TSTP Solution File: SEU711^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU711^2 : 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 : n019.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 03:50:57 EDT 2024
% Result : Theorem 0.16s 0.35s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU711^2 : TPTP v8.2.0. Released v3.7.0.
% 0.00/0.11 % 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
% 0.11/0.32 % Computer : n019.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sun May 19 15:25:23 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 This is a TH0_THM_EQU_NAR problem
% 0.11/0.32 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
% 0.16/0.34 % (2716)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.16/0.34 % (2714)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)
% 0.16/0.34 % (2713)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.16/0.34 % (2715)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)
% 0.16/0.34 % (2717)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)
% 0.16/0.34 % (2718)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)
% 0.16/0.34 % (2719)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.16/0.34 % (2716)Instruction limit reached!
% 0.16/0.34 % (2716)------------------------------
% 0.16/0.34 % (2716)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (2720)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)
% 0.16/0.34 % (2716)Termination reason: Unknown
% 0.16/0.34 % (2716)Termination phase: Saturation
% 0.16/0.34 % (2717)Instruction limit reached!
% 0.16/0.34 % (2717)------------------------------
% 0.16/0.34 % (2717)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (2717)Termination reason: Unknown
% 0.16/0.34 % (2717)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (2717)Memory used [KB]: 1023
% 0.16/0.34 % (2717)Time elapsed: 0.003 s
% 0.16/0.34 % (2717)Instructions burned: 3 (million)
% 0.16/0.34 % (2717)------------------------------
% 0.16/0.34 % (2717)------------------------------
% 0.16/0.34
% 0.16/0.34 % (2716)Memory used [KB]: 1023
% 0.16/0.34 % (2716)Time elapsed: 0.003 s
% 0.16/0.34 % (2716)Instructions burned: 3 (million)
% 0.16/0.34 % (2716)------------------------------
% 0.16/0.34 % (2716)------------------------------
% 0.16/0.34 % (2714)Instruction limit reached!
% 0.16/0.34 % (2714)------------------------------
% 0.16/0.34 % (2714)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (2714)Termination reason: Unknown
% 0.16/0.34 % (2714)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (2714)Memory used [KB]: 5500
% 0.16/0.34 % (2714)Time elapsed: 0.004 s
% 0.16/0.34 % (2714)Instructions burned: 4 (million)
% 0.16/0.34 % (2714)------------------------------
% 0.16/0.34 % (2714)------------------------------
% 0.16/0.34 % (2720)Instruction limit reached!
% 0.16/0.34 % (2720)------------------------------
% 0.16/0.34 % (2720)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (2720)Termination reason: Unknown
% 0.16/0.34 % (2720)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (2720)Memory used [KB]: 5500
% 0.16/0.34 % (2720)Time elapsed: 0.003 s
% 0.16/0.34 % (2720)Instructions burned: 3 (million)
% 0.16/0.34 % (2720)------------------------------
% 0.16/0.34 % (2720)------------------------------
% 0.16/0.35 % (2719)First to succeed.
% 0.16/0.35 % (2719)Refutation found. Thanks to Tanya!
% 0.16/0.35 % SZS status Theorem for theBenchmark
% 0.16/0.35 % SZS output start Proof for theBenchmark
% 0.16/0.35 thf(func_def_0, type, in: $i > $i > $o).
% 0.16/0.35 thf(func_def_1, type, powerset: $i > $i).
% 0.16/0.35 thf(func_def_5, type, binunion: $i > $i > $i).
% 0.16/0.35 thf(func_def_9, type, sK0: $i > $i > $i).
% 0.16/0.35 thf(f118,plain,(
% 0.16/0.35 $false),
% 0.16/0.35 inference(avatar_sat_refutation,[],[f105,f111,f117])).
% 0.16/0.35 thf(f117,plain,(
% 0.16/0.35 ~spl13_1),
% 0.16/0.35 inference(avatar_contradiction_clause,[],[f116])).
% 0.16/0.35 thf(f116,plain,(
% 0.16/0.35 $false | ~spl13_1),
% 0.16/0.35 inference(subsumption_resolution,[],[f115,f57])).
% 0.16/0.35 thf(f57,plain,(
% 0.16/0.35 ($true != (in @ (binunion @ sK10 @ sK12) @ (powerset @ sK11)))),
% 0.16/0.35 inference(cnf_transformation,[],[f37])).
% 0.16/0.35 thf(f37,plain,(
% 0.16/0.35 (powersetI = $true) & ((($true = (in @ sK12 @ (powerset @ sK11))) & ($true != (in @ (binunion @ sK10 @ sK12) @ (powerset @ sK11)))) & ((in @ sK10 @ (powerset @ sK11)) = $true)) & (powersetE = $true) & (binunionEcases = $true)),
% 0.16/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f21,f36,f35])).
% 0.16/0.35 thf(f35,plain,(
% 0.16/0.35 ? [X0,X1] : (? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ($true != (in @ (binunion @ X0 @ X2) @ (powerset @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) => (? [X2] : (($true = (in @ X2 @ (powerset @ sK11))) & ($true != (in @ (binunion @ sK10 @ X2) @ (powerset @ sK11)))) & ((in @ sK10 @ (powerset @ sK11)) = $true))),
% 0.16/0.35 introduced(choice_axiom,[])).
% 0.16/0.35 thf(f36,plain,(
% 0.16/0.35 ? [X2] : (($true = (in @ X2 @ (powerset @ sK11))) & ($true != (in @ (binunion @ sK10 @ X2) @ (powerset @ sK11)))) => (($true = (in @ sK12 @ (powerset @ sK11))) & ($true != (in @ (binunion @ sK10 @ sK12) @ (powerset @ sK11))))),
% 0.16/0.35 introduced(choice_axiom,[])).
% 0.16/0.35 thf(f21,plain,(
% 0.16/0.35 (powersetI = $true) & ? [X0,X1] : (? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ($true != (in @ (binunion @ X0 @ X2) @ (powerset @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) & (powersetE = $true) & (binunionEcases = $true)),
% 0.16/0.35 inference(flattening,[],[f20])).
% 0.16/0.35 thf(f20,plain,(
% 0.16/0.35 ((? [X0,X1] : (? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ($true != (in @ (binunion @ X0 @ X2) @ (powerset @ X1)))) & ($true = (in @ X0 @ (powerset @ X1)))) & (binunionEcases = $true)) & (powersetE = $true)) & (powersetI = $true)),
% 0.16/0.35 inference(ennf_transformation,[],[f8])).
% 0.16/0.35 thf(f8,plain,(
% 0.16/0.35 ~((powersetI = $true) => ((powersetE = $true) => ((binunionEcases = $true) => ! [X0,X1] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2] : (($true = (in @ X2 @ (powerset @ X1))) => ($true = (in @ (binunion @ X0 @ X2) @ (powerset @ X1))))))))),
% 0.16/0.35 inference(fool_elimination,[],[f7])).
% 0.16/0.35 thf(f7,plain,(
% 0.16/0.35 ~(powersetI => (powersetE => (binunionEcases => ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => (in @ (binunion @ X0 @ X2) @ (powerset @ X1)))))))),
% 0.16/0.35 inference(rectify,[],[f5])).
% 0.16/0.35 thf(f5,negated_conjecture,(
% 0.16/0.35 ~(powersetI => (powersetE => (binunionEcases => ! [X4,X0] : ((in @ X4 @ (powerset @ X0)) => ! [X5] : ((in @ X5 @ (powerset @ X0)) => (in @ (binunion @ X4 @ X5) @ (powerset @ X0)))))))),
% 0.16/0.35 inference(negated_conjecture,[],[f4])).
% 0.16/0.35 thf(f4,conjecture,(
% 0.16/0.35 powersetI => (powersetE => (binunionEcases => ! [X4,X0] : ((in @ X4 @ (powerset @ X0)) => ! [X5] : ((in @ X5 @ (powerset @ X0)) => (in @ (binunion @ X4 @ X5) @ (powerset @ X0))))))),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionT_lem)).
% 0.16/0.35 thf(f115,plain,(
% 0.16/0.35 ($true = (in @ (binunion @ sK10 @ sK12) @ (powerset @ sK11))) | ~spl13_1),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f114])).
% 0.16/0.35 thf(f114,plain,(
% 0.16/0.35 ($true = (in @ (binunion @ sK10 @ sK12) @ (powerset @ sK11))) | ($true != $true) | ~spl13_1),
% 0.16/0.35 inference(superposition,[],[f82,f113])).
% 0.16/0.35 thf(f113,plain,(
% 0.16/0.35 ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK11)) | ~spl13_1),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f112])).
% 0.16/0.35 thf(f112,plain,(
% 0.16/0.35 ($true != $true) | ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK11)) | ~spl13_1),
% 0.16/0.35 inference(superposition,[],[f93,f100])).
% 0.16/0.35 thf(f100,plain,(
% 0.16/0.35 ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK10)) | ~spl13_1),
% 0.16/0.35 inference(avatar_component_clause,[],[f98])).
% 0.16/0.35 thf(f98,plain,(
% 0.16/0.35 spl13_1 <=> ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK10))),
% 0.16/0.35 introduced(avatar_definition,[new_symbols(naming,[spl13_1])])).
% 0.16/0.35 thf(f93,plain,(
% 0.16/0.35 ( ! [X0 : $i] : (($true != (in @ X0 @ sK10)) | ($true = (in @ X0 @ sK11))) )),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f89])).
% 0.16/0.35 thf(f89,plain,(
% 0.16/0.35 ( ! [X0 : $i] : (($true != $true) | ($true = (in @ X0 @ sK11)) | ($true != (in @ X0 @ sK10))) )),
% 0.16/0.35 inference(superposition,[],[f79,f56])).
% 0.16/0.35 thf(f56,plain,(
% 0.16/0.35 ((in @ sK10 @ (powerset @ sK11)) = $true)),
% 0.16/0.35 inference(cnf_transformation,[],[f37])).
% 0.16/0.35 thf(f79,plain,(
% 0.16/0.35 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (powerset @ X4))) | ($true = (in @ X3 @ X4)) | ($true != (in @ X3 @ X5))) )),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f67])).
% 0.16/0.35 thf(f67,plain,(
% 0.16/0.35 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X3 @ X5)) | ($true != $true) | ($true = (in @ X3 @ X4)) | ($true != (in @ X5 @ (powerset @ X4)))) )),
% 0.16/0.35 inference(definition_unfolding,[],[f42,f55])).
% 0.16/0.35 thf(f55,plain,(
% 0.16/0.35 (powersetE = $true)),
% 0.16/0.35 inference(cnf_transformation,[],[f37])).
% 0.16/0.35 thf(f42,plain,(
% 0.16/0.35 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X3 @ X4)) | ($true != (in @ X3 @ X5)) | ($true != (in @ X5 @ (powerset @ X4))) | (powersetE != $true)) )),
% 0.16/0.35 inference(cnf_transformation,[],[f30])).
% 0.16/0.35 thf(f30,plain,(
% 0.16/0.35 ((powersetE = $true) | (($true != (in @ sK3 @ sK4)) & ($true = (in @ sK3 @ sK5)) & ($true = (in @ sK5 @ (powerset @ sK4))))) & (! [X3,X4,X5] : (($true = (in @ X3 @ X4)) | ($true != (in @ X3 @ X5)) | ($true != (in @ X5 @ (powerset @ X4)))) | (powersetE != $true))),
% 0.16/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f28,f29])).
% 0.16/0.35 thf(f29,plain,(
% 0.16/0.35 ? [X0,X1,X2] : (($true != (in @ X0 @ X1)) & ($true = (in @ X0 @ X2)) & ($true = (in @ X2 @ (powerset @ X1)))) => (($true != (in @ sK3 @ sK4)) & ($true = (in @ sK3 @ sK5)) & ($true = (in @ sK5 @ (powerset @ sK4))))),
% 0.16/0.35 introduced(choice_axiom,[])).
% 0.16/0.35 thf(f28,plain,(
% 0.16/0.35 ((powersetE = $true) | ? [X0,X1,X2] : (($true != (in @ X0 @ X1)) & ($true = (in @ X0 @ X2)) & ($true = (in @ X2 @ (powerset @ X1))))) & (! [X3,X4,X5] : (($true = (in @ X3 @ X4)) | ($true != (in @ X3 @ X5)) | ($true != (in @ X5 @ (powerset @ X4)))) | (powersetE != $true))),
% 0.16/0.35 inference(rectify,[],[f27])).
% 0.16/0.35 thf(f27,plain,(
% 0.16/0.35 ((powersetE = $true) | ? [X2,X1,X0] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true) & ($true = (in @ X0 @ (powerset @ X1))))) & (! [X2,X1,X0] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true) | ($true != (in @ X0 @ (powerset @ X1)))) | (powersetE != $true))),
% 0.16/0.35 inference(nnf_transformation,[],[f16])).
% 0.16/0.35 thf(f16,plain,(
% 0.16/0.35 (powersetE = $true) <=> ! [X2,X1,X0] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true) | ($true != (in @ X0 @ (powerset @ X1))))),
% 0.16/0.35 inference(flattening,[],[f15])).
% 0.16/0.35 thf(f15,plain,(
% 0.16/0.35 ! [X1,X2,X0] : ((((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (powersetE = $true)),
% 0.16/0.35 inference(ennf_transformation,[],[f12])).
% 0.16/0.35 thf(f12,plain,(
% 0.16/0.35 ! [X1,X2,X0] : (($true = (in @ X0 @ (powerset @ X1))) => (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true))) <=> (powersetE = $true)),
% 0.16/0.35 inference(fool_elimination,[],[f11])).
% 0.16/0.35 thf(f11,plain,(
% 0.16/0.35 (! [X0,X1,X2] : ((in @ X0 @ (powerset @ X1)) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = powersetE)),
% 0.16/0.35 inference(rectify,[],[f2])).
% 0.16/0.35 thf(f2,axiom,(
% 0.16/0.35 (! [X1,X0,X2] : ((in @ X1 @ (powerset @ X0)) => ((in @ X2 @ X1) => (in @ X2 @ X0))) = powersetE)),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE)).
% 0.16/0.35 thf(f82,plain,(
% 0.16/0.35 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK0 @ X1 @ X0) @ X0)) | ((in @ X1 @ (powerset @ X0)) = $true)) )),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f60])).
% 0.16/0.35 thf(f60,plain,(
% 0.16/0.35 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ($true != $true) | ($true != (in @ (sK0 @ X1 @ X0) @ X0))) )),
% 0.16/0.35 inference(definition_unfolding,[],[f41,f59])).
% 0.16/0.35 thf(f59,plain,(
% 0.16/0.35 (powersetI = $true)),
% 0.16/0.35 inference(cnf_transformation,[],[f37])).
% 0.16/0.35 thf(f41,plain,(
% 0.16/0.35 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ($true != (in @ (sK0 @ X1 @ X0) @ X0)) | (powersetI != $true)) )),
% 0.16/0.35 inference(cnf_transformation,[],[f26])).
% 0.16/0.35 thf(f26,plain,(
% 0.16/0.35 (! [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) | (($true != (in @ (sK0 @ X1 @ X0) @ X0)) & ($true = (in @ (sK0 @ X1 @ X0) @ X1)))) | (powersetI != $true)) & ((powersetI = $true) | (($true != (in @ sK2 @ (powerset @ sK1))) & ! [X5] : (($true = (in @ X5 @ sK1)) | ($true != (in @ X5 @ sK2)))))),
% 0.16/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f23,f25,f24])).
% 0.16/0.35 thf(f24,plain,(
% 0.16/0.35 ! [X0,X1] : (? [X2] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) => (($true != (in @ (sK0 @ X1 @ X0) @ X0)) & ($true = (in @ (sK0 @ X1 @ X0) @ X1))))),
% 0.16/0.35 introduced(choice_axiom,[])).
% 0.16/0.35 thf(f25,plain,(
% 0.16/0.35 ? [X3,X4] : (($true != (in @ X4 @ (powerset @ X3))) & ! [X5] : (($true = (in @ X5 @ X3)) | ($true != (in @ X5 @ X4)))) => (($true != (in @ sK2 @ (powerset @ sK1))) & ! [X5] : (($true = (in @ X5 @ sK1)) | ($true != (in @ X5 @ sK2))))),
% 0.16/0.35 introduced(choice_axiom,[])).
% 0.16/0.35 thf(f23,plain,(
% 0.16/0.35 (! [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) | ? [X2] : (((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true))) | (powersetI != $true)) & ((powersetI = $true) | ? [X3,X4] : (($true != (in @ X4 @ (powerset @ X3))) & ! [X5] : (($true = (in @ X5 @ X3)) | ($true != (in @ X5 @ X4)))))),
% 0.16/0.35 inference(rectify,[],[f22])).
% 0.16/0.35 thf(f22,plain,(
% 0.16/0.35 (! [X1,X0] : (($true = (in @ X0 @ (powerset @ X1))) | ? [X2] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) | (powersetI != $true)) & ((powersetI = $true) | ? [X1,X0] : (($true != (in @ X0 @ (powerset @ X1))) & ! [X2] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true))))),
% 0.16/0.35 inference(nnf_transformation,[],[f19])).
% 0.16/0.35 thf(f19,plain,(
% 0.16/0.35 ! [X1,X0] : (($true = (in @ X0 @ (powerset @ X1))) | ? [X2] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) <=> (powersetI = $true)),
% 0.16/0.35 inference(ennf_transformation,[],[f10])).
% 0.16/0.35 thf(f10,plain,(
% 0.16/0.35 ! [X0,X1] : (! [X2] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ($true = (in @ X0 @ (powerset @ X1)))) <=> (powersetI = $true)),
% 0.16/0.35 inference(fool_elimination,[],[f9])).
% 0.16/0.35 thf(f9,plain,(
% 0.16/0.35 (powersetI = ! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (in @ X0 @ (powerset @ X1))))),
% 0.16/0.35 inference(rectify,[],[f1])).
% 0.16/0.35 thf(f1,axiom,(
% 0.16/0.35 (powersetI = ! [X1,X0] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (in @ X1 @ (powerset @ X0))))),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI)).
% 0.16/0.35 thf(f111,plain,(
% 0.16/0.35 ~spl13_2),
% 0.16/0.35 inference(avatar_contradiction_clause,[],[f110])).
% 0.16/0.35 thf(f110,plain,(
% 0.16/0.35 $false | ~spl13_2),
% 0.16/0.35 inference(subsumption_resolution,[],[f109,f57])).
% 0.16/0.35 thf(f109,plain,(
% 0.16/0.35 ($true = (in @ (binunion @ sK10 @ sK12) @ (powerset @ sK11))) | ~spl13_2),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f108])).
% 0.16/0.35 thf(f108,plain,(
% 0.16/0.35 ($true != $true) | ($true = (in @ (binunion @ sK10 @ sK12) @ (powerset @ sK11))) | ~spl13_2),
% 0.16/0.35 inference(superposition,[],[f82,f107])).
% 0.16/0.35 thf(f107,plain,(
% 0.16/0.35 ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK11)) | ~spl13_2),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f106])).
% 0.16/0.35 thf(f106,plain,(
% 0.16/0.35 ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK11)) | ($true != $true) | ~spl13_2),
% 0.16/0.35 inference(superposition,[],[f94,f104])).
% 0.16/0.35 thf(f104,plain,(
% 0.16/0.35 ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK12)) | ~spl13_2),
% 0.16/0.35 inference(avatar_component_clause,[],[f102])).
% 0.16/0.35 thf(f102,plain,(
% 0.16/0.35 spl13_2 <=> ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK12))),
% 0.16/0.35 introduced(avatar_definition,[new_symbols(naming,[spl13_2])])).
% 0.16/0.35 thf(f94,plain,(
% 0.16/0.35 ( ! [X0 : $i] : (($true != (in @ X0 @ sK12)) | ($true = (in @ X0 @ sK11))) )),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f90])).
% 0.16/0.35 thf(f90,plain,(
% 0.16/0.35 ( ! [X0 : $i] : (($true = (in @ X0 @ sK11)) | ($true != (in @ X0 @ sK12)) | ($true != $true)) )),
% 0.16/0.35 inference(superposition,[],[f79,f58])).
% 0.16/0.35 thf(f58,plain,(
% 0.16/0.35 ($true = (in @ sK12 @ (powerset @ sK11)))),
% 0.16/0.35 inference(cnf_transformation,[],[f37])).
% 0.16/0.35 thf(f105,plain,(
% 0.16/0.35 spl13_1 | spl13_2),
% 0.16/0.35 inference(avatar_split_clause,[],[f96,f102,f98])).
% 0.16/0.35 thf(f96,plain,(
% 0.16/0.35 ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK10)) | ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK12))),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f95])).
% 0.16/0.35 thf(f95,plain,(
% 0.16/0.35 ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK12)) | ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ sK10)) | ($true != $true)),
% 0.16/0.35 inference(superposition,[],[f81,f88])).
% 0.16/0.35 thf(f88,plain,(
% 0.16/0.35 ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ (binunion @ sK10 @ sK12)))),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f85])).
% 0.16/0.35 thf(f85,plain,(
% 0.16/0.35 ($true = (in @ (sK0 @ (binunion @ sK10 @ sK12) @ sK11) @ (binunion @ sK10 @ sK12))) | ($true != $true)),
% 0.16/0.35 inference(superposition,[],[f57,f84])).
% 0.16/0.35 thf(f84,plain,(
% 0.16/0.35 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ($true = (in @ (sK0 @ X1 @ X0) @ X1))) )),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f61])).
% 0.16/0.35 thf(f61,plain,(
% 0.16/0.35 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK0 @ X1 @ X0) @ X1)) | ((in @ X1 @ (powerset @ X0)) = $true) | ($true != $true)) )),
% 0.16/0.35 inference(definition_unfolding,[],[f40,f59])).
% 0.16/0.35 thf(f40,plain,(
% 0.16/0.35 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ($true = (in @ (sK0 @ X1 @ X0) @ X1)) | (powersetI != $true)) )),
% 0.16/0.35 inference(cnf_transformation,[],[f26])).
% 0.16/0.35 thf(f81,plain,(
% 0.16/0.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ (binunion @ X2 @ X1))) | ($true = (in @ X0 @ X1)) | ($true = (in @ X0 @ X2))) )),
% 0.16/0.35 inference(condensation,[],[f80])).
% 0.16/0.35 thf(f80,plain,(
% 0.16/0.35 ( ! [X2 : $o,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ X3 @ X0)) | ($true = (in @ X3 @ X1)) | ($true != (in @ X3 @ (binunion @ X1 @ X0))) | ($true = X2)) )),
% 0.16/0.35 inference(trivial_inequality_removal,[],[f68])).
% 0.16/0.35 thf(f68,plain,(
% 0.16/0.35 ( ! [X2 : $o,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ X3 @ X0)) | ($true != (in @ X3 @ (binunion @ X1 @ X0))) | ($true = (in @ X3 @ X1)) | ($true != $true) | ($true = X2)) )),
% 0.16/0.35 inference(definition_unfolding,[],[f53,f54])).
% 0.16/0.35 thf(f54,plain,(
% 0.16/0.35 (binunionEcases = $true)),
% 0.16/0.35 inference(cnf_transformation,[],[f37])).
% 0.16/0.35 thf(f53,plain,(
% 0.16/0.35 ( ! [X2 : $o,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ X3 @ X0)) | ($true = (in @ X3 @ X1)) | ($true = X2) | ($true != (in @ X3 @ (binunion @ X1 @ X0))) | (binunionEcases != $true)) )),
% 0.16/0.35 inference(cnf_transformation,[],[f34])).
% 0.16/0.35 thf(f34,plain,(
% 0.16/0.35 (! [X0,X1,X2 : $o,X3] : ((($true = (in @ X3 @ X0)) & ($true != X2)) | (($true = (in @ X3 @ X1)) & ($true != X2)) | ($true = X2) | ($true != (in @ X3 @ (binunion @ X1 @ X0)))) | (binunionEcases != $true)) & ((binunionEcases = $true) | ((($true != (in @ sK9 @ sK6)) | ($true = sK8)) & (($true != (in @ sK9 @ sK7)) | ($true = sK8)) & ($true != sK8) & ($true = (in @ sK9 @ (binunion @ sK7 @ sK6)))))),
% 0.16/0.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f32,f33])).
% 0.16/0.35 thf(f33,plain,(
% 0.16/0.35 ? [X4,X5,X6 : $o,X7] : ((($true != (in @ X7 @ X4)) | ($true = X6)) & (($true != (in @ X7 @ X5)) | ($true = X6)) & ($true != X6) & ($true = (in @ X7 @ (binunion @ X5 @ X4)))) => ((($true != (in @ sK9 @ sK6)) | ($true = sK8)) & (($true != (in @ sK9 @ sK7)) | ($true = sK8)) & ($true != sK8) & ($true = (in @ sK9 @ (binunion @ sK7 @ sK6))))),
% 0.16/0.35 introduced(choice_axiom,[])).
% 0.16/0.35 thf(f32,plain,(
% 0.16/0.35 (! [X0,X1,X2 : $o,X3] : ((($true = (in @ X3 @ X0)) & ($true != X2)) | (($true = (in @ X3 @ X1)) & ($true != X2)) | ($true = X2) | ($true != (in @ X3 @ (binunion @ X1 @ X0)))) | (binunionEcases != $true)) & ((binunionEcases = $true) | ? [X4,X5,X6 : $o,X7] : ((($true != (in @ X7 @ X4)) | ($true = X6)) & (($true != (in @ X7 @ X5)) | ($true = X6)) & ($true != X6) & ($true = (in @ X7 @ (binunion @ X5 @ X4)))))),
% 0.16/0.35 inference(rectify,[],[f31])).
% 0.16/0.35 thf(f31,plain,(
% 0.16/0.35 (! [X2,X3,X1 : $o,X0] : ((($true = (in @ X0 @ X2)) & ($true != X1)) | (($true = (in @ X0 @ X3)) & ($true != X1)) | ($true = X1) | ($true != (in @ X0 @ (binunion @ X3 @ X2)))) | (binunionEcases != $true)) & ((binunionEcases = $true) | ? [X2,X3,X1 : $o,X0] : ((($true != (in @ X0 @ X2)) | ($true = X1)) & (($true != (in @ X0 @ X3)) | ($true = X1)) & ($true != X1) & ($true = (in @ X0 @ (binunion @ X3 @ X2)))))),
% 0.16/0.35 inference(nnf_transformation,[],[f18])).
% 0.16/0.35 thf(f18,plain,(
% 0.16/0.35 ! [X2,X3,X1 : $o,X0] : ((($true = (in @ X0 @ X2)) & ($true != X1)) | (($true = (in @ X0 @ X3)) & ($true != X1)) | ($true = X1) | ($true != (in @ X0 @ (binunion @ X3 @ X2)))) <=> (binunionEcases = $true)),
% 0.16/0.35 inference(flattening,[],[f17])).
% 0.16/0.35 thf(f17,plain,(
% 0.16/0.35 ! [X1 : $o,X2,X0,X3] : (((($true = X1) | (($true = (in @ X0 @ X2)) & ($true != X1))) | (($true = (in @ X0 @ X3)) & ($true != X1))) | ($true != (in @ X0 @ (binunion @ X3 @ X2)))) <=> (binunionEcases = $true)),
% 0.16/0.35 inference(ennf_transformation,[],[f14])).
% 0.16/0.35 thf(f14,plain,(
% 0.16/0.35 ! [X1 : $o,X2,X0,X3] : (($true = (in @ X0 @ (binunion @ X3 @ X2))) => ((($true = (in @ X0 @ X3)) => ($true = X1)) => ((($true = (in @ X0 @ X2)) => ($true = X1)) => ($true = X1)))) <=> (binunionEcases = $true)),
% 0.16/0.35 inference(fool_elimination,[],[f13])).
% 0.16/0.35 thf(f13,plain,(
% 0.16/0.35 (! [X0,X1 : $o,X2,X3] : ((in @ X0 @ (binunion @ X3 @ X2)) => (((in @ X0 @ X3) => X1) => (((in @ X0 @ X2) => X1) => X1))) = binunionEcases)),
% 0.16/0.35 inference(rectify,[],[f3])).
% 0.16/0.35 thf(f3,axiom,(
% 0.16/0.35 (! [X2,X3 : $o,X1,X0] : ((in @ X2 @ (binunion @ X0 @ X1)) => (((in @ X2 @ X0) => X3) => (((in @ X2 @ X1) => X3) => X3))) = binunionEcases)),
% 0.16/0.35 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases)).
% 0.16/0.35 % SZS output end Proof for theBenchmark
% 0.16/0.35 % (2719)------------------------------
% 0.16/0.35 % (2719)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (2719)Termination reason: Refutation
% 0.16/0.35
% 0.16/0.35 % (2719)Memory used [KB]: 5628
% 0.16/0.35 % (2719)Time elapsed: 0.010 s
% 0.16/0.35 % (2719)Instructions burned: 9 (million)
% 0.16/0.35 % (2719)------------------------------
% 0.16/0.35 % (2719)------------------------------
% 0.16/0.35 % (2712)Success in time 0.01 s
% 0.16/0.35 % Vampire---4.8 exiting
%------------------------------------------------------------------------------