%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU689^2 : 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 : n003.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 08:30:47 AM UTC 2026
% Result : Theorem 0.46s 0.38s
% Output : Refutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU689^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n003.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 14:11:28 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.29 Running higher-order theorem proving
% 0.26/0.30 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
% 0.46/0.38 % (2563426)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.46/0.38 % (2563437)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.46/0.38 % (2563437)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
% 0.46/0.38 % (2563437)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=3327028242:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.46/0.38 % (2563432)lrs+10_16_si=on:nwc=1.5:random_seed=3379467292:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.46/0.38 % (2563435)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1782827509:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.46/0.38 % (2563431)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2799774372:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.46/0.38 % (2563436)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2385373845:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.46/0.38 % (2563433)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1901865855:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.46/0.38 % (2563434)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=623522854: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)
% 0.46/0.38 % (2563433)Instruction limit reached!
% 0.46/0.38 % (2563433)------------------------------
% 0.46/0.38 % (2563433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.38 % (2563433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.38 % (2563433)CaDiCaL version: 2.1.3
% 0.46/0.38 % (2563433)Termination reason: Instruction limit
% 0.46/0.38 % (2563433)Termination phase: Saturation
% 0.46/0.38 % (2563433)Time elapsed: 0.004 s
% 0.46/0.38 % (2563433)Peak memory usage: 11 MB
% 0.46/0.38 % (2563433)Instructions burned: 3 (million)
% 0.46/0.38 % (2563437)Refutation not found, incomplete strategy
% 0.46/0.38 % (2563437)------------------------------
% 0.46/0.38 % (2563437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.38 % (2563437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.38 % (2563437)CaDiCaL version: 2.1.3
% 0.46/0.38 % (2563437)Termination reason: Refutation not found, incomplete strategy
% 0.46/0.38 % (2563437)Time elapsed: 0.021 s
% 0.46/0.38 % (2563437)Peak memory usage: 12 MB
% 0.46/0.38 % (2563437)Instructions burned: 41 (million)
% 0.46/0.38 % (2563432)Instruction limit reached!
% 0.46/0.38 % (2563432)------------------------------
% 0.46/0.38 % (2563432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.38 % (2563432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.38 % (2563432)CaDiCaL version: 2.1.3
% 0.46/0.38 % (2563432)Termination reason: Instruction limit
% 0.46/0.38 % (2563432)Termination phase: Saturation
% 0.46/0.38 % (2563432)Time elapsed: 0.019 s
% 0.46/0.38 % (2563432)Peak memory usage: 12 MB
% 0.46/0.38 % (2563432)Instructions burned: 18 (million)
% 0.46/0.38 % (2563437)------------------------------
% 0.46/0.38 % (2563437)------------------------------
% 0.46/0.38 % (2563435)Instruction limit reached!
% 0.46/0.38 % (2563435)------------------------------
% 0.46/0.38 % (2563435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.38 % (2563435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.38 % (2563435)CaDiCaL version: 2.1.3
% 0.46/0.38 % (2563435)Termination reason: Instruction limit
% 0.46/0.38 % (2563435)Termination phase: Saturation
% 0.46/0.38 % (2563435)Time elapsed: 0.023 s
% 0.46/0.38 % (2563435)Peak memory usage: 12 MB
% 0.46/0.38 % (2563435)Instructions burned: 24 (million)
% 0.46/0.38 % (2563447)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.46/0.38 % (2563434) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2563426-2563434"...
% 0.46/0.38 % (2563447)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3626436320:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.46/0.38 % (2563447)Instruction limit reached!
% 0.46/0.38 % (2563447)------------------------------
% 0.46/0.38 % (2563447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.38 % (2563447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.38 % (2563447)CaDiCaL version: 2.1.3
% 0.46/0.38 % (2563447)Termination reason: Instruction limit
% 0.46/0.38 % (2563447)Termination phase: Saturation
% 0.46/0.38 % (2563447)Time elapsed: 0.004 s
% 0.46/0.38 % (2563447)Peak memory usage: 12 MB
% 0.46/0.38 % (2563447)Instructions burned: 8 (million)
% 0.46/0.38 % (2563434)...printing done.
% 0.46/0.38 % (2563434)Refutation found. Thanks to Tanya!
% 0.46/0.38 % SZS status Theorem for theBenchmark
% 0.46/0.38 % SZS output start Proof for theBenchmark
% 0.46/0.38 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.46/0.38 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.46/0.38 thf(func_def_1, type, subset: ($i > $i > $o)).
% 0.46/0.38 thf(func_def_2, type, subsetI1: $o).
% 0.46/0.38 thf(func_def_4, type, kpair: ($i > $i > $i)).
% 0.46/0.38 thf(func_def_5, type, cartprod: ($i > $i > $i)).
% 0.46/0.38 thf(func_def_6, type, breln: ($i > $i > $i > $o)).
% 0.46/0.38 thf(func_def_7, type, brelnall1: $o).
% 0.46/0.38 thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
% 0.46/0.38 thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
% 0.46/0.38 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.46/0.38 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.46/0.38 thf(func_def_14, type, sK0: (($i > $o) > $i > $i > $i > $i)).
% 0.46/0.38 thf(func_def_15, type, sK1: (($i > $o) > $i > $i > $i > $i)).
% 0.46/0.38 thf(func_def_19, type, sK5: ($i > $o)).
% 0.46/0.38 thf(func_def_23, type, sK9: ($i > $i > $i)).
% 0.46/0.38 thf(func_def_28, type, vNOT: ($o > $o)).
% 0.46/0.38 thf(func_def_30, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.46/0.38 thf(f1,axiom,(
% 0.46/0.38 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.46/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1)).
% 0.46/0.38 thf(f3,axiom,(
% 0.46/0.38 (! [X2 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X4 : $i] : ((in @ X4 @ X2) => (X3 @ X4)))) = brelnall1)),
% 0.46/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1)).
% 0.46/0.38 thf(f4,conjecture,(
% 0.46/0.38 subsetI1 => (brelnall1 => ! [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)))))),
% 0.46/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln)).
% 0.46/0.38 thf(f5,negated_conjecture,(
% 0.46/0.38 ~(subsetI1 => (brelnall1 => ! [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))))))),
% 0.46/0.38 inference(negated_conjecture,[status(cth)],[f4])).
% 0.46/0.38 thf(f6,plain,(
% 0.46/0.38 (subsetI1 = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.46/0.38 inference(rectify,[],[f1])).
% 0.46/0.38 thf(f7,plain,(
% 0.46/0.38 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) => (((in @ X2 @ X1)) = $true)) => (((subset @ X0 @ X1)) = $true))),
% 0.46/0.38 inference(fool_elimination,[],[f6])).
% 0.46/0.38 thf(f8,plain,(
% 0.46/0.38 (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X2 @ X0) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X0) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X0) => (X3 @ X6)))) = brelnall1)),
% 0.46/0.38 inference(rectify,[],[f3])).
% 0.46/0.38 thf(f9,plain,(
% 0.46/0.38 (brelnall1 = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (($true = ((breln @ X1 @ X2 @ X0))) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((((in @ X4 @ X1)) = $true) => ! [X5 : $i] : ((((in @ X5 @ X2)) = $true) => ((((in @ (kpair @ X4 @ X5) @ X0)) = $true) => (((X3 @ (kpair @ X4 @ X5))) = $true)))) => ! [X6 : $i] : ((((in @ X6 @ X0)) = $true) => (((X3 @ X6)) = $true))))),
% 0.46/0.38 inference(fool_elimination,[],[f8])).
% 0.46/0.38 thf(f10,plain,(
% 0.46/0.38 ~(subsetI1 => (brelnall1 => ! [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))))))),
% 0.46/0.38 inference(rectify,[],[f5])).
% 0.46/0.38 thf(f11,plain,(
% 0.46/0.38 ~((subsetI1 = $true) => ((brelnall1 = $true) => ! [X2 : $i,X1 : $i,X0 : $i] : (($true = ((breln @ X2 @ X0 @ X1))) => ! [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))))))),
% 0.46/0.38 inference(fool_elimination,[],[f10])).
% 0.46/0.38 thf(f13,plain,(
% 0.46/0.38 (brelnall1 = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (! [X3 : ($i > $o)] : (! [X6 : $i] : ((((X3 @ X6)) = $true) | (((in @ X6 @ X0)) != $true)) | ? [X4 : $i] : (? [X5 : $i] : (((((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X0)) = $true)) & (((in @ X5 @ X2)) = $true)) & (((in @ X4 @ X1)) = $true))) | ($true != ((breln @ X1 @ X2 @ X0))))),
% 0.46/0.38 inference(ennf_transformation,[],[f9])).
% 0.46/0.38 thf(f14,plain,(
% 0.46/0.38 ! [X2 : $i,X0 : $i,X1 : $i] : (! [X3 : ($i > $o)] : (? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & ? [X5 : $i] : ((((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ X5 @ X2)) = $true) & (((in @ (kpair @ X4 @ X5) @ X0)) = $true))) | ! [X6 : $i] : ((((X3 @ X6)) = $true) | (((in @ X6 @ X0)) != $true))) | ($true != ((breln @ X1 @ X2 @ X0)))) <=> (brelnall1 = $true)),
% 0.46/0.38 inference(flattening,[],[f13])).
% 0.46/0.38 thf(f15,plain,(
% 0.46/0.38 (? [X2 : $i,X1 : $i,X0 : $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)))) & ($true = ((breln @ X2 @ X0 @ X1)))) & (brelnall1 = $true)) & (subsetI1 = $true)),
% 0.46/0.38 inference(ennf_transformation,[],[f11])).
% 0.46/0.38 thf(f16,plain,(
% 0.46/0.38 ? [X1 : $i,X2 : $i,X0 : $i] : (? [X3 : $i] : (! [X4 : $i] : (! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X1)) != $true) | (((in @ (kpair @ X4 @ X5) @ X3)) = $true) | (((in @ X5 @ X0)) != $true)) | (((in @ X4 @ X2)) != $true)) & ($true = ((breln @ X2 @ X0 @ X3))) & (((subset @ X1 @ X3)) != $true)) & ($true = ((breln @ X2 @ X0 @ X1)))) & (brelnall1 = $true) & (subsetI1 = $true)),
% 0.46/0.38 inference(flattening,[],[f15])).
% 0.46/0.38 thf(f17,plain,(
% 0.46/0.38 (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true))),
% 0.46/0.38 inference(ennf_transformation,[],[f7])).
% 0.46/0.38 thf(f18,plain,(
% 0.46/0.38 (! [X2 : $i,X0 : $i,X1 : $i] : (! [X3 : ($i > $o)] : (? [X4 : $i] : ((((in @ X4 @ X1)) = $true) & ? [X5 : $i] : ((((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ X5 @ X2)) = $true) & (((in @ (kpair @ X4 @ X5) @ X0)) = $true))) | ! [X6 : $i] : ((((X3 @ X6)) = $true) | (((in @ X6 @ X0)) != $true))) | ($true != ((breln @ X1 @ X2 @ X0)))) | (brelnall1 != $true)) & ((brelnall1 = $true) | ? [X2 : $i,X0 : $i,X1 : $i] : (? [X3 : ($i > $o)] : (! [X4 : $i] : ((((in @ X4 @ X1)) != $true) | ! [X5 : $i] : ((((X3 @ (kpair @ X4 @ X5))) = $true) | (((in @ X5 @ X2)) != $true) | (((in @ (kpair @ X4 @ X5) @ X0)) != $true))) & ? [X6 : $i] : ((((X3 @ X6)) != $true) & (((in @ X6 @ X0)) = $true))) & ($true = ((breln @ X1 @ X2 @ X0)))))),
% 0.46/0.38 inference(nnf_transformation,[],[f14])).
% 0.46/0.38 thf(f19,plain,(
% 0.46/0.38 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : ($i > $o)] : (? [X4 : $i] : ((((in @ X4 @ X2)) = $true) & ? [X5 : $i] : ((((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ X5 @ X0)) = $true) & (((in @ (kpair @ X4 @ X5) @ X1)) = $true))) | ! [X6 : $i] : ((((X3 @ X6)) = $true) | (((in @ X6 @ X1)) != $true))) | ($true != ((breln @ X2 @ X0 @ X1)))) | (brelnall1 != $true)) & ((brelnall1 = $true) | ? [X7 : $i,X8 : $i,X9 : $i] : (? [X10 : ($i > $o)] : (! [X11 : $i] : ((((in @ X11 @ X9)) != $true) | ! [X12 : $i] : ((((X10 @ (kpair @ X11 @ X12))) = $true) | (((in @ X12 @ X7)) != $true) | (((in @ (kpair @ X11 @ X12) @ X8)) != $true))) & ? [X13 : $i] : ((((X10 @ X13)) != $true) & (((in @ X13 @ X8)) = $true))) & (((breln @ X9 @ X7 @ X8)) = $true)))),
% 0.46/0.38 inference(rectify,[],[f18])).
% 0.46/0.38 thf(f20,plain,(
% 0.46/0.38 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : ($i > $o)] : (((((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X2)) = $true) & ((((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) & (((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X0)) = $true) & (((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X1)) = $true))) | ! [X6 : $i] : ((((X3 @ X6)) = $true) | (((in @ X6 @ X1)) != $true))) | ($true != ((breln @ X2 @ X0 @ X1)))) | (brelnall1 != $true)) & ((brelnall1 = $true) | ((! [X11 : $i] : (($true != ((in @ X11 @ sK4))) | ! [X12 : $i] : ((((sK5 @ (kpair @ X11 @ X12))) = $true) | (((in @ X12 @ sK2)) != $true) | (((in @ (kpair @ X11 @ X12) @ sK3)) != $true))) & ((((sK5 @ sK6)) != $true) & (((in @ sK6 @ sK3)) = $true))) & (((breln @ sK4 @ sK2 @ sK3)) = $true)))),
% 0.46/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2,sK3,sK4,sK5,sK6]),skolemize(X5,sK1 @ X3 @ X2 @ X1 @ X0),skolemize(X5,sK1 @ X3 @ X2 @ X1 @ X0),skolemize(X7,sK2),skolemize(X8,sK3),skolemize(X9,sK4),skolemize(X10,sK5),skolemize(X13,sK6)],[f19])).
% 0.46/0.38 thf(f21,plain,(
% 0.46/0.38 ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) | (((in @ X2 @ X0)) != $true)) & (((subset @ X0 @ X1)) != $true))) & (! [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) != $true) & (((in @ X2 @ X0)) = $true)) | (((subset @ X0 @ X1)) = $true)) | (subsetI1 != $true))),
% 0.46/0.38 inference(nnf_transformation,[],[f17])).
% 0.46/0.38 thf(f22,plain,(
% 0.46/0.38 ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) = $true) | (((in @ X2 @ X1)) != $true)) & ($true != ((subset @ X1 @ X0))))) & (! [X3 : $i,X4 : $i] : (? [X5 : $i] : ((((in @ X5 @ X3)) != $true) & (((in @ X5 @ X4)) = $true)) | (((subset @ X4 @ X3)) = $true)) | (subsetI1 != $true))),
% 0.46/0.38 inference(rectify,[],[f21])).
% 0.46/0.38 thf(f23,plain,(
% 0.46/0.38 ((subsetI1 = $true) | (! [X2 : $i] : ((((in @ X2 @ sK7)) = $true) | (((in @ X2 @ sK8)) != $true)) & (((subset @ sK8 @ sK7)) != $true))) & (! [X3 : $i,X4 : $i] : (((((in @ (sK9 @ X4 @ X3) @ X3)) != $true) & (((in @ (sK9 @ X4 @ X3) @ X4)) = $true)) | (((subset @ X4 @ X3)) = $true)) | (subsetI1 != $true))),
% 0.46/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,vAPP]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X5,sK1 @ X3 @ X2 @ X1 @ X0)],[f22])).
% 0.46/0.38 thf(f24,plain,(
% 0.46/0.38 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (! [X4 : $i] : (! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X0)) != $true) | (((in @ (kpair @ X4 @ X5) @ X3)) = $true) | (((in @ X5 @ X2)) != $true)) | (((in @ X4 @ X1)) != $true)) & ($true = ((breln @ X1 @ X2 @ X3))) & ($true != ((subset @ X0 @ X3)))) & ($true = ((breln @ X1 @ X2 @ X0)))) & (brelnall1 = $true) & (subsetI1 = $true)),
% 0.46/0.38 inference(rectify,[],[f16])).
% 0.46/0.38 thf(f25,plain,(
% 0.46/0.38 ((! [X4 : $i] : (! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ sK10)) != $true) | (((in @ (kpair @ X4 @ X5) @ sK13)) = $true) | ($true != ((in @ X5 @ sK12)))) | ($true != ((in @ X4 @ sK11)))) & (((breln @ sK11 @ sK12 @ sK13)) = $true) & (((subset @ sK10 @ sK13)) != $true)) & (((breln @ sK11 @ sK12 @ sK10)) = $true)) & (brelnall1 = $true) & (subsetI1 = $true)),
% 0.46/0.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12),skolemize(X3,sK13)],[f24])).
% 0.46/0.38 thf(f32,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((((X3 @ X6)) = $true) | (((in @ X6 @ X1)) != $true) | (brelnall1 != $true) | (((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X0)) = $true) | ($true != ((breln @ X2 @ X0 @ X1)))) )),
% 0.46/0.38 inference(cnf_transformation,[],[f20])).
% 0.46/0.38 thf(f33,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : (($true != ((breln @ X2 @ X0 @ X1))) | (((in @ X6 @ X1)) != $true) | (((X3 @ X6)) = $true) | (((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) | (brelnall1 != $true)) )),
% 0.46/0.38 inference(cnf_transformation,[],[f20])).
% 0.46/0.38 thf(f34,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((brelnall1 != $true) | (((X3 @ X6)) = $true) | (((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X2)) = $true) | ($true != ((breln @ X2 @ X0 @ X1))) | (((in @ X6 @ X1)) != $true)) )),
% 0.46/0.38 inference(cnf_transformation,[],[f20])).
% 0.46/0.38 thf(f35,plain,(
% 0.46/0.38 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK9 @ X4 @ X3) @ X4)) = $true) | (subsetI1 != $true) | (((subset @ X4 @ X3)) = $true)) )),
% 0.46/0.38 inference(cnf_transformation,[],[f23])).
% 0.46/0.38 thf(f36,plain,(
% 0.46/0.38 ( ! [X3 : $i,X4 : $i] : ((((subset @ X4 @ X3)) = $true) | (((in @ (sK9 @ X4 @ X3) @ X3)) != $true) | (subsetI1 != $true)) )),
% 0.46/0.38 inference(cnf_transformation,[],[f23])).
% 0.46/0.38 thf(f39,plain,(
% 0.46/0.38 (subsetI1 = $true)),
% 0.46/0.38 inference(cnf_transformation,[],[f25])).
% 0.46/0.38 thf(f40,plain,(
% 0.46/0.38 (brelnall1 = $true)),
% 0.46/0.38 inference(cnf_transformation,[],[f25])).
% 0.46/0.38 thf(f41,plain,(
% 0.46/0.38 (((breln @ sK11 @ sK12 @ sK10)) = $true)),
% 0.46/0.38 inference(cnf_transformation,[],[f25])).
% 0.46/0.38 thf(f42,plain,(
% 0.46/0.38 (((subset @ sK10 @ sK13)) != $true)),
% 0.46/0.38 inference(cnf_transformation,[],[f25])).
% 0.46/0.38 thf(f44,plain,(
% 0.46/0.38 ( ! [X4 : $i,X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ sK13)) = $true) | ($true != ((in @ X5 @ sK12))) | ($true != ((in @ X4 @ sK11))) | (((in @ (kpair @ X4 @ X5) @ sK10)) != $true)) )),
% 0.46/0.38 inference(cnf_transformation,[],[f25])).
% 0.46/0.38 thf(f47,definition,(
% 0.46/0.38 spl14_1 <=> ! [X4 : $i,X3 : $i] : ((((in @ (sK9 @ X4 @ X3) @ X4)) = $true) | (((subset @ X4 @ X3)) = $true))),
% 0.46/0.38 introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition])).
% 0.46/0.38 thf(f48,plain,(
% 0.46/0.38 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK9 @ X4 @ X3) @ X4)) = $true) | (((subset @ X4 @ X3)) = $true)) ) | ~spl14_1),
% 0.46/0.38 inference(avatar_component_clause,[],[f47])).
% 0.46/0.38 thf(f50,definition,(
% 0.46/0.38 spl14_2 <=> (subsetI1 = $true)),
% 0.46/0.38 introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition])).
% 0.46/0.38 thf(f53,plain,(
% 0.46/0.38 spl14_1 | ~spl14_2),
% 0.46/0.38 inference(avatar_split_clause,[],[f35,f50,f47])).
% 0.46/0.38 thf(f55,definition,(
% 0.46/0.38 spl14_3 <=> ! [X4 : $i,X3 : $i] : ((((subset @ X4 @ X3)) = $true) | (((in @ (sK9 @ X4 @ X3) @ X3)) != $true))),
% 0.46/0.38 introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition])).
% 0.46/0.38 thf(f56,plain,(
% 0.46/0.38 ( ! [X3 : $i,X4 : $i] : ((((in @ (sK9 @ X4 @ X3) @ X3)) != $true) | (((subset @ X4 @ X3)) = $true)) ) | ~spl14_3),
% 0.46/0.38 inference(avatar_component_clause,[],[f55])).
% 0.46/0.38 thf(f57,plain,(
% 0.46/0.38 spl14_3 | ~spl14_2),
% 0.46/0.38 inference(avatar_split_clause,[],[f36,f50,f55])).
% 0.46/0.38 thf(f59,definition,(
% 0.46/0.38 spl14_4 <=> (brelnall1 = $true)),
% 0.46/0.38 introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition])).
% 0.46/0.38 thf(f76,plain,(
% 0.46/0.38 spl14_2),
% 0.46/0.38 inference(avatar_split_clause,[],[f39,f50])).
% 0.46/0.38 thf(f82,plain,(
% 0.46/0.38 spl14_4),
% 0.46/0.38 inference(avatar_split_clause,[],[f40,f59])).
% 0.46/0.38 thf(f84,definition,(
% 0.46/0.38 spl14_9 <=> (((subset @ sK10 @ sK13)) = $true)),
% 0.46/0.38 introduced(definition,[new_symbols(definition,[spl14_9])],[avatar_definition])).
% 0.46/0.38 thf(f86,plain,(
% 0.46/0.38 (((subset @ sK10 @ sK13)) != $true) | spl14_9),
% 0.46/0.38 inference(avatar_component_clause,[],[f84])).
% 0.46/0.38 thf(f87,plain,(
% 0.46/0.38 ~spl14_9),
% 0.46/0.38 inference(avatar_split_clause,[],[f42,f84])).
% 0.46/0.38 thf(f94,definition,(
% 0.46/0.38 spl14_11 <=> ! [X2 : $i,X3 : ($i > $o),X0 : $i,X6 : $i,X1 : $i] : ((((X3 @ X6)) = $true) | (((in @ X6 @ X1)) != $true) | ($true != ((breln @ X2 @ X0 @ X1))) | (((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X2)) = $true))),
% 0.46/0.38 introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition])).
% 0.46/0.38 thf(f95,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X2)) = $true) | (((X3 @ X6)) = $true) | ($true != ((breln @ X2 @ X0 @ X1))) | (((in @ X6 @ X1)) != $true)) ) | ~spl14_11),
% 0.46/0.38 inference(avatar_component_clause,[],[f94])).
% 0.46/0.38 thf(f96,plain,(
% 0.46/0.38 spl14_11 | ~spl14_4),
% 0.46/0.38 inference(avatar_split_clause,[],[f34,f59,f94])).
% 0.46/0.38 thf(f116,definition,(
% 0.46/0.38 spl14_16 <=> ! [X2 : $i,X3 : ($i > $o),X0 : $i,X6 : $i,X1 : $i] : ((((X3 @ X6)) = $true) | ($true != ((breln @ X2 @ X0 @ X1))) | (((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X0)) = $true) | (((in @ X6 @ X1)) != $true))),
% 0.46/0.38 introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition])).
% 0.46/0.38 thf(f117,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X0)) = $true) | ($true != ((breln @ X2 @ X0 @ X1))) | (((X3 @ X6)) = $true) | (((in @ X6 @ X1)) != $true)) ) | ~spl14_16),
% 0.46/0.38 inference(avatar_component_clause,[],[f116])).
% 0.46/0.38 thf(f118,plain,(
% 0.46/0.38 ~spl14_4 | spl14_16),
% 0.46/0.38 inference(avatar_split_clause,[],[f32,f116,f59])).
% 0.46/0.38 thf(f120,definition,(
% 0.46/0.38 spl14_17 <=> (((breln @ sK11 @ sK12 @ sK10)) = $true)),
% 0.46/0.38 introduced(definition,[new_symbols(definition,[spl14_17])],[avatar_definition])).
% 0.46/0.38 thf(f122,plain,(
% 0.46/0.38 (((breln @ sK11 @ sK12 @ sK10)) = $true) | ~spl14_17),
% 0.46/0.38 inference(avatar_component_clause,[],[f120])).
% 0.46/0.38 thf(f123,plain,(
% 0.46/0.38 spl14_17),
% 0.46/0.38 inference(avatar_split_clause,[],[f41,f120])).
% 0.46/0.38 thf(f125,definition,(
% 0.46/0.38 spl14_18 <=> ! [X6 : $i,X0 : $i,X3 : ($i > $o),X2 : $i,X1 : $i] : (($true != ((breln @ X2 @ X0 @ X1))) | (((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) | (((X3 @ X6)) = $true) | (((in @ X6 @ X1)) != $true))),
% 0.46/0.38 introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition])).
% 0.46/0.38 thf(f126,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) | (((in @ X6 @ X1)) != $true) | (((X3 @ X6)) = $true) | ($true != ((breln @ X2 @ X0 @ X1)))) ) | ~spl14_18),
% 0.46/0.38 inference(avatar_component_clause,[],[f125])).
% 0.46/0.38 thf(f127,plain,(
% 0.46/0.38 spl14_18 | ~spl14_4),
% 0.46/0.38 inference(avatar_split_clause,[],[f33,f59,f125])).
% 0.46/0.38 thf(f135,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((kpair @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3) @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3))) = X0) | (((breln @ X1 @ X3 @ X2)) != $true) | (((in @ X0 @ X2)) != $true)) ) | ~spl14_18),
% 0.46/0.38 inference(leibniz_equality_elimination,[],[f126])).
% 0.46/0.38 thf(f162,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3) @ sK12))) | (((in @ X0 @ sK13)) = $true) | (((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3) @ sK11)) != $true) | (((breln @ X1 @ X3 @ X2)) != $true) | (((in @ X0 @ X2)) != $true) | ($true != ((in @ X0 @ sK10)))) ) | ~spl14_18),
% 0.46/0.38 inference(superposition,[],[f44,f135])).
% 0.46/0.38 thf(f170,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ sK12) @ sK11)) != $true) | ((((^[Y0 : $i]: (~ (Y0 = X0))) @ X3)) = $true) | ($true != ((in @ X3 @ X2))) | ($true != ((in @ X0 @ sK10))) | (((in @ X0 @ sK13)) = $true) | ($true != $true) | (((in @ X0 @ X2)) != $true) | ($true != ((breln @ X1 @ sK12 @ X2))) | ($true != ((breln @ X1 @ sK12 @ X2)))) ) | (~spl14_16 | ~spl14_18)),
% 0.46/0.38 inference(superposition,[],[f162,f117])).
% 0.46/0.38 thf(f171,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((breln @ X1 @ sK12 @ X2))) | (((in @ X0 @ sK13)) = $true) | ((((^[Y0 : $i]: (~ (Y0 = X0))) @ X3)) = $true) | ($true != ((in @ X3 @ X2))) | (((in @ X0 @ X2)) != $true) | ($true != ((in @ X0 @ sK10))) | ($true != $true) | (((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ sK12) @ sK11)) != $true)) ) | (~spl14_16 | ~spl14_18)),
% 0.46/0.38 inference(duplicate_literal_removal,[],[f170])).
% 0.46/0.38 thf(f172,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((((^[Y0 : $i]: (~ (Y0 = X0))) @ X3)) = $true) | (((in @ X0 @ X2)) != $true) | ($true != ((in @ X3 @ X2))) | (((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ sK12) @ sK11)) != $true) | ($true != ((in @ X0 @ sK10))) | (((in @ X0 @ sK13)) = $true) | ($true != ((breln @ X1 @ sK12 @ X2)))) ) | (~spl14_16 | ~spl14_18)),
% 0.46/0.38 inference(trivial_inequality_removal,[],[f171])).
% 0.46/0.38 thf(f173,plain,(
% 0.46/0.38 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ sK13)) = $true) | ($true != ((in @ X3 @ X2))) | ($true != ((in @ X0 @ sK10))) | (((~ (X3 = X0))) = $true) | (((in @ X0 @ X2)) != $true) | (((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ sK12) @ sK11)) != $true) | ($true != ((breln @ X1 @ sK12 @ X2)))) ) | (~spl14_16 | ~spl14_18)),
% 0.46/0.38 inference(beta-eta_normalization,[],[f172])).
% 0.46/0.39 thf(f174,plain,(
% 0.46/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X2)) != $true) | ($true != ((in @ X0 @ sK10))) | ($true != ((breln @ X1 @ sK12 @ X2))) | (((in @ X0 @ sK13)) = $true) | ($true != ((in @ X3 @ X2))) | (((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ sK12) @ sK11)) != $true) | (((X3 = X0)) = $false)) ) | (~spl14_16 | ~spl14_18)),
% 0.46/0.39 inference(not_proxy_clausification,[],[f173])).
% 0.46/0.39 thf(f175,plain,(
% 0.46/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ sK12) @ sK11)) != $true) | ($true != ((in @ X0 @ sK10))) | (((in @ X0 @ sK13)) = $true) | ($true != ((breln @ X1 @ sK12 @ X2))) | (((in @ X0 @ X2)) != $true) | ($true != ((in @ X3 @ X2))) | (X0 != X3)) ) | (~spl14_16 | ~spl14_18)),
% 0.46/0.39 inference(equality_proxy_clausification,[],[f174])).
% 0.46/0.39 thf(f187,plain,(
% 0.46/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | (X0 != X2) | (((in @ X3 @ X1)) != $true) | ($true != ((breln @ sK11 @ sK12 @ X1))) | ($true != ((in @ X0 @ sK10))) | ((((^[Y0 : $i]: (~ (Y0 = X0))) @ X3)) = $true) | (((in @ X0 @ X1)) != $true) | ($true != ((breln @ sK11 @ sK12 @ X1))) | (((in @ X2 @ X1)) != $true) | (((in @ X0 @ sK13)) = $true)) ) | (~spl14_11 | ~spl14_16 | ~spl14_18)),
% 0.46/0.39 inference(superposition,[],[f175,f95])).
% 0.46/0.39 thf(f188,plain,(
% 0.46/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((((^[Y0 : $i]: (~ (Y0 = X0))) @ X3)) = $true) | (((in @ X0 @ X1)) != $true) | ($true != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X0 @ sK13)) = $true) | (X0 != X2) | ($true != ((in @ X0 @ sK10))) | ($true != ((breln @ sK11 @ sK12 @ X1))) | (((in @ X3 @ X1)) != $true)) ) | (~spl14_11 | ~spl14_16 | ~spl14_18)),
% 0.46/0.39 inference(duplicate_literal_removal,[],[f187])).
% 0.46/0.39 thf(f189,plain,(
% 0.46/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ X1)) != $true) | ($true != ((in @ X0 @ sK10))) | (((in @ X0 @ X1)) != $true) | ($true != ((breln @ sK11 @ sK12 @ X1))) | (X0 != X2) | (((in @ X0 @ sK13)) = $true) | (((in @ X3 @ X1)) != $true) | ((((^[Y0 : $i]: (~ (Y0 = X0))) @ X3)) = $true)) ) | (~spl14_11 | ~spl14_16 | ~spl14_18)),
% 0.46/0.39 inference(trivial_inequality_removal,[],[f188])).
% 0.46/0.39 thf(f190,plain,(
% 0.46/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | ($true != ((breln @ sK11 @ sK12 @ X1))) | (((in @ X0 @ sK13)) = $true) | (X0 != X2) | (((in @ X3 @ X1)) != $true) | (((~ (X3 = X0))) = $true) | (((in @ X2 @ X1)) != $true) | ($true != ((in @ X0 @ sK10)))) ) | (~spl14_11 | ~spl14_16 | ~spl14_18)),
% 0.46/0.39 inference(beta-eta_normalization,[],[f189])).
% 0.46/0.39 thf(f191,plain,(
% 0.46/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X3 @ X1)) != $true) | (X0 != X2) | ($true != ((in @ X0 @ sK10))) | (((X3 = X0)) = $false) | (((in @ X2 @ X1)) != $true) | (((in @ X0 @ X1)) != $true) | ($true != ((breln @ sK11 @ sK12 @ X1))) | (((in @ X0 @ sK13)) = $true)) ) | (~spl14_11 | ~spl14_16 | ~spl14_18)),
% 0.46/0.39 inference(not_proxy_clausification,[],[f190])).
% 0.46/0.39 thf(f192,plain,(
% 0.46/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((breln @ sK11 @ sK12 @ X1))) | (((in @ X0 @ sK13)) = $true) | ($true != ((in @ X0 @ sK10))) | (((in @ X3 @ X1)) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X0 @ X1)) != $true) | (X0 != X2) | (X0 != X3)) ) | (~spl14_11 | ~spl14_16 | ~spl14_18)),
% 0.46/0.39 inference(equality_proxy_clausification,[],[f191])).
% 0.46/0.39 thf(f194,plain,(
% 0.46/0.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 != X2) | (((in @ X0 @ sK13)) = $true) | ($true != ((in @ X0 @ sK10))) | ($true != ((in @ X0 @ sK10))) | (((in @ X2 @ sK10)) != $true) | (X0 != X1) | ($true != ((in @ X1 @ sK10))) | ($true != $true)) ) | (~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
% 0.46/0.39 inference(superposition,[],[f192,f122])).
% 0.46/0.39 thf(f198,plain,(
% 0.46/0.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK10))) | (((in @ X2 @ sK10)) != $true) | (X0 != X2) | (X0 != X1) | ($true != $true) | (((in @ X0 @ sK13)) = $true) | ($true != ((in @ X0 @ sK10)))) ) | (~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
% 0.46/0.39 inference(duplicate_literal_removal,[],[f194])).
% 0.46/0.39 thf(f199,plain,(
% 0.46/0.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ sK13)) = $true) | (((in @ X2 @ sK10)) != $true) | ($true != ((in @ X1 @ sK10))) | ($true != ((in @ X0 @ sK10))) | (X0 != X2) | (X0 != X1)) ) | (~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
% 0.46/0.39 inference(trivial_inequality_removal,[],[f198])).
% 0.46/0.39 thf(f201,plain,(
% 0.46/0.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ sK10)) != $true) | (((in @ (sK9 @ X0 @ sK13) @ sK10)) != $true) | (((sK9 @ X0 @ sK13)) != X2) | ($true = ((subset @ X0 @ sK13))) | ($true != $true) | (((sK9 @ X0 @ sK13)) != X1) | ($true != ((in @ X1 @ sK10)))) ) | (~spl14_3 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
% 0.46/0.39 inference(superposition,[],[f56,f199])).
% 0.46/0.39 thf(f202,plain,(
% 0.46/0.39 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK9 @ X0 @ sK13) @ sK10)) != $true) | (((in @ X2 @ sK10)) != $true) | (((sK9 @ X0 @ sK13)) != X1) | (((sK9 @ X0 @ sK13)) != X2) | ($true != ((in @ X1 @ sK10))) | ($true = ((subset @ X0 @ sK13)))) ) | (~spl14_3 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
% 0.46/0.39 inference(trivial_inequality_removal,[],[f201])).
% 0.46/0.39 thf(f203,plain,(
% 0.46/0.39 ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ sK10))) | (((subset @ sK10 @ sK13)) = $true) | (((subset @ sK10 @ sK13)) = $true) | ($true != ((in @ X1 @ sK10))) | (((sK9 @ sK10 @ sK13)) != X1) | ($true != $true) | (((sK9 @ sK10 @ sK13)) != X0)) ) | (~spl14_1 | ~spl14_3 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
% 0.46/0.39 inference(superposition,[],[f202,f48])).
% 0.46/0.39 thf(f204,plain,(
% 0.46/0.39 ( ! [X0 : $i,X1 : $i] : ((((sK9 @ sK10 @ sK13)) != X0) | (((subset @ sK10 @ sK13)) = $true) | ($true != ((in @ X0 @ sK10))) | (((sK9 @ sK10 @ sK13)) != X1) | ($true != $true) | ($true != ((in @ X1 @ sK10)))) ) | (~spl14_1 | ~spl14_3 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
% 0.46/0.39 inference(duplicate_literal_removal,[],[f203])).
% 0.46/0.39 thf(f205,plain,(
% 0.46/0.39 ( ! [X0 : $i,X1 : $i] : ((((sK9 @ sK10 @ sK13)) != X1) | ($true != ((in @ X0 @ sK10))) | (((subset @ sK10 @ sK13)) = $true) | ($true != ((in @ X1 @ sK10))) | (((sK9 @ sK10 @ sK13)) != X0)) ) | (~spl14_1 | ~spl14_3 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
% 0.46/0.39 inference(trivial_inequality_removal,[],[f204])).
% 0.46/0.39 thf(f206,plain,(
% 0.46/0.39 ( ! [X0 : $i,X1 : $i] : ((((sK9 @ sK10 @ sK13)) != X0) | ($true != ((in @ X0 @ sK10))) | ($true != ((in @ X1 @ sK10))) | (((sK9 @ sK10 @ sK13)) != X1)) ) | (~spl14_1 | ~spl14_3 | spl14_9 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
% 0.46/0.39 inference(forward_subsumption_resolution,[],[f205,f86])).
% 0.46/0.39 thf(f208,definition,(
% 0.46/0.39 spl14_19 <=> ! [X1 : $i] : (($true != ((in @ X1 @ sK10))) | (((sK9 @ sK10 @ sK13)) != X1))),
% 0.46/0.39 introduced(definition,[new_symbols(definition,[spl14_19])],[avatar_definition])).
% 0.46/0.39 thf(f209,plain,(
% 0.46/0.39 ( ! [X1 : $i] : (($true != ((in @ X1 @ sK10))) | (((sK9 @ sK10 @ sK13)) != X1)) ) | ~spl14_19),
% 0.46/0.39 inference(avatar_component_clause,[],[f208])).
% 0.46/0.39 thf(f210,plain,(
% 0.46/0.39 spl14_19 | spl14_19 | ~spl14_1 | ~spl14_3 | spl14_9 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18),
% 0.46/0.39 inference(avatar_split_clause,[],[f206,f125,f120,f116,f94,f84,f55,f47,f208,f208])).
% 0.46/0.39 thf(f227,plain,(
% 0.46/0.39 ( ! [X0 : $i] : (($true = ((subset @ sK10 @ X0))) | (((sK9 @ sK10 @ sK13)) != ((sK9 @ sK10 @ X0))) | ($true != $true)) ) | (~spl14_1 | ~spl14_19)),
% 0.46/0.39 inference(superposition,[],[f209,f48])).
% 0.46/0.39 thf(f234,plain,(
% 0.46/0.39 ( ! [X0 : $i] : ((((sK9 @ sK10 @ sK13)) != ((sK9 @ sK10 @ X0))) | ($true = ((subset @ sK10 @ X0)))) ) | (~spl14_1 | ~spl14_19)),
% 0.46/0.39 inference(trivial_inequality_removal,[],[f227])).
% 0.46/0.39 thf(f235,plain,(
% 0.46/0.39 (((subset @ sK10 @ sK13)) = $true) | (~spl14_1 | ~spl14_19)),
% 0.46/0.39 inference(equality_resolution,[],[f234])).
% 0.46/0.39 thf(f236,plain,(
% 0.46/0.39 $false | (~spl14_1 | spl14_9 | ~spl14_19)),
% 0.46/0.39 inference(forward_subsumption_resolution,[],[f235,f86])).
% 0.46/0.39 thf(f237,plain,(
% 0.46/0.39 ~spl14_1 | spl14_9 | ~spl14_19),
% 0.46/0.39 inference(avatar_contradiction_clause,[],[f236])).
% 0.46/0.39 cnf(s1, plain, spl14_1 | ~spl14_2, inference(sat_conversion,[],[f53])).
% 0.46/0.39 cnf(s2, plain, ~spl14_2 | spl14_3, inference(sat_conversion,[],[f57])).
% 0.46/0.39 cnf(s6, plain, spl14_2, inference(sat_conversion,[],[f76])).
% 0.46/0.39 cnf(s8, plain, spl14_4, inference(sat_conversion,[],[f82])).
% 0.46/0.39 cnf(s9, plain, ~spl14_9, inference(sat_conversion,[],[f87])).
% 0.46/0.39 cnf(s11, plain, ~spl14_4 | spl14_11, inference(sat_conversion,[],[f96])).
% 0.46/0.39 cnf(s16, plain, ~spl14_4 | spl14_16, inference(sat_conversion,[],[f118])).
% 0.46/0.39 cnf(s17, plain, spl14_17, inference(sat_conversion,[],[f123])).
% 0.46/0.39 cnf(s18, plain, ~spl14_4 | spl14_18, inference(sat_conversion,[],[f127])).
% 0.46/0.39 cnf(s19, plain, spl14_19 | ~spl14_3 | spl14_9 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18 | ~spl14_1 | spl14_19, inference(sat_conversion,[],[f210])).
% 0.46/0.39 cnf(s20, plain, ~spl14_1 | ~spl14_3 | spl14_9 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18 | spl14_19, inference(rat,[],[s19])).
% 0.46/0.39 cnf(s21, plain, ~spl14_1 | spl14_9 | ~spl14_19, inference(sat_conversion,[],[f237])).
% 0.46/0.39 cnf(s22, plain, spl14_18, inference(rat,[],[s18,s8])).
% 0.46/0.39 cnf(s23, plain, spl14_16, inference(rat,[],[s16,s8])).
% 0.46/0.39 cnf(s25, plain, spl14_11, inference(rat,[],[s11,s8])).
% 0.46/0.39 cnf(s26, plain, spl14_3, inference(rat,[],[s2,s6])).
% 0.46/0.39 cnf(s27, plain, spl14_1, inference(rat,[],[s1,s6])).
% 0.46/0.39 cnf(s28, plain, ~spl14_19, inference(rat,[],[s21,s9,s27])).
% 0.46/0.39 cnf(s29, plain, $false, inference(rat,[],[s20,s26,s22,s17,s23,s25,s9,s28,s27])).
% 0.46/0.39 thf(f238,plain,(
% 0.46/0.39 $false),
% 0.46/0.39 inference(avatar_sat_refutation,[],[s29])).
% 0.46/0.39 % SZS output end Proof for theBenchmark
% 0.46/0.39 % (2563434)------------------------------
% 0.46/0.39 % (2563434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.46/0.39 % (2563434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.46/0.39 % (2563434)CaDiCaL version: 2.1.3
% 0.46/0.39 % (2563434)Termination reason: Refutation
% 0.46/0.39 % (2563434)Time elapsed: 0.030 s
% 0.46/0.39 % (2563434)Peak memory usage: 13 MB
% 0.46/0.39 % (2563434)Instructions burned: 31 (million)
% 0.46/0.39 % (2563426)Success in time 0.07 s
% 0.46/0.39 % Vampire exiting
%------------------------------------------------------------------------------