20/0.28 thf(f38,plain,(
% 0.20/0.28 ($true != ((subset @ (setunion @ (setadjoin @ sK6 @ emptyset)) @ sK6)))),
% 0.20/0.28 inference(cnf_transformation,[],[f25])).
% 0.20/0.28 thf(f39,plain,(
% 0.20/0.28 (subsetI2 = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f25])).
% 0.20/0.28 thf(f40,plain,(
% 0.20/0.28 (uniqinunit = $true)),
% 0.20/0.28 inference(cnf_transformation,[],[f25])).
% 0.20/0.28 thf(f43,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | (((in @ X1 @ (setadjoin @ X0 @ emptyset))) != $true) | (uniqinunit != $true)) )),
% 0.20/0.28 inference(cnf_transformation,[],[f28])).
% 0.20/0.28 thf(f48,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ emptyset))) != $true) | (X0 = X1)) )),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f43,f40])).
% 0.20/0.28 thf(f49,plain,(
% 0.20/0.28 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X3)) = $true) | (((subset @ X3 @ X4)) = $true)) )),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f29,f39])).
% 0.20/0.28 thf(f54,plain,(
% 0.20/0.28 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK2 @ X4 @ X3) @ X4)) != $true) | (((subset @ X3 @ X4)) = $true)) )),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f30,f39])).
% 0.20/0.28 thf(f60,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X1 @ X0) @ X1))) | ($true != ((in @ X0 @ (setunion @ X1))))) )),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f35,f37])).
% 0.20/0.28 thf(f61,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((((sK3 @ (setadjoin @ X0 @ emptyset) @ X1)) = X0) | ($true != $true) | (((in @ X1 @ (setunion @ (setadjoin @ X0 @ emptyset)))) != $true)) )),
% 0.20/0.28 inference(superposition,[],[f48,f60])).
% 0.20/0.28 thf(f62,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (setunion @ (setadjoin @ X0 @ emptyset)))) != $true) | (((sK3 @ (setadjoin @ X0 @ emptyset) @ X1)) = X0)) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f61])).
% 0.20/0.28 thf(f63,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((((subset @ (setunion @ (setadjoin @ X1 @ emptyset)) @ X0)) = $true) | (((sK3 @ (setadjoin @ X1 @ emptyset) @ (sK2 @ X0 @ (setunion @ (setadjoin @ X1 @ emptyset))))) = X1) | ($true != $true)) )),
% 0.20/0.28 inference(superposition,[],[f62,f49])).
% 0.20/0.28 thf(f65,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((((sK3 @ (setadjoin @ X1 @ emptyset) @ (sK2 @ X0 @ (setunion @ (setadjoin @ X1 @ emptyset))))) = X1) | (((subset @ (setunion @ (setadjoin @ X1 @ emptyset)) @ X0)) = $true)) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f63])).
% 0.20/0.28 thf(f71,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (sK3 @ X1 @ X0))) = $true) | ($true != ((in @ X0 @ (setunion @ X1))))) )),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f36,f37])).
% 0.20/0.28 thf(f72,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK2 @ X1 @ (setunion @ (setadjoin @ X0 @ emptyset))) @ X0)) = $true) | (((in @ (sK2 @ X1 @ (setunion @ (setadjoin @ X0 @ emptyset))) @ (setunion @ (setadjoin @ X0 @ emptyset)))) != $true) | ($true = ((subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X1)))) )),
% 0.20/0.28 inference(superposition,[],[f71,f65])).
% 0.20/0.28 thf(f73,plain,(
% 0.20/0.28 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK2 @ X1 @ (setunion @ (setadjoin @ X0 @ emptyset))) @ X0)) = $true) | ($true = ((subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X1)))) )),
% 0.20/0.28 inference(forward_subsumption_resolution,[],[f72,f49])).
% 0.20/0.28 thf(f74,plain,(
% 0.20/0.28 ( ! [X0 : $i] : ((((subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) = $true) | (((subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) = $true) | ($true != $true)) )),
% 0.20/0.28 inference(superposition,[],[f54,f73])).
% 0.20/0.28 thf(f78,plain,(
% 0.20/0.28 ( ! [X0 : $i] : ((((subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) = $true) | ($true != $true)) )),
% 0.20/0.28 inference(duplicate_literal_removal,[],[f74])).
% 0.20/0.28 thf(f79,plain,(
% 0.20/0.28 ( ! [X0 : $i] : ((((subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) = $true)) )),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f78])).
% 0.20/0.28 thf(f81,plain,(
% 0.20/0.28 ($true != $true)),
% 0.20/0.28 inference(superposition,[],[f38,f79])).
% 0.20/0.28 thf(f82,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f81])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (2164610)------------------------------
% 0.20/0.28 % (2164610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2164610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2164610)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2164610)Termination reason: Refutation
% 0.20/0.28 % (2164610)Time elapsed: 0.007 s
% 0.20/0.28 % (2164610)Peak memory usage: 12 MB
% 0.20/0.28 % (2164610)Instructions burned: 10 (million)
% 0.20/0.28 % (2164601)Success in time 0.045 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------