%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU574^2 : 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 : n014.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 08:30:08 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU574^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n014.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 13:51:15 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.21 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
% 0.08/0.26 % (2696454)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.26 % (2696460)lrs+10_16_si=on:nwc=1.5:random_seed=1009977171:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.26 % (2696465)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.26 % (2696465)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
% 0.08/0.26 % (2696460)Instruction limit reached!
% 0.08/0.26 % (2696460)------------------------------
% 0.08/0.26 % (2696460)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (2696460)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (2696460)CaDiCaL version: 2.1.3
% 0.08/0.26 % (2696460)Termination reason: Instruction limit
% 0.08/0.26 % (2696460)Termination phase: Saturation
% 0.08/0.26 % (2696460)Time elapsed: 0.006 s
% 0.08/0.26 % (2696460)Peak memory usage: 12 MB
% 0.08/0.26 % (2696460)Instructions burned: 20 (million)
% 0.08/0.26 % (2696459)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4069359802:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.26 % (2696461)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3952759400:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.26 % (2696463)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=907628958:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.26 % (2696464)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=486659416:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.26 % (2696462)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=3253655363: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)
% 0.08/0.26 % (2696465)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=3715505842:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.26 % (2696461)Refutation not found, incomplete strategy
% 0.08/0.26 % (2696461)------------------------------
% 0.08/0.26 % (2696461)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (2696461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (2696461)CaDiCaL version: 2.1.3
% 0.08/0.26 % (2696461)Termination reason: Refutation not found, incomplete strategy
% 0.08/0.26 % (2696461)Time elapsed: 0.002 s
% 0.08/0.26 % (2696461)Peak memory usage: 12 MB
% 0.08/0.26 % (2696461)Instructions burned: 2 (million)
% 0.08/0.26 % (2696461)------------------------------
% 0.08/0.26 % (2696461)------------------------------
% 0.08/0.26 % (2696459) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2696454-2696459"...
% 0.08/0.26 % (2696463) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2696454-2696463"...
% 0.08/0.26 % (2696464) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2696454-2696464"...
% 0.08/0.26 % (2696459)...printing done.
% 0.08/0.26 % (2696463)...printing done.
% 0.08/0.26 % (2696459)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% 0.08/0.26 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.26 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.08/0.26 thf(func_def_1, type, setext: $o).
% 0.08/0.26 thf(func_def_3, type, subset: ($i > $i > $o)).
% 0.08/0.26 thf(func_def_4, type, subsetE: $o).
% 0.08/0.26 thf(func_def_9, type, sK2: ($i > $i > $i)).
% 0.08/0.26 thf(func_def_10, type, sK3: ($i > $i > $i)).
% 0.08/0.26 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.08/0.26 thf(f1,axiom,(
% 0.08/0.26 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))) = setext)),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext)).
% 0.08/0.26 thf(f2,axiom,(
% 0.08/0.26 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE)).
% 0.08/0.26 thf(f3,conjecture,(
% 0.08/0.26 setext => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 0.08/0.26 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub)).
% 0.08/0.26 thf(f4,negated_conjecture,(
% 0.08/0.26 ~(setext => (subsetE => ! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1)))))),
% 0.08/0.26 inference(negated_conjecture,[status(cth)],[f3])).
% 0.08/0.26 thf(f5,plain,(
% 0.08/0.26 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.08/0.26 inference(rectify,[],[f2])).
% 0.08/0.26 thf(f6,plain,(
% 0.08/0.26 (subsetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((subset @ X0 @ X1)) = $true) => ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)))),
% 0.08/0.26 inference(fool_elimination,[],[f5])).
% 0.08/0.26 thf(f7,plain,(
% 0.08/0.26 (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => (in @ X3 @ X0)) => (X0 = X1))) = setext)),
% 0.08/0.26 inference(rectify,[],[f1])).
% 0.08/0.26 thf(f8,plain,(
% 0.08/0.26 (setext = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => (((in @ X3 @ X0)) = $true)) => (X0 = X1)))),
% 0.08/0.26 inference(fool_elimination,[],[f7])).
% 0.08/0.26 thf(f9,plain,(
% 0.08/0.26 ~(setext => (subsetE => ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1)))))),
% 0.08/0.26 inference(rectify,[],[f4])).
% 0.08/0.26 thf(f10,plain,(
% 0.08/0.26 ~((setext = $true) => ((subsetE = $true) => ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) => ((((subset @ X0 @ X1)) = $true) => (X0 = X1)))))),
% 0.08/0.26 inference(fool_elimination,[],[f9])).
% 0.08/0.26 thf(f11,plain,(
% 0.08/0.26 (? [X0 : $i,X1 : $i] : (((X0 != X1) & (((subset @ X0 @ X1)) = $true)) & (((subset @ X1 @ X0)) = $true)) & (subsetE = $true)) & (setext = $true)),
% 0.08/0.26 inference(ennf_transformation,[],[f10])).
% 0.08/0.26 thf(f12,plain,(
% 0.08/0.26 (subsetE = $true) & ? [X0 : $i,X1 : $i] : ((X0 != X1) & (((subset @ X0 @ X1)) = $true) & (((subset @ X1 @ X0)) = $true)) & (setext = $true)),
% 0.08/0.26 inference(flattening,[],[f11])).
% 0.08/0.26 thf(f13,plain,(
% 0.08/0.26 (setext = $true) <=> ! [X0 : $i,X1 : $i] : (((X0 = X1) | ? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((in @ X3 @ X0)) != $true))) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)))),
% 0.08/0.26 inference(ennf_transformation,[],[f8])).
% 0.08/0.26 thf(f14,plain,(
% 0.08/0.26 (setext = $true) <=> ! [X1 : $i,X0 : $i] : ((X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)) | ? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((in @ X3 @ X0)) != $true)))),
% 0.08/0.26 inference(flattening,[],[f13])).
% 0.08/0.26 thf(f15,plain,(
% 0.08/0.26 (subsetE = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) | (((subset @ X0 @ X1)) != $true))),
% 0.08/0.26 inference(ennf_transformation,[],[f6])).
% 0.08/0.26 thf(f16,plain,(
% 0.08/0.26 ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ X0)) != $true) | (((subset @ X0 @ X1)) != $true) | (((in @ X2 @ X1)) = $true)) <=> (subsetE = $true)),
% 0.08/0.26 inference(flattening,[],[f15])).
% 0.08/0.26 thf(f17,plain,(
% 0.08/0.26 ((setext = $true) | ? [X1 : $i,X0 : $i] : ((X0 != X1) & ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true)) & ! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((in @ X3 @ X0)) = $true)))) & (! [X1 : $i,X0 : $i] : ((X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & (((in @ X2 @ X1)) != $true)) | ? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((in @ X3 @ X0)) != $true))) | (setext != $true))),
% 0.08/0.26 inference(nnf_transformation,[],[f14])).
% 0.08/0.26 thf(f18,plain,(
% 0.08/0.26 ((setext = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)) & ! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ X1)) = $true)))) & (! [X4 : $i,X5 : $i] : ((X4 = X5) | ? [X6 : $i] : ((((in @ X6 @ X5)) = $true) & (((in @ X6 @ X4)) != $true)) | ? [X7 : $i] : ((((in @ X7 @ X4)) = $true) & (((in @ X7 @ X5)) != $true))) | (setext != $true))),
% 0.08/0.26 inference(rectify,[],[f17])).
% 0.08/0.26 thf(f19,plain,(
% 0.08/0.26 ((setext = $true) | ((sK0 != sK1) & ! [X2 : $i] : ((((in @ X2 @ sK1)) != $true) | (((in @ X2 @ sK0)) = $true)) & ! [X3 : $i] : ((((in @ X3 @ sK0)) != $true) | (((in @ X3 @ sK1)) = $true)))) & (! [X4 : $i,X5 : $i] : ((X4 = X5) | ((((in @ (sK2 @ X5 @ X4) @ X5)) = $true) & (((in @ (sK2 @ X5 @ X4) @ X4)) != $true)) | ((((in @ (sK3 @ X5 @ X4) @ X4)) = $true) & (((in @ (sK3 @ X5 @ X4) @ X5)) != $true))) | (setext != $true))),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP,vAPP]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X7,sK3 @ X5 @ X4),skolemize(X7,sK3 @ X5 @ X4)],[f18])).
% 0.08/0.26 thf(f20,plain,(
% 0.08/0.26 (! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ X0)) != $true) | (((subset @ X0 @ X1)) != $true) | (((in @ X2 @ X1)) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X2 @ X0)) = $true) & (((subset @ X0 @ X1)) = $true) & (((in @ X2 @ X1)) != $true)))),
% 0.08/0.26 inference(nnf_transformation,[],[f16])).
% 0.08/0.26 thf(f21,plain,(
% 0.08/0.26 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | (((subset @ X0 @ X2)) != $true) | (((in @ X1 @ X2)) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X4 @ X3)) = $true) & (((subset @ X3 @ X5)) = $true) & (((in @ X4 @ X5)) != $true)))),
% 0.08/0.26 inference(rectify,[],[f20])).
% 0.08/0.26 thf(f22,plain,(
% 0.08/0.26 (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X1 @ X0)) != $true) | (((subset @ X0 @ X2)) != $true) | (((in @ X1 @ X2)) = $true)) | (subsetE != $true)) & ((subsetE = $true) | ((((in @ sK5 @ sK4)) = $true) & (((subset @ sK4 @ sK6)) = $true) & (((in @ sK5 @ sK6)) != $true)))),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X3,sK4),skolemize(X4,sK5),skolemize(X5,sK6)],[f21])).
% 0.08/0.26 thf(f23,plain,(
% 0.08/0.26 (subsetE = $true) & ((sK7 != sK8) & (((subset @ sK7 @ sK8)) = $true) & (((subset @ sK8 @ sK7)) = $true)) & (setext = $true)),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f12])).
% 0.08/0.26 thf(f24,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | (((in @ (sK2 @ X5 @ X4) @ X4)) != $true) | (((in @ (sK3 @ X5 @ X4) @ X5)) != $true) | (setext != $true)) )),
% 0.08/0.26 inference(cnf_transformation,[],[f19])).
% 0.08/0.26 thf(f25,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | (((in @ (sK2 @ X5 @ X4) @ X4)) != $true) | (((in @ (sK3 @ X5 @ X4) @ X4)) = $true) | (setext != $true)) )),
% 0.08/0.26 inference(cnf_transformation,[],[f19])).
% 0.08/0.26 thf(f26,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | (((in @ (sK2 @ X5 @ X4) @ X5)) = $true) | (((in @ (sK3 @ X5 @ X4) @ X5)) != $true) | (setext != $true)) )),
% 0.08/0.26 inference(cnf_transformation,[],[f19])).
% 0.08/0.26 thf(f27,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | (((in @ (sK2 @ X5 @ X4) @ X5)) = $true) | (((in @ (sK3 @ X5 @ X4) @ X4)) = $true) | (setext != $true)) )),
% 0.08/0.26 inference(cnf_transformation,[],[f19])).
% 0.08/0.26 thf(f34,plain,(
% 0.08/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) != $true) | (((subset @ X0 @ X2)) != $true) | (((in @ X1 @ X2)) = $true) | (subsetE != $true)) )),
% 0.08/0.26 inference(cnf_transformation,[],[f22])).
% 0.08/0.26 thf(f35,plain,(
% 0.08/0.26 (setext = $true)),
% 0.08/0.26 inference(cnf_transformation,[],[f23])).
% 0.08/0.26 thf(f36,plain,(
% 0.08/0.26 (((subset @ sK8 @ sK7)) = $true)),
% 0.08/0.26 inference(cnf_transformation,[],[f23])).
% 0.08/0.26 thf(f37,plain,(
% 0.08/0.26 (((subset @ sK7 @ sK8)) = $true)),
% 0.08/0.26 inference(cnf_transformation,[],[f23])).
% 0.08/0.26 thf(f38,plain,(
% 0.08/0.26 (sK7 != sK8)),
% 0.08/0.26 inference(cnf_transformation,[],[f23])).
% 0.08/0.26 thf(f39,plain,(
% 0.08/0.26 (subsetE = $true)),
% 0.08/0.26 inference(cnf_transformation,[],[f23])).
% 0.08/0.26 thf(f45,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | (((in @ (sK3 @ X5 @ X4) @ X4)) = $true) | (((in @ (sK2 @ X5 @ X4) @ X5)) = $true) | ($true != $true)) )),
% 0.08/0.26 inference(definition_unfolding,[],[f27,f35])).
% 0.08/0.26 thf(f46,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | (((in @ (sK3 @ X5 @ X4) @ X5)) != $true) | (((in @ (sK2 @ X5 @ X4) @ X5)) = $true) | ($true != $true)) )),
% 0.08/0.26 inference(definition_unfolding,[],[f26,f35])).
% 0.08/0.26 thf(f47,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK2 @ X5 @ X4) @ X4)) != $true) | (((in @ (sK3 @ X5 @ X4) @ X4)) = $true) | ($true != $true) | (X4 = X5)) )),
% 0.08/0.26 inference(definition_unfolding,[],[f25,f35])).
% 0.08/0.26 thf(f48,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | ($true != $true) | (((in @ (sK2 @ X5 @ X4) @ X4)) != $true) | (((in @ (sK3 @ X5 @ X4) @ X5)) != $true)) )),
% 0.08/0.26 inference(definition_unfolding,[],[f24,f35])).
% 0.08/0.26 thf(f49,plain,(
% 0.08/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X2)) != $true) | ($true != $true) | (((in @ X1 @ X0)) != $true) | (((in @ X1 @ X2)) = $true)) )),
% 0.08/0.26 inference(definition_unfolding,[],[f34,f39])).
% 0.08/0.26 thf(f53,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK3 @ X5 @ X4) @ X5)) != $true) | (X4 = X5) | (((in @ (sK2 @ X5 @ X4) @ X5)) = $true)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f46])).
% 0.08/0.26 thf(f54,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK3 @ X5 @ X4) @ X5)) != $true) | (X4 = X5) | (((in @ (sK2 @ X5 @ X4) @ X4)) != $true)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f48])).
% 0.08/0.26 thf(f55,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK3 @ X5 @ X4) @ X4)) = $true) | (((in @ (sK2 @ X5 @ X4) @ X5)) = $true) | (X4 = X5)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f45])).
% 0.08/0.26 thf(f56,plain,(
% 0.08/0.26 ( ! [X4 : $i,X5 : $i] : ((((in @ (sK2 @ X5 @ X4) @ X4)) != $true) | (X4 = X5) | (((in @ (sK3 @ X5 @ X4) @ X4)) = $true)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f47])).
% 0.08/0.26 thf(f57,plain,(
% 0.08/0.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((subset @ X0 @ X2)) != $true) | (((in @ X1 @ X0)) != $true) | (((in @ X1 @ X2)) = $true)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f49])).
% 0.08/0.26 thf(f58,plain,(
% 0.08/0.26 ( ! [X0 : $i] : (($true != $true) | (((in @ X0 @ sK7)) = $true) | (((in @ X0 @ sK8)) != $true)) )),
% 0.08/0.26 inference(constrained_superposition,[],[f57,f36])).
% 0.08/0.26 thf(f59,plain,(
% 0.08/0.26 ( ! [X0 : $i] : ((((in @ X0 @ sK7)) != $true) | (((in @ X0 @ sK8)) = $true) | ($true != $true)) )),
% 0.08/0.26 inference(constrained_superposition,[],[f57,f37])).
% 0.08/0.26 thf(f60,plain,(
% 0.08/0.26 ( ! [X0 : $i] : ((((in @ X0 @ sK7)) != $true) | (((in @ X0 @ sK8)) = $true)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f59])).
% 0.08/0.26 thf(f61,plain,(
% 0.08/0.26 ( ! [X0 : $i] : ((((in @ X0 @ sK8)) != $true) | (((in @ X0 @ sK7)) = $true)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f58])).
% 0.08/0.26 thf(f62,plain,(
% 0.08/0.26 ( ! [X0 : $i] : ((sK7 = X0) | (((in @ (sK2 @ X0 @ sK7) @ X0)) = $true) | ($true != $true) | (((in @ (sK3 @ X0 @ sK7) @ sK8)) = $true)) )),
% 0.08/0.26 inference(constrained_superposition,[],[f60,f55])).
% 0.08/0.26 thf(f64,plain,(
% 0.08/0.26 ( ! [X0 : $i] : ((((in @ (sK3 @ X0 @ sK7) @ sK8)) = $true) | (((in @ (sK2 @ X0 @ sK7) @ X0)) = $true) | (sK7 = X0)) )),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f62])).
% 0.08/0.26 thf(f68,plain,(
% 0.08/0.26 (((in @ (sK2 @ sK8 @ sK7) @ sK8)) = $true) | (sK7 = sK8) | (sK7 = sK8) | ($true != $true) | (((in @ (sK2 @ sK8 @ sK7) @ sK8)) = $true)),
% 0.08/0.26 inference(constrained_superposition,[],[f53,f64])).
% 0.08/0.26 thf(f72,plain,(
% 0.08/0.26 (sK7 = sK8) | ($true != $true) | (((in @ (sK2 @ sK8 @ sK7) @ sK8)) = $true)),
% 0.08/0.26 inference(duplicate_literal_removal,[],[f68])).
% 0.08/0.26 thf(f73,plain,(
% 0.08/0.26 (((in @ (sK2 @ sK8 @ sK7) @ sK8)) = $true) | (sK7 = sK8)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f72])).
% 0.08/0.26 thf(f74,plain,(
% 0.08/0.26 (((in @ (sK2 @ sK8 @ sK7) @ sK8)) = $true)),
% 0.08/0.26 inference(forward_subsumption_resolution,[],[f73,f38])).
% 0.08/0.26 thf(f75,plain,(
% 0.08/0.26 ($true != $true) | (((in @ (sK2 @ sK8 @ sK7) @ sK7)) = $true)),
% 0.08/0.26 inference(constrained_superposition,[],[f61,f74])).
% 0.08/0.26 thf(f76,plain,(
% 0.08/0.26 (((in @ (sK2 @ sK8 @ sK7) @ sK7)) = $true)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f75])).
% 0.08/0.26 thf(f78,plain,(
% 0.08/0.26 ($true != $true) | (sK7 = sK8) | (((in @ (sK3 @ sK8 @ sK7) @ sK7)) = $true)),
% 0.08/0.26 inference(constrained_superposition,[],[f56,f76])).
% 0.08/0.26 thf(f80,plain,(
% 0.08/0.26 (((in @ (sK3 @ sK8 @ sK7) @ sK7)) = $true) | (sK7 = sK8)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f78])).
% 0.08/0.26 thf(f81,plain,(
% 0.08/0.26 (((in @ (sK3 @ sK8 @ sK7) @ sK7)) = $true)),
% 0.08/0.26 inference(forward_subsumption_resolution,[],[f80,f38])).
% 0.08/0.26 thf(f82,plain,(
% 0.08/0.26 (((in @ (sK3 @ sK8 @ sK7) @ sK8)) = $true) | ($true != $true)),
% 0.08/0.26 inference(constrained_superposition,[],[f60,f81])).
% 0.08/0.26 thf(f83,plain,(
% 0.08/0.26 (((in @ (sK3 @ sK8 @ sK7) @ sK8)) = $true)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f82])).
% 0.08/0.26 thf(f85,plain,(
% 0.08/0.26 ($true != $true) | (((in @ (sK2 @ sK8 @ sK7) @ sK7)) != $true) | (sK7 = sK8)),
% 0.08/0.26 inference(constrained_superposition,[],[f54,f83])).
% 0.08/0.26 thf(f89,plain,(
% 0.08/0.26 (((in @ (sK2 @ sK8 @ sK7) @ sK7)) != $true) | (sK7 = sK8)),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f85])).
% 0.08/0.26 thf(f90,plain,(
% 0.08/0.26 (sK7 = sK8)),
% 0.08/0.26 inference(forward_subsumption_resolution,[],[f89,f76])).
% 0.08/0.26 thf(f91,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(forward_subsumption_resolution,[],[f90,f38])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (2696459)------------------------------
% 0.08/0.26 % (2696459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (2696459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (2696459)CaDiCaL version: 2.1.3
% 0.08/0.26 % (2696459)Termination reason: Refutation
% 0.08/0.26 % (2696459)Time elapsed: 0.006 s
% 0.08/0.26 % (2696459)Peak memory usage: 12 MB
% 0.08/0.26 % (2696459)Instructions burned: 9 (million)
% 0.08/0.26 % (2696454)Success in time 0.037 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------