TSTP Solution File: SEU623^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU623^2 : 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 : n003.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 03:50:05 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
% 0.06/0.12 % Problem : SEU623^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.14 % 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
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 16:09:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 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
% 0.14/0.37 % (24032)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (24032)Instruction limit reached!
% 0.14/0.37 % (24032)------------------------------
% 0.14/0.37 % (24032)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (24032)Termination reason: Unknown
% 0.14/0.37 % (24032)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (24032)Memory used [KB]: 1023
% 0.14/0.37 % (24032)Time elapsed: 0.002 s
% 0.14/0.37 % (24032)Instructions burned: 3 (million)
% 0.14/0.37 % (24032)------------------------------
% 0.14/0.37 % (24032)------------------------------
% 0.14/0.37 % (24029)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (24030)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)
% 0.14/0.37 % (24033)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)
% 0.14/0.37 % (24034)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)
% 0.14/0.37 % (24031)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)
% 0.14/0.37 % (24035)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (24036)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)
% 0.14/0.37 % (24033)Instruction limit reached!
% 0.14/0.37 % (24033)------------------------------
% 0.14/0.37 % (24033)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (24033)Termination reason: Unknown
% 0.14/0.37 % (24033)Termination phase: Property scanning
% 0.14/0.37
% 0.14/0.37 % (24033)Memory used [KB]: 895
% 0.14/0.37 % (24033)Time elapsed: 0.003 s
% 0.14/0.37 % (24033)Instructions burned: 2 (million)
% 0.14/0.37 % (24033)------------------------------
% 0.14/0.37 % (24033)------------------------------
% 0.14/0.38 % (24036)Instruction limit reached!
% 0.14/0.38 % (24036)------------------------------
% 0.14/0.38 % (24036)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (24036)Termination reason: Unknown
% 0.14/0.38 % (24036)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (24036)Memory used [KB]: 1023
% 0.14/0.38 % (24036)Time elapsed: 0.003 s
% 0.14/0.38 % (24036)Instructions burned: 3 (million)
% 0.14/0.38 % (24036)------------------------------
% 0.14/0.38 % (24036)------------------------------
% 0.21/0.38 % (24030)Instruction limit reached!
% 0.21/0.38 % (24030)------------------------------
% 0.21/0.38 % (24030)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (24030)Termination reason: Unknown
% 0.21/0.38 % (24030)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (24030)Memory used [KB]: 5500
% 0.21/0.38 % (24030)Time elapsed: 0.005 s
% 0.21/0.38 % (24030)Instructions burned: 4 (million)
% 0.21/0.38 % (24030)------------------------------
% 0.21/0.38 % (24030)------------------------------
% 0.21/0.38 % (24041)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 % (24034)First to succeed.
% 0.21/0.38 % (24029)Also succeeded, but the first one will report.
% 0.21/0.38 % (24031)Also succeeded, but the first one will report.
% 0.21/0.38 % (24034)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_2, type, setadjoin: $i > $i > $i).
% 0.21/0.38 thf(func_def_3, type, powerset: $i > $i).
% 0.21/0.38 thf(func_def_4, type, subset: $i > $i > $o).
% 0.21/0.38 thf(func_def_8, type, binunion: $i > $i > $i).
% 0.21/0.38 thf(f87,plain,(
% 0.21/0.38 $false),
% 0.21/0.38 inference(subsumption_resolution,[],[f86,f53])).
% 0.21/0.38 thf(f53,plain,(
% 0.21/0.38 ($true = (in @ sK9 @ sK8))),
% 0.21/0.38 inference(cnf_transformation,[],[f38])).
% 0.21/0.38 thf(f38,plain,(
% 0.21/0.38 (powersetsubset = $true) & (binunionLsub = $true) & (singletoninpowerset = $true) & (($true != (in @ (setadjoin @ sK9 @ emptyset) @ (powerset @ (binunion @ sK8 @ sK7)))) & ($true = (in @ sK9 @ sK8))) & (subsetE = $true)),
% 0.21/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f36,f37])).
% 0.21/0.38 thf(f37,plain,(
% 0.21/0.38 ? [X0,X1,X2] : (($true != (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X0)))) & ((in @ X2 @ X1) = $true)) => (($true != (in @ (setadjoin @ sK9 @ emptyset) @ (powerset @ (binunion @ sK8 @ sK7)))) & ($true = (in @ sK9 @ sK8)))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f36,plain,(
% 0.21/0.38 (powersetsubset = $true) & (binunionLsub = $true) & (singletoninpowerset = $true) & ? [X0,X1,X2] : (($true != (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X1 @ X0)))) & ((in @ X2 @ X1) = $true)) & (subsetE = $true)),
% 0.21/0.38 inference(rectify,[],[f21])).
% 0.21/0.38 thf(f21,plain,(
% 0.21/0.38 (powersetsubset = $true) & (binunionLsub = $true) & (singletoninpowerset = $true) & ? [X0,X2,X1] : (($true != (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X2 @ X0)))) & ($true = (in @ X1 @ X2))) & (subsetE = $true)),
% 0.21/0.38 inference(flattening,[],[f20])).
% 0.21/0.38 thf(f20,plain,(
% 0.21/0.38 (((? [X0,X2,X1] : (($true != (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X2 @ X0)))) & ($true = (in @ X1 @ X2))) & (singletoninpowerset = $true)) & (binunionLsub = $true)) & (powersetsubset = $true)) & (subsetE = $true)),
% 0.21/0.38 inference(ennf_transformation,[],[f17])).
% 0.21/0.38 thf(f17,plain,(
% 0.21/0.38 ~((subsetE = $true) => ((powersetsubset = $true) => ((binunionLsub = $true) => ((singletoninpowerset = $true) => ! [X2,X0,X1] : (($true = (in @ X1 @ X2)) => ($true = (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X2 @ X0)))))))))),
% 0.21/0.38 inference(fool_elimination,[],[f16])).
% 0.21/0.38 thf(f16,plain,(
% 0.21/0.38 ~(subsetE => (powersetsubset => (binunionLsub => (singletoninpowerset => ! [X0,X1,X2] : ((in @ X1 @ X2) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ (binunion @ X2 @ X0))))))))),
% 0.21/0.38 inference(rectify,[],[f6])).
% 0.21/0.38 thf(f6,negated_conjecture,(
% 0.21/0.38 ~(subsetE => (powersetsubset => (binunionLsub => (singletoninpowerset => ! [X1,X2,X0] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1))))))))),
% 0.21/0.38 inference(negated_conjecture,[],[f5])).
% 0.21/0.38 thf(f5,conjecture,(
% 0.21/0.38 subsetE => (powersetsubset => (binunionLsub => (singletoninpowerset => ! [X1,X2,X0] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X0 @ X1)))))))),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion)).
% 0.21/0.38 thf(f86,plain,(
% 0.21/0.38 ($true != (in @ sK9 @ sK8))),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f85])).
% 0.21/0.38 thf(f85,plain,(
% 0.21/0.38 ($true != $true) | ($true != (in @ sK9 @ sK8))),
% 0.21/0.38 inference(superposition,[],[f82,f75])).
% 0.21/0.38 thf(f75,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ (binunion @ X1 @ X0)) = $true)) )),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f68])).
% 0.21/0.38 thf(f68,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((subset @ X1 @ (binunion @ X1 @ X0)) = $true)) )),
% 0.21/0.38 inference(definition_unfolding,[],[f51,f56])).
% 0.21/0.38 thf(f56,plain,(
% 0.21/0.38 (binunionLsub = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f38])).
% 0.21/0.38 thf(f51,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ (binunion @ X1 @ X0)) = $true) | (binunionLsub != $true)) )),
% 0.21/0.38 inference(cnf_transformation,[],[f35])).
% 0.21/0.38 thf(f35,plain,(
% 0.21/0.38 (! [X0,X1] : ((subset @ X1 @ (binunion @ X1 @ X0)) = $true) | (binunionLsub != $true)) & ((binunionLsub = $true) | ($true != (subset @ sK6 @ (binunion @ sK6 @ sK5))))),
% 0.21/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f33,f34])).
% 0.21/0.38 thf(f34,plain,(
% 0.21/0.38 ? [X2,X3] : ($true != (subset @ X3 @ (binunion @ X3 @ X2))) => ($true != (subset @ sK6 @ (binunion @ sK6 @ sK5)))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f33,plain,(
% 0.21/0.38 (! [X0,X1] : ((subset @ X1 @ (binunion @ X1 @ X0)) = $true) | (binunionLsub != $true)) & ((binunionLsub = $true) | ? [X2,X3] : ($true != (subset @ X3 @ (binunion @ X3 @ X2))))),
% 0.21/0.38 inference(rectify,[],[f32])).
% 0.21/0.38 thf(f32,plain,(
% 0.21/0.38 (! [X1,X0] : ((subset @ X0 @ (binunion @ X0 @ X1)) = $true) | (binunionLsub != $true)) & ((binunionLsub = $true) | ? [X1,X0] : ((subset @ X0 @ (binunion @ X0 @ X1)) != $true))),
% 0.21/0.38 inference(nnf_transformation,[],[f15])).
% 0.21/0.38 thf(f15,plain,(
% 0.21/0.38 ! [X1,X0] : ((subset @ X0 @ (binunion @ X0 @ X1)) = $true) <=> (binunionLsub = $true)),
% 0.21/0.38 inference(fool_elimination,[],[f14])).
% 0.21/0.38 thf(f14,plain,(
% 0.21/0.38 (! [X0,X1] : (subset @ X0 @ (binunion @ X0 @ X1)) = binunionLsub)),
% 0.21/0.38 inference(rectify,[],[f3])).
% 0.21/0.38 thf(f3,axiom,(
% 0.21/0.38 (! [X0,X1] : (subset @ X0 @ (binunion @ X0 @ X1)) = binunionLsub)),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub)).
% 0.21/0.38 thf(f82,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true != (subset @ X0 @ (binunion @ sK8 @ sK7))) | ($true != (in @ sK9 @ X0))) )),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f81])).
% 0.21/0.38 thf(f81,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true != (in @ sK9 @ X0)) | ($true != $true) | ($true != (subset @ X0 @ (binunion @ sK8 @ sK7)))) )),
% 0.21/0.38 inference(superposition,[],[f80,f74])).
% 0.21/0.38 thf(f74,plain,(
% 0.21/0.38 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) | ((in @ X5 @ X3) != $true) | ($true != (subset @ X3 @ X4))) )),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f64])).
% 0.21/0.38 thf(f64,plain,(
% 0.21/0.38 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (subset @ X3 @ X4)) | ((in @ X5 @ X3) != $true) | ((in @ X5 @ X4) = $true) | ($true != $true)) )),
% 0.21/0.38 inference(definition_unfolding,[],[f43,f52])).
% 0.21/0.38 thf(f52,plain,(
% 0.21/0.38 (subsetE = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f38])).
% 0.21/0.38 thf(f43,plain,(
% 0.21/0.38 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X4) = $true) | ($true != (subset @ X3 @ X4)) | ((in @ X5 @ X3) != $true) | (subsetE != $true)) )),
% 0.21/0.38 inference(cnf_transformation,[],[f27])).
% 0.21/0.38 thf(f27,plain,(
% 0.21/0.38 ((subsetE = $true) | (($true != (in @ sK2 @ sK1)) & ($true = (subset @ sK0 @ sK1)) & ($true = (in @ sK2 @ sK0)))) & (! [X3,X4,X5] : (((in @ X5 @ X4) = $true) | ($true != (subset @ X3 @ X4)) | ((in @ X5 @ X3) != $true)) | (subsetE != $true))),
% 0.21/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f25,f26])).
% 0.21/0.38 thf(f26,plain,(
% 0.21/0.38 ? [X0,X1,X2] : (((in @ X2 @ X1) != $true) & ((subset @ X0 @ X1) = $true) & ((in @ X2 @ X0) = $true)) => (($true != (in @ sK2 @ sK1)) & ($true = (subset @ sK0 @ sK1)) & ($true = (in @ sK2 @ sK0)))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f25,plain,(
% 0.21/0.38 ((subsetE = $true) | ? [X0,X1,X2] : (((in @ X2 @ X1) != $true) & ((subset @ X0 @ X1) = $true) & ((in @ X2 @ X0) = $true))) & (! [X3,X4,X5] : (((in @ X5 @ X4) = $true) | ($true != (subset @ X3 @ X4)) | ((in @ X5 @ X3) != $true)) | (subsetE != $true))),
% 0.21/0.38 inference(rectify,[],[f24])).
% 0.21/0.38 thf(f24,plain,(
% 0.21/0.38 ((subsetE = $true) | ? [X0,X1,X2] : (((in @ X2 @ X1) != $true) & ((subset @ X0 @ X1) = $true) & ((in @ X2 @ X0) = $true))) & (! [X0,X1,X2] : (((in @ X2 @ X1) = $true) | ((subset @ X0 @ X1) != $true) | ((in @ X2 @ X0) != $true)) | (subsetE != $true))),
% 0.21/0.38 inference(nnf_transformation,[],[f19])).
% 0.21/0.38 thf(f19,plain,(
% 0.21/0.38 (subsetE = $true) <=> ! [X0,X1,X2] : (((in @ X2 @ X1) = $true) | ((subset @ X0 @ X1) != $true) | ((in @ X2 @ X0) != $true))),
% 0.21/0.38 inference(flattening,[],[f18])).
% 0.21/0.38 thf(f18,plain,(
% 0.21/0.38 (subsetE = $true) <=> ! [X2,X0,X1] : ((((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) | ((subset @ X0 @ X1) != $true))),
% 0.21/0.38 inference(ennf_transformation,[],[f9])).
% 0.21/0.38 thf(f9,plain,(
% 0.21/0.38 (subsetE = $true) <=> ! [X2,X0,X1] : (((subset @ X0 @ X1) = $true) => (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)))),
% 0.21/0.38 inference(fool_elimination,[],[f8])).
% 0.21/0.38 thf(f8,plain,(
% 0.21/0.38 (! [X0,X1,X2] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.21/0.38 inference(rectify,[],[f1])).
% 0.21/0.38 thf(f1,axiom,(
% 0.21/0.38 (! [X0,X1,X2] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
% 0.21/0.38 thf(f80,plain,(
% 0.21/0.38 ($true != (in @ sK9 @ (binunion @ sK8 @ sK7)))),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f79])).
% 0.21/0.38 thf(f79,plain,(
% 0.21/0.38 ($true != $true) | ($true != (in @ sK9 @ (binunion @ sK8 @ sK7)))),
% 0.21/0.38 inference(superposition,[],[f54,f76])).
% 0.21/0.38 thf(f76,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0))) | ($true != (in @ X1 @ X0))) )),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f70])).
% 0.21/0.38 thf(f70,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0))) | ($true != (in @ X1 @ X0)) | ($true != $true)) )),
% 0.21/0.38 inference(definition_unfolding,[],[f60,f55])).
% 0.21/0.38 thf(f55,plain,(
% 0.21/0.38 (singletoninpowerset = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f38])).
% 0.21/0.38 thf(f60,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ X0)) | ($true = (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0))) | (singletoninpowerset != $true)) )),
% 0.21/0.38 inference(cnf_transformation,[],[f42])).
% 0.21/0.38 thf(f42,plain,(
% 0.21/0.38 (! [X0,X1] : (($true != (in @ X1 @ X0)) | ($true = (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0)))) | (singletoninpowerset != $true)) & ((singletoninpowerset = $true) | (((in @ sK11 @ sK10) = $true) & ((in @ (setadjoin @ sK11 @ emptyset) @ (powerset @ sK10)) != $true)))),
% 0.21/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f40,f41])).
% 0.21/0.38 thf(f41,plain,(
% 0.21/0.38 ? [X2,X3] : (((in @ X3 @ X2) = $true) & ($true != (in @ (setadjoin @ X3 @ emptyset) @ (powerset @ X2)))) => (((in @ sK11 @ sK10) = $true) & ((in @ (setadjoin @ sK11 @ emptyset) @ (powerset @ sK10)) != $true))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f40,plain,(
% 0.21/0.38 (! [X0,X1] : (($true != (in @ X1 @ X0)) | ($true = (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0)))) | (singletoninpowerset != $true)) & ((singletoninpowerset = $true) | ? [X2,X3] : (((in @ X3 @ X2) = $true) & ($true != (in @ (setadjoin @ X3 @ emptyset) @ (powerset @ X2)))))),
% 0.21/0.38 inference(rectify,[],[f39])).
% 0.21/0.38 thf(f39,plain,(
% 0.21/0.38 (! [X0,X1] : (($true != (in @ X1 @ X0)) | ($true = (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0)))) | (singletoninpowerset != $true)) & ((singletoninpowerset = $true) | ? [X0,X1] : (($true = (in @ X1 @ X0)) & ($true != (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0)))))),
% 0.21/0.38 inference(nnf_transformation,[],[f22])).
% 0.21/0.38 thf(f22,plain,(
% 0.21/0.38 ! [X0,X1] : (($true != (in @ X1 @ X0)) | ($true = (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0)))) <=> (singletoninpowerset = $true)),
% 0.21/0.38 inference(ennf_transformation,[],[f13])).
% 0.21/0.38 thf(f13,plain,(
% 0.21/0.38 ! [X0,X1] : (($true = (in @ X1 @ X0)) => ($true = (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0)))) <=> (singletoninpowerset = $true)),
% 0.21/0.38 inference(fool_elimination,[],[f12])).
% 0.21/0.38 thf(f12,plain,(
% 0.21/0.38 (singletoninpowerset = ! [X0,X1] : ((in @ X1 @ X0) => (in @ (setadjoin @ X1 @ emptyset) @ (powerset @ X0))))),
% 0.21/0.38 inference(rectify,[],[f4])).
% 0.21/0.38 thf(f4,axiom,(
% 0.21/0.38 (singletoninpowerset = ! [X0,X2] : ((in @ X2 @ X0) => (in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X0))))),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset)).
% 0.21/0.38 thf(f54,plain,(
% 0.21/0.38 ($true != (in @ (setadjoin @ sK9 @ emptyset) @ (powerset @ (binunion @ sK8 @ sK7))))),
% 0.21/0.38 inference(cnf_transformation,[],[f38])).
% 0.21/0.38 % SZS output end Proof for theBenchmark
% 0.21/0.38 % (24034)------------------------------
% 0.21/0.38 % (24034)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (24034)Termination reason: Refutation
% 0.21/0.38
% 0.21/0.38 % (24034)Memory used [KB]: 5500
% 0.21/0.38 % (24034)Time elapsed: 0.008 s
% 0.21/0.38 % (24034)Instructions burned: 5 (million)
% 0.21/0.38 % (24034)------------------------------
% 0.21/0.38 % (24034)------------------------------
% 0.21/0.38 % (24026)Success in time 0.013 s
% 0.21/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------