TSTP Solution File: SEU604^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU604^2 : 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 : n024.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 03:49:55 EDT 2024
% Result : Theorem 0.11s 0.36s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SEU604^2 : TPTP v8.2.0. Released v3.7.0.
% 0.08/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.11/0.32 % Computer : n024.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 15:49:07 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 This is a TH0_THM_EQU_NAR problem
% 0.11/0.33 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.34 % (12030)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (3000ds/275Mi)
% 0.11/0.34 % (12027)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (3000ds/27Mi)
% 0.11/0.34 % (12032)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)
% 0.11/0.34 % (12029)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.11/0.34 % (12028)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.11/0.34 % (12031)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.11/0.34 % (12026)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi)
% 0.11/0.34 % (12025)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.11/0.34 % (12028)Instruction limit reached!
% 0.11/0.34 % (12028)------------------------------
% 0.11/0.34 % (12028)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (12028)Termination reason: Unknown
% 0.11/0.34 % (12029)Instruction limit reached!
% 0.11/0.34 % (12029)------------------------------
% 0.11/0.34 % (12029)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (12028)Termination phase: Preprocessing 3
% 0.11/0.34
% 0.11/0.34 % (12028)Memory used [KB]: 895
% 0.11/0.34 % (12028)Time elapsed: 0.003 s
% 0.11/0.34 % (12028)Instructions burned: 2 (million)
% 0.11/0.34 % (12028)------------------------------
% 0.11/0.34 % (12028)------------------------------
% 0.11/0.34 % (12029)Termination reason: Unknown
% 0.11/0.34 % (12029)Termination phase: Property scanning
% 0.11/0.34
% 0.11/0.34 % (12029)Memory used [KB]: 895
% 0.11/0.34 % (12029)Time elapsed: 0.003 s
% 0.11/0.34 % (12029)Instructions burned: 2 (million)
% 0.11/0.34 % (12029)------------------------------
% 0.11/0.34 % (12029)------------------------------
% 0.11/0.34 % (12032)Instruction limit reached!
% 0.11/0.34 % (12032)------------------------------
% 0.11/0.34 % (12032)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (12032)Termination reason: Unknown
% 0.11/0.34 % (12032)Termination phase: Function definition elimination
% 0.11/0.34
% 0.11/0.34 % (12032)Memory used [KB]: 1023
% 0.11/0.34 % (12032)Time elapsed: 0.003 s
% 0.11/0.34 % (12032)Instructions burned: 3 (million)
% 0.11/0.34 % (12032)------------------------------
% 0.11/0.34 % (12032)------------------------------
% 0.11/0.34 % (12026)Instruction limit reached!
% 0.11/0.34 % (12026)------------------------------
% 0.11/0.34 % (12026)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.34 % (12026)Termination reason: Unknown
% 0.11/0.34 % (12026)Termination phase: Saturation
% 0.11/0.34
% 0.11/0.34 % (12026)Memory used [KB]: 5500
% 0.11/0.34 % (12026)Time elapsed: 0.004 s
% 0.11/0.34 % (12026)Instructions burned: 5 (million)
% 0.11/0.34 % (12026)------------------------------
% 0.11/0.34 % (12026)------------------------------
% 0.11/0.35 % (12031)First to succeed.
% 0.11/0.36 % (12031)Refutation found. Thanks to Tanya!
% 0.11/0.36 % SZS status Theorem for theBenchmark
% 0.11/0.36 % SZS output start Proof for theBenchmark
% 0.11/0.36 thf(func_def_0, type, in: $i > $i > $o).
% 0.11/0.36 thf(func_def_2, type, subset: $i > $i > $o).
% 0.11/0.36 thf(func_def_7, type, setminus: $i > $i > $i).
% 0.11/0.36 thf(func_def_20, type, sK8: $i > $i > $i).
% 0.11/0.36 thf(f187,plain,(
% 0.11/0.36 $false),
% 0.11/0.36 inference(subsumption_resolution,[],[f186,f70])).
% 0.11/0.36 thf(f70,plain,(
% 0.11/0.36 (emptyset != (setminus @ sK12 @ sK13))),
% 0.11/0.36 inference(cnf_transformation,[],[f49])).
% 0.11/0.36 thf(f49,plain,(
% 0.11/0.36 (subsetE = $true) & (subsetI2 = $true) & (setminusER = $true) & (setminusEL = $true) & ((emptyset != (setminus @ sK12 @ sK13)) & ((subset @ sK12 @ sK13) = $true)) & (subsetemptysetimpeq = $true)),
% 0.11/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f47,f48])).
% 0.11/0.36 thf(f48,plain,(
% 0.11/0.36 ? [X0,X1] : ((emptyset != (setminus @ X0 @ X1)) & ((subset @ X0 @ X1) = $true)) => ((emptyset != (setminus @ sK12 @ sK13)) & ((subset @ sK12 @ sK13) = $true))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f47,plain,(
% 0.11/0.36 (subsetE = $true) & (subsetI2 = $true) & (setminusER = $true) & (setminusEL = $true) & ? [X0,X1] : ((emptyset != (setminus @ X0 @ X1)) & ((subset @ X0 @ X1) = $true)) & (subsetemptysetimpeq = $true)),
% 0.11/0.36 inference(rectify,[],[f27])).
% 0.11/0.36 thf(f27,plain,(
% 0.11/0.36 (subsetE = $true) & (subsetI2 = $true) & (setminusER = $true) & (setminusEL = $true) & ? [X1,X0] : ((emptyset != (setminus @ X1 @ X0)) & ((subset @ X1 @ X0) = $true)) & (subsetemptysetimpeq = $true)),
% 0.11/0.36 inference(flattening,[],[f26])).
% 0.11/0.36 thf(f26,plain,(
% 0.11/0.36 ((((? [X1,X0] : ((emptyset != (setminus @ X1 @ X0)) & ((subset @ X1 @ X0) = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (subsetemptysetimpeq = $true)) & (subsetE = $true)) & (subsetI2 = $true)),
% 0.11/0.36 inference(ennf_transformation,[],[f12])).
% 0.11/0.36 thf(f12,plain,(
% 0.11/0.36 ~((subsetI2 = $true) => ((subsetE = $true) => ((subsetemptysetimpeq = $true) => ((setminusEL = $true) => ((setminusER = $true) => ! [X0,X1] : (((subset @ X1 @ X0) = $true) => (emptyset = (setminus @ X1 @ X0))))))))),
% 0.11/0.36 inference(fool_elimination,[],[f11])).
% 0.11/0.36 thf(f11,plain,(
% 0.11/0.36 ~(subsetI2 => (subsetE => (subsetemptysetimpeq => (setminusEL => (setminusER => ! [X0,X1] : ((subset @ X1 @ X0) => (emptyset = (setminus @ X1 @ X0))))))))),
% 0.11/0.36 inference(rectify,[],[f7])).
% 0.11/0.36 thf(f7,negated_conjecture,(
% 0.11/0.36 ~(subsetI2 => (subsetE => (subsetemptysetimpeq => (setminusEL => (setminusER => ! [X1,X0] : ((subset @ X0 @ X1) => (emptyset = (setminus @ X0 @ X1))))))))),
% 0.11/0.36 inference(negated_conjecture,[],[f6])).
% 0.11/0.36 thf(f6,conjecture,(
% 0.11/0.36 subsetI2 => (subsetE => (subsetemptysetimpeq => (setminusEL => (setminusER => ! [X1,X0] : ((subset @ X0 @ X1) => (emptyset = (setminus @ X0 @ X1)))))))),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2)).
% 0.11/0.36 thf(f186,plain,(
% 0.11/0.36 (emptyset = (setminus @ sK12 @ sK13))),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f185])).
% 0.11/0.36 thf(f185,plain,(
% 0.11/0.36 ($true != $true) | (emptyset = (setminus @ sK12 @ sK13))),
% 0.11/0.36 inference(superposition,[],[f171,f102])).
% 0.11/0.36 thf(f102,plain,(
% 0.11/0.36 ( ! [X0 : $i] : (($true = (in @ (sK8 @ X0 @ emptyset) @ X0)) | (emptyset = X0)) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f101])).
% 0.11/0.36 thf(f101,plain,(
% 0.11/0.36 ( ! [X0 : $i] : ((emptyset = X0) | ($true = (in @ (sK8 @ X0 @ emptyset) @ X0)) | ($true != $true)) )),
% 0.11/0.36 inference(superposition,[],[f99,f98])).
% 0.11/0.36 thf(f98,plain,(
% 0.11/0.36 ( ! [X3 : $i,X4 : $i] : (((subset @ X4 @ X3) = $true) | ($true = (in @ (sK8 @ X4 @ X3) @ X4))) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f87])).
% 0.11/0.36 thf(f87,plain,(
% 0.11/0.36 ( ! [X3 : $i,X4 : $i] : (($true = (in @ (sK8 @ X4 @ X3) @ X4)) | ($true != $true) | ((subset @ X4 @ X3) = $true)) )),
% 0.11/0.36 inference(definition_unfolding,[],[f62,f73])).
% 0.11/0.36 thf(f73,plain,(
% 0.11/0.36 (subsetI2 = $true)),
% 0.11/0.36 inference(cnf_transformation,[],[f49])).
% 0.11/0.36 thf(f62,plain,(
% 0.11/0.36 ( ! [X3 : $i,X4 : $i] : (($true = (in @ (sK8 @ X4 @ X3) @ X4)) | ((subset @ X4 @ X3) = $true) | (subsetI2 != $true)) )),
% 0.11/0.36 inference(cnf_transformation,[],[f42])).
% 0.11/0.36 thf(f42,plain,(
% 0.11/0.36 ((subsetI2 = $true) | (! [X2] : (((in @ X2 @ sK7) != $true) | ($true = (in @ X2 @ sK6))) & ((subset @ sK7 @ sK6) != $true))) & (! [X3,X4] : ((($true = (in @ (sK8 @ X4 @ X3) @ X4)) & ((in @ (sK8 @ X4 @ X3) @ X3) != $true)) | ((subset @ X4 @ X3) = $true)) | (subsetI2 != $true))),
% 0.11/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f39,f41,f40])).
% 0.11/0.36 thf(f40,plain,(
% 0.11/0.36 ? [X0,X1] : (! [X2] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ((subset @ X1 @ X0) != $true)) => (! [X2] : (((in @ X2 @ sK7) != $true) | ($true = (in @ X2 @ sK6))) & ((subset @ sK7 @ sK6) != $true))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f41,plain,(
% 0.11/0.36 ! [X3,X4] : (? [X5] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) != $true)) => (($true = (in @ (sK8 @ X4 @ X3) @ X4)) & ((in @ (sK8 @ X4 @ X3) @ X3) != $true)))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f39,plain,(
% 0.11/0.36 ((subsetI2 = $true) | ? [X0,X1] : (! [X2] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ((subset @ X1 @ X0) != $true))) & (! [X3,X4] : (? [X5] : (((in @ X5 @ X4) = $true) & ((in @ X5 @ X3) != $true)) | ((subset @ X4 @ X3) = $true)) | (subsetI2 != $true))),
% 0.11/0.36 inference(rectify,[],[f38])).
% 0.11/0.36 thf(f38,plain,(
% 0.11/0.36 ((subsetI2 = $true) | ? [X0,X1] : (! [X2] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true)) & ((subset @ X1 @ X0) != $true))) & (! [X0,X1] : (? [X2] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | ((subset @ X1 @ X0) = $true)) | (subsetI2 != $true))),
% 0.11/0.36 inference(nnf_transformation,[],[f29])).
% 0.11/0.36 thf(f29,plain,(
% 0.11/0.36 (subsetI2 = $true) <=> ! [X0,X1] : (? [X2] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true)) | ((subset @ X1 @ X0) = $true))),
% 0.11/0.36 inference(ennf_transformation,[],[f10])).
% 0.11/0.36 thf(f10,plain,(
% 0.11/0.36 ! [X0,X1] : (! [X2] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ((subset @ X1 @ X0) = $true)) <=> (subsetI2 = $true)),
% 0.11/0.36 inference(fool_elimination,[],[f9])).
% 0.11/0.36 thf(f9,plain,(
% 0.11/0.36 (! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI2)),
% 0.11/0.36 inference(rectify,[],[f1])).
% 0.11/0.36 thf(f1,axiom,(
% 0.11/0.36 (! [X1,X0] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2)).
% 0.11/0.36 thf(f99,plain,(
% 0.11/0.36 ( ! [X0 : $i] : (((subset @ X0 @ emptyset) != $true) | (emptyset = X0)) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f92])).
% 0.11/0.36 thf(f92,plain,(
% 0.11/0.36 ( ! [X0 : $i] : ((emptyset = X0) | ($true != $true) | ((subset @ X0 @ emptyset) != $true)) )),
% 0.11/0.36 inference(definition_unfolding,[],[f77,f68])).
% 0.11/0.36 thf(f68,plain,(
% 0.11/0.36 (subsetemptysetimpeq = $true)),
% 0.11/0.36 inference(cnf_transformation,[],[f49])).
% 0.11/0.36 thf(f77,plain,(
% 0.11/0.36 ( ! [X0 : $i] : ((emptyset = X0) | ((subset @ X0 @ emptyset) != $true) | (subsetemptysetimpeq != $true)) )),
% 0.11/0.36 inference(cnf_transformation,[],[f53])).
% 0.11/0.36 thf(f53,plain,(
% 0.11/0.36 (! [X0] : ((emptyset = X0) | ((subset @ X0 @ emptyset) != $true)) | (subsetemptysetimpeq != $true)) & ((subsetemptysetimpeq = $true) | ((emptyset != sK14) & ($true = (subset @ sK14 @ emptyset))))),
% 0.11/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f51,f52])).
% 0.11/0.36 thf(f52,plain,(
% 0.11/0.36 ? [X1] : ((emptyset != X1) & ((subset @ X1 @ emptyset) = $true)) => ((emptyset != sK14) & ($true = (subset @ sK14 @ emptyset)))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f51,plain,(
% 0.11/0.36 (! [X0] : ((emptyset = X0) | ((subset @ X0 @ emptyset) != $true)) | (subsetemptysetimpeq != $true)) & ((subsetemptysetimpeq = $true) | ? [X1] : ((emptyset != X1) & ((subset @ X1 @ emptyset) = $true)))),
% 0.11/0.36 inference(rectify,[],[f50])).
% 0.11/0.36 thf(f50,plain,(
% 0.11/0.36 (! [X0] : ((emptyset = X0) | ((subset @ X0 @ emptyset) != $true)) | (subsetemptysetimpeq != $true)) & ((subsetemptysetimpeq = $true) | ? [X0] : ((emptyset != X0) & ((subset @ X0 @ emptyset) = $true)))),
% 0.11/0.36 inference(nnf_transformation,[],[f28])).
% 0.11/0.36 thf(f28,plain,(
% 0.11/0.36 ! [X0] : ((emptyset = X0) | ((subset @ X0 @ emptyset) != $true)) <=> (subsetemptysetimpeq = $true)),
% 0.11/0.36 inference(ennf_transformation,[],[f20])).
% 0.11/0.36 thf(f20,plain,(
% 0.11/0.36 ! [X0] : (((subset @ X0 @ emptyset) = $true) => (emptyset = X0)) <=> (subsetemptysetimpeq = $true)),
% 0.11/0.36 inference(fool_elimination,[],[f19])).
% 0.11/0.36 thf(f19,plain,(
% 0.11/0.36 (! [X0] : ((subset @ X0 @ emptyset) => (emptyset = X0)) = subsetemptysetimpeq)),
% 0.11/0.36 inference(rectify,[],[f3])).
% 0.11/0.36 thf(f3,axiom,(
% 0.11/0.36 (! [X0] : ((subset @ X0 @ emptyset) => (emptyset = X0)) = subsetemptysetimpeq)),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq)).
% 0.11/0.36 thf(f171,plain,(
% 0.11/0.36 ( ! [X0 : $i] : (($true != (in @ (sK8 @ (setminus @ sK12 @ sK13) @ emptyset) @ (setminus @ X0 @ sK13)))) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f170])).
% 0.11/0.36 thf(f170,plain,(
% 0.11/0.36 ( ! [X0 : $i] : (($true != (in @ (sK8 @ (setminus @ sK12 @ sK13) @ emptyset) @ (setminus @ X0 @ sK13))) | ($true != $true)) )),
% 0.11/0.36 inference(superposition,[],[f95,f159])).
% 0.11/0.36 thf(f159,plain,(
% 0.11/0.36 ($true = (in @ (sK8 @ (setminus @ sK12 @ sK13) @ emptyset) @ sK13))),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f156])).
% 0.11/0.36 thf(f156,plain,(
% 0.11/0.36 ($true != $true) | ($true = (in @ (sK8 @ (setminus @ sK12 @ sK13) @ emptyset) @ sK13))),
% 0.11/0.36 inference(superposition,[],[f110,f150])).
% 0.11/0.36 thf(f150,plain,(
% 0.11/0.36 ((in @ (sK8 @ (setminus @ sK12 @ sK13) @ emptyset) @ sK12) = $true)),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f149])).
% 0.11/0.36 thf(f149,plain,(
% 0.11/0.36 ((in @ (sK8 @ (setminus @ sK12 @ sK13) @ emptyset) @ sK12) = $true) | (emptyset != emptyset)),
% 0.11/0.36 inference(superposition,[],[f70,f106])).
% 0.11/0.36 thf(f106,plain,(
% 0.11/0.36 ( ! [X0 : $i,X1 : $i] : ((emptyset = (setminus @ X0 @ X1)) | ((in @ (sK8 @ (setminus @ X0 @ X1) @ emptyset) @ X0) = $true)) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f104])).
% 0.11/0.36 thf(f104,plain,(
% 0.11/0.36 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK8 @ (setminus @ X0 @ X1) @ emptyset) @ X0) = $true) | (emptyset = (setminus @ X0 @ X1))) )),
% 0.11/0.36 inference(superposition,[],[f96,f102])).
% 0.11/0.36 thf(f96,plain,(
% 0.11/0.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X5 @ X3)) != $true) | ((in @ X4 @ X5) = $true)) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f80])).
% 0.11/0.36 thf(f80,plain,(
% 0.11/0.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X4 @ (setminus @ X5 @ X3)) != $true) | ((in @ X4 @ X5) = $true)) )),
% 0.11/0.36 inference(definition_unfolding,[],[f54,f71])).
% 0.11/0.36 thf(f71,plain,(
% 0.11/0.36 (setminusEL = $true)),
% 0.11/0.36 inference(cnf_transformation,[],[f49])).
% 0.11/0.36 thf(f54,plain,(
% 0.11/0.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X5) = $true) | ((in @ X4 @ (setminus @ X5 @ X3)) != $true) | (setminusEL != $true)) )),
% 0.11/0.36 inference(cnf_transformation,[],[f33])).
% 0.11/0.36 thf(f33,plain,(
% 0.11/0.36 ((setminusEL = $true) | (($true != (in @ sK1 @ sK2)) & ($true = (in @ sK1 @ (setminus @ sK2 @ sK0))))) & (! [X3,X4,X5] : (((in @ X4 @ X5) = $true) | ((in @ X4 @ (setminus @ X5 @ X3)) != $true)) | (setminusEL != $true))),
% 0.11/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f31,f32])).
% 0.11/0.36 thf(f32,plain,(
% 0.11/0.36 ? [X0,X1,X2] : (((in @ X1 @ X2) != $true) & ((in @ X1 @ (setminus @ X2 @ X0)) = $true)) => (($true != (in @ sK1 @ sK2)) & ($true = (in @ sK1 @ (setminus @ sK2 @ sK0))))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f31,plain,(
% 0.11/0.36 ((setminusEL = $true) | ? [X0,X1,X2] : (((in @ X1 @ X2) != $true) & ((in @ X1 @ (setminus @ X2 @ X0)) = $true))) & (! [X3,X4,X5] : (((in @ X4 @ X5) = $true) | ((in @ X4 @ (setminus @ X5 @ X3)) != $true)) | (setminusEL != $true))),
% 0.11/0.36 inference(rectify,[],[f30])).
% 0.11/0.36 thf(f30,plain,(
% 0.11/0.36 ((setminusEL = $true) | ? [X1,X0,X2] : (((in @ X0 @ X2) != $true) & ((in @ X0 @ (setminus @ X2 @ X1)) = $true))) & (! [X1,X0,X2] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ (setminus @ X2 @ X1)) != $true)) | (setminusEL != $true))),
% 0.11/0.36 inference(nnf_transformation,[],[f24])).
% 0.11/0.36 thf(f24,plain,(
% 0.11/0.36 (setminusEL = $true) <=> ! [X1,X0,X2] : (((in @ X0 @ X2) = $true) | ((in @ X0 @ (setminus @ X2 @ X1)) != $true))),
% 0.11/0.36 inference(ennf_transformation,[],[f16])).
% 0.11/0.36 thf(f16,plain,(
% 0.11/0.36 (setminusEL = $true) <=> ! [X0,X1,X2] : (((in @ X0 @ (setminus @ X2 @ X1)) = $true) => ((in @ X0 @ X2) = $true))),
% 0.11/0.36 inference(fool_elimination,[],[f15])).
% 0.11/0.36 thf(f15,plain,(
% 0.11/0.36 (setminusEL = ! [X0,X1,X2] : ((in @ X0 @ (setminus @ X2 @ X1)) => (in @ X0 @ X2)))),
% 0.11/0.36 inference(rectify,[],[f4])).
% 0.11/0.36 thf(f4,axiom,(
% 0.11/0.36 (setminusEL = ! [X2,X1,X0] : ((in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X0)))),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL)).
% 0.11/0.36 thf(f110,plain,(
% 0.11/0.36 ( ! [X0 : $i] : (((in @ X0 @ sK12) != $true) | ((in @ X0 @ sK13) = $true)) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f108])).
% 0.11/0.36 thf(f108,plain,(
% 0.11/0.36 ( ! [X0 : $i] : (((in @ X0 @ sK12) != $true) | ($true != $true) | ((in @ X0 @ sK13) = $true)) )),
% 0.11/0.36 inference(superposition,[],[f97,f69])).
% 0.11/0.36 thf(f69,plain,(
% 0.11/0.36 ((subset @ sK12 @ sK13) = $true)),
% 0.11/0.36 inference(cnf_transformation,[],[f49])).
% 0.11/0.36 thf(f97,plain,(
% 0.11/0.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f81])).
% 0.11/0.36 thf(f81,plain,(
% 0.11/0.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((in @ X2 @ X0) != $true) | ($true != $true) | ((in @ X2 @ X1) = $true)) )),
% 0.11/0.36 inference(definition_unfolding,[],[f60,f74])).
% 0.11/0.36 thf(f74,plain,(
% 0.11/0.36 (subsetE = $true)),
% 0.11/0.36 inference(cnf_transformation,[],[f49])).
% 0.11/0.36 thf(f60,plain,(
% 0.11/0.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true) | (subsetE != $true)) )),
% 0.11/0.36 inference(cnf_transformation,[],[f37])).
% 0.11/0.36 thf(f37,plain,(
% 0.11/0.36 (! [X0,X1,X2] : (((subset @ X0 @ X1) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) | (subsetE != $true)) & ((subsetE = $true) | (((subset @ sK3 @ sK4) = $true) & ((in @ sK5 @ sK4) != $true) & ((in @ sK5 @ sK3) = $true)))),
% 0.11/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f35,f36])).
% 0.11/0.36 thf(f36,plain,(
% 0.11/0.36 ? [X3,X4,X5] : (((subset @ X3 @ X4) = $true) & ((in @ X5 @ X4) != $true) & ((in @ X5 @ X3) = $true)) => (((subset @ sK3 @ sK4) = $true) & ((in @ sK5 @ sK4) != $true) & ((in @ sK5 @ sK3) = $true))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f35,plain,(
% 0.11/0.36 (! [X0,X1,X2] : (((subset @ X0 @ X1) != $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X3,X4,X5] : (((subset @ X3 @ X4) = $true) & ((in @ X5 @ X4) != $true) & ((in @ X5 @ X3) = $true)))),
% 0.11/0.36 inference(rectify,[],[f34])).
% 0.11/0.36 thf(f34,plain,(
% 0.11/0.36 (! [X1,X2,X0] : (((subset @ X1 @ X2) != $true) | ((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true)) | (subsetE != $true)) & ((subsetE = $true) | ? [X1,X2,X0] : (((subset @ X1 @ X2) = $true) & ((in @ X0 @ X2) != $true) & ((in @ X0 @ X1) = $true)))),
% 0.11/0.36 inference(nnf_transformation,[],[f23])).
% 0.11/0.36 thf(f23,plain,(
% 0.11/0.36 ! [X1,X2,X0] : (((subset @ X1 @ X2) != $true) | ((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true)) <=> (subsetE = $true)),
% 0.11/0.36 inference(flattening,[],[f22])).
% 0.11/0.36 thf(f22,plain,(
% 0.11/0.36 (subsetE = $true) <=> ! [X2,X0,X1] : ((((in @ X0 @ X2) = $true) | ((in @ X0 @ X1) != $true)) | ((subset @ X1 @ X2) != $true))),
% 0.11/0.36 inference(ennf_transformation,[],[f14])).
% 0.11/0.36 thf(f14,plain,(
% 0.11/0.36 (subsetE = $true) <=> ! [X2,X0,X1] : (((subset @ X1 @ X2) = $true) => (((in @ X0 @ X1) = $true) => ((in @ X0 @ X2) = $true)))),
% 0.11/0.36 inference(fool_elimination,[],[f13])).
% 0.11/0.36 thf(f13,plain,(
% 0.11/0.36 (! [X0,X1,X2] : ((subset @ X1 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ X2))) = subsetE)),
% 0.11/0.36 inference(rectify,[],[f2])).
% 0.11/0.36 thf(f2,axiom,(
% 0.11/0.36 (! [X2,X0,X1] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
% 0.11/0.36 thf(f95,plain,(
% 0.11/0.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) | ((in @ X3 @ (setminus @ X5 @ X4)) != $true)) )),
% 0.11/0.36 inference(trivial_inequality_removal,[],[f91])).
% 0.11/0.36 thf(f91,plain,(
% 0.11/0.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X3 @ (setminus @ X5 @ X4)) != $true) | ((in @ X3 @ X4) != $true)) )),
% 0.11/0.36 inference(definition_unfolding,[],[f65,f72])).
% 0.11/0.36 thf(f72,plain,(
% 0.11/0.36 (setminusER = $true)),
% 0.11/0.36 inference(cnf_transformation,[],[f49])).
% 0.11/0.36 thf(f65,plain,(
% 0.11/0.36 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X4) != $true) | ((in @ X3 @ (setminus @ X5 @ X4)) != $true) | (setminusER != $true)) )),
% 0.11/0.36 inference(cnf_transformation,[],[f46])).
% 0.11/0.36 thf(f46,plain,(
% 0.11/0.36 ((setminusER = $true) | (((in @ sK9 @ sK10) = $true) & ((in @ sK9 @ (setminus @ sK11 @ sK10)) = $true))) & (! [X3,X4,X5] : (((in @ X3 @ X4) != $true) | ((in @ X3 @ (setminus @ X5 @ X4)) != $true)) | (setminusER != $true))),
% 0.11/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f44,f45])).
% 0.11/0.36 thf(f45,plain,(
% 0.11/0.36 ? [X0,X1,X2] : (((in @ X0 @ X1) = $true) & ((in @ X0 @ (setminus @ X2 @ X1)) = $true)) => (((in @ sK9 @ sK10) = $true) & ((in @ sK9 @ (setminus @ sK11 @ sK10)) = $true))),
% 0.11/0.36 introduced(choice_axiom,[])).
% 0.11/0.36 thf(f44,plain,(
% 0.11/0.36 ((setminusER = $true) | ? [X0,X1,X2] : (((in @ X0 @ X1) = $true) & ((in @ X0 @ (setminus @ X2 @ X1)) = $true))) & (! [X3,X4,X5] : (((in @ X3 @ X4) != $true) | ((in @ X3 @ (setminus @ X5 @ X4)) != $true)) | (setminusER != $true))),
% 0.11/0.36 inference(rectify,[],[f43])).
% 0.11/0.36 thf(f43,plain,(
% 0.11/0.36 ((setminusER = $true) | ? [X1,X2,X0] : (((in @ X1 @ X2) = $true) & ((in @ X1 @ (setminus @ X0 @ X2)) = $true))) & (! [X1,X2,X0] : (((in @ X1 @ X2) != $true) | ((in @ X1 @ (setminus @ X0 @ X2)) != $true)) | (setminusER != $true))),
% 0.11/0.36 inference(nnf_transformation,[],[f25])).
% 0.11/0.36 thf(f25,plain,(
% 0.11/0.36 (setminusER = $true) <=> ! [X1,X2,X0] : (((in @ X1 @ X2) != $true) | ((in @ X1 @ (setminus @ X0 @ X2)) != $true))),
% 0.11/0.36 inference(ennf_transformation,[],[f21])).
% 0.11/0.36 thf(f21,plain,(
% 0.11/0.36 ! [X0,X2,X1] : (((in @ X1 @ (setminus @ X0 @ X2)) = $true) => ((in @ X1 @ X2) != $true)) <=> (setminusER = $true)),
% 0.11/0.36 inference(flattening,[],[f18])).
% 0.11/0.36 thf(f18,plain,(
% 0.11/0.36 (setminusER = $true) <=> ! [X0,X1,X2] : (((in @ X1 @ (setminus @ X0 @ X2)) = $true) => ~((in @ X1 @ X2) = $true))),
% 0.11/0.36 inference(fool_elimination,[],[f17])).
% 0.11/0.36 thf(f17,plain,(
% 0.11/0.36 (setminusER = ! [X0,X1,X2] : ((in @ X1 @ (setminus @ X0 @ X2)) => ~(in @ X1 @ X2)))),
% 0.11/0.36 inference(rectify,[],[f5])).
% 0.11/0.36 thf(f5,axiom,(
% 0.11/0.36 (setminusER = ! [X0,X2,X1] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 0.11/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER)).
% 0.11/0.36 % SZS output end Proof for theBenchmark
% 0.11/0.36 % (12031)------------------------------
% 0.11/0.36 % (12031)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.11/0.36 % (12031)Termination reason: Refutation
% 0.11/0.36
% 0.11/0.36 % (12031)Memory used [KB]: 5628
% 0.11/0.36 % (12031)Time elapsed: 0.014 s
% 0.11/0.36 % (12031)Instructions burned: 16 (million)
% 0.11/0.36 % (12031)------------------------------
% 0.11/0.36 % (12031)------------------------------
% 0.11/0.36 % (12024)Success in time 0.015 s
% 0.11/0.36 % Vampire---4.8 exiting
%------------------------------------------------------------------------------