TSTP Solution File: SEU759^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU759^2 : 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 : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:51:19 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU759^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.14 % 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
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 17:58:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 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
% 0.14/0.37 % (32267)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)
% 0.14/0.37 % (32268)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (32269)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)
% 0.14/0.37 % (32266)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)
% 0.14/0.37 % (32265)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (32270)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)
% 0.14/0.37 % (32272)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 % (32268)Instruction limit reached!
% 0.14/0.37 % (32268)------------------------------
% 0.14/0.37 % (32268)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (32268)Termination reason: Unknown
% 0.14/0.37 % (32268)Termination phase: Property scanning
% 0.14/0.37 % (32269)Instruction limit reached!
% 0.14/0.37 % (32269)------------------------------
% 0.14/0.37 % (32269)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37
% 0.14/0.37 % (32268)Memory used [KB]: 895
% 0.14/0.37 % (32268)Time elapsed: 0.003 s
% 0.14/0.37 % (32268)Instructions burned: 2 (million)
% 0.14/0.37 % (32268)------------------------------
% 0.14/0.37 % (32268)------------------------------
% 0.14/0.37 % (32269)Termination reason: Unknown
% 0.14/0.37 % (32269)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (32269)Memory used [KB]: 895
% 0.14/0.37 % (32269)Time elapsed: 0.003 s
% 0.14/0.37 % (32269)Instructions burned: 2 (million)
% 0.14/0.37 % (32269)------------------------------
% 0.14/0.37 % (32269)------------------------------
% 0.14/0.37 % (32272)Instruction limit reached!
% 0.14/0.37 % (32272)------------------------------
% 0.14/0.37 % (32272)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (32272)Termination reason: Unknown
% 0.14/0.37 % (32272)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (32272)Memory used [KB]: 1023
% 0.14/0.37 % (32272)Time elapsed: 0.004 s
% 0.14/0.37 % (32272)Instructions burned: 3 (million)
% 0.14/0.37 % (32272)------------------------------
% 0.14/0.37 % (32272)------------------------------
% 0.14/0.37 % (32266)Instruction limit reached!
% 0.14/0.37 % (32266)------------------------------
% 0.14/0.37 % (32266)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (32266)Termination reason: Unknown
% 0.14/0.37 % (32266)Termination phase: Saturation
% 0.14/0.37
% 0.14/0.37 % (32266)Memory used [KB]: 5500
% 0.14/0.37 % (32266)Time elapsed: 0.004 s
% 0.14/0.37 % (32266)Instructions burned: 4 (million)
% 0.14/0.37 % (32266)------------------------------
% 0.14/0.37 % (32266)------------------------------
% 0.14/0.37 % (32271)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (32267)First to succeed.
% 0.14/0.38 % (32270)Also succeeded, but the first one will report.
% 0.14/0.38 % (32267)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% 0.14/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.14/0.38 thf(func_def_1, type, powerset: $i > $i).
% 0.14/0.38 thf(func_def_2, type, subset: $i > $i > $o).
% 0.14/0.38 thf(func_def_6, type, binintersect: $i > $i > $i).
% 0.14/0.38 thf(func_def_8, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.14/0.38 thf(func_def_22, type, sK5: $i > $i > $i).
% 0.14/0.38 thf(f118,plain,(
% 0.14/0.38 $false),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f115])).
% 0.14/0.38 thf(f115,plain,(
% 0.14/0.38 ($true != $true)),
% 0.14/0.38 inference(superposition,[],[f28,f105])).
% 0.14/0.38 thf(f105,plain,(
% 0.14/0.38 ( ! [X0 : $i] : (((subset @ (binintersect @ sK0 @ X0) @ sK3) = $true)) )),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f104])).
% 0.14/0.38 thf(f104,plain,(
% 0.14/0.38 ( ! [X0 : $i] : (((subset @ (binintersect @ sK0 @ X0) @ sK3) = $true) | ($false = $true)) )),
% 0.14/0.38 inference(duplicate_literal_removal,[],[f99])).
% 0.14/0.38 thf(f99,plain,(
% 0.14/0.38 ( ! [X0 : $i] : (((subset @ (binintersect @ sK0 @ X0) @ sK3) = $true) | ((subset @ (binintersect @ sK0 @ X0) @ sK3) = $true) | ($false = $true)) )),
% 0.14/0.38 inference(superposition,[],[f74,f66])).
% 0.14/0.38 thf(f66,plain,(
% 0.14/0.38 ( ! [X0 : $i] : (((in @ (sK5 @ X0 @ sK3) @ sK0) = $false) | ((subset @ X0 @ sK3) = $true)) )),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f64])).
% 0.14/0.38 thf(f64,plain,(
% 0.14/0.38 ( ! [X0 : $i] : (((subset @ X0 @ sK3) = $true) | ($false = $true) | ((in @ (sK5 @ X0 @ sK3) @ sK0) = $false)) )),
% 0.14/0.38 inference(superposition,[],[f50,f62])).
% 0.14/0.38 thf(f62,plain,(
% 0.14/0.38 ( ! [X0 : $i] : (((in @ X0 @ sK3) = $true) | ((in @ X0 @ sK0) = $false)) )),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f59])).
% 0.14/0.38 thf(f59,plain,(
% 0.14/0.38 ( ! [X0 : $i] : (($false = $true) | ((in @ X0 @ sK0) = $false) | ((in @ X0 @ sK3) = $true)) )),
% 0.14/0.38 inference(superposition,[],[f42,f27])).
% 0.14/0.38 thf(f27,plain,(
% 0.14/0.38 ((subset @ sK0 @ sK3) = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f20])).
% 0.14/0.38 thf(f20,plain,(
% 0.14/0.38 (binintersectEL = $true) & (((($true = (in @ sK3 @ (powerset @ sK1))) & ((subset @ (binintersect @ sK0 @ sK2) @ sK3) != $true) & ((subset @ sK0 @ sK3) = $true)) & ((in @ sK2 @ (powerset @ sK1)) = $true)) & ((in @ sK0 @ (powerset @ sK1)) = $true)) & (subsetE = $true) & (subsetI1 = $true)),
% 0.14/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f16,f19,f18,f17])).
% 0.14/0.38 thf(f17,plain,(
% 0.14/0.38 ? [X0,X1] : (? [X2] : (? [X3] : (($true = (in @ X3 @ (powerset @ X1))) & ($true != (subset @ (binintersect @ X0 @ X2) @ X3)) & ((subset @ X0 @ X3) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) => (? [X2] : (? [X3] : (($true = (in @ X3 @ (powerset @ sK1))) & ((subset @ (binintersect @ sK0 @ X2) @ X3) != $true) & ($true = (subset @ sK0 @ X3))) & ($true = (in @ X2 @ (powerset @ sK1)))) & ((in @ sK0 @ (powerset @ sK1)) = $true))),
% 0.14/0.38 introduced(choice_axiom,[])).
% 0.14/0.38 thf(f18,plain,(
% 0.14/0.38 ? [X2] : (? [X3] : (($true = (in @ X3 @ (powerset @ sK1))) & ((subset @ (binintersect @ sK0 @ X2) @ X3) != $true) & ($true = (subset @ sK0 @ X3))) & ($true = (in @ X2 @ (powerset @ sK1)))) => (? [X3] : (($true = (in @ X3 @ (powerset @ sK1))) & ((subset @ (binintersect @ sK0 @ sK2) @ X3) != $true) & ($true = (subset @ sK0 @ X3))) & ((in @ sK2 @ (powerset @ sK1)) = $true))),
% 0.14/0.38 introduced(choice_axiom,[])).
% 0.14/0.38 thf(f19,plain,(
% 0.14/0.38 ? [X3] : (($true = (in @ X3 @ (powerset @ sK1))) & ((subset @ (binintersect @ sK0 @ sK2) @ X3) != $true) & ($true = (subset @ sK0 @ X3))) => (($true = (in @ sK3 @ (powerset @ sK1))) & ((subset @ (binintersect @ sK0 @ sK2) @ sK3) != $true) & ((subset @ sK0 @ sK3) = $true))),
% 0.14/0.38 introduced(choice_axiom,[])).
% 0.14/0.38 thf(f16,plain,(
% 0.14/0.38 (binintersectEL = $true) & ? [X0,X1] : (? [X2] : (? [X3] : (($true = (in @ X3 @ (powerset @ X1))) & ($true != (subset @ (binintersect @ X0 @ X2) @ X3)) & ((subset @ X0 @ X3) = $true)) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (subsetE = $true) & (subsetI1 = $true)),
% 0.14/0.38 inference(flattening,[],[f15])).
% 0.14/0.38 thf(f15,plain,(
% 0.14/0.38 ((? [X0,X1] : (? [X2] : (? [X3] : ((($true != (subset @ (binintersect @ X0 @ X2) @ X3)) & ((subset @ X0 @ X3) = $true)) & ($true = (in @ X3 @ (powerset @ X1)))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (binintersectEL = $true)) & (subsetE = $true)) & (subsetI1 = $true)),
% 0.14/0.38 inference(ennf_transformation,[],[f12])).
% 0.14/0.38 thf(f12,plain,(
% 0.14/0.38 ~((subsetI1 = $true) => ((subsetE = $true) => ((binintersectEL = $true) => ! [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3] : (($true = (in @ X3 @ (powerset @ X1))) => (((subset @ X0 @ X3) = $true) => ($true = (subset @ (binintersect @ X0 @ X2) @ X3)))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f11])).
% 0.14/0.38 thf(f11,plain,(
% 0.14/0.38 ~(subsetI1 => (subsetE => (binintersectEL => ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => ! [X3] : ((in @ X3 @ (powerset @ X1)) => ((subset @ X0 @ X3) => (subset @ (binintersect @ X0 @ X2) @ X3))))))))),
% 0.14/0.38 inference(rectify,[],[f5])).
% 0.14/0.38 thf(f5,negated_conjecture,(
% 0.14/0.38 ~(subsetI1 => (subsetE => (binintersectEL => ! [X3,X0] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X5] : ((in @ X5 @ (powerset @ X0)) => ((subset @ X3 @ X5) => (subset @ (binintersect @ X3 @ X4) @ X5))))))))),
% 0.14/0.38 inference(negated_conjecture,[],[f4])).
% 0.14/0.38 thf(f4,conjecture,(
% 0.14/0.38 subsetI1 => (subsetE => (binintersectEL => ! [X3,X0] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X5] : ((in @ X5 @ (powerset @ X0)) => ((subset @ X3 @ X5) => (subset @ (binintersect @ X3 @ X4) @ X5)))))))),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule1)).
% 0.14/0.38 thf(f42,plain,(
% 0.14/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((subset @ X1 @ X2) = $false) | ((in @ X3 @ X1) = $false) | ((in @ X3 @ X2) = $true)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f41])).
% 0.14/0.38 thf(f41,plain,(
% 0.14/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ X1) => (in @ X3 @ X2))) | ((subset @ X1 @ X2) = $false)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f40])).
% 0.14/0.38 thf(f40,plain,(
% 0.14/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((subset @ X1 @ X2) => ((in @ X3 @ X1) => (in @ X3 @ X2))))) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f39])).
% 0.14/0.38 thf(f39,plain,(
% 0.14/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ X1 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) @ X3))) )),
% 0.14/0.38 inference(pi_clausification,[],[f38])).
% 0.14/0.38 thf(f38,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X2))))))) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f37])).
% 0.14/0.38 thf(f37,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y0) => ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))))) @ X2) = $true)) )),
% 0.14/0.38 inference(pi_clausification,[],[f36])).
% 0.14/0.38 thf(f36,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ X1 @ Y0) => ((in @ Y1 @ X1) => (in @ Y1 @ Y0))))))) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f35])).
% 0.14/0.38 thf(f35,plain,(
% 0.14/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))))))) @ X1) = $true)) )),
% 0.14/0.38 inference(pi_clausification,[],[f33])).
% 0.14/0.38 thf(f33,plain,(
% 0.14/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))),
% 0.14/0.38 inference(definition_unfolding,[],[f24,f22])).
% 0.14/0.38 thf(f22,plain,(
% 0.14/0.38 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f10])).
% 0.14/0.38 thf(f10,plain,(
% 0.14/0.38 (subsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((subset @ Y0 @ Y1) => ((in @ Y2 @ Y0) => (in @ Y2 @ Y1))))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f9])).
% 0.14/0.38 thf(f9,plain,(
% 0.14/0.38 (subsetE = ! [X0,X1,X2] : ((subset @ X2 @ X1) => ((in @ X0 @ X2) => (in @ X0 @ X1))))),
% 0.14/0.38 inference(rectify,[],[f2])).
% 0.14/0.38 thf(f2,axiom,(
% 0.14/0.38 (subsetE = ! [X2,X1,X0] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))))),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE)).
% 0.14/0.38 thf(f24,plain,(
% 0.14/0.38 (subsetE = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f20])).
% 0.14/0.38 thf(f50,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (($false = (in @ (sK5 @ X1 @ X2) @ X2)) | ((subset @ X1 @ X2) = $true)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f49])).
% 0.14/0.38 thf(f49,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (((subset @ X1 @ X2) = $true) | ($false = ((in @ (sK5 @ X1 @ X2) @ X1) => (in @ (sK5 @ X1 @ X2) @ X2)))) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f48])).
% 0.14/0.38 thf(f48,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))) @ (sK5 @ X1 @ X2)) = $false) | ((subset @ X1 @ X2) = $true)) )),
% 0.14/0.38 inference(sigma_clausification,[],[f47])).
% 0.14/0.38 thf(f47,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2))))) | ((subset @ X1 @ X2) = $true)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f46])).
% 0.14/0.38 thf(f46,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (in @ Y0 @ X2)))) => (subset @ X1 @ X2)))) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f45])).
% 0.14/0.38 thf(f45,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0))) @ X2) = $true)) )),
% 0.14/0.38 inference(pi_clausification,[],[f44])).
% 0.14/0.38 thf(f44,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (in @ Y1 @ Y0)))) => (subset @ X1 @ Y0)))) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f43])).
% 0.14/0.38 thf(f43,plain,(
% 0.14/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1))))) @ X1) = $true)) )),
% 0.14/0.38 inference(pi_clausification,[],[f34])).
% 0.14/0.38 thf(f34,plain,(
% 0.14/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))) = $true)),
% 0.14/0.38 inference(definition_unfolding,[],[f31,f23])).
% 0.14/0.38 thf(f23,plain,(
% 0.14/0.38 (subsetI1 = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f20])).
% 0.14/0.38 thf(f31,plain,(
% 0.14/0.38 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f8])).
% 0.14/0.38 thf(f8,plain,(
% 0.14/0.38 (subsetI1 = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (in @ Y2 @ Y1)))) => (subset @ Y0 @ Y1)))))))),
% 0.14/0.38 inference(fool_elimination,[],[f7])).
% 0.14/0.38 thf(f7,plain,(
% 0.14/0.38 (subsetI1 = ! [X0,X1] : (! [X2] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)))),
% 0.14/0.38 inference(rectify,[],[f1])).
% 0.14/0.38 thf(f1,axiom,(
% 0.14/0.38 (subsetI1 = ! [X1,X0] : (! [X2] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)))),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1)).
% 0.14/0.38 thf(f74,plain,(
% 0.14/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK5 @ (binintersect @ X0 @ X1) @ X2) @ X0) = $true) | ($true = (subset @ (binintersect @ X0 @ X1) @ X2))) )),
% 0.14/0.38 inference(trivial_inequality_removal,[],[f71])).
% 0.14/0.38 thf(f71,plain,(
% 0.14/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (sK5 @ (binintersect @ X0 @ X1) @ X2) @ X0) = $true) | ($false = $true) | ($true = (subset @ (binintersect @ X0 @ X1) @ X2))) )),
% 0.14/0.38 inference(superposition,[],[f58,f51])).
% 0.14/0.38 thf(f51,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (((in @ (sK5 @ X1 @ X2) @ X1) = $true) | ((subset @ X1 @ X2) = $true)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f49])).
% 0.14/0.38 thf(f58,plain,(
% 0.14/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X3 @ (binintersect @ X1 @ X2))) | ((in @ X3 @ X1) = $true)) )),
% 0.14/0.38 inference(binary_proxy_clausification,[],[f57])).
% 0.14/0.38 thf(f57,plain,(
% 0.14/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ (binintersect @ X1 @ X2)) => (in @ X3 @ X1)) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f56])).
% 0.14/0.38 thf(f56,plain,(
% 0.14/0.38 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (binintersect @ X1 @ X2)) => (in @ Y0 @ X1))) @ X3))) )),
% 0.14/0.38 inference(pi_clausification,[],[f55])).
% 0.14/0.38 thf(f55,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (binintersect @ X1 @ X2)) => (in @ Y0 @ X1)))) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f54])).
% 0.14/0.38 thf(f54,plain,(
% 0.14/0.38 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (binintersect @ X1 @ Y0)) => (in @ Y1 @ X1))))) @ X2) = $true)) )),
% 0.14/0.38 inference(pi_clausification,[],[f53])).
% 0.14/0.38 thf(f53,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (binintersect @ X1 @ Y0)) => (in @ Y1 @ X1)))))) = $true)) )),
% 0.14/0.38 inference(beta_eta_normalization,[],[f52])).
% 0.14/0.38 thf(f52,plain,(
% 0.14/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y0))))))) @ X1))) )),
% 0.14/0.38 inference(pi_clausification,[],[f32])).
% 0.14/0.38 thf(f32,plain,(
% 0.14/0.38 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))),
% 0.14/0.38 inference(definition_unfolding,[],[f30,f21])).
% 0.14/0.38 thf(f21,plain,(
% 0.14/0.38 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))),
% 0.14/0.38 inference(cnf_transformation,[],[f14])).
% 0.14/0.38 thf(f14,plain,(
% 0.14/0.38 (binintersectEL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (binintersect @ Y0 @ Y1)) => (in @ Y2 @ Y0)))))))))),
% 0.14/0.38 inference(fool_elimination,[],[f13])).
% 0.14/0.38 thf(f13,plain,(
% 0.14/0.38 (binintersectEL = ! [X0,X1,X2] : ((in @ X0 @ (binintersect @ X2 @ X1)) => (in @ X0 @ X2)))),
% 0.14/0.38 inference(rectify,[],[f3])).
% 0.14/0.38 thf(f3,axiom,(
% 0.14/0.38 (binintersectEL = ! [X2,X1,X0] : ((in @ X2 @ (binintersect @ X0 @ X1)) => (in @ X2 @ X0)))),
% 0.14/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL)).
% 0.14/0.38 thf(f30,plain,(
% 0.14/0.38 (binintersectEL = $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f20])).
% 0.14/0.38 thf(f28,plain,(
% 0.14/0.38 ((subset @ (binintersect @ sK0 @ sK2) @ sK3) != $true)),
% 0.14/0.38 inference(cnf_transformation,[],[f20])).
% 0.14/0.38 % SZS output end Proof for theBenchmark
% 0.14/0.38 % (32267)------------------------------
% 0.14/0.38 % (32267)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (32267)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (32267)Memory used [KB]: 5628
% 0.14/0.38 % (32267)Time elapsed: 0.012 s
% 0.14/0.38 % (32267)Instructions burned: 13 (million)
% 0.14/0.38 % (32267)------------------------------
% 0.14/0.38 % (32267)------------------------------
% 0.14/0.38 % (32264)Success in time 0.01 s
% 0.14/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------