%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU774^2 : 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 : n026.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 08:31:17 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU774^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n026.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 14:30:34 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 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
% 0.19/0.28 % (673998)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (674008)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1223964891:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.19/0.28 % (674009)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.28 % (674009)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
% 0.19/0.28 % (674003)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2587782055:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.28 % (674004)lrs+10_16_si=on:nwc=1.5:random_seed=4201739187:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.19/0.28 % (674005)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3553643951:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.19/0.28 % (674006)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=3485600886: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)
% 0.19/0.28 % (674007)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3915816620:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.19/0.28 % (674009)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=2354120405:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.19/0.28 % (674005)Instruction limit reached!
% 0.19/0.28 % (674005)------------------------------
% 0.19/0.28 % (674005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (674005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (674005)CaDiCaL version: 2.1.3
% 0.19/0.28 % (674005)Termination reason: Instruction limit
% 0.19/0.28 % (674005)Termination phase: Saturation
% 0.19/0.28 % (674005)Time elapsed: 0.002 s
% 0.19/0.28 % (674005)Peak memory usage: 11 MB
% 0.19/0.28 % (674005)Instructions burned: 3 (million)
% 0.19/0.28 % (674004)Instruction limit reached!
% 0.19/0.28 % (674004)------------------------------
% 0.19/0.28 % (674004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (674004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (674004)CaDiCaL version: 2.1.3
% 0.19/0.28 % (674004)Termination reason: Instruction limit
% 0.19/0.28 % (674004)Termination phase: Saturation
% 0.19/0.28 % (674004)Time elapsed: 0.010 s
% 0.19/0.28 % (674008) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-673998-674008"...
% 0.19/0.28 % (674004)Peak memory usage: 12 MB
% 0.19/0.28 % (674004)Instructions burned: 19 (million)
% 0.19/0.28 % (674003) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-673998-674003"...
% 0.19/0.28 % (674008)...printing done.
% 0.19/0.28 % (674008)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% 0.19/0.28 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.28 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.19/0.28 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.19/0.28 thf(func_def_2, type, kpair: ($i > $i > $i)).
% 0.19/0.28 thf(func_def_3, type, cartprod: ($i > $i > $i)).
% 0.19/0.28 thf(func_def_4, type, breln: ($i > $i > $i > $o)).
% 0.19/0.28 thf(func_def_6, type, eqbreln: $o).
% 0.19/0.28 thf(func_def_7, type, breln1: ($i > $i > $o)).
% 0.19/0.28 thf(func_def_8, type, db0: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_9, type, db2: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_10, type, db1: !>[X0: $tType]:(X0)).
% 0.19/0.28 thf(func_def_11, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.19/0.28 thf(func_def_14, type, sP0: ($i > $i > $i > $i > $o)).
% 0.19/0.28 thf(func_def_15, type, sP1: $o).
% 0.19/0.28 thf(func_def_20, type, sK6: ($i > $i > $i > $i > $i)).
% 0.19/0.28 thf(func_def_21, type, sK7: ($i > $i > $i > $i > $i)).
% 0.19/0.28 thf(func_def_22, type, sK8: ($i > $i > $i > $i > $i)).
% 0.19/0.28 thf(func_def_23, type, sK9: ($i > $i > $i > $i > $i)).
% 0.19/0.28 thf(func_def_27, type, vNOT: ($o > $o)).
% 0.19/0.28 thf(f1,axiom,(
% 0.19/0.28 ((^[X0 : $i, X1 : $i, X2 : $i] : ((subset @ X2 @ (cartprod @ X0 @ X1)))) = breln)),
% 0.19/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 0.19/0.28 thf(f2,axiom,(
% 0.19/0.28 (! [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))))) = eqbreln)),
% 0.19/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln)).
% 0.19/0.28 thf(f3,axiom,(
% 0.19/0.28 (breln1 = (^[X0 : $i, X1 : $i] : ((breln @ X0 @ X0 @ X1))))),
% 0.19/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1)).
% 0.19/0.28 thf(f4,conjecture,(
% 0.19/0.28 eqbreln => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ X2)))) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X2) => (in @ (kpair @ X3 @ X4) @ X1)))) => (X1 = X2)))))),
% 0.19/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln1)).
% 0.19/0.28 thf(f5,negated_conjecture,(
% 0.19/0.28 ~(eqbreln => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ X2)))) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X2) => (in @ (kpair @ X3 @ X4) @ X1)))) => (X1 = X2))))))),
% 0.19/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.19/0.28 thf(f6,plain,(
% 0.19/0.28 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.19/0.28 inference(fool_elimination,[],[f1])).
% 0.19/0.28 thf(f7,plain,(
% 0.19/0.28 ~(eqbreln => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ X2)))) => (! [X5 : $i] : ((in @ X5 @ X0) => ! [X6 : $i] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ X2) => (in @ (kpair @ X5 @ X6) @ X1)))) => (X1 = X2))))))),
% 0.19/0.28 inference(rectify,[],[f5])).
% 0.19/0.28 thf(f8,plain,(
% 0.19/0.28 ~((eqbreln = $true) => ! [X1 : $i,X0 : $i] : ((((breln1 @ X0 @ X1)) = $true) => ! [X2 : $i] : ((((breln1 @ X0 @ X2)) = $true) => (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => ((((in @ (kpair @ X3 @ X4) @ X1)) = $true) => (((in @ (kpair @ X3 @ X4) @ X2)) = $true)))) => (! [X5 : $i] : (($true = ((in @ X5 @ X0))) => ! [X6 : $i] : (($true = ((in @ X6 @ X0))) => ((((in @ (kpair @ X5 @ X6) @ X2)) = $true) => ($true = ((in @ (kpair @ X5 @ X6) @ X1)))))) => (X1 = X2))))))),
% 0.19/0.28 inference(fool_elimination,[],[f7])).
% 0.19/0.28 thf(f9,plain,(
% 0.19/0.28 (! [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))))) = eqbreln)),
% 0.19/0.28 inference(rectify,[],[f2])).
% 0.19/0.28 thf(f10,plain,(
% 0.19/0.28 (eqbreln = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((breln @ X2 @ X1 @ X0))) => ! [X3 : $i] : (($true = ((breln @ X2 @ X1 @ X3))) => (! [X4 : $i] : (($true = ((in @ X4 @ X2))) => ! [X5 : $i] : ((((in @ X5 @ X1)) = $true) => (($true = ((in @ (kpair @ X4 @ X5) @ X0))) => (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))) => (! [X6 : $i] : (($true = ((in @ X6 @ X2))) => ! [X7 : $i] : (($true = ((in @ X7 @ X1))) => (($true = ((in @ (kpair @ X6 @ X7) @ X3))) => ($true = ((in @ (kpair @ X6 @ X7) @ X0)))))) => (X0 = X3)))))),
% 0.19/0.28 inference(fool_elimination,[],[f9])).
% 0.19/0.28 thf(f11,plain,(
% 0.19/0.28 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 0.19/0.28 inference(fool_elimination,[],[f3])).
% 0.19/0.28 thf(f12,plain,(
% 0.19/0.28 (eqbreln = $true) <=> ! [X0 : $i,X1 : $i,X2 : $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)))) & ($true = ((in @ X6 @ X2))))) | ? [X4 : $i] : (? [X5 : $i] : (((((in @ (kpair @ X4 @ X5) @ X3)) != $true) & ($true = ((in @ (kpair @ X4 @ X5) @ X0)))) & (((in @ X5 @ X1)) = $true)) & ($true = ((in @ X4 @ X2))))) | ($true != ((breln @ X2 @ X1 @ X3)))) | ($true != ((breln @ X2 @ X1 @ X0))))),
% 0.19/0.28 inference(ennf_transformation,[],[f10])).
% 0.19/0.28 thf(f13,plain,(
% 0.19/0.28 ! [X2 : $i,X1 : $i,X0 : $i] : (($true != ((breln @ X2 @ X1 @ X0))) | ! [X3 : $i] : ((X0 = X3) | ($true != ((breln @ X2 @ X1 @ X3))) | ? [X6 : $i] : (($true = ((in @ X6 @ X2))) & ? [X7 : $i] : (($true = ((in @ X7 @ X1))) & ($true != ((in @ (kpair @ X6 @ X7) @ X0))) & ($true = ((in @ (kpair @ X6 @ X7) @ X3))))) | ? [X4 : $i] : (($true = ((in @ X4 @ X2))) & ? [X5 : $i] : ((((in @ X5 @ X1)) = $true) & ($true = ((in @ (kpair @ X4 @ X5) @ X0))) & (((in @ (kpair @ X4 @ X5) @ X3)) != $true))))) <=> (eqbreln = $true)),
% 0.19/0.28 inference(flattening,[],[f12])).
% 0.19/0.28 thf(f14,plain,(
% 0.19/0.28 ? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((X1 != X2) & ! [X5 : $i] : (! [X6 : $i] : ((($true = ((in @ (kpair @ X5 @ X6) @ X1))) | (((in @ (kpair @ X5 @ X6) @ X2)) != $true)) | ($true != ((in @ X6 @ X0)))) | ($true != ((in @ X5 @ X0))))) & ! [X3 : $i] : (! [X4 : $i] : (((((in @ (kpair @ X3 @ X4) @ X2)) = $true) | (((in @ (kpair @ X3 @ X4) @ X1)) != $true)) | (((in @ X4 @ X0)) != $true)) | (((in @ X3 @ X0)) != $true))) & (((breln1 @ X0 @ X2)) = $true)) & (((breln1 @ X0 @ X1)) = $true)) & (eqbreln = $true)),
% 0.19/0.28 inference(ennf_transformation,[],[f8])).
% 0.19/0.28 thf(f15,plain,(
% 0.19/0.28 (eqbreln = $true) & ? [X1 : $i,X0 : $i] : ((((breln1 @ X0 @ X1)) = $true) & ? [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | ! [X4 : $i] : ((((in @ X4 @ X0)) != $true) | (((in @ (kpair @ X3 @ X4) @ X1)) != $true) | (((in @ (kpair @ X3 @ X4) @ X2)) = $true))) & (((breln1 @ X0 @ X2)) = $true) & (X1 != X2) & ! [X5 : $i] : (! [X6 : $i] : (($true = ((in @ (kpair @ X5 @ X6) @ X1))) | (((in @ (kpair @ X5 @ X6) @ X2)) != $true) | ($true != ((in @ X6 @ X0)))) | ($true != ((in @ X5 @ X0))))))),
% 0.19/0.29 inference(flattening,[],[f14])).
% 0.19/0.29 thf(f16,definition,(
% 0.19/0.29 ! [X2 : $i,X1 : $i,X0 : $i,X3 : $i] : (($true = ((sP0 @ X3 @ X0 @ X1 @ X2))) <=> ? [X4 : $i] : (($true = ((in @ X4 @ X2))) & ? [X5 : $i] : ((((in @ X5 @ X1)) = $true) & ($true = ((in @ (kpair @ X4 @ X5) @ X0))) & (((in @ (kpair @ X4 @ X5) @ X3)) != $true))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.19/0.29 thf(f17,definition,(
% 0.19/0.29 ($true = sP1) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (($true != ((breln @ X2 @ X1 @ X0))) | ! [X3 : $i] : ((X0 = X3) | ($true != ((breln @ X2 @ X1 @ X3))) | ? [X6 : $i] : (($true = ((in @ X6 @ X2))) & ? [X7 : $i] : (($true = ((in @ X7 @ X1))) & ($true != ((in @ (kpair @ X6 @ X7) @ X0))) & ($true = ((in @ (kpair @ X6 @ X7) @ X3))))) | ($true = ((sP0 @ X3 @ X0 @ X1 @ X2)))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
% 0.19/0.29 thf(f18,plain,(
% 0.19/0.29 ($true = sP1) <=> (eqbreln = $true)),
% 0.19/0.29 inference(definition_folding,[],[f13,f17,f16])).
% 0.19/0.29 thf(f19,plain,(
% 0.19/0.29 (($true = sP1) | ? [X2 : $i,X1 : $i,X0 : $i] : (($true = ((breln @ X2 @ X1 @ X0))) & ? [X3 : $i] : ((X0 != X3) & ($true = ((breln @ X2 @ X1 @ X3))) & ! [X6 : $i] : (($true != ((in @ X6 @ X2))) | ! [X7 : $i] : (($true != ((in @ X7 @ X1))) | ($true = ((in @ (kpair @ X6 @ X7) @ X0))) | ($true != ((in @ (kpair @ X6 @ X7) @ X3))))) & ($true != ((sP0 @ X3 @ X0 @ X1 @ X2)))))) & (! [X2 : $i,X1 : $i,X0 : $i] : (($true != ((breln @ X2 @ X1 @ X0))) | ! [X3 : $i] : ((X0 = X3) | ($true != ((breln @ X2 @ X1 @ X3))) | ? [X6 : $i] : (($true = ((in @ X6 @ X2))) & ? [X7 : $i] : (($true = ((in @ X7 @ X1))) & ($true != ((in @ (kpair @ X6 @ X7) @ X0))) & ($true = ((in @ (kpair @ X6 @ X7) @ X3))))) | ($true = ((sP0 @ X3 @ X0 @ X1 @ X2))))) | ($true != sP1))),
% 0.19/0.29 inference(nnf_transformation,[],[f17])).
% 0.19/0.29 thf(f20,plain,(
% 0.19/0.29 (($true = sP1) | ? [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X0 @ X1 @ X2)) = $true) & ? [X3 : $i] : ((X2 != X3) & (((breln @ X0 @ X1 @ X3)) = $true) & ! [X4 : $i] : ((((in @ X4 @ X0)) != $true) | ! [X5 : $i] : ((((in @ X5 @ X1)) != $true) | (((in @ (kpair @ X4 @ X5) @ X2)) = $true) | (((in @ (kpair @ X4 @ X5) @ X3)) != $true))) & ($true != ((sP0 @ X3 @ X2 @ X1 @ X0)))))) & (! [X6 : $i,X7 : $i,X8 : $i] : (($true != ((breln @ X6 @ X7 @ X8))) | ! [X9 : $i] : ((X8 = X9) | ($true != ((breln @ X6 @ X7 @ X9))) | ? [X10 : $i] : (($true = ((in @ X10 @ X6))) & ? [X11 : $i] : (($true = ((in @ X11 @ X7))) & (((in @ (kpair @ X10 @ X11) @ X8)) != $true) & ($true = ((in @ (kpair @ X10 @ X11) @ X9))))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))))) | ($true != sP1))),
% 0.19/0.29 inference(rectify,[],[f19])).
% 0.19/0.29 thf(f21,plain,(
% 0.19/0.29 (($true = sP1) | (($true = ((breln @ sK2 @ sK3 @ sK4))) & ((sK4 != sK5) & ($true = ((breln @ sK2 @ sK3 @ sK5))) & ! [X4 : $i] : (($true != ((in @ X4 @ sK2))) | ! [X5 : $i] : (($true != ((in @ X5 @ sK3))) | ($true = ((in @ (kpair @ X4 @ X5) @ sK4))) | ($true != ((in @ (kpair @ X4 @ X5) @ sK5))))) & (((sP0 @ sK5 @ sK4 @ sK3 @ sK2)) != $true)))) & (! [X6 : $i,X7 : $i,X8 : $i] : (($true != ((breln @ X6 @ X7 @ X8))) | ! [X9 : $i] : ((X8 = X9) | ($true != ((breln @ X6 @ X7 @ X9))) | (($true = ((in @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X6))) & ((((in @ (sK7 @ X9 @ X8 @ X7 @ X6) @ X7)) = $true) & ($true != ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X8))) & ($true = ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X9))))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))))) | ($true != sP1))),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,vAPP,vAPP]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5),skolemize(X11,sK7 @ X9 @ X8 @ X7 @ X6),skolemize(X11,sK7 @ X9 @ X8 @ X7 @ X6)],[f20])).
% 0.19/0.29 thf(f22,plain,(
% 0.19/0.29 ! [X2 : $i,X1 : $i,X0 : $i,X3 : $i] : ((($true = ((sP0 @ X3 @ X0 @ X1 @ X2))) | ! [X4 : $i] : (($true != ((in @ X4 @ X2))) | ! [X5 : $i] : ((((in @ X5 @ X1)) != $true) | ($true != ((in @ (kpair @ X4 @ X5) @ X0))) | (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))) & (? [X4 : $i] : (($true = ((in @ X4 @ X2))) & ? [X5 : $i] : ((((in @ X5 @ X1)) = $true) & ($true = ((in @ (kpair @ X4 @ X5) @ X0))) & (((in @ (kpair @ X4 @ X5) @ X3)) != $true))) | ($true != ((sP0 @ X3 @ X0 @ X1 @ X2)))))),
% 0.19/0.29 inference(nnf_transformation,[],[f16])).
% 0.19/0.29 thf(f23,plain,(
% 0.19/0.29 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((($true = ((sP0 @ X3 @ X2 @ X1 @ X0))) | ! [X4 : $i] : ((((in @ X4 @ X0)) != $true) | ! [X5 : $i] : ((((in @ X5 @ X1)) != $true) | (((in @ (kpair @ X4 @ X5) @ X2)) != $true) | (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))) & (? [X6 : $i] : (($true = ((in @ X6 @ X0))) & ? [X7 : $i] : (($true = ((in @ X7 @ X1))) & ($true = ((in @ (kpair @ X6 @ X7) @ X2))) & ($true != ((in @ (kpair @ X6 @ X7) @ X3))))) | ($true != ((sP0 @ X3 @ X2 @ X1 @ X0)))))),
% 0.19/0.29 inference(rectify,[],[f22])).
% 0.19/0.29 thf(f24,plain,(
% 0.19/0.29 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((($true = ((sP0 @ X3 @ X2 @ X1 @ X0))) | ! [X4 : $i] : ((((in @ X4 @ X0)) != $true) | ! [X5 : $i] : ((((in @ X5 @ X1)) != $true) | (((in @ (kpair @ X4 @ X5) @ X2)) != $true) | (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))) & ((($true = ((in @ (sK8 @ X3 @ X2 @ X1 @ X0) @ X0))) & (($true = ((in @ (sK9 @ X3 @ X2 @ X1 @ X0) @ X1))) & ($true = ((in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ (sK9 @ X3 @ X2 @ X1 @ X0)) @ X2))) & ($true != ((in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ (sK9 @ X3 @ X2 @ X1 @ X0)) @ X3))))) | ($true != ((sP0 @ X3 @ X2 @ X1 @ X0)))))),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP]),skolemize(X11,sK7 @ X9 @ X8 @ X7 @ X6),skolemize(X11,sK7 @ X9 @ X8 @ X7 @ X6)],[f23])).
% 0.19/0.29 thf(f25,plain,(
% 0.19/0.29 (($true = sP1) | (eqbreln != $true)) & ((eqbreln = $true) | ($true != sP1))),
% 0.19/0.29 inference(nnf_transformation,[],[f18])).
% 0.19/0.29 thf(f26,plain,(
% 0.19/0.29 (eqbreln = $true) & ? [X0 : $i,X1 : $i] : (($true = ((breln1 @ X1 @ X0))) & ? [X2 : $i] : (! [X3 : $i] : (($true != ((in @ X3 @ X1))) | ! [X4 : $i] : (($true != ((in @ X4 @ X1))) | ($true != ((in @ (kpair @ X3 @ X4) @ X0))) | (((in @ (kpair @ X3 @ X4) @ X2)) = $true))) & ($true = ((breln1 @ X1 @ X2))) & (X0 != X2) & ! [X5 : $i] : (! [X6 : $i] : (($true = ((in @ (kpair @ X5 @ X6) @ X0))) | (((in @ (kpair @ X5 @ X6) @ X2)) != $true) | ($true != ((in @ X6 @ X1)))) | (((in @ X5 @ X1)) != $true))))),
% 0.19/0.29 inference(rectify,[],[f15])).
% 0.19/0.29 thf(f27,plain,(
% 0.19/0.29 (eqbreln = $true) & (($true = ((breln1 @ sK11 @ sK10))) & (! [X3 : $i] : (($true != ((in @ X3 @ sK11))) | ! [X4 : $i] : (($true != ((in @ X4 @ sK11))) | ($true != ((in @ (kpair @ X3 @ X4) @ sK10))) | ($true = ((in @ (kpair @ X3 @ X4) @ sK12))))) & ($true = ((breln1 @ sK11 @ sK12))) & (sK12 != sK10) & ! [X5 : $i] : (! [X6 : $i] : (($true = ((in @ (kpair @ X5 @ X6) @ sK10))) | ($true != ((in @ (kpair @ X5 @ X6) @ sK12))) | ($true != ((in @ X6 @ sK11)))) | ($true != ((in @ X5 @ sK11))))))),
% 0.19/0.29 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f26])).
% 0.19/0.29 thf(f28,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((breln @ X6 @ X7 @ X8))) | (X8 = X9) | ($true != ((breln @ X6 @ X7 @ X9))) | ($true = ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X9))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ($true != sP1)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f29,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((breln @ X6 @ X7 @ X8))) | (X8 = X9) | ($true != ((breln @ X6 @ X7 @ X9))) | ($true != ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X8))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ($true != sP1)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f30,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((breln @ X6 @ X7 @ X8))) | (X8 = X9) | ($true != ((breln @ X6 @ X7 @ X9))) | (((in @ (sK7 @ X9 @ X8 @ X7 @ X6) @ X7)) = $true) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ($true != sP1)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f31,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((breln @ X6 @ X7 @ X8))) | (X8 = X9) | ($true != ((breln @ X6 @ X7 @ X9))) | ($true = ((in @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X6))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ($true != sP1)) )),
% 0.19/0.29 inference(cnf_transformation,[],[f21])).
% 0.19/0.29 thf(f37,plain,(
% 0.19/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ (sK9 @ X3 @ X2 @ X1 @ X0)) @ X3))) | ($true != ((sP0 @ X3 @ X2 @ X1 @ X0)))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f24])).
% 0.19/0.29 thf(f38,plain,(
% 0.19/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((sP0 @ X3 @ X2 @ X1 @ X0))) | ($true = ((in @ (kpair @ (sK8 @ X3 @ X2 @ X1 @ X0) @ (sK9 @ X3 @ X2 @ X1 @ X0)) @ X2)))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f24])).
% 0.19/0.29 thf(f39,plain,(
% 0.19/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((sP0 @ X3 @ X2 @ X1 @ X0))) | ($true = ((in @ (sK9 @ X3 @ X2 @ X1 @ X0) @ X1)))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f24])).
% 0.19/0.29 thf(f40,plain,(
% 0.19/0.29 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((sP0 @ X3 @ X2 @ X1 @ X0))) | ($true = ((in @ (sK8 @ X3 @ X2 @ X1 @ X0) @ X0)))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f24])).
% 0.19/0.29 thf(f43,plain,(
% 0.19/0.29 ($true = sP1) | (eqbreln != $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f25])).
% 0.19/0.29 thf(f44,plain,(
% 0.19/0.29 ( ! [X6 : $i,X5 : $i] : (($true != ((in @ (kpair @ X5 @ X6) @ sK12))) | ($true != ((in @ X6 @ sK11))) | ($true = ((in @ (kpair @ X5 @ X6) @ sK10))) | ($true != ((in @ X5 @ sK11)))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f27])).
% 0.19/0.29 thf(f45,plain,(
% 0.19/0.29 (sK12 != sK10)),
% 0.19/0.29 inference(cnf_transformation,[],[f27])).
% 0.19/0.29 thf(f46,plain,(
% 0.19/0.29 ($true = ((breln1 @ sK11 @ sK12)))),
% 0.19/0.29 inference(cnf_transformation,[],[f27])).
% 0.19/0.29 thf(f47,plain,(
% 0.19/0.29 ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (kpair @ X3 @ X4) @ sK10))) | ($true = ((in @ (kpair @ X3 @ X4) @ sK12))) | ($true != ((in @ X3 @ sK11))) | ($true != ((in @ X4 @ sK11)))) )),
% 0.19/0.29 inference(cnf_transformation,[],[f27])).
% 0.19/0.29 thf(f48,plain,(
% 0.19/0.29 ($true = ((breln1 @ sK11 @ sK10)))),
% 0.19/0.29 inference(cnf_transformation,[],[f27])).
% 0.19/0.29 thf(f49,plain,(
% 0.19/0.29 (eqbreln = $true)),
% 0.19/0.29 inference(cnf_transformation,[],[f27])).
% 0.19/0.29 thf(f50,plain,(
% 0.19/0.29 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 0.19/0.29 inference(cnf_transformation,[],[f11])).
% 0.19/0.29 thf(f51,plain,(
% 0.19/0.29 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.19/0.29 inference(cnf_transformation,[],[f6])).
% 0.19/0.29 thf(f53,definition,(
% 0.19/0.29 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.29 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.29 thf(f54,plain,(
% 0.19/0.29 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 0.19/0.29 inference(definition_unfolding,[],[f50,f51])).
% 0.19/0.29 thf(f57,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : ((X8 = X9) | ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X7 @ X9))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X7 @ X8)) != $true) | ($true != sP1) | ($true = ((in @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X6)))) )),
% 0.19/0.29 inference(definition_unfolding,[],[f31,f51,f51])).
% 0.19/0.29 thf(f58,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != sP1) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X7 @ X9))) | (((in @ (sK7 @ X9 @ X8 @ X7 @ X6) @ X7)) = $true) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X7 @ X8)) != $true) | (X8 = X9)) )),
% 0.19/0.29 inference(definition_unfolding,[],[f30,f51,f51])).
% 0.19/0.29 thf(f59,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != sP1) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X7 @ X8)) != $true) | ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X7 @ X9))) | (X8 = X9) | ($true != ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X8))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6)))) )),
% 0.19/0.29 inference(definition_unfolding,[],[f29,f51,f51])).
% 0.19/0.29 thf(f60,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X9))) | ($true != (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X7 @ X9))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | (X8 = X9) | ((((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ X6 @ X7 @ X8)) != $true) | ($true != sP1)) )),
% 0.19/0.29 inference(definition_unfolding,[],[f28,f51,f51])).
% 0.19/0.29 thf(f61,plain,(
% 0.19/0.29 ($true = sP1) | ($true != $true)),
% 0.19/0.29 inference(definition_unfolding,[],[f43,f49])).
% 0.19/0.29 thf(f63,plain,(
% 0.19/0.29 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK11 @ sK10)))),
% 0.19/0.29 inference(definition_unfolding,[],[f48,f54])).
% 0.19/0.29 thf(f64,plain,(
% 0.19/0.29 ($true = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK11 @ sK12)))),
% 0.19/0.29 inference(definition_unfolding,[],[f46,f54])).
% 0.19/0.29 thf(f65,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7)))) | ($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | ($true != sP1) | ($true != ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X8))) | (X8 = X9)) )),
% 0.19/0.29 inference(beta-eta_normalization,[],[f59])).
% 0.19/0.29 thf(f67,plain,(
% 0.19/0.29 ($true = sP1)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f61])).
% 0.19/0.29 thf(f68,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != sP1) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | (X8 = X9) | ($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | ($true = ((in @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X6))) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7))))) )),
% 0.19/0.29 inference(beta-eta_normalization,[],[f57])).
% 0.19/0.29 thf(f69,plain,(
% 0.19/0.29 ($true = ((subset @ sK12 @ (cartprod @ sK11 @ sK11))))),
% 0.19/0.29 inference(beta-eta_normalization,[],[f64])).
% 0.19/0.29 thf(f70,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7)))) | (((in @ (sK7 @ X9 @ X8 @ X7 @ X6) @ X7)) = $true) | (X8 = X9) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ($true != sP1)) )),
% 0.19/0.29 inference(beta-eta_normalization,[],[f58])).
% 0.19/0.29 thf(f71,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X9))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | (X8 = X9) | ($true != sP1) | ($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7))))) )),
% 0.19/0.29 inference(beta-eta_normalization,[],[f60])).
% 0.19/0.29 thf(f72,plain,(
% 0.19/0.29 ($true = ((subset @ sK10 @ (cartprod @ sK11 @ sK11))))),
% 0.19/0.29 inference(beta-eta_normalization,[],[f63])).
% 0.19/0.29 thf(f78,definition,(
% 0.19/0.29 spl13_2 <=> ($true = sP1)),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition])).
% 0.19/0.29 thf(f82,definition,(
% 0.19/0.29 spl13_3 <=> ! [X9 : $i,X7 : $i,X6 : $i,X8 : $i] : (($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | (X8 = X9) | ($true != ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X8))) | ($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7)))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition])).
% 0.19/0.29 thf(f83,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X8))) | ($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7)))) | (X8 = X9)) ) | ~spl13_3),
% 0.19/0.29 inference(avatar_component_clause,[],[f82])).
% 0.19/0.29 thf(f85,plain,(
% 0.19/0.29 spl13_3 | ~spl13_2),
% 0.19/0.29 inference(avatar_split_clause,[],[f65,f78,f82])).
% 0.19/0.29 thf(f90,plain,(
% 0.19/0.29 spl13_2),
% 0.19/0.29 inference(avatar_split_clause,[],[f67,f78])).
% 0.19/0.29 thf(f100,definition,(
% 0.19/0.29 spl13_7 <=> ! [X9 : $i,X7 : $i,X6 : $i,X8 : $i] : (($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7)))) | ($true = ((in @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X6))) | ($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | (X8 = X9))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition])).
% 0.19/0.29 thf(f101,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | (X8 = X9) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ($true = ((in @ (sK6 @ X9 @ X8 @ X7 @ X6) @ X6))) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7))))) ) | ~spl13_7),
% 0.19/0.29 inference(avatar_component_clause,[],[f100])).
% 0.19/0.29 thf(f102,plain,(
% 0.19/0.29 spl13_7 | ~spl13_2),
% 0.19/0.29 inference(avatar_split_clause,[],[f68,f78,f100])).
% 0.19/0.29 thf(f104,definition,(
% 0.19/0.29 spl13_8 <=> ! [X9 : $i,X7 : $i,X6 : $i,X8 : $i] : (($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | (X8 = X9) | (((in @ (sK7 @ X9 @ X8 @ X7 @ X6) @ X7)) = $true) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7)))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition])).
% 0.19/0.29 thf(f105,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | (X8 = X9) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7)))) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | (((in @ (sK7 @ X9 @ X8 @ X7 @ X6) @ X7)) = $true)) ) | ~spl13_8),
% 0.19/0.29 inference(avatar_component_clause,[],[f104])).
% 0.19/0.29 thf(f106,plain,(
% 0.19/0.29 ~spl13_2 | spl13_8),
% 0.19/0.29 inference(avatar_split_clause,[],[f70,f104,f78])).
% 0.19/0.29 thf(f108,definition,(
% 0.19/0.29 spl13_9 <=> ! [X9 : $i,X7 : $i,X6 : $i,X8 : $i] : (($true = ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X9))) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7)))) | ($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | (X8 = X9) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition])).
% 0.19/0.29 thf(f109,plain,(
% 0.19/0.29 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true != ((subset @ X9 @ (cartprod @ X6 @ X7)))) | (X8 = X9) | ($true = ((sP0 @ X9 @ X8 @ X7 @ X6))) | ($true != ((subset @ X8 @ (cartprod @ X6 @ X7)))) | ($true = ((in @ (kpair @ (sK6 @ X9 @ X8 @ X7 @ X6) @ (sK7 @ X9 @ X8 @ X7 @ X6)) @ X9)))) ) | ~spl13_9),
% 0.19/0.29 inference(avatar_component_clause,[],[f108])).
% 0.19/0.29 thf(f110,plain,(
% 0.19/0.29 spl13_9 | ~spl13_2),
% 0.19/0.29 inference(avatar_split_clause,[],[f71,f78,f108])).
% 0.19/0.29 thf(f115,plain,(
% 0.19/0.29 ( ! [X0 : $i] : (($true != ((subset @ X0 @ (cartprod @ sK11 @ sK11)))) | (sK12 = X0) | ($true != $true) | (((in @ (sK6 @ sK12 @ X0 @ sK11 @ sK11) @ sK11)) = $true) | ($true = ((sP0 @ sK12 @ X0 @ sK11 @ sK11)))) ) | ~spl13_7),
% 0.19/0.29 inference(constrained_superposition,[],[f101,f69])).
% 0.19/0.29 thf(f117,plain,(
% 0.19/0.29 ( ! [X0 : $i] : (($true != ((subset @ X0 @ (cartprod @ sK11 @ sK11)))) | ($true = ((sP0 @ sK12 @ X0 @ sK11 @ sK11))) | (sK12 = X0) | (((in @ (sK6 @ sK12 @ X0 @ sK11 @ sK11) @ sK11)) = $true)) ) | ~spl13_7),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f115])).
% 0.19/0.29 thf(f123,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ (kpair @ X0 @ X1) @ sK10))) | ($true != $true) | ($true = ((in @ (kpair @ X0 @ X1) @ sK12))) | ($true != ((in @ X0 @ sK11))) | ($true != ((in @ X1 @ sK11)))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f47,f53])).
% 0.19/0.29 thf(f125,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK11))) | ($false = ((in @ (kpair @ X0 @ X1) @ sK10))) | ($true != ((in @ X0 @ sK11))) | ($true = ((in @ (kpair @ X0 @ X1) @ sK12)))) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f123])).
% 0.19/0.29 thf(f133,plain,(
% 0.19/0.29 ( ! [X0 : $i] : (($true = ((in @ (sK7 @ sK12 @ X0 @ sK11 @ sK11) @ sK11))) | ($true != ((subset @ X0 @ (cartprod @ sK11 @ sK11)))) | (sK12 = X0) | ($true = ((sP0 @ sK12 @ X0 @ sK11 @ sK11))) | ($true != $true)) ) | ~spl13_8),
% 0.19/0.29 inference(constrained_superposition,[],[f105,f69])).
% 0.19/0.29 thf(f137,plain,(
% 0.19/0.29 ( ! [X0 : $i] : (($true != ((subset @ X0 @ (cartprod @ sK11 @ sK11)))) | ($true = ((sP0 @ sK12 @ X0 @ sK11 @ sK11))) | ($true = ((in @ (sK7 @ sK12 @ X0 @ sK11 @ sK11) @ sK11))) | (sK12 = X0)) ) | ~spl13_8),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f133])).
% 0.19/0.29 thf(f138,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (kpair @ X1 @ X0) @ sK12))) | (((in @ X0 @ sK11)) = $false) | ($true != $true) | ($true != ((in @ X1 @ sK11))) | (((in @ (kpair @ X1 @ X0) @ sK10)) = $false)) )),
% 0.19/0.29 inference(constrained_superposition,[],[f125,f53])).
% 0.19/0.29 thf(f139,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK11))) | (((in @ X0 @ sK11)) = $false) | ($true = ((in @ (kpair @ X1 @ X0) @ sK12))) | (((in @ (kpair @ X1 @ X0) @ sK10)) = $false)) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f138])).
% 0.19/0.29 thf(f145,plain,(
% 0.19/0.29 ( ! [X0 : $i] : (($true = ((sP0 @ sK12 @ X0 @ sK11 @ sK11))) | ($true != $true) | (sK12 = X0) | ($true != ((subset @ X0 @ (cartprod @ sK11 @ sK11)))) | ($true = ((in @ (kpair @ (sK6 @ sK12 @ X0 @ sK11 @ sK11) @ (sK7 @ sK12 @ X0 @ sK11 @ sK11)) @ sK12)))) ) | ~spl13_9),
% 0.19/0.29 inference(constrained_superposition,[],[f109,f69])).
% 0.19/0.29 thf(f149,plain,(
% 0.19/0.29 ( ! [X0 : $i] : (($true != ((subset @ X0 @ (cartprod @ sK11 @ sK11)))) | (sK12 = X0) | ($true = ((in @ (kpair @ (sK6 @ sK12 @ X0 @ sK11 @ sK11) @ (sK7 @ sK12 @ X0 @ sK11 @ sK11)) @ sK12))) | ($true = ((sP0 @ sK12 @ X0 @ sK11 @ sK11)))) ) | ~spl13_9),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f145])).
% 0.19/0.29 thf(f150,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ sK11)) = $false) | ($true = ((in @ (kpair @ X0 @ X1) @ sK12))) | (((in @ X1 @ sK11)) = $false) | ($true != $true) | ($false = ((in @ (kpair @ X0 @ X1) @ sK10)))) )),
% 0.19/0.29 inference(constrained_superposition,[],[f139,f53])).
% 0.19/0.29 thf(f151,plain,(
% 0.19/0.29 ( ! [X0 : $i,X1 : $i] : (($false = ((in @ (kpair @ X0 @ X1) @ sK10))) | ($true = ((in @ (kpair @ X0 @ X1) @ sK12))) | (((in @ X0 @ sK11)) = $false) | (((in @ X1 @ sK11)) = $false)) )),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f150])).
% 0.19/0.29 thf(f153,plain,(
% 0.19/0.29 ($true != $true) | (sK12 = sK10) | ($true = ((in @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ~spl13_7),
% 0.19/0.29 inference(constrained_superposition,[],[f117,f72])).
% 0.19/0.29 thf(f154,plain,(
% 0.19/0.29 ($true = ((in @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | (sK12 = sK10) | ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ~spl13_7),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f153])).
% 0.19/0.29 thf(f156,plain,(
% 0.19/0.29 ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ($true = ((in @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ~spl13_7),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f154,f45])).
% 0.19/0.29 thf(f158,definition,(
% 0.19/0.29 spl13_11 <=> ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition])).
% 0.19/0.29 thf(f159,plain,(
% 0.19/0.29 ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ~spl13_11),
% 0.19/0.29 inference(avatar_component_clause,[],[f158])).
% 0.19/0.29 thf(f161,definition,(
% 0.19/0.29 spl13_12 <=> ($true = ((in @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition])).
% 0.19/0.29 thf(f162,plain,(
% 0.19/0.29 ($true = ((in @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ~spl13_12),
% 0.19/0.29 inference(avatar_component_clause,[],[f161])).
% 0.19/0.29 thf(f163,plain,(
% 0.19/0.29 spl13_11 | spl13_12 | ~spl13_7),
% 0.19/0.29 inference(avatar_split_clause,[],[f156,f100,f161,f158])).
% 0.19/0.29 thf(f192,plain,(
% 0.19/0.29 ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ($true = ((in @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ($true != $true) | (sK12 = sK10) | ~spl13_8),
% 0.19/0.29 inference(constrained_superposition,[],[f137,f72])).
% 0.19/0.29 thf(f193,plain,(
% 0.19/0.29 (sK12 = sK10) | ($true = ((in @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ~spl13_8),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f192])).
% 0.19/0.29 thf(f209,plain,(
% 0.19/0.29 ($true != $true) | (sK12 = sK10) | ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ($true = ((in @ (kpair @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK12))) | ~spl13_9),
% 0.19/0.29 inference(constrained_superposition,[],[f149,f72])).
% 0.19/0.29 thf(f211,plain,(
% 0.19/0.29 ($true = ((in @ (kpair @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK12))) | ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | (sK12 = sK10) | ~spl13_9),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f209])).
% 0.19/0.29 thf(f223,plain,(
% 0.19/0.29 ($true = ((in @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ($true != $true) | ~spl13_11),
% 0.19/0.29 inference(constrained_superposition,[],[f39,f159])).
% 0.19/0.29 thf(f225,plain,(
% 0.19/0.29 ($true = ((in @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ~spl13_11),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f223])).
% 0.19/0.29 thf(f237,plain,(
% 0.19/0.29 (((in @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11)) = $true) | ($true != $true) | ~spl13_11),
% 0.19/0.29 inference(constrained_superposition,[],[f40,f159])).
% 0.19/0.29 thf(f241,plain,(
% 0.19/0.29 (((in @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11)) = $true) | ~spl13_11),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f237])).
% 0.19/0.29 thf(f277,plain,(
% 0.19/0.29 ($true != $true) | ($true = ((in @ (kpair @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK10))) | ~spl13_11),
% 0.19/0.29 inference(constrained_superposition,[],[f38,f159])).
% 0.19/0.29 thf(f281,plain,(
% 0.19/0.29 ($true = ((in @ (kpair @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK10))) | ~spl13_11),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f277])).
% 0.19/0.29 thf(f289,plain,(
% 0.19/0.29 (((in @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11)) = $false) | ($true = $false) | (((in @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11)) = $false) | ($true = ((in @ (kpair @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK12))) | ~spl13_11),
% 0.19/0.29 inference(constrained_superposition,[],[f151,f281])).
% 0.19/0.29 thf(f293,plain,(
% 0.19/0.29 (((in @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11)) = $false) | (((in @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11)) = $false) | ($true = ((in @ (kpair @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK12))) | ~spl13_11),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f289])).
% 0.19/0.29 thf(f296,plain,(
% 0.19/0.29 ($true = $false) | ($true = ((in @ (kpair @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK12))) | (((in @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11)) = $false) | ~spl13_11),
% 0.19/0.29 inference(forward_demodulation,[],[f293,f241])).
% 0.19/0.29 thf(f297,plain,(
% 0.19/0.29 (((in @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11)) = $false) | ($true = ((in @ (kpair @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK12))) | ~spl13_11),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f296])).
% 0.19/0.29 thf(f301,plain,(
% 0.19/0.29 ($true = ((in @ (kpair @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK12))) | ($true = $false) | ~spl13_11),
% 0.19/0.29 inference(forward_demodulation,[],[f297,f225])).
% 0.19/0.29 thf(f302,plain,(
% 0.19/0.29 ($true = ((in @ (kpair @ (sK8 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK9 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK12))) | ~spl13_11),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f301])).
% 0.19/0.29 thf(f359,plain,(
% 0.19/0.29 ($true != $true) | ($true != ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ~spl13_11),
% 0.19/0.29 inference(constrained_superposition,[],[f37,f302])).
% 0.19/0.29 thf(f360,plain,(
% 0.19/0.29 ($true != ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ~spl13_11),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f359])).
% 0.19/0.29 thf(f363,plain,(
% 0.19/0.29 $false | ~spl13_11),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f360,f159])).
% 0.19/0.29 thf(f364,plain,(
% 0.19/0.29 ~spl13_11),
% 0.19/0.29 inference(avatar_contradiction_clause,[],[f363])).
% 0.19/0.29 thf(f365,plain,(
% 0.19/0.29 ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ($true = ((in @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ~spl13_8),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f193,f45])).
% 0.19/0.29 thf(f366,plain,(
% 0.19/0.29 ($true = ((in @ (kpair @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK12))) | ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ~spl13_9),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f211,f45])).
% 0.19/0.29 thf(f368,definition,(
% 0.19/0.29 spl13_17 <=> ($true = ((in @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl13_17])],[avatar_definition])).
% 0.19/0.29 thf(f369,plain,(
% 0.19/0.29 ($true = ((in @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ~spl13_17),
% 0.19/0.29 inference(avatar_component_clause,[],[f368])).
% 0.19/0.29 thf(f370,plain,(
% 0.19/0.29 spl13_11 | spl13_17 | ~spl13_8),
% 0.19/0.29 inference(avatar_split_clause,[],[f365,f104,f368,f158])).
% 0.19/0.29 thf(f372,definition,(
% 0.19/0.29 spl13_18 <=> ($true = ((in @ (kpair @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK12)))),
% 0.19/0.29 introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition])).
% 0.19/0.29 thf(f373,plain,(
% 0.19/0.29 ($true = ((in @ (kpair @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK12))) | ~spl13_18),
% 0.19/0.29 inference(avatar_component_clause,[],[f372])).
% 0.19/0.29 thf(f374,plain,(
% 0.19/0.29 spl13_11 | spl13_18 | ~spl13_9),
% 0.19/0.29 inference(avatar_split_clause,[],[f366,f108,f372,f158])).
% 0.19/0.29 thf(f391,plain,(
% 0.19/0.29 ($true != ((in @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ($true != $true) | ($true != ((in @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ($true = ((in @ (kpair @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK10))) | ~spl13_18),
% 0.19/0.29 inference(constrained_superposition,[],[f44,f373])).
% 0.19/0.29 thf(f394,plain,(
% 0.19/0.29 ($true = ((in @ (kpair @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK10))) | ($true != ((in @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ($true != ((in @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ~spl13_18),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f391])).
% 0.19/0.29 thf(f395,plain,(
% 0.19/0.29 ($true != ((in @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11) @ sK11))) | ($true = ((in @ (kpair @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK10))) | (~spl13_12 | ~spl13_18)),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f394,f162])).
% 0.19/0.29 thf(f396,plain,(
% 0.19/0.29 ($true = ((in @ (kpair @ (sK6 @ sK12 @ sK10 @ sK11 @ sK11) @ (sK7 @ sK12 @ sK10 @ sK11 @ sK11)) @ sK10))) | (~spl13_12 | ~spl13_17 | ~spl13_18)),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f395,f369])).
% 0.19/0.29 thf(f401,plain,(
% 0.19/0.29 ($true != ((subset @ sK12 @ (cartprod @ sK11 @ sK11)))) | ($true != ((subset @ sK10 @ (cartprod @ sK11 @ sK11)))) | (sK12 = sK10) | ($true != $true) | ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | (~spl13_3 | ~spl13_12 | ~spl13_17 | ~spl13_18)),
% 0.19/0.29 inference(constrained_superposition,[],[f83,f396])).
% 0.19/0.29 thf(f406,plain,(
% 0.19/0.29 ($true != ((subset @ sK12 @ (cartprod @ sK11 @ sK11)))) | (sK12 = sK10) | ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ($true != ((subset @ sK10 @ (cartprod @ sK11 @ sK11)))) | (~spl13_3 | ~spl13_12 | ~spl13_17 | ~spl13_18)),
% 0.19/0.29 inference(trivial_inequality_removal,[],[f401])).
% 0.19/0.29 thf(f407,plain,(
% 0.19/0.29 ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | (sK12 = sK10) | ($true != ((subset @ sK10 @ (cartprod @ sK11 @ sK11)))) | (~spl13_3 | ~spl13_12 | ~spl13_17 | ~spl13_18)),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f406,f69])).
% 0.19/0.29 thf(f408,plain,(
% 0.19/0.29 ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | ($true != ((subset @ sK10 @ (cartprod @ sK11 @ sK11)))) | (~spl13_3 | ~spl13_12 | ~spl13_17 | ~spl13_18)),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f407,f45])).
% 0.19/0.29 thf(f409,plain,(
% 0.19/0.29 ($true = ((sP0 @ sK12 @ sK10 @ sK11 @ sK11))) | (~spl13_3 | ~spl13_12 | ~spl13_17 | ~spl13_18)),
% 0.19/0.29 inference(forward_subsumption_resolution,[],[f408,f72])).
% 0.19/0.29 thf(f410,plain,(
% 0.19/0.29 spl13_11 | ~spl13_3 | ~spl13_12 | ~spl13_17 | ~spl13_18),
% 0.19/0.29 inference(avatar_split_clause,[],[f409,f372,f368,f161,f82,f158])).
% 0.19/0.29 cnf(s2, plain, ~spl13_2 | spl13_3, inference(sat_conversion,[],[f85])).
% 0.19/0.29 cnf(s4, plain, spl13_2, inference(sat_conversion,[],[f90])).
% 0.19/0.29 cnf(s7, plain, ~spl13_2 | spl13_7, inference(sat_conversion,[],[f102])).
% 0.19/0.29 cnf(s8, plain, ~spl13_2 | spl13_8, inference(sat_conversion,[],[f106])).
% 0.19/0.29 cnf(s9, plain, ~spl13_2 | spl13_9, inference(sat_conversion,[],[f110])).
% 0.19/0.29 cnf(s11, plain, ~spl13_7 | spl13_11 | spl13_12, inference(sat_conversion,[],[f163])).
% 0.19/0.29 cnf(s16, plain, ~spl13_11, inference(sat_conversion,[],[f364])).
% 0.19/0.29 cnf(s17, plain, ~spl13_8 | spl13_11 | spl13_17, inference(sat_conversion,[],[f370])).
% 0.19/0.29 cnf(s18, plain, ~spl13_9 | spl13_11 | spl13_18, inference(sat_conversion,[],[f374])).
% 0.19/0.29 cnf(s19, plain, ~spl13_3 | spl13_11 | ~spl13_12 | ~spl13_17 | ~spl13_18, inference(sat_conversion,[],[f410])).
% 0.19/0.29 cnf(s22, plain, ~spl13_7 | spl13_12, inference(rat,[],[s11,s16])).
% 0.19/0.29 cnf(s23, plain, spl13_9, inference(rat,[],[s9,s4])).
% 0.19/0.29 cnf(s24, plain, spl13_8, inference(rat,[],[s8,s4])).
% 0.19/0.29 cnf(s25, plain, spl13_7, inference(rat,[],[s7,s4])).
% 0.19/0.29 cnf(s26, plain, spl13_18, inference(rat,[],[s18,s16,s23])).
% 0.19/0.29 cnf(s28, plain, spl13_17, inference(rat,[],[s17,s16,s24])).
% 0.19/0.29 cnf(s31, plain, spl13_12, inference(rat,[],[s22,s25])).
% 0.19/0.29 cnf(s32, plain, ~spl13_3, inference(rat,[],[s19,s26,s28,s16,s31])).
% 0.19/0.29 cnf(s33, plain, $false, inference(rat,[],[s2,s32,s4])).
% 0.19/0.29 thf(f411,plain,(
% 0.19/0.29 $false),
% 0.19/0.29 inference(avatar_sat_refutation,[],[s33])).
% 0.19/0.29 % SZS output end Proof for theBenchmark
% 0.19/0.29 % (674008)------------------------------
% 0.19/0.29 % (674008)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.29 % (674008)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.29 % (674008)CaDiCaL version: 2.1.3
% 0.19/0.29 % (674008)Termination reason: Refutation
% 0.19/0.29 % (674008)Time elapsed: 0.020 s
% 0.19/0.29 % (674008)Peak memory usage: 13 MB
% 0.19/0.29 % (674008)Instructions burned: 70 (million)
% 0.19/0.29 % (673998)Success in time 0.05 s
% 0.19/0.29 % Vampire exiting
%------------------------------------------------------------------------------