TSTP Solution File: SEU768^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU768^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:51:22 EDT 2024
% Result : Theorem 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU768^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.35 % Computer : n011.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sun May 19 18:06:08 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.37 % (20255)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.37 % (20256)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.37 % (20257)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.21/0.37 % (20258)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (20259)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (20260)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.21/0.37 % (20258)Instruction limit reached!
% 0.21/0.37 % (20258)------------------------------
% 0.21/0.37 % (20258)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (20258)Termination reason: Unknown
% 0.21/0.37 % (20258)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (20258)Memory used [KB]: 895
% 0.21/0.37 % (20258)Time elapsed: 0.003 s
% 0.21/0.37 % (20258)Instructions burned: 2 (million)
% 0.21/0.37 % (20258)------------------------------
% 0.21/0.37 % (20258)------------------------------
% 0.21/0.38 % (20259)Instruction limit reached!
% 0.21/0.38 % (20259)------------------------------
% 0.21/0.38 % (20259)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (20259)Termination reason: Unknown
% 0.21/0.38 % (20259)Termination phase: Function definition elimination
% 0.21/0.38
% 0.21/0.38 % (20259)Memory used [KB]: 895
% 0.21/0.38 % (20259)Time elapsed: 0.003 s
% 0.21/0.38 % (20259)Instructions burned: 3 (million)
% 0.21/0.38 % (20259)------------------------------
% 0.21/0.38 % (20259)------------------------------
% 0.21/0.38 % (20256)Instruction limit reached!
% 0.21/0.38 % (20256)------------------------------
% 0.21/0.38 % (20256)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (20256)Termination reason: Unknown
% 0.21/0.38 % (20256)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (20256)Memory used [KB]: 5500
% 0.21/0.38 % (20256)Time elapsed: 0.005 s
% 0.21/0.38 % (20256)Instructions burned: 4 (million)
% 0.21/0.38 % (20256)------------------------------
% 0.21/0.38 % (20256)------------------------------
% 0.21/0.38 % (20262)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.38 % (20262)Instruction limit reached!
% 0.21/0.38 % (20262)------------------------------
% 0.21/0.38 % (20262)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (20262)Termination reason: Unknown
% 0.21/0.38 % (20262)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (20262)Memory used [KB]: 5500
% 0.21/0.38 % (20262)Time elapsed: 0.004 s
% 0.21/0.38 % (20262)Instructions burned: 4 (million)
% 0.21/0.38 % (20262)------------------------------
% 0.21/0.38 % (20262)------------------------------
% 0.21/0.38 % (20261)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.39 % (20263)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.39 % (20257)First to succeed.
% 0.21/0.39 % (20264)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.39 % (20266)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.39 % (20268)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.39 % (20260)Also succeeded, but the first one will report.
% 0.21/0.40 % (20261)Instruction limit reached!
% 0.21/0.40 % (20261)------------------------------
% 0.21/0.40 % (20261)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (20261)Termination reason: Unknown
% 0.21/0.40 % (20261)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (20261)Memory used [KB]: 5628
% 0.21/0.40 % (20261)Time elapsed: 0.016 s
% 0.21/0.40 % (20261)Instructions burned: 18 (million)
% 0.21/0.40 % (20261)------------------------------
% 0.21/0.40 % (20261)------------------------------
% 0.21/0.40 % (20266)Instruction limit reached!
% 0.21/0.40 % (20266)------------------------------
% 0.21/0.40 % (20266)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (20266)Termination reason: Unknown
% 0.21/0.40 % (20266)Termination phase: Function definition elimination
% 0.21/0.40
% 0.21/0.40 % (20266)Memory used [KB]: 1023
% 0.21/0.40 % (20266)Time elapsed: 0.003 s
% 0.21/0.40 % (20266)Instructions burned: 3 (million)
% 0.21/0.40 % (20266)------------------------------
% 0.21/0.40 % (20266)------------------------------
% 0.21/0.40 % (20257)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Theorem for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% 0.21/0.40 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.40 thf(func_def_1, type, subset: $i > $i > $o).
% 0.21/0.40 thf(func_def_2, type, kpair: $i > $i > $i).
% 0.21/0.40 thf(func_def_3, type, cartprod: $i > $i > $i).
% 0.21/0.40 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 0.21/0.40 thf(func_def_7, type, breln1: $i > $i > $o).
% 0.21/0.40 thf(func_def_8, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.21/0.40 thf(func_def_21, type, sK2: $i > $o).
% 0.21/0.40 thf(func_def_24, type, sK5: $i > $i > ($i > $o) > $i > $i).
% 0.21/0.40 thf(func_def_25, type, sK6: $i > $i > $i > ($i > $o) > $i).
% 0.21/0.40 thf(func_def_26, type, ph7: !>[X0: $tType]:(X0)).
% 0.21/0.40 thf(f124,plain,(
% 0.21/0.40 $false),
% 0.21/0.40 inference(avatar_sat_refutation,[],[f98,f120,f123])).
% 0.21/0.40 thf(f123,plain,(
% 0.21/0.40 ~spl4_4),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f122])).
% 0.21/0.40 thf(f122,plain,(
% 0.21/0.40 $false | ~spl4_4),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f121])).
% 0.21/0.40 thf(f121,plain,(
% 0.21/0.40 ($false = $true) | ~spl4_4),
% 0.21/0.40 inference(backward_demodulation,[],[f55,f96])).
% 0.21/0.40 thf(f96,plain,(
% 0.21/0.40 ($false = (subset @ sK1 @ (cartprod @ sK0 @ sK0))) | ~spl4_4),
% 0.21/0.40 inference(avatar_component_clause,[],[f94])).
% 0.21/0.40 thf(f94,plain,(
% 0.21/0.40 spl4_4 <=> ($false = (subset @ sK1 @ (cartprod @ sK0 @ sK0)))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl4_4])])).
% 0.21/0.40 thf(f55,plain,(
% 0.21/0.40 ($true = (subset @ sK1 @ (cartprod @ sK0 @ sK0)))),
% 0.21/0.40 inference(beta_eta_normalization,[],[f29])).
% 0.21/0.40 thf(f29,plain,(
% 0.21/0.40 (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))) @ sK0 @ sK1) = $true)),
% 0.21/0.40 inference(definition_unfolding,[],[f24,f28])).
% 0.21/0.40 thf(f28,plain,(
% 0.21/0.40 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: (subset @ Y4 @ (cartprod @ Y2 @ Y3))))))) @ Y0 @ Y0 @ Y1)))))),
% 0.21/0.40 inference(definition_unfolding,[],[f25,f27])).
% 0.21/0.40 thf(f27,plain,(
% 0.21/0.40 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f7])).
% 0.21/0.40 thf(f7,plain,(
% 0.21/0.40 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f1])).
% 0.21/0.40 thf(f1,axiom,(
% 0.21/0.40 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 0.21/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln)).
% 0.21/0.40 thf(f25,plain,(
% 0.21/0.40 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 0.21/0.40 inference(cnf_transformation,[],[f13])).
% 0.21/0.40 thf(f13,plain,(
% 0.21/0.40 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))),
% 0.21/0.40 inference(fool_elimination,[],[f12])).
% 0.21/0.40 thf(f12,plain,(
% 0.21/0.40 (breln1 = (^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)))),
% 0.21/0.40 inference(rectify,[],[f3])).
% 0.21/0.40 thf(f3,axiom,(
% 0.21/0.40 (breln1 = (^[X0 : $i, X3 : $i] : (breln @ X0 @ X0 @ X3)))),
% 0.21/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1)).
% 0.21/0.40 thf(f24,plain,(
% 0.21/0.40 ((breln1 @ sK0 @ sK1) = $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f19])).
% 0.21/0.40 thf(f19,plain,(
% 0.21/0.40 (((breln1 @ sK0 @ sK1) = $true) & (! [X3] : (((in @ X3 @ sK0) != $true) | ! [X4] : (((sK2 @ (kpair @ X3 @ X4)) = $true) | ($true != (in @ (kpair @ X3 @ X4) @ sK1)) | ((in @ X4 @ sK0) != $true))) & (((in @ sK3 @ sK1) = $true) & ((sK2 @ sK3) != $true)))) & (brelnall2 = $true)),
% 0.21/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f15,f18,f17,f16])).
% 0.21/0.40 thf(f16,plain,(
% 0.21/0.40 ? [X0,X1] : (((breln1 @ X0 @ X1) = $true) & ? [X2 : $i > $o] : (! [X3] : (((in @ X3 @ X0) != $true) | ! [X4] : (((X2 @ (kpair @ X3 @ X4)) = $true) | ($true != (in @ (kpair @ X3 @ X4) @ X1)) | ($true != (in @ X4 @ X0)))) & ? [X5] : (((in @ X5 @ X1) = $true) & ((X2 @ X5) != $true)))) => (((breln1 @ sK0 @ sK1) = $true) & ? [X2 : $i > $o] : (! [X3] : (((in @ X3 @ sK0) != $true) | ! [X4] : (((X2 @ (kpair @ X3 @ X4)) = $true) | ($true != (in @ (kpair @ X3 @ X4) @ sK1)) | ((in @ X4 @ sK0) != $true))) & ? [X5] : (((in @ X5 @ sK1) = $true) & ((X2 @ X5) != $true))))),
% 0.21/0.40 introduced(choice_axiom,[])).
% 0.21/0.40 thf(f17,plain,(
% 0.21/0.40 ? [X2 : $i > $o] : (! [X3] : (((in @ X3 @ sK0) != $true) | ! [X4] : (((X2 @ (kpair @ X3 @ X4)) = $true) | ($true != (in @ (kpair @ X3 @ X4) @ sK1)) | ((in @ X4 @ sK0) != $true))) & ? [X5] : (((in @ X5 @ sK1) = $true) & ((X2 @ X5) != $true))) => (! [X3] : (((in @ X3 @ sK0) != $true) | ! [X4] : (((sK2 @ (kpair @ X3 @ X4)) = $true) | ($true != (in @ (kpair @ X3 @ X4) @ sK1)) | ((in @ X4 @ sK0) != $true))) & ? [X5] : (((in @ X5 @ sK1) = $true) & ((sK2 @ X5) != $true)))),
% 0.21/0.40 introduced(choice_axiom,[])).
% 0.21/0.40 thf(f18,plain,(
% 0.21/0.40 ? [X5] : (((in @ X5 @ sK1) = $true) & ((sK2 @ X5) != $true)) => (((in @ sK3 @ sK1) = $true) & ((sK2 @ sK3) != $true))),
% 0.21/0.40 introduced(choice_axiom,[])).
% 0.21/0.40 thf(f15,plain,(
% 0.21/0.40 ? [X0,X1] : (((breln1 @ X0 @ X1) = $true) & ? [X2 : $i > $o] : (! [X3] : (((in @ X3 @ X0) != $true) | ! [X4] : (((X2 @ (kpair @ X3 @ X4)) = $true) | ($true != (in @ (kpair @ X3 @ X4) @ X1)) | ($true != (in @ X4 @ X0)))) & ? [X5] : (((in @ X5 @ X1) = $true) & ((X2 @ X5) != $true)))) & (brelnall2 = $true)),
% 0.21/0.40 inference(flattening,[],[f14])).
% 0.21/0.40 thf(f14,plain,(
% 0.21/0.40 ? [X0,X1] : (? [X2 : $i > $o] : (? [X5] : (((in @ X5 @ X1) = $true) & ((X2 @ X5) != $true)) & ! [X3] : (! [X4] : ((((X2 @ (kpair @ X3 @ X4)) = $true) | ($true != (in @ (kpair @ X3 @ X4) @ X1))) | ($true != (in @ X4 @ X0))) | ((in @ X3 @ X0) != $true))) & ((breln1 @ X0 @ X1) = $true)) & (brelnall2 = $true)),
% 0.21/0.40 inference(ennf_transformation,[],[f11])).
% 0.21/0.40 thf(f11,plain,(
% 0.21/0.40 ~((brelnall2 = $true) => ! [X0,X1] : (((breln1 @ X0 @ X1) = $true) => ! [X2 : $i > $o] : (! [X3] : (((in @ X3 @ X0) = $true) => ! [X4] : (($true = (in @ X4 @ X0)) => (($true = (in @ (kpair @ X3 @ X4) @ X1)) => ((X2 @ (kpair @ X3 @ X4)) = $true)))) => ! [X5] : (((in @ X5 @ X1) = $true) => ((X2 @ X5) = $true)))))),
% 0.21/0.40 inference(fool_elimination,[],[f10])).
% 0.21/0.40 thf(f10,plain,(
% 0.21/0.40 ~(brelnall2 => ! [X0,X1] : ((breln1 @ X0 @ X1) => ! [X2 : $i > $o] : (! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (X2 @ (kpair @ X3 @ X4))))) => ! [X5] : ((in @ X5 @ X1) => (X2 @ X5)))))),
% 0.21/0.40 inference(rectify,[],[f5])).
% 0.21/0.40 thf(f5,negated_conjecture,(
% 0.21/0.40 ~(brelnall2 => ! [X0,X3] : ((breln1 @ X0 @ X3) => ! [X4 : $i > $o] : (! [X5] : ((in @ X5 @ X0) => ! [X6] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ X3) => (X4 @ (kpair @ X5 @ X6))))) => ! [X5] : ((in @ X5 @ X3) => (X4 @ X5)))))),
% 0.21/0.40 inference(negated_conjecture,[],[f4])).
% 0.21/0.40 thf(f4,conjecture,(
% 0.21/0.40 brelnall2 => ! [X0,X3] : ((breln1 @ X0 @ X3) => ! [X4 : $i > $o] : (! [X5] : ((in @ X5 @ X0) => ! [X6] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ X3) => (X4 @ (kpair @ X5 @ X6))))) => ! [X5] : ((in @ X5 @ X3) => (X4 @ X5))))),
% 0.21/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1all2)).
% 0.21/0.40 thf(f120,plain,(
% 0.21/0.40 ~spl4_2),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f119])).
% 0.21/0.40 thf(f119,plain,(
% 0.21/0.40 $false | ~spl4_2),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f118])).
% 0.21/0.40 thf(f118,plain,(
% 0.21/0.40 ($true != $true) | ~spl4_2),
% 0.21/0.40 inference(superposition,[],[f21,f114])).
% 0.21/0.40 thf(f114,plain,(
% 0.21/0.40 ((sK2 @ sK3) = $true) | ~spl4_2),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f104])).
% 0.21/0.40 thf(f104,plain,(
% 0.21/0.40 ((sK2 @ sK3) = $true) | ($false = $true) | ~spl4_2),
% 0.21/0.40 inference(superposition,[],[f22,f86])).
% 0.21/0.40 thf(f86,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (($false = (in @ X1 @ sK1)) | ((sK2 @ X1) = $true)) ) | ~spl4_2),
% 0.21/0.40 inference(avatar_component_clause,[],[f85])).
% 0.21/0.40 thf(f85,plain,(
% 0.21/0.40 spl4_2 <=> ! [X1] : (($false = (in @ X1 @ sK1)) | ((sK2 @ X1) = $true))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl4_2])])).
% 0.21/0.40 thf(f22,plain,(
% 0.21/0.40 ((in @ sK3 @ sK1) = $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f19])).
% 0.21/0.40 thf(f21,plain,(
% 0.21/0.40 ((sK2 @ sK3) != $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f19])).
% 0.21/0.40 thf(f98,plain,(
% 0.21/0.40 spl4_2 | spl4_4 | spl4_2 | spl4_2 | spl4_2),
% 0.21/0.40 inference(avatar_split_clause,[],[f76,f85,f85,f85,f94,f85])).
% 0.21/0.40 thf(f76,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = (in @ X2 @ sK1)) | ((sK2 @ X2) = $true) | ($false = (subset @ sK1 @ (cartprod @ sK0 @ sK0))) | ((sK2 @ X1) = $true) | ((sK2 @ X0) = $true) | ($false = (in @ X1 @ sK1)) | ($false = (in @ X3 @ sK1)) | ((sK2 @ X3) = $true) | ($false = (in @ X0 @ sK1))) )),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f71])).
% 0.21/0.40 thf(f71,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((sK2 @ X3) = $true) | ((sK2 @ X0) = $true) | ((sK2 @ X1) = $true) | ($false = (in @ X0 @ sK1)) | ($false = (subset @ sK1 @ (cartprod @ sK0 @ sK0))) | ($false = $true) | ($false = (in @ X2 @ sK1)) | ($false = (in @ X1 @ sK1)) | ((sK2 @ X2) = $true) | ($false = (in @ X3 @ sK1))) )),
% 0.21/0.40 inference(superposition,[],[f53,f69])).
% 0.21/0.40 thf(f69,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((sK2 @ (kpair @ (sK5 @ sK1 @ sK0 @ X0 @ sK0) @ (sK6 @ sK0 @ sK0 @ sK1 @ X0))) = $true) | ((X0 @ X1) = $true) | ($false = (in @ X2 @ sK1)) | ($false = (in @ X1 @ sK1)) | ((X0 @ X3) = $true) | ($false = (in @ X3 @ sK1)) | ((X0 @ X2) = $true)) )),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f68])).
% 0.21/0.40 thf(f68,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X2) = $true) | ($false = $true) | ((X0 @ X3) = $true) | ((sK2 @ (kpair @ (sK5 @ sK1 @ sK0 @ X0 @ sK0) @ (sK6 @ sK0 @ sK0 @ sK1 @ X0))) = $true) | ((X0 @ X1) = $true) | ($false = (in @ X2 @ sK1)) | ($false = (in @ X1 @ sK1)) | ($false = (in @ X3 @ sK1))) )),
% 0.21/0.40 inference(forward_demodulation,[],[f67,f55])).
% 0.21/0.40 thf(f67,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($false = (in @ X1 @ sK1)) | ((X0 @ X3) = $true) | ((sK2 @ (kpair @ (sK5 @ sK1 @ sK0 @ X0 @ sK0) @ (sK6 @ sK0 @ sK0 @ sK1 @ X0))) = $true) | ((X0 @ X1) = $true) | ($false = (in @ X3 @ sK1)) | ($false = (subset @ sK1 @ (cartprod @ sK0 @ sK0))) | ($false = (in @ X2 @ sK1)) | ((X0 @ X2) = $true)) )),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f66])).
% 0.21/0.40 thf(f66,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((X0 @ X1) = $true) | ((sK2 @ (kpair @ (sK5 @ sK1 @ sK0 @ X0 @ sK0) @ (sK6 @ sK0 @ sK0 @ sK1 @ X0))) = $true) | ((X0 @ X3) = $true) | ($false = (subset @ sK1 @ (cartprod @ sK0 @ sK0))) | ((X0 @ X2) = $true) | ($false = (in @ X1 @ sK1)) | ($true != $true) | ($false = (in @ X2 @ sK1)) | ($false = (in @ X3 @ sK1))) )),
% 0.21/0.40 inference(duplicate_literal_removal,[],[f65])).
% 0.21/0.40 thf(f65,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($false = (in @ X3 @ sK1)) | ((X0 @ X1) = $true) | ((X0 @ X3) = $true) | ($false = (in @ X2 @ sK1)) | ($false = (in @ X1 @ sK1)) | ((sK2 @ (kpair @ (sK5 @ sK1 @ sK0 @ X0 @ sK0) @ (sK6 @ sK0 @ sK0 @ sK1 @ X0))) = $true) | ($false = (subset @ sK1 @ (cartprod @ sK0 @ sK0))) | ($false = (subset @ sK1 @ (cartprod @ sK0 @ sK0))) | ($true != $true) | ((X0 @ X2) = $true)) )),
% 0.21/0.40 inference(superposition,[],[f64,f48])).
% 0.21/0.40 thf(f48,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X1) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((X4 @ X5) = $true) | ((in @ X5 @ X3) = $false)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f46])).
% 0.21/0.40 thf(f46,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((in @ X5 @ X3) = $false) | ((X4 @ X5) = $true) | ($false = ((in @ (sK5 @ X3 @ X1 @ X4 @ X2) @ X1) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0))))))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f45])).
% 0.21/0.40 thf(f45,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((X4 @ X5) = $true) | ((in @ X5 @ X3) = $false) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1)))))))) @ (sK5 @ X3 @ X1 @ X4 @ X2)))) )),
% 0.21/0.40 inference(sigma_clausification,[],[f44])).
% 0.21/0.40 thf(f44,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ X3) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1)))))))))) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((X4 @ X5) = $true)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f43])).
% 0.21/0.40 thf(f43,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = ((in @ X5 @ X3) => (X4 @ X5))) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1))))))))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f42])).
% 0.21/0.40 thf(f42,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1)))))))))) | (((^[Y0 : $i]: ((in @ Y0 @ X3) => (X4 @ Y0))) @ X5) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f41])).
% 0.21/0.40 thf(f41,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (X4 @ Y0))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1)))))))))) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f40])).
% 0.21/0.40 thf(f40,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X3) => (X4 @ (kpair @ Y0 @ Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (X4 @ Y0)))))) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f39])).
% 0.21/0.40 thf(f39,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | (((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (Y0 @ Y1)))))) @ X4) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f38])).
% 0.21/0.40 thf(f38,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (Y0 @ Y1))))))) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f37])).
% 0.21/0.40 thf(f37,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((subset @ X3 @ (cartprod @ X1 @ X2)) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X3) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (Y0 @ Y1)))))))) = $true)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f36])).
% 0.21/0.40 thf(f36,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X1 @ X2)) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (Y1 @ (kpair @ Y2 @ Y3))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2))))))))) @ X3))) )),
% 0.21/0.40 inference(pi_clausification,[],[f35])).
% 0.21/0.40 thf(f35,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((subset @ Y0 @ (cartprod @ X1 @ X2)) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ Y0) => (Y1 @ (kpair @ Y2 @ Y3))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (Y1 @ Y2)))))))))) = $true)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f34])).
% 0.21/0.40 thf(f34,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X1 @ Y0)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3))))))))))) @ X2) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f33])).
% 0.21/0.40 thf(f33,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y1 @ (cartprod @ X1 @ Y0)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ Y1) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (Y2 @ Y3)))))))))))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f32])).
% 0.21/0.40 thf(f32,plain,(
% 0.21/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4))))))))))))) @ X1) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f31])).
% 0.21/0.40 thf(f31,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y2 @ (cartprod @ Y0 @ Y1)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))) = $true)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f30])).
% 0.21/0.40 thf(f30,plain,(
% 0.21/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y0 @ Y1 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f26,f20,f27])).
% 0.21/0.40 thf(f20,plain,(
% 0.21/0.40 (brelnall2 = $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f19])).
% 0.21/0.40 thf(f26,plain,(
% 0.21/0.40 (brelnall2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f9])).
% 0.21/0.40 thf(f9,plain,(
% 0.21/0.40 (brelnall2 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y2) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (Y3 @ Y4)))))))))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f8])).
% 0.21/0.40 thf(f8,plain,(
% 0.21/0.40 (brelnall2 = ! [X0,X1,X2] : ((breln @ X2 @ X1 @ X0) => ! [X3 : $i > $o] : (! [X4] : ((in @ X4 @ X2) => ! [X5] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X0) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6] : ((in @ X6 @ X0) => (X3 @ X6)))))),
% 0.21/0.40 inference(rectify,[],[f2])).
% 0.21/0.40 thf(f2,axiom,(
% 0.21/0.40 (brelnall2 = ! [X3,X1,X0] : ((breln @ X0 @ X1 @ X3) => ! [X4 : $i > $o] : (! [X5] : ((in @ X5 @ X0) => ! [X6] : ((in @ X6 @ X1) => ((in @ (kpair @ X5 @ X6) @ X3) => (X4 @ (kpair @ X5 @ X6))))) => ! [X5] : ((in @ X5 @ X3) => (X4 @ X5)))))),
% 0.21/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall2)).
% 0.21/0.40 thf(f64,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ sK0)) | ($false = (in @ X3 @ sK1)) | ((X1 @ X3) = $true) | ((sK2 @ (kpair @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ (sK6 @ X0 @ sK0 @ sK1 @ X1))) = $true) | ($false = (in @ X2 @ sK1)) | ($false = (subset @ sK1 @ (cartprod @ X0 @ sK0))) | ((X1 @ X2) = $true)) )),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f63])).
% 0.21/0.40 thf(f63,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($false = (subset @ sK1 @ (cartprod @ X0 @ sK0))) | ((sK2 @ (kpair @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ (sK6 @ X0 @ sK0 @ sK1 @ X1))) = $true) | ((X1 @ X2) = $true) | ($false = (in @ X3 @ sK1)) | ((X1 @ X3) = $true) | ($true != $true) | ($false = (in @ X2 @ sK1)) | ($true != (in @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ sK0))) )),
% 0.21/0.40 inference(duplicate_literal_removal,[],[f62])).
% 0.21/0.40 thf(f62,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (((sK2 @ (kpair @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ (sK6 @ X0 @ sK0 @ sK1 @ X1))) = $true) | ((X1 @ X3) = $true) | ($false = (in @ X2 @ sK1)) | ($false = (subset @ sK1 @ (cartprod @ X0 @ sK0))) | ($true != (in @ (sK5 @ sK1 @ X0 @ X1 @ sK0) @ sK0)) | ((X1 @ X2) = $true) | ($false = (subset @ sK1 @ (cartprod @ X0 @ sK0))) | ($false = (in @ X3 @ sK1)) | ($true != $true)) )),
% 0.21/0.40 inference(superposition,[],[f61,f52])).
% 0.21/0.40 thf(f52,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = (in @ (sK6 @ X1 @ X2 @ X3 @ X4) @ X2)) | ((in @ X5 @ X3) = $false) | ((X4 @ X5) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2)))) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f50])).
% 0.21/0.40 thf(f50,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ X3) = $false) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((X4 @ X5) = $true) | ($false = ((in @ (sK6 @ X1 @ X2 @ X3 @ X4) @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4))))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f49])).
% 0.21/0.40 thf(f49,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0))))) @ (sK6 @ X1 @ X2 @ X3 @ X4))) | ((in @ X5 @ X3) = $false) | ((X4 @ X5) = $true)) )),
% 0.21/0.40 inference(sigma_clausification,[],[f47])).
% 0.21/0.40 thf(f47,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((X4 @ X5) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((in @ X5 @ X3) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ Y0)))))))) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f46])).
% 0.21/0.40 thf(f61,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (((in @ (sK6 @ X0 @ X2 @ sK1 @ X1) @ sK0) != $true) | ($false = (subset @ sK1 @ (cartprod @ X0 @ X2))) | ($false = (in @ X3 @ sK1)) | ((X1 @ X3) = $true) | ((in @ (sK5 @ sK1 @ X0 @ X1 @ X2) @ sK0) != $true) | ($true = (sK2 @ (kpair @ (sK5 @ sK1 @ X0 @ X1 @ X2) @ (sK6 @ X0 @ X2 @ sK1 @ X1))))) )),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f59])).
% 0.21/0.40 thf(f59,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (((in @ (sK6 @ X0 @ X2 @ sK1 @ X1) @ sK0) != $true) | ($false = (in @ X3 @ sK1)) | ($true != $true) | ((in @ (sK5 @ sK1 @ X0 @ X1 @ X2) @ sK0) != $true) | ($true = (sK2 @ (kpair @ (sK5 @ sK1 @ X0 @ X1 @ X2) @ (sK6 @ X0 @ X2 @ sK1 @ X1)))) | ((X1 @ X3) = $true) | ($false = (subset @ sK1 @ (cartprod @ X0 @ X2)))) )),
% 0.21/0.40 inference(superposition,[],[f23,f54])).
% 0.21/0.40 thf(f54,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = (in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X3)) | ((X4 @ X5) = $true) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((in @ X5 @ X3) = $false)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f51])).
% 0.21/0.40 thf(f51,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((in @ X5 @ X3) = $false) | ($false = ((in @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)) @ X3) => (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4))))) | ((X4 @ X5) = $true)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f50])).
% 0.21/0.40 thf(f23,plain,(
% 0.21/0.40 ( ! [X3 : $i,X4 : $i] : (($true != (in @ (kpair @ X3 @ X4) @ sK1)) | ((sK2 @ (kpair @ X3 @ X4)) = $true) | ((in @ X4 @ sK0) != $true) | ((in @ X3 @ sK0) != $true)) )),
% 0.21/0.40 inference(cnf_transformation,[],[f19])).
% 0.21/0.40 thf(f53,plain,(
% 0.21/0.40 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($false = (X4 @ (kpair @ (sK5 @ X3 @ X1 @ X4 @ X2) @ (sK6 @ X1 @ X2 @ X3 @ X4)))) | ((in @ X5 @ X3) = $false) | ($false = (subset @ X3 @ (cartprod @ X1 @ X2))) | ((X4 @ X5) = $true)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f51])).
% 0.21/0.40 % SZS output end Proof for theBenchmark
% 0.21/0.40 % (20257)------------------------------
% 0.21/0.40 % (20257)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (20257)Termination reason: Refutation
% 0.21/0.40
% 0.21/0.40 % (20257)Memory used [KB]: 5756
% 0.21/0.40 % (20257)Time elapsed: 0.023 s
% 0.21/0.40 % (20257)Instructions burned: 24 (million)
% 0.21/0.40 % (20257)------------------------------
% 0.21/0.40 % (20257)------------------------------
% 0.21/0.40 % (20250)Success in time 0.03 s
% 0.21/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------