TSTP Solution File: SEU755^2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU755^2 : 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 03:51:17 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
% 0.11/0.12 % Problem : SEU755^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.14 % 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
% 0.15/0.35 % Computer : n024.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 16:05:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 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
% 0.15/0.39 % (20184)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.39 % (20187)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39 % (20186)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)
% 0.15/0.39 % (20185)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)
% 0.15/0.39 % (20189)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)
% 0.15/0.39 % (20188)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)
% 0.15/0.39 % (20190)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.39 % (20191)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)
% 0.15/0.39 % (20187)Instruction limit reached!
% 0.15/0.39 % (20187)------------------------------
% 0.15/0.39 % (20187)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (20187)Termination reason: Unknown
% 0.15/0.39 % (20187)Termination phase: Preprocessing 1
% 0.15/0.39 % (20188)Instruction limit reached!
% 0.15/0.39 % (20188)------------------------------
% 0.15/0.39 % (20188)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (20188)Termination reason: Unknown
% 0.15/0.39 % (20188)Termination phase: Property scanning
% 0.15/0.39
% 0.15/0.39 % (20188)Memory used [KB]: 895
% 0.15/0.39 % (20188)Time elapsed: 0.004 s
% 0.15/0.39 % (20188)Instructions burned: 2 (million)
% 0.15/0.39 % (20188)------------------------------
% 0.15/0.39 % (20188)------------------------------
% 0.15/0.40
% 0.15/0.40 % (20187)Memory used [KB]: 895
% 0.15/0.40 % (20187)Time elapsed: 0.005 s
% 0.15/0.40 % (20187)Instructions burned: 2 (million)
% 0.15/0.40 % (20187)------------------------------
% 0.15/0.40 % (20187)------------------------------
% 0.15/0.40 % (20185)Instruction limit reached!
% 0.15/0.40 % (20185)------------------------------
% 0.15/0.40 % (20185)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (20185)Termination reason: Unknown
% 0.15/0.40 % (20185)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (20185)Memory used [KB]: 5500
% 0.15/0.40 % (20185)Time elapsed: 0.006 s
% 0.15/0.40 % (20185)Instructions burned: 4 (million)
% 0.15/0.40 % (20185)------------------------------
% 0.15/0.40 % (20185)------------------------------
% 0.15/0.40 % (20191)Instruction limit reached!
% 0.15/0.40 % (20191)------------------------------
% 0.15/0.40 % (20191)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (20191)Termination reason: Unknown
% 0.15/0.40 % (20191)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (20191)Memory used [KB]: 1023
% 0.15/0.40 % (20191)Time elapsed: 0.006 s
% 0.15/0.40 % (20191)Instructions burned: 4 (million)
% 0.15/0.40 % (20191)------------------------------
% 0.15/0.40 % (20191)------------------------------
% 0.15/0.40 % (20189)First to succeed.
% 0.22/0.41 % (20189)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_3, type, setminus: $i > $i > $i).
% 0.22/0.41 thf(f99,plain,(
% 0.22/0.41 $false),
% 0.22/0.41 inference(subsumption_resolution,[],[f98,f51])).
% 0.22/0.41 thf(f51,plain,(
% 0.22/0.41 ((in @ sK0 @ (powerset @ sK1)) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f29])).
% 0.22/0.41 thf(f29,plain,(
% 0.22/0.41 (setminusI = $true) & (((in @ sK0 @ (powerset @ sK1)) = $true) & (($true = (in @ sK2 @ (powerset @ sK1))) & (((in @ sK3 @ (setminus @ sK1 @ sK2)) = $true) & ((in @ sK3 @ sK1) = $true) & ((in @ sK3 @ (setminus @ sK1 @ (binunion @ sK0 @ sK2))) != $true) & ((in @ sK3 @ (setminus @ sK1 @ sK0)) = $true)))) & (binunionTEcontra = $true) & (setminusER = $true)),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f28,f27,f26])).
% 0.22/0.41 thf(f26,plain,(
% 0.22/0.41 ? [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ X1 @ X2)) = $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) != $true) & ((in @ X3 @ (setminus @ X1 @ X0)) = $true)))) => (((in @ sK0 @ (powerset @ sK1)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ sK1)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ sK1 @ X2)) = $true) & ((in @ X3 @ sK1) = $true) & ((in @ X3 @ (setminus @ sK1 @ (binunion @ sK0 @ X2))) != $true) & ((in @ X3 @ (setminus @ sK1 @ sK0)) = $true))))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f27,plain,(
% 0.22/0.41 ? [X2] : (((in @ X2 @ (powerset @ sK1)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ sK1 @ X2)) = $true) & ((in @ X3 @ sK1) = $true) & ((in @ X3 @ (setminus @ sK1 @ (binunion @ sK0 @ X2))) != $true) & ((in @ X3 @ (setminus @ sK1 @ sK0)) = $true))) => (($true = (in @ sK2 @ (powerset @ sK1))) & ? [X3] : (((in @ X3 @ (setminus @ sK1 @ sK2)) = $true) & ((in @ X3 @ sK1) = $true) & ((in @ X3 @ (setminus @ sK1 @ (binunion @ sK0 @ sK2))) != $true) & ((in @ X3 @ (setminus @ sK1 @ sK0)) = $true)))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f28,plain,(
% 0.22/0.41 ? [X3] : (((in @ X3 @ (setminus @ sK1 @ sK2)) = $true) & ((in @ X3 @ sK1) = $true) & ((in @ X3 @ (setminus @ sK1 @ (binunion @ sK0 @ sK2))) != $true) & ((in @ X3 @ (setminus @ sK1 @ sK0)) = $true)) => (((in @ sK3 @ (setminus @ sK1 @ sK2)) = $true) & ((in @ sK3 @ sK1) = $true) & ((in @ sK3 @ (setminus @ sK1 @ (binunion @ sK0 @ sK2))) != $true) & ((in @ sK3 @ (setminus @ sK1 @ sK0)) = $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f25,plain,(
% 0.22/0.41 (setminusI = $true) & ? [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ X1 @ X2)) = $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ (setminus @ X1 @ (binunion @ X0 @ X2))) != $true) & ((in @ X3 @ (setminus @ X1 @ X0)) = $true)))) & (binunionTEcontra = $true) & (setminusER = $true)),
% 0.22/0.41 inference(rectify,[],[f19])).
% 0.22/0.41 thf(f19,plain,(
% 0.22/0.41 (setminusI = $true) & ? [X1,X0] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3] : (((in @ X3 @ (setminus @ X0 @ X2)) = $true) & ((in @ X3 @ X0) = $true) & ($true != (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) & ((in @ X3 @ (setminus @ X0 @ X1)) = $true)))) & (binunionTEcontra = $true) & (setminusER = $true)),
% 0.22/0.41 inference(flattening,[],[f18])).
% 0.22/0.41 thf(f18,plain,(
% 0.22/0.41 ((? [X0,X1] : (? [X2] : (? [X3] : (((($true != (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))) & ((in @ X3 @ (setminus @ X0 @ X2)) = $true)) & ((in @ X3 @ (setminus @ X0 @ X1)) = $true)) & ((in @ X3 @ X0) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binunionTEcontra = $true)) & (setminusER = $true)) & (setminusI = $true)),
% 0.22/0.41 inference(ennf_transformation,[],[f10])).
% 0.22/0.41 thf(f10,plain,(
% 0.22/0.41 ~((setminusI = $true) => ((setminusER = $true) => ((binunionTEcontra = $true) => ! [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ (setminus @ X0 @ X1)) = $true) => (((in @ X3 @ (setminus @ X0 @ X2)) = $true) => ($true = (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))))))))))))),
% 0.22/0.41 inference(fool_elimination,[],[f9])).
% 0.22/0.41 thf(f9,plain,(
% 0.22/0.41 ~(setminusI => (setminusER => (binunionTEcontra => ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ X1)) => ((in @ X3 @ (setminus @ X0 @ X2)) => (in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2)))))))))))),
% 0.22/0.41 inference(rectify,[],[f5])).
% 0.22/0.41 thf(f5,negated_conjecture,(
% 0.22/0.41 ~(setminusI => (setminusER => (binunionTEcontra => ! [X0,X3] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ X3)) => ((in @ X2 @ (setminus @ X0 @ X4)) => (in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4)))))))))))),
% 0.22/0.41 inference(negated_conjecture,[],[f4])).
% 0.22/0.41 thf(f4,conjecture,(
% 0.22/0.41 setminusI => (setminusER => (binunionTEcontra => ! [X0,X3] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => ((in @ X2 @ (setminus @ X0 @ X3)) => ((in @ X2 @ (setminus @ X0 @ X4)) => (in @ X2 @ (setminus @ X0 @ (binunion @ X3 @ X4))))))))))),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b2)).
% 0.22/0.41 thf(f98,plain,(
% 0.22/0.41 ((in @ sK0 @ (powerset @ sK1)) != $true)),
% 0.22/0.41 inference(subsumption_resolution,[],[f97,f48])).
% 0.22/0.41 thf(f48,plain,(
% 0.22/0.41 ((in @ sK3 @ sK1) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f29])).
% 0.22/0.41 thf(f97,plain,(
% 0.22/0.41 ((in @ sK3 @ sK1) != $true) | ((in @ sK0 @ (powerset @ sK1)) != $true)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f96])).
% 0.22/0.41 thf(f96,plain,(
% 0.22/0.41 ($true != $true) | ((in @ sK3 @ sK1) != $true) | ((in @ sK0 @ (powerset @ sK1)) != $true)),
% 0.22/0.41 inference(superposition,[],[f95,f50])).
% 0.22/0.41 thf(f50,plain,(
% 0.22/0.41 ($true = (in @ sK2 @ (powerset @ sK1)))),
% 0.22/0.41 inference(cnf_transformation,[],[f29])).
% 0.22/0.41 thf(f95,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (((in @ sK2 @ (powerset @ X0)) != $true) | ((in @ sK0 @ (powerset @ X0)) != $true) | ((in @ sK3 @ X0) != $true)) )),
% 0.22/0.41 inference(subsumption_resolution,[],[f94,f86])).
% 0.22/0.41 thf(f86,plain,(
% 0.22/0.41 ((in @ sK3 @ sK0) != $true)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f84])).
% 0.22/0.41 thf(f84,plain,(
% 0.22/0.41 ((in @ sK3 @ sK0) != $true) | ($true != $true)),
% 0.22/0.41 inference(superposition,[],[f83,f46])).
% 0.22/0.41 thf(f46,plain,(
% 0.22/0.41 ((in @ sK3 @ (setminus @ sK1 @ sK0)) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f29])).
% 0.22/0.41 thf(f83,plain,(
% 0.22/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) != $true) | ((in @ X1 @ X0) != $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f78])).
% 0.22/0.41 thf(f78,plain,(
% 0.22/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ (setminus @ X2 @ X0)) != $true) | ((in @ X1 @ X0) != $true) | ($true != $true)) )),
% 0.22/0.41 inference(definition_unfolding,[],[f66,f44])).
% 0.22/0.41 thf(f44,plain,(
% 0.22/0.41 (setminusER = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f29])).
% 0.22/0.41 thf(f66,plain,(
% 0.22/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (setminus @ X2 @ X0)) != $true) | (setminusER != $true)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f43])).
% 0.22/0.41 thf(f43,plain,(
% 0.22/0.41 (! [X0,X1,X2] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (setminus @ X2 @ X0)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | (((in @ sK12 @ sK11) = $true) & ((in @ sK12 @ (setminus @ sK13 @ sK11)) = $true)))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f41,f42])).
% 0.22/0.41 thf(f42,plain,(
% 0.22/0.41 ? [X3,X4,X5] : (((in @ X4 @ X3) = $true) & ((in @ X4 @ (setminus @ X5 @ X3)) = $true)) => (((in @ sK12 @ sK11) = $true) & ((in @ sK12 @ (setminus @ sK13 @ sK11)) = $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f41,plain,(
% 0.22/0.41 (! [X0,X1,X2] : (((in @ X1 @ X0) != $true) | ((in @ X1 @ (setminus @ X2 @ X0)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X3,X4,X5] : (((in @ X4 @ X3) = $true) & ((in @ X4 @ (setminus @ X5 @ X3)) = $true)))),
% 0.22/0.41 inference(rectify,[],[f40])).
% 0.22/0.41 thf(f40,plain,(
% 0.22/0.41 (! [X0,X2,X1] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ (setminus @ X1 @ X0)) != $true)) | (setminusER != $true)) & ((setminusER = $true) | ? [X0,X2,X1] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ (setminus @ X1 @ X0)) = $true)))),
% 0.22/0.41 inference(nnf_transformation,[],[f20])).
% 0.22/0.41 thf(f20,plain,(
% 0.22/0.41 ! [X0,X2,X1] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ (setminus @ X1 @ X0)) != $true)) <=> (setminusER = $true)),
% 0.22/0.41 inference(ennf_transformation,[],[f17])).
% 0.22/0.41 thf(f17,plain,(
% 0.22/0.41 ! [X2,X0,X1] : (((in @ X2 @ (setminus @ X1 @ X0)) = $true) => ((in @ X2 @ X0) != $true)) <=> (setminusER = $true)),
% 0.22/0.41 inference(flattening,[],[f12])).
% 0.22/0.41 thf(f12,plain,(
% 0.22/0.41 (setminusER = $true) <=> ! [X0,X1,X2] : (((in @ X2 @ (setminus @ X1 @ X0)) = $true) => ~((in @ X2 @ X0) = $true))),
% 0.22/0.41 inference(fool_elimination,[],[f11])).
% 0.22/0.41 thf(f11,plain,(
% 0.22/0.41 (setminusER = ! [X0,X1,X2] : ((in @ X2 @ (setminus @ X1 @ X0)) => ~(in @ X2 @ X0)))),
% 0.22/0.41 inference(rectify,[],[f2])).
% 0.22/0.41 thf(f2,axiom,(
% 0.22/0.41 (setminusER = ! [X1,X0,X2] : ((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(f94,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (((in @ sK2 @ (powerset @ X0)) != $true) | ((in @ sK3 @ X0) != $true) | ((in @ sK3 @ sK0) = $true) | ((in @ sK0 @ (powerset @ X0)) != $true)) )),
% 0.22/0.41 inference(subsumption_resolution,[],[f93,f87])).
% 0.22/0.41 thf(f87,plain,(
% 0.22/0.41 ((in @ sK3 @ sK2) != $true)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f85])).
% 0.22/0.41 thf(f85,plain,(
% 0.22/0.41 ($true != $true) | ((in @ sK3 @ sK2) != $true)),
% 0.22/0.41 inference(superposition,[],[f83,f49])).
% 0.22/0.41 thf(f49,plain,(
% 0.22/0.41 ((in @ sK3 @ (setminus @ sK1 @ sK2)) = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f29])).
% 0.22/0.41 thf(f93,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (((in @ sK2 @ (powerset @ X0)) != $true) | ((in @ sK0 @ (powerset @ X0)) != $true) | ((in @ sK3 @ sK2) = $true) | ((in @ sK3 @ sK0) = $true) | ((in @ sK3 @ X0) != $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f92])).
% 0.22/0.41 thf(f92,plain,(
% 0.22/0.41 ( ! [X0 : $i] : (($true != $true) | ((in @ sK3 @ X0) != $true) | ((in @ sK2 @ (powerset @ X0)) != $true) | ((in @ sK3 @ sK0) = $true) | ((in @ sK0 @ (powerset @ X0)) != $true) | ((in @ sK3 @ sK2) = $true)) )),
% 0.22/0.41 inference(superposition,[],[f81,f91])).
% 0.22/0.41 thf(f91,plain,(
% 0.22/0.41 ((in @ sK3 @ (binunion @ sK0 @ sK2)) = $true)),
% 0.22/0.41 inference(subsumption_resolution,[],[f90,f48])).
% 0.22/0.41 thf(f90,plain,(
% 0.22/0.41 ((in @ sK3 @ (binunion @ sK0 @ sK2)) = $true) | ((in @ sK3 @ sK1) != $true)),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f89])).
% 0.22/0.41 thf(f89,plain,(
% 0.22/0.41 ((in @ sK3 @ sK1) != $true) | ((in @ sK3 @ (binunion @ sK0 @ sK2)) = $true) | ($true != $true)),
% 0.22/0.41 inference(superposition,[],[f47,f82])).
% 0.22/0.41 thf(f82,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (setminus @ X4 @ X3)) = $true) | ((in @ X5 @ X4) != $true) | ((in @ X5 @ X3) = $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f70])).
% 0.22/0.41 thf(f70,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) | ($true != $true) | ((in @ X5 @ X4) != $true) | ((in @ X5 @ (setminus @ X4 @ X3)) = $true)) )),
% 0.22/0.41 inference(definition_unfolding,[],[f53,f52])).
% 0.22/0.41 thf(f52,plain,(
% 0.22/0.41 (setminusI = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f29])).
% 0.22/0.41 thf(f53,plain,(
% 0.22/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (setminus @ X4 @ X3)) = $true) | ((in @ X5 @ X3) = $true) | ((in @ X5 @ X4) != $true) | (setminusI != $true)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f33])).
% 0.22/0.41 thf(f33,plain,(
% 0.22/0.41 ((setminusI = $true) | (((in @ sK6 @ (setminus @ sK5 @ sK4)) != $true) & ((in @ sK6 @ sK4) != $true) & ((in @ sK6 @ sK5) = $true))) & (! [X3,X4,X5] : (((in @ X5 @ (setminus @ X4 @ X3)) = $true) | ((in @ X5 @ X3) = $true) | ((in @ X5 @ X4) != $true)) | (setminusI != $true))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f31,f32])).
% 0.22/0.41 thf(f32,plain,(
% 0.22/0.41 ? [X0,X1,X2] : (((in @ X2 @ (setminus @ X1 @ X0)) != $true) & ((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true)) => (((in @ sK6 @ (setminus @ sK5 @ sK4)) != $true) & ((in @ sK6 @ sK4) != $true) & ((in @ sK6 @ sK5) = $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f31,plain,(
% 0.22/0.41 ((setminusI = $true) | ? [X0,X1,X2] : (((in @ X2 @ (setminus @ X1 @ X0)) != $true) & ((in @ X2 @ X0) != $true) & ((in @ X2 @ X1) = $true))) & (! [X3,X4,X5] : (((in @ X5 @ (setminus @ X4 @ X3)) = $true) | ((in @ X5 @ X3) = $true) | ((in @ X5 @ X4) != $true)) | (setminusI != $true))),
% 0.22/0.41 inference(rectify,[],[f30])).
% 0.22/0.41 thf(f30,plain,(
% 0.22/0.41 ((setminusI = $true) | ? [X1,X0,X2] : (((in @ X2 @ (setminus @ X0 @ X1)) != $true) & ((in @ X2 @ X1) != $true) & ((in @ X2 @ X0) = $true))) & (! [X1,X0,X2] : (((in @ X2 @ (setminus @ X0 @ X1)) = $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true)) | (setminusI != $true))),
% 0.22/0.41 inference(nnf_transformation,[],[f22])).
% 0.22/0.41 thf(f22,plain,(
% 0.22/0.41 (setminusI = $true) <=> ! [X1,X0,X2] : (((in @ X2 @ (setminus @ X0 @ X1)) = $true) | ((in @ X2 @ X1) = $true) | ((in @ X2 @ X0) != $true))),
% 0.22/0.41 inference(flattening,[],[f21])).
% 0.22/0.41 thf(f21,plain,(
% 0.22/0.41 ! [X1,X0,X2] : ((((in @ X2 @ (setminus @ X0 @ X1)) = $true) | ((in @ X2 @ X1) = $true)) | ((in @ X2 @ X0) != $true)) <=> (setminusI = $true)),
% 0.22/0.41 inference(ennf_transformation,[],[f16])).
% 0.22/0.41 thf(f16,plain,(
% 0.22/0.41 ! [X1,X0,X2] : (((in @ X2 @ X0) = $true) => (((in @ X2 @ X1) != $true) => ((in @ X2 @ (setminus @ X0 @ X1)) = $true))) <=> (setminusI = $true)),
% 0.22/0.41 inference(flattening,[],[f14])).
% 0.22/0.41 thf(f14,plain,(
% 0.22/0.41 (setminusI = $true) <=> ! [X0,X1,X2] : (((in @ X2 @ X0) = $true) => (~((in @ X2 @ X1) = $true) => ((in @ X2 @ (setminus @ X0 @ X1)) = $true)))),
% 0.22/0.41 inference(fool_elimination,[],[f13])).
% 0.22/0.41 thf(f13,plain,(
% 0.22/0.41 (setminusI = ! [X0,X1,X2] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))))),
% 0.22/0.41 inference(rectify,[],[f1])).
% 0.22/0.41 thf(f1,axiom,(
% 0.22/0.41 (setminusI = ! [X0,X1,X2] : ((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(f47,plain,(
% 0.22/0.41 ((in @ sK3 @ (setminus @ sK1 @ (binunion @ sK0 @ sK2))) != $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f29])).
% 0.22/0.41 thf(f81,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ((in @ X3 @ X0) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X0 @ (powerset @ X1)) != $true)) )),
% 0.22/0.41 inference(trivial_inequality_removal,[],[f71])).
% 0.22/0.41 thf(f71,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ X0) = $true) | ((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ((in @ X0 @ (powerset @ X1)) != $true) | ((in @ X3 @ X2) = $true) | ($true != $true) | ((in @ X3 @ X1) != $true) | ((in @ X2 @ (powerset @ X1)) != $true)) )),
% 0.22/0.41 inference(definition_unfolding,[],[f63,f45])).
% 0.22/0.41 thf(f45,plain,(
% 0.22/0.41 (binunionTEcontra = $true)),
% 0.22/0.41 inference(cnf_transformation,[],[f29])).
% 0.22/0.41 thf(f63,plain,(
% 0.22/0.41 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X0) = $true) | ((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ((in @ X0 @ (powerset @ X1)) != $true) | (binunionTEcontra != $true)) )),
% 0.22/0.41 inference(cnf_transformation,[],[f39])).
% 0.22/0.41 thf(f39,plain,(
% 0.22/0.41 (! [X0,X1] : (! [X2] : (! [X3] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X0) = $true) | ((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) | (binunionTEcontra != $true)) & ((binunionTEcontra = $true) | (((((in @ sK10 @ sK8) = $true) & ((in @ sK10 @ sK7) != $true) & ((in @ sK10 @ (binunion @ sK7 @ sK9)) = $true) & ((in @ sK10 @ sK9) != $true)) & ((in @ sK9 @ (powerset @ sK8)) = $true)) & ((in @ sK7 @ (powerset @ sK8)) = $true)))),
% 0.22/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10])],[f35,f38,f37,f36])).
% 0.22/0.41 thf(f36,plain,(
% 0.22/0.41 ? [X4,X5] : (? [X6] : (? [X7] : (((in @ X7 @ X5) = $true) & ((in @ X7 @ X4) != $true) & ((in @ X7 @ (binunion @ X4 @ X6)) = $true) & ((in @ X7 @ X6) != $true)) & ((in @ X6 @ (powerset @ X5)) = $true)) & ((in @ X4 @ (powerset @ X5)) = $true)) => (? [X6] : (? [X7] : (((in @ X7 @ sK8) = $true) & ((in @ X7 @ sK7) != $true) & ((in @ X7 @ (binunion @ sK7 @ X6)) = $true) & ((in @ X7 @ X6) != $true)) & ((in @ X6 @ (powerset @ sK8)) = $true)) & ((in @ sK7 @ (powerset @ sK8)) = $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f37,plain,(
% 0.22/0.41 ? [X6] : (? [X7] : (((in @ X7 @ sK8) = $true) & ((in @ X7 @ sK7) != $true) & ((in @ X7 @ (binunion @ sK7 @ X6)) = $true) & ((in @ X7 @ X6) != $true)) & ((in @ X6 @ (powerset @ sK8)) = $true)) => (? [X7] : (((in @ X7 @ sK8) = $true) & ((in @ X7 @ sK7) != $true) & ((in @ X7 @ (binunion @ sK7 @ sK9)) = $true) & ((in @ X7 @ sK9) != $true)) & ((in @ sK9 @ (powerset @ sK8)) = $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f38,plain,(
% 0.22/0.41 ? [X7] : (((in @ X7 @ sK8) = $true) & ((in @ X7 @ sK7) != $true) & ((in @ X7 @ (binunion @ sK7 @ sK9)) = $true) & ((in @ X7 @ sK9) != $true)) => (((in @ sK10 @ sK8) = $true) & ((in @ sK10 @ sK7) != $true) & ((in @ sK10 @ (binunion @ sK7 @ sK9)) = $true) & ((in @ sK10 @ sK9) != $true))),
% 0.22/0.41 introduced(choice_axiom,[])).
% 0.22/0.41 thf(f35,plain,(
% 0.22/0.41 (! [X0,X1] : (! [X2] : (! [X3] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X0) = $true) | ((in @ X3 @ (binunion @ X0 @ X2)) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) | (binunionTEcontra != $true)) & ((binunionTEcontra = $true) | ? [X4,X5] : (? [X6] : (? [X7] : (((in @ X7 @ X5) = $true) & ((in @ X7 @ X4) != $true) & ((in @ X7 @ (binunion @ X4 @ X6)) = $true) & ((in @ X7 @ X6) != $true)) & ((in @ X6 @ (powerset @ X5)) = $true)) & ((in @ X4 @ (powerset @ X5)) = $true)))),
% 0.22/0.41 inference(rectify,[],[f34])).
% 0.22/0.41 thf(f34,plain,(
% 0.22/0.41 (! [X1,X0] : (! [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) = $true) | ((in @ X3 @ (binunion @ X1 @ X2)) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) | (binunionTEcontra != $true)) & ((binunionTEcontra = $true) | ? [X1,X0] : (? [X2] : (? [X3] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) != $true) & ((in @ X3 @ (binunion @ X1 @ X2)) = $true) & ((in @ X3 @ X2) != $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)))),
% 0.22/0.41 inference(nnf_transformation,[],[f24])).
% 0.22/0.41 thf(f24,plain,(
% 0.22/0.41 ! [X1,X0] : (! [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X1) = $true) | ((in @ X3 @ (binunion @ X1 @ X2)) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (binunionTEcontra = $true)),
% 0.22/0.41 inference(flattening,[],[f23])).
% 0.22/0.41 thf(f23,plain,(
% 0.22/0.41 ! [X0,X1] : (! [X2] : (! [X3] : (((((in @ X3 @ (binunion @ X1 @ X2)) != $true) | ((in @ X3 @ X2) = $true)) | ((in @ X3 @ X1) = $true)) | ((in @ X3 @ X0) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true)) <=> (binunionTEcontra = $true)),
% 0.22/0.41 inference(ennf_transformation,[],[f15])).
% 0.22/0.41 thf(f15,plain,(
% 0.22/0.41 ! [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3] : (((in @ X3 @ X0) = $true) => (((in @ X3 @ X1) != $true) => (((in @ X3 @ X2) != $true) => ((in @ X3 @ (binunion @ X1 @ X2)) != $true)))))) <=> (binunionTEcontra = $true)),
% 0.22/0.41 inference(flattening,[],[f8])).
% 0.22/0.41 thf(f8,plain,(
% 0.22/0.41 ! [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3] : (((in @ X3 @ X0) = $true) => (~((in @ X3 @ X1) = $true) => (~((in @ X3 @ X2) = $true) => ~((in @ X3 @ (binunion @ X1 @ X2)) = $true)))))) <=> (binunionTEcontra = $true)),
% 0.22/0.41 inference(fool_elimination,[],[f7])).
% 0.22/0.41 thf(f7,plain,(
% 0.22/0.41 (! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ X0) => (~(in @ X3 @ X1) => (~(in @ X3 @ X2) => ~(in @ X3 @ (binunion @ X1 @ X2))))))) = binunionTEcontra)),
% 0.22/0.41 inference(rectify,[],[f3])).
% 0.22/0.41 thf(f3,axiom,(
% 0.22/0.41 (! [X0,X3] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => (~(in @ X2 @ X3) => (~(in @ X2 @ X4) => ~(in @ X2 @ (binunion @ X3 @ X4))))))) = binunionTEcontra)),
% 0.22/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTEcontra)).
% 0.22/0.41 % SZS output end Proof for theBenchmark
% 0.22/0.41 % (20189)------------------------------
% 0.22/0.41 % (20189)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.41 % (20189)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (20189)Memory used [KB]: 5628
% 0.22/0.41 % (20189)Time elapsed: 0.019 s
% 0.22/0.41 % (20189)Instructions burned: 8 (million)
% 0.22/0.41 % (20189)------------------------------
% 0.22/0.41 % (20189)------------------------------
% 0.22/0.41 % (20183)Success in time 0.042 s
% 0.22/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------