TSTP Solution File: SEU610^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU610^2 : 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/sandbox2/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 03:49:58 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : SEU610^2 : TPTP v8.2.0. Released v3.7.0.
% 0.05/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 17:54:08 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.36 This is a TH0_THM_EQU_NAR problem
% 0.13/0.36 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/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 % (32228)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.38 % (32229)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)
% 0.13/0.38 % (32232)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)
% 0.13/0.38 % (32231)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.38 % (32230)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)
% 0.13/0.38 % (32234)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.38 % (32233)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)
% 0.13/0.38 % (32235)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)
% 0.13/0.38 % (32231)Instruction limit reached!
% 0.13/0.38 % (32231)------------------------------
% 0.13/0.38 % (32231)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (32231)Termination reason: Unknown
% 0.13/0.38 % (32231)Termination phase: Property scanning
% 0.13/0.38 % (32232)Instruction limit reached!
% 0.13/0.38 % (32232)------------------------------
% 0.13/0.38 % (32232)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (32232)Termination reason: Unknown
% 0.13/0.38 % (32232)Termination phase: Function definition elimination
% 0.13/0.38
% 0.13/0.38 % (32232)Memory used [KB]: 895
% 0.13/0.38 % (32232)Time elapsed: 0.003 s
% 0.13/0.38 % (32232)Instructions burned: 3 (million)
% 0.13/0.38 % (32232)------------------------------
% 0.13/0.38 % (32232)------------------------------
% 0.13/0.38
% 0.13/0.38 % (32231)Memory used [KB]: 1023
% 0.13/0.38 % (32231)Time elapsed: 0.003 s
% 0.13/0.38 % (32231)Instructions burned: 2 (million)
% 0.13/0.38 % (32231)------------------------------
% 0.13/0.38 % (32231)------------------------------
% 0.13/0.38 % (32235)Instruction limit reached!
% 0.13/0.38 % (32235)------------------------------
% 0.13/0.38 % (32235)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (32235)Termination reason: Unknown
% 0.13/0.38 % (32235)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (32235)Memory used [KB]: 5500
% 0.13/0.38 % (32235)Time elapsed: 0.003 s
% 0.13/0.38 % (32235)Instructions burned: 3 (million)
% 0.13/0.38 % (32235)------------------------------
% 0.13/0.38 % (32235)------------------------------
% 0.21/0.38 % (32229)Instruction limit reached!
% 0.21/0.38 % (32229)------------------------------
% 0.21/0.38 % (32229)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (32229)Termination reason: Unknown
% 0.21/0.38 % (32229)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (32229)Memory used [KB]: 5500
% 0.21/0.38 % (32229)Time elapsed: 0.005 s
% 0.21/0.38 % (32229)Instructions burned: 5 (million)
% 0.21/0.38 % (32229)------------------------------
% 0.21/0.38 % (32229)------------------------------
% 0.21/0.38 % (32233)First to succeed.
% 0.21/0.38 % (32233)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% 0.21/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.38 thf(func_def_5, type, subset: $i > $i > $o).
% 0.21/0.38 thf(func_def_7, type, setminus: $i > $i > $i).
% 0.21/0.38 thf(func_def_20, type, sK9: $i > $i > $i).
% 0.21/0.38 thf(f121,plain,(
% 0.21/0.38 $false),
% 0.21/0.38 inference(avatar_sat_refutation,[],[f96,f112,f120])).
% 0.21/0.38 thf(f120,plain,(
% 0.21/0.38 ~spl14_1),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f119])).
% 0.21/0.38 thf(f119,plain,(
% 0.21/0.38 $false | ~spl14_1),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f114])).
% 0.21/0.38 thf(f114,plain,(
% 0.21/0.38 ($true != $true) | ~spl14_1),
% 0.21/0.38 inference(superposition,[],[f65,f92])).
% 0.21/0.38 thf(f92,plain,(
% 0.21/0.38 ( ! [X3 : $o] : (($true = X3)) ) | ~spl14_1),
% 0.21/0.38 inference(avatar_component_clause,[],[f91])).
% 0.21/0.38 thf(f91,plain,(
% 0.21/0.38 spl14_1 <=> ! [X3 : $o] : ($true = X3)),
% 0.21/0.38 introduced(avatar_definition,[new_symbols(naming,[spl14_1])])).
% 0.21/0.38 thf(f65,plain,(
% 0.21/0.38 ((subset @ sK13 @ sK12) != $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f47])).
% 0.21/0.38 thf(f47,plain,(
% 0.21/0.38 (subsetI2 = $true) & (setminusI = $true) & (emptysetE = $true) & (((subset @ sK13 @ sK12) != $true) & (emptyset = (setminus @ sK13 @ sK12))) & (in__Cong = $true)),
% 0.21/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f45,f46])).
% 0.21/0.38 thf(f46,plain,(
% 0.21/0.38 ? [X0,X1] : (((subset @ X1 @ X0) != $true) & (emptyset = (setminus @ X1 @ X0))) => (((subset @ sK13 @ sK12) != $true) & (emptyset = (setminus @ sK13 @ sK12)))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f45,plain,(
% 0.21/0.38 (subsetI2 = $true) & (setminusI = $true) & (emptysetE = $true) & ? [X0,X1] : (((subset @ X1 @ X0) != $true) & (emptyset = (setminus @ X1 @ X0))) & (in__Cong = $true)),
% 0.21/0.38 inference(rectify,[],[f23])).
% 0.21/0.38 thf(f23,plain,(
% 0.21/0.38 (subsetI2 = $true) & (setminusI = $true) & (emptysetE = $true) & ? [X1,X0] : (((subset @ X0 @ X1) != $true) & (emptyset = (setminus @ X0 @ X1))) & (in__Cong = $true)),
% 0.21/0.38 inference(flattening,[],[f22])).
% 0.21/0.38 thf(f22,plain,(
% 0.21/0.38 (((? [X1,X0] : (((subset @ X0 @ X1) != $true) & (emptyset = (setminus @ X0 @ X1))) & (setminusI = $true)) & (subsetI2 = $true)) & (in__Cong = $true)) & (emptysetE = $true)),
% 0.21/0.38 inference(ennf_transformation,[],[f15])).
% 0.21/0.38 thf(f15,plain,(
% 0.21/0.38 ~((emptysetE = $true) => ((in__Cong = $true) => ((subsetI2 = $true) => ((setminusI = $true) => ! [X1,X0] : ((emptyset = (setminus @ X0 @ X1)) => ((subset @ X0 @ X1) = $true))))))),
% 0.21/0.38 inference(fool_elimination,[],[f14])).
% 0.21/0.38 thf(f14,plain,(
% 0.21/0.38 ~(emptysetE => (in__Cong => (subsetI2 => (setminusI => ! [X0,X1] : ((emptyset = (setminus @ X0 @ X1)) => (subset @ X0 @ X1))))))),
% 0.21/0.38 inference(rectify,[],[f6])).
% 0.21/0.38 thf(f6,negated_conjecture,(
% 0.21/0.38 ~(emptysetE => (in__Cong => (subsetI2 => (setminusI => ! [X2,X3] : ((emptyset = (setminus @ X2 @ X3)) => (subset @ X2 @ X3))))))),
% 0.21/0.38 inference(negated_conjecture,[],[f5])).
% 0.21/0.38 thf(f5,conjecture,(
% 0.21/0.38 emptysetE => (in__Cong => (subsetI2 => (setminusI => ! [X2,X3] : ((emptyset = (setminus @ X2 @ X3)) => (subset @ X2 @ X3)))))),
% 0.21/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1)).
% 0.21/0.38 thf(f112,plain,(
% 0.21/0.38 ~spl14_2),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f111])).
% 0.21/0.38 thf(f111,plain,(
% 0.21/0.38 $false | ~spl14_2),
% 0.21/0.38 inference(subsumption_resolution,[],[f110,f65])).
% 0.21/0.38 thf(f110,plain,(
% 0.21/0.38 ((subset @ sK13 @ sK12) = $true) | ~spl14_2),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f109])).
% 0.21/0.38 thf(f109,plain,(
% 0.21/0.38 ((subset @ sK13 @ sK12) = $true) | ($true != $true) | ~spl14_2),
% 0.21/0.38 inference(duplicate_literal_removal,[],[f108])).
% 0.21/0.38 thf(f108,plain,(
% 0.21/0.38 ($true != $true) | ((subset @ sK13 @ sK12) = $true) | ((subset @ sK13 @ sK12) = $true) | ~spl14_2),
% 0.21/0.38 inference(superposition,[],[f107,f87])).
% 0.21/0.38 thf(f87,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : (((in @ (sK9 @ X1 @ X0) @ X0) = $true) | ((subset @ X0 @ X1) = $true)) )),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f80])).
% 0.21/0.38 thf(f80,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : (((in @ (sK9 @ X1 @ X0) @ X0) = $true) | ($true != $true) | ((subset @ X0 @ X1) = $true)) )),
% 0.21/0.38 inference(definition_unfolding,[],[f62,f68])).
% 0.21/0.38 thf(f68,plain,(
% 0.21/0.38 (subsetI2 = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f47])).
% 0.21/0.38 thf(f62,plain,(
% 0.21/0.38 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK9 @ X1 @ X0) @ X0) = $true) | (subsetI2 != $true)) )),
% 0.21/0.38 inference(cnf_transformation,[],[f44])).
% 0.21/0.38 thf(f44,plain,(
% 0.21/0.38 (! [X0,X1] : (((subset @ X0 @ X1) = $true) | (((in @ (sK9 @ X1 @ X0) @ X0) = $true) & ((in @ (sK9 @ X1 @ X0) @ X1) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | (((subset @ sK10 @ sK11) != $true) & ! [X5] : (((in @ X5 @ sK10) != $true) | ((in @ X5 @ sK11) = $true))))),
% 0.21/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f41,f43,f42])).
% 0.21/0.38 thf(f42,plain,(
% 0.21/0.38 ! [X0,X1] : (? [X2] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) => (((in @ (sK9 @ X1 @ X0) @ X0) = $true) & ((in @ (sK9 @ X1 @ X0) @ X1) != $true)))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f43,plain,(
% 0.21/0.38 ? [X3,X4] : (((subset @ X3 @ X4) != $true) & ! [X5] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ X4) = $true))) => (((subset @ sK10 @ sK11) != $true) & ! [X5] : (((in @ X5 @ sK10) != $true) | ((in @ X5 @ sK11) = $true)))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f41,plain,(
% 0.21/0.38 (! [X0,X1] : (((subset @ X0 @ X1) = $true) | ? [X2] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X3,X4] : (((subset @ X3 @ X4) != $true) & ! [X5] : (((in @ X5 @ X3) != $true) | ((in @ X5 @ X4) = $true))))),
% 0.21/0.39 inference(rectify,[],[f40])).
% 0.21/0.39 thf(f40,plain,(
% 0.21/0.39 (! [X0,X1] : (((subset @ X0 @ X1) = $true) | ? [X2] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) | (subsetI2 != $true)) & ((subsetI2 = $true) | ? [X0,X1] : (((subset @ X0 @ X1) != $true) & ! [X2] : (((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true))))),
% 0.21/0.39 inference(nnf_transformation,[],[f24])).
% 0.21/0.39 thf(f24,plain,(
% 0.21/0.39 ! [X0,X1] : (((subset @ X0 @ X1) = $true) | ? [X2] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) <=> (subsetI2 = $true)),
% 0.21/0.39 inference(ennf_transformation,[],[f9])).
% 0.21/0.39 thf(f9,plain,(
% 0.21/0.39 (subsetI2 = $true) <=> ! [X0,X1] : (! [X2] : (((in @ X2 @ X0) = $true) => ((in @ X2 @ X1) = $true)) => ((subset @ X0 @ X1) = $true))),
% 0.21/0.39 inference(fool_elimination,[],[f8])).
% 0.21/0.39 thf(f8,plain,(
% 0.21/0.39 (subsetI2 = ! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.21/0.39 inference(rectify,[],[f3])).
% 0.21/0.39 thf(f3,axiom,(
% 0.21/0.39 (subsetI2 = ! [X2,X3] : (! [X0] : ((in @ X0 @ X2) => (in @ X0 @ X3)) => (subset @ X2 @ X3)))),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 0.21/0.39 thf(f107,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (((in @ (sK9 @ sK12 @ X0) @ sK13) != $true) | ((subset @ X0 @ sK12) = $true)) ) | ~spl14_2),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f106])).
% 0.21/0.39 thf(f106,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (((subset @ X0 @ sK12) = $true) | ($true != $true) | ((in @ (sK9 @ sK12 @ X0) @ sK13) != $true)) ) | ~spl14_2),
% 0.21/0.39 inference(superposition,[],[f88,f105])).
% 0.21/0.39 thf(f105,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (((in @ X0 @ sK12) = $true) | ((in @ X0 @ sK13) != $true)) ) | ~spl14_2),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f102])).
% 0.21/0.39 thf(f102,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($true != $true) | ((in @ X0 @ sK13) != $true) | ((in @ X0 @ sK12) = $true)) ) | ~spl14_2),
% 0.21/0.39 inference(superposition,[],[f95,f86])).
% 0.21/0.39 thf(f86,plain,(
% 0.21/0.39 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X5) = $true) | ((in @ X3 @ X4) != $true)) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f76])).
% 0.21/0.39 thf(f76,plain,(
% 0.21/0.39 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != $true) | ((in @ X3 @ X4) != $true) | ((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X5) = $true)) )),
% 0.21/0.39 inference(definition_unfolding,[],[f52,f67])).
% 0.21/0.39 thf(f67,plain,(
% 0.21/0.39 (setminusI = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f47])).
% 0.21/0.39 thf(f52,plain,(
% 0.21/0.39 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X4) != $true) | ((in @ X3 @ X5) = $true) | (setminusI != $true)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f34])).
% 0.21/0.39 thf(f34,plain,(
% 0.21/0.39 ((setminusI = $true) | (((in @ sK4 @ (setminus @ sK5 @ sK6)) != $true) & ((in @ sK4 @ sK5) = $true) & ((in @ sK4 @ sK6) != $true))) & (! [X3,X4,X5] : (((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X4) != $true) | ((in @ X3 @ X5) = $true)) | (setminusI != $true))),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f32,f33])).
% 0.21/0.39 thf(f33,plain,(
% 0.21/0.39 ? [X0,X1,X2] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ((in @ X0 @ X1) = $true) & ((in @ X0 @ X2) != $true)) => (((in @ sK4 @ (setminus @ sK5 @ sK6)) != $true) & ((in @ sK4 @ sK5) = $true) & ((in @ sK4 @ sK6) != $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f32,plain,(
% 0.21/0.39 ((setminusI = $true) | ? [X0,X1,X2] : (((in @ X0 @ (setminus @ X1 @ X2)) != $true) & ((in @ X0 @ X1) = $true) & ((in @ X0 @ X2) != $true))) & (! [X3,X4,X5] : (((in @ X3 @ (setminus @ X4 @ X5)) = $true) | ((in @ X3 @ X4) != $true) | ((in @ X3 @ X5) = $true)) | (setminusI != $true))),
% 0.21/0.39 inference(rectify,[],[f31])).
% 0.21/0.39 thf(f31,plain,(
% 0.21/0.39 ((setminusI = $true) | ? [X2,X0,X1] : (((in @ X2 @ (setminus @ X0 @ X1)) != $true) & ((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) & (! [X2,X0,X1] : (((in @ X2 @ (setminus @ X0 @ X1)) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true)) | (setminusI != $true))),
% 0.21/0.39 inference(nnf_transformation,[],[f21])).
% 0.21/0.39 thf(f21,plain,(
% 0.21/0.39 (setminusI = $true) <=> ! [X2,X0,X1] : (((in @ X2 @ (setminus @ X0 @ X1)) = $true) | ((in @ X2 @ X0) != $true) | ((in @ X2 @ X1) = $true))),
% 0.21/0.39 inference(flattening,[],[f20])).
% 0.21/0.39 thf(f20,plain,(
% 0.21/0.39 ! [X2,X1,X0] : ((((in @ X2 @ (setminus @ X0 @ X1)) = $true) | ((in @ X2 @ X1) = $true)) | ((in @ X2 @ X0) != $true)) <=> (setminusI = $true)),
% 0.21/0.39 inference(ennf_transformation,[],[f18])).
% 0.21/0.39 thf(f18,plain,(
% 0.21/0.39 ! [X2,X1,X0] : (((in @ X2 @ X0) = $true) => (((in @ X2 @ X1) != $true) => ((in @ X2 @ (setminus @ X0 @ X1)) = $true))) <=> (setminusI = $true)),
% 0.21/0.39 inference(flattening,[],[f11])).
% 0.21/0.39 thf(f11,plain,(
% 0.21/0.39 ! [X0,X1,X2] : (((in @ X2 @ X0) = $true) => (~((in @ X2 @ X1) = $true) => ((in @ X2 @ (setminus @ X0 @ X1)) = $true))) <=> (setminusI = $true)),
% 0.21/0.39 inference(fool_elimination,[],[f10])).
% 0.21/0.39 thf(f10,plain,(
% 0.21/0.39 (! [X0,X1,X2] : ((in @ X2 @ X0) => (~(in @ X2 @ X1) => (in @ X2 @ (setminus @ X0 @ X1)))) = setminusI)),
% 0.21/0.39 inference(rectify,[],[f4])).
% 0.21/0.39 thf(f4,axiom,(
% 0.21/0.39 (! [X2,X3,X0] : ((in @ X0 @ X2) => (~(in @ X0 @ X3) => (in @ X0 @ (setminus @ X2 @ X3)))) = setminusI)),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI)).
% 0.21/0.39 thf(f95,plain,(
% 0.21/0.39 ( ! [X2 : $i] : (((in @ X2 @ (setminus @ sK13 @ sK12)) != $true)) ) | ~spl14_2),
% 0.21/0.39 inference(avatar_component_clause,[],[f94])).
% 0.21/0.39 thf(f94,plain,(
% 0.21/0.39 spl14_2 <=> ! [X2] : ((in @ X2 @ (setminus @ sK13 @ sK12)) != $true)),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl14_2])])).
% 0.21/0.39 thf(f88,plain,(
% 0.21/0.39 ( ! [X0 : $i,X1 : $i] : (((in @ (sK9 @ X1 @ X0) @ X1) != $true) | ((subset @ X0 @ X1) = $true)) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f81])).
% 0.21/0.39 thf(f81,plain,(
% 0.21/0.39 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((in @ (sK9 @ X1 @ X0) @ X1) != $true) | ((subset @ X0 @ X1) = $true)) )),
% 0.21/0.39 inference(definition_unfolding,[],[f61,f68])).
% 0.21/0.39 thf(f61,plain,(
% 0.21/0.39 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ((in @ (sK9 @ X1 @ X0) @ X1) != $true) | (subsetI2 != $true)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f44])).
% 0.21/0.39 thf(f96,plain,(
% 0.21/0.39 spl14_1 | spl14_2),
% 0.21/0.39 inference(avatar_split_clause,[],[f89,f94,f91])).
% 0.21/0.39 thf(f89,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $o] : (((in @ X2 @ (setminus @ sK13 @ sK12)) != $true) | ($true = X3)) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f79])).
% 0.21/0.39 thf(f79,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $o] : (((in @ X2 @ (setminus @ sK13 @ sK12)) != $true) | ($true = X3) | ($true != $true)) )),
% 0.21/0.39 inference(definition_unfolding,[],[f56,f64,f66])).
% 0.21/0.39 thf(f66,plain,(
% 0.21/0.39 (emptysetE = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f47])).
% 0.21/0.39 thf(f64,plain,(
% 0.21/0.39 (emptyset = (setminus @ sK13 @ sK12))),
% 0.21/0.39 inference(cnf_transformation,[],[f47])).
% 0.21/0.39 thf(f56,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $o] : (($true = X3) | ((in @ X2 @ emptyset) != $true) | (emptysetE != $true)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f39])).
% 0.21/0.39 thf(f39,plain,(
% 0.21/0.39 ((emptysetE = $true) | ((sK8 != $true) & ((in @ sK7 @ emptyset) = $true))) & (! [X2] : (! [X3 : $o] : ($true = X3) | ((in @ X2 @ emptyset) != $true)) | (emptysetE != $true))),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f36,f38,f37])).
% 0.21/0.39 thf(f37,plain,(
% 0.21/0.39 ? [X0] : (? [X1 : $o] : ($true != X1) & ((in @ X0 @ emptyset) = $true)) => (? [X1 : $o] : ($true != X1) & ((in @ sK7 @ emptyset) = $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f38,plain,(
% 0.21/0.39 ? [X1 : $o] : ($true != X1) => (sK8 != $true)),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f36,plain,(
% 0.21/0.39 ((emptysetE = $true) | ? [X0] : (? [X1 : $o] : ($true != X1) & ((in @ X0 @ emptyset) = $true))) & (! [X2] : (! [X3 : $o] : ($true = X3) | ((in @ X2 @ emptyset) != $true)) | (emptysetE != $true))),
% 0.21/0.39 inference(rectify,[],[f35])).
% 0.21/0.39 thf(f35,plain,(
% 0.21/0.39 ((emptysetE = $true) | ? [X0] : (? [X1 : $o] : ($true != X1) & ((in @ X0 @ emptyset) = $true))) & (! [X0] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true)) | (emptysetE != $true))),
% 0.21/0.39 inference(nnf_transformation,[],[f25])).
% 0.21/0.39 thf(f25,plain,(
% 0.21/0.39 (emptysetE = $true) <=> ! [X0] : (! [X1 : $o] : ($true = X1) | ((in @ X0 @ emptyset) != $true))),
% 0.21/0.39 inference(ennf_transformation,[],[f17])).
% 0.21/0.39 thf(f17,plain,(
% 0.21/0.39 ! [X0] : (((in @ X0 @ emptyset) = $true) => ! [X1 : $o] : ($true = X1)) <=> (emptysetE = $true)),
% 0.21/0.39 inference(fool_elimination,[],[f16])).
% 0.21/0.39 thf(f16,plain,(
% 0.21/0.39 (emptysetE = ! [X0] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.21/0.39 inference(rectify,[],[f1])).
% 0.21/0.39 thf(f1,axiom,(
% 0.21/0.39 (emptysetE = ! [X0] : ((in @ X0 @ emptyset) => ! [X1 : $o] : X1))),
% 0.21/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE)).
% 0.21/0.39 % SZS output end Proof for theBenchmark
% 0.21/0.39 % (32233)------------------------------
% 0.21/0.39 % (32233)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (32233)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (32233)Memory used [KB]: 5628
% 0.21/0.39 % (32233)Time elapsed: 0.009 s
% 0.21/0.39 % (32233)Instructions burned: 6 (million)
% 0.21/0.39 % (32233)------------------------------
% 0.21/0.39 % (32233)------------------------------
% 0.21/0.39 % (32227)Success in time 0.013 s
% 0.21/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------