TSTP Solution File: SYO061^4 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO061^4 : 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 : 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 09:02:35 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
% 0.07/0.12 % Problem : SYO061^4 : 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
% 0.14/0.35 % 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 : Mon May 20 10:31:23 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 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
% 0.14/0.39 % (21562)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)
% 0.14/0.39 % (21562)Instruction limit reached!
% 0.14/0.39 % (21562)------------------------------
% 0.14/0.39 % (21562)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (21562)Termination reason: Unknown
% 0.14/0.39 % (21562)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (21562)Memory used [KB]: 1023
% 0.14/0.39 % (21562)Time elapsed: 0.005 s
% 0.14/0.39 % (21562)Instructions burned: 3 (million)
% 0.14/0.39 % (21562)------------------------------
% 0.14/0.39 % (21562)------------------------------
% 0.14/0.39 % (21558)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39 % (21555)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.39 % (21556)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)
% 0.14/0.39 % (21559)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)
% 0.14/0.39 % (21561)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.39 % (21557)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)
% 0.14/0.39 % (21560)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)
% 0.14/0.39 % (21558)Instruction limit reached!
% 0.14/0.39 % (21558)------------------------------
% 0.14/0.39 % (21558)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (21558)Termination reason: Unknown
% 0.14/0.39 % (21558)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (21558)Memory used [KB]: 1023
% 0.14/0.39 % (21558)Time elapsed: 0.004 s
% 0.14/0.39 % (21559)Instruction limit reached!
% 0.14/0.39 % (21559)------------------------------
% 0.14/0.39 % (21559)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (21559)Termination reason: Unknown
% 0.14/0.39 % (21559)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (21559)Memory used [KB]: 1023
% 0.14/0.39 % (21559)Time elapsed: 0.004 s
% 0.14/0.39 % (21559)Instructions burned: 2 (million)
% 0.14/0.39 % (21559)------------------------------
% 0.14/0.39 % (21559)------------------------------
% 0.14/0.39 % (21558)Instructions burned: 2 (million)
% 0.14/0.40 % (21558)------------------------------
% 0.14/0.40 % (21558)------------------------------
% 0.14/0.40 % (21556)Instruction limit reached!
% 0.14/0.40 % (21556)------------------------------
% 0.14/0.40 % (21556)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (21556)Termination reason: Unknown
% 0.14/0.40 % (21556)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (21556)Memory used [KB]: 1023
% 0.14/0.40 % (21556)Time elapsed: 0.006 s
% 0.14/0.40 % (21556)Instructions burned: 4 (million)
% 0.14/0.40 % (21556)------------------------------
% 0.14/0.40 % (21556)------------------------------
% 0.21/0.40 % (21560)Refutation not found, incomplete strategy
% 0.21/0.40 % (21560)------------------------------
% 0.21/0.40 % (21560)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.40 % (21560)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.40
% 0.21/0.40
% 0.21/0.40 % (21560)Memory used [KB]: 5500
% 0.21/0.40 % (21560)Time elapsed: 0.007 s
% 0.21/0.40 % (21560)Instructions burned: 4 (million)
% 0.21/0.40 % (21560)------------------------------
% 0.21/0.40 % (21560)------------------------------
% 0.21/0.41 % (21561)First to succeed.
% 0.21/0.41 % (21563)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)
% 0.21/0.41 % (21557)Also succeeded, but the first one will report.
% 0.21/0.41 % (21561)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, irel: $i > $i > $o).
% 0.21/0.41 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_9, type, itrue: $i > $o).
% 0.21/0.41 thf(func_def_10, type, ifalse: $i > $o).
% 0.21/0.41 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.41 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 0.21/0.41 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 0.21/0.41 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 0.21/0.41 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 0.21/0.41 thf(func_def_21, type, a: $i > $o).
% 0.21/0.41 thf(func_def_22, type, b: $i > $o).
% 0.21/0.41 thf(func_def_36, type, sK1: $i > $i).
% 0.21/0.41 thf(f173,plain,(
% 0.21/0.41 $false),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f172])).
% 0.21/0.41 thf(f172,plain,(
% 0.21/0.41 ($true = $false)),
% 0.21/0.41 inference(forward_demodulation,[],[f169,f130])).
% 0.21/0.41 thf(f130,plain,(
% 0.21/0.41 ($false = (b @ sK3))),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f129])).
% 0.21/0.41 thf(f129,plain,(
% 0.21/0.41 ($false = ((irel @ sK2 @ sK3) => (b @ sK3)))),
% 0.21/0.41 inference(beta_eta_normalization,[],[f128])).
% 0.21/0.41 thf(f128,plain,(
% 0.21/0.41 ($false = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (b @ Y0))) @ sK3))),
% 0.21/0.41 inference(sigma_clausification,[],[f122])).
% 0.21/0.41 thf(f122,plain,(
% 0.21/0.41 ((!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (b @ Y0)))) = $false)),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f121])).
% 0.21/0.41 thf(f121,plain,(
% 0.21/0.41 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (b @ Y0))))))),
% 0.21/0.41 inference(beta_eta_normalization,[],[f120])).
% 0.21/0.41 thf(f120,plain,(
% 0.21/0.41 ($false = ((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (b @ Y1)))))) @ sK2))),
% 0.21/0.41 inference(sigma_clausification,[],[f119])).
% 0.21/0.41 thf(f119,plain,(
% 0.21/0.41 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (b @ Y1))))))))),
% 0.21/0.41 inference(beta_eta_normalization,[],[f105])).
% 0.21/0.41 thf(f105,plain,(
% 0.21/0.41 (((^[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)) @ a) @ ((^[Y0 : $i > $o]: (Y0)) @ b))) != $true)),
% 0.21/0.41 inference(definition_unfolding,[],[f80,f82,f101,f89,f89])).
% 0.21/0.41 thf(f89,plain,(
% 0.21/0.41 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.21/0.41 inference(cnf_transformation,[],[f69])).
% 0.21/0.41 thf(f69,plain,(
% 0.21/0.41 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.21/0.41 inference(fool_elimination,[],[f68])).
% 0.21/0.41 thf(f68,plain,(
% 0.21/0.41 ((^[X0 : $i > $o] : (X0)) = iatom)),
% 0.21/0.41 inference(rectify,[],[f8])).
% 0.21/0.41 thf(f8,axiom,(
% 0.21/0.41 ((^[X5 : $i > $o] : (X5)) = iatom)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iatom)).
% 0.21/0.41 thf(f101,plain,(
% 0.21/0.41 (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))))))),
% 0.21/0.41 inference(definition_unfolding,[],[f90,f96,f95,f95])).
% 0.21/0.41 thf(f95,plain,(
% 0.21/0.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f37])).
% 0.21/0.41 thf(f37,plain,(
% 0.21/0.41 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.21/0.41 inference(fool_elimination,[],[f36])).
% 0.21/0.41 thf(f36,plain,(
% 0.21/0.41 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((irel @ X1 @ X2) => (X0 @ X2)))) = mbox_s4)),
% 0.21/0.41 inference(rectify,[],[f7])).
% 0.21/0.41 thf(f7,axiom,(
% 0.21/0.41 ((^[X5 : $i > $o, X0 : $i] : (! [X1] : ((irel @ X0 @ X1) => (X5 @ X1)))) = mbox_s4)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s4)).
% 0.21/0.41 thf(f96,plain,(
% 0.21/0.41 (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)))))),
% 0.21/0.41 inference(definition_unfolding,[],[f84,f88,f85])).
% 0.21/0.41 thf(f85,plain,(
% 0.21/0.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f39])).
% 0.21/0.41 thf(f39,plain,(
% 0.21/0.41 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.41 inference(fool_elimination,[],[f38])).
% 0.21/0.41 thf(f38,plain,(
% 0.21/0.41 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.41 inference(rectify,[],[f3])).
% 0.21/0.41 thf(f3,axiom,(
% 0.21/0.41 ((^[X0 : $i > $o, X3 : $i] : (~(X0 @ X3))) = mnot)),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.21/0.41 thf(f88,plain,(
% 0.21/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f45])).
% 0.21/0.41 thf(f45,plain,(
% 0.21/0.41 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.21/0.41 inference(fool_elimination,[],[f44])).
% 0.21/0.41 thf(f44,plain,(
% 0.21/0.41 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.21/0.41 inference(rectify,[],[f4])).
% 0.21/0.41 thf(f4,axiom,(
% 0.21/0.41 (mor = (^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X1 @ X3) | (X0 @ X3))))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.21/0.41 thf(f84,plain,(
% 0.21/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.41 inference(cnf_transformation,[],[f63])).
% 0.21/0.41 thf(f63,plain,(
% 0.21/0.41 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.41 inference(fool_elimination,[],[f62])).
% 0.21/0.41 thf(f62,plain,(
% 0.21/0.41 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.21/0.41 inference(rectify,[],[f6])).
% 0.21/0.41 thf(f6,axiom,(
% 0.21/0.41 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.41 thf(f90,plain,(
% 0.21/0.41 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.21/0.41 inference(cnf_transformation,[],[f67])).
% 0.21/0.41 thf(f67,plain,(
% 0.21/0.41 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.21/0.41 inference(fool_elimination,[],[f66])).
% 0.21/0.41 thf(f66,plain,(
% 0.21/0.41 (iimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))))),
% 0.21/0.41 inference(rectify,[],[f14])).
% 0.21/0.41 thf(f14,axiom,(
% 0.21/0.41 (iimplies = (^[X5 : $i > $o, X7 : $i > $o] : (mimplies @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplies)).
% 0.21/0.41 thf(f82,plain,(
% 0.21/0.41 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.41 inference(cnf_transformation,[],[f47])).
% 0.21/0.41 thf(f47,plain,(
% 0.21/0.41 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.41 inference(fool_elimination,[],[f46])).
% 0.21/0.41 thf(f46,plain,(
% 0.21/0.41 (ivalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.21/0.41 inference(rectify,[],[f18])).
% 0.21/0.41 thf(f18,axiom,(
% 0.21/0.41 (ivalid = (^[X8 : $i > $o] : (! [X6] : (X8 @ X6))))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ivalid)).
% 0.21/0.41 thf(f80,plain,(
% 0.21/0.41 ((ivalid @ (iimplies @ (iatom @ a) @ (iatom @ b))) != $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f70])).
% 0.21/0.41 thf(f70,plain,(
% 0.21/0.41 ((ivalid @ (iimplies @ (iatom @ a) @ (iatom @ b))) != $true)),
% 0.21/0.41 inference(flattening,[],[f41])).
% 0.21/0.41 thf(f41,plain,(
% 0.21/0.41 ~((ivalid @ (iimplies @ (iatom @ a) @ (iatom @ b))) = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f40])).
% 0.21/0.41 thf(f40,plain,(
% 0.21/0.41 ~(ivalid @ (iimplies @ (iatom @ a) @ (iatom @ b)))),
% 0.21/0.41 inference(rectify,[],[f24])).
% 0.21/0.41 thf(f24,negated_conjecture,(
% 0.21/0.41 ~(ivalid @ (iimplies @ (iatom @ a) @ (iatom @ b)))),
% 0.21/0.41 inference(negated_conjecture,[],[f23])).
% 0.21/0.41 thf(f23,conjecture,(
% 0.21/0.41 (ivalid @ (iimplies @ (iatom @ a) @ (iatom @ b)))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',con)).
% 0.21/0.41 thf(f169,plain,(
% 0.21/0.41 ($true = (b @ sK3))),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f161])).
% 0.21/0.41 thf(f161,plain,(
% 0.21/0.41 ($true = $false) | ($true = (b @ sK3))),
% 0.21/0.41 inference(superposition,[],[f159,f131])).
% 0.21/0.41 thf(f131,plain,(
% 0.21/0.41 ($true = (irel @ sK2 @ sK3))),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f129])).
% 0.21/0.41 thf(f159,plain,(
% 0.21/0.41 ( ! [X0 : $i] : (($false = (irel @ sK2 @ X0)) | ($true = (b @ X0))) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f156])).
% 0.21/0.41 thf(f156,plain,(
% 0.21/0.41 ( ! [X0 : $i] : (($true = $false) | ($false = (irel @ sK2 @ X0)) | ($true = (b @ X0))) )),
% 0.21/0.41 inference(superposition,[],[f155,f117])).
% 0.21/0.41 thf(f117,plain,(
% 0.21/0.41 ( ! [X2 : $i,X1 : $i] : (((a @ (sK1 @ X1)) = $false) | ($true = (b @ X2)) | ((irel @ X1 @ X2) = $false)) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f116])).
% 0.21/0.41 thf(f116,plain,(
% 0.21/0.41 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ (sK1 @ X1)) => (a @ (sK1 @ X1))) = $false) | ($true = (b @ X2)) | ((irel @ X1 @ X2) = $false)) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f115])).
% 0.21/0.41 thf(f115,plain,(
% 0.21/0.41 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => (a @ Y0))) @ (sK1 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (b @ X2))) )),
% 0.21/0.41 inference(sigma_clausification,[],[f114])).
% 0.21/0.41 thf(f114,plain,(
% 0.21/0.41 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a @ Y0))))) | ((irel @ X1 @ X2) = $false) | ($true = (b @ X2))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f113])).
% 0.21/0.41 thf(f113,plain,(
% 0.21/0.41 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => (b @ X2))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a @ Y0)))))) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f112])).
% 0.21/0.41 thf(f112,plain,(
% 0.21/0.41 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a @ Y0))))) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (b @ Y0))) @ X2) = $true)) )),
% 0.21/0.41 inference(pi_clausification,[],[f111])).
% 0.21/0.41 thf(f111,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (b @ Y0))))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a @ Y0)))))) )),
% 0.21/0.41 inference(not_proxy_clausification,[],[f110])).
% 0.21/0.41 thf(f110,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (b @ Y0)))))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f109])).
% 0.21/0.41 thf(f109,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (a @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (b @ Y0))))))) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f108])).
% 0.21/0.41 thf(f108,plain,(
% 0.21/0.41 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (b @ Y1)))))) @ X1) = $true)) )),
% 0.21/0.41 inference(pi_clausification,[],[f107])).
% 0.21/0.41 thf(f107,plain,(
% 0.21/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (a @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (b @ Y1))))))))),
% 0.21/0.41 inference(beta_eta_normalization,[],[f106])).
% 0.21/0.41 thf(f106,plain,(
% 0.21/0.41 (((^[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)) @ a) @ ((^[Y0 : $i > $o]: (Y0)) @ b))) = $true)),
% 0.21/0.41 inference(definition_unfolding,[],[f83,f82,f101,f89,f89])).
% 0.21/0.41 thf(f83,plain,(
% 0.21/0.41 ((ivalid @ (iimplies @ (iatom @ a) @ (iatom @ b))) = $true)),
% 0.21/0.41 inference(cnf_transformation,[],[f57])).
% 0.21/0.41 thf(f57,plain,(
% 0.21/0.41 ((ivalid @ (iimplies @ (iatom @ a) @ (iatom @ b))) = $true)),
% 0.21/0.41 inference(fool_elimination,[],[f56])).
% 0.21/0.41 thf(f56,plain,(
% 0.21/0.41 (ivalid @ (iimplies @ (iatom @ a) @ (iatom @ b)))),
% 0.21/0.41 inference(rectify,[],[f22])).
% 0.21/0.41 thf(f22,axiom,(
% 0.21/0.41 (ivalid @ (iimplies @ (iatom @ a) @ (iatom @ b)))),
% 0.21/0.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1)).
% 0.21/0.41 thf(f155,plain,(
% 0.21/0.41 ($true = (a @ (sK1 @ sK2)))),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f152])).
% 0.21/0.41 thf(f152,plain,(
% 0.21/0.41 ($true = $false) | ($true = (a @ (sK1 @ sK2)))),
% 0.21/0.41 inference(superposition,[],[f150,f127])).
% 0.21/0.41 thf(f127,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (((irel @ sK2 @ X1) = $false) | ($true = (a @ X1))) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f126])).
% 0.21/0.41 thf(f126,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($true = ((irel @ sK2 @ X1) => (a @ X1)))) )),
% 0.21/0.41 inference(beta_eta_normalization,[],[f125])).
% 0.21/0.41 thf(f125,plain,(
% 0.21/0.41 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a @ Y0))) @ X1))) )),
% 0.21/0.41 inference(pi_clausification,[],[f124])).
% 0.21/0.41 thf(f124,plain,(
% 0.21/0.41 ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a @ Y0)))))),
% 0.21/0.41 inference(not_proxy_clausification,[],[f123])).
% 0.21/0.41 thf(f123,plain,(
% 0.21/0.41 ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ sK2 @ Y0) => (a @ Y0))))) = $false)),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f121])).
% 0.21/0.41 thf(f150,plain,(
% 0.21/0.41 ($true = (irel @ sK2 @ (sK1 @ sK2)))),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f144])).
% 0.21/0.41 thf(f144,plain,(
% 0.21/0.41 ($true = (irel @ sK2 @ (sK1 @ sK2))) | ($true = $false)),
% 0.21/0.41 inference(superposition,[],[f143,f131])).
% 0.21/0.41 thf(f143,plain,(
% 0.21/0.41 ( ! [X0 : $i] : (($false = (irel @ X0 @ sK3)) | ($true = (irel @ X0 @ (sK1 @ X0)))) )),
% 0.21/0.41 inference(trivial_inequality_removal,[],[f141])).
% 0.21/0.41 thf(f141,plain,(
% 0.21/0.41 ( ! [X0 : $i] : (($true = (irel @ X0 @ (sK1 @ X0))) | ($true = $false) | ($false = (irel @ X0 @ sK3))) )),
% 0.21/0.41 inference(superposition,[],[f130,f118])).
% 0.21/0.41 thf(f118,plain,(
% 0.21/0.41 ( ! [X2 : $i,X1 : $i] : (($true = (b @ X2)) | ((irel @ X1 @ (sK1 @ X1)) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.21/0.41 inference(binary_proxy_clausification,[],[f116])).
% 0.21/0.41 % SZS output end Proof for theBenchmark
% 0.21/0.41 % (21561)------------------------------
% 0.21/0.41 % (21561)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.41 % (21561)Termination reason: Refutation
% 0.21/0.41
% 0.21/0.41 % (21561)Memory used [KB]: 5628
% 0.21/0.41 % (21561)Time elapsed: 0.018 s
% 0.21/0.41 % (21561)Instructions burned: 10 (million)
% 0.21/0.41 % (21561)------------------------------
% 0.21/0.41 % (21561)------------------------------
% 0.21/0.41 % (21554)Success in time 0.031 s
% 0.21/0.41 % Vampire---4.8 exiting
%------------------------------------------------------------------------------