TSTP Solution File: SEU628^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU628^2 : 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 : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:50:07 EDT 2024
% Result : Theorem 0.14s 0.37s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : SEU628^2 : TPTP v8.2.0. Released v3.7.0.
% 0.13/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 17:42:53 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 This is a TH0_THM_EQU_NAR problem
% 0.14/0.34 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % (28764)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.14/0.36 % (28764)Instruction limit reached!
% 0.14/0.36 % (28764)------------------------------
% 0.14/0.36 % (28764)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (28764)Termination reason: Unknown
% 0.14/0.36 % (28764)Termination phase: Saturation
% 0.14/0.36
% 0.14/0.36 % (28764)Memory used [KB]: 5500
% 0.14/0.36 % (28764)Time elapsed: 0.003 s
% 0.14/0.36 % (28764)Instructions burned: 5 (million)
% 0.14/0.36 % (28764)------------------------------
% 0.14/0.36 % (28764)------------------------------
% 0.14/0.36 % (28763)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.36 % (28767)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.36 % (28765)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.36 % (28766)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.36 % (28769)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.36 % (28767)Instruction limit reached!
% 0.14/0.36 % (28767)------------------------------
% 0.14/0.36 % (28767)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.36 % (28767)Termination reason: Unknown
% 0.14/0.36 % (28767)Termination phase: shuffling
% 0.14/0.36
% 0.14/0.36 % (28767)Memory used [KB]: 895
% 0.14/0.36 % (28767)Time elapsed: 0.003 s
% 0.14/0.36 % (28767)Instructions burned: 2 (million)
% 0.14/0.36 % (28767)------------------------------
% 0.14/0.36 % (28767)------------------------------
% 0.14/0.37 % (28771)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.37 % (28766)Instruction limit reached!
% 0.14/0.37 % (28766)------------------------------
% 0.14/0.37 % (28766)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28766)Termination reason: Unknown
% 0.14/0.37 % (28766)Termination phase: Function definition elimination
% 0.14/0.37
% 0.14/0.37 % (28766)Memory used [KB]: 895
% 0.14/0.37 % (28766)Time elapsed: 0.003 s
% 0.14/0.37 % (28766)Instructions burned: 3 (million)
% 0.14/0.37 % (28766)------------------------------
% 0.14/0.37 % (28766)------------------------------
% 0.14/0.37 % (28771)Instruction limit reached!
% 0.14/0.37 % (28771)------------------------------
% 0.14/0.37 % (28771)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28771)Termination reason: Unknown
% 0.14/0.37 % (28771)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (28771)Memory used [KB]: 5500
% 0.14/0.37 % (28771)Time elapsed: 0.004 s
% 0.14/0.37 % (28771)Instructions burned: 3 (million)
% 0.14/0.37 % (28771)------------------------------
% 0.14/0.37 % (28771)------------------------------
% 0.14/0.37 % (28775)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)
% 0.14/0.37 % (28770)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (28769)First to succeed.
% 0.14/0.37 % (28765)Also succeeded, but the first one will report.
% 0.14/0.37 % (28763)Also succeeded, but the first one will report.
% 0.14/0.37 % (28769)Refutation found. Thanks to Tanya!
% 0.14/0.37 % SZS status Theorem for theBenchmark
% 0.14/0.37 % SZS output start Proof for theBenchmark
% 0.14/0.37 thf(func_def_0, type, in: $i > $i > $o).
% 0.14/0.37 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.14/0.37 thf(func_def_3, type, powerset: $i > $i).
% 0.14/0.37 thf(func_def_4, type, subset: $i > $i > $o).
% 0.14/0.37 thf(func_def_7, type, binunion: $i > $i > $i).
% 0.14/0.37 thf(f55,plain,(
% 0.14/0.37 $false),
% 0.14/0.37 inference(subsumption_resolution,[],[f54,f35])).
% 0.14/0.37 thf(f35,plain,(
% 0.14/0.37 ((in @ sK5 @ sK4) = $true)),
% 0.14/0.37 inference(cnf_transformation,[],[f23])).
% 0.14/0.37 thf(f23,plain,(
% 0.14/0.37 ((($true != (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK3 @ sK4))))) & ((in @ sK5 @ sK4) = $true)) & ($true = (in @ sK2 @ sK3))) & (powersetI1 = $true) & (ubforcartprodlem1 = $true)),
% 0.14/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f20,f22,f21])).
% 0.14/0.37 thf(f21,plain,(
% 0.14/0.37 ? [X0,X1,X2] : (? [X3] : (((in @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X2)))) != $true) & ($true = (in @ X3 @ X2))) & ((in @ X0 @ X1) = $true)) => (? [X3] : (($true != (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK3 @ sK4))))) & ($true = (in @ X3 @ sK4))) & ($true = (in @ sK2 @ sK3)))),
% 0.14/0.37 introduced(choice_axiom,[])).
% 0.14/0.37 thf(f22,plain,(
% 0.14/0.37 ? [X3] : (($true != (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK3 @ sK4))))) & ($true = (in @ X3 @ sK4))) => (($true != (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK3 @ sK4))))) & ((in @ sK5 @ sK4) = $true))),
% 0.14/0.37 introduced(choice_axiom,[])).
% 0.14/0.37 thf(f20,plain,(
% 0.14/0.37 ? [X0,X1,X2] : (? [X3] : (((in @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X2)))) != $true) & ($true = (in @ X3 @ X2))) & ((in @ X0 @ X1) = $true)) & (powersetI1 = $true) & (ubforcartprodlem1 = $true)),
% 0.14/0.37 inference(rectify,[],[f14])).
% 0.14/0.37 thf(f14,plain,(
% 0.14/0.37 ? [X2,X1,X0] : (? [X3] : (($true != (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X0))))) & ((in @ X3 @ X0) = $true)) & ($true = (in @ X2 @ X1))) & (powersetI1 = $true) & (ubforcartprodlem1 = $true)),
% 0.14/0.37 inference(flattening,[],[f13])).
% 0.14/0.37 thf(f13,plain,(
% 0.14/0.37 (? [X2,X1,X0] : (? [X3] : (($true != (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X0))))) & ((in @ X3 @ X0) = $true)) & ($true = (in @ X2 @ X1))) & (ubforcartprodlem1 = $true)) & (powersetI1 = $true)),
% 0.14/0.37 inference(ennf_transformation,[],[f9])).
% 0.14/0.37 thf(f9,plain,(
% 0.14/0.37 ~((powersetI1 = $true) => ((ubforcartprodlem1 = $true) => ! [X0,X2,X1] : (($true = (in @ X2 @ X1)) => ! [X3] : (((in @ X3 @ X0) = $true) => ($true = (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X0)))))))))),
% 0.14/0.37 inference(fool_elimination,[],[f8])).
% 0.14/0.37 thf(f8,plain,(
% 0.14/0.37 ~(powersetI1 => (ubforcartprodlem1 => ! [X0,X1,X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X0) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1 @ X0))))))))),
% 0.14/0.37 inference(rectify,[],[f4])).
% 0.14/0.37 thf(f4,negated_conjecture,(
% 0.14/0.37 ~(powersetI1 => (ubforcartprodlem1 => ! [X1,X0,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X0 @ X1))))))))),
% 0.14/0.37 inference(negated_conjecture,[],[f3])).
% 0.14/0.37 thf(f3,conjecture,(
% 0.14/0.37 powersetI1 => (ubforcartprodlem1 => ! [X1,X0,X2] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X0 @ X1)))))))),
% 0.14/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2)).
% 0.14/0.37 thf(f54,plain,(
% 0.14/0.37 ((in @ sK5 @ sK4) != $true)),
% 0.14/0.37 inference(subsumption_resolution,[],[f53,f34])).
% 0.14/0.37 thf(f34,plain,(
% 0.14/0.37 ($true = (in @ sK2 @ sK3))),
% 0.14/0.37 inference(cnf_transformation,[],[f23])).
% 0.14/0.37 thf(f53,plain,(
% 0.14/0.37 ($true != (in @ sK2 @ sK3)) | ((in @ sK5 @ sK4) != $true)),
% 0.14/0.37 inference(trivial_inequality_removal,[],[f52])).
% 0.14/0.37 thf(f52,plain,(
% 0.14/0.37 ($true != (in @ sK2 @ sK3)) | ($true != $true) | ((in @ sK5 @ sK4) != $true)),
% 0.14/0.37 inference(superposition,[],[f51,f48])).
% 0.14/0.37 thf(f48,plain,(
% 0.14/0.37 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((subset @ (setadjoin @ (setadjoin @ X6 @ emptyset) @ (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X7 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))) = $true) | ((in @ X7 @ X5) != $true) | ($true != (in @ X6 @ X4))) )),
% 0.14/0.37 inference(trivial_inequality_removal,[],[f47])).
% 0.14/0.37 thf(f47,plain,(
% 0.14/0.37 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((subset @ (setadjoin @ (setadjoin @ X6 @ emptyset) @ (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X7 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))) = $true) | ($true != $true) | ((in @ X7 @ X5) != $true) | ($true != (in @ X6 @ X4))) )),
% 0.14/0.37 inference(definition_unfolding,[],[f37,f32])).
% 0.14/0.37 thf(f32,plain,(
% 0.14/0.37 (ubforcartprodlem1 = $true)),
% 0.14/0.37 inference(cnf_transformation,[],[f23])).
% 0.14/0.37 thf(f37,plain,(
% 0.14/0.37 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((subset @ (setadjoin @ (setadjoin @ X6 @ emptyset) @ (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X7 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))) = $true) | ((in @ X7 @ X5) != $true) | ($true != (in @ X6 @ X4)) | (ubforcartprodlem1 != $true)) )),
% 0.14/0.37 inference(cnf_transformation,[],[f28])).
% 0.14/0.37 thf(f28,plain,(
% 0.14/0.37 ((ubforcartprodlem1 = $true) | ((($true != (subset @ (setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK6 @ sK7)))) & ($true = (in @ sK9 @ sK7))) & ((in @ sK8 @ sK6) = $true))) & (! [X4,X5,X6] : (! [X7] : (((subset @ (setadjoin @ (setadjoin @ X6 @ emptyset) @ (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X7 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))) = $true) | ((in @ X7 @ X5) != $true)) | ($true != (in @ X6 @ X4))) | (ubforcartprodlem1 != $true))),
% 0.14/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9])],[f25,f27,f26])).
% 0.14/0.37 thf(f26,plain,(
% 0.14/0.37 ? [X0,X1,X2] : (? [X3] : (((subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))) != $true) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ X0) = $true)) => (? [X3] : (((subset @ (setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK6 @ sK7))) != $true) & ($true = (in @ X3 @ sK7))) & ((in @ sK8 @ sK6) = $true))),
% 0.14/0.37 introduced(choice_axiom,[])).
% 0.14/0.37 thf(f27,plain,(
% 0.14/0.37 ? [X3] : (((subset @ (setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK6 @ sK7))) != $true) & ($true = (in @ X3 @ sK7))) => (($true != (subset @ (setadjoin @ (setadjoin @ sK8 @ emptyset) @ (setadjoin @ (setadjoin @ sK8 @ (setadjoin @ sK9 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK6 @ sK7)))) & ($true = (in @ sK9 @ sK7)))),
% 0.14/0.37 introduced(choice_axiom,[])).
% 0.14/0.37 thf(f25,plain,(
% 0.14/0.37 ((ubforcartprodlem1 = $true) | ? [X0,X1,X2] : (? [X3] : (((subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))) != $true) & ((in @ X3 @ X1) = $true)) & ((in @ X2 @ X0) = $true))) & (! [X4,X5,X6] : (! [X7] : (((subset @ (setadjoin @ (setadjoin @ X6 @ emptyset) @ (setadjoin @ (setadjoin @ X6 @ (setadjoin @ X7 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5))) = $true) | ((in @ X7 @ X5) != $true)) | ($true != (in @ X6 @ X4))) | (ubforcartprodlem1 != $true))),
% 0.14/0.37 inference(rectify,[],[f24])).
% 0.14/0.37 thf(f24,plain,(
% 0.14/0.37 ((ubforcartprodlem1 = $true) | ? [X2,X1,X0] : (? [X3] : (((subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X2 @ X1))) != $true) & ((in @ X3 @ X1) = $true)) & ((in @ X0 @ X2) = $true))) & (! [X2,X1,X0] : (! [X3] : (((subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X2 @ X1))) = $true) | ((in @ X3 @ X1) != $true)) | ((in @ X0 @ X2) != $true)) | (ubforcartprodlem1 != $true))),
% 0.14/0.37 inference(nnf_transformation,[],[f15])).
% 0.14/0.37 thf(f15,plain,(
% 0.14/0.37 (ubforcartprodlem1 = $true) <=> ! [X2,X1,X0] : (! [X3] : (((subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X2 @ X1))) = $true) | ((in @ X3 @ X1) != $true)) | ((in @ X0 @ X2) != $true))),
% 0.14/0.37 inference(ennf_transformation,[],[f11])).
% 0.14/0.37 thf(f11,plain,(
% 0.14/0.37 ! [X1,X0,X2] : (((in @ X0 @ X2) = $true) => ! [X3] : (((in @ X3 @ X1) = $true) => ((subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X2 @ X1))) = $true))) <=> (ubforcartprodlem1 = $true)),
% 0.14/0.37 inference(fool_elimination,[],[f10])).
% 0.14/0.37 thf(f10,plain,(
% 0.14/0.37 (! [X0,X1,X2] : ((in @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => (subset @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X2 @ X1))))) = ubforcartprodlem1)),
% 0.14/0.37 inference(rectify,[],[f2])).
% 0.14/0.37 thf(f2,axiom,(
% 0.14/0.37 (! [X2,X1,X0] : ((in @ X2 @ X0) => ! [X3] : ((in @ X3 @ X1) => (subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X0 @ X1))))) = ubforcartprodlem1)),
% 0.14/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1)).
% 0.14/0.37 thf(f51,plain,(
% 0.14/0.37 ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK3 @ sK4))) != $true)),
% 0.14/0.37 inference(trivial_inequality_removal,[],[f50])).
% 0.14/0.37 thf(f50,plain,(
% 0.14/0.37 ((subset @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ sK3 @ sK4))) != $true) | ($true != $true)),
% 0.14/0.37 inference(superposition,[],[f36,f49])).
% 0.14/0.37 thf(f49,plain,(
% 0.14/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true)) )),
% 0.14/0.37 inference(trivial_inequality_removal,[],[f41])).
% 0.14/0.37 thf(f41,plain,(
% 0.14/0.37 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ((in @ X1 @ (powerset @ X0)) = $true) | ($true != $true)) )),
% 0.14/0.37 inference(definition_unfolding,[],[f31,f33])).
% 0.14/0.37 thf(f33,plain,(
% 0.14/0.37 (powersetI1 = $true)),
% 0.14/0.37 inference(cnf_transformation,[],[f23])).
% 0.14/0.37 thf(f31,plain,(
% 0.14/0.37 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true) | (powersetI1 != $true)) )),
% 0.14/0.37 inference(cnf_transformation,[],[f19])).
% 0.14/0.37 thf(f19,plain,(
% 0.14/0.37 (! [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | (($true != (in @ sK1 @ (powerset @ sK0))) & ((subset @ sK1 @ sK0) = $true)))),
% 0.14/0.37 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18])).
% 0.14/0.37 thf(f18,plain,(
% 0.14/0.37 ? [X2,X3] : (($true != (in @ X3 @ (powerset @ X2))) & ((subset @ X3 @ X2) = $true)) => (($true != (in @ sK1 @ (powerset @ sK0))) & ((subset @ sK1 @ sK0) = $true))),
% 0.14/0.37 introduced(choice_axiom,[])).
% 0.14/0.37 thf(f17,plain,(
% 0.14/0.37 (! [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) | ((subset @ X1 @ X0) != $true)) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X2,X3] : (($true != (in @ X3 @ (powerset @ X2))) & ((subset @ X3 @ X2) = $true)))),
% 0.14/0.37 inference(rectify,[],[f16])).
% 0.14/0.37 thf(f16,plain,(
% 0.14/0.37 (! [X1,X0] : (((in @ X0 @ (powerset @ X1)) = $true) | ($true != (subset @ X0 @ X1))) | (powersetI1 != $true)) & ((powersetI1 = $true) | ? [X1,X0] : (((in @ X0 @ (powerset @ X1)) != $true) & ($true = (subset @ X0 @ X1))))),
% 0.14/0.37 inference(nnf_transformation,[],[f12])).
% 0.14/0.37 thf(f12,plain,(
% 0.14/0.37 ! [X1,X0] : (((in @ X0 @ (powerset @ X1)) = $true) | ($true != (subset @ X0 @ X1))) <=> (powersetI1 = $true)),
% 0.14/0.37 inference(ennf_transformation,[],[f7])).
% 0.14/0.37 thf(f7,plain,(
% 0.14/0.37 (powersetI1 = $true) <=> ! [X0,X1] : (($true = (subset @ X0 @ X1)) => ((in @ X0 @ (powerset @ X1)) = $true))),
% 0.14/0.37 inference(fool_elimination,[],[f6])).
% 0.14/0.37 thf(f6,plain,(
% 0.14/0.37 (powersetI1 = ! [X0,X1] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))))),
% 0.14/0.37 inference(rectify,[],[f1])).
% 0.14/0.37 thf(f1,axiom,(
% 0.14/0.37 (powersetI1 = ! [X1,X0] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 0.14/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1)).
% 0.14/0.37 thf(f36,plain,(
% 0.14/0.37 ($true != (in @ (setadjoin @ (setadjoin @ sK2 @ emptyset) @ (setadjoin @ (setadjoin @ sK2 @ (setadjoin @ sK5 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ sK3 @ sK4)))))),
% 0.14/0.37 inference(cnf_transformation,[],[f23])).
% 0.14/0.37 % SZS output end Proof for theBenchmark
% 0.14/0.37 % (28769)------------------------------
% 0.14/0.37 % (28769)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (28769)Termination reason: Refutation
% 0.14/0.37
% 0.14/0.37 % (28769)Memory used [KB]: 5500
% 0.14/0.37 % (28769)Time elapsed: 0.008 s
% 0.14/0.37 % (28769)Instructions burned: 5 (million)
% 0.14/0.37 % (28769)------------------------------
% 0.14/0.37 % (28769)------------------------------
% 0.14/0.37 % (28761)Success in time 0.015 s
% 0.14/0.37 % Vampire---4.8 exiting
%------------------------------------------------------------------------------