TSTP Solution File: SEU682^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU682^2 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n032.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 03:50:42 EDT 2024
% Result : Theorem 0.15s 0.32s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.09 % Problem : SEU682^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.10 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Sun May 19 16:02:22 EDT 2024
% 0.11/0.30 % CPUTime :
% 0.11/0.30 This is a TH0_THM_EQU_NAR problem
% 0.11/0.30 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/sandbox/benchmark/theBenchmark.p
% 0.11/0.31 % (4772)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.11/0.31 % (4769)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.11/0.31 % (4770)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 (3000ds/4Mi)
% 0.11/0.31 % (4771)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 (3000ds/27Mi)
% 0.11/0.31 % (4773)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 (3000ds/2Mi)
% 0.11/0.31 % (4774)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 (3000ds/275Mi)
% 0.11/0.31 % (4775)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.11/0.31 % (4772)Instruction limit reached!
% 0.11/0.31 % (4772)------------------------------
% 0.11/0.31 % (4772)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.31 % (4773)Instruction limit reached!
% 0.11/0.31 % (4773)------------------------------
% 0.11/0.31 % (4773)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.31 % (4773)Termination reason: Unknown
% 0.11/0.31 % (4773)Termination phase: Saturation
% 0.11/0.31
% 0.11/0.31 % (4773)Memory used [KB]: 1023
% 0.11/0.31 % (4773)Time elapsed: 0.002 s
% 0.11/0.31 % (4773)Instructions burned: 4 (million)
% 0.11/0.31 % (4773)------------------------------
% 0.11/0.31 % (4773)------------------------------
% 0.11/0.31 % (4772)Termination reason: Unknown
% 0.11/0.31 % (4772)Termination phase: Saturation
% 0.11/0.31
% 0.11/0.31 % (4772)Memory used [KB]: 5500
% 0.11/0.31 % (4772)Time elapsed: 0.003 s
% 0.11/0.31 % (4772)Instructions burned: 3 (million)
% 0.11/0.31 % (4772)------------------------------
% 0.11/0.31 % (4772)------------------------------
% 0.11/0.31 % (4770)Instruction limit reached!
% 0.11/0.31 % (4770)------------------------------
% 0.11/0.31 % (4770)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.31 % (4770)Termination reason: Unknown
% 0.11/0.31 % (4770)Termination phase: Saturation
% 0.11/0.31
% 0.11/0.31 % (4770)Memory used [KB]: 5500
% 0.11/0.31 % (4770)Time elapsed: 0.003 s
% 0.11/0.31 % (4770)Instructions burned: 5 (million)
% 0.11/0.31 % (4770)------------------------------
% 0.11/0.31 % (4770)------------------------------
% 0.15/0.32 % (4775)Instruction limit reached!
% 0.15/0.32 % (4775)------------------------------
% 0.15/0.32 % (4775)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (4775)Termination reason: Unknown
% 0.15/0.32 % (4775)Termination phase: Saturation
% 0.15/0.32
% 0.15/0.32 % (4775)Memory used [KB]: 5628
% 0.15/0.32 % (4775)Time elapsed: 0.008 s
% 0.15/0.32 % (4775)Instructions burned: 20 (million)
% 0.15/0.32 % (4775)------------------------------
% 0.15/0.32 % (4775)------------------------------
% 0.15/0.32 % (4771)First to succeed.
% 0.15/0.32 % (4776)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.15/0.32 % (4777)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)
% 0.15/0.32 % (4776)Instruction limit reached!
% 0.15/0.32 % (4776)------------------------------
% 0.15/0.32 % (4776)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (4776)Termination reason: Unknown
% 0.15/0.32 % (4776)Termination phase: Saturation
% 0.15/0.32
% 0.15/0.32 % (4776)Memory used [KB]: 5500
% 0.15/0.32 % (4776)Time elapsed: 0.003 s
% 0.15/0.32 % (4776)Instructions burned: 5 (million)
% 0.15/0.32 % (4776)------------------------------
% 0.15/0.32 % (4776)------------------------------
% 0.15/0.32 % (4779)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)
% 0.15/0.32 % (4779)Instruction limit reached!
% 0.15/0.32 % (4779)------------------------------
% 0.15/0.32 % (4779)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (4779)Termination reason: Unknown
% 0.15/0.32 % (4779)Termination phase: Property scanning
% 0.15/0.32
% 0.15/0.32 % (4779)Memory used [KB]: 1023
% 0.15/0.32 % (4779)Time elapsed: 0.002 s
% 0.15/0.32 % (4779)Instructions burned: 3 (million)
% 0.15/0.32 % (4779)------------------------------
% 0.15/0.32 % (4779)------------------------------
% 0.15/0.32 % (4771)Refutation found. Thanks to Tanya!
% 0.15/0.32 % SZS status Theorem for theBenchmark
% 0.15/0.32 % SZS output start Proof for theBenchmark
% 0.15/0.32 thf(func_def_0, type, in: $i > $i > $o).
% 0.15/0.32 thf(func_def_1, type, subset: $i > $i > $o).
% 0.15/0.32 thf(func_def_2, type, kpair: $i > $i > $i).
% 0.15/0.32 thf(func_def_3, type, cartprod: $i > $i > $i).
% 0.15/0.32 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 0.15/0.32 thf(func_def_7, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.15/0.32 thf(func_def_22, type, sK3: $i > $o).
% 0.15/0.32 thf(func_def_25, type, sK6: $i > $i > ($i > $o) > $i > $i).
% 0.15/0.32 thf(func_def_26, type, sK7: $i > $i > $i > ($i > $o) > $i).
% 0.15/0.32 thf(func_def_27, type, ph8: !>[X0: $tType]:(X0)).
% 0.15/0.32 thf(f121,plain,(
% 0.15/0.32 $false),
% 0.15/0.32 inference(avatar_sat_refutation,[],[f96,f99,f120])).
% 0.15/0.32 thf(f120,plain,(
% 0.15/0.32 ~spl5_1),
% 0.15/0.32 inference(avatar_contradiction_clause,[],[f119])).
% 0.15/0.32 thf(f119,plain,(
% 0.15/0.32 $false | ~spl5_1),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f118])).
% 0.15/0.32 thf(f118,plain,(
% 0.15/0.32 ($true != $true) | ~spl5_1),
% 0.15/0.32 inference(superposition,[],[f22,f111])).
% 0.15/0.32 thf(f111,plain,(
% 0.15/0.32 ($true = (sK3 @ sK4)) | ~spl5_1),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f100])).
% 0.15/0.32 thf(f100,plain,(
% 0.15/0.32 ($true = (sK3 @ sK4)) | ($true = $false) | ~spl5_1),
% 0.15/0.32 inference(superposition,[],[f79,f21])).
% 0.15/0.32 thf(f21,plain,(
% 0.15/0.32 ((in @ sK4 @ sK2) = $true)),
% 0.15/0.32 inference(cnf_transformation,[],[f17])).
% 0.15/0.32 thf(f17,plain,(
% 0.15/0.32 (brelnall1 = $true) & (($true = (breln @ sK1 @ sK0 @ sK2)) & ((($true != (sK3 @ sK4)) & ((in @ sK4 @ sK2) = $true)) & ! [X5] : (! [X6] : (($true = (sK3 @ (kpair @ X5 @ X6))) | ($true != (in @ (kpair @ X5 @ X6) @ sK2)) | ((in @ X6 @ sK0) != $true)) | ($true != (in @ X5 @ sK1)))))),
% 0.15/0.32 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f13,f16,f15,f14])).
% 0.15/0.32 thf(f14,plain,(
% 0.15/0.32 ? [X0,X1,X2] : (($true = (breln @ X1 @ X0 @ X2)) & ? [X3 : $i > $o] : (? [X4] : (($true != (X3 @ X4)) & ($true = (in @ X4 @ X2))) & ! [X5] : (! [X6] : (($true = (X3 @ (kpair @ X5 @ X6))) | ($true != (in @ (kpair @ X5 @ X6) @ X2)) | ($true != (in @ X6 @ X0))) | ($true != (in @ X5 @ X1))))) => (($true = (breln @ sK1 @ sK0 @ sK2)) & ? [X3 : $i > $o] : (? [X4] : (($true != (X3 @ X4)) & ((in @ X4 @ sK2) = $true)) & ! [X5] : (! [X6] : (($true = (X3 @ (kpair @ X5 @ X6))) | ($true != (in @ (kpair @ X5 @ X6) @ sK2)) | ((in @ X6 @ sK0) != $true)) | ($true != (in @ X5 @ sK1)))))),
% 0.15/0.32 introduced(choice_axiom,[])).
% 0.15/0.32 thf(f15,plain,(
% 0.15/0.32 ? [X3 : $i > $o] : (? [X4] : (($true != (X3 @ X4)) & ((in @ X4 @ sK2) = $true)) & ! [X5] : (! [X6] : (($true = (X3 @ (kpair @ X5 @ X6))) | ($true != (in @ (kpair @ X5 @ X6) @ sK2)) | ((in @ X6 @ sK0) != $true)) | ($true != (in @ X5 @ sK1)))) => (? [X4] : (($true != (sK3 @ X4)) & ((in @ X4 @ sK2) = $true)) & ! [X5] : (! [X6] : (($true = (sK3 @ (kpair @ X5 @ X6))) | ($true != (in @ (kpair @ X5 @ X6) @ sK2)) | ((in @ X6 @ sK0) != $true)) | ($true != (in @ X5 @ sK1))))),
% 0.15/0.32 introduced(choice_axiom,[])).
% 0.15/0.32 thf(f16,plain,(
% 0.15/0.32 ? [X4] : (($true != (sK3 @ X4)) & ((in @ X4 @ sK2) = $true)) => (($true != (sK3 @ sK4)) & ((in @ sK4 @ sK2) = $true))),
% 0.15/0.32 introduced(choice_axiom,[])).
% 0.15/0.32 thf(f13,plain,(
% 0.15/0.32 (brelnall1 = $true) & ? [X0,X1,X2] : (($true = (breln @ X1 @ X0 @ X2)) & ? [X3 : $i > $o] : (? [X4] : (($true != (X3 @ X4)) & ($true = (in @ X4 @ X2))) & ! [X5] : (! [X6] : (($true = (X3 @ (kpair @ X5 @ X6))) | ($true != (in @ (kpair @ X5 @ X6) @ X2)) | ($true != (in @ X6 @ X0))) | ($true != (in @ X5 @ X1)))))),
% 0.15/0.32 inference(rectify,[],[f12])).
% 0.15/0.32 thf(f12,plain,(
% 0.15/0.32 (brelnall1 = $true) & ? [X0,X1,X2] : (($true = (breln @ X1 @ X0 @ X2)) & ? [X3 : $i > $o] : (? [X6] : (($true != (X3 @ X6)) & ($true = (in @ X6 @ X2))) & ! [X4] : (! [X5] : (($true = (X3 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ X2) != $true) | ((in @ X5 @ X0) != $true)) | ($true != (in @ X4 @ X1)))))),
% 0.15/0.32 inference(flattening,[],[f11])).
% 0.15/0.32 thf(f11,plain,(
% 0.15/0.32 ? [X0,X1,X2] : (? [X3 : $i > $o] : (? [X6] : (($true != (X3 @ X6)) & ($true = (in @ X6 @ X2))) & ! [X4] : (! [X5] : ((($true = (X3 @ (kpair @ X4 @ X5))) | ((in @ (kpair @ X4 @ X5) @ X2) != $true)) | ((in @ X5 @ X0) != $true)) | ($true != (in @ X4 @ X1)))) & ($true = (breln @ X1 @ X0 @ X2))) & (brelnall1 = $true)),
% 0.15/0.32 inference(ennf_transformation,[],[f7])).
% 0.15/0.32 thf(f7,plain,(
% 0.15/0.32 ~((brelnall1 = $true) => ! [X0,X1,X2] : (($true = (breln @ X1 @ X0 @ X2)) => ! [X3 : $i > $o] : (! [X4] : (($true = (in @ X4 @ X1)) => ! [X5] : (((in @ X5 @ X0) = $true) => (((in @ (kpair @ X4 @ X5) @ X2) = $true) => ($true = (X3 @ (kpair @ X4 @ X5)))))) => ! [X6] : (($true = (in @ X6 @ X2)) => ($true = (X3 @ X6))))))),
% 0.15/0.32 inference(fool_elimination,[],[f6])).
% 0.15/0.32 thf(f6,plain,(
% 0.15/0.32 ~(brelnall1 => ! [X0,X1,X2] : ((breln @ X1 @ X0 @ X2) => ! [X3 : $i > $o] : (! [X4] : ((in @ X4 @ X1) => ! [X5] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6] : ((in @ X6 @ X2) => (X3 @ X6)))))),
% 0.15/0.32 inference(rectify,[],[f4])).
% 0.15/0.32 thf(f4,negated_conjecture,(
% 0.15/0.32 ~(brelnall1 => ! [X1,X0,X3] : ((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)))))),
% 0.15/0.32 inference(negated_conjecture,[],[f3])).
% 0.15/0.32 thf(f3,conjecture,(
% 0.15/0.32 brelnall1 => ! [X1,X0,X3] : ((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))))),
% 0.15/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2)).
% 0.15/0.32 thf(f79,plain,(
% 0.15/0.32 ( ! [X3 : $i] : (((in @ X3 @ sK2) = $false) | ($true = (sK3 @ X3))) ) | ~spl5_1),
% 0.15/0.32 inference(avatar_component_clause,[],[f78])).
% 0.15/0.32 thf(f78,plain,(
% 0.15/0.32 spl5_1 <=> ! [X3] : (($true = (sK3 @ X3)) | ((in @ X3 @ sK2) = $false))),
% 0.15/0.32 introduced(avatar_definition,[new_symbols(naming,[spl5_1])])).
% 0.15/0.32 thf(f22,plain,(
% 0.15/0.32 ($true != (sK3 @ sK4))),
% 0.15/0.32 inference(cnf_transformation,[],[f17])).
% 0.15/0.32 thf(f99,plain,(
% 0.15/0.32 ~spl5_2),
% 0.15/0.32 inference(avatar_contradiction_clause,[],[f98])).
% 0.15/0.32 thf(f98,plain,(
% 0.15/0.32 $false | ~spl5_2),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f97])).
% 0.15/0.32 thf(f97,plain,(
% 0.15/0.32 ($true = $false) | ~spl5_2),
% 0.15/0.32 inference(backward_demodulation,[],[f52,f83])).
% 0.15/0.32 thf(f83,plain,(
% 0.15/0.32 ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ~spl5_2),
% 0.15/0.32 inference(avatar_component_clause,[],[f81])).
% 0.15/0.32 thf(f81,plain,(
% 0.15/0.32 spl5_2 <=> ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false)),
% 0.15/0.32 introduced(avatar_definition,[new_symbols(naming,[spl5_2])])).
% 0.15/0.32 thf(f52,plain,(
% 0.15/0.32 ($true = (subset @ sK2 @ (cartprod @ sK1 @ sK0)))),
% 0.15/0.32 inference(beta_eta_normalization,[],[f27])).
% 0.15/0.32 thf(f27,plain,(
% 0.15/0.32 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))) @ sK1 @ sK0 @ sK2))),
% 0.15/0.32 inference(definition_unfolding,[],[f23,f18])).
% 0.15/0.32 thf(f18,plain,(
% 0.15/0.32 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.15/0.32 inference(cnf_transformation,[],[f8])).
% 0.15/0.32 thf(f8,plain,(
% 0.15/0.32 (breln = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (subset @ Y2 @ (cartprod @ Y0 @ Y1))))))))),
% 0.15/0.32 inference(fool_elimination,[],[f1])).
% 0.15/0.32 thf(f1,axiom,(
% 0.15/0.32 ((^[X0 : $i, X1 : $i, X2 : $i] : (subset @ X2 @ (cartprod @ X0 @ X1))) = breln)),
% 0.15/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln)).
% 0.15/0.32 thf(f23,plain,(
% 0.15/0.32 ($true = (breln @ sK1 @ sK0 @ sK2))),
% 0.15/0.32 inference(cnf_transformation,[],[f17])).
% 0.15/0.32 thf(f96,plain,(
% 0.15/0.32 spl5_1 | spl5_1 | spl5_2 | spl5_1 | spl5_1),
% 0.15/0.32 inference(avatar_split_clause,[],[f72,f78,f78,f81,f78,f78])).
% 0.15/0.32 thf(f72,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (sK3 @ X0)) | ((in @ X3 @ sK2) = $false) | ($true = (sK3 @ X2)) | ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ($true = (sK3 @ X1)) | ($false = (in @ X2 @ sK2)) | ((in @ X1 @ sK2) = $false) | ($true = (sK3 @ X3)) | ((in @ X0 @ sK2) = $false)) )),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f67])).
% 0.15/0.32 thf(f67,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X0 @ sK2) = $false) | ($true = (sK3 @ X1)) | ($true = $false) | ($true = (sK3 @ X3)) | ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ((in @ X1 @ sK2) = $false) | ($true = (sK3 @ X0)) | ($true = (sK3 @ X2)) | ($false = (in @ X2 @ sK2)) | ((in @ X3 @ sK2) = $false)) )),
% 0.15/0.32 inference(superposition,[],[f66,f50])).
% 0.15/0.32 thf(f50,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4))) = $false) | ((in @ X5 @ X2) = $false) | ((X4 @ X5) = $true) | ((subset @ X2 @ (cartprod @ X3 @ X1)) = $false)) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f48])).
% 0.15/0.32 thf(f48,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ((in @ X5 @ X2) = $false) | ((X4 @ X5) = $true) | (((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4)) @ X2) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4)))) = $false)) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f47])).
% 0.15/0.32 thf(f47,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((X4 @ X5) = $true) | ((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ((in @ X5 @ X2) = $false) | ($false = ((in @ (sK7 @ X1 @ X2 @ X3 @ X4) @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4)) @ X2) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4))))))) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f46])).
% 0.15/0.32 thf(f46,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X2) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0))))) @ (sK7 @ X1 @ X2 @ X3 @ X4)) = $false) | ((in @ X5 @ X2) = $false) | ((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ((X4 @ X5) = $true)) )),
% 0.15/0.32 inference(sigma_clausification,[],[f44])).
% 0.15/0.32 thf(f44,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((in @ X5 @ X2) = $false) | ((X4 @ X5) = $true) | ((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X2) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0)))))))) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f43])).
% 0.15/0.32 thf(f43,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ((in @ X5 @ X2) = $false) | ($false = ((in @ (sK6 @ X3 @ X1 @ X4 @ X2) @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X2) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0)))))))) | ((X4 @ X5) = $true)) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f42])).
% 0.15/0.32 thf(f42,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ($true = ((in @ X5 @ X2) => (X4 @ X5))) | ($false = ((in @ (sK6 @ X3 @ X1 @ X4 @ X2) @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X2) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0))))))))) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f41])).
% 0.15/0.32 thf(f41,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ($true = ((^[Y0 : $i]: ((in @ Y0 @ X2) => (X4 @ Y0))) @ X5)) | ($false = ((in @ (sK6 @ X3 @ X1 @ X4 @ X2) @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X2) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0))))))))) )),
% 0.15/0.32 inference(pi_clausification,[],[f40])).
% 0.15/0.32 thf(f40,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (X4 @ Y0))))) | ($false = ((in @ (sK6 @ X3 @ X1 @ X4 @ X2) @ X3) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0) @ X2) => (X4 @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ Y0)))))))) | ((subset @ X2 @ (cartprod @ X3 @ X1)) = $false)) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f39])).
% 0.15/0.32 thf(f39,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (X4 @ Y0))))) | ($false = ((^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X2) => (X4 @ (kpair @ Y0 @ Y1)))))))) @ (sK6 @ X3 @ X1 @ X4 @ X2)))) )),
% 0.15/0.32 inference(sigma_clausification,[],[f38])).
% 0.15/0.32 thf(f38,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X2) => (X4 @ (kpair @ Y0 @ Y1)))))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (X4 @ Y0)))))) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f37])).
% 0.15/0.32 thf(f37,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((in @ (kpair @ Y0 @ Y1) @ X2) => (X4 @ (kpair @ Y0 @ Y1))))))))) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => (X4 @ Y0))))))) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f36])).
% 0.15/0.32 thf(f36,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o] : (($true = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ (kpair @ Y1 @ Y2) @ X2) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (Y0 @ Y1)))))) @ X4)) | ((subset @ X2 @ (cartprod @ X3 @ X1)) = $false)) )),
% 0.15/0.32 inference(pi_clausification,[],[f35])).
% 0.15/0.32 thf(f35,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ (kpair @ Y1 @ Y2) @ X2) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (Y0 @ Y1))))))))) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f34])).
% 0.15/0.32 thf(f34,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X2 @ (cartprod @ X3 @ X1)) => (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => ((in @ (kpair @ Y1 @ Y2) @ X2) => (Y0 @ (kpair @ Y1 @ Y2))))))))) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => (Y0 @ Y1)))))))))) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f33])).
% 0.15/0.32 thf(f33,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ X2 @ (cartprod @ Y0 @ X1)) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((in @ (kpair @ Y2 @ Y3) @ X2) => (Y1 @ (kpair @ Y2 @ Y3))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (Y1 @ Y2))))))))) @ X3))) )),
% 0.15/0.32 inference(pi_clausification,[],[f32])).
% 0.15/0.32 thf(f32,plain,(
% 0.15/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ X2 @ (cartprod @ Y0 @ X1)) => (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X1) => ((in @ (kpair @ Y2 @ Y3) @ X2) => (Y1 @ (kpair @ Y2 @ Y3))))))))) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => (Y1 @ Y2)))))))))))) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f31])).
% 0.15/0.32 thf(f31,plain,(
% 0.15/0.32 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ X1)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ X1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 @ Y3))))))))))) @ X2))) )),
% 0.15/0.32 inference(pi_clausification,[],[f30])).
% 0.15/0.32 thf(f30,plain,(
% 0.15/0.32 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ (cartprod @ Y1 @ X1)) => (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ X1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (Y2 @ (kpair @ Y3 @ Y4))))))))) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (Y2 @ Y3)))))))))))))) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f29])).
% 0.15/0.32 thf(f29,plain,(
% 0.15/0.32 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ (cartprod @ Y2 @ Y0)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y1) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (Y3 @ Y4))))))))))))) @ X1))) )),
% 0.15/0.32 inference(pi_clausification,[],[f28])).
% 0.15/0.32 thf(f28,plain,(
% 0.15/0.32 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y1 @ (cartprod @ Y2 @ Y0)) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y1) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (Y3 @ Y4)))))))))))))))),
% 0.15/0.32 inference(beta_eta_normalization,[],[f26])).
% 0.15/0.32 thf(f26,plain,(
% 0.15/0.32 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y2 @ Y0 @ Y1) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y1) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (Y3 @ Y4)))))))))))))))),
% 0.15/0.32 inference(definition_unfolding,[],[f24,f25])).
% 0.15/0.32 thf(f25,plain,(
% 0.15/0.32 (brelnall1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (subset @ Y5 @ (cartprod @ Y3 @ Y4))))))) @ Y2 @ Y0 @ Y1) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y1) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (Y3 @ Y4)))))))))))))))),
% 0.15/0.32 inference(definition_unfolding,[],[f19,f18])).
% 0.15/0.32 thf(f19,plain,(
% 0.15/0.32 (brelnall1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y0 @ Y1) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y1) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (Y3 @ Y4)))))))))))))))),
% 0.15/0.32 inference(cnf_transformation,[],[f10])).
% 0.15/0.32 thf(f10,plain,(
% 0.15/0.32 (brelnall1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y0 @ Y1) => (!! @ ($i > $o) @ (^[Y3 : $i > $o]: ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y0) => ((in @ (kpair @ Y4 @ Y5) @ Y1) => (Y3 @ (kpair @ Y4 @ Y5))))))))) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => (Y3 @ Y4)))))))))))))))),
% 0.15/0.32 inference(fool_elimination,[],[f9])).
% 0.15/0.32 thf(f9,plain,(
% 0.15/0.32 (brelnall1 = ! [X0,X1,X2] : ((breln @ X0 @ X2 @ X1) => ! [X3 : $i > $o] : (! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X1) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6] : ((in @ X6 @ X1) => (X3 @ X6)))))),
% 0.15/0.32 inference(rectify,[],[f2])).
% 0.15/0.32 thf(f2,axiom,(
% 0.15/0.32 (brelnall1 = ! [X0,X3,X1] : ((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)))))),
% 0.15/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1)).
% 0.15/0.32 thf(f24,plain,(
% 0.15/0.32 (brelnall1 = $true)),
% 0.15/0.32 inference(cnf_transformation,[],[f17])).
% 0.15/0.32 thf(f66,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($true = (sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X0 @ sK2) @ (sK7 @ sK0 @ sK2 @ sK1 @ X0)))) | ($true = (X0 @ X2)) | ($false = (in @ X2 @ sK2)) | ($true = (X0 @ X3)) | ((in @ X3 @ sK2) = $false) | ($true = (X0 @ X1)) | ((in @ X1 @ sK2) = $false)) )),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f65])).
% 0.15/0.32 thf(f65,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($true = (X0 @ X3)) | ((in @ X3 @ sK2) = $false) | ($true = (sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X0 @ sK2) @ (sK7 @ sK0 @ sK2 @ sK1 @ X0)))) | ($false = (in @ X2 @ sK2)) | ($true = (X0 @ X1)) | ((in @ X1 @ sK2) = $false) | ($true = $false) | ($true = (X0 @ X2))) )),
% 0.15/0.32 inference(forward_demodulation,[],[f64,f52])).
% 0.15/0.32 thf(f64,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ($true = (X0 @ X3)) | ($false = (in @ X2 @ sK2)) | ($true = (X0 @ X2)) | ($true = (X0 @ X1)) | ($true = (sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X0 @ sK2) @ (sK7 @ sK0 @ sK2 @ sK1 @ X0)))) | ((in @ X3 @ sK2) = $false) | ((in @ X1 @ sK2) = $false)) )),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f63])).
% 0.15/0.32 thf(f63,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($false = (in @ X2 @ sK2)) | ($true = (sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X0 @ sK2) @ (sK7 @ sK0 @ sK2 @ sK1 @ X0)))) | ($true != $true) | ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ($true = (X0 @ X1)) | ((in @ X3 @ sK2) = $false) | ((in @ X1 @ sK2) = $false) | ($true = (X0 @ X3)) | ($true = (X0 @ X2))) )),
% 0.15/0.32 inference(duplicate_literal_removal,[],[f62])).
% 0.15/0.32 thf(f62,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X0 : $i > $o,X1 : $i] : (($true = (sK3 @ (kpair @ (sK6 @ sK1 @ sK0 @ X0 @ sK2) @ (sK7 @ sK0 @ sK2 @ sK1 @ X0)))) | ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ((subset @ sK2 @ (cartprod @ sK1 @ sK0)) = $false) | ((in @ X3 @ sK2) = $false) | ($true != $true) | ($true = (X0 @ X3)) | ((in @ X1 @ sK2) = $false) | ($true = (X0 @ X2)) | ($false = (in @ X2 @ sK2)) | ($true = (X0 @ X1))) )),
% 0.15/0.32 inference(superposition,[],[f61,f45])).
% 0.15/0.32 thf(f45,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = (in @ (sK6 @ X3 @ X1 @ X4 @ X2) @ X3)) | ((in @ X5 @ X2) = $false) | ((subset @ X2 @ (cartprod @ X3 @ X1)) = $false) | ((X4 @ X5) = $true)) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f43])).
% 0.15/0.32 thf(f61,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ (sK6 @ X0 @ sK0 @ X1 @ sK2) @ sK1)) | ($true = (sK3 @ (kpair @ (sK6 @ X0 @ sK0 @ X1 @ sK2) @ (sK7 @ sK0 @ sK2 @ X0 @ X1)))) | ($true = (X1 @ X2)) | ((in @ X3 @ sK2) = $false) | ($false = (in @ X2 @ sK2)) | ($false = (subset @ sK2 @ (cartprod @ X0 @ sK0))) | ($true = (X1 @ X3))) )),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f60])).
% 0.15/0.32 thf(f60,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($false = (subset @ sK2 @ (cartprod @ X0 @ sK0))) | ($true != (in @ (sK6 @ X0 @ sK0 @ X1 @ sK2) @ sK1)) | ($false = (in @ X2 @ sK2)) | ($true = (sK3 @ (kpair @ (sK6 @ X0 @ sK0 @ X1 @ sK2) @ (sK7 @ sK0 @ sK2 @ X0 @ X1)))) | ((in @ X3 @ sK2) = $false) | ($true != $true) | ($true = (X1 @ X2)) | ($true = (X1 @ X3))) )),
% 0.15/0.32 inference(duplicate_literal_removal,[],[f59])).
% 0.15/0.32 thf(f59,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ (sK6 @ X0 @ sK0 @ X1 @ sK2) @ sK1)) | ($false = (subset @ sK2 @ (cartprod @ X0 @ sK0))) | ($true != $true) | ($false = (in @ X2 @ sK2)) | ((in @ X3 @ sK2) = $false) | ($true = (X1 @ X2)) | ($true = (sK3 @ (kpair @ (sK6 @ X0 @ sK0 @ X1 @ sK2) @ (sK7 @ sK0 @ sK2 @ X0 @ X1)))) | ($false = (subset @ sK2 @ (cartprod @ X0 @ sK0))) | ($true = (X1 @ X3))) )),
% 0.15/0.32 inference(superposition,[],[f58,f49])).
% 0.15/0.32 thf(f49,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (((in @ (sK7 @ X1 @ X2 @ X3 @ X4) @ X1) = $true) | ((X4 @ X5) = $true) | ((in @ X5 @ X2) = $false) | ((subset @ X2 @ (cartprod @ X3 @ X1)) = $false)) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f47])).
% 0.15/0.32 thf(f58,plain,(
% 0.15/0.32 ( ! [X2 : $i > $o,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK7 @ X1 @ sK2 @ X0 @ X2) @ sK0)) | ($true != (in @ (sK6 @ X0 @ X1 @ X2 @ sK2) @ sK1)) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ($true = (sK3 @ (kpair @ (sK6 @ X0 @ X1 @ X2 @ sK2) @ (sK7 @ X1 @ sK2 @ X0 @ X2)))) | ((in @ X3 @ sK2) = $false) | ($true = (X2 @ X3))) )),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f56])).
% 0.15/0.32 thf(f56,plain,(
% 0.15/0.32 ( ! [X2 : $i > $o,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ sK2) = $false) | ((subset @ sK2 @ (cartprod @ X0 @ X1)) = $false) | ($true != $true) | ($true = (X2 @ X3)) | ($true = (sK3 @ (kpair @ (sK6 @ X0 @ X1 @ X2 @ sK2) @ (sK7 @ X1 @ sK2 @ X0 @ X2)))) | ($true != (in @ (sK7 @ X1 @ sK2 @ X0 @ X2) @ sK0)) | ($true != (in @ (sK6 @ X0 @ X1 @ X2 @ sK2) @ sK1))) )),
% 0.15/0.32 inference(superposition,[],[f20,f51])).
% 0.15/0.32 thf(f51,plain,(
% 0.15/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i > $o,X5 : $i] : (($true = (in @ (kpair @ (sK6 @ X3 @ X1 @ X4 @ X2) @ (sK7 @ X1 @ X2 @ X3 @ X4)) @ X2)) | ((X4 @ X5) = $true) | ((in @ X5 @ X2) = $false) | ((subset @ X2 @ (cartprod @ X3 @ X1)) = $false)) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f48])).
% 0.15/0.32 thf(f20,plain,(
% 0.15/0.32 ( ! [X6 : $i,X5 : $i] : (($true != (in @ (kpair @ X5 @ X6) @ sK2)) | ($true = (sK3 @ (kpair @ X5 @ X6))) | ($true != (in @ X5 @ sK1)) | ((in @ X6 @ sK0) != $true)) )),
% 0.15/0.32 inference(cnf_transformation,[],[f17])).
% 0.15/0.32 % SZS output end Proof for theBenchmark
% 0.15/0.32 % (4771)------------------------------
% 0.15/0.32 % (4771)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.32 % (4771)Termination reason: Refutation
% 0.15/0.32
% 0.15/0.32 % (4771)Memory used [KB]: 5756
% 0.15/0.32 % (4771)Time elapsed: 0.012 s
% 0.15/0.32 % (4771)Instructions burned: 21 (million)
% 0.15/0.32 % (4771)------------------------------
% 0.15/0.32 % (4771)------------------------------
% 0.15/0.32 % (4768)Success in time 0.009 s
% 0.15/0.32 % Vampire---4.8 exiting
%------------------------------------------------------------------------------