TSTP Solution File: SEU734^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU734^2 : 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 : n004.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 03:51:07 EDT 2024
% Result : Theorem 0.22s 0.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU734^2 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.14 % 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
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 18:13:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 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
% 0.22/0.37 % (11265)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.38 % (11260)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)
% 0.22/0.38 % (11259)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.38 % (11262)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.38 % (11261)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)
% 0.22/0.38 % (11263)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)
% 0.22/0.38 % (11264)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)
% 0.22/0.38 % (11262)Instruction limit reached!
% 0.22/0.38 % (11262)------------------------------
% 0.22/0.38 % (11262)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (11263)Instruction limit reached!
% 0.22/0.38 % (11263)------------------------------
% 0.22/0.38 % (11263)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (11263)Termination reason: Unknown
% 0.22/0.38 % (11263)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (11263)Memory used [KB]: 895
% 0.22/0.38 % (11263)Time elapsed: 0.003 s
% 0.22/0.38 % (11263)Instructions burned: 2 (million)
% 0.22/0.38 % (11263)------------------------------
% 0.22/0.38 % (11263)------------------------------
% 0.22/0.38 % (11262)Termination reason: Unknown
% 0.22/0.38 % (11262)Termination phase: shuffling
% 0.22/0.38
% 0.22/0.38 % (11262)Memory used [KB]: 895
% 0.22/0.38 % (11262)Time elapsed: 0.003 s
% 0.22/0.38 % (11262)Instructions burned: 2 (million)
% 0.22/0.38 % (11265)Instruction limit reached!
% 0.22/0.38 % (11265)------------------------------
% 0.22/0.38 % (11265)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (11265)Termination reason: Unknown
% 0.22/0.38 % (11265)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (11265)Memory used [KB]: 5628
% 0.22/0.38 % (11265)Time elapsed: 0.008 s
% 0.22/0.38 % (11265)Instructions burned: 20 (million)
% 0.22/0.38 % (11265)------------------------------
% 0.22/0.38 % (11265)------------------------------
% 0.22/0.38 % (11262)------------------------------
% 0.22/0.38 % (11262)------------------------------
% 0.22/0.38 % (11266)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)
% 0.22/0.38 % (11266)Instruction limit reached!
% 0.22/0.38 % (11266)------------------------------
% 0.22/0.38 % (11266)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (11266)Termination reason: Unknown
% 0.22/0.38 % (11266)Termination phase: Property scanning
% 0.22/0.38
% 0.22/0.38 % (11266)Memory used [KB]: 895
% 0.22/0.38 % (11266)Time elapsed: 0.003 s
% 0.22/0.38 % (11266)Instructions burned: 3 (million)
% 0.22/0.38 % (11266)------------------------------
% 0.22/0.38 % (11266)------------------------------
% 0.22/0.38 % (11260)Instruction limit reached!
% 0.22/0.38 % (11260)------------------------------
% 0.22/0.38 % (11260)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.38 % (11260)Termination reason: Unknown
% 0.22/0.38 % (11260)Termination phase: Saturation
% 0.22/0.38
% 0.22/0.38 % (11260)Memory used [KB]: 5500
% 0.22/0.38 % (11260)Time elapsed: 0.005 s
% 0.22/0.38 % (11260)Instructions burned: 5 (million)
% 0.22/0.38 % (11260)------------------------------
% 0.22/0.38 % (11260)------------------------------
% 0.22/0.39 % (11273)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)
% 0.22/0.40 % (11274)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)
% 0.22/0.40 % (11276)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)
% 0.22/0.40 % (11261)Instruction limit reached!
% 0.22/0.40 % (11261)------------------------------
% 0.22/0.40 % (11261)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (11277)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)
% 0.22/0.40 % (11261)Termination reason: Unknown
% 0.22/0.40 % (11261)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (11261)Memory used [KB]: 5628
% 0.22/0.40 % (11276)Instruction limit reached!
% 0.22/0.40 % (11276)------------------------------
% 0.22/0.40 % (11276)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (11261)Time elapsed: 0.020 s
% 0.22/0.40 % (11261)Instructions burned: 27 (million)
% 0.22/0.40 % (11261)------------------------------
% 0.22/0.40 % (11261)------------------------------
% 0.22/0.40 % (11278)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.40 % (11276)Termination reason: Unknown
% 0.22/0.40 % (11276)Termination phase: Property scanning
% 0.22/0.40
% 0.22/0.40 % (11276)Memory used [KB]: 1023
% 0.22/0.40 % (11276)Time elapsed: 0.004 s
% 0.22/0.40 % (11276)Instructions burned: 4 (million)
% 0.22/0.40 % (11276)------------------------------
% 0.22/0.40 % (11276)------------------------------
% 0.22/0.40 % (11278)Instruction limit reached!
% 0.22/0.40 % (11278)------------------------------
% 0.22/0.40 % (11278)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (11278)Termination reason: Unknown
% 0.22/0.40 % (11278)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (11278)Memory used [KB]: 1023
% 0.22/0.40 % (11278)Time elapsed: 0.006 s
% 0.22/0.40 % (11278)Instructions burned: 7 (million)
% 0.22/0.40 % (11278)------------------------------
% 0.22/0.40 % (11278)------------------------------
% 0.22/0.40 % (11273)Instruction limit reached!
% 0.22/0.40 % (11273)------------------------------
% 0.22/0.40 % (11273)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (11273)Termination reason: Unknown
% 0.22/0.40 % (11273)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (11273)Memory used [KB]: 5756
% 0.22/0.40 % (11273)Time elapsed: 0.014 s
% 0.22/0.40 % (11273)Instructions burned: 38 (million)
% 0.22/0.40 % (11273)------------------------------
% 0.22/0.40 % (11273)------------------------------
% 0.22/0.40 % (11274)Instruction limit reached!
% 0.22/0.40 % (11274)------------------------------
% 0.22/0.40 % (11274)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (11274)Termination reason: Unknown
% 0.22/0.40 % (11274)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (11274)Memory used [KB]: 5628
% 0.22/0.40 % (11274)Time elapsed: 0.012 s
% 0.22/0.40 % (11274)Instructions burned: 15 (million)
% 0.22/0.41 % (11274)------------------------------
% 0.22/0.41 % (11274)------------------------------
% 0.22/0.41 % (11264)First to succeed.
% 0.22/0.41 % (11288)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.41 % (11288)Instruction limit reached!
% 0.22/0.41 % (11288)------------------------------
% 0.22/0.41 % (11288)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (11288)Termination reason: Unknown
% 0.22/0.41 % (11288)Termination phase: Saturation
% 0.22/0.41
% 0.22/0.41 % (11288)Memory used [KB]: 1023
% 0.22/0.41 % (11288)Time elapsed: 0.003 s
% 0.22/0.41 % (11288)Instructions burned: 5 (million)
% 0.22/0.41 % (11288)------------------------------
% 0.22/0.41 % (11288)------------------------------
% 0.22/0.41 % (11285)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.22/0.41 % (11286)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.41 % (11286)Instruction limit reached!
% 0.22/0.41 % (11286)------------------------------
% 0.22/0.41 % (11286)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (11286)Termination reason: Unknown
% 0.22/0.41 % (11286)Termination phase: Property scanning
% 0.22/0.41
% 0.22/0.41 % (11286)Memory used [KB]: 1023
% 0.22/0.41 % (11286)Time elapsed: 0.004 s
% 0.22/0.41 % (11286)Instructions burned: 3 (million)
% 0.22/0.41 % (11286)------------------------------
% 0.22/0.41 % (11286)------------------------------
% 0.22/0.41 % (11264)Refutation found. Thanks to Tanya!
% 0.22/0.41 % SZS status Theorem for theBenchmark
% 0.22/0.41 % SZS output start Proof for theBenchmark
% 0.22/0.41 thf(func_def_0, type, in: $i > $i > $o).
% 0.22/0.41 thf(func_def_1, type, powerset: $i > $i).
% 0.22/0.41 thf(func_def_2, type, subset: $i > $i > $o).
% 0.22/0.41 thf(func_def_3, type, binintersect: $i > $i > $i).
% 0.22/0.41 thf(func_def_4, type, setminus: $i > $i > $i).
% 0.22/0.41 thf(func_def_20, type, sK8: $i > $i > $i > $i).
% 0.22/0.41 thf(f196,plain,(
% 0.22/0.41 $false),
% 0.22/0.41 inference(subsumption_resolution,[],[f195,f70])).
% 0.22/0.41 thf(f70,plain,(
% 0.22/0.41 ((in @ sK11 @ (powerset @ sK10)) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f44])).
% 0.22/0.41 thf(f44,plain,(
% 0.22/0.41 (complementT_lem = $true) & ((((in @ sK11 @ (powerset @ sK10)) = $true) & ((subset @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ (binintersect @ sK9 @ sK11))) != $true)) & ((in @ sK9 @ (powerset @ sK10)) = $true)) & (complementImpComplementIntersect = $true) & (subsetTI = $true) & (binintersectT_lem = $true)),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f41,f43,f42])).
% 0.22/0.41 thf(f42,plain,(
% 0.22/0.41 ? [X0,X1] : (? [X2] : (((in @ X2 @ (powerset @ X1)) = $true) & ((subset @ (setminus @ X1 @ X0) @ (setminus @ X1 @ (binintersect @ X0 @ X2))) != $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2] : (((in @ X2 @ (powerset @ sK10)) = $true) & ((subset @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ (binintersect @ sK9 @ X2))) != $true)) & ((in @ sK9 @ (powerset @ sK10)) = $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f43,plain,(
% 0.22/0.41 ? [X2] : (((in @ X2 @ (powerset @ sK10)) = $true) & ((subset @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ (binintersect @ sK9 @ X2))) != $true)) => (((in @ sK11 @ (powerset @ sK10)) = $true) & ((subset @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ (binintersect @ sK9 @ sK11))) != $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f41,plain,(
% 0.22/0.41 (complementT_lem = $true) & ? [X0,X1] : (? [X2] : (((in @ X2 @ (powerset @ X1)) = $true) & ((subset @ (setminus @ X1 @ X0) @ (setminus @ X1 @ (binintersect @ X0 @ X2))) != $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (complementImpComplementIntersect = $true) & (subsetTI = $true) & (binintersectT_lem = $true)),
% 0.22/0.41 inference(rectify,[],[f21])).
% 0.22/0.41 thf(f21,plain,(
% 0.22/0.41 (complementT_lem = $true) & ? [X1,X0] : (? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (complementImpComplementIntersect = $true) & (subsetTI = $true) & (binintersectT_lem = $true)),
% 0.22/0.41 inference(flattening,[],[f20])).
% 0.22/0.41 thf(f20,plain,(
% 0.22/0.41 (((? [X1,X0] : (? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (complementImpComplementIntersect = $true)) & (subsetTI = $true)) & (complementT_lem = $true)) & (binintersectT_lem = $true)),
% 0.22/0.41 inference(ennf_transformation,[],[f17])).
% 0.22/0.41 thf(f17,plain,(
% 0.22/0.41 ~((binintersectT_lem = $true) => ((complementT_lem = $true) => ((subsetTI = $true) => ((complementImpComplementIntersect = $true) => ! [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X0)) = $true) => ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true)))))))),
% 0.22/0.41 inference(fool_elimination,[],[f16])).
% 0.22/0.41 thf(f16,plain,(
% 0.22/0.41 ~(binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))))))),
% 0.22/0.41 inference(rectify,[],[f6])).
% 0.22/0.41 thf(f6,negated_conjecture,(
% 0.22/0.41 ~(binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))))))),
% 0.22/0.41 inference(negated_conjecture,[],[f5])).
% 0.22/0.41 thf(f5,conjecture,(
% 0.22/0.41 binintersectT_lem => (complementT_lem => (subsetTI => (complementImpComplementIntersect => ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => (subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))))),
% 0.22/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementSubsetComplementIntersect)).
% 0.22/0.41 thf(f195,plain,(
% 0.22/0.41 ((in @ sK11 @ (powerset @ sK10)) != $true)),
% 0.22/0.41 inference(subsumption_resolution,[],[f194,f68])).
% 0.22/0.41 thf(f68,plain,(
% 0.22/0.41 ((in @ sK9 @ (powerset @ sK10)) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f44])).
% 0.22/0.41 thf(f194,plain,(
% 0.22/0.41 ((in @ sK9 @ (powerset @ sK10)) != $true) | ((in @ sK11 @ (powerset @ sK10)) != $true)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f193])).
% 0.22/0.41 thf(f193,plain,(
% 0.22/0.41 ((in @ sK9 @ (powerset @ sK10)) != $true) | ((in @ sK11 @ (powerset @ sK10)) != $true) | ($true != $true)),
% 0.22/0.41 inference(superposition,[],[f186,f100])).
% 0.22/0.41 thf(f100,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | ((in @ X4 @ (powerset @ X3)) != $true) | ((in @ X5 @ (powerset @ X3)) != $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f81])).
% 0.22/0.41 thf(f81,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X3)) != $true) | ((in @ X4 @ (powerset @ X3)) != $true) | ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | ($true != $true)) )),
% 0.22/0.41 inference(definition_unfolding,[],[f51,f65])).
% 0.22/0.41 thf(f65,plain,(
% 0.22/0.41 (binintersectT_lem = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f44])).
% 0.22/0.41 thf(f51,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X3)) != $true) | ((in @ X5 @ (powerset @ X3)) != $true) | ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | (binintersectT_lem != $true)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f30])).
% 0.22/0.41 thf(f30,plain,(
% 0.22/0.41 ((binintersectT_lem = $true) | (((in @ sK1 @ (powerset @ sK0)) = $true) & (((in @ sK2 @ (powerset @ sK0)) = $true) & ((in @ (binintersect @ sK1 @ sK2) @ (powerset @ sK0)) != $true)))) & (! [X3,X4] : (((in @ X4 @ (powerset @ X3)) != $true) | ! [X5] : (((in @ X5 @ (powerset @ X3)) != $true) | ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true))) | (binintersectT_lem != $true))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f27,f29,f28])).
% 0.22/0.41 thf(f28,plain,(
% 0.22/0.41 ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) != $true))) => (((in @ sK1 @ (powerset @ sK0)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ sK0)) = $true) & ((in @ (binintersect @ sK1 @ X2) @ (powerset @ sK0)) != $true)))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f29,plain,(
% 0.22/0.41 ? [X2] : (((in @ X2 @ (powerset @ sK0)) = $true) & ((in @ (binintersect @ sK1 @ X2) @ (powerset @ sK0)) != $true)) => (((in @ sK2 @ (powerset @ sK0)) = $true) & ((in @ (binintersect @ sK1 @ sK2) @ (powerset @ sK0)) != $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f27,plain,(
% 0.22/0.41 ((binintersectT_lem = $true) | ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) != $true)))) & (! [X3,X4] : (((in @ X4 @ (powerset @ X3)) != $true) | ! [X5] : (((in @ X5 @ (powerset @ X3)) != $true) | ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true))) | (binintersectT_lem != $true))),
% 0.22/0.41 inference(rectify,[],[f26])).
% 0.22/0.41 thf(f26,plain,(
% 0.22/0.41 ((binintersectT_lem = $true) | ? [X1,X0] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X1)) = $true) & ($true != (in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))))) & (! [X1,X0] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2] : (((in @ X2 @ (powerset @ X1)) != $true) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ X1))))) | (binintersectT_lem != $true))),
% 0.22/0.41 inference(nnf_transformation,[],[f18])).
% 0.22/0.41 thf(f18,plain,(
% 0.22/0.41 (binintersectT_lem = $true) <=> ! [X1,X0] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2] : (((in @ X2 @ (powerset @ X1)) != $true) | ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))))),
% 0.22/0.41 inference(ennf_transformation,[],[f11])).
% 0.22/0.41 thf(f11,plain,(
% 0.22/0.41 (binintersectT_lem = $true) <=> ! [X1,X0] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X1)) = $true) => ($true = (in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))))),
% 0.22/0.41 inference(fool_elimination,[],[f10])).
% 0.22/0.41 thf(f10,plain,(
% 0.22/0.41 (binintersectT_lem = ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => (in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))))),
% 0.22/0.41 inference(rectify,[],[f1])).
% 0.22/0.41 thf(f1,axiom,(
% 0.22/0.41 (binintersectT_lem = ! [X1,X0] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 0.22/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem)).
% 0.22/0.41 thf(f186,plain,(
% 0.22/0.41 ((in @ (binintersect @ sK9 @ sK11) @ (powerset @ sK10)) != $true)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f185])).
% 0.22/0.41 thf(f185,plain,(
% 0.22/0.41 ($true != $true) | ((in @ (binintersect @ sK9 @ sK11) @ (powerset @ sK10)) != $true)),
% 0.22/0.41 inference(superposition,[],[f174,f98])).
% 0.22/0.41 thf(f98,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i] : (((in @ (setminus @ X3 @ X2) @ (powerset @ X3)) = $true) | ((in @ X2 @ (powerset @ X3)) != $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f84])).
% 0.22/0.41 thf(f84,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i] : (((in @ (setminus @ X3 @ X2) @ (powerset @ X3)) = $true) | ((in @ X2 @ (powerset @ X3)) != $true) | ($true != $true)) )),
% 0.22/0.41 inference(definition_unfolding,[],[f55,f71])).
% 0.22/0.41 thf(f71,plain,(
% 0.22/0.41 (complementT_lem = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f44])).
% 0.22/0.41 thf(f55,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i] : (((in @ (setminus @ X3 @ X2) @ (powerset @ X3)) = $true) | ((in @ X2 @ (powerset @ X3)) != $true) | (complementT_lem != $true)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f34])).
% 0.22/0.41 thf(f34,plain,(
% 0.22/0.41 ((complementT_lem = $true) | (((in @ (setminus @ sK4 @ sK3) @ (powerset @ sK4)) != $true) & ((in @ sK3 @ (powerset @ sK4)) = $true))) & (! [X2,X3] : (((in @ (setminus @ X3 @ X2) @ (powerset @ X3)) = $true) | ((in @ X2 @ (powerset @ X3)) != $true)) | (complementT_lem != $true))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f32,f33])).
% 0.22/0.41 thf(f33,plain,(
% 0.22/0.41 ? [X0,X1] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) != $true) & ((in @ X0 @ (powerset @ X1)) = $true)) => (((in @ (setminus @ sK4 @ sK3) @ (powerset @ sK4)) != $true) & ((in @ sK3 @ (powerset @ sK4)) = $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f32,plain,(
% 0.22/0.41 ((complementT_lem = $true) | ? [X0,X1] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) != $true) & ((in @ X0 @ (powerset @ X1)) = $true))) & (! [X2,X3] : (((in @ (setminus @ X3 @ X2) @ (powerset @ X3)) = $true) | ((in @ X2 @ (powerset @ X3)) != $true)) | (complementT_lem != $true))),
% 0.22/0.41 inference(rectify,[],[f31])).
% 0.22/0.41 thf(f31,plain,(
% 0.22/0.41 ((complementT_lem = $true) | ? [X0,X1] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) != $true) & ((in @ X0 @ (powerset @ X1)) = $true))) & (! [X0,X1] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true) | ((in @ X0 @ (powerset @ X1)) != $true)) | (complementT_lem != $true))),
% 0.22/0.41 inference(nnf_transformation,[],[f19])).
% 0.22/0.41 thf(f19,plain,(
% 0.22/0.41 (complementT_lem = $true) <=> ! [X0,X1] : (((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 0.22/0.41 inference(ennf_transformation,[],[f15])).
% 0.22/0.41 thf(f15,plain,(
% 0.22/0.41 (complementT_lem = $true) <=> ! [X1,X0] : (((in @ X0 @ (powerset @ X1)) = $true) => ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)) = $true))),
% 0.22/0.41 inference(fool_elimination,[],[f14])).
% 0.22/0.41 thf(f14,plain,(
% 0.22/0.41 (complementT_lem = ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))))),
% 0.22/0.41 inference(rectify,[],[f2])).
% 0.22/0.41 thf(f2,axiom,(
% 0.22/0.41 (complementT_lem = ! [X1,X0] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.22/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem)).
% 0.22/0.41 thf(f174,plain,(
% 0.22/0.41 ((in @ (setminus @ sK10 @ (binintersect @ sK9 @ sK11)) @ (powerset @ sK10)) != $true)),
% 0.22/0.41 inference(subsumption_resolution,[],[f173,f70])).
% 0.22/0.41 thf(f173,plain,(
% 0.22/0.41 ((in @ (setminus @ sK10 @ (binintersect @ sK9 @ sK11)) @ (powerset @ sK10)) != $true) | ((in @ sK11 @ (powerset @ sK10)) != $true)),
% 0.22/0.41 inference(subsumption_resolution,[],[f172,f68])).
% 0.22/0.41 thf(f172,plain,(
% 0.22/0.41 ((in @ (setminus @ sK10 @ (binintersect @ sK9 @ sK11)) @ (powerset @ sK10)) != $true) | ((in @ sK9 @ (powerset @ sK10)) != $true) | ((in @ sK11 @ (powerset @ sK10)) != $true)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f171])).
% 0.22/0.41 thf(f171,plain,(
% 0.22/0.41 ((in @ sK9 @ (powerset @ sK10)) != $true) | ((in @ (setminus @ sK10 @ (binintersect @ sK9 @ sK11)) @ (powerset @ sK10)) != $true) | ($true != $true) | ((in @ sK11 @ (powerset @ sK10)) != $true)),
% 0.22/0.41 inference(superposition,[],[f69,f170])).
% 0.22/0.41 thf(f170,plain,(
% 0.22/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true)) )),
% 0.22/0.41 inference(subsumption_resolution,[],[f169,f98])).
% 0.22/0.41 thf(f169,plain,(
% 0.22/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f168])).
% 0.22/0.41 thf(f168,plain,(
% 0.22/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true)) )),
% 0.22/0.41 inference(duplicate_literal_removal,[],[f166])).
% 0.22/0.41 thf(f166,plain,(
% 0.22/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X0)) != $true)) )),
% 0.22/0.41 inference(superposition,[],[f156,f102])).
% 0.22/0.41 thf(f102,plain,(
% 0.22/0.41 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK8 @ X6 @ X5 @ X4) @ X4) = $true) | ((subset @ X5 @ X6) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f90])).
% 0.22/0.41 thf(f90,plain,(
% 0.22/0.41 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) = $true) | ($true != $true) | ((in @ (sK8 @ X6 @ X5 @ X4) @ X4) = $true)) )),
% 0.22/0.41 inference(definition_unfolding,[],[f59,f66])).
% 0.22/0.41 thf(f66,plain,(
% 0.22/0.41 (subsetTI = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f44])).
% 0.22/0.41 thf(f59,plain,(
% 0.22/0.41 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK8 @ X6 @ X5 @ X4) @ X4) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) = $true) | ((in @ X5 @ (powerset @ X4)) != $true) | (subsetTI != $true)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f40])).
% 0.22/0.41 thf(f40,plain,(
% 0.22/0.41 ((subsetTI = $true) | ((! [X3] : (((in @ X3 @ sK7) = $true) | ((in @ X3 @ sK5) != $true) | ((in @ X3 @ sK6) != $true)) & ((in @ sK7 @ (powerset @ sK5)) = $true) & ((subset @ sK6 @ sK7) != $true)) & ((in @ sK6 @ (powerset @ sK5)) = $true))) & (! [X4,X5] : (! [X6] : ((((in @ (sK8 @ X6 @ X5 @ X4) @ X6) != $true) & ((in @ (sK8 @ X6 @ X5 @ X4) @ X4) = $true) & ((in @ (sK8 @ X6 @ X5 @ X4) @ X5) = $true)) | ((in @ X6 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) = $true)) | ((in @ X5 @ (powerset @ X4)) != $true)) | (subsetTI != $true))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f36,f39,f38,f37])).
% 0.22/0.41 thf(f37,plain,(
% 0.22/0.41 ? [X0,X1] : (? [X2] : (! [X3] : (((in @ X3 @ X2) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) != $true)) & ((in @ X2 @ (powerset @ X0)) = $true) & ((subset @ X1 @ X2) != $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2] : (! [X3] : (((in @ X3 @ X2) = $true) | ((in @ X3 @ sK5) != $true) | ((in @ X3 @ sK6) != $true)) & ((in @ X2 @ (powerset @ sK5)) = $true) & ((subset @ sK6 @ X2) != $true)) & ((in @ sK6 @ (powerset @ sK5)) = $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f38,plain,(
% 0.22/0.41 ? [X2] : (! [X3] : (((in @ X3 @ X2) = $true) | ((in @ X3 @ sK5) != $true) | ((in @ X3 @ sK6) != $true)) & ((in @ X2 @ (powerset @ sK5)) = $true) & ((subset @ sK6 @ X2) != $true)) => (! [X3] : (((in @ X3 @ sK7) = $true) | ((in @ X3 @ sK5) != $true) | ((in @ X3 @ sK6) != $true)) & ((in @ sK7 @ (powerset @ sK5)) = $true) & ((subset @ sK6 @ sK7) != $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f39,plain,(
% 0.22/0.41 ! [X4,X5,X6] : (? [X7] : (((in @ X7 @ X6) != $true) & ((in @ X7 @ X4) = $true) & ((in @ X7 @ X5) = $true)) => (((in @ (sK8 @ X6 @ X5 @ X4) @ X6) != $true) & ((in @ (sK8 @ X6 @ X5 @ X4) @ X4) = $true) & ((in @ (sK8 @ X6 @ X5 @ X4) @ X5) = $true)))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f36,plain,(
% 0.22/0.41 ((subsetTI = $true) | ? [X0,X1] : (? [X2] : (! [X3] : (((in @ X3 @ X2) = $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) != $true)) & ((in @ X2 @ (powerset @ X0)) = $true) & ((subset @ X1 @ X2) != $true)) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X4,X5] : (! [X6] : (? [X7] : (((in @ X7 @ X6) != $true) & ((in @ X7 @ X4) = $true) & ((in @ X7 @ X5) = $true)) | ((in @ X6 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) = $true)) | ((in @ X5 @ (powerset @ X4)) != $true)) | (subsetTI != $true))),
% 0.22/0.41 inference(rectify,[],[f35])).
% 0.22/0.41 thf(f35,plain,(
% 0.22/0.41 ((subsetTI = $true) | ? [X1,X0] : (? [X2] : (! [X3] : (((in @ X3 @ X2) = $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X0) != $true)) & ((in @ X2 @ (powerset @ X1)) = $true) & ((subset @ X0 @ X2) != $true)) & ((in @ X0 @ (powerset @ X1)) = $true))) & (! [X1,X0] : (! [X2] : (? [X3] : (((in @ X3 @ X2) != $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true)) | ((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) | (subsetTI != $true))),
% 0.22/0.42 inference(nnf_transformation,[],[f23])).
% 0.22/0.42 thf(f23,plain,(
% 0.22/0.42 (subsetTI = $true) <=> ! [X1,X0] : (! [X2] : (? [X3] : (((in @ X3 @ X2) != $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X0) = $true)) | ((in @ X2 @ (powerset @ X1)) != $true) | ((subset @ X0 @ X2) = $true)) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 0.22/0.42 inference(flattening,[],[f22])).
% 0.22/0.42 thf(f22,plain,(
% 0.22/0.42 (subsetTI = $true) <=> ! [X1,X0] : (! [X2] : ((((subset @ X0 @ X2) = $true) | ? [X3] : ((((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X3 @ X1) = $true))) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 0.22/0.42 inference(ennf_transformation,[],[f13])).
% 0.22/0.42 thf(f13,plain,(
% 0.22/0.42 (subsetTI = $true) <=> ! [X1,X0] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X1)) = $true) => (! [X3] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ X0) = $true) => ((in @ X3 @ X2) = $true))) => ((subset @ X0 @ X2) = $true))))),
% 0.22/0.42 inference(fool_elimination,[],[f12])).
% 0.22/0.42 thf(f12,plain,(
% 0.22/0.42 (subsetTI = ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => (! [X3] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (subset @ X0 @ X2)))))),
% 0.22/0.42 inference(rectify,[],[f3])).
% 0.22/0.42 thf(f3,axiom,(
% 0.22/0.42 (subsetTI = ! [X1,X0] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => (! [X3] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (subset @ X1 @ X2)))))),
% 0.22/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI)).
% 0.22/0.42 thf(f156,plain,(
% 0.22/0.42 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK8 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (setminus @ X0 @ X1) @ X3) @ X0) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true)) )),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f155])).
% 0.22/0.42 thf(f155,plain,(
% 0.22/0.42 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)) != $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (sK8 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (setminus @ X0 @ X1) @ X3) @ X0) != $true) | ($true != $true)) )),
% 0.22/0.42 inference(duplicate_literal_removal,[],[f151])).
% 0.22/0.42 thf(f151,plain,(
% 0.22/0.42 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK8 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (setminus @ X0 @ X1) @ X3) @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)) != $true) | ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)) != $true) | ($true != $true) | ((subset @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true)) )),
% 0.22/0.42 inference(superposition,[],[f123,f101])).
% 0.22/0.42 thf(f101,plain,(
% 0.22/0.42 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK8 @ X6 @ X5 @ X4) @ X5) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) = $true)) )),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f91])).
% 0.22/0.42 thf(f91,plain,(
% 0.22/0.42 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK8 @ X6 @ X5 @ X4) @ X5) = $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ($true != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) = $true)) )),
% 0.22/0.42 inference(definition_unfolding,[],[f58,f66])).
% 0.22/0.42 thf(f58,plain,(
% 0.22/0.42 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK8 @ X6 @ X5 @ X4) @ X5) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) = $true) | ((in @ X5 @ (powerset @ X4)) != $true) | (subsetTI != $true)) )),
% 0.22/0.42 inference(cnf_transformation,[],[f40])).
% 0.22/0.42 thf(f123,plain,(
% 0.22/0.42 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ (sK8 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ X1)) != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X4)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((subset @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ (sK8 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ X0) != $true) | ((in @ X3 @ (powerset @ X4)) != $true)) )),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f122])).
% 0.22/0.42 thf(f122,plain,(
% 0.22/0.42 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((subset @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ (sK8 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ X0) != $true) | ((in @ X3 @ (powerset @ X4)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((in @ (sK8 @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ X1)) != $true) | ($true != $true) | ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X4)) != $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 0.22/0.42 inference(superposition,[],[f99,f103])).
% 0.22/0.42 thf(f103,plain,(
% 0.22/0.42 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ (setminus @ X5 @ (binintersect @ X4 @ X6))) = $true) | ((in @ X7 @ X5) != $true) | ((in @ X6 @ (powerset @ X5)) != $true) | ((in @ X7 @ (setminus @ X5 @ X4)) != $true) | ((in @ X4 @ (powerset @ X5)) != $true)) )),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f97])).
% 0.22/0.42 thf(f97,plain,(
% 0.22/0.42 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X4 @ (powerset @ X5)) != $true) | ((in @ X7 @ (setminus @ X5 @ (binintersect @ X4 @ X6))) = $true) | ((in @ X6 @ (powerset @ X5)) != $true) | ((in @ X7 @ X5) != $true) | ((in @ X7 @ (setminus @ X5 @ X4)) != $true)) )),
% 0.22/0.42 inference(definition_unfolding,[],[f72,f67])).
% 0.22/0.42 thf(f67,plain,(
% 0.22/0.42 (complementImpComplementIntersect = $true)),
% 0.22/0.42 inference(cnf_transformation,[],[f44])).
% 0.22/0.42 thf(f72,plain,(
% 0.22/0.42 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X5)) != $true) | ((in @ X6 @ (powerset @ X5)) != $true) | ((in @ X7 @ (setminus @ X5 @ X4)) != $true) | ((in @ X7 @ (setminus @ X5 @ (binintersect @ X4 @ X6))) = $true) | ((in @ X7 @ X5) != $true) | (complementImpComplementIntersect != $true)) )),
% 0.22/0.42 inference(cnf_transformation,[],[f50])).
% 0.22/0.42 thf(f50,plain,(
% 0.22/0.42 ((complementImpComplementIntersect = $true) | (((in @ sK12 @ (powerset @ sK13)) = $true) & (((in @ sK14 @ (powerset @ sK13)) = $true) & (((in @ sK15 @ (setminus @ sK13 @ sK12)) = $true) & ((in @ sK15 @ (setminus @ sK13 @ (binintersect @ sK12 @ sK14))) != $true) & ((in @ sK15 @ sK13) = $true))))) & (! [X4,X5] : (((in @ X4 @ (powerset @ X5)) != $true) | ! [X6] : (((in @ X6 @ (powerset @ X5)) != $true) | ! [X7] : (((in @ X7 @ (setminus @ X5 @ X4)) != $true) | ((in @ X7 @ (setminus @ X5 @ (binintersect @ X4 @ X6))) = $true) | ((in @ X7 @ X5) != $true)))) | (complementImpComplementIntersect != $true))),
% 0.22/0.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15])],[f46,f49,f48,f47])).
% 0.22/0.42 thf(f47,plain,(
% 0.22/0.42 ? [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ X1 @ X0)) = $true) & ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) != $true) & ((in @ X3 @ X1) = $true)))) => (((in @ sK12 @ (powerset @ sK13)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ sK13)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ sK13 @ sK12)) = $true) & ((in @ X3 @ (setminus @ sK13 @ (binintersect @ sK12 @ X2))) != $true) & ((in @ X3 @ sK13) = $true))))),
% 0.22/0.42 introduced(choice_axiom,[])).
% 0.22/0.42 thf(f48,plain,(
% 0.22/0.42 ? [X2] : (((in @ X2 @ (powerset @ sK13)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ sK13 @ sK12)) = $true) & ((in @ X3 @ (setminus @ sK13 @ (binintersect @ sK12 @ X2))) != $true) & ((in @ X3 @ sK13) = $true))) => (((in @ sK14 @ (powerset @ sK13)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ sK13 @ sK12)) = $true) & ((in @ X3 @ (setminus @ sK13 @ (binintersect @ sK12 @ sK14))) != $true) & ((in @ X3 @ sK13) = $true)))),
% 0.22/0.42 introduced(choice_axiom,[])).
% 0.22/0.42 thf(f49,plain,(
% 0.22/0.42 ? [X3] : (((in @ X3 @ (setminus @ sK13 @ sK12)) = $true) & ((in @ X3 @ (setminus @ sK13 @ (binintersect @ sK12 @ sK14))) != $true) & ((in @ X3 @ sK13) = $true)) => (((in @ sK15 @ (setminus @ sK13 @ sK12)) = $true) & ((in @ sK15 @ (setminus @ sK13 @ (binintersect @ sK12 @ sK14))) != $true) & ((in @ sK15 @ sK13) = $true))),
% 0.22/0.42 introduced(choice_axiom,[])).
% 0.22/0.42 thf(f46,plain,(
% 0.22/0.42 ((complementImpComplementIntersect = $true) | ? [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ X1 @ X0)) = $true) & ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) != $true) & ((in @ X3 @ X1) = $true))))) & (! [X4,X5] : (((in @ X4 @ (powerset @ X5)) != $true) | ! [X6] : (((in @ X6 @ (powerset @ X5)) != $true) | ! [X7] : (((in @ X7 @ (setminus @ X5 @ X4)) != $true) | ((in @ X7 @ (setminus @ X5 @ (binintersect @ X4 @ X6))) = $true) | ((in @ X7 @ X5) != $true)))) | (complementImpComplementIntersect != $true))),
% 0.22/0.42 inference(rectify,[],[f45])).
% 0.22/0.42 thf(f45,plain,(
% 0.22/0.42 ((complementImpComplementIntersect = $true) | ? [X1,X0] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ X0 @ X1)) = $true) & ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) != $true) & ((in @ X3 @ X0) = $true))))) & (! [X1,X0] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3] : (((in @ X3 @ (setminus @ X0 @ X1)) != $true) | ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X3 @ X0) != $true)))) | (complementImpComplementIntersect != $true))),
% 0.22/0.42 inference(nnf_transformation,[],[f25])).
% 0.22/0.42 thf(f25,plain,(
% 0.22/0.42 (complementImpComplementIntersect = $true) <=> ! [X1,X0] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3] : (((in @ X3 @ (setminus @ X0 @ X1)) != $true) | ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X3 @ X0) != $true))))),
% 0.22/0.42 inference(flattening,[],[f24])).
% 0.22/0.42 thf(f24,plain,(
% 0.22/0.42 (complementImpComplementIntersect = $true) <=> ! [X0,X1] : (! [X2] : (! [X3] : ((((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true) | ((in @ X3 @ (setminus @ X0 @ X1)) != $true)) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 0.22/0.42 inference(ennf_transformation,[],[f9])).
% 0.22/0.42 thf(f9,plain,(
% 0.22/0.42 (complementImpComplementIntersect = $true) <=> ! [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ (setminus @ X0 @ X1)) = $true) => ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) = $true)))))),
% 0.22/0.42 inference(fool_elimination,[],[f8])).
% 0.22/0.42 thf(f8,plain,(
% 0.22/0.42 (! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))) = complementImpComplementIntersect)),
% 0.22/0.42 inference(rectify,[],[f4])).
% 0.22/0.42 thf(f4,axiom,(
% 0.22/0.42 (! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))) = complementImpComplementIntersect)),
% 0.22/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementImpComplementIntersect)).
% 0.22/0.42 thf(f99,plain,(
% 0.22/0.42 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK8 @ X6 @ X5 @ X4) @ X6) != $true) | ((subset @ X5 @ X6) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true)) )),
% 0.22/0.42 inference(trivial_inequality_removal,[],[f89])).
% 0.22/0.42 thf(f89,plain,(
% 0.22/0.42 ( ! [X6 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ (sK8 @ X6 @ X5 @ X4) @ X6) != $true)) )),
% 0.22/0.42 inference(definition_unfolding,[],[f60,f66])).
% 0.22/0.42 thf(f60,plain,(
% 0.22/0.42 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK8 @ X6 @ X5 @ X4) @ X6) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) = $true) | ((in @ X5 @ (powerset @ X4)) != $true) | (subsetTI != $true)) )),
% 0.22/0.42 inference(cnf_transformation,[],[f40])).
% 0.22/0.42 thf(f69,plain,(
% 0.22/0.42 ((subset @ (setminus @ sK10 @ sK9) @ (setminus @ sK10 @ (binintersect @ sK9 @ sK11))) != $true)),
% 0.22/0.42 inference(cnf_transformation,[],[f44])).
% 0.22/0.42 % SZS output end Proof for theBenchmark
% 0.22/0.42 % (11264)------------------------------
% 0.22/0.42 % (11264)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.42 % (11264)Termination reason: Refutation
% 0.22/0.42
% 0.22/0.42 % (11264)Memory used [KB]: 5756
% 0.22/0.42 % (11264)Time elapsed: 0.035 s
% 0.22/0.42 % (11264)Instructions burned: 44 (million)
% 0.22/0.42 % (11264)------------------------------
% 0.22/0.42 % (11264)------------------------------
% 0.22/0.42 % (11256)Success in time 0.038 s
% 0.22/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------