TSTP Solution File: SEU802^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU802^2 : 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 : n021.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 03:51:39 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SEU802^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.15 % 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 : n021.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 17:33:08 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 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/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % (27279)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)
% 0.13/0.37 % (27276)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)
% 0.13/0.37 % (27279)Instruction limit reached!
% 0.13/0.37 % (27279)------------------------------
% 0.13/0.37 % (27279)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (27279)Termination reason: Unknown
% 0.13/0.37 % (27279)Termination phase: Property scanning
% 0.13/0.37
% 0.13/0.37 % (27279)Memory used [KB]: 895
% 0.13/0.37 % (27279)Time elapsed: 0.003 s
% 0.13/0.37 % (27279)Instructions burned: 2 (million)
% 0.13/0.37 % (27279)------------------------------
% 0.13/0.37 % (27279)------------------------------
% 0.13/0.37 % (27278)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (27280)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)
% 0.13/0.37 % (27277)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)
% 0.13/0.37 % (27282)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)
% 0.13/0.37 % (27281)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37 % (27275)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (27278)Instruction limit reached!
% 0.13/0.37 % (27278)------------------------------
% 0.13/0.37 % (27278)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (27278)Termination reason: Unknown
% 0.13/0.37 % (27278)Termination phase: Preprocessing 3
% 0.13/0.37
% 0.13/0.37 % (27278)Memory used [KB]: 895
% 0.13/0.37 % (27278)Time elapsed: 0.003 s
% 0.13/0.37 % (27278)Instructions burned: 2 (million)
% 0.13/0.37 % (27278)------------------------------
% 0.13/0.37 % (27278)------------------------------
% 0.13/0.37 % (27280)Refutation not found, incomplete strategy
% 0.13/0.37 % (27280)------------------------------
% 0.13/0.37 % (27280)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (27282)Instruction limit reached!
% 0.13/0.37 % (27282)------------------------------
% 0.13/0.37 % (27282)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (27282)Termination reason: Unknown
% 0.13/0.37 % (27282)Termination phase: Saturation
% 0.13/0.37
% 0.13/0.37 % (27282)Memory used [KB]: 5500
% 0.13/0.37 % (27282)Time elapsed: 0.004 s
% 0.13/0.37 % (27282)Instructions burned: 4 (million)
% 0.13/0.37 % (27282)------------------------------
% 0.13/0.37 % (27282)------------------------------
% 0.13/0.37 % (27280)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.37
% 0.13/0.37
% 0.13/0.37 % (27280)Memory used [KB]: 5500
% 0.13/0.37 % (27280)Time elapsed: 0.004 s
% 0.13/0.37 % (27280)Instructions burned: 3 (million)
% 0.13/0.37 % (27280)------------------------------
% 0.13/0.37 % (27280)------------------------------
% 0.13/0.37 % (27276)Instruction limit reached!
% 0.13/0.37 % (27276)------------------------------
% 0.13/0.37 % (27276)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (27276)Termination reason: Unknown
% 0.13/0.37 % (27276)Termination phase: Saturation
% 0.13/0.37
% 0.13/0.37 % (27276)Memory used [KB]: 5500
% 0.13/0.37 % (27276)Time elapsed: 0.005 s
% 0.13/0.37 % (27276)Instructions burned: 5 (million)
% 0.13/0.37 % (27276)------------------------------
% 0.13/0.37 % (27276)------------------------------
% 0.13/0.38 % (27281)First to succeed.
% 0.13/0.38 % (27277)Also succeeded, but the first one will report.
% 0.13/0.38 % (27275)Also succeeded, but the first one will report.
% 0.13/0.38 % (27281)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% 0.13/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.13/0.38 thf(func_def_1, type, dsetconstr: $i > ($i > $o) > $i).
% 0.13/0.38 thf(func_def_4, type, funcSet: $i > $i > $i).
% 0.13/0.38 thf(func_def_5, type, ap: $i > $i > $i > $i > $i).
% 0.13/0.38 thf(func_def_6, type, surjective: $i > $i > $i > $o).
% 0.13/0.38 thf(func_def_7, type, surjFuncSet: $i > $i > $i).
% 0.13/0.38 thf(func_def_21, type, sK0: $i > $o).
% 0.13/0.38 thf(func_def_30, type, ph8: !>[X0: $tType]:(X0)).
% 0.13/0.38 thf(func_def_31, type, sK9: $i > $i).
% 0.13/0.38 thf(f71,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f70])).
% 0.13/0.38 thf(f70,plain,(
% 0.13/0.38 ($true = $false)),
% 0.13/0.38 inference(backward_demodulation,[],[f41,f69])).
% 0.13/0.38 thf(f69,plain,(
% 0.13/0.38 ((in @ sK7 @ sK3) = $false)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f67])).
% 0.13/0.38 thf(f67,plain,(
% 0.13/0.38 ($true = $false) | ((in @ sK7 @ sK3) = $false)),
% 0.13/0.38 inference(superposition,[],[f57,f65])).
% 0.13/0.38 thf(f65,plain,(
% 0.13/0.38 ($false = (in @ (sK9 @ sK7) @ sK5))),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f64])).
% 0.13/0.38 thf(f64,plain,(
% 0.13/0.38 ($false = (in @ (sK9 @ sK7) @ sK5)) | (sK7 != sK7)),
% 0.13/0.38 inference(superposition,[],[f45,f63])).
% 0.13/0.38 thf(f63,plain,(
% 0.13/0.38 (sK7 = (ap @ sK5 @ sK3 @ sK4 @ (sK9 @ sK7)))),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f61])).
% 0.13/0.38 thf(f61,plain,(
% 0.13/0.38 (sK7 = (ap @ sK5 @ sK3 @ sK4 @ (sK9 @ sK7))) | ($true = $false)),
% 0.13/0.38 inference(superposition,[],[f41,f59])).
% 0.13/0.38 thf(f59,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($false = (in @ X1 @ sK3)) | ((ap @ sK5 @ sK3 @ sK4 @ (sK9 @ X1)) = X1)) )),
% 0.13/0.38 inference(equality_proxy_clausification,[],[f58])).
% 0.13/0.38 thf(f58,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((ap @ sK5 @ sK3 @ sK4 @ (sK9 @ X1)) = X1)) | ($false = (in @ X1 @ sK3))) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f56])).
% 0.13/0.38 thf(f56,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = (((ap @ sK5 @ sK3 @ sK4 @ (sK9 @ X1)) = X1) & (in @ (sK9 @ X1) @ sK5))) | ($false = (in @ X1 @ sK3))) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f55])).
% 0.13/0.38 thf(f55,plain,(
% 0.13/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((ap @ sK5 @ sK3 @ sK4 @ Y0) = X1) & (in @ Y0 @ sK5))) @ (sK9 @ X1)) = $true) | ($false = (in @ X1 @ sK3))) )),
% 0.13/0.38 inference(sigma_clausification,[],[f54])).
% 0.13/0.38 thf(f54,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = (?? @ $i @ (^[Y0 : $i]: (((ap @ sK5 @ sK3 @ sK4 @ Y0) = X1) & (in @ Y0 @ sK5))))) | ($false = (in @ X1 @ sK3))) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f53])).
% 0.13/0.38 thf(f53,plain,(
% 0.13/0.38 ( ! [X1 : $i] : ((((in @ X1 @ sK3) => (?? @ $i @ (^[Y0 : $i]: (((ap @ sK5 @ sK3 @ sK4 @ Y0) = X1) & (in @ Y0 @ sK5))))) = $true)) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f52])).
% 0.13/0.38 thf(f52,plain,(
% 0.13/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((ap @ sK5 @ sK3 @ sK4 @ Y1) = Y0) & (in @ Y1 @ sK5)))))) @ X1) = $true)) )),
% 0.13/0.38 inference(pi_clausification,[],[f51])).
% 0.13/0.38 thf(f51,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((ap @ sK5 @ sK3 @ sK4 @ Y1) = Y0) & (in @ Y1 @ sK5))))))) = $true)),
% 0.13/0.38 inference(beta_eta_normalization,[],[f50])).
% 0.13/0.38 thf(f50,plain,(
% 0.13/0.38 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: (((ap @ sK5 @ sK3 @ Y0 @ Y2) = Y1) & (in @ Y2 @ sK5)))))))) @ sK4) = $true)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f49])).
% 0.13/0.38 thf(f49,plain,(
% 0.13/0.38 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: (((ap @ sK5 @ sK3 @ Y0 @ Y2) = Y1) & (in @ Y2 @ sK5)))))))) @ sK4) = $true) | ($true != $true)),
% 0.13/0.38 inference(superposition,[],[f47,f48])).
% 0.13/0.38 thf(f48,plain,(
% 0.13/0.38 ((in @ sK4 @ (dsetconstr @ (funcSet @ sK5 @ sK3) @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (?? @ $i @ (^[Y2 : $i]: (((ap @ sK5 @ sK3 @ Y0 @ Y2) = Y1) & (in @ Y2 @ sK5)))))))))) = $true)),
% 0.13/0.38 inference(beta_eta_normalization,[],[f36])).
% 0.13/0.38 thf(f36,plain,(
% 0.13/0.38 ($true = (in @ sK4 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y4) => (?? @ $i @ (^[Y7 : $i]: (((ap @ Y3 @ Y4 @ Y5 @ Y7) = Y6) & (in @ Y7 @ Y3)))))))))))) @ Y0 @ Y1 @ Y2)))))) @ sK5 @ sK3)))),
% 0.13/0.38 inference(definition_unfolding,[],[f28,f31])).
% 0.13/0.38 thf(f31,plain,(
% 0.13/0.38 (surjFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: ((^[Y3 : $i]: ((^[Y4 : $i]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((in @ Y6 @ Y4) => (?? @ $i @ (^[Y7 : $i]: (((ap @ Y3 @ Y4 @ Y5 @ Y7) = Y6) & (in @ Y7 @ Y3)))))))))))) @ Y0 @ Y1 @ Y2)))))))),
% 0.13/0.38 inference(definition_unfolding,[],[f23,f24])).
% 0.13/0.38 thf(f24,plain,(
% 0.13/0.38 (surjective = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3) & (in @ Y4 @ Y0)))))))))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f12])).
% 0.13/0.38 thf(f12,plain,(
% 0.13/0.38 (surjective = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3) & (in @ Y4 @ Y0)))))))))))))),
% 0.13/0.38 inference(fool_elimination,[],[f11])).
% 0.13/0.38 thf(f11,plain,(
% 0.13/0.38 ((^[X0 : $i, X1 : $i, X2 : $i] : (! [X3] : ((in @ X3 @ X1) => ? [X4] : ((in @ X4 @ X0) & ((ap @ X0 @ X1 @ X2 @ X4) = X3))))) = surjective)),
% 0.13/0.38 inference(rectify,[],[f2])).
% 0.13/0.38 thf(f2,axiom,(
% 0.13/0.38 ((^[X0 : $i, X4 : $i, X5 : $i] : (! [X2] : ((in @ X2 @ X4) => ? [X3] : ((in @ X3 @ X0) & ((ap @ X0 @ X4 @ X5 @ X3) = X2))))) = surjective)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjective)).
% 0.13/0.38 thf(f23,plain,(
% 0.13/0.38 (surjFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (surjective @ Y0 @ Y1 @ Y2)))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f10])).
% 0.13/0.38 thf(f10,plain,(
% 0.13/0.38 (surjFuncSet = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ (funcSet @ Y0 @ Y1) @ (^[Y2 : $i]: (surjective @ Y0 @ Y1 @ Y2)))))))),
% 0.13/0.38 inference(fool_elimination,[],[f9])).
% 0.13/0.38 thf(f9,plain,(
% 0.13/0.38 ((^[X0 : $i, X1 : $i] : (dsetconstr @ (funcSet @ X0 @ X1) @ (^[X2 : $i] : (surjective @ X0 @ X1 @ X2)))) = surjFuncSet)),
% 0.13/0.38 inference(rectify,[],[f3])).
% 0.13/0.38 thf(f3,axiom,(
% 0.13/0.38 ((^[X0 : $i, X4 : $i] : (dsetconstr @ (funcSet @ X0 @ X4) @ (^[X5 : $i] : (surjective @ X0 @ X4 @ X5)))) = surjFuncSet)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjFuncSet)).
% 0.13/0.38 thf(f28,plain,(
% 0.13/0.38 ((in @ sK4 @ (surjFuncSet @ sK5 @ sK3)) = $true)),
% 0.13/0.38 inference(cnf_transformation,[],[f22])).
% 0.13/0.38 thf(f22,plain,(
% 0.13/0.38 (dsetconstrER = $true) & (((surjective @ sK5 @ sK3 @ sK4) != $true) & ((in @ sK4 @ (surjFuncSet @ sK5 @ sK3)) = $true))),
% 0.13/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f15,f21])).
% 0.13/0.38 thf(f21,plain,(
% 0.13/0.38 ? [X0,X1,X2] : (((surjective @ X2 @ X0 @ X1) != $true) & ((in @ X1 @ (surjFuncSet @ X2 @ X0)) = $true)) => (((surjective @ sK5 @ sK3 @ sK4) != $true) & ((in @ sK4 @ (surjFuncSet @ sK5 @ sK3)) = $true))),
% 0.13/0.38 introduced(choice_axiom,[])).
% 0.13/0.38 thf(f15,plain,(
% 0.13/0.38 (dsetconstrER = $true) & ? [X0,X1,X2] : (((surjective @ X2 @ X0 @ X1) != $true) & ((in @ X1 @ (surjFuncSet @ X2 @ X0)) = $true))),
% 0.13/0.38 inference(ennf_transformation,[],[f8])).
% 0.13/0.38 thf(f8,plain,(
% 0.13/0.38 ~((dsetconstrER = $true) => ! [X0,X1,X2] : (((in @ X1 @ (surjFuncSet @ X2 @ X0)) = $true) => ((surjective @ X2 @ X0 @ X1) = $true)))),
% 0.13/0.38 inference(fool_elimination,[],[f7])).
% 0.13/0.38 thf(f7,plain,(
% 0.13/0.38 ~(dsetconstrER => ! [X0,X1,X2] : ((in @ X1 @ (surjFuncSet @ X2 @ X0)) => (surjective @ X2 @ X0 @ X1)))),
% 0.13/0.38 inference(rectify,[],[f5])).
% 0.13/0.38 thf(f5,negated_conjecture,(
% 0.13/0.38 ~(dsetconstrER => ! [X3,X5,X2] : ((in @ X5 @ (surjFuncSet @ X2 @ X3)) => (surjective @ X2 @ X3 @ X5)))),
% 0.13/0.38 inference(negated_conjecture,[],[f4])).
% 0.13/0.38 thf(f4,conjecture,(
% 0.13/0.38 dsetconstrER => ! [X3,X5,X2] : ((in @ X5 @ (surjFuncSet @ X2 @ X3)) => (surjective @ X2 @ X3 @ X5))),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',surjFuncSetFuncSurj)).
% 0.13/0.38 thf(f47,plain,(
% 0.13/0.38 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X5 @ (dsetconstr @ X4 @ X3)) != $true) | ($true = (X3 @ X5))) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f46])).
% 0.13/0.38 thf(f46,plain,(
% 0.13/0.38 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true) | ($true = (X3 @ X5))) )),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f34])).
% 0.13/0.38 thf(f34,plain,(
% 0.13/0.38 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true) | ($true != $true) | ($true = (X3 @ X5))) )),
% 0.13/0.38 inference(definition_unfolding,[],[f25,f30])).
% 0.13/0.38 thf(f30,plain,(
% 0.13/0.38 (dsetconstrER = $true)),
% 0.13/0.38 inference(cnf_transformation,[],[f22])).
% 0.13/0.38 thf(f25,plain,(
% 0.13/0.38 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true) | ($true = (X3 @ X5)) | (dsetconstrER != $true)) )),
% 0.13/0.38 inference(cnf_transformation,[],[f20])).
% 0.13/0.38 thf(f20,plain,(
% 0.13/0.38 ((dsetconstrER = $true) | (($true = (in @ sK2 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))))) & ($true != (sK0 @ sK2)))) & (! [X3 : $i > $o,X4,X5] : (((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true) | ($true = (X3 @ X5))) | (dsetconstrER != $true))),
% 0.13/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f18,f19])).
% 0.13/0.38 thf(f19,plain,(
% 0.13/0.38 ? [X0 : $i > $o,X1,X2] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) & ($true != (X0 @ X2))) => (($true = (in @ sK2 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (sK0 @ Y0))))) & ($true != (sK0 @ sK2)))),
% 0.13/0.38 introduced(choice_axiom,[])).
% 0.13/0.38 thf(f18,plain,(
% 0.13/0.38 ((dsetconstrER = $true) | ? [X0 : $i > $o,X1,X2] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) & ($true != (X0 @ X2)))) & (! [X3 : $i > $o,X4,X5] : (((in @ X5 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true) | ($true = (X3 @ X5))) | (dsetconstrER != $true))),
% 0.13/0.38 inference(rectify,[],[f17])).
% 0.13/0.38 thf(f17,plain,(
% 0.13/0.38 ((dsetconstrER = $true) | ? [X0 : $i > $o,X1,X2] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) & ($true != (X0 @ X2)))) & (! [X0 : $i > $o,X1,X2] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (X0 @ X2))) | (dsetconstrER != $true))),
% 0.13/0.38 inference(nnf_transformation,[],[f16])).
% 0.13/0.38 thf(f16,plain,(
% 0.13/0.38 (dsetconstrER = $true) <=> ! [X0 : $i > $o,X1,X2] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) != $true) | ($true = (X0 @ X2)))),
% 0.13/0.38 inference(ennf_transformation,[],[f14])).
% 0.13/0.38 thf(f14,plain,(
% 0.13/0.38 (dsetconstrER = $true) <=> ! [X0 : $i > $o,X1,X2] : (((in @ X2 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X0 @ Y0)))) = $true) => ($true = (X0 @ X2)))),
% 0.13/0.38 inference(fool_elimination,[],[f13])).
% 0.13/0.38 thf(f13,plain,(
% 0.13/0.38 (! [X0 : $i > $o,X1,X2] : ((in @ X2 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X2)) = dsetconstrER)),
% 0.13/0.38 inference(rectify,[],[f1])).
% 0.13/0.38 thf(f1,axiom,(
% 0.13/0.38 (! [X1 : $i > $o,X0,X2] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 0.13/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER)).
% 0.13/0.38 thf(f45,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (((ap @ sK5 @ sK3 @ sK4 @ X1) != sK7) | ($false = (in @ X1 @ sK5))) )),
% 0.13/0.38 inference(equality_proxy_clausification,[],[f44])).
% 0.13/0.38 thf(f44,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($false = (in @ X1 @ sK5)) | (((ap @ sK5 @ sK3 @ sK4 @ X1) = sK7) = $false)) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f43])).
% 0.13/0.38 thf(f43,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($false = (((ap @ sK5 @ sK3 @ sK4 @ X1) = sK7) & (in @ X1 @ sK5)))) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f42])).
% 0.13/0.38 thf(f42,plain,(
% 0.13/0.38 ( ! [X1 : $i] : ((((^[Y0 : $i]: (((ap @ sK5 @ sK3 @ sK4 @ Y0) = sK7) & (in @ Y0 @ sK5))) @ X1) = $false)) )),
% 0.13/0.38 inference(pi_clausification,[],[f40])).
% 0.13/0.38 thf(f40,plain,(
% 0.13/0.38 ($false = (?? @ $i @ (^[Y0 : $i]: (((ap @ sK5 @ sK3 @ sK4 @ Y0) = sK7) & (in @ Y0 @ sK5)))))),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f39])).
% 0.13/0.38 thf(f39,plain,(
% 0.13/0.38 (((in @ sK7 @ sK3) => (?? @ $i @ (^[Y0 : $i]: (((ap @ sK5 @ sK3 @ sK4 @ Y0) = sK7) & (in @ Y0 @ sK5))))) = $false)),
% 0.13/0.38 inference(beta_eta_normalization,[],[f38])).
% 0.13/0.38 thf(f38,plain,(
% 0.13/0.38 (((^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((ap @ sK5 @ sK3 @ sK4 @ Y1) = Y0) & (in @ Y1 @ sK5)))))) @ sK7) = $false)),
% 0.13/0.38 inference(sigma_clausification,[],[f37])).
% 0.13/0.38 thf(f37,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (?? @ $i @ (^[Y1 : $i]: (((ap @ sK5 @ sK3 @ sK4 @ Y1) = Y0) & (in @ Y1 @ sK5))))))) != $true)),
% 0.13/0.38 inference(beta_eta_normalization,[],[f35])).
% 0.13/0.38 thf(f35,plain,(
% 0.13/0.38 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (?? @ $i @ (^[Y4 : $i]: (((ap @ Y0 @ Y1 @ Y2 @ Y4) = Y3) & (in @ Y4 @ Y0)))))))))))) @ sK5 @ sK3 @ sK4))),
% 0.13/0.38 inference(definition_unfolding,[],[f29,f24])).
% 0.13/0.38 thf(f29,plain,(
% 0.13/0.38 ((surjective @ sK5 @ sK3 @ sK4) != $true)),
% 0.13/0.38 inference(cnf_transformation,[],[f22])).
% 0.13/0.38 thf(f57,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (((in @ (sK9 @ X1) @ sK5) = $true) | ($false = (in @ X1 @ sK3))) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f56])).
% 0.13/0.38 thf(f41,plain,(
% 0.13/0.38 ((in @ sK7 @ sK3) = $true)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f39])).
% 0.13/0.38 % SZS output end Proof for theBenchmark
% 0.13/0.38 % (27281)------------------------------
% 0.13/0.38 % (27281)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (27281)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (27281)Memory used [KB]: 5500
% 0.13/0.38 % (27281)Time elapsed: 0.009 s
% 0.13/0.38 % (27281)Instructions burned: 6 (million)
% 0.13/0.38 % (27281)------------------------------
% 0.13/0.38 % (27281)------------------------------
% 0.13/0.38 % (27274)Success in time 0.021 s
% 0.13/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------