%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU690^2 : 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 : 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 08:30:48 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU690^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n014.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 14:10:32 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.23 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
% 0.22/0.30 % (2721674)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (2721681)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=661907265:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (2721681)Refutation not found, incomplete strategy
% 0.22/0.30 % (2721681)------------------------------
% 0.22/0.30 % (2721681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2721681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2721681)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2721681)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.30 % (2721681)Time elapsed: 0.002 s
% 0.22/0.30 % (2721681)Peak memory usage: 12 MB
% 0.22/0.30 % (2721681)Instructions burned: 5 (million)
% 0.22/0.30 % (2721681)------------------------------
% 0.22/0.30 % (2721681)------------------------------
% 0.22/0.30 % (2721680)lrs+10_16_si=on:nwc=1.5:random_seed=696340499:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (2721679)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1537399611:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (2721682)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=3674483904: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)
% 0.22/0.30 % (2721683)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3934907387:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (2721685)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (2721685)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
% 0.22/0.30 % (2721685)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=3110680122:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (2721679) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2721674-2721679"...
% 0.22/0.30 % (2721684)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3208042904:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (2721680)Instruction limit reached!
% 0.22/0.30 % (2721680)------------------------------
% 0.22/0.30 % (2721680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2721680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2721680)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2721680)Termination reason: Instruction limit
% 0.22/0.30 % (2721680)Termination phase: Saturation
% 0.22/0.30 % (2721680)Time elapsed: 0.011 s
% 0.22/0.30 % (2721680)Peak memory usage: 12 MB
% 0.22/0.30 % (2721680)Instructions burned: 18 (million)
% 0.22/0.30 % (2721687)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1368226025:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.30 % (2721683) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2721674-2721683"...
% 0.22/0.30 % (2721682) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2721674-2721682"...
% 0.22/0.30 % (2721687)Instruction limit reached!
% 0.22/0.30 % (2721687)------------------------------
% 0.22/0.30 % (2721687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2721687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2721687)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2721687)Termination reason: Instruction limit
% 0.22/0.30 % (2721687)Termination phase: Saturation
% 0.22/0.30 % (2721687)Time elapsed: 0.001 s
% 0.22/0.30 % (2721687)Peak memory usage: 12 MB
% 0.22/0.30 % (2721687)Instructions burned: 4 (million)
% 0.22/0.30 % (2721683)...printing done.
% 0.22/0.30 % (2721679)...printing done.
% 0.22/0.30 % (2721683)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% 0.22/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.30 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.22/0.30 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.22/0.30 thf(func_def_2, type, setextsub: $o).
% 0.22/0.30 thf(func_def_4, type, kpair: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_5, type, cartprod: ($i > $i > $i)).
% 0.22/0.30 thf(func_def_6, type, breln: ($i > $i > $i > $o)).
% 0.22/0.30 thf(func_def_7, type, subbreln: $o).
% 0.22/0.30 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.22/0.30 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.30 thf(func_def_22, type, sK8: ($i > $i > $i > $i > $i)).
% 0.22/0.30 thf(func_def_23, type, sK9: ($i > $i > $i > $i > $i)).
% 0.22/0.30 thf(f1,axiom,(
% 0.22/0.30 (! [X1 : $i,X0 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))) = setextsub)),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub)).
% 0.22/0.30 thf(f3,axiom,(
% 0.22/0.30 (! [X1 : $i,X2 : $i,X0 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3)))) = subbreln)),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln)).
% 0.22/0.30 thf(f4,conjecture,(
% 0.22/0.30 setextsub => (subbreln => ! [X2 : $i,X1 : $i,X0 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X3) => (in @ (kpair @ X4 @ X5) @ X2)))) => (X2 = X3))))))),
% 0.22/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln)).
% 0.22/0.30 thf(f5,negated_conjecture,(
% 0.22/0.30 ~(setextsub => (subbreln => ! [X2 : $i,X1 : $i,X0 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X3) => (in @ (kpair @ X4 @ X5) @ X2)))) => (X2 = X3)))))))),
% 0.22/0.30 inference(negated_conjecture,[status(cth)],[f4])).
% 0.22/0.30 thf(f6,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X2 @ X0 @ X1) => ! [X3 : $i] : ((breln @ X2 @ X0 @ X3) => (! [X4 : $i] : ((in @ X4 @ X2) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X1) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X1 @ X3)))) = subbreln)),
% 0.22/0.30 inference(rectify,[],[f3])).
% 0.22/0.30 thf(f7,plain,(
% 0.22/0.30 ! [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X2 @ X0 @ X1)) = $true) => ! [X3 : $i] : (($true = ((breln @ X2 @ X0 @ X3))) => (! [X4 : $i] : ((((in @ X4 @ X2)) = $true) => ! [X5 : $i] : ((((in @ X5 @ X0)) = $true) => ((((in @ (kpair @ X4 @ X5) @ X1)) = $true) => (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))) => (((subset @ X1 @ X3)) = $true)))) <=> (subbreln = $true)),
% 0.22/0.30 inference(fool_elimination,[],[f6])).
% 0.22/0.30 thf(f8,plain,(
% 0.22/0.30 ~(setextsub => (subbreln => ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X2 @ X1 @ X0) => ! [X3 : $i] : ((breln @ X2 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X2) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X0) => (in @ (kpair @ X4 @ X5) @ X3)))) => (! [X6 : $i] : ((in @ X6 @ X2) => ! [X7 : $i] : ((in @ X7 @ X1) => ((in @ (kpair @ X6 @ X7) @ X3) => (in @ (kpair @ X6 @ X7) @ X0)))) => (X0 = X3)))))))),
% 0.22/0.30 inference(rectify,[],[f5])).
% 0.22/0.30 thf(f9,plain,(
% 0.22/0.30 ~((setextsub = $true) => ((subbreln = $true) => ! [X0 : $i,X2 : $i,X1 : $i] : (($true = ((breln @ X2 @ X1 @ X0))) => ! [X3 : $i] : ((((breln @ X2 @ X1 @ X3)) = $true) => (! [X4 : $i] : ((((in @ X4 @ X2)) = $true) => ! [X5 : $i] : ((((in @ X5 @ X1)) = $true) => (($true = ((in @ (kpair @ X4 @ X5) @ X0))) => (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))) => (! [X6 : $i] : ((((in @ X6 @ X2)) = $true) => ! [X7 : $i] : (($true = ((in @ X7 @ X1))) => (($true = ((in @ (kpair @ X6 @ X7) @ X3))) => ($true = ((in @ (kpair @ X6 @ X7) @ X0)))))) => (X0 = X3)))))))),
% 0.22/0.30 inference(fool_elimination,[],[f8])).
% 0.22/0.30 thf(f10,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))) = setextsub)),
% 0.22/0.30 inference(rectify,[],[f1])).
% 0.22/0.30 thf(f11,plain,(
% 0.22/0.30 ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) = $true) => ((((subset @ X0 @ X1)) = $true) => (X0 = X1))) <=> (setextsub = $true)),
% 0.22/0.30 inference(fool_elimination,[],[f10])).
% 0.22/0.30 thf(f13,plain,(
% 0.22/0.30 (? [X0 : $i,X2 : $i,X1 : $i] : (? [X3 : $i] : ((((X0 != X3) & ! [X6 : $i] : (! [X7 : $i] : ((($true = ((in @ (kpair @ X6 @ X7) @ X0))) | ($true != ((in @ (kpair @ X6 @ X7) @ X3)))) | ($true != ((in @ X7 @ X1)))) | (((in @ X6 @ X2)) != $true))) & ! [X4 : $i] : (! [X5 : $i] : (((((in @ (kpair @ X4 @ X5) @ X3)) = $true) | ($true != ((in @ (kpair @ X4 @ X5) @ X0)))) | (((in @ X5 @ X1)) != $true)) | (((in @ X4 @ X2)) != $true))) & (((breln @ X2 @ X1 @ X3)) = $true)) & ($true = ((breln @ X2 @ X1 @ X0)))) & (subbreln = $true)) & (setextsub = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f9])).
% 0.22/0.30 thf(f14,plain,(
% 0.22/0.30 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((breln @ X2 @ X1 @ X3)) = $true) & (X0 != X3) & ! [X6 : $i] : ((((in @ X6 @ X2)) != $true) | ! [X7 : $i] : (($true != ((in @ X7 @ X1))) | ($true != ((in @ (kpair @ X6 @ X7) @ X3))) | ($true = ((in @ (kpair @ X6 @ X7) @ X0))))) & ! [X4 : $i] : (! [X5 : $i] : (($true != ((in @ (kpair @ X4 @ X5) @ X0))) | (((in @ (kpair @ X4 @ X5) @ X3)) = $true) | (((in @ X5 @ X1)) != $true)) | (((in @ X4 @ X2)) != $true))) & ($true = ((breln @ X2 @ X1 @ X0)))) & (setextsub = $true) & (subbreln = $true)),
% 0.22/0.30 inference(flattening,[],[f13])).
% 0.22/0.30 thf(f15,plain,(
% 0.22/0.30 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (((((subset @ X1 @ X3)) = $true) | ? [X4 : $i] : (? [X5 : $i] : (((((in @ (kpair @ X4 @ X5) @ X3)) != $true) & (((in @ (kpair @ X4 @ X5) @ X1)) = $true)) & (((in @ X5 @ X0)) = $true)) & (((in @ X4 @ X2)) = $true))) | ($true != ((breln @ X2 @ X0 @ X3)))) | (((breln @ X2 @ X0 @ X1)) != $true)) <=> (subbreln = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f7])).
% 0.22/0.30 thf(f16,plain,(
% 0.22/0.30 (subbreln = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : ((((breln @ X2 @ X0 @ X1)) != $true) | ! [X3 : $i] : ((((subset @ X1 @ X3)) = $true) | ($true != ((breln @ X2 @ X0 @ X3))) | ? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & ? [X5 : $i] : ((((in @ X5 @ X0)) = $true) & (((in @ (kpair @ X4 @ X5) @ X1)) = $true) & (((in @ (kpair @ X4 @ X5) @ X3)) != $true)))))),
% 0.22/0.30 inference(flattening,[],[f15])).
% 0.22/0.30 thf(f17,plain,(
% 0.22/0.30 ! [X0 : $i,X1 : $i] : (((X0 = X1) | (((subset @ X0 @ X1)) != $true)) | (((subset @ X1 @ X0)) != $true)) <=> (setextsub = $true)),
% 0.22/0.30 inference(ennf_transformation,[],[f11])).
% 0.22/0.30 thf(f18,plain,(
% 0.22/0.30 ! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) | (((subset @ X0 @ X1)) != $true) | (X0 = X1)) <=> (setextsub = $true)),
% 0.22/0.30 inference(flattening,[],[f17])).
% 0.22/0.30 thf(f19,plain,(
% 0.22/0.30 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((breln @ X2 @ X1 @ X3)) = $true) & (X0 != X3) & ! [X4 : $i] : ((((in @ X4 @ X2)) != $true) | ! [X5 : $i] : ((((in @ X5 @ X1)) != $true) | (((in @ (kpair @ X4 @ X5) @ X3)) != $true) | ($true = ((in @ (kpair @ X4 @ X5) @ X0))))) & ! [X6 : $i] : (! [X7 : $i] : (($true != ((in @ (kpair @ X6 @ X7) @ X0))) | ($true = ((in @ (kpair @ X6 @ X7) @ X3))) | ($true != ((in @ X7 @ X1)))) | (((in @ X6 @ X2)) != $true))) & ($true = ((breln @ X2 @ X1 @ X0)))) & (setextsub = $true) & (subbreln = $true)),
% 0.22/0.30 inference(rectify,[],[f14])).
% 0.22/0.30 thf(f20,plain,(
% 0.22/0.30 ((($true = ((breln @ sK2 @ sK1 @ sK3))) & (sK3 != sK0) & ! [X4 : $i] : (($true != ((in @ X4 @ sK2))) | ! [X5 : $i] : (($true != ((in @ X5 @ sK1))) | ($true != ((in @ (kpair @ X4 @ X5) @ sK3))) | (((in @ (kpair @ X4 @ X5) @ sK0)) = $true))) & ! [X6 : $i] : (! [X7 : $i] : (($true != ((in @ (kpair @ X6 @ X7) @ sK0))) | (((in @ (kpair @ X6 @ X7) @ sK3)) = $true) | ($true != ((in @ X7 @ sK1)))) | ($true != ((in @ X6 @ sK2))))) & ($true = ((breln @ sK2 @ sK1 @ sK0)))) & (setextsub = $true) & (subbreln = $true)),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f19])).
% 0.22/0.30 thf(f21,plain,(
% 0.22/0.30 ((subbreln = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : ((((breln @ X2 @ X0 @ X1)) = $true) & ? [X3 : $i] : ((((subset @ X1 @ X3)) != $true) & ($true = ((breln @ X2 @ X0 @ X3))) & ! [X4 : $i] : ((((in @ X4 @ X2)) != $true) | ! [X5 : $i] : ((((in @ X5 @ X0)) != $true) | (((in @ (kpair @ X4 @ X5) @ X1)) != $true) | (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))))) & (! [X2 : $i,X1 : $i,X0 : $i] : ((((breln @ X2 @ X0 @ X1)) != $true) | ! [X3 : $i] : ((((subset @ X1 @ X3)) = $true) | ($true != ((breln @ X2 @ X0 @ X3))) | ? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & ? [X5 : $i] : ((((in @ X5 @ X0)) = $true) & (((in @ (kpair @ X4 @ X5) @ X1)) = $true) & (((in @ (kpair @ X4 @ X5) @ X3)) != $true))))) | (subbreln != $true))),
% 0.22/0.30 inference(nnf_transformation,[],[f16])).
% 0.22/0.30 thf(f22,plain,(
% 0.22/0.30 ((subbreln = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X0 @ X2 @ X1)) = $true) & ? [X3 : $i] : ((((subset @ X1 @ X3)) != $true) & ($true = ((breln @ X0 @ X2 @ X3))) & ! [X4 : $i] : ((((in @ X4 @ X0)) != $true) | ! [X5 : $i] : (($true != ((in @ X5 @ X2))) | (((in @ (kpair @ X4 @ X5) @ X1)) != $true) | (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))))) & (! [X6 : $i,X7 : $i,X8 : $i] : ((((breln @ X6 @ X8 @ X7)) != $true) | ! [X9 : $i] : (($true = ((subset @ X7 @ X9))) | ($true != ((breln @ X6 @ X8 @ X9))) | ? [X10 : $i] : (($true = ((in @ X10 @ X6))) & ? [X11 : $i] : ((((in @ X11 @ X8)) = $true) & ($true = ((in @ (kpair @ X10 @ X11) @ X7))) & ($true != ((in @ (kpair @ X10 @ X11) @ X9))))))) | (subbreln != $true))),
% 0.22/0.30 inference(rectify,[],[f21])).
% 0.22/0.30 thf(f23,plain,(
% 0.22/0.30 ((subbreln = $true) | ((((breln @ sK4 @ sK6 @ sK5)) = $true) & (($true != ((subset @ sK5 @ sK7))) & (((breln @ sK4 @ sK6 @ sK7)) = $true) & ! [X4 : $i] : (($true != ((in @ X4 @ sK4))) | ! [X5 : $i] : ((((in @ X5 @ sK6)) != $true) | ($true != ((in @ (kpair @ X4 @ X5) @ sK5))) | ($true = ((in @ (kpair @ X4 @ X5) @ sK7)))))))) & (! [X6 : $i,X7 : $i,X8 : $i] : ((((breln @ X6 @ X8 @ X7)) != $true) | ! [X9 : $i] : (($true = ((subset @ X7 @ X9))) | ($true != ((breln @ X6 @ X8 @ X9))) | (($true = ((in @ (sK8 @ X9 @ X8 @ X7 @ X6) @ X6))) & (($true = ((in @ (sK9 @ X9 @ X8 @ X7 @ X6) @ X8))) & ($true = ((in @ (kpair @ (sK8 @ X9 @ X8 @ X7 @ X6) @ (sK9 @ X9 @ X8 @ X7 @ X6)) @ X7))) & ($true != ((in @ (kpair @ (sK8 @ X9 @ X8 @ X7 @ X6) @ (sK9 @ X9 @ X8 @ X7 @ X6)) @ X9))))))) | (subbreln != $true))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,vAPP,vAPP]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7),skolemize(X11,sK9 @ X9 @ X8 @ X7 @ X6),skolemize(X11,sK9 @ X9 @ X8 @ X7 @ X6)],[f22])).
% 0.22/0.30 thf(f24,plain,(
% 0.22/0.30 (! [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) != $true) | (((subset @ X0 @ X1)) != $true) | (X0 = X1)) | (setextsub != $true)) & ((setextsub = $true) | ? [X1 : $i,X0 : $i] : ((((subset @ X1 @ X0)) = $true) & (((subset @ X0 @ X1)) = $true) & (X0 != X1)))),
% 0.22/0.30 inference(nnf_transformation,[],[f18])).
% 0.22/0.30 thf(f25,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) | (((subset @ X1 @ X0)) != $true) | (X0 = X1)) | (setextsub != $true)) & ((setextsub = $true) | ? [X2 : $i,X3 : $i] : ((((subset @ X2 @ X3)) = $true) & ($true = ((subset @ X3 @ X2))) & (X2 != X3)))),
% 0.22/0.30 inference(rectify,[],[f24])).
% 0.22/0.30 thf(f26,plain,(
% 0.22/0.30 (! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) | (((subset @ X1 @ X0)) != $true) | (X0 = X1)) | (setextsub != $true)) & ((setextsub = $true) | ((((subset @ sK10 @ sK11)) = $true) & (((subset @ sK11 @ sK10)) = $true) & (sK11 != sK10)))),
% 0.22/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X2,sK10),skolemize(X3,sK11)],[f25])).
% 0.22/0.30 thf(f28,plain,(
% 0.22/0.30 (subbreln = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f20])).
% 0.22/0.30 thf(f29,plain,(
% 0.22/0.30 (setextsub = $true)),
% 0.22/0.30 inference(cnf_transformation,[],[f20])).
% 0.22/0.30 thf(f30,plain,(
% 0.22/0.30 ($true = ((breln @ sK2 @ sK1 @ sK0)))),
% 0.22/0.30 inference(cnf_transformation,[],[f20])).
% 0.22/0.30 thf(f31,plain,(
% 0.22/0.30 ( ! [X6 : $i,X7 : $i] : (($true != ((in @ (kpair @ X6 @ X7) @ sK0))) | ($true != ((in @ X6 @ sK2))) | ($true != ((in @ X7 @ sK1))) | (((in @ (kpair @ X6 @ X7) @ sK3)) = $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f20])).
% 0.22/0.30 thf(f32,plain,(
% 0.22/0.30 ( ! [X4 : $i,X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ sK0)) = $true) | ($true != ((in @ (kpair @ X4 @ X5) @ sK3))) | ($true != ((in @ X5 @ sK1))) | ($true != ((in @ X4 @ sK2)))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f20])).
% 0.22/0.30 thf(f33,plain,(
% 0.22/0.30 (sK3 != sK0)),
% 0.22/0.30 inference(cnf_transformation,[],[f20])).
% 0.22/0.30 thf(f34,plain,(
% 0.22/0.30 ($true = ((breln @ sK2 @ sK1 @ sK3)))),
% 0.22/0.30 inference(cnf_transformation,[],[f20])).
% 0.22/0.30 thf(f35,plain,(
% 0.22/0.30 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((subbreln != $true) | ($true != ((in @ (kpair @ (sK8 @ X9 @ X8 @ X7 @ X6) @ (sK9 @ X9 @ X8 @ X7 @ X6)) @ X9))) | ($true != ((breln @ X6 @ X8 @ X9))) | (((breln @ X6 @ X8 @ X7)) != $true) | ($true = ((subset @ X7 @ X9)))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f23])).
% 0.22/0.30 thf(f36,plain,(
% 0.22/0.30 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((subbreln != $true) | ($true != ((breln @ X6 @ X8 @ X9))) | ($true = ((in @ (kpair @ (sK8 @ X9 @ X8 @ X7 @ X6) @ (sK9 @ X9 @ X8 @ X7 @ X6)) @ X7))) | (((breln @ X6 @ X8 @ X7)) != $true) | ($true = ((subset @ X7 @ X9)))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f23])).
% 0.22/0.30 thf(f37,plain,(
% 0.22/0.30 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((breln @ X6 @ X8 @ X9))) | ($true = ((in @ (sK9 @ X9 @ X8 @ X7 @ X6) @ X8))) | (subbreln != $true) | (((breln @ X6 @ X8 @ X7)) != $true) | ($true = ((subset @ X7 @ X9)))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f23])).
% 0.22/0.30 thf(f38,plain,(
% 0.22/0.30 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = ((in @ (sK8 @ X9 @ X8 @ X7 @ X6) @ X6))) | (subbreln != $true) | ($true != ((breln @ X6 @ X8 @ X9))) | (((breln @ X6 @ X8 @ X7)) != $true) | ($true = ((subset @ X7 @ X9)))) )),
% 0.22/0.30 inference(cnf_transformation,[],[f23])).
% 0.22/0.30 thf(f46,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : ((((subset @ X1 @ X0)) != $true) | (((subset @ X0 @ X1)) != $true) | (X0 = X1) | (setextsub != $true)) )),
% 0.22/0.30 inference(cnf_transformation,[],[f26])).
% 0.22/0.30 thf(f52,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) | (X0 = X1) | (((subset @ X1 @ X0)) != $true)) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f46,f29])).
% 0.22/0.30 thf(f79,plain,(
% 0.22/0.30 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = ((in @ (sK9 @ X9 @ X8 @ X7 @ X6) @ X8))) | ($true = ((subset @ X7 @ X9))) | ($true != ((breln @ X6 @ X8 @ X9))) | (((breln @ X6 @ X8 @ X7)) != $true)) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f37,f28])).
% 0.22/0.30 thf(f80,plain,(
% 0.22/0.30 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = ((in @ (sK8 @ X9 @ X8 @ X7 @ X6) @ X6))) | ($true = ((subset @ X7 @ X9))) | ($true != ((breln @ X6 @ X8 @ X9))) | (((breln @ X6 @ X8 @ X7)) != $true)) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f38,f28])).
% 0.22/0.30 thf(f81,plain,(
% 0.22/0.30 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((in @ (kpair @ (sK8 @ X9 @ X8 @ X7 @ X6) @ (sK9 @ X9 @ X8 @ X7 @ X6)) @ X9))) | (((breln @ X6 @ X8 @ X7)) != $true) | ($true != ((breln @ X6 @ X8 @ X9))) | ($true = ((subset @ X7 @ X9)))) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f35,f28])).
% 0.22/0.30 thf(f82,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK9 @ sK0 @ X0 @ X1 @ X2) @ sK1))) | (((breln @ X2 @ X0 @ sK0)) != $true) | (((breln @ X2 @ X0 @ X1)) != $true) | (((in @ (sK8 @ sK0 @ X0 @ X1 @ X2) @ sK2)) != $true) | (((subset @ X1 @ sK0)) = $true) | ($true != $true) | (((in @ (kpair @ (sK8 @ sK0 @ X0 @ X1 @ X2) @ (sK9 @ sK0 @ X0 @ X1 @ X2)) @ sK3)) != $true)) )),
% 0.22/0.30 inference(superposition,[],[f81,f32])).
% 0.22/0.30 thf(f83,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (kpair @ (sK8 @ sK0 @ X0 @ X1 @ X2) @ (sK9 @ sK0 @ X0 @ X1 @ X2)) @ sK3)) != $true) | ($true != ((in @ (sK9 @ sK0 @ X0 @ X1 @ X2) @ sK1))) | (((breln @ X2 @ X0 @ X1)) != $true) | (((subset @ X1 @ sK0)) = $true) | (((breln @ X2 @ X0 @ sK0)) != $true) | (((in @ (sK8 @ sK0 @ X0 @ X1 @ X2) @ sK2)) != $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f82])).
% 0.22/0.30 thf(f84,plain,(
% 0.22/0.30 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = ((in @ (kpair @ (sK8 @ X9 @ X8 @ X7 @ X6) @ (sK9 @ X9 @ X8 @ X7 @ X6)) @ X7))) | ($true = ((subset @ X7 @ X9))) | (((breln @ X6 @ X8 @ X7)) != $true) | ($true != ((breln @ X6 @ X8 @ X9)))) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f36,f28])).
% 0.22/0.30 thf(f86,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK8 @ X0 @ X1 @ sK0 @ X2) @ sK2))) | ($true != ((in @ (sK9 @ X0 @ X1 @ sK0 @ X2) @ sK1))) | ($true = ((subset @ sK0 @ X0))) | ($true != $true) | ($true != ((breln @ X2 @ X1 @ sK0))) | ($true != ((breln @ X2 @ X1 @ X0))) | (((in @ (kpair @ (sK8 @ X0 @ X1 @ sK0 @ X2) @ (sK9 @ X0 @ X1 @ sK0 @ X2)) @ sK3)) = $true)) )),
% 0.22/0.30 inference(superposition,[],[f31,f84])).
% 0.22/0.30 thf(f87,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : ((((subset @ sK3 @ sK0)) = $true) | ($true != ((in @ (sK8 @ sK0 @ X0 @ sK3 @ X1) @ sK2))) | (((breln @ X1 @ X0 @ sK3)) != $true) | (((breln @ X1 @ X0 @ sK3)) != $true) | (((subset @ sK3 @ sK0)) = $true) | ($true != $true) | ($true != ((breln @ X1 @ X0 @ sK0))) | ($true != ((breln @ X1 @ X0 @ sK0))) | (((in @ (sK9 @ sK0 @ X0 @ sK3 @ X1) @ sK1)) != $true)) )),
% 0.22/0.30 inference(superposition,[],[f83,f84])).
% 0.22/0.30 thf(f90,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK8 @ sK0 @ X0 @ sK3 @ X1) @ sK2))) | (((subset @ sK3 @ sK0)) = $true) | (((breln @ X1 @ X0 @ sK3)) != $true) | ($true != $true) | ($true != ((breln @ X1 @ X0 @ sK0))) | (((in @ (sK9 @ sK0 @ X0 @ sK3 @ X1) @ sK1)) != $true)) )),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f87])).
% 0.22/0.30 thf(f91,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK9 @ sK0 @ X0 @ sK3 @ X1) @ sK1)) != $true) | (((breln @ X1 @ X0 @ sK3)) != $true) | ($true != ((in @ (sK8 @ sK0 @ X0 @ sK3 @ X1) @ sK2))) | (((subset @ sK3 @ sK0)) = $true) | ($true != ((breln @ X1 @ X0 @ sK0)))) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f90])).
% 0.22/0.30 thf(f92,plain,(
% 0.22/0.30 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (kpair @ (sK8 @ X0 @ X1 @ sK0 @ X2) @ (sK9 @ X0 @ X1 @ sK0 @ X2)) @ sK3)) = $true) | ($true != ((in @ (sK9 @ X0 @ X1 @ sK0 @ X2) @ sK1))) | ($true = ((subset @ sK0 @ X0))) | ($true != ((breln @ X2 @ X1 @ sK0))) | ($true != ((in @ (sK8 @ X0 @ X1 @ sK0 @ X2) @ sK2))) | ($true != ((breln @ X2 @ X1 @ X0)))) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f86])).
% 0.22/0.30 thf(f102,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : ((((in @ (sK8 @ sK3 @ X0 @ sK0 @ X1) @ sK2)) != $true) | ($true != ((in @ (sK9 @ sK3 @ X0 @ sK0 @ X1) @ sK1))) | ($true != ((breln @ X1 @ X0 @ sK0))) | ($true = ((subset @ sK0 @ sK3))) | ($true = ((subset @ sK0 @ sK3))) | (((breln @ X1 @ X0 @ sK3)) != $true) | ($true != ((breln @ X1 @ X0 @ sK0))) | ($true != $true) | (((breln @ X1 @ X0 @ sK3)) != $true)) )),
% 0.22/0.30 inference(superposition,[],[f81,f92])).
% 0.22/0.30 thf(f105,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : (($true != ((breln @ X1 @ X0 @ sK0))) | ($true != $true) | ($true != ((in @ (sK9 @ sK3 @ X0 @ sK0 @ X1) @ sK1))) | (((in @ (sK8 @ sK3 @ X0 @ sK0 @ X1) @ sK2)) != $true) | ($true = ((subset @ sK0 @ sK3))) | (((breln @ X1 @ X0 @ sK3)) != $true)) )),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f102])).
% 0.22/0.30 thf(f106,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : (($true != ((breln @ X1 @ X0 @ sK0))) | ($true = ((subset @ sK0 @ sK3))) | ($true != ((in @ (sK9 @ sK3 @ X0 @ sK0 @ X1) @ sK1))) | (((breln @ X1 @ X0 @ sK3)) != $true) | (((in @ (sK8 @ sK3 @ X0 @ sK0 @ X1) @ sK2)) != $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f105])).
% 0.22/0.30 thf(f129,plain,(
% 0.22/0.30 ( ! [X0 : $i] : ((((subset @ sK3 @ sK0)) = $true) | ($true != ((in @ (sK8 @ sK0 @ sK1 @ sK3 @ X0) @ sK2))) | ($true != ((breln @ X0 @ sK1 @ sK3))) | ($true != $true) | ($true != ((breln @ X0 @ sK1 @ sK0))) | ($true != ((breln @ X0 @ sK1 @ sK3))) | ($true != ((breln @ X0 @ sK1 @ sK0))) | (((subset @ sK3 @ sK0)) = $true)) )),
% 0.22/0.30 inference(superposition,[],[f91,f79])).
% 0.22/0.30 thf(f130,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != ((breln @ X0 @ sK1 @ sK3))) | ($true != $true) | ($true != ((in @ (sK8 @ sK0 @ sK1 @ sK3 @ X0) @ sK2))) | (((subset @ sK3 @ sK0)) = $true) | ($true != ((breln @ X0 @ sK1 @ sK0)))) )),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f129])).
% 0.22/0.30 thf(f131,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != ((in @ (sK8 @ sK0 @ sK1 @ sK3 @ X0) @ sK2))) | ($true != ((breln @ X0 @ sK1 @ sK3))) | ($true != ((breln @ X0 @ sK1 @ sK0))) | (((subset @ sK3 @ sK0)) = $true)) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f130])).
% 0.22/0.30 thf(f132,plain,(
% 0.22/0.30 (((subset @ sK3 @ sK0)) = $true) | (((subset @ sK3 @ sK0)) = $true) | ($true != ((breln @ sK2 @ sK1 @ sK3))) | ($true != ((breln @ sK2 @ sK1 @ sK3))) | ($true != ((breln @ sK2 @ sK1 @ sK0))) | ($true != $true) | ($true != ((breln @ sK2 @ sK1 @ sK0)))),
% 0.22/0.30 inference(superposition,[],[f131,f80])).
% 0.22/0.30 thf(f133,plain,(
% 0.22/0.30 (((subset @ sK3 @ sK0)) = $true) | ($true != ((breln @ sK2 @ sK1 @ sK0))) | ($true != $true) | ($true != ((breln @ sK2 @ sK1 @ sK3)))),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f132])).
% 0.22/0.30 thf(f134,plain,(
% 0.22/0.30 ($true != ((breln @ sK2 @ sK1 @ sK3))) | (((subset @ sK3 @ sK0)) = $true) | ($true != ((breln @ sK2 @ sK1 @ sK0)))),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f133])).
% 0.22/0.30 thf(f135,plain,(
% 0.22/0.30 (((subset @ sK3 @ sK0)) = $true) | ($true != ((breln @ sK2 @ sK1 @ sK0)))),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f134,f34])).
% 0.22/0.30 thf(f136,plain,(
% 0.22/0.30 (((subset @ sK3 @ sK0)) = $true)),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f135,f30])).
% 0.22/0.30 thf(f137,plain,(
% 0.22/0.30 ($true != ((subset @ sK0 @ sK3))) | (sK3 = sK0) | ($true != $true)),
% 0.22/0.30 inference(superposition,[],[f52,f136])).
% 0.22/0.30 thf(f138,plain,(
% 0.22/0.30 ($true != ((subset @ sK0 @ sK3))) | (sK3 = sK0)),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f137])).
% 0.22/0.30 thf(f139,plain,(
% 0.22/0.30 ($true != ((subset @ sK0 @ sK3)))),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f138,f33])).
% 0.22/0.30 thf(f140,plain,(
% 0.22/0.30 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK9 @ sK3 @ X0 @ sK0 @ X1) @ sK1))) | (((breln @ X1 @ X0 @ sK3)) != $true) | ($true != ((breln @ X1 @ X0 @ sK0))) | (((in @ (sK8 @ sK3 @ X0 @ sK0 @ X1) @ sK2)) != $true)) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f106,f139])).
% 0.22/0.30 thf(f141,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != $true) | ($true = ((subset @ sK0 @ sK3))) | ($true != ((breln @ X0 @ sK1 @ sK0))) | ($true != ((breln @ X0 @ sK1 @ sK0))) | ($true != ((in @ (sK8 @ sK3 @ sK1 @ sK0 @ X0) @ sK2))) | ($true != ((breln @ X0 @ sK1 @ sK3))) | ($true != ((breln @ X0 @ sK1 @ sK3)))) )),
% 0.22/0.30 inference(superposition,[],[f140,f79])).
% 0.22/0.30 thf(f142,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != $true) | ($true = ((subset @ sK0 @ sK3))) | ($true != ((in @ (sK8 @ sK3 @ sK1 @ sK0 @ X0) @ sK2))) | ($true != ((breln @ X0 @ sK1 @ sK3))) | ($true != ((breln @ X0 @ sK1 @ sK0)))) )),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f141])).
% 0.22/0.30 thf(f143,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true = ((subset @ sK0 @ sK3))) | ($true != ((in @ (sK8 @ sK3 @ sK1 @ sK0 @ X0) @ sK2))) | ($true != ((breln @ X0 @ sK1 @ sK3))) | ($true != ((breln @ X0 @ sK1 @ sK0)))) )),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f142])).
% 0.22/0.30 thf(f144,plain,(
% 0.22/0.30 ( ! [X0 : $i] : (($true != ((in @ (sK8 @ sK3 @ sK1 @ sK0 @ X0) @ sK2))) | ($true != ((breln @ X0 @ sK1 @ sK3))) | ($true != ((breln @ X0 @ sK1 @ sK0)))) )),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f143,f139])).
% 0.22/0.30 thf(f145,plain,(
% 0.22/0.30 ($true != ((breln @ sK2 @ sK1 @ sK0))) | ($true != ((breln @ sK2 @ sK1 @ sK3))) | ($true = ((subset @ sK0 @ sK3))) | ($true != ((breln @ sK2 @ sK1 @ sK3))) | ($true != $true) | ($true != ((breln @ sK2 @ sK1 @ sK0)))),
% 0.22/0.30 inference(superposition,[],[f144,f80])).
% 0.22/0.30 thf(f146,plain,(
% 0.22/0.30 ($true != $true) | ($true != ((breln @ sK2 @ sK1 @ sK3))) | ($true != ((breln @ sK2 @ sK1 @ sK0))) | ($true = ((subset @ sK0 @ sK3)))),
% 0.22/0.30 inference(duplicate_literal_removal,[],[f145])).
% 0.22/0.30 thf(f147,plain,(
% 0.22/0.30 ($true != ((breln @ sK2 @ sK1 @ sK0))) | ($true = ((subset @ sK0 @ sK3))) | ($true != ((breln @ sK2 @ sK1 @ sK3)))),
% 0.22/0.30 inference(trivial_inequality_removal,[],[f146])).
% 0.22/0.30 thf(f148,plain,(
% 0.22/0.30 ($true = ((subset @ sK0 @ sK3))) | ($true != ((breln @ sK2 @ sK1 @ sK3)))),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f147,f30])).
% 0.22/0.30 thf(f149,plain,(
% 0.22/0.30 ($true != ((breln @ sK2 @ sK1 @ sK3)))),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f148,f139])).
% 0.22/0.30 thf(f150,plain,(
% 0.22/0.30 $false),
% 0.22/0.30 inference(forward_subsumption_resolution,[],[f149,f34])).
% 0.22/0.30 % SZS output end Proof for theBenchmark
% 0.22/0.30 % (2721683)------------------------------
% 0.22/0.30 % (2721683)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (2721683)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (2721683)CaDiCaL version: 2.1.3
% 0.22/0.30 % (2721683)Termination reason: Refutation
% 0.22/0.30 % (2721683)Time elapsed: 0.014 s
% 0.22/0.30 % (2721683)Peak memory usage: 12 MB
% 0.22/0.30 % (2721683)Instructions burned: 25 (million)
% 0.22/0.30 % (2721674)Success in time 0.054 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------