TSTP Solution File: SEU598^2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU598^2 : 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 : n006.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 03:49:52 EDT 2024
% Result : Theorem 0.21s 0.41s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU598^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.14 % 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
% 0.13/0.35 % Computer : n006.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 18:20:08 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 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/sandbox/benchmark/theBenchmark.p
% 0.13/0.37 % (9145)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 % (9141)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 % (9140)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 % (9139)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 % (9142)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.38 % (9143)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 % (9144)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 % (9146)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 % (9143)Instruction limit reached!
% 0.13/0.38 % (9143)------------------------------
% 0.13/0.38 % (9143)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (9143)Termination reason: Unknown
% 0.13/0.38 % (9143)Termination phase: shuffling
% 0.13/0.38
% 0.13/0.38 % (9143)Memory used [KB]: 895
% 0.13/0.38 % (9143)Time elapsed: 0.003 s
% 0.13/0.38 % (9143)Instructions burned: 2 (million)
% 0.13/0.38 % (9143)------------------------------
% 0.13/0.38 % (9143)------------------------------
% 0.13/0.38 % (9142)Instruction limit reached!
% 0.13/0.38 % (9142)------------------------------
% 0.13/0.38 % (9142)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (9142)Termination reason: Unknown
% 0.13/0.38 % (9142)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (9142)Memory used [KB]: 1023
% 0.13/0.38 % (9142)Time elapsed: 0.004 s
% 0.13/0.38 % (9142)Instructions burned: 3 (million)
% 0.13/0.38 % (9142)------------------------------
% 0.13/0.38 % (9142)------------------------------
% 0.13/0.38 % (9146)Instruction limit reached!
% 0.13/0.38 % (9146)------------------------------
% 0.13/0.38 % (9146)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (9146)Termination reason: Unknown
% 0.13/0.38 % (9146)Termination phase: Property scanning
% 0.13/0.38
% 0.13/0.38 % (9146)Memory used [KB]: 895
% 0.13/0.38 % (9146)Time elapsed: 0.004 s
% 0.13/0.38 % (9146)Instructions burned: 3 (million)
% 0.13/0.38 % (9146)------------------------------
% 0.13/0.38 % (9146)------------------------------
% 0.13/0.38 % (9140)Instruction limit reached!
% 0.13/0.38 % (9140)------------------------------
% 0.13/0.38 % (9140)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (9140)Termination reason: Unknown
% 0.13/0.38 % (9140)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (9140)Memory used [KB]: 5500
% 0.13/0.38 % (9140)Time elapsed: 0.005 s
% 0.13/0.38 % (9140)Instructions burned: 4 (million)
% 0.13/0.38 % (9140)------------------------------
% 0.13/0.38 % (9140)------------------------------
% 0.21/0.39 % (9145)Instruction limit reached!
% 0.21/0.39 % (9145)------------------------------
% 0.21/0.39 % (9145)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (9145)Termination reason: Unknown
% 0.21/0.39 % (9145)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (9145)Memory used [KB]: 5628
% 0.21/0.39 % (9145)Time elapsed: 0.014 s
% 0.21/0.39 % (9145)Instructions burned: 18 (million)
% 0.21/0.39 % (9145)------------------------------
% 0.21/0.39 % (9145)------------------------------
% 0.21/0.39 % (9147)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)
% 0.21/0.39 % (9148)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.39 % (9149)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.39 % (9141)Instruction limit reached!
% 0.21/0.39 % (9141)------------------------------
% 0.21/0.39 % (9141)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (9150)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.21/0.39 % (9141)Termination reason: Unknown
% 0.21/0.39 % (9141)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (9141)Memory used [KB]: 5628
% 0.21/0.39 % (9141)Time elapsed: 0.020 s
% 0.21/0.39 % (9141)Instructions burned: 27 (million)
% 0.21/0.39 % (9141)------------------------------
% 0.21/0.39 % (9141)------------------------------
% 0.21/0.39 % (9149)Instruction limit reached!
% 0.21/0.39 % (9149)------------------------------
% 0.21/0.39 % (9149)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (9149)Termination reason: Unknown
% 0.21/0.39 % (9149)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (9149)Memory used [KB]: 5500
% 0.21/0.39 % (9149)Time elapsed: 0.004 s
% 0.21/0.39 % (9149)Instructions burned: 4 (million)
% 0.21/0.39 % (9149)------------------------------
% 0.21/0.39 % (9149)------------------------------
% 0.21/0.40 % (9151)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.40 % (9144)First to succeed.
% 0.21/0.40 % (9148)Instruction limit reached!
% 0.21/0.40 % (9148)------------------------------
% 0.21/0.40 % (9148)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (9148)Termination reason: Unknown
% 0.21/0.40 % (9148)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (9148)Memory used [KB]: 5628
% 0.21/0.40 % (9148)Time elapsed: 0.013 s
% 0.21/0.40 % (9148)Instructions burned: 16 (million)
% 0.21/0.40 % (9148)------------------------------
% 0.21/0.40 % (9148)------------------------------
% 0.21/0.40 % (9151)Instruction limit reached!
% 0.21/0.40 % (9151)------------------------------
% 0.21/0.40 % (9151)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (9151)Termination reason: Unknown
% 0.21/0.40 % (9151)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (9151)Memory used [KB]: 1023
% 0.21/0.40 % (9151)Time elapsed: 0.006 s
% 0.21/0.40 % (9151)Instructions burned: 7 (million)
% 0.21/0.40 % (9151)------------------------------
% 0.21/0.40 % (9151)------------------------------
% 0.21/0.41 % (9144)Refutation found. Thanks to Tanya!
% 0.21/0.41 % SZS status Theorem for theBenchmark
% 0.21/0.41 % SZS output start Proof for theBenchmark
% 0.21/0.41 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.41 thf(func_def_1, type, subset: $i > $i > $o).
% 0.21/0.41 thf(func_def_6, type, binintersect: $i > $i > $i).
% 0.21/0.41 thf(func_def_15, type, sK4: $i > $i > $i).
% 0.21/0.41 thf(f257,plain,(
% 0.21/0.41 $false),
% 0.21/0.41 inference(subsumption_resolution,[],[f256,f69])).
% 0.21/0.41 thf(f69,plain,(
% 0.21/0.41 ($true = (subset @ sK10 @ sK11))),
% 0.21/0.41 inference(cnf_transformation,[],[f48])).
% 0.21/0.41 thf(f48,plain,(
% 0.21/0.41 (subsetE = $true) & (binintersectRsub = $true) & (setextsub = $true) & ((sK10 != (binintersect @ sK11 @ sK10)) & ($true = (subset @ sK10 @ sK11))) & (subsetI1 = $true) & (binintersectI = $true)),
% 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11])],[f29,f47])).
% 0.21/0.41 thf(f47,plain,(
% 0.21/0.41 ? [X0,X1] : (((binintersect @ X1 @ X0) != X0) & ((subset @ X0 @ X1) = $true)) => ((sK10 != (binintersect @ sK11 @ sK10)) & ($true = (subset @ sK10 @ sK11)))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f29,plain,(
% 0.21/0.41 (subsetE = $true) & (binintersectRsub = $true) & (setextsub = $true) & ? [X0,X1] : (((binintersect @ X1 @ X0) != X0) & ((subset @ X0 @ X1) = $true)) & (subsetI1 = $true) & (binintersectI = $true)),
% 0.21/0.41 inference(flattening,[],[f28])).
% 0.21/0.41 thf(f28,plain,(
% 0.21/0.41 ((((? [X0,X1] : (((binintersect @ X1 @ X0) != X0) & ((subset @ X0 @ X1) = $true)) & (binintersectRsub = $true)) & (binintersectI = $true)) & (setextsub = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 0.21/0.41 inference(ennf_transformation,[],[f18])).
% 0.21/0.41 thf(f18,plain,(
% 0.21/0.41 ~((subsetI1 = $true) => ((subsetE = $true) => ((setextsub = $true) => ((binintersectI = $true) => ((binintersectRsub = $true) => ! [X0,X1] : (((subset @ X0 @ X1) = $true) => ((binintersect @ X1 @ X0) = X0)))))))),
% 0.21/0.41 inference(fool_elimination,[],[f17])).
% 0.21/0.41 thf(f17,plain,(
% 0.21/0.41 ~(subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectRsub => ! [X0,X1] : ((subset @ X0 @ X1) => ((binintersect @ X1 @ X0) = X0)))))))),
% 0.21/0.41 inference(rectify,[],[f7])).
% 0.21/0.41 thf(f7,negated_conjecture,(
% 0.21/0.41 ~(subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectRsub => ! [X1,X0] : ((subset @ X1 @ X0) => ((binintersect @ X0 @ X1) = X1)))))))),
% 0.21/0.41 inference(negated_conjecture,[],[f6])).
% 0.21/0.41 thf(f6,conjecture,(
% 0.21/0.41 subsetI1 => (subsetE => (setextsub => (binintersectI => (binintersectRsub => ! [X1,X0] : ((subset @ X1 @ X0) => ((binintersect @ X0 @ X1) = X1))))))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4)).
% 0.21/0.41 thf(f256,plain,(
% 0.21/0.41 ($true != (subset @ sK10 @ sK11))),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f241])).
% 0.21/0.41 thf(f241,plain,(
% 0.21/0.41 (sK10 != sK10) | ($true != (subset @ sK10 @ sK11))),
% 0.21/0.41 inference(superposition,[],[f70,f232])).
% 0.21/0.41 thf(f232,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) = X0) | ((subset @ X0 @ X1) != $true)) )),
% 0.21/0.41 inference(subsumption_resolution,[],[f230,f99])).
% 0.21/0.41 thf(f99,plain,(
% 0.21/0.41 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ (binintersect @ X3 @ X2) @ X2))) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f79])).
% 0.21/0.41 thf(f79,plain,(
% 0.21/0.41 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ (binintersect @ X3 @ X2) @ X2)) | ($true != $true)) )),
% 0.21/0.41 inference(definition_unfolding,[],[f53,f72])).
% 0.21/0.41 thf(f72,plain,(
% 0.21/0.41 (binintersectRsub = $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f48])).
% 0.21/0.41 thf(f53,plain,(
% 0.21/0.41 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ (binintersect @ X3 @ X2) @ X2)) | (binintersectRsub != $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f33])).
% 0.21/0.41 thf(f33,plain,(
% 0.21/0.41 ((binintersectRsub = $true) | ($true != (subset @ (binintersect @ sK1 @ sK0) @ sK0))) & (! [X2,X3] : ($true = (subset @ (binintersect @ X3 @ X2) @ X2)) | (binintersectRsub != $true))),
% 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f31,f32])).
% 0.21/0.41 thf(f32,plain,(
% 0.21/0.41 ? [X0,X1] : ((subset @ (binintersect @ X1 @ X0) @ X0) != $true) => ($true != (subset @ (binintersect @ sK1 @ sK0) @ sK0))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f31,plain,(
% 0.21/0.41 ((binintersectRsub = $true) | ? [X0,X1] : ((subset @ (binintersect @ X1 @ X0) @ X0) != $true)) & (! [X2,X3] : ($true = (subset @ (binintersect @ X3 @ X2) @ X2)) | (binintersectRsub != $true))),
% 0.21/0.41 inference(rectify,[],[f30])).
% 0.21/0.41 thf(f30,plain,(
% 0.21/0.41 ((binintersectRsub = $true) | ? [X1,X0] : ((subset @ (binintersect @ X0 @ X1) @ X1) != $true)) & (! [X1,X0] : ((subset @ (binintersect @ X0 @ X1) @ X1) = $true) | (binintersectRsub != $true))),
% 0.21/0.41 inference(nnf_transformation,[],[f16])).
% 0.21/0.41 thf(f16,plain,(
% 0.21/0.41 (binintersectRsub = $true) <=> ! [X1,X0] : ((subset @ (binintersect @ X0 @ X1) @ X1) = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f15])).
% 0.21/0.41 thf(f15,plain,(
% 0.21/0.41 (binintersectRsub = ! [X0,X1] : (subset @ (binintersect @ X0 @ X1) @ X1))),
% 0.21/0.41 inference(rectify,[],[f5])).
% 0.21/0.41 thf(f5,axiom,(
% 0.21/0.41 (binintersectRsub = ! [X0,X1] : (subset @ (binintersect @ X0 @ X1) @ X1))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub)).
% 0.21/0.41 thf(f230,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X1 @ X0) @ X0) != $true) | ((binintersect @ X1 @ X0) = X0) | ((subset @ X0 @ X1) != $true)) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f223])).
% 0.21/0.41 thf(f223,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((subset @ (binintersect @ X1 @ X0) @ X0) != $true) | ((binintersect @ X1 @ X0) = X0) | ((subset @ X0 @ X1) != $true)) )),
% 0.21/0.41 inference(superposition,[],[f100,f220])).
% 0.21/0.41 thf(f220,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binintersect @ X0 @ X1))) | ((subset @ X1 @ X0) != $true)) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f219])).
% 0.21/0.41 thf(f219,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ($true != $true) | ($true = (subset @ X1 @ (binintersect @ X0 @ X1)))) )),
% 0.21/0.41 inference(duplicate_literal_removal,[],[f214])).
% 0.21/0.41 thf(f214,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) != $true) | ($true = (subset @ X1 @ (binintersect @ X0 @ X1))) | ($true = (subset @ X1 @ (binintersect @ X0 @ X1))) | ($true != $true)) )),
% 0.21/0.41 inference(superposition,[],[f154,f98])).
% 0.21/0.41 thf(f98,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK4 @ X1 @ X0) @ X0)) | ((subset @ X0 @ X1) = $true)) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f84])).
% 0.21/0.41 thf(f84,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true = (in @ (sK4 @ X1 @ X0) @ X0)) | ($true != $true)) )),
% 0.21/0.41 inference(definition_unfolding,[],[f62,f68])).
% 0.21/0.41 thf(f68,plain,(
% 0.21/0.41 (subsetI1 = $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f48])).
% 0.21/0.41 thf(f62,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true = (in @ (sK4 @ X1 @ X0) @ X0)) | (subsetI1 != $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f42])).
% 0.21/0.41 thf(f42,plain,(
% 0.21/0.41 (! [X0,X1] : (((subset @ X0 @ X1) = $true) | (($true = (in @ (sK4 @ X1 @ X0) @ X0)) & ($true != (in @ (sK4 @ X1 @ X0) @ X1)))) | (subsetI1 != $true)) & ((subsetI1 = $true) | (($true != (subset @ sK5 @ sK6)) & ! [X5] : (($true != (in @ X5 @ sK5)) | ((in @ X5 @ sK6) = $true))))),
% 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f39,f41,f40])).
% 0.21/0.41 thf(f40,plain,(
% 0.21/0.41 ! [X0,X1] : (? [X2] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true)) => (($true = (in @ (sK4 @ X1 @ X0) @ X0)) & ($true != (in @ (sK4 @ X1 @ X0) @ X1))))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f41,plain,(
% 0.21/0.41 ? [X3,X4] : (($true != (subset @ X3 @ X4)) & ! [X5] : (($true != (in @ X5 @ X3)) | ($true = (in @ X5 @ X4)))) => (($true != (subset @ sK5 @ sK6)) & ! [X5] : (($true != (in @ X5 @ sK5)) | ((in @ X5 @ sK6) = $true)))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f39,plain,(
% 0.21/0.41 (! [X0,X1] : (((subset @ X0 @ X1) = $true) | ? [X2] : (((in @ X2 @ X0) = $true) & ((in @ X2 @ X1) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X3,X4] : (($true != (subset @ X3 @ X4)) & ! [X5] : (($true != (in @ X5 @ X3)) | ($true = (in @ X5 @ X4)))))),
% 0.21/0.41 inference(rectify,[],[f38])).
% 0.21/0.41 thf(f38,plain,(
% 0.21/0.41 (! [X1,X0] : (((subset @ X1 @ X0) = $true) | ? [X2] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) | (subsetI1 != $true)) & ((subsetI1 = $true) | ? [X1,X0] : (((subset @ X1 @ X0) != $true) & ! [X2] : (((in @ X2 @ X1) != $true) | ((in @ X2 @ X0) = $true))))),
% 0.21/0.41 inference(nnf_transformation,[],[f21])).
% 0.21/0.41 thf(f21,plain,(
% 0.21/0.41 ! [X1,X0] : (((subset @ X1 @ X0) = $true) | ? [X2] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) != $true))) <=> (subsetI1 = $true)),
% 0.21/0.41 inference(ennf_transformation,[],[f20])).
% 0.21/0.41 thf(f20,plain,(
% 0.21/0.41 ! [X1,X0] : (! [X2] : (((in @ X2 @ X1) = $true) => ((in @ X2 @ X0) = $true)) => ((subset @ X1 @ X0) = $true)) <=> (subsetI1 = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f19])).
% 0.21/0.41 thf(f19,plain,(
% 0.21/0.41 (! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
% 0.21/0.41 inference(rectify,[],[f1])).
% 0.21/0.41 thf(f1,axiom,(
% 0.21/0.41 (! [X1,X0] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1)).
% 0.21/0.41 thf(f154,plain,(
% 0.21/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK4 @ (binintersect @ X0 @ X1) @ X1) @ X2)) | ($true != (subset @ X2 @ X0)) | ($true = (subset @ X1 @ (binintersect @ X0 @ X1)))) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f150])).
% 0.21/0.41 thf(f150,plain,(
% 0.21/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (in @ (sK4 @ (binintersect @ X0 @ X1) @ X1) @ X2)) | ($true != (subset @ X2 @ X0)) | ($true = (subset @ X1 @ (binintersect @ X0 @ X1)))) )),
% 0.21/0.41 inference(superposition,[],[f142,f96])).
% 0.21/0.41 thf(f96,plain,(
% 0.21/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (in @ X0 @ X2)) | ($true != (subset @ X1 @ X2)) | ($true != (in @ X0 @ X1))) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f88])).
% 0.21/0.41 thf(f88,plain,(
% 0.21/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != (subset @ X1 @ X2)) | ($true = (in @ X0 @ X2)) | ($true != (in @ X0 @ X1))) )),
% 0.21/0.41 inference(definition_unfolding,[],[f66,f73])).
% 0.21/0.41 thf(f73,plain,(
% 0.21/0.41 (subsetE = $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f48])).
% 0.21/0.41 thf(f66,plain,(
% 0.21/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ X2)) | ($true != (subset @ X1 @ X2)) | (subsetE != $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f46])).
% 0.21/0.41 thf(f46,plain,(
% 0.21/0.41 (! [X0,X1,X2] : (($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ X2)) | ($true != (subset @ X1 @ X2))) | (subsetE != $true)) & ((subsetE = $true) | (($true = (in @ sK7 @ sK8)) & ($true != (in @ sK7 @ sK9)) & ((subset @ sK8 @ sK9) = $true)))),
% 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f44,f45])).
% 0.21/0.41 thf(f45,plain,(
% 0.21/0.41 ? [X3,X4,X5] : (($true = (in @ X3 @ X4)) & ($true != (in @ X3 @ X5)) & ($true = (subset @ X4 @ X5))) => (($true = (in @ sK7 @ sK8)) & ($true != (in @ sK7 @ sK9)) & ((subset @ sK8 @ sK9) = $true))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f44,plain,(
% 0.21/0.41 (! [X0,X1,X2] : (($true != (in @ X0 @ X1)) | ($true = (in @ X0 @ X2)) | ($true != (subset @ X1 @ X2))) | (subsetE != $true)) & ((subsetE = $true) | ? [X3,X4,X5] : (($true = (in @ X3 @ X4)) & ($true != (in @ X3 @ X5)) & ($true = (subset @ X4 @ X5))))),
% 0.21/0.41 inference(rectify,[],[f43])).
% 0.21/0.41 thf(f43,plain,(
% 0.21/0.41 (! [X0,X2,X1] : (($true != (in @ X0 @ X2)) | ($true = (in @ X0 @ X1)) | ($true != (subset @ X2 @ X1))) | (subsetE != $true)) & ((subsetE = $true) | ? [X0,X2,X1] : (($true = (in @ X0 @ X2)) & ($true != (in @ X0 @ X1)) & ($true = (subset @ X2 @ X1))))),
% 0.21/0.41 inference(nnf_transformation,[],[f23])).
% 0.21/0.41 thf(f23,plain,(
% 0.21/0.41 ! [X0,X2,X1] : (($true != (in @ X0 @ X2)) | ($true = (in @ X0 @ X1)) | ($true != (subset @ X2 @ X1))) <=> (subsetE = $true)),
% 0.21/0.41 inference(flattening,[],[f22])).
% 0.21/0.41 thf(f22,plain,(
% 0.21/0.41 ! [X2,X1,X0] : ((($true = (in @ X0 @ X1)) | ($true != (in @ X0 @ X2))) | ($true != (subset @ X2 @ X1))) <=> (subsetE = $true)),
% 0.21/0.41 inference(ennf_transformation,[],[f14])).
% 0.21/0.41 thf(f14,plain,(
% 0.21/0.41 ! [X2,X1,X0] : (($true = (subset @ X2 @ X1)) => (($true = (in @ X0 @ X2)) => ($true = (in @ X0 @ X1)))) <=> (subsetE = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f13])).
% 0.21/0.41 thf(f13,plain,(
% 0.21/0.41 (subsetE = ! [X0,X1,X2] : ((subset @ X2 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ X1))))),
% 0.21/0.41 inference(rectify,[],[f2])).
% 0.21/0.41 thf(f2,axiom,(
% 0.21/0.41 (subsetE = ! [X2,X1,X0] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
% 0.21/0.41 thf(f142,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK4 @ (binintersect @ X0 @ X1) @ X1) @ X0)) | ($true = (subset @ X1 @ (binintersect @ X0 @ X1)))) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f141])).
% 0.21/0.41 thf(f141,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK4 @ (binintersect @ X0 @ X1) @ X1) @ X0)) | ($true = (subset @ X1 @ (binintersect @ X0 @ X1))) | ($true != $true)) )),
% 0.21/0.41 inference(duplicate_literal_removal,[],[f136])).
% 0.21/0.41 thf(f136,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ (binintersect @ X0 @ X1))) | ($true != $true) | ($true = (subset @ X1 @ (binintersect @ X0 @ X1))) | ($true != (in @ (sK4 @ (binintersect @ X0 @ X1) @ X1) @ X0))) )),
% 0.21/0.41 inference(superposition,[],[f122,f98])).
% 0.21/0.41 thf(f122,plain,(
% 0.21/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK4 @ (binintersect @ X0 @ X1) @ X2) @ X1)) | ($true != (in @ (sK4 @ (binintersect @ X0 @ X1) @ X2) @ X0)) | ($true = (subset @ X2 @ (binintersect @ X0 @ X1)))) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f121])).
% 0.21/0.41 thf(f121,plain,(
% 0.21/0.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK4 @ (binintersect @ X0 @ X1) @ X2) @ X0)) | ($true = (subset @ X2 @ (binintersect @ X0 @ X1))) | ($true != (in @ (sK4 @ (binintersect @ X0 @ X1) @ X2) @ X1)) | ($true != $true)) )),
% 0.21/0.41 inference(superposition,[],[f101,f97])).
% 0.21/0.41 thf(f97,plain,(
% 0.21/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ (binintersect @ X3 @ X4))) | ($true != (in @ X5 @ X3)) | ($true != (in @ X5 @ X4))) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f95])).
% 0.21/0.41 thf(f95,plain,(
% 0.21/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true = (in @ X5 @ (binintersect @ X3 @ X4))) | ($true != (in @ X5 @ X3)) | ($true != (in @ X5 @ X4)) | ($true != $true)) )),
% 0.21/0.41 inference(definition_unfolding,[],[f74,f67])).
% 0.21/0.41 thf(f67,plain,(
% 0.21/0.41 (binintersectI = $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f48])).
% 0.21/0.41 thf(f74,plain,(
% 0.21/0.41 ( ! [X3 : $i,X4 : $i,X5 : $i] : (($true != (in @ X5 @ X4)) | ($true != (in @ X5 @ X3)) | ($true = (in @ X5 @ (binintersect @ X3 @ X4))) | (binintersectI != $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f52])).
% 0.21/0.41 thf(f52,plain,(
% 0.21/0.41 ((binintersectI = $true) | (($true = (in @ sK14 @ sK13)) & ($true = (in @ sK14 @ sK12)) & ($true != (in @ sK14 @ (binintersect @ sK12 @ sK13))))) & (! [X3,X4,X5] : (($true != (in @ X5 @ X4)) | ($true != (in @ X5 @ X3)) | ($true = (in @ X5 @ (binintersect @ X3 @ X4)))) | (binintersectI != $true))),
% 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f50,f51])).
% 0.21/0.41 thf(f51,plain,(
% 0.21/0.41 ? [X0,X1,X2] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) = $true) & ((in @ X2 @ (binintersect @ X0 @ X1)) != $true)) => (($true = (in @ sK14 @ sK13)) & ($true = (in @ sK14 @ sK12)) & ($true != (in @ sK14 @ (binintersect @ sK12 @ sK13))))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f50,plain,(
% 0.21/0.41 ((binintersectI = $true) | ? [X0,X1,X2] : (((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) = $true) & ((in @ X2 @ (binintersect @ X0 @ X1)) != $true))) & (! [X3,X4,X5] : (($true != (in @ X5 @ X4)) | ($true != (in @ X5 @ X3)) | ($true = (in @ X5 @ (binintersect @ X3 @ X4)))) | (binintersectI != $true))),
% 0.21/0.41 inference(rectify,[],[f49])).
% 0.21/0.41 thf(f49,plain,(
% 0.21/0.41 ((binintersectI = $true) | ? [X1,X2,X0] : (($true = (in @ X0 @ X2)) & ($true = (in @ X0 @ X1)) & ((in @ X0 @ (binintersect @ X1 @ X2)) != $true))) & (! [X1,X2,X0] : (($true != (in @ X0 @ X2)) | ($true != (in @ X0 @ X1)) | ((in @ X0 @ (binintersect @ X1 @ X2)) = $true)) | (binintersectI != $true))),
% 0.21/0.41 inference(nnf_transformation,[],[f25])).
% 0.21/0.41 thf(f25,plain,(
% 0.21/0.41 (binintersectI = $true) <=> ! [X1,X2,X0] : (($true != (in @ X0 @ X2)) | ($true != (in @ X0 @ X1)) | ((in @ X0 @ (binintersect @ X1 @ X2)) = $true))),
% 0.21/0.41 inference(flattening,[],[f24])).
% 0.21/0.41 thf(f24,plain,(
% 0.21/0.41 (binintersectI = $true) <=> ! [X0,X2,X1] : ((((in @ X0 @ (binintersect @ X1 @ X2)) = $true) | ($true != (in @ X0 @ X2))) | ($true != (in @ X0 @ X1)))),
% 0.21/0.41 inference(ennf_transformation,[],[f12])).
% 0.21/0.41 thf(f12,plain,(
% 0.21/0.41 (binintersectI = $true) <=> ! [X0,X2,X1] : (($true = (in @ X0 @ X1)) => (($true = (in @ X0 @ X2)) => ((in @ X0 @ (binintersect @ X1 @ X2)) = $true)))),
% 0.21/0.41 inference(fool_elimination,[],[f11])).
% 0.21/0.41 thf(f11,plain,(
% 0.21/0.41 (binintersectI = ! [X0,X1,X2] : ((in @ X0 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ (binintersect @ X1 @ X2)))))),
% 0.21/0.41 inference(rectify,[],[f4])).
% 0.21/0.41 thf(f4,axiom,(
% 0.21/0.41 (binintersectI = ! [X2,X0,X1] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI)).
% 0.21/0.41 thf(f101,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK4 @ X1 @ X0) @ X1)) | ((subset @ X0 @ X1) = $true)) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f85])).
% 0.21/0.41 thf(f85,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK4 @ X1 @ X0) @ X1)) | ((subset @ X0 @ X1) = $true) | ($true != $true)) )),
% 0.21/0.41 inference(definition_unfolding,[],[f61,f68])).
% 0.21/0.41 thf(f61,plain,(
% 0.21/0.41 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | ($true != (in @ (sK4 @ X1 @ X0) @ X1)) | (subsetI1 != $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f42])).
% 0.21/0.41 thf(f100,plain,(
% 0.21/0.41 ( ! [X2 : $i,X3 : $i] : (($true != (subset @ X3 @ X2)) | ((subset @ X2 @ X3) != $true) | (X2 = X3)) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f83])).
% 0.21/0.41 thf(f83,plain,(
% 0.21/0.41 ( ! [X2 : $i,X3 : $i] : (($true != (subset @ X3 @ X2)) | ($true != $true) | (X2 = X3) | ((subset @ X2 @ X3) != $true)) )),
% 0.21/0.41 inference(definition_unfolding,[],[f55,f71])).
% 0.21/0.41 thf(f71,plain,(
% 0.21/0.41 (setextsub = $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f48])).
% 0.21/0.41 thf(f55,plain,(
% 0.21/0.41 ( ! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | ($true != (subset @ X3 @ X2)) | (X2 = X3) | (setextsub != $true)) )),
% 0.21/0.41 inference(cnf_transformation,[],[f37])).
% 0.21/0.41 thf(f37,plain,(
% 0.21/0.41 ((setextsub = $true) | (($true = (subset @ sK2 @ sK3)) & ($true = (subset @ sK3 @ sK2)) & (sK3 != sK2))) & (! [X2,X3] : (((subset @ X2 @ X3) != $true) | ($true != (subset @ X3 @ X2)) | (X2 = X3)) | (setextsub != $true))),
% 0.21/0.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f35,f36])).
% 0.21/0.41 thf(f36,plain,(
% 0.21/0.41 ? [X0,X1] : (((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X0) = $true) & (X0 != X1)) => (($true = (subset @ sK2 @ sK3)) & ($true = (subset @ sK3 @ sK2)) & (sK3 != sK2))),
% 0.21/0.41 introduced(choice_axiom,[])).
% 0.21/0.41 thf(f35,plain,(
% 0.21/0.41 ((setextsub = $true) | ? [X0,X1] : (((subset @ X0 @ X1) = $true) & ((subset @ X1 @ X0) = $true) & (X0 != X1))) & (! [X2,X3] : (((subset @ X2 @ X3) != $true) | ($true != (subset @ X3 @ X2)) | (X2 = X3)) | (setextsub != $true))),
% 0.21/0.41 inference(rectify,[],[f34])).
% 0.21/0.41 thf(f34,plain,(
% 0.21/0.41 ((setextsub = $true) | ? [X1,X0] : (((subset @ X1 @ X0) = $true) & ((subset @ X0 @ X1) = $true) & (X0 != X1))) & (! [X1,X0] : (((subset @ X1 @ X0) != $true) | ((subset @ X0 @ X1) != $true) | (X0 = X1)) | (setextsub != $true))),
% 0.21/0.41 inference(nnf_transformation,[],[f27])).
% 0.21/0.41 thf(f27,plain,(
% 0.21/0.41 (setextsub = $true) <=> ! [X1,X0] : (((subset @ X1 @ X0) != $true) | ((subset @ X0 @ X1) != $true) | (X0 = X1))),
% 0.21/0.41 inference(flattening,[],[f26])).
% 0.21/0.41 thf(f26,plain,(
% 0.21/0.41 ! [X0,X1] : (((X0 = X1) | ((subset @ X0 @ X1) != $true)) | ((subset @ X1 @ X0) != $true)) <=> (setextsub = $true)),
% 0.21/0.41 inference(ennf_transformation,[],[f10])).
% 0.21/0.41 thf(f10,plain,(
% 0.21/0.41 ! [X0,X1] : (((subset @ X1 @ X0) = $true) => (((subset @ X0 @ X1) = $true) => (X0 = X1))) <=> (setextsub = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f9])).
% 0.21/0.41 thf(f9,plain,(
% 0.21/0.41 (setextsub = ! [X0,X1] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))))),
% 0.21/0.41 inference(rectify,[],[f3])).
% 0.21/0.41 thf(f3,axiom,(
% 0.21/0.41 (setextsub = ! [X1,X0] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub)).
% 0.21/0.41 thf(f70,plain,(
% 0.21/0.41 (sK10 != (binintersect @ sK11 @ sK10))),
% 0.21/0.41 inference(cnf_transformation,[],[f48])).
% 0.21/0.41 % SZS output end Proof for theBenchmark
% 0.21/0.41 % (9144)------------------------------
% 0.21/0.41 % (9144)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (9144)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (9144)Memory used [KB]: 5628
% 0.21/0.41 % (9144)Time elapsed: 0.032 s
% 0.21/0.41 % (9144)Instructions burned: 43 (million)
% 0.21/0.41 % (9144)------------------------------
% 0.21/0.41 % (9144)------------------------------
% 0.21/0.41 % (9138)Success in time 0.031 s
% 0.21/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------