TSTP Solution File: SEU634^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU634^2 : 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 : n032.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 03:50:10 EDT 2024
% Result : Theorem 0.15s 0.34s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SEU634^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.12 % 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
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun May 19 15:27:53 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.11/0.31 This is a TH0_THM_EQU_NAR problem
% 0.15/0.31 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
% 0.15/0.33 % (28197)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.15/0.33 % (28195)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.15/0.33 % (28193)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (3000ds/27Mi)
% 0.15/0.33 % (28196)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (3000ds/275Mi)
% 0.15/0.33 % (28195)Instruction limit reached!
% 0.15/0.33 % (28195)------------------------------
% 0.15/0.33 % (28195)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (28194)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.15/0.33 % (28198)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.15/0.33 % (28195)Termination reason: Unknown
% 0.15/0.33 % (28195)Termination phase: Saturation
% 0.15/0.33
% 0.15/0.33 % (28195)Memory used [KB]: 5500
% 0.15/0.33 % (28195)Time elapsed: 0.003 s
% 0.15/0.33 % (28195)Instructions burned: 3 (million)
% 0.15/0.33 % (28195)------------------------------
% 0.15/0.33 % (28195)------------------------------
% 0.15/0.33 % (28191)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.15/0.33 % (28194)Instruction limit reached!
% 0.15/0.33 % (28194)------------------------------
% 0.15/0.33 % (28194)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (28194)Termination reason: Unknown
% 0.15/0.33 % (28192)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (3000ds/4Mi)
% 0.15/0.33 % (28194)Termination phase: Property scanning
% 0.15/0.33
% 0.15/0.33 % (28194)Memory used [KB]: 895
% 0.15/0.33 % (28194)Time elapsed: 0.003 s
% 0.15/0.33 % (28194)Instructions burned: 2 (million)
% 0.15/0.33 % (28194)------------------------------
% 0.15/0.33 % (28194)------------------------------
% 0.15/0.33 % (28198)Instruction limit reached!
% 0.15/0.33 % (28198)------------------------------
% 0.15/0.33 % (28198)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (28198)Termination reason: Unknown
% 0.15/0.33 % (28198)Termination phase: Saturation
% 0.15/0.33
% 0.15/0.33 % (28198)Memory used [KB]: 5500
% 0.15/0.33 % (28198)Time elapsed: 0.003 s
% 0.15/0.33 % (28198)Instructions burned: 3 (million)
% 0.15/0.33 % (28198)------------------------------
% 0.15/0.33 % (28198)------------------------------
% 0.15/0.33 % (28197)First to succeed.
% 0.15/0.33 % (28192)Instruction limit reached!
% 0.15/0.33 % (28192)------------------------------
% 0.15/0.33 % (28192)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.33 % (28192)Termination reason: Unknown
% 0.15/0.33 % (28192)Termination phase: Saturation
% 0.15/0.33
% 0.15/0.33 % (28192)Memory used [KB]: 5500
% 0.15/0.33 % (28192)Time elapsed: 0.005 s
% 0.15/0.33 % (28192)Instructions burned: 5 (million)
% 0.15/0.33 % (28192)------------------------------
% 0.15/0.33 % (28192)------------------------------
% 0.15/0.34 % (28197)Refutation found. Thanks to Tanya!
% 0.15/0.34 % SZS status Theorem for theBenchmark
% 0.15/0.34 % SZS output start Proof for theBenchmark
% 0.15/0.34 thf(func_def_0, type, in: $i > $i > $o).
% 0.15/0.34 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.15/0.34 thf(func_def_3, type, setunion: $i > $i).
% 0.15/0.34 thf(func_def_6, type, subset: $i > $i > $o).
% 0.15/0.34 thf(func_def_13, type, sK2: $i > $i > $i).
% 0.15/0.34 thf(func_def_19, type, sK8: $i > $i > $i).
% 0.15/0.34 thf(f80,plain,(
% 0.15/0.34 $false),
% 0.15/0.34 inference(subsumption_resolution,[],[f79,f41])).
% 0.15/0.34 thf(f41,plain,(
% 0.15/0.34 ((subset @ (setunion @ (setadjoin @ sK3 @ emptyset)) @ sK3) != $true)),
% 0.15/0.34 inference(cnf_transformation,[],[f26])).
% 0.15/0.34 thf(f26,plain,(
% 0.15/0.34 (setunionE2 = $true) & (subsetI2 = $true) & ((subset @ (setunion @ (setadjoin @ sK3 @ emptyset)) @ sK3) != $true) & (uniqinunit = $true)),
% 0.15/0.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f17,f25])).
% 0.15/0.34 thf(f25,plain,(
% 0.15/0.34 ? [X0] : ($true != (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) => ((subset @ (setunion @ (setadjoin @ sK3 @ emptyset)) @ sK3) != $true)),
% 0.15/0.34 introduced(choice_axiom,[])).
% 0.15/0.34 thf(f17,plain,(
% 0.15/0.34 (setunionE2 = $true) & (subsetI2 = $true) & ? [X0] : ($true != (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) & (uniqinunit = $true)),
% 0.15/0.34 inference(flattening,[],[f16])).
% 0.15/0.34 thf(f16,plain,(
% 0.15/0.34 ((? [X0] : ($true != (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)) & (setunionE2 = $true)) & (subsetI2 = $true)) & (uniqinunit = $true)),
% 0.15/0.34 inference(ennf_transformation,[],[f12])).
% 0.15/0.34 thf(f12,plain,(
% 0.15/0.34 ~((uniqinunit = $true) => ((subsetI2 = $true) => ((setunionE2 = $true) => ! [X0] : ($true = (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0)))))),
% 0.15/0.34 inference(fool_elimination,[],[f11])).
% 0.15/0.34 thf(f11,plain,(
% 0.15/0.34 ~(uniqinunit => (subsetI2 => (setunionE2 => ! [X0] : (subset @ (setunion @ (setadjoin @ X0 @ emptyset)) @ X0))))),
% 0.15/0.34 inference(rectify,[],[f5])).
% 0.15/0.34 thf(f5,negated_conjecture,(
% 0.15/0.34 ~(uniqinunit => (subsetI2 => (setunionE2 => ! [X2] : (subset @ (setunion @ (setadjoin @ X2 @ emptyset)) @ X2))))),
% 0.15/0.34 inference(negated_conjecture,[],[f4])).
% 0.15/0.34 thf(f4,conjecture,(
% 0.15/0.34 uniqinunit => (subsetI2 => (setunionE2 => ! [X2] : (subset @ (setunion @ (setadjoin @ X2 @ emptyset)) @ X2)))),
% 0.15/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1)).
% 0.15/0.34 thf(f79,plain,(
% 0.15/0.34 ((subset @ (setunion @ (setadjoin @ sK3 @ emptyset)) @ sK3) = $true)),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f78])).
% 0.15/0.34 thf(f78,plain,(
% 0.15/0.34 ($true != $true) | ((subset @ (setunion @ (setadjoin @ sK3 @ emptyset)) @ sK3) = $true)),
% 0.15/0.34 inference(superposition,[],[f62,f75])).
% 0.15/0.34 thf(f75,plain,(
% 0.15/0.34 ($true = (in @ (sK2 @ sK3 @ (setunion @ (setadjoin @ sK3 @ emptyset))) @ sK3))),
% 0.15/0.34 inference(backward_demodulation,[],[f71,f74])).
% 0.15/0.34 thf(f74,plain,(
% 0.15/0.34 (sK3 = (sK8 @ (setadjoin @ sK3 @ emptyset) @ (sK2 @ sK3 @ (setunion @ (setadjoin @ sK3 @ emptyset)))))),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f73])).
% 0.15/0.34 thf(f73,plain,(
% 0.15/0.34 ($true != $true) | (sK3 = (sK8 @ (setadjoin @ sK3 @ emptyset) @ (sK2 @ sK3 @ (setunion @ (setadjoin @ sK3 @ emptyset)))))),
% 0.15/0.34 inference(superposition,[],[f66,f72])).
% 0.15/0.34 thf(f72,plain,(
% 0.15/0.34 ($true = (in @ (sK8 @ (setadjoin @ sK3 @ emptyset) @ (sK2 @ sK3 @ (setunion @ (setadjoin @ sK3 @ emptyset)))) @ (setadjoin @ sK3 @ emptyset)))),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f70])).
% 0.15/0.34 thf(f70,plain,(
% 0.15/0.34 ($true = (in @ (sK8 @ (setadjoin @ sK3 @ emptyset) @ (sK2 @ sK3 @ (setunion @ (setadjoin @ sK3 @ emptyset)))) @ (setadjoin @ sK3 @ emptyset))) | ($true != $true)),
% 0.15/0.34 inference(superposition,[],[f63,f68])).
% 0.15/0.34 thf(f68,plain,(
% 0.15/0.34 ($true = (in @ (sK2 @ sK3 @ (setunion @ (setadjoin @ sK3 @ emptyset))) @ (setunion @ (setadjoin @ sK3 @ emptyset))))),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f67])).
% 0.15/0.34 thf(f67,plain,(
% 0.15/0.34 ($true = (in @ (sK2 @ sK3 @ (setunion @ (setadjoin @ sK3 @ emptyset))) @ (setunion @ (setadjoin @ sK3 @ emptyset)))) | ($true != $true)),
% 0.15/0.34 inference(superposition,[],[f41,f65])).
% 0.15/0.34 thf(f65,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (($true = (subset @ X3 @ X4)) | ((in @ (sK2 @ X4 @ X3) @ X3) = $true)) )),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f53])).
% 0.15/0.34 thf(f53,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (((in @ (sK2 @ X4 @ X3) @ X3) = $true) | ($true != $true) | ($true = (subset @ X3 @ X4))) )),
% 0.15/0.34 inference(definition_unfolding,[],[f37,f42])).
% 0.15/0.34 thf(f42,plain,(
% 0.15/0.34 (subsetI2 = $true)),
% 0.15/0.34 inference(cnf_transformation,[],[f26])).
% 0.15/0.34 thf(f37,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (($true = (subset @ X3 @ X4)) | ((in @ (sK2 @ X4 @ X3) @ X3) = $true) | (subsetI2 != $true)) )),
% 0.15/0.34 inference(cnf_transformation,[],[f24])).
% 0.15/0.34 thf(f24,plain,(
% 0.15/0.34 ((subsetI2 = $true) | (((subset @ sK0 @ sK1) != $true) & ! [X2] : (($true != (in @ X2 @ sK0)) | ($true = (in @ X2 @ sK1))))) & (! [X3,X4] : (($true = (subset @ X3 @ X4)) | (((in @ (sK2 @ X4 @ X3) @ X3) = $true) & ($true != (in @ (sK2 @ X4 @ X3) @ X4)))) | (subsetI2 != $true))),
% 0.15/0.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f21,f23,f22])).
% 0.15/0.34 thf(f22,plain,(
% 0.15/0.34 ? [X0,X1] : (($true != (subset @ X0 @ X1)) & ! [X2] : (($true != (in @ X2 @ X0)) | ($true = (in @ X2 @ X1)))) => (((subset @ sK0 @ sK1) != $true) & ! [X2] : (($true != (in @ X2 @ sK0)) | ($true = (in @ X2 @ sK1))))),
% 0.15/0.34 introduced(choice_axiom,[])).
% 0.15/0.34 thf(f23,plain,(
% 0.15/0.34 ! [X3,X4] : (? [X5] : (((in @ X5 @ X3) = $true) & ((in @ X5 @ X4) != $true)) => (((in @ (sK2 @ X4 @ X3) @ X3) = $true) & ($true != (in @ (sK2 @ X4 @ X3) @ X4))))),
% 0.15/0.34 introduced(choice_axiom,[])).
% 0.15/0.34 thf(f21,plain,(
% 0.15/0.34 ((subsetI2 = $true) | ? [X0,X1] : (($true != (subset @ X0 @ X1)) & ! [X2] : (($true != (in @ X2 @ X0)) | ($true = (in @ X2 @ X1))))) & (! [X3,X4] : (($true = (subset @ X3 @ X4)) | ? [X5] : (((in @ X5 @ X3) = $true) & ((in @ X5 @ X4) != $true))) | (subsetI2 != $true))),
% 0.15/0.34 inference(rectify,[],[f20])).
% 0.15/0.34 thf(f20,plain,(
% 0.15/0.34 ((subsetI2 = $true) | ? [X0,X1] : (($true != (subset @ X0 @ X1)) & ! [X2] : (($true != (in @ X2 @ X0)) | ($true = (in @ X2 @ X1))))) & (! [X0,X1] : (($true = (subset @ X0 @ X1)) | ? [X2] : (($true = (in @ X2 @ X0)) & ($true != (in @ X2 @ X1)))) | (subsetI2 != $true))),
% 0.15/0.34 inference(nnf_transformation,[],[f19])).
% 0.15/0.34 thf(f19,plain,(
% 0.15/0.34 (subsetI2 = $true) <=> ! [X0,X1] : (($true = (subset @ X0 @ X1)) | ? [X2] : (($true = (in @ X2 @ X0)) & ($true != (in @ X2 @ X1))))),
% 0.15/0.34 inference(ennf_transformation,[],[f10])).
% 0.15/0.34 thf(f10,plain,(
% 0.15/0.34 ! [X0,X1] : (! [X2] : (($true = (in @ X2 @ X0)) => ($true = (in @ X2 @ X1))) => ($true = (subset @ X0 @ X1))) <=> (subsetI2 = $true)),
% 0.15/0.34 inference(fool_elimination,[],[f9])).
% 0.15/0.34 thf(f9,plain,(
% 0.15/0.34 (! [X0,X1] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI2)),
% 0.15/0.34 inference(rectify,[],[f2])).
% 0.15/0.34 thf(f2,axiom,(
% 0.15/0.34 (! [X2,X3] : (! [X0] : ((in @ X0 @ X2) => (in @ X0 @ X3)) => (subset @ X2 @ X3)) = subsetI2)),
% 0.15/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2)).
% 0.15/0.34 thf(f63,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (((in @ X3 @ (setunion @ X4)) != $true) | ($true = (in @ (sK8 @ X4 @ X3) @ X4))) )),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f60])).
% 0.15/0.34 thf(f60,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (((in @ X3 @ (setunion @ X4)) != $true) | ($true != $true) | ($true = (in @ (sK8 @ X4 @ X3) @ X4))) )),
% 0.15/0.34 inference(definition_unfolding,[],[f48,f43])).
% 0.15/0.34 thf(f43,plain,(
% 0.15/0.34 (setunionE2 = $true)),
% 0.15/0.34 inference(cnf_transformation,[],[f26])).
% 0.15/0.34 thf(f48,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (((in @ X3 @ (setunion @ X4)) != $true) | ($true = (in @ (sK8 @ X4 @ X3) @ X4)) | (setunionE2 != $true)) )),
% 0.15/0.34 inference(cnf_transformation,[],[f35])).
% 0.15/0.34 thf(f35,plain,(
% 0.15/0.34 ((setunionE2 = $true) | (($true = (in @ sK6 @ (setunion @ sK7))) & ! [X2] : (($true != (in @ X2 @ sK7)) | ($true != (in @ sK6 @ X2))))) & (! [X3,X4] : (((in @ X3 @ (setunion @ X4)) != $true) | (($true = (in @ (sK8 @ X4 @ X3) @ X4)) & ($true = (in @ X3 @ (sK8 @ X4 @ X3))))) | (setunionE2 != $true))),
% 0.15/0.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f32,f34,f33])).
% 0.15/0.34 thf(f33,plain,(
% 0.15/0.34 ? [X0,X1] : (($true = (in @ X0 @ (setunion @ X1))) & ! [X2] : (($true != (in @ X2 @ X1)) | ((in @ X0 @ X2) != $true))) => (($true = (in @ sK6 @ (setunion @ sK7))) & ! [X2] : (($true != (in @ X2 @ sK7)) | ($true != (in @ sK6 @ X2))))),
% 0.15/0.34 introduced(choice_axiom,[])).
% 0.15/0.34 thf(f34,plain,(
% 0.15/0.34 ! [X3,X4] : (? [X5] : (((in @ X5 @ X4) = $true) & ($true = (in @ X3 @ X5))) => (($true = (in @ (sK8 @ X4 @ X3) @ X4)) & ($true = (in @ X3 @ (sK8 @ X4 @ X3)))))),
% 0.15/0.34 introduced(choice_axiom,[])).
% 0.15/0.34 thf(f32,plain,(
% 0.15/0.34 ((setunionE2 = $true) | ? [X0,X1] : (($true = (in @ X0 @ (setunion @ X1))) & ! [X2] : (($true != (in @ X2 @ X1)) | ((in @ X0 @ X2) != $true)))) & (! [X3,X4] : (((in @ X3 @ (setunion @ X4)) != $true) | ? [X5] : (((in @ X5 @ X4) = $true) & ($true = (in @ X3 @ X5)))) | (setunionE2 != $true))),
% 0.15/0.34 inference(rectify,[],[f31])).
% 0.15/0.34 thf(f31,plain,(
% 0.15/0.34 ((setunionE2 = $true) | ? [X0,X1] : (($true = (in @ X0 @ (setunion @ X1))) & ! [X2] : (($true != (in @ X2 @ X1)) | ((in @ X0 @ X2) != $true)))) & (! [X0,X1] : (($true != (in @ X0 @ (setunion @ X1))) | ? [X2] : (($true = (in @ X2 @ X1)) & ((in @ X0 @ X2) = $true))) | (setunionE2 != $true))),
% 0.15/0.34 inference(nnf_transformation,[],[f15])).
% 0.15/0.34 thf(f15,plain,(
% 0.15/0.34 (setunionE2 = $true) <=> ! [X0,X1] : (($true != (in @ X0 @ (setunion @ X1))) | ? [X2] : (($true = (in @ X2 @ X1)) & ((in @ X0 @ X2) = $true)))),
% 0.15/0.34 inference(ennf_transformation,[],[f8])).
% 0.15/0.34 thf(f8,plain,(
% 0.15/0.34 (setunionE2 = $true) <=> ! [X1,X0] : (($true = (in @ X0 @ (setunion @ X1))) => ? [X2] : (($true = (in @ X2 @ X1)) & ((in @ X0 @ X2) = $true)))),
% 0.15/0.34 inference(fool_elimination,[],[f7])).
% 0.15/0.34 thf(f7,plain,(
% 0.15/0.34 (! [X0,X1] : ((in @ X0 @ (setunion @ X1)) => ? [X2] : ((in @ X2 @ X1) & (in @ X0 @ X2))) = setunionE2)),
% 0.15/0.34 inference(rectify,[],[f3])).
% 0.15/0.34 thf(f3,axiom,(
% 0.15/0.34 (! [X0,X2] : ((in @ X0 @ (setunion @ X2)) => ? [X4] : ((in @ X4 @ X2) & (in @ X0 @ X4))) = setunionE2)),
% 0.15/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2)).
% 0.15/0.34 thf(f66,plain,(
% 0.15/0.34 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | (X0 = X1)) )),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f55])).
% 0.15/0.34 thf(f55,plain,(
% 0.15/0.34 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | ($true != $true)) )),
% 0.15/0.34 inference(definition_unfolding,[],[f46,f40])).
% 0.15/0.34 thf(f40,plain,(
% 0.15/0.34 (uniqinunit = $true)),
% 0.15/0.34 inference(cnf_transformation,[],[f26])).
% 0.15/0.34 thf(f46,plain,(
% 0.15/0.34 ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | ($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))) | (uniqinunit != $true)) )),
% 0.15/0.34 inference(cnf_transformation,[],[f30])).
% 0.15/0.34 thf(f30,plain,(
% 0.15/0.34 (! [X0,X1] : ((X0 = X1) | ($true != (in @ X1 @ (setadjoin @ X0 @ emptyset)))) | (uniqinunit != $true)) & ((uniqinunit = $true) | ((sK4 != sK5) & ($true = (in @ sK5 @ (setadjoin @ sK4 @ emptyset)))))),
% 0.15/0.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f28,f29])).
% 0.15/0.34 thf(f29,plain,(
% 0.15/0.34 ? [X2,X3] : ((X2 != X3) & ($true = (in @ X3 @ (setadjoin @ X2 @ emptyset)))) => ((sK4 != sK5) & ($true = (in @ sK5 @ (setadjoin @ sK4 @ emptyset))))),
% 0.15/0.34 introduced(choice_axiom,[])).
% 0.15/0.34 thf(f28,plain,(
% 0.15/0.34 (! [X0,X1] : ((X0 = X1) | ($true != (in @ X1 @ (setadjoin @ X0 @ emptyset)))) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X2,X3] : ((X2 != X3) & ($true = (in @ X3 @ (setadjoin @ X2 @ emptyset)))))),
% 0.15/0.34 inference(rectify,[],[f27])).
% 0.15/0.34 thf(f27,plain,(
% 0.15/0.34 (! [X1,X0] : ((X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X1,X0] : ((X0 != X1) & ((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true)))),
% 0.15/0.34 inference(nnf_transformation,[],[f18])).
% 0.15/0.34 thf(f18,plain,(
% 0.15/0.34 ! [X1,X0] : ((X0 = X1) | ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true)) <=> (uniqinunit = $true)),
% 0.15/0.34 inference(ennf_transformation,[],[f14])).
% 0.15/0.34 thf(f14,plain,(
% 0.15/0.34 ! [X0,X1] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) => (X0 = X1)) <=> (uniqinunit = $true)),
% 0.15/0.34 inference(fool_elimination,[],[f13])).
% 0.15/0.34 thf(f13,plain,(
% 0.15/0.34 (uniqinunit = ! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.15/0.34 inference(rectify,[],[f1])).
% 0.15/0.34 thf(f1,axiom,(
% 0.15/0.34 (uniqinunit = ! [X0,X1] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 0.15/0.34 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit)).
% 0.15/0.34 thf(f71,plain,(
% 0.15/0.34 ($true = (in @ (sK2 @ sK3 @ (setunion @ (setadjoin @ sK3 @ emptyset))) @ (sK8 @ (setadjoin @ sK3 @ emptyset) @ (sK2 @ sK3 @ (setunion @ (setadjoin @ sK3 @ emptyset))))))),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f69])).
% 0.15/0.34 thf(f69,plain,(
% 0.15/0.34 ($true = (in @ (sK2 @ sK3 @ (setunion @ (setadjoin @ sK3 @ emptyset))) @ (sK8 @ (setadjoin @ sK3 @ emptyset) @ (sK2 @ sK3 @ (setunion @ (setadjoin @ sK3 @ emptyset)))))) | ($true != $true)),
% 0.15/0.34 inference(superposition,[],[f64,f68])).
% 0.15/0.34 thf(f64,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (((in @ X3 @ (setunion @ X4)) != $true) | ($true = (in @ X3 @ (sK8 @ X4 @ X3)))) )),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f61])).
% 0.15/0.34 thf(f61,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (($true != $true) | ((in @ X3 @ (setunion @ X4)) != $true) | ($true = (in @ X3 @ (sK8 @ X4 @ X3)))) )),
% 0.15/0.34 inference(definition_unfolding,[],[f47,f43])).
% 0.15/0.34 thf(f47,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (((in @ X3 @ (setunion @ X4)) != $true) | ($true = (in @ X3 @ (sK8 @ X4 @ X3))) | (setunionE2 != $true)) )),
% 0.15/0.34 inference(cnf_transformation,[],[f35])).
% 0.15/0.34 thf(f62,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (($true != (in @ (sK2 @ X4 @ X3) @ X4)) | ($true = (subset @ X3 @ X4))) )),
% 0.15/0.34 inference(trivial_inequality_removal,[],[f54])).
% 0.15/0.34 thf(f54,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (($true = (subset @ X3 @ X4)) | ($true != $true) | ($true != (in @ (sK2 @ X4 @ X3) @ X4))) )),
% 0.15/0.34 inference(definition_unfolding,[],[f36,f42])).
% 0.15/0.34 thf(f36,plain,(
% 0.15/0.34 ( ! [X3 : $i,X4 : $i] : (($true = (subset @ X3 @ X4)) | ($true != (in @ (sK2 @ X4 @ X3) @ X4)) | (subsetI2 != $true)) )),
% 0.15/0.34 inference(cnf_transformation,[],[f24])).
% 0.15/0.34 % SZS output end Proof for theBenchmark
% 0.15/0.34 % (28197)------------------------------
% 0.15/0.34 % (28197)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.34 % (28197)Termination reason: Refutation
% 0.15/0.34
% 0.15/0.34 % (28197)Memory used [KB]: 5500
% 0.15/0.34 % (28197)Time elapsed: 0.007 s
% 0.15/0.34 % (28197)Instructions burned: 6 (million)
% 0.15/0.34 % (28197)------------------------------
% 0.15/0.34 % (28197)------------------------------
% 0.15/0.34 % (28190)Success in time 0.004 s
% 0.15/0.34 % Vampire---4.8 exiting
%------------------------------------------------------------------------------