TSTP Solution File: SYO068^4.001 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO068^4.001 : TPTP v8.2.0. Released v4.0.0.
% 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 : n022.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 09:02:41 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO068^4.001 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % 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
% 0.15/0.35 % Computer : n022.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Mon May 20 10:41:38 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 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
% 0.15/0.37 % (8754)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)
% 0.15/0.38 % (8748)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)
% 0.15/0.38 % (8747)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.38 % (8749)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)
% 0.15/0.38 % (8754)Instruction limit reached!
% 0.15/0.38 % (8754)------------------------------
% 0.15/0.38 % (8754)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (8752)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)
% 0.15/0.38 % (8754)Termination reason: Unknown
% 0.15/0.38 % (8754)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (8754)Memory used [KB]: 1023
% 0.15/0.38 % (8754)Time elapsed: 0.003 s
% 0.15/0.38 % (8754)Instructions burned: 3 (million)
% 0.15/0.38 % (8754)------------------------------
% 0.15/0.38 % (8754)------------------------------
% 0.15/0.38 % (8753)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.38 % (8751)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)
% 0.15/0.38 % (8748)Instruction limit reached!
% 0.15/0.38 % (8748)------------------------------
% 0.15/0.38 % (8748)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (8748)Termination reason: Unknown
% 0.15/0.38 % (8748)Termination phase: Function definition elimination
% 0.15/0.38
% 0.15/0.38 % (8748)Memory used [KB]: 1023
% 0.15/0.38 % (8748)Time elapsed: 0.004 s
% 0.15/0.38 % (8748)Instructions burned: 4 (million)
% 0.15/0.38 % (8748)------------------------------
% 0.15/0.38 % (8748)------------------------------
% 0.15/0.38 % (8751)Instruction limit reached!
% 0.15/0.38 % (8751)------------------------------
% 0.15/0.38 % (8751)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (8751)Termination reason: Unknown
% 0.15/0.38 % (8751)Termination phase: Preprocessing 3
% 0.15/0.38
% 0.15/0.38 % (8751)Memory used [KB]: 1023
% 0.15/0.38 % (8751)Time elapsed: 0.004 s
% 0.15/0.38 % (8751)Instructions burned: 3 (million)
% 0.15/0.38 % (8751)------------------------------
% 0.15/0.38 % (8751)------------------------------
% 0.15/0.38 % (8752)Refutation not found, incomplete strategy
% 0.15/0.38 % (8752)------------------------------
% 0.15/0.38 % (8752)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (8752)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.38
% 0.15/0.38
% 0.15/0.38 % (8752)Memory used [KB]: 5500
% 0.15/0.38 % (8752)Time elapsed: 0.004 s
% 0.15/0.38 % (8752)Instructions burned: 3 (million)
% 0.15/0.38 % (8752)------------------------------
% 0.15/0.38 % (8752)------------------------------
% 0.15/0.38 % (8750)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.38 % (8750)Instruction limit reached!
% 0.15/0.38 % (8750)------------------------------
% 0.15/0.38 % (8750)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.38 % (8750)Termination reason: Unknown
% 0.15/0.38 % (8750)Termination phase: Property scanning
% 0.15/0.38
% 0.15/0.38 % (8750)Memory used [KB]: 1023
% 0.15/0.38 % (8750)Time elapsed: 0.003 s
% 0.15/0.38 % (8750)Instructions burned: 2 (million)
% 0.15/0.38 % (8750)------------------------------
% 0.15/0.38 % (8750)------------------------------
% 0.15/0.38 % (8749)First to succeed.
% 0.15/0.39 % (8753)Also succeeded, but the first one will report.
% 0.15/0.39 % (8749)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% 0.15/0.39 thf(func_def_0, type, irel: $i > $i > $o).
% 0.15/0.39 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_9, type, itrue: $i > $o).
% 0.15/0.39 thf(func_def_10, type, ifalse: $i > $o).
% 0.15/0.39 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.39 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 0.15/0.39 thf(func_def_21, type, p0: $i > $o).
% 0.15/0.39 thf(func_def_22, type, p1: $i > $o).
% 0.15/0.39 thf(func_def_23, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.15/0.39 thf(func_def_37, type, sK1: $i > $i).
% 0.15/0.39 thf(func_def_38, type, sK2: $i > $i).
% 0.15/0.39 thf(func_def_39, type, sK3: $i > $i).
% 0.15/0.39 thf(f166,plain,(
% 0.15/0.39 $false),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f165])).
% 0.15/0.39 thf(f165,plain,(
% 0.15/0.39 ($true = $false)),
% 0.15/0.39 inference(superposition,[],[f146,f162])).
% 0.15/0.39 thf(f162,plain,(
% 0.15/0.39 ( ! [X0 : $i] : (((p0 @ X0) = $true)) )),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f159])).
% 0.15/0.39 thf(f159,plain,(
% 0.15/0.39 ( ! [X0 : $i] : (($true = $false) | ((p0 @ X0) = $true)) )),
% 0.15/0.39 inference(superposition,[],[f156,f91])).
% 0.15/0.39 thf(f91,plain,(
% 0.15/0.39 ( ! [X0 : $i] : (((irel @ X0 @ X0) = $true)) )),
% 0.15/0.39 inference(cnf_transformation,[],[f66])).
% 0.15/0.39 thf(f66,plain,(
% 0.15/0.39 ! [X0] : ((irel @ X0 @ X0) = $true)),
% 0.15/0.39 inference(fool_elimination,[],[f65])).
% 0.15/0.39 thf(f65,plain,(
% 0.15/0.39 ! [X0] : (irel @ X0 @ X0)),
% 0.15/0.39 inference(rectify,[],[f1])).
% 0.15/0.39 thf(f1,axiom,(
% 0.15/0.39 ! [X0] : (irel @ X0 @ X0)),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',refl_axiom)).
% 0.15/0.39 thf(f156,plain,(
% 0.15/0.39 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p0 @ X0) = $true)) )),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f152])).
% 0.15/0.39 thf(f152,plain,(
% 0.15/0.39 ( ! [X0 : $i,X1 : $i] : (((p0 @ X0) = $true) | ($true = $false) | ((irel @ X1 @ X0) = $false)) )),
% 0.15/0.39 inference(superposition,[],[f151,f91])).
% 0.15/0.39 thf(f151,plain,(
% 0.15/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((irel @ X1 @ X2) = $false) | ((p0 @ X3) = $true)) )),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f150])).
% 0.15/0.39 thf(f150,plain,(
% 0.15/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((p0 @ X3) = $true) | ($true = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.15/0.39 inference(forward_demodulation,[],[f149,f144])).
% 0.15/0.39 thf(f144,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((p1 @ X1) = $true)) )),
% 0.15/0.39 inference(pi_clausification,[],[f143])).
% 0.15/0.39 thf(f143,plain,(
% 0.15/0.39 ((!! @ $i @ p1) = $true)),
% 0.15/0.39 inference(beta_eta_normalization,[],[f109])).
% 0.15/0.39 thf(f109,plain,(
% 0.15/0.39 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p1)))),
% 0.15/0.39 inference(definition_unfolding,[],[f87,f84,f81])).
% 0.15/0.39 thf(f81,plain,(
% 0.15/0.39 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.15/0.39 inference(cnf_transformation,[],[f70])).
% 0.15/0.39 thf(f70,plain,(
% 0.15/0.39 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.15/0.39 inference(fool_elimination,[],[f69])).
% 0.15/0.39 thf(f69,plain,(
% 0.15/0.39 ((^[X0 : $i > $o] : (X0)) = iatom)),
% 0.15/0.39 inference(rectify,[],[f8])).
% 0.15/0.39 thf(f8,axiom,(
% 0.15/0.39 ((^[X5 : $i > $o] : (X5)) = iatom)),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iatom)).
% 0.15/0.39 thf(f84,plain,(
% 0.15/0.39 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.39 inference(cnf_transformation,[],[f62])).
% 0.15/0.39 thf(f62,plain,(
% 0.15/0.39 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.39 inference(fool_elimination,[],[f61])).
% 0.15/0.39 thf(f61,plain,(
% 0.15/0.39 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = ivalid)),
% 0.15/0.39 inference(rectify,[],[f18])).
% 0.15/0.39 thf(f18,axiom,(
% 0.15/0.39 ((^[X8 : $i > $o] : (! [X6] : (X8 @ X6))) = ivalid)),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ivalid)).
% 0.15/0.39 thf(f87,plain,(
% 0.15/0.39 ((ivalid @ (iatom @ p1)) = $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f64])).
% 0.15/0.39 thf(f64,plain,(
% 0.15/0.39 ((ivalid @ (iatom @ p1)) = $true)),
% 0.15/0.39 inference(fool_elimination,[],[f63])).
% 0.15/0.39 thf(f63,plain,(
% 0.15/0.39 (ivalid @ (iatom @ p1))),
% 0.15/0.39 inference(rectify,[],[f22])).
% 0.15/0.39 thf(f22,axiom,(
% 0.15/0.39 (ivalid @ (iatom @ p1))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1)).
% 0.15/0.39 thf(f149,plain,(
% 0.15/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p0 @ X3) = $true) | ((p1 @ (sK3 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false)) )),
% 0.15/0.39 inference(trivial_inequality_removal,[],[f148])).
% 0.15/0.39 thf(f148,plain,(
% 0.15/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = $false) | ((p1 @ (sK3 @ X2)) = $false) | ((p0 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ((irel @ X2 @ X3) = $false)) )),
% 0.15/0.39 inference(forward_demodulation,[],[f141,f144])).
% 0.15/0.39 thf(f141,plain,(
% 0.15/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((p1 @ (sK1 @ X1)) = $false) | ((irel @ X2 @ X3) = $false) | ((p1 @ (sK3 @ X2)) = $false) | ((p0 @ X3) = $true)) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f140])).
% 0.15/0.39 thf(f140,plain,(
% 0.15/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | (((irel @ X2 @ (sK3 @ X2)) => (p1 @ (sK3 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | ((p1 @ (sK1 @ X1)) = $false) | ((p0 @ X3) = $true)) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f139])).
% 0.15/0.39 thf(f139,plain,(
% 0.15/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p1 @ (sK1 @ X1)) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))) @ (sK3 @ X2)) = $false) | ((irel @ X1 @ X2) = $false) | ((p0 @ X3) = $true) | ((irel @ X2 @ X3) = $false)) )),
% 0.15/0.39 inference(sigma_clausification,[],[f138])).
% 0.15/0.39 thf(f138,plain,(
% 0.15/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $false) | ((irel @ X2 @ X3) = $false) | ((p0 @ X3) = $true) | ((p1 @ (sK1 @ X1)) = $false)) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f137])).
% 0.15/0.39 thf(f137,plain,(
% 0.15/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X2 @ X3) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) = $true) | ((p0 @ X3) = $true) | ((p1 @ (sK1 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f136])).
% 0.15/0.39 thf(f136,plain,(
% 0.15/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p0 @ X3)) = $true) | ((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) = $true) | ((p1 @ (sK1 @ X1)) = $false)) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f135])).
% 0.15/0.39 thf(f135,plain,(
% 0.15/0.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false) | ((p1 @ (sK1 @ X1)) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))) @ X3) = $true)) )),
% 0.15/0.39 inference(pi_clausification,[],[f134])).
% 0.15/0.39 thf(f134,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false) | ((p1 @ (sK1 @ X1)) = $false)) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f133])).
% 0.15/0.39 thf(f133,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : (((p1 @ (sK1 @ X1)) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f121])).
% 0.15/0.39 thf(f121,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))))) = $true) | ((p1 @ (sK1 @ X1)) = $false)) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f120])).
% 0.15/0.39 thf(f120,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK1 @ X1)) => (p1 @ (sK1 @ X1))) = $false) | (((irel @ X1 @ X2) => ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))))) = $true)) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f119])).
% 0.15/0.39 thf(f119,plain,(
% 0.15/0.39 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK1 @ X1)) => (p1 @ (sK1 @ X1))) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1))))))) @ X2))) )),
% 0.15/0.39 inference(pi_clausification,[],[f118])).
% 0.15/0.39 thf(f118,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))))))) = $true) | (((irel @ X1 @ (sK1 @ X1)) => (p1 @ (sK1 @ X1))) = $false)) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f117])).
% 0.15/0.39 thf(f117,plain,(
% 0.15/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))) @ (sK1 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))))))) = $true)) )),
% 0.15/0.39 inference(sigma_clausification,[],[f116])).
% 0.15/0.39 thf(f116,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))))))) = $true)) )),
% 0.15/0.39 inference(not_proxy_clausification,[],[f115])).
% 0.15/0.39 thf(f115,plain,(
% 0.15/0.39 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))))))) = $true)) )),
% 0.15/0.39 inference(binary_proxy_clausification,[],[f114])).
% 0.15/0.39 thf(f114,plain,(
% 0.15/0.39 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1))))))))) = $true)) )),
% 0.15/0.39 inference(beta_eta_normalization,[],[f113])).
% 0.15/0.39 thf(f113,plain,(
% 0.15/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p0 @ Y2)))))))))) @ X1) = $true)) )),
% 0.15/0.39 inference(pi_clausification,[],[f112])).
% 0.15/0.39 thf(f112,plain,(
% 0.15/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p0 @ Y2))))))))))))),
% 0.15/0.39 inference(beta_eta_normalization,[],[f111])).
% 0.15/0.39 thf(f111,plain,(
% 0.15/0.39 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p1) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p1) @ ((^[Y0 : $i > $o]: (Y0)) @ p0)))))),
% 0.15/0.39 inference(definition_unfolding,[],[f95,f84,f105,f81,f105,f81,f81])).
% 0.15/0.39 thf(f105,plain,(
% 0.15/0.39 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.15/0.39 inference(definition_unfolding,[],[f90,f100,f77,f77])).
% 0.15/0.39 thf(f77,plain,(
% 0.15/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f38])).
% 0.15/0.39 thf(f38,plain,(
% 0.15/0.39 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.15/0.39 inference(fool_elimination,[],[f37])).
% 0.15/0.39 thf(f37,plain,(
% 0.15/0.39 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((irel @ X1 @ X2) => (X0 @ X2)))) = mbox_s4)),
% 0.15/0.39 inference(rectify,[],[f7])).
% 0.15/0.39 thf(f7,axiom,(
% 0.15/0.39 ((^[X5 : $i > $o, X0 : $i] : (! [X1] : ((irel @ X0 @ X1) => (X5 @ X1)))) = mbox_s4)),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.15/0.39 thf(f100,plain,(
% 0.15/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.15/0.39 inference(definition_unfolding,[],[f99,f80,f93])).
% 0.15/0.39 thf(f93,plain,(
% 0.15/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f52])).
% 0.15/0.39 thf(f52,plain,(
% 0.15/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.39 inference(fool_elimination,[],[f51])).
% 0.15/0.39 thf(f51,plain,(
% 0.15/0.39 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.15/0.39 inference(rectify,[],[f3])).
% 0.15/0.39 thf(f3,axiom,(
% 0.15/0.39 (mnot = (^[X0 : $i > $o, X3 : $i] : (~(X0 @ X3))))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.15/0.39 thf(f80,plain,(
% 0.15/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f60])).
% 0.15/0.39 thf(f60,plain,(
% 0.15/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.39 inference(fool_elimination,[],[f59])).
% 0.15/0.39 thf(f59,plain,(
% 0.15/0.39 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.15/0.39 inference(rectify,[],[f4])).
% 0.15/0.39 thf(f4,axiom,(
% 0.15/0.39 (mor = (^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X1 @ X3) | (X0 @ X3))))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.15/0.39 thf(f99,plain,(
% 0.15/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.39 inference(cnf_transformation,[],[f44])).
% 0.15/0.39 thf(f44,plain,(
% 0.15/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.39 inference(fool_elimination,[],[f43])).
% 0.15/0.39 thf(f43,plain,(
% 0.15/0.39 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.15/0.39 inference(rectify,[],[f6])).
% 0.15/0.39 thf(f6,axiom,(
% 0.15/0.39 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.15/0.39 thf(f90,plain,(
% 0.15/0.39 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.15/0.39 inference(cnf_transformation,[],[f40])).
% 0.15/0.39 thf(f40,plain,(
% 0.15/0.39 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.15/0.39 inference(fool_elimination,[],[f39])).
% 0.15/0.39 thf(f39,plain,(
% 0.15/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))) = iimplies)),
% 0.15/0.39 inference(rectify,[],[f14])).
% 0.15/0.39 thf(f14,axiom,(
% 0.15/0.39 ((^[X5 : $i > $o, X7 : $i > $o] : (mimplies @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))) = iimplies)),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplies)).
% 0.15/0.39 thf(f95,plain,(
% 0.15/0.39 ((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0)))) = $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f48])).
% 0.15/0.39 thf(f48,plain,(
% 0.15/0.39 ((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0)))) = $true)),
% 0.15/0.39 inference(fool_elimination,[],[f47])).
% 0.15/0.39 thf(f47,plain,(
% 0.15/0.39 (ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),
% 0.15/0.39 inference(rectify,[],[f23])).
% 0.15/0.39 thf(f23,axiom,(
% 0.15/0.39 (ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2)).
% 0.15/0.39 thf(f146,plain,(
% 0.15/0.39 ((p0 @ sK4) = $false)),
% 0.15/0.39 inference(sigma_clausification,[],[f145])).
% 0.15/0.39 thf(f145,plain,(
% 0.15/0.39 ((!! @ $i @ p0) != $true)),
% 0.15/0.39 inference(beta_eta_normalization,[],[f110])).
% 0.15/0.39 thf(f110,plain,(
% 0.15/0.39 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p0)) != $true)),
% 0.15/0.39 inference(definition_unfolding,[],[f88,f84,f81])).
% 0.15/0.39 thf(f88,plain,(
% 0.15/0.39 ((ivalid @ (iatom @ p0)) != $true)),
% 0.15/0.39 inference(cnf_transformation,[],[f73])).
% 0.15/0.39 thf(f73,plain,(
% 0.15/0.39 ((ivalid @ (iatom @ p0)) != $true)),
% 0.15/0.39 inference(flattening,[],[f34])).
% 0.15/0.39 thf(f34,plain,(
% 0.15/0.39 ~((ivalid @ (iatom @ p0)) = $true)),
% 0.15/0.39 inference(fool_elimination,[],[f33])).
% 0.15/0.39 thf(f33,plain,(
% 0.15/0.39 ~(ivalid @ (iatom @ p0))),
% 0.15/0.39 inference(rectify,[],[f25])).
% 0.15/0.39 thf(f25,negated_conjecture,(
% 0.15/0.39 ~(ivalid @ (iatom @ p0))),
% 0.15/0.39 inference(negated_conjecture,[],[f24])).
% 0.15/0.39 thf(f24,conjecture,(
% 0.15/0.39 (ivalid @ (iatom @ p0))),
% 0.15/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 0.15/0.39 % SZS output end Proof for theBenchmark
% 0.15/0.39 % (8749)------------------------------
% 0.15/0.39 % (8749)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (8749)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (8749)Memory used [KB]: 5628
% 0.15/0.39 % (8749)Time elapsed: 0.011 s
% 0.15/0.39 % (8749)Instructions burned: 10 (million)
% 0.15/0.39 % (8749)------------------------------
% 0.15/0.39 % (8749)------------------------------
% 0.15/0.39 % (8746)Success in time 0.011 s
% 0.15/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------