TSTP Solution File: SEU752^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU752^2 : 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 : n018.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 03:51:16 EDT 2024
% Result : Theorem 0.22s 0.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU752^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.15 % 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
% 0.15/0.37 % Computer : n018.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 16:06:08 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a TH0_THM_EQU_NAR problem
% 0.15/0.37 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
% 0.22/0.39 % (24801)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.22/0.39 % (24804)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39 % (24805)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.22/0.39 % (24803)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.22/0.39 % (24802)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.39 % (24807)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.22/0.39 % (24804)Instruction limit reached!
% 0.22/0.39 % (24804)------------------------------
% 0.22/0.39 % (24804)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (24805)Instruction limit reached!
% 0.22/0.39 % (24805)------------------------------
% 0.22/0.39 % (24805)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (24804)Termination reason: Unknown
% 0.22/0.39 % (24804)Termination phase: shuffling
% 0.22/0.39
% 0.22/0.39 % (24804)Memory used [KB]: 895
% 0.22/0.39 % (24804)Time elapsed: 0.003 s
% 0.22/0.39 % (24804)Instructions burned: 2 (million)
% 0.22/0.39 % (24804)------------------------------
% 0.22/0.39 % (24804)------------------------------
% 0.22/0.39 % (24805)Termination reason: Unknown
% 0.22/0.39 % (24805)Termination phase: shuffling
% 0.22/0.39
% 0.22/0.39 % (24805)Memory used [KB]: 1023
% 0.22/0.39 % (24805)Time elapsed: 0.003 s
% 0.22/0.39 % (24805)Instructions burned: 2 (million)
% 0.22/0.39 % (24805)------------------------------
% 0.22/0.39 % (24805)------------------------------
% 0.22/0.39 % (24802)Instruction limit reached!
% 0.22/0.39 % (24802)------------------------------
% 0.22/0.39 % (24802)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (24802)Termination reason: Unknown
% 0.22/0.39 % (24802)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (24802)Memory used [KB]: 5500
% 0.22/0.39 % (24802)Time elapsed: 0.005 s
% 0.22/0.39 % (24802)Instructions burned: 5 (million)
% 0.22/0.39 % (24802)------------------------------
% 0.22/0.39 % (24802)------------------------------
% 0.22/0.39 % (24806)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.22/0.40 % (24806)First to succeed.
% 0.22/0.40 % (24807)Instruction limit reached!
% 0.22/0.40 % (24807)------------------------------
% 0.22/0.40 % (24807)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (24807)Termination reason: Unknown
% 0.22/0.40 % (24807)Termination phase: Saturation
% 0.22/0.40
% 0.22/0.40 % (24807)Memory used [KB]: 5628
% 0.22/0.40 % (24807)Time elapsed: 0.014 s
% 0.22/0.40 % (24807)Instructions burned: 18 (million)
% 0.22/0.40 % (24807)------------------------------
% 0.22/0.40 % (24807)------------------------------
% 0.22/0.40 % (24808)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.40 % (24808)Instruction limit reached!
% 0.22/0.40 % (24808)------------------------------
% 0.22/0.40 % (24808)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (24808)Termination reason: Unknown
% 0.22/0.40 % (24808)Termination phase: Function definition elimination
% 0.22/0.40
% 0.22/0.40 % (24808)Memory used [KB]: 1023
% 0.22/0.40 % (24808)Time elapsed: 0.004 s
% 0.22/0.40 % (24808)Instructions burned: 4 (million)
% 0.22/0.40 % (24808)------------------------------
% 0.22/0.40 % (24808)------------------------------
% 0.22/0.41 % (24811)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.22/0.41 % (24809)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.22/0.41 % (24811)Instruction limit reached!
% 0.22/0.41 % (24811)------------------------------
% 0.22/0.41 % (24811)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (24811)Termination reason: Unknown
% 0.22/0.41 % (24811)Termination phase: Preprocessing 3
% 0.22/0.41
% 0.22/0.41 % (24811)Memory used [KB]: 1023
% 0.22/0.41 % (24811)Time elapsed: 0.003 s
% 0.22/0.41 % (24811)Instructions burned: 3 (million)
% 0.22/0.41 % (24811)------------------------------
% 0.22/0.41 % (24811)------------------------------
% 0.22/0.41 % (24806)Refutation found. Thanks to Tanya!
% 0.22/0.41 % SZS status Theorem for theBenchmark
% 0.22/0.41 % SZS output start Proof for theBenchmark
% 0.22/0.41 thf(func_def_0, type, in: $i > $i > $o).
% 0.22/0.41 thf(func_def_1, type, powerset: $i > $i).
% 0.22/0.41 thf(func_def_2, type, binunion: $i > $i > $i).
% 0.22/0.41 thf(func_def_5, type, binintersect: $i > $i > $i).
% 0.22/0.41 thf(func_def_6, type, setminus: $i > $i > $i).
% 0.22/0.41 thf(f170,plain,(
% 0.22/0.41 $false),
% 0.22/0.41 inference(avatar_sat_refutation,[],[f139,f149,f158,f160,f169])).
% 0.22/0.41 thf(f169,plain,(
% 0.22/0.41 ~spl21_1 | ~spl21_4),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f168])).
% 0.22/0.41 thf(f168,plain,(
% 0.22/0.41 $false | (~spl21_1 | ~spl21_4)),
% 0.22/0.41 inference(subsumption_resolution,[],[f167,f148])).
% 0.22/0.41 thf(f148,plain,(
% 0.22/0.41 ((in @ sK9 @ sK6) = $true) | ~spl21_4),
% 0.22/0.41 inference(avatar_component_clause,[],[f146])).
% 0.22/0.41 thf(f146,plain,(
% 0.22/0.41 spl21_4 <=> ((in @ sK9 @ sK6) = $true)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl21_4])])).
% 0.22/0.41 thf(f167,plain,(
% 0.22/0.41 ((in @ sK9 @ sK6) != $true) | ~spl21_1),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f166])).
% 0.22/0.41 thf(f166,plain,(
% 0.22/0.41 ((in @ sK9 @ sK6) != $true) | ($true != $true) | ~spl21_1),
% 0.22/0.41 inference(superposition,[],[f121,f134])).
% 0.22/0.41 thf(f134,plain,(
% 0.22/0.41 ($true = (in @ sK9 @ (setminus @ sK7 @ sK6))) | ~spl21_1),
% 0.22/0.41 inference(avatar_component_clause,[],[f132])).
% 0.22/0.41 thf(f132,plain,(
% 0.22/0.41 spl21_1 <=> ($true = (in @ sK9 @ (setminus @ sK7 @ sK6)))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl21_1])])).
% 0.22/0.41 thf(f121,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ (setminus @ X3 @ X4))) | ($true != (in @ X5 @ X4))) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f99])).
% 0.22/0.41 thf(f99,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != (in @ X5 @ (setminus @ X3 @ X4))) | ($true != (in @ X5 @ X4))) )),
% 0.22/0.41 inference(definition_unfolding,[],[f64,f77])).
% 0.22/0.41 thf(f77,plain,(
% 0.22/0.41 (setminusER = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f47])).
% 0.22/0.41 thf(f47,plain,(
% 0.22/0.41 (binintersectTERcontra = $true) & (binunionE = $true) & (binintersectTELcontra = $true) & (setminusER = $true) & (setminusI = $true) & (($true = (in @ sK6 @ (powerset @ sK7))) & (((in @ sK8 @ (powerset @ sK7)) = $true) & (((in @ sK9 @ (setminus @ sK7 @ (binintersect @ sK6 @ sK8))) != $true) & ((in @ sK9 @ sK7) = $true) & ($true = (in @ sK9 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ sK8)))))))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f26,f46,f45,f44])).
% 0.22/0.41 thf(f44,plain,(
% 0.22/0.41 ? [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3] : (($true != (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true)))) => (($true = (in @ sK6 @ (powerset @ sK7))) & ? [X2] : (((in @ X2 @ (powerset @ sK7)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ sK7 @ (binintersect @ sK6 @ X2))) != $true) & ($true = (in @ X3 @ sK7)) & ($true = (in @ X3 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ X2)))))))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f45,plain,(
% 0.22/0.41 ? [X2] : (((in @ X2 @ (powerset @ sK7)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ sK7 @ (binintersect @ sK6 @ X2))) != $true) & ($true = (in @ X3 @ sK7)) & ($true = (in @ X3 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ X2)))))) => (((in @ sK8 @ (powerset @ sK7)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ sK7 @ (binintersect @ sK6 @ sK8))) != $true) & ($true = (in @ X3 @ sK7)) & ((in @ X3 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ sK8))) = $true)))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f46,plain,(
% 0.22/0.41 ? [X3] : (((in @ X3 @ (setminus @ sK7 @ (binintersect @ sK6 @ sK8))) != $true) & ($true = (in @ X3 @ sK7)) & ((in @ X3 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ sK8))) = $true)) => (((in @ sK9 @ (setminus @ sK7 @ (binintersect @ sK6 @ sK8))) != $true) & ((in @ sK9 @ sK7) = $true) & ($true = (in @ sK9 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ sK8)))))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f26,plain,(
% 0.22/0.41 (binintersectTERcontra = $true) & (binunionE = $true) & (binintersectTELcontra = $true) & (setminusER = $true) & (setminusI = $true) & ? [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (($true = (in @ X2 @ (powerset @ X1))) & ? [X3] : (($true != (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true))))),
% 0.22/0.41 inference(flattening,[],[f25])).
% 0.22/0.41 thf(f25,plain,(
% 0.22/0.41 ((((? [X1,X0] : (? [X2] : (? [X3] : ((($true != (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) & ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true)) & ((in @ X3 @ X1) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))) & ((in @ X0 @ (powerset @ X1)) = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (setminusER = $true)) & (setminusI = $true)) & (binunionE = $true)),
% 0.22/0.41 inference(ennf_transformation,[],[f14])).
% 0.22/0.41 thf(f14,plain,(
% 0.22/0.41 ~((binunionE = $true) => ((setminusI = $true) => ((setminusER = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ! [X1,X0] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = $true) => ($true = (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))))))))))))),
% 0.22/0.41 inference(fool_elimination,[],[f13])).
% 0.22/0.41 thf(f13,plain,(
% 0.22/0.41 ~(binunionE => (setminusI => (setminusER => (binintersectTELcontra => (binintersectTERcontra => ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => ! [X3] : ((in @ X3 @ X1) => ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) => (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))))))))))))),
% 0.22/0.41 inference(rectify,[],[f7])).
% 0.22/0.41 thf(f7,negated_conjecture,(
% 0.22/0.41 ~(binunionE => (setminusI => (setminusER => (binintersectTELcontra => (binintersectTERcontra => ! [X3,X0] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => ((in @ X2 @ (binunion @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4))) => (in @ X2 @ (setminus @ X0 @ (binintersect @ X3 @ X4))))))))))))),
% 0.22/0.41 inference(negated_conjecture,[],[f6])).
% 0.22/0.41 thf(f6,conjecture,(
% 0.22/0.41 binunionE => (setminusI => (setminusER => (binintersectTELcontra => (binintersectTERcontra => ! [X3,X0] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => ((in @ X2 @ (binunion @ (setminus @ X0 @ X3) @ (setminus @ X0 @ X4))) => (in @ X2 @ (setminus @ X0 @ (binintersect @ X3 @ X4)))))))))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1b)).
% 0.22/0.41 thf(f64,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X4)) | ($true != (in @ X5 @ (setminus @ X3 @ X4))) | (setminusER != $true)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f39])).
% 0.22/0.41 thf(f39,plain,(
% 0.22/0.41 ((setminusER = $true) | (((in @ sK2 @ sK1) = $true) & ($true = (in @ sK2 @ (setminus @ sK0 @ sK1))))) & (! [X3,X4,X5] : (($true != (in @ X5 @ X4)) | ($true != (in @ X5 @ (setminus @ X3 @ X4)))) | (setminusER != $true))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f37,f38])).
% 0.22/0.41 thf(f38,plain,(
% 0.22/0.41 ? [X0,X1,X2] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ (setminus @ X0 @ X1)) = $true)) => (((in @ sK2 @ sK1) = $true) & ($true = (in @ sK2 @ (setminus @ sK0 @ sK1))))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f37,plain,(
% 0.22/0.41 ((setminusER = $true) | ? [X0,X1,X2] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ (setminus @ X0 @ X1)) = $true))) & (! [X3,X4,X5] : (($true != (in @ X5 @ X4)) | ($true != (in @ X5 @ (setminus @ X3 @ X4)))) | (setminusER != $true))),
% 0.22/0.41 inference(rectify,[],[f36])).
% 0.22/0.41 thf(f36,plain,(
% 0.22/0.41 ((setminusER = $true) | ? [X2,X0,X1] : (((in @ X1 @ X0) = $true) & ($true = (in @ X1 @ (setminus @ X2 @ X0))))) & (! [X2,X0,X1] : (((in @ X1 @ X0) != $true) | ($true != (in @ X1 @ (setminus @ X2 @ X0)))) | (setminusER != $true))),
% 0.22/0.41 inference(nnf_transformation,[],[f29])).
% 0.22/0.41 thf(f29,plain,(
% 0.22/0.41 (setminusER = $true) <=> ! [X2,X0,X1] : (((in @ X1 @ X0) != $true) | ($true != (in @ X1 @ (setminus @ X2 @ X0))))),
% 0.22/0.41 inference(ennf_transformation,[],[f22])).
% 0.22/0.41 thf(f22,plain,(
% 0.22/0.41 ! [X0,X2,X1] : (($true = (in @ X1 @ (setminus @ X2 @ X0))) => ((in @ X1 @ X0) != $true)) <=> (setminusER = $true)),
% 0.22/0.41 inference(flattening,[],[f18])).
% 0.22/0.41 thf(f18,plain,(
% 0.22/0.41 (setminusER = $true) <=> ! [X0,X1,X2] : (($true = (in @ X1 @ (setminus @ X2 @ X0))) => ~((in @ X1 @ X0) = $true))),
% 0.22/0.41 inference(fool_elimination,[],[f17])).
% 0.22/0.41 thf(f17,plain,(
% 0.22/0.41 (setminusER = ! [X0,X1,X2] : ((in @ X1 @ (setminus @ X2 @ X0)) => ~(in @ X1 @ X0)))),
% 0.22/0.41 inference(rectify,[],[f3])).
% 0.22/0.41 thf(f3,axiom,(
% 0.22/0.41 (setminusER = ! [X1,X2,X0] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER)).
% 0.22/0.41 thf(f160,plain,(
% 0.22/0.41 spl21_3 | ~spl21_2),
% 0.22/0.41 inference(avatar_split_clause,[],[f159,f136,f143])).
% 0.22/0.41 thf(f143,plain,(
% 0.22/0.41 spl21_3 <=> ! [X0] : (($true != (in @ sK8 @ (powerset @ X0))) | ((in @ sK9 @ X0) != $true) | ($true != (in @ sK6 @ (powerset @ X0))))),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl21_3])])).
% 0.22/0.41 thf(f136,plain,(
% 0.22/0.41 spl21_2 <=> ((in @ sK9 @ (setminus @ sK7 @ sK8)) = $true)),
% 0.22/0.41 introduced(avatar_definition,[new_symbols(naming,[spl21_2])])).
% 0.22/0.41 thf(f159,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($true != (in @ sK6 @ (powerset @ X0))) | ($true != (in @ sK8 @ (powerset @ X0))) | ((in @ sK9 @ X0) != $true)) ) | ~spl21_2),
% 0.22/0.41 inference(subsumption_resolution,[],[f153,f151])).
% 0.22/0.41 thf(f151,plain,(
% 0.22/0.41 ($true != (in @ sK9 @ sK8)) | ~spl21_2),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f150])).
% 0.22/0.41 thf(f150,plain,(
% 0.22/0.41 ($true != $true) | ($true != (in @ sK9 @ sK8)) | ~spl21_2),
% 0.22/0.41 inference(superposition,[],[f121,f138])).
% 0.22/0.41 thf(f138,plain,(
% 0.22/0.41 ((in @ sK9 @ (setminus @ sK7 @ sK8)) = $true) | ~spl21_2),
% 0.22/0.41 inference(avatar_component_clause,[],[f136])).
% 0.22/0.41 thf(f153,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($true = (in @ sK9 @ sK8)) | ($true != (in @ sK8 @ (powerset @ X0))) | ($true != (in @ sK6 @ (powerset @ X0))) | ((in @ sK9 @ X0) != $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f152])).
% 0.22/0.41 thf(f152,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($true = (in @ sK9 @ sK8)) | ((in @ sK9 @ X0) != $true) | ($true != $true) | ($true != (in @ sK8 @ (powerset @ X0))) | ($true != (in @ sK6 @ (powerset @ X0)))) )),
% 0.22/0.41 inference(superposition,[],[f123,f128])).
% 0.22/0.41 thf(f128,plain,(
% 0.22/0.41 ($true = (in @ sK9 @ (binintersect @ sK6 @ sK8)))),
% 0.22/0.41 inference(subsumption_resolution,[],[f127,f72])).
% 0.22/0.41 thf(f72,plain,(
% 0.22/0.41 ((in @ sK9 @ sK7) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f47])).
% 0.22/0.41 thf(f127,plain,(
% 0.22/0.41 ((in @ sK9 @ sK7) != $true) | ($true = (in @ sK9 @ (binintersect @ sK6 @ sK8)))),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f126])).
% 0.22/0.41 thf(f126,plain,(
% 0.22/0.41 ((in @ sK9 @ sK7) != $true) | ($true = (in @ sK9 @ (binintersect @ sK6 @ sK8))) | ($true != $true)),
% 0.22/0.41 inference(superposition,[],[f73,f120])).
% 0.22/0.41 thf(f120,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X5) = $true) | ((in @ X3 @ X4) != $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f103])).
% 0.22/0.41 thf(f103,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) = $true) | ((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X4) != $true) | ($true != $true)) )),
% 0.22/0.41 inference(definition_unfolding,[],[f67,f76])).
% 0.22/0.41 thf(f76,plain,(
% 0.22/0.41 (setminusI = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f47])).
% 0.22/0.41 thf(f67,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X5) = $true) | ((in @ X3 @ X4) != $true) | (setminusI != $true)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f43])).
% 0.22/0.41 thf(f43,plain,(
% 0.22/0.41 ((setminusI = $true) | (((in @ sK3 @ (setminus @ sK4 @ sK5)) != $true) & ((in @ sK3 @ sK5) != $true) & ($true = (in @ sK3 @ sK4)))) & (! [X3,X4,X5] : (((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X5) = $true) | ((in @ X3 @ X4) != $true)) | (setminusI != $true))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f41,f42])).
% 0.22/0.41 thf(f42,plain,(
% 0.22/0.41 ? [X0,X1,X2] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ((in @ X0 @ X2) != $true) & ($true = (in @ X0 @ X1))) => (((in @ sK3 @ (setminus @ sK4 @ sK5)) != $true) & ((in @ sK3 @ sK5) != $true) & ($true = (in @ sK3 @ sK4)))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f41,plain,(
% 0.22/0.41 ((setminusI = $true) | ? [X0,X1,X2] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ((in @ X0 @ X2) != $true) & ($true = (in @ X0 @ X1)))) & (! [X3,X4,X5] : (((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X5) = $true) | ((in @ X3 @ X4) != $true)) | (setminusI != $true))),
% 0.22/0.41 inference(rectify,[],[f40])).
% 0.22/0.41 thf(f40,plain,(
% 0.22/0.41 ((setminusI = $true) | ? [X0,X1,X2] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ((in @ X0 @ X2) != $true) & ($true = (in @ X0 @ X1)))) & (! [X0,X1,X2] : (((in @ X0 @ (setminus @ X1 @ X2)) = $true) | ((in @ X0 @ X2) = $true) | ($true != (in @ X0 @ X1))) | (setminusI != $true))),
% 0.22/0.41 inference(nnf_transformation,[],[f33])).
% 0.22/0.41 thf(f33,plain,(
% 0.22/0.41 (setminusI = $true) <=> ! [X0,X1,X2] : (((in @ X0 @ (setminus @ X1 @ X2)) = $true) | ((in @ X0 @ X2) = $true) | ($true != (in @ X0 @ X1)))),
% 0.22/0.41 inference(flattening,[],[f32])).
% 0.22/0.41 thf(f32,plain,(
% 0.22/0.41 ! [X0,X2,X1] : ((((in @ X0 @ (setminus @ X1 @ X2)) = $true) | ((in @ X0 @ X2) = $true)) | ($true != (in @ X0 @ X1))) <=> (setminusI = $true)),
% 0.22/0.41 inference(ennf_transformation,[],[f21])).
% 0.22/0.41 thf(f21,plain,(
% 0.22/0.41 ! [X0,X2,X1] : (($true = (in @ X0 @ X1)) => (((in @ X0 @ X2) != $true) => ((in @ X0 @ (setminus @ X1 @ X2)) = $true))) <=> (setminusI = $true)),
% 0.22/0.41 inference(flattening,[],[f10])).
% 0.22/0.41 thf(f10,plain,(
% 0.22/0.41 (setminusI = $true) <=> ! [X0,X1,X2] : (($true = (in @ X0 @ X1)) => (~((in @ X0 @ X2) = $true) => ((in @ X0 @ (setminus @ X1 @ X2)) = $true)))),
% 0.22/0.41 inference(fool_elimination,[],[f9])).
% 0.22/0.41 thf(f9,plain,(
% 0.22/0.41 (setminusI = ! [X0,X1,X2] : ((in @ X0 @ X1) => (~(in @ X0 @ X2) => (in @ X0 @ (setminus @ X1 @ X2)))))),
% 0.22/0.41 inference(rectify,[],[f2])).
% 0.22/0.41 thf(f2,axiom,(
% 0.22/0.41 (setminusI = ! [X2,X0,X1] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI)).
% 0.22/0.41 thf(f73,plain,(
% 0.22/0.41 ((in @ sK9 @ (setminus @ sK7 @ (binintersect @ sK6 @ sK8))) != $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f47])).
% 0.22/0.41 thf(f123,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ X1 @ (powerset @ X0))) | ($true != (in @ X3 @ X0)) | ((in @ X3 @ X2) = $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f104])).
% 0.22/0.41 thf(f104,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ (powerset @ X0)) != $true) | ($true != (in @ X3 @ X0)) | ($true != $true) | ((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X2) = $true) | ($true != (in @ X1 @ (powerset @ X0)))) )),
% 0.22/0.41 inference(definition_unfolding,[],[f86,f80])).
% 0.22/0.41 thf(f80,plain,(
% 0.22/0.41 (binintersectTERcontra = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f47])).
% 0.22/0.41 thf(f86,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ X1 @ (powerset @ X0))) | ($true != (in @ X3 @ X0)) | ((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X2 @ (powerset @ X0)) != $true) | (binintersectTERcontra != $true)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f53])).
% 0.22/0.41 thf(f53,plain,(
% 0.22/0.41 (! [X0,X1] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2] : (! [X3] : (($true != (in @ X3 @ X0)) | ((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (binintersectTERcontra != $true)) & ((binintersectTERcontra = $true) | (($true = (in @ sK11 @ (powerset @ sK10))) & ((((in @ sK13 @ sK10) = $true) & ($true = (in @ sK13 @ (binintersect @ sK11 @ sK12))) & ((in @ sK13 @ sK12) != $true)) & ((in @ sK12 @ (powerset @ sK10)) = $true))))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13])],[f49,f52,f51,f50])).
% 0.22/0.41 thf(f50,plain,(
% 0.22/0.41 ? [X4,X5] : (((in @ X5 @ (powerset @ X4)) = $true) & ? [X6] : (? [X7] : (($true = (in @ X7 @ X4)) & ((in @ X7 @ (binintersect @ X5 @ X6)) = $true) & ($true != (in @ X7 @ X6))) & ($true = (in @ X6 @ (powerset @ X4))))) => (($true = (in @ sK11 @ (powerset @ sK10))) & ? [X6] : (? [X7] : (((in @ X7 @ sK10) = $true) & ($true = (in @ X7 @ (binintersect @ sK11 @ X6))) & ($true != (in @ X7 @ X6))) & ((in @ X6 @ (powerset @ sK10)) = $true)))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f51,plain,(
% 0.22/0.41 ? [X6] : (? [X7] : (((in @ X7 @ sK10) = $true) & ($true = (in @ X7 @ (binintersect @ sK11 @ X6))) & ($true != (in @ X7 @ X6))) & ((in @ X6 @ (powerset @ sK10)) = $true)) => (? [X7] : (((in @ X7 @ sK10) = $true) & ((in @ X7 @ (binintersect @ sK11 @ sK12)) = $true) & ($true != (in @ X7 @ sK12))) & ((in @ sK12 @ (powerset @ sK10)) = $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f52,plain,(
% 0.22/0.41 ? [X7] : (((in @ X7 @ sK10) = $true) & ((in @ X7 @ (binintersect @ sK11 @ sK12)) = $true) & ($true != (in @ X7 @ sK12))) => (((in @ sK13 @ sK10) = $true) & ($true = (in @ sK13 @ (binintersect @ sK11 @ sK12))) & ((in @ sK13 @ sK12) != $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f49,plain,(
% 0.22/0.41 (! [X0,X1] : (($true != (in @ X1 @ (powerset @ X0))) | ! [X2] : (! [X3] : (($true != (in @ X3 @ X0)) | ((in @ X3 @ (binintersect @ X1 @ X2)) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X2 @ (powerset @ X0)) != $true))) | (binintersectTERcontra != $true)) & ((binintersectTERcontra = $true) | ? [X4,X5] : (((in @ X5 @ (powerset @ X4)) = $true) & ? [X6] : (? [X7] : (($true = (in @ X7 @ X4)) & ((in @ X7 @ (binintersect @ X5 @ X6)) = $true) & ($true != (in @ X7 @ X6))) & ($true = (in @ X6 @ (powerset @ X4))))))),
% 0.22/0.41 inference(rectify,[],[f48])).
% 0.22/0.41 thf(f48,plain,(
% 0.22/0.41 (! [X1,X0] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2] : (! [X3] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ (binintersect @ X0 @ X2)) != $true) | ((in @ X3 @ X2) = $true)) | ($true != (in @ X2 @ (powerset @ X1))))) | (binintersectTERcontra != $true)) & ((binintersectTERcontra = $true) | ? [X1,X0] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (? [X3] : (((in @ X3 @ X1) = $true) & ((in @ X3 @ (binintersect @ X0 @ X2)) = $true) & ((in @ X3 @ X2) != $true)) & ($true = (in @ X2 @ (powerset @ X1))))))),
% 0.22/0.41 inference(nnf_transformation,[],[f35])).
% 0.22/0.41 thf(f35,plain,(
% 0.22/0.41 ! [X1,X0] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2] : (! [X3] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ (binintersect @ X0 @ X2)) != $true) | ((in @ X3 @ X2) = $true)) | ($true != (in @ X2 @ (powerset @ X1))))) <=> (binintersectTERcontra = $true)),
% 0.22/0.41 inference(flattening,[],[f34])).
% 0.22/0.41 thf(f34,plain,(
% 0.22/0.41 (binintersectTERcontra = $true) <=> ! [X0,X1] : (! [X2] : (! [X3] : ((((in @ X3 @ (binintersect @ X0 @ X2)) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X3 @ X1) != $true)) | ($true != (in @ X2 @ (powerset @ X1)))) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 0.22/0.41 inference(ennf_transformation,[],[f24])).
% 0.22/0.41 thf(f24,plain,(
% 0.22/0.41 (binintersectTERcontra = $true) <=> ! [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ X2) != $true) => ((in @ X3 @ (binintersect @ X0 @ X2)) != $true)))))),
% 0.22/0.41 inference(flattening,[],[f12])).
% 0.22/0.41 thf(f12,plain,(
% 0.22/0.41 ! [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3] : (((in @ X3 @ X1) = $true) => (~((in @ X3 @ X2) = $true) => ~((in @ X3 @ (binintersect @ X0 @ X2)) = $true))))) <=> (binintersectTERcontra = $true)),
% 0.22/0.41 inference(fool_elimination,[],[f11])).
% 0.22/0.41 thf(f11,plain,(
% 0.22/0.41 (! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => ! [X3] : ((in @ X3 @ X1) => (~(in @ X3 @ X2) => ~(in @ X3 @ (binintersect @ X0 @ X2)))))) = binintersectTERcontra)),
% 0.22/0.41 inference(rectify,[],[f5])).
% 0.22/0.41 thf(f5,axiom,(
% 0.22/0.41 (! [X3,X0] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => (~(in @ X2 @ X4) => ~(in @ X2 @ (binintersect @ X3 @ X4)))))) = binintersectTERcontra)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTERcontra)).
% 0.22/0.41 thf(f158,plain,(
% 0.22/0.41 ~spl21_3),
% 0.22/0.41 inference(avatar_contradiction_clause,[],[f157])).
% 0.22/0.41 thf(f157,plain,(
% 0.22/0.41 $false | ~spl21_3),
% 0.22/0.41 inference(subsumption_resolution,[],[f156,f75])).
% 0.22/0.41 thf(f75,plain,(
% 0.22/0.41 ($true = (in @ sK6 @ (powerset @ sK7)))),
% 0.22/0.41 inference(cnf_transformation,[],[f47])).
% 0.22/0.41 thf(f156,plain,(
% 0.22/0.41 ($true != (in @ sK6 @ (powerset @ sK7))) | ~spl21_3),
% 0.22/0.41 inference(subsumption_resolution,[],[f155,f72])).
% 0.22/0.41 thf(f155,plain,(
% 0.22/0.41 ((in @ sK9 @ sK7) != $true) | ($true != (in @ sK6 @ (powerset @ sK7))) | ~spl21_3),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f154])).
% 0.22/0.41 thf(f154,plain,(
% 0.22/0.41 ($true != $true) | ($true != (in @ sK6 @ (powerset @ sK7))) | ((in @ sK9 @ sK7) != $true) | ~spl21_3),
% 0.22/0.41 inference(superposition,[],[f144,f74])).
% 0.22/0.41 thf(f74,plain,(
% 0.22/0.41 ((in @ sK8 @ (powerset @ sK7)) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f47])).
% 0.22/0.41 thf(f144,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($true != (in @ sK8 @ (powerset @ X0))) | ($true != (in @ sK6 @ (powerset @ X0))) | ((in @ sK9 @ X0) != $true)) ) | ~spl21_3),
% 0.22/0.41 inference(avatar_component_clause,[],[f143])).
% 0.22/0.41 thf(f149,plain,(
% 0.22/0.41 spl21_3 | spl21_4),
% 0.22/0.41 inference(avatar_split_clause,[],[f141,f146,f143])).
% 0.22/0.41 thf(f141,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($true != (in @ sK8 @ (powerset @ X0))) | ((in @ sK9 @ sK6) = $true) | ($true != (in @ sK6 @ (powerset @ X0))) | ((in @ sK9 @ X0) != $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f140])).
% 0.22/0.41 thf(f140,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($true != (in @ sK8 @ (powerset @ X0))) | ((in @ sK9 @ sK6) = $true) | ($true != $true) | ($true != (in @ sK6 @ (powerset @ X0))) | ((in @ sK9 @ X0) != $true)) )),
% 0.22/0.41 inference(superposition,[],[f122,f128])).
% 0.22/0.41 thf(f122,plain,(
% 0.22/0.41 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ X7 @ (binintersect @ X4 @ X6)) != $true) | ((in @ X6 @ (powerset @ X5)) != $true) | ((in @ X7 @ X5) != $true) | ($true != (in @ X4 @ (powerset @ X5))) | ($true = (in @ X7 @ X4))) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f115])).
% 0.22/0.41 thf(f115,plain,(
% 0.22/0.41 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != $true) | ($true != (in @ X4 @ (powerset @ X5))) | ((in @ X7 @ (binintersect @ X4 @ X6)) != $true) | ((in @ X6 @ (powerset @ X5)) != $true) | ($true = (in @ X7 @ X4)) | ((in @ X7 @ X5) != $true)) )),
% 0.22/0.41 inference(definition_unfolding,[],[f87,f78])).
% 0.22/0.41 thf(f78,plain,(
% 0.22/0.41 (binintersectTELcontra = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f47])).
% 0.22/0.41 thf(f87,plain,(
% 0.22/0.41 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (in @ X4 @ (powerset @ X5))) | ((in @ X7 @ (binintersect @ X4 @ X6)) != $true) | ($true = (in @ X7 @ X4)) | ((in @ X7 @ X5) != $true) | ((in @ X6 @ (powerset @ X5)) != $true) | (binintersectTELcontra != $true)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f59])).
% 0.22/0.41 thf(f59,plain,(
% 0.22/0.41 ((binintersectTELcontra = $true) | (((in @ sK14 @ (powerset @ sK15)) = $true) & ((((in @ sK17 @ (binintersect @ sK14 @ sK16)) = $true) & ((in @ sK17 @ sK14) != $true) & ((in @ sK17 @ sK15) = $true)) & ((in @ sK16 @ (powerset @ sK15)) = $true)))) & (! [X4,X5] : (($true != (in @ X4 @ (powerset @ X5))) | ! [X6] : (! [X7] : (((in @ X7 @ (binintersect @ X4 @ X6)) != $true) | ($true = (in @ X7 @ X4)) | ((in @ X7 @ X5) != $true)) | ((in @ X6 @ (powerset @ X5)) != $true))) | (binintersectTELcontra != $true))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17])],[f55,f58,f57,f56])).
% 0.22/0.41 thf(f56,plain,(
% 0.22/0.41 ? [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (? [X3] : (((in @ X3 @ (binintersect @ X0 @ X2)) = $true) & ($true != (in @ X3 @ X0)) & ((in @ X3 @ X1) = $true)) & ($true = (in @ X2 @ (powerset @ X1))))) => (((in @ sK14 @ (powerset @ sK15)) = $true) & ? [X2] : (? [X3] : (((in @ X3 @ (binintersect @ sK14 @ X2)) = $true) & ((in @ X3 @ sK14) != $true) & ((in @ X3 @ sK15) = $true)) & ((in @ X2 @ (powerset @ sK15)) = $true)))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f57,plain,(
% 0.22/0.41 ? [X2] : (? [X3] : (((in @ X3 @ (binintersect @ sK14 @ X2)) = $true) & ((in @ X3 @ sK14) != $true) & ((in @ X3 @ sK15) = $true)) & ((in @ X2 @ (powerset @ sK15)) = $true)) => (? [X3] : (($true = (in @ X3 @ (binintersect @ sK14 @ sK16))) & ((in @ X3 @ sK14) != $true) & ((in @ X3 @ sK15) = $true)) & ((in @ sK16 @ (powerset @ sK15)) = $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f58,plain,(
% 0.22/0.41 ? [X3] : (($true = (in @ X3 @ (binintersect @ sK14 @ sK16))) & ((in @ X3 @ sK14) != $true) & ((in @ X3 @ sK15) = $true)) => (((in @ sK17 @ (binintersect @ sK14 @ sK16)) = $true) & ((in @ sK17 @ sK14) != $true) & ((in @ sK17 @ sK15) = $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f55,plain,(
% 0.22/0.41 ((binintersectTELcontra = $true) | ? [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (? [X3] : (((in @ X3 @ (binintersect @ X0 @ X2)) = $true) & ($true != (in @ X3 @ X0)) & ((in @ X3 @ X1) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))))) & (! [X4,X5] : (($true != (in @ X4 @ (powerset @ X5))) | ! [X6] : (! [X7] : (((in @ X7 @ (binintersect @ X4 @ X6)) != $true) | ($true = (in @ X7 @ X4)) | ((in @ X7 @ X5) != $true)) | ((in @ X6 @ (powerset @ X5)) != $true))) | (binintersectTELcontra != $true))),
% 0.22/0.41 inference(rectify,[],[f54])).
% 0.22/0.41 thf(f54,plain,(
% 0.22/0.41 ((binintersectTELcontra = $true) | ? [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (? [X3] : (((in @ X3 @ (binintersect @ X0 @ X2)) = $true) & ($true != (in @ X3 @ X0)) & ((in @ X3 @ X1) = $true)) & ($true = (in @ X2 @ (powerset @ X1)))))) & (! [X0,X1] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2] : (! [X3] : (((in @ X3 @ (binintersect @ X0 @ X2)) != $true) | ($true = (in @ X3 @ X0)) | ((in @ X3 @ X1) != $true)) | ($true != (in @ X2 @ (powerset @ X1))))) | (binintersectTELcontra != $true))),
% 0.22/0.41 inference(nnf_transformation,[],[f28])).
% 0.22/0.41 thf(f28,plain,(
% 0.22/0.41 (binintersectTELcontra = $true) <=> ! [X0,X1] : (((in @ X0 @ (powerset @ X1)) != $true) | ! [X2] : (! [X3] : (((in @ X3 @ (binintersect @ X0 @ X2)) != $true) | ($true = (in @ X3 @ X0)) | ((in @ X3 @ X1) != $true)) | ($true != (in @ X2 @ (powerset @ X1)))))),
% 0.22/0.41 inference(flattening,[],[f27])).
% 0.22/0.41 thf(f27,plain,(
% 0.22/0.41 ! [X1,X0] : (! [X2] : (! [X3] : ((((in @ X3 @ (binintersect @ X0 @ X2)) != $true) | ($true = (in @ X3 @ X0))) | ((in @ X3 @ X1) != $true)) | ($true != (in @ X2 @ (powerset @ X1)))) | ((in @ X0 @ (powerset @ X1)) != $true)) <=> (binintersectTELcontra = $true)),
% 0.22/0.41 inference(ennf_transformation,[],[f23])).
% 0.22/0.41 thf(f23,plain,(
% 0.22/0.41 ! [X1,X0] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3] : (((in @ X3 @ X1) = $true) => (($true != (in @ X3 @ X0)) => ((in @ X3 @ (binintersect @ X0 @ X2)) != $true))))) <=> (binintersectTELcontra = $true)),
% 0.22/0.41 inference(flattening,[],[f20])).
% 0.22/0.41 thf(f20,plain,(
% 0.22/0.41 ! [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (($true = (in @ X2 @ (powerset @ X1))) => ! [X3] : (((in @ X3 @ X1) = $true) => (~($true = (in @ X3 @ X0)) => ~((in @ X3 @ (binintersect @ X0 @ X2)) = $true))))) <=> (binintersectTELcontra = $true)),
% 0.22/0.41 inference(fool_elimination,[],[f19])).
% 0.22/0.41 thf(f19,plain,(
% 0.22/0.41 (! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => ! [X3] : ((in @ X3 @ X1) => (~(in @ X3 @ X0) => ~(in @ X3 @ (binintersect @ X0 @ X2)))))) = binintersectTELcontra)),
% 0.22/0.41 inference(rectify,[],[f4])).
% 0.22/0.41 thf(f4,axiom,(
% 0.22/0.41 (! [X3,X0] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => (~(in @ X2 @ X3) => ~(in @ X2 @ (binintersect @ X3 @ X4)))))) = binintersectTELcontra)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTELcontra)).
% 0.22/0.41 thf(f139,plain,(
% 0.22/0.41 spl21_1 | spl21_2),
% 0.22/0.41 inference(avatar_split_clause,[],[f130,f136,f132])).
% 0.22/0.41 thf(f130,plain,(
% 0.22/0.41 ((in @ sK9 @ (setminus @ sK7 @ sK8)) = $true) | ($true = (in @ sK9 @ (setminus @ sK7 @ sK6)))),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f129])).
% 0.22/0.41 thf(f129,plain,(
% 0.22/0.41 ((in @ sK9 @ (setminus @ sK7 @ sK8)) = $true) | ($true = (in @ sK9 @ (setminus @ sK7 @ sK6))) | ($true != $true)),
% 0.22/0.41 inference(superposition,[],[f124,f71])).
% 0.22/0.41 thf(f71,plain,(
% 0.22/0.41 ($true = (in @ sK9 @ (binunion @ (setminus @ sK7 @ sK6) @ (setminus @ sK7 @ sK8))))),
% 0.22/0.41 inference(cnf_transformation,[],[f47])).
% 0.22/0.41 thf(f124,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (binunion @ X4 @ X3)) != $true) | ((in @ X5 @ X3) = $true) | ($true = (in @ X5 @ X4))) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f119])).
% 0.22/0.41 thf(f119,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) | ($true != $true) | ($true = (in @ X5 @ X4)) | ((in @ X5 @ (binunion @ X4 @ X3)) != $true)) )),
% 0.22/0.41 inference(definition_unfolding,[],[f93,f79])).
% 0.22/0.41 thf(f79,plain,(
% 0.22/0.41 (binunionE = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f47])).
% 0.22/0.41 thf(f93,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ (binunion @ X4 @ X3)) != $true) | ($true = (in @ X5 @ X4)) | (binunionE != $true)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f63])).
% 0.22/0.41 thf(f63,plain,(
% 0.22/0.41 ((binunionE = $true) | (((in @ sK20 @ sK18) != $true) & ((in @ sK20 @ (binunion @ sK19 @ sK18)) = $true) & ((in @ sK20 @ sK19) != $true))) & (! [X3,X4,X5] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ (binunion @ X4 @ X3)) != $true) | ($true = (in @ X5 @ X4))) | (binunionE != $true))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20])],[f61,f62])).
% 0.22/0.41 thf(f62,plain,(
% 0.22/0.41 ? [X0,X1,X2] : (((in @ X2 @ X0) != $true) & ($true = (in @ X2 @ (binunion @ X1 @ X0))) & ((in @ X2 @ X1) != $true)) => (((in @ sK20 @ sK18) != $true) & ((in @ sK20 @ (binunion @ sK19 @ sK18)) = $true) & ((in @ sK20 @ sK19) != $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f61,plain,(
% 0.22/0.41 ((binunionE = $true) | ? [X0,X1,X2] : (((in @ X2 @ X0) != $true) & ($true = (in @ X2 @ (binunion @ X1 @ X0))) & ((in @ X2 @ X1) != $true))) & (! [X3,X4,X5] : (((in @ X5 @ X3) = $true) | ((in @ X5 @ (binunion @ X4 @ X3)) != $true) | ($true = (in @ X5 @ X4))) | (binunionE != $true))),
% 0.22/0.41 inference(rectify,[],[f60])).
% 0.22/0.41 thf(f60,plain,(
% 0.22/0.41 ((binunionE = $true) | ? [X1,X0,X2] : (((in @ X2 @ X1) != $true) & ((in @ X2 @ (binunion @ X0 @ X1)) = $true) & ((in @ X2 @ X0) != $true))) & (! [X1,X0,X2] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ (binunion @ X0 @ X1)) != $true) | ((in @ X2 @ X0) = $true)) | (binunionE != $true))),
% 0.22/0.41 inference(nnf_transformation,[],[f31])).
% 0.22/0.41 thf(f31,plain,(
% 0.22/0.41 (binunionE = $true) <=> ! [X1,X0,X2] : (((in @ X2 @ X1) = $true) | ((in @ X2 @ (binunion @ X0 @ X1)) != $true) | ((in @ X2 @ X0) = $true))),
% 0.22/0.41 inference(flattening,[],[f30])).
% 0.22/0.41 thf(f30,plain,(
% 0.22/0.41 ! [X0,X2,X1] : ((((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) = $true)) | ((in @ X2 @ (binunion @ X0 @ X1)) != $true)) <=> (binunionE = $true)),
% 0.22/0.41 inference(ennf_transformation,[],[f16])).
% 0.22/0.41 thf(f16,plain,(
% 0.22/0.41 ! [X0,X2,X1] : (((in @ X2 @ (binunion @ X0 @ X1)) = $true) => (((in @ X2 @ X0) = $true) | ((in @ X2 @ X1) = $true))) <=> (binunionE = $true)),
% 0.22/0.41 inference(fool_elimination,[],[f15])).
% 0.22/0.41 thf(f15,plain,(
% 0.22/0.41 (binunionE = ! [X0,X1,X2] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X1) | (in @ X2 @ X0))))),
% 0.22/0.41 inference(rectify,[],[f1])).
% 0.22/0.41 thf(f1,axiom,(
% 0.22/0.41 (binunionE = ! [X0,X1,X2] : ((in @ X2 @ (binunion @ X0 @ X1)) => ((in @ X2 @ X1) | (in @ X2 @ X0))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE)).
% 0.22/0.41 % SZS output end Proof for theBenchmark
% 0.22/0.41 % (24806)------------------------------
% 0.22/0.41 % (24806)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (24806)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (24806)Memory used [KB]: 5628
% 0.22/0.41 % (24806)Time elapsed: 0.016 s
% 0.22/0.41 % (24806)Instructions burned: 11 (million)
% 0.22/0.41 % (24806)------------------------------
% 0.22/0.41 % (24806)------------------------------
% 0.22/0.41 % (24800)Success in time 0.018 s
% 0.22/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------