TSTP Solution File: SEU762^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU762^2 : 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 : n010.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 03:51:20 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU762^2 : TPTP v8.2.0. Released v3.7.0.
% 0.12/0.14 % 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
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 16:05:52 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.21/0.35 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
% 0.21/0.37 % (31972)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 % (31975)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 % (31976)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 % (31971)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 % (31975)Instruction limit reached!
% 0.21/0.37 % (31975)------------------------------
% 0.21/0.37 % (31975)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (31975)Termination reason: Unknown
% 0.21/0.37 % (31975)Termination phase: shuffling
% 0.21/0.37
% 0.21/0.37 % (31975)Memory used [KB]: 1023
% 0.21/0.37 % (31975)Time elapsed: 0.003 s
% 0.21/0.37 % (31975)Instructions burned: 2 (million)
% 0.21/0.37 % (31975)------------------------------
% 0.21/0.37 % (31975)------------------------------
% 0.21/0.37 % (31972)Instruction limit reached!
% 0.21/0.37 % (31972)------------------------------
% 0.21/0.37 % (31972)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (31972)Termination reason: Unknown
% 0.21/0.37 % (31972)Termination phase: Saturation
% 0.21/0.37
% 0.21/0.37 % (31972)Memory used [KB]: 5500
% 0.21/0.37 % (31972)Time elapsed: 0.005 s
% 0.21/0.37 % (31972)Instructions burned: 5 (million)
% 0.21/0.37 % (31972)------------------------------
% 0.21/0.37 % (31972)------------------------------
% 0.21/0.37 % (31973)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)
% 0.21/0.38 % (31976)First to succeed.
% 0.21/0.38 % (31977)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (31978)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 % (31979)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)
% 0.21/0.38 % (31974)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (31974)Instruction limit reached!
% 0.21/0.38 % (31974)------------------------------
% 0.21/0.38 % (31974)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (31974)Termination reason: Unknown
% 0.21/0.38 % (31974)Termination phase: Property scanning
% 0.21/0.38
% 0.21/0.38 % (31974)Memory used [KB]: 895
% 0.21/0.38 % (31974)Time elapsed: 0.003 s
% 0.21/0.38 % (31974)Instructions burned: 2 (million)
% 0.21/0.38 % (31974)------------------------------
% 0.21/0.38 % (31974)------------------------------
% 0.21/0.38 % (31978)Instruction limit reached!
% 0.21/0.38 % (31978)------------------------------
% 0.21/0.38 % (31978)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (31978)Termination reason: Unknown
% 0.21/0.38 % (31978)Termination phase: Function definition elimination
% 0.21/0.38
% 0.21/0.38 % (31978)Memory used [KB]: 1023
% 0.21/0.38 % (31978)Time elapsed: 0.004 s
% 0.21/0.38 % (31978)Instructions burned: 4 (million)
% 0.21/0.38 % (31978)------------------------------
% 0.21/0.38 % (31978)------------------------------
% 0.21/0.38 % (31980)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)
% 0.21/0.38 % (31976)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% 0.21/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.38 thf(func_def_1, type, powerset: $i > $i).
% 0.21/0.38 thf(func_def_2, type, subset: $i > $i > $o).
% 0.21/0.38 thf(func_def_3, type, binintersect: $i > $i > $i).
% 0.21/0.38 thf(f197,plain,(
% 0.21/0.38 $false),
% 0.21/0.38 inference(avatar_sat_refutation,[],[f148,f178,f188,f196])).
% 0.21/0.38 thf(f196,plain,(
% 0.21/0.38 ~spl20_5),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f195])).
% 0.21/0.38 thf(f195,plain,(
% 0.21/0.38 $false | ~spl20_5),
% 0.21/0.38 inference(subsumption_resolution,[],[f194,f68])).
% 0.21/0.38 thf(f68,plain,(
% 0.21/0.38 ($true = (in @ sK4 @ (powerset @ sK5)))),
% 0.21/0.38 inference(cnf_transformation,[],[f37])).
% 0.21/0.38 thf(f37,plain,(
% 0.21/0.38 (woz13rule1 = $true) & (woz13rule3 = $true) & (woz13rule2 = $true) & (($true = (in @ sK4 @ (powerset @ sK5))) & (($true = (in @ sK6 @ (powerset @ sK5))) & (($true = (in @ sK7 @ (powerset @ sK5))) & (($true != (subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ sK7 @ sK8))) & ((in @ sK8 @ (powerset @ sK5)) = $true) & ((subset @ sK4 @ sK7) = $true) & ((subset @ sK6 @ sK8) = $true))))) & (binintersectT_lem = $true)),
% 0.21/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f24,f36,f35,f34,f33])).
% 0.21/0.38 thf(f33,plain,(
% 0.21/0.38 ? [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3] : (($true = (in @ X3 @ (powerset @ X1))) & ? [X4] : (((subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4)) != $true) & ($true = (in @ X4 @ (powerset @ X1))) & ($true = (subset @ X0 @ X3)) & ((subset @ X2 @ X4) = $true))))) => (($true = (in @ sK4 @ (powerset @ sK5))) & ? [X2] : (($true = (in @ X2 @ (powerset @ sK5))) & ? [X3] : (((in @ X3 @ (powerset @ sK5)) = $true) & ? [X4] : (($true != (subset @ (binintersect @ sK4 @ X2) @ (binintersect @ X3 @ X4))) & ($true = (in @ X4 @ (powerset @ sK5))) & ($true = (subset @ sK4 @ X3)) & ((subset @ X2 @ X4) = $true)))))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f34,plain,(
% 0.21/0.38 ? [X2] : (($true = (in @ X2 @ (powerset @ sK5))) & ? [X3] : (((in @ X3 @ (powerset @ sK5)) = $true) & ? [X4] : (($true != (subset @ (binintersect @ sK4 @ X2) @ (binintersect @ X3 @ X4))) & ($true = (in @ X4 @ (powerset @ sK5))) & ($true = (subset @ sK4 @ X3)) & ((subset @ X2 @ X4) = $true)))) => (($true = (in @ sK6 @ (powerset @ sK5))) & ? [X3] : (((in @ X3 @ (powerset @ sK5)) = $true) & ? [X4] : (($true != (subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ X3 @ X4))) & ($true = (in @ X4 @ (powerset @ sK5))) & ($true = (subset @ sK4 @ X3)) & ($true = (subset @ sK6 @ X4)))))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f35,plain,(
% 0.21/0.38 ? [X3] : (((in @ X3 @ (powerset @ sK5)) = $true) & ? [X4] : (($true != (subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ X3 @ X4))) & ($true = (in @ X4 @ (powerset @ sK5))) & ($true = (subset @ sK4 @ X3)) & ($true = (subset @ sK6 @ X4)))) => (($true = (in @ sK7 @ (powerset @ sK5))) & ? [X4] : (($true != (subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ sK7 @ X4))) & ($true = (in @ X4 @ (powerset @ sK5))) & ((subset @ sK4 @ sK7) = $true) & ($true = (subset @ sK6 @ X4))))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f36,plain,(
% 0.21/0.38 ? [X4] : (($true != (subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ sK7 @ X4))) & ($true = (in @ X4 @ (powerset @ sK5))) & ((subset @ sK4 @ sK7) = $true) & ($true = (subset @ sK6 @ X4))) => (($true != (subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ sK7 @ sK8))) & ((in @ sK8 @ (powerset @ sK5)) = $true) & ((subset @ sK4 @ sK7) = $true) & ((subset @ sK6 @ sK8) = $true))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f24,plain,(
% 0.21/0.38 (woz13rule1 = $true) & (woz13rule3 = $true) & (woz13rule2 = $true) & ? [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3] : (($true = (in @ X3 @ (powerset @ X1))) & ? [X4] : (((subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4)) != $true) & ($true = (in @ X4 @ (powerset @ X1))) & ($true = (subset @ X0 @ X3)) & ((subset @ X2 @ X4) = $true))))) & (binintersectT_lem = $true)),
% 0.21/0.38 inference(flattening,[],[f23])).
% 0.21/0.38 thf(f23,plain,(
% 0.21/0.38 (((? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (((((subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4)) != $true) & ((subset @ X2 @ X4) = $true)) & ($true = (subset @ X0 @ X3))) & ($true = (in @ X4 @ (powerset @ X1)))) & ($true = (in @ X3 @ (powerset @ X1)))) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (binintersectT_lem = $true)),
% 0.21/0.38 inference(ennf_transformation,[],[f15])).
% 0.21/0.38 thf(f15,plain,(
% 0.21/0.38 ~((binintersectT_lem = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ! [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3] : (($true = (in @ X3 @ (powerset @ X1))) => ! [X4] : (($true = (in @ X4 @ (powerset @ X1))) => (($true = (subset @ X0 @ X3)) => (((subset @ X2 @ X4) = $true) => ((subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4)) = $true)))))))))))),
% 0.21/0.38 inference(fool_elimination,[],[f14])).
% 0.21/0.38 thf(f14,plain,(
% 0.21/0.38 ~(binintersectT_lem => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => ! [X3] : ((in @ X3 @ (powerset @ X1)) => ! [X4] : ((in @ X4 @ (powerset @ X1)) => ((subset @ X0 @ X3) => ((subset @ X2 @ X4) => (subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4))))))))))))),
% 0.21/0.38 inference(rectify,[],[f6])).
% 0.21/0.38 thf(f6,negated_conjecture,(
% 0.21/0.38 ~(binintersectT_lem => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X1,X0] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ((subset @ X1 @ X3) => ((subset @ X2 @ X4) => (subset @ (binintersect @ X1 @ X2) @ (binintersect @ X3 @ X4))))))))))))),
% 0.21/0.38 inference(negated_conjecture,[],[f5])).
% 0.21/0.38 thf(f5,conjecture,(
% 0.21/0.38 binintersectT_lem => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X1,X0] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ((subset @ X1 @ X3) => ((subset @ X2 @ X4) => (subset @ (binintersect @ X1 @ X2) @ (binintersect @ X3 @ X4)))))))))))),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule4)).
% 0.21/0.38 thf(f194,plain,(
% 0.21/0.38 ($true != (in @ sK4 @ (powerset @ sK5))) | ~spl20_5),
% 0.21/0.38 inference(subsumption_resolution,[],[f193,f66])).
% 0.21/0.38 thf(f66,plain,(
% 0.21/0.38 ($true = (in @ sK7 @ (powerset @ sK5)))),
% 0.21/0.38 inference(cnf_transformation,[],[f37])).
% 0.21/0.38 thf(f193,plain,(
% 0.21/0.38 ($true != (in @ sK7 @ (powerset @ sK5))) | ($true != (in @ sK4 @ (powerset @ sK5))) | ~spl20_5),
% 0.21/0.38 inference(subsumption_resolution,[],[f192,f67])).
% 0.21/0.38 thf(f67,plain,(
% 0.21/0.38 ($true = (in @ sK6 @ (powerset @ sK5)))),
% 0.21/0.38 inference(cnf_transformation,[],[f37])).
% 0.21/0.38 thf(f192,plain,(
% 0.21/0.38 ($true != (in @ sK6 @ (powerset @ sK5))) | ($true != (in @ sK4 @ (powerset @ sK5))) | ($true != (in @ sK7 @ (powerset @ sK5))) | ~spl20_5),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f191])).
% 0.21/0.38 thf(f191,plain,(
% 0.21/0.38 ($true != $true) | ($true != (in @ sK4 @ (powerset @ sK5))) | ($true != (in @ sK6 @ (powerset @ sK5))) | ($true != (in @ sK7 @ (powerset @ sK5))) | ~spl20_5),
% 0.21/0.38 inference(superposition,[],[f190,f64])).
% 0.21/0.38 thf(f64,plain,(
% 0.21/0.38 ((in @ sK8 @ (powerset @ sK5)) = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f37])).
% 0.21/0.38 thf(f190,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true != (in @ sK8 @ (powerset @ X0))) | ($true != (in @ sK4 @ (powerset @ X0))) | ($true != (in @ sK6 @ (powerset @ X0))) | ($true != (in @ sK7 @ (powerset @ X0)))) ) | ~spl20_5),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f189])).
% 0.21/0.38 thf(f189,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true != (in @ sK4 @ (powerset @ X0))) | ($true != (in @ sK8 @ (powerset @ X0))) | ($true != (in @ sK6 @ (powerset @ X0))) | ($true != (in @ sK7 @ (powerset @ X0))) | ($true != $true)) ) | ~spl20_5),
% 0.21/0.38 inference(superposition,[],[f143,f113])).
% 0.21/0.38 thf(f113,plain,(
% 0.21/0.38 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | ((in @ X4 @ (powerset @ X3)) != $true) | ($true != (in @ X5 @ (powerset @ X3)))) )),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f104])).
% 0.21/0.38 thf(f104,plain,(
% 0.21/0.38 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X3)) != $true) | ($true != (in @ X5 @ (powerset @ X3))) | ($true != $true) | ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true)) )),
% 0.21/0.38 inference(definition_unfolding,[],[f78,f61])).
% 0.21/0.38 thf(f61,plain,(
% 0.21/0.38 (binintersectT_lem = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f37])).
% 0.21/0.38 thf(f78,plain,(
% 0.21/0.38 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (powerset @ X3)) != $true) | ((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | ($true != (in @ X5 @ (powerset @ X3))) | (binintersectT_lem != $true)) )),
% 0.21/0.38 inference(cnf_transformation,[],[f48])).
% 0.21/0.38 thf(f48,plain,(
% 0.21/0.38 ((binintersectT_lem = $true) | (($true = (in @ sK14 @ (powerset @ sK13))) & (($true != (in @ (binintersect @ sK14 @ sK15) @ (powerset @ sK13))) & ((in @ sK15 @ (powerset @ sK13)) = $true)))) & (! [X3,X4] : (((in @ X4 @ (powerset @ X3)) != $true) | ! [X5] : (((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | ($true != (in @ X5 @ (powerset @ X3))))) | (binintersectT_lem != $true))),
% 0.21/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f45,f47,f46])).
% 0.21/0.38 thf(f46,plain,(
% 0.21/0.38 ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) != $true) & ((in @ X2 @ (powerset @ X0)) = $true))) => (($true = (in @ sK14 @ (powerset @ sK13))) & ? [X2] : (($true != (in @ (binintersect @ sK14 @ X2) @ (powerset @ sK13))) & ($true = (in @ X2 @ (powerset @ sK13)))))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f47,plain,(
% 0.21/0.38 ? [X2] : (($true != (in @ (binintersect @ sK14 @ X2) @ (powerset @ sK13))) & ($true = (in @ X2 @ (powerset @ sK13)))) => (($true != (in @ (binintersect @ sK14 @ sK15) @ (powerset @ sK13))) & ((in @ sK15 @ (powerset @ sK13)) = $true))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f45,plain,(
% 0.21/0.38 ((binintersectT_lem = $true) | ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)))) & (! [X3,X4] : (((in @ X4 @ (powerset @ X3)) != $true) | ! [X5] : (((in @ (binintersect @ X4 @ X5) @ (powerset @ X3)) = $true) | ($true != (in @ X5 @ (powerset @ X3))))) | (binintersectT_lem != $true))),
% 0.21/0.38 inference(rectify,[],[f44])).
% 0.21/0.38 thf(f44,plain,(
% 0.21/0.38 ((binintersectT_lem = $true) | ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)))) & (! [X0,X1] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true))) | (binintersectT_lem != $true))),
% 0.21/0.38 inference(nnf_transformation,[],[f22])).
% 0.21/0.38 thf(f22,plain,(
% 0.21/0.38 (binintersectT_lem = $true) <=> ! [X0,X1] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2] : (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true) | ((in @ X2 @ (powerset @ X0)) != $true)))),
% 0.21/0.38 inference(ennf_transformation,[],[f9])).
% 0.21/0.38 thf(f9,plain,(
% 0.21/0.38 ! [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X0)) = $true) => ((in @ (binintersect @ X1 @ X2) @ (powerset @ X0)) = $true))) <=> (binintersectT_lem = $true)),
% 0.21/0.38 inference(fool_elimination,[],[f8])).
% 0.21/0.38 thf(f8,plain,(
% 0.21/0.38 (binintersectT_lem = ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 0.21/0.38 inference(rectify,[],[f1])).
% 0.21/0.38 thf(f1,axiom,(
% 0.21/0.38 (binintersectT_lem = ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem)).
% 0.21/0.38 thf(f143,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true != (in @ (binintersect @ sK4 @ sK6) @ (powerset @ X0))) | ($true != (in @ sK7 @ (powerset @ X0))) | ($true != (in @ sK8 @ (powerset @ X0)))) ) | ~spl20_5),
% 0.21/0.38 inference(avatar_component_clause,[],[f142])).
% 0.21/0.38 thf(f142,plain,(
% 0.21/0.38 spl20_5 <=> ! [X0] : (($true != (in @ (binintersect @ sK4 @ sK6) @ (powerset @ X0))) | ($true != (in @ sK7 @ (powerset @ X0))) | ($true != (in @ sK8 @ (powerset @ X0))))),
% 0.21/0.38 introduced(avatar_definition,[new_symbols(naming,[spl20_5])])).
% 0.21/0.38 thf(f188,plain,(
% 0.21/0.38 spl20_6),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f187])).
% 0.21/0.38 thf(f187,plain,(
% 0.21/0.38 $false | spl20_6),
% 0.21/0.38 inference(subsumption_resolution,[],[f186,f67])).
% 0.21/0.38 thf(f186,plain,(
% 0.21/0.38 ($true != (in @ sK6 @ (powerset @ sK5))) | spl20_6),
% 0.21/0.38 inference(subsumption_resolution,[],[f185,f68])).
% 0.21/0.38 thf(f185,plain,(
% 0.21/0.38 ($true != (in @ sK4 @ (powerset @ sK5))) | ($true != (in @ sK6 @ (powerset @ sK5))) | spl20_6),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f184])).
% 0.21/0.38 thf(f184,plain,(
% 0.21/0.38 ($true != (in @ sK6 @ (powerset @ sK5))) | ($true != $true) | ($true != (in @ sK4 @ (powerset @ sK5))) | spl20_6),
% 0.21/0.38 inference(superposition,[],[f183,f64])).
% 0.21/0.38 thf(f183,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true != (in @ sK8 @ (powerset @ X0))) | ($true != (in @ sK6 @ (powerset @ X0))) | ($true != (in @ sK4 @ (powerset @ X0)))) ) | spl20_6),
% 0.21/0.38 inference(subsumption_resolution,[],[f181,f62])).
% 0.21/0.38 thf(f62,plain,(
% 0.21/0.38 ((subset @ sK6 @ sK8) = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f37])).
% 0.21/0.38 thf(f181,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true != (in @ sK8 @ (powerset @ X0))) | ((subset @ sK6 @ sK8) != $true) | ($true != (in @ sK6 @ (powerset @ X0))) | ($true != (in @ sK4 @ (powerset @ X0)))) ) | spl20_6),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f180])).
% 0.21/0.38 thf(f180,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true != (in @ sK6 @ (powerset @ X0))) | ($true != (in @ sK4 @ (powerset @ X0))) | ($true != $true) | ($true != (in @ sK8 @ (powerset @ X0))) | ((subset @ sK6 @ sK8) != $true)) ) | spl20_6),
% 0.21/0.38 inference(superposition,[],[f147,f112])).
% 0.21/0.38 thf(f112,plain,(
% 0.21/0.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((subset @ (binintersect @ X4 @ X6) @ X7) = $true) | ($true != (subset @ X6 @ X7)) | ($true != (in @ X7 @ (powerset @ X5))) | ($true != (in @ X4 @ (powerset @ X5))) | ($true != (in @ X6 @ (powerset @ X5)))) )),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f94])).
% 0.21/0.38 thf(f94,plain,(
% 0.21/0.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (in @ X7 @ (powerset @ X5))) | ($true != (subset @ X6 @ X7)) | ($true != (in @ X6 @ (powerset @ X5))) | ($true != (in @ X4 @ (powerset @ X5))) | ((subset @ (binintersect @ X4 @ X6) @ X7) = $true) | ($true != $true)) )),
% 0.21/0.38 inference(definition_unfolding,[],[f55,f69])).
% 0.21/0.38 thf(f69,plain,(
% 0.21/0.38 (woz13rule2 = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f37])).
% 0.21/0.38 thf(f55,plain,(
% 0.21/0.38 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (in @ X6 @ (powerset @ X5))) | ($true != (in @ X7 @ (powerset @ X5))) | ((subset @ (binintersect @ X4 @ X6) @ X7) = $true) | ($true != (subset @ X6 @ X7)) | ($true != (in @ X4 @ (powerset @ X5))) | (woz13rule2 != $true)) )),
% 0.21/0.38 inference(cnf_transformation,[],[f32])).
% 0.21/0.38 thf(f32,plain,(
% 0.21/0.38 ((woz13rule2 = $true) | ((((in @ sK2 @ (powerset @ sK1)) = $true) & (($true = (in @ sK3 @ (powerset @ sK1))) & ($true != (subset @ (binintersect @ sK0 @ sK2) @ sK3)) & ($true = (subset @ sK2 @ sK3)))) & ($true = (in @ sK0 @ (powerset @ sK1))))) & (! [X4,X5] : (! [X6] : (($true != (in @ X6 @ (powerset @ X5))) | ! [X7] : (($true != (in @ X7 @ (powerset @ X5))) | ((subset @ (binintersect @ X4 @ X6) @ X7) = $true) | ($true != (subset @ X6 @ X7)))) | ($true != (in @ X4 @ (powerset @ X5)))) | (woz13rule2 != $true))),
% 0.21/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f28,f31,f30,f29])).
% 0.21/0.38 thf(f29,plain,(
% 0.21/0.38 ? [X0,X1] : (? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3] : (($true = (in @ X3 @ (powerset @ X1))) & ($true != (subset @ (binintersect @ X0 @ X2) @ X3)) & ((subset @ X2 @ X3) = $true))) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2] : (((in @ X2 @ (powerset @ sK1)) = $true) & ? [X3] : (((in @ X3 @ (powerset @ sK1)) = $true) & ($true != (subset @ (binintersect @ sK0 @ X2) @ X3)) & ((subset @ X2 @ X3) = $true))) & ($true = (in @ sK0 @ (powerset @ sK1))))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f30,plain,(
% 0.21/0.38 ? [X2] : (((in @ X2 @ (powerset @ sK1)) = $true) & ? [X3] : (((in @ X3 @ (powerset @ sK1)) = $true) & ($true != (subset @ (binintersect @ sK0 @ X2) @ X3)) & ((subset @ X2 @ X3) = $true))) => (((in @ sK2 @ (powerset @ sK1)) = $true) & ? [X3] : (((in @ X3 @ (powerset @ sK1)) = $true) & ($true != (subset @ (binintersect @ sK0 @ sK2) @ X3)) & ($true = (subset @ sK2 @ X3))))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f31,plain,(
% 0.21/0.38 ? [X3] : (((in @ X3 @ (powerset @ sK1)) = $true) & ($true != (subset @ (binintersect @ sK0 @ sK2) @ X3)) & ($true = (subset @ sK2 @ X3))) => (($true = (in @ sK3 @ (powerset @ sK1))) & ($true != (subset @ (binintersect @ sK0 @ sK2) @ sK3)) & ($true = (subset @ sK2 @ sK3)))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f28,plain,(
% 0.21/0.38 ((woz13rule2 = $true) | ? [X0,X1] : (? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3] : (($true = (in @ X3 @ (powerset @ X1))) & ($true != (subset @ (binintersect @ X0 @ X2) @ X3)) & ((subset @ X2 @ X3) = $true))) & ((in @ X0 @ (powerset @ X1)) = $true))) & (! [X4,X5] : (! [X6] : (($true != (in @ X6 @ (powerset @ X5))) | ! [X7] : (($true != (in @ X7 @ (powerset @ X5))) | ((subset @ (binintersect @ X4 @ X6) @ X7) = $true) | ($true != (subset @ X6 @ X7)))) | ($true != (in @ X4 @ (powerset @ X5)))) | (woz13rule2 != $true))),
% 0.21/0.38 inference(rectify,[],[f27])).
% 0.21/0.38 thf(f27,plain,(
% 0.21/0.38 ((woz13rule2 = $true) | ? [X0,X1] : (? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3] : (($true = (in @ X3 @ (powerset @ X1))) & ($true != (subset @ (binintersect @ X0 @ X2) @ X3)) & ((subset @ X2 @ X3) = $true))) & ((in @ X0 @ (powerset @ X1)) = $true))) & (! [X0,X1] : (! [X2] : (($true != (in @ X2 @ (powerset @ X1))) | ! [X3] : (($true != (in @ X3 @ (powerset @ X1))) | ($true = (subset @ (binintersect @ X0 @ X2) @ X3)) | ((subset @ X2 @ X3) != $true))) | ((in @ X0 @ (powerset @ X1)) != $true)) | (woz13rule2 != $true))),
% 0.21/0.38 inference(nnf_transformation,[],[f26])).
% 0.21/0.38 thf(f26,plain,(
% 0.21/0.38 (woz13rule2 = $true) <=> ! [X0,X1] : (! [X2] : (($true != (in @ X2 @ (powerset @ X1))) | ! [X3] : (($true != (in @ X3 @ (powerset @ X1))) | ($true = (subset @ (binintersect @ X0 @ X2) @ X3)) | ((subset @ X2 @ X3) != $true))) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 0.21/0.38 inference(flattening,[],[f25])).
% 0.21/0.38 thf(f25,plain,(
% 0.21/0.38 (woz13rule2 = $true) <=> ! [X0,X1] : (! [X2] : (! [X3] : ((($true = (subset @ (binintersect @ X0 @ X2) @ X3)) | ((subset @ X2 @ X3) != $true)) | ($true != (in @ X3 @ (powerset @ X1)))) | ($true != (in @ X2 @ (powerset @ X1)))) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 0.21/0.38 inference(ennf_transformation,[],[f17])).
% 0.21/0.38 thf(f17,plain,(
% 0.21/0.38 (woz13rule2 = $true) <=> ! [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3] : (($true = (in @ X3 @ (powerset @ X1))) => (((subset @ X2 @ X3) = $true) => ($true = (subset @ (binintersect @ X0 @ X2) @ X3))))))),
% 0.21/0.38 inference(fool_elimination,[],[f16])).
% 0.21/0.38 thf(f16,plain,(
% 0.21/0.38 (woz13rule2 = ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => ! [X3] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X0 @ X2) @ X3))))))),
% 0.21/0.38 inference(rectify,[],[f3])).
% 0.21/0.38 thf(f3,axiom,(
% 0.21/0.38 (woz13rule2 = ! [X1,X0] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X2 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule2)).
% 0.21/0.39 thf(f147,plain,(
% 0.21/0.39 ($true != (subset @ (binintersect @ sK4 @ sK6) @ sK8)) | spl20_6),
% 0.21/0.39 inference(avatar_component_clause,[],[f145])).
% 0.21/0.39 thf(f145,plain,(
% 0.21/0.39 spl20_6 <=> ($true = (subset @ (binintersect @ sK4 @ sK6) @ sK8))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl20_6])])).
% 0.21/0.39 thf(f178,plain,(
% 0.21/0.39 spl20_4),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f177])).
% 0.21/0.39 thf(f177,plain,(
% 0.21/0.39 $false | spl20_4),
% 0.21/0.39 inference(subsumption_resolution,[],[f176,f67])).
% 0.21/0.39 thf(f176,plain,(
% 0.21/0.39 ($true != (in @ sK6 @ (powerset @ sK5))) | spl20_4),
% 0.21/0.39 inference(subsumption_resolution,[],[f175,f68])).
% 0.21/0.39 thf(f175,plain,(
% 0.21/0.39 ($true != (in @ sK4 @ (powerset @ sK5))) | ($true != (in @ sK6 @ (powerset @ sK5))) | spl20_4),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f174])).
% 0.21/0.39 thf(f174,plain,(
% 0.21/0.39 ($true != (in @ sK4 @ (powerset @ sK5))) | ($true != $true) | ($true != (in @ sK6 @ (powerset @ sK5))) | spl20_4),
% 0.21/0.39 inference(superposition,[],[f173,f66])).
% 0.21/0.39 thf(f173,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($true != (in @ sK7 @ (powerset @ X0))) | ($true != (in @ sK4 @ (powerset @ X0))) | ($true != (in @ sK6 @ (powerset @ X0)))) ) | spl20_4),
% 0.21/0.39 inference(subsumption_resolution,[],[f171,f63])).
% 0.21/0.39 thf(f63,plain,(
% 0.21/0.39 ((subset @ sK4 @ sK7) = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f37])).
% 0.21/0.39 thf(f171,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($true != (in @ sK7 @ (powerset @ X0))) | ($true != (in @ sK4 @ (powerset @ X0))) | ((subset @ sK4 @ sK7) != $true) | ($true != (in @ sK6 @ (powerset @ X0)))) ) | spl20_4),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f169])).
% 0.21/0.39 thf(f169,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ sK7 @ (powerset @ X0))) | ((subset @ sK4 @ sK7) != $true) | ($true != (in @ sK6 @ (powerset @ X0))) | ($true != (in @ sK4 @ (powerset @ X0)))) ) | spl20_4),
% 0.21/0.39 inference(superposition,[],[f140,f115])).
% 0.21/0.39 thf(f115,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X2) @ X3) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ((subset @ X1 @ X3) != $true) | ((in @ X1 @ (powerset @ X0)) != $true) | ((in @ X3 @ (powerset @ X0)) != $true)) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f95])).
% 0.21/0.39 thf(f95,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != $true) | ((subset @ X1 @ X3) != $true) | ((subset @ (binintersect @ X1 @ X2) @ X3) = $true) | ((in @ X1 @ (powerset @ X0)) != $true)) )),
% 0.21/0.39 inference(definition_unfolding,[],[f77,f71])).
% 0.21/0.39 thf(f71,plain,(
% 0.21/0.39 (woz13rule1 = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f37])).
% 0.21/0.39 thf(f77,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) != $true) | ((subset @ (binintersect @ X1 @ X2) @ X3) = $true) | ((subset @ X1 @ X3) != $true) | ((in @ X3 @ (powerset @ X0)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | (woz13rule1 != $true)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f43])).
% 0.21/0.39 thf(f43,plain,(
% 0.21/0.39 (! [X0,X1] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2] : (! [X3] : (((subset @ (binintersect @ X1 @ X2) @ X3) = $true) | ((subset @ X1 @ X3) != $true) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (woz13rule1 != $true)) & ((woz13rule1 = $true) | (((in @ sK10 @ (powerset @ sK9)) = $true) & ((((subset @ (binintersect @ sK10 @ sK11) @ sK12) != $true) & ((subset @ sK10 @ sK12) = $true) & ((in @ sK12 @ (powerset @ sK9)) = $true)) & ($true = (in @ sK11 @ (powerset @ sK9))))))),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f39,f42,f41,f40])).
% 0.21/0.39 thf(f40,plain,(
% 0.21/0.39 ? [X4,X5] : (($true = (in @ X5 @ (powerset @ X4))) & ? [X6] : (? [X7] : (((subset @ (binintersect @ X5 @ X6) @ X7) != $true) & ($true = (subset @ X5 @ X7)) & ($true = (in @ X7 @ (powerset @ X4)))) & ($true = (in @ X6 @ (powerset @ X4))))) => (((in @ sK10 @ (powerset @ sK9)) = $true) & ? [X6] : (? [X7] : (($true != (subset @ (binintersect @ sK10 @ X6) @ X7)) & ((subset @ sK10 @ X7) = $true) & ($true = (in @ X7 @ (powerset @ sK9)))) & ((in @ X6 @ (powerset @ sK9)) = $true)))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f41,plain,(
% 0.21/0.39 ? [X6] : (? [X7] : (($true != (subset @ (binintersect @ sK10 @ X6) @ X7)) & ((subset @ sK10 @ X7) = $true) & ($true = (in @ X7 @ (powerset @ sK9)))) & ((in @ X6 @ (powerset @ sK9)) = $true)) => (? [X7] : (($true != (subset @ (binintersect @ sK10 @ sK11) @ X7)) & ((subset @ sK10 @ X7) = $true) & ($true = (in @ X7 @ (powerset @ sK9)))) & ($true = (in @ sK11 @ (powerset @ sK9))))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f42,plain,(
% 0.21/0.39 ? [X7] : (($true != (subset @ (binintersect @ sK10 @ sK11) @ X7)) & ((subset @ sK10 @ X7) = $true) & ($true = (in @ X7 @ (powerset @ sK9)))) => (((subset @ (binintersect @ sK10 @ sK11) @ sK12) != $true) & ((subset @ sK10 @ sK12) = $true) & ((in @ sK12 @ (powerset @ sK9)) = $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f39,plain,(
% 0.21/0.39 (! [X0,X1] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2] : (! [X3] : (((subset @ (binintersect @ X1 @ X2) @ X3) = $true) | ((subset @ X1 @ X3) != $true) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (woz13rule1 != $true)) & ((woz13rule1 = $true) | ? [X4,X5] : (($true = (in @ X5 @ (powerset @ X4))) & ? [X6] : (? [X7] : (((subset @ (binintersect @ X5 @ X6) @ X7) != $true) & ($true = (subset @ X5 @ X7)) & ($true = (in @ X7 @ (powerset @ X4)))) & ($true = (in @ X6 @ (powerset @ X4))))))),
% 0.21/0.39 inference(rectify,[],[f38])).
% 0.21/0.39 thf(f38,plain,(
% 0.21/0.39 (! [X0,X1] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2] : (! [X3] : (((subset @ (binintersect @ X1 @ X2) @ X3) = $true) | ((subset @ X1 @ X3) != $true) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (woz13rule1 != $true)) & ((woz13rule1 = $true) | ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (? [X3] : (((subset @ (binintersect @ X1 @ X2) @ X3) != $true) & ((subset @ X1 @ X3) = $true) & ((in @ X3 @ (powerset @ X0)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true))))),
% 0.21/0.39 inference(nnf_transformation,[],[f21])).
% 0.21/0.39 thf(f21,plain,(
% 0.21/0.39 ! [X0,X1] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2] : (! [X3] : (((subset @ (binintersect @ X1 @ X2) @ X3) = $true) | ((subset @ X1 @ X3) != $true) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) <=> (woz13rule1 = $true)),
% 0.21/0.39 inference(flattening,[],[f20])).
% 0.21/0.39 thf(f20,plain,(
% 0.21/0.39 ! [X1,X0] : (! [X2] : (! [X3] : ((((subset @ (binintersect @ X1 @ X2) @ X3) = $true) | ((subset @ X1 @ X3) != $true)) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (woz13rule1 = $true)),
% 0.21/0.39 inference(ennf_transformation,[],[f13])).
% 0.21/0.39 thf(f13,plain,(
% 0.21/0.39 ! [X1,X0] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3] : (((in @ X3 @ (powerset @ X0)) = $true) => (((subset @ X1 @ X3) = $true) => ((subset @ (binintersect @ X1 @ X2) @ X3) = $true))))) <=> (woz13rule1 = $true)),
% 0.21/0.39 inference(fool_elimination,[],[f12])).
% 0.21/0.39 thf(f12,plain,(
% 0.21/0.39 (woz13rule1 = ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))),
% 0.21/0.39 inference(rectify,[],[f2])).
% 0.21/0.39 thf(f2,axiom,(
% 0.21/0.39 (woz13rule1 = ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X3) => (subset @ (binintersect @ X1 @ X2) @ X3))))))),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule1)).
% 0.21/0.39 thf(f140,plain,(
% 0.21/0.39 ($true != (subset @ (binintersect @ sK4 @ sK6) @ sK7)) | spl20_4),
% 0.21/0.39 inference(avatar_component_clause,[],[f138])).
% 0.21/0.39 thf(f138,plain,(
% 0.21/0.39 spl20_4 <=> ($true = (subset @ (binintersect @ sK4 @ sK6) @ sK7))),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl20_4])])).
% 0.21/0.39 thf(f148,plain,(
% 0.21/0.39 ~spl20_4 | spl20_5 | ~spl20_6),
% 0.21/0.39 inference(avatar_split_clause,[],[f136,f145,f142,f138])).
% 0.21/0.39 thf(f136,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($true != (subset @ (binintersect @ sK4 @ sK6) @ sK7)) | ($true != (subset @ (binintersect @ sK4 @ sK6) @ sK8)) | ($true != (in @ (binintersect @ sK4 @ sK6) @ (powerset @ X0))) | ($true != (in @ sK8 @ (powerset @ X0))) | ($true != (in @ sK7 @ (powerset @ X0)))) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f133])).
% 0.21/0.39 thf(f133,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($true != $true) | ($true != (in @ sK7 @ (powerset @ X0))) | ($true != (in @ (binintersect @ sK4 @ sK6) @ (powerset @ X0))) | ($true != (subset @ (binintersect @ sK4 @ sK6) @ sK7)) | ($true != (in @ sK8 @ (powerset @ X0))) | ($true != (subset @ (binintersect @ sK4 @ sK6) @ sK8))) )),
% 0.21/0.39 inference(superposition,[],[f65,f114])).
% 0.21/0.39 thf(f114,plain,(
% 0.21/0.39 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (subset @ X5 @ (binintersect @ X6 @ X7))) | ($true != (in @ X7 @ (powerset @ X4))) | ($true != (in @ X6 @ (powerset @ X4))) | ($true != (subset @ X5 @ X6)) | ($true != (in @ X5 @ (powerset @ X4))) | ($true != (subset @ X5 @ X7))) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f111])).
% 0.21/0.39 thf(f111,plain,(
% 0.21/0.39 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (powerset @ X4))) | ($true != $true) | ($true != (subset @ X5 @ X7)) | ($true = (subset @ X5 @ (binintersect @ X6 @ X7))) | ($true != (subset @ X5 @ X6)) | ($true != (in @ X7 @ (powerset @ X4))) | ($true != (in @ X6 @ (powerset @ X4)))) )),
% 0.21/0.39 inference(definition_unfolding,[],[f82,f70])).
% 0.21/0.39 thf(f70,plain,(
% 0.21/0.39 (woz13rule3 = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f37])).
% 0.21/0.39 thf(f82,plain,(
% 0.21/0.39 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (in @ X6 @ (powerset @ X4))) | ($true != (in @ X7 @ (powerset @ X4))) | ($true != (subset @ X5 @ X6)) | ($true = (subset @ X5 @ (binintersect @ X6 @ X7))) | ($true != (subset @ X5 @ X7)) | ($true != (in @ X5 @ (powerset @ X4))) | (woz13rule3 != $true)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f54])).
% 0.21/0.39 thf(f54,plain,(
% 0.21/0.39 ((woz13rule3 = $true) | ((($true = (in @ sK18 @ (powerset @ sK16))) & (((in @ sK19 @ (powerset @ sK16)) = $true) & ($true = (subset @ sK17 @ sK18)) & ($true != (subset @ sK17 @ (binintersect @ sK18 @ sK19))) & ($true = (subset @ sK17 @ sK19)))) & ($true = (in @ sK17 @ (powerset @ sK16))))) & (! [X4,X5] : (! [X6] : (($true != (in @ X6 @ (powerset @ X4))) | ! [X7] : (($true != (in @ X7 @ (powerset @ X4))) | ($true != (subset @ X5 @ X6)) | ($true = (subset @ X5 @ (binintersect @ X6 @ X7))) | ($true != (subset @ X5 @ X7)))) | ($true != (in @ X5 @ (powerset @ X4)))) | (woz13rule3 != $true))),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19])],[f50,f53,f52,f51])).
% 0.21/0.39 thf(f51,plain,(
% 0.21/0.39 ? [X0,X1] : (? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3] : (((in @ X3 @ (powerset @ X0)) = $true) & ((subset @ X1 @ X2) = $true) & ((subset @ X1 @ (binintersect @ X2 @ X3)) != $true) & ((subset @ X1 @ X3) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2] : (((in @ X2 @ (powerset @ sK16)) = $true) & ? [X3] : (((in @ X3 @ (powerset @ sK16)) = $true) & ($true = (subset @ sK17 @ X2)) & ($true != (subset @ sK17 @ (binintersect @ X2 @ X3))) & ($true = (subset @ sK17 @ X3)))) & ($true = (in @ sK17 @ (powerset @ sK16))))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f52,plain,(
% 0.21/0.39 ? [X2] : (((in @ X2 @ (powerset @ sK16)) = $true) & ? [X3] : (((in @ X3 @ (powerset @ sK16)) = $true) & ($true = (subset @ sK17 @ X2)) & ($true != (subset @ sK17 @ (binintersect @ X2 @ X3))) & ($true = (subset @ sK17 @ X3)))) => (($true = (in @ sK18 @ (powerset @ sK16))) & ? [X3] : (((in @ X3 @ (powerset @ sK16)) = $true) & ($true = (subset @ sK17 @ sK18)) & ($true != (subset @ sK17 @ (binintersect @ sK18 @ X3))) & ($true = (subset @ sK17 @ X3))))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f53,plain,(
% 0.21/0.39 ? [X3] : (((in @ X3 @ (powerset @ sK16)) = $true) & ($true = (subset @ sK17 @ sK18)) & ($true != (subset @ sK17 @ (binintersect @ sK18 @ X3))) & ($true = (subset @ sK17 @ X3))) => (((in @ sK19 @ (powerset @ sK16)) = $true) & ($true = (subset @ sK17 @ sK18)) & ($true != (subset @ sK17 @ (binintersect @ sK18 @ sK19))) & ($true = (subset @ sK17 @ sK19)))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f50,plain,(
% 0.21/0.39 ((woz13rule3 = $true) | ? [X0,X1] : (? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3] : (((in @ X3 @ (powerset @ X0)) = $true) & ((subset @ X1 @ X2) = $true) & ((subset @ X1 @ (binintersect @ X2 @ X3)) != $true) & ((subset @ X1 @ X3) = $true))) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X4,X5] : (! [X6] : (($true != (in @ X6 @ (powerset @ X4))) | ! [X7] : (($true != (in @ X7 @ (powerset @ X4))) | ($true != (subset @ X5 @ X6)) | ($true = (subset @ X5 @ (binintersect @ X6 @ X7))) | ($true != (subset @ X5 @ X7)))) | ($true != (in @ X5 @ (powerset @ X4)))) | (woz13rule3 != $true))),
% 0.21/0.39 inference(rectify,[],[f49])).
% 0.21/0.39 thf(f49,plain,(
% 0.21/0.39 ((woz13rule3 = $true) | ? [X1,X0] : (? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3] : (($true = (in @ X3 @ (powerset @ X1))) & ($true = (subset @ X0 @ X2)) & ($true != (subset @ X0 @ (binintersect @ X2 @ X3))) & ($true = (subset @ X0 @ X3)))) & ((in @ X0 @ (powerset @ X1)) = $true))) & (! [X1,X0] : (! [X2] : (($true != (in @ X2 @ (powerset @ X1))) | ! [X3] : (($true != (in @ X3 @ (powerset @ X1))) | ($true != (subset @ X0 @ X2)) | ($true = (subset @ X0 @ (binintersect @ X2 @ X3))) | ($true != (subset @ X0 @ X3)))) | ((in @ X0 @ (powerset @ X1)) != $true)) | (woz13rule3 != $true))),
% 0.21/0.39 inference(nnf_transformation,[],[f19])).
% 0.21/0.39 thf(f19,plain,(
% 0.21/0.39 (woz13rule3 = $true) <=> ! [X1,X0] : (! [X2] : (($true != (in @ X2 @ (powerset @ X1))) | ! [X3] : (($true != (in @ X3 @ (powerset @ X1))) | ($true != (subset @ X0 @ X2)) | ($true = (subset @ X0 @ (binintersect @ X2 @ X3))) | ($true != (subset @ X0 @ X3)))) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 0.21/0.39 inference(flattening,[],[f18])).
% 0.21/0.39 thf(f18,plain,(
% 0.21/0.39 (woz13rule3 = $true) <=> ! [X1,X0] : (! [X2] : (! [X3] : (((($true = (subset @ X0 @ (binintersect @ X2 @ X3))) | ($true != (subset @ X0 @ X3))) | ($true != (subset @ X0 @ X2))) | ($true != (in @ X3 @ (powerset @ X1)))) | ($true != (in @ X2 @ (powerset @ X1)))) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 0.21/0.39 inference(ennf_transformation,[],[f11])).
% 0.21/0.39 thf(f11,plain,(
% 0.21/0.39 (woz13rule3 = $true) <=> ! [X1,X0] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3] : (($true = (in @ X3 @ (powerset @ X1))) => (($true = (subset @ X0 @ X2)) => (($true = (subset @ X0 @ X3)) => ($true = (subset @ X0 @ (binintersect @ X2 @ X3))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f10])).
% 0.21/0.39 thf(f10,plain,(
% 0.21/0.39 (! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => ! [X3] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X0 @ X2) => ((subset @ X0 @ X3) => (subset @ X0 @ (binintersect @ X2 @ X3))))))) = woz13rule3)),
% 0.21/0.39 inference(rectify,[],[f4])).
% 0.21/0.39 thf(f4,axiom,(
% 0.21/0.39 (! [X1,X0] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ (powerset @ X0)) => ((subset @ X1 @ X2) => ((subset @ X1 @ X3) => (subset @ X1 @ (binintersect @ X2 @ X3))))))) = woz13rule3)),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule3)).
% 0.21/0.39 thf(f65,plain,(
% 0.21/0.39 ($true != (subset @ (binintersect @ sK4 @ sK6) @ (binintersect @ sK7 @ sK8)))),
% 0.21/0.39 inference(cnf_transformation,[],[f37])).
% 0.21/0.39 % SZS output end Proof for theBenchmark
% 0.21/0.39 % (31976)------------------------------
% 0.21/0.39 % (31976)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (31976)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (31976)Memory used [KB]: 5628
% 0.21/0.39 % (31976)Time elapsed: 0.019 s
% 0.21/0.39 % (31976)Instructions burned: 17 (million)
% 0.21/0.39 % (31976)------------------------------
% 0.21/0.39 % (31976)------------------------------
% 0.21/0.39 % (31970)Success in time 0.019 s
% 0.21/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------