TSTP Solution File: LCL588^1 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : LCL588^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n032.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 : Mon Jun 24 11:27:01 EDT 2024
% Result : Theorem 0.15s 0.32s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : LCL588^1 : TPTP v8.2.0. Released v3.6.0.
% 0.03/0.10 % Command : run_vampire %s %d THM
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Sat Jun 22 16:08:09 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.09/0.30 This is a TH0_THM_EQU_NAR problem
% 0.09/0.30 Running higher-order theorem proving
% 0.09/0.30 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.09/0.31 % (12292)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.09/0.31 % (12293)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)
% 0.09/0.31 % (12294)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)
% 0.09/0.31 % (12296)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)
% 0.09/0.31 % (12297)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)
% 0.09/0.31 % (12295)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.09/0.31 % (12298)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.09/0.31 % (12295)Instruction limit reached!
% 0.09/0.31 % (12295)------------------------------
% 0.09/0.31 % (12295)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.09/0.31 % (12295)Termination reason: Unknown
% 0.09/0.31 % (12295)Termination phase: Function definition elimination
% 0.09/0.31
% 0.09/0.31 % (12295)Memory used [KB]: 1023
% 0.09/0.31 % (12295)Time elapsed: 0.003 s
% 0.09/0.31 % (12295)Instructions burned: 3 (million)
% 0.09/0.31 % (12295)------------------------------
% 0.09/0.31 % (12295)------------------------------
% 0.09/0.31 % (12296)Instruction limit reached!
% 0.09/0.31 % (12296)------------------------------
% 0.09/0.31 % (12296)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.09/0.31 % (12296)Termination reason: Unknown
% 0.09/0.31 % (12296)Termination phase: Property scanning
% 0.09/0.31
% 0.09/0.31 % (12296)Memory used [KB]: 1023
% 0.09/0.31 % (12296)Time elapsed: 0.003 s
% 0.09/0.31 % (12296)Instructions burned: 3 (million)
% 0.09/0.31 % (12296)------------------------------
% 0.09/0.31 % (12296)------------------------------
% 0.15/0.31 % (12297)Refutation not found, incomplete strategy
% 0.15/0.31 % (12297)------------------------------
% 0.15/0.31 % (12297)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.31 % (12297)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.31
% 0.15/0.31
% 0.15/0.31 % (12297)Memory used [KB]: 5500
% 0.15/0.31 % (12297)Time elapsed: 0.003 s
% 0.15/0.31 % (12297)Instructions burned: 3 (million)
% 0.15/0.31 % (12297)------------------------------
% 0.15/0.31 % (12297)------------------------------
% 0.15/0.31 % (12293)Instruction limit reached!
% 0.15/0.31 % (12293)------------------------------
% 0.15/0.31 % (12293)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.31 % (12293)Termination reason: Unknown
% 0.15/0.31 % (12293)Termination phase: Saturation
% 0.15/0.31
% 0.15/0.31 % (12293)Memory used [KB]: 5500
% 0.15/0.31 % (12293)Time elapsed: 0.004 s
% 0.15/0.31 % (12293)Instructions burned: 5 (million)
% 0.15/0.31 % (12293)------------------------------
% 0.15/0.31 % (12293)------------------------------
% 0.15/0.31 % (12292)First to succeed.
% 0.15/0.32 % (12298)Also succeeded, but the first one will report.
% 0.15/0.32 % (12292)Refutation found. Thanks to Tanya!
% 0.15/0.32 % SZS status Theorem for theBenchmark
% 0.15/0.32 % SZS output start Proof for theBenchmark
% 0.15/0.32 thf(type_def_6, type, individuals: $tType).
% 0.15/0.32 thf(func_def_1, type, prop_a: $i > $o).
% 0.15/0.32 thf(func_def_2, type, prop_b: $i > $o).
% 0.15/0.32 thf(func_def_3, type, prop_c: $i > $o).
% 0.15/0.32 thf(func_def_4, type, mfalse: $i > $o).
% 0.15/0.32 thf(func_def_5, type, mtrue: $i > $o).
% 0.15/0.32 thf(func_def_6, type, mnot: ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_8, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_9, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_10, type, mimpl: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_11, type, miff: ($i > $o) > ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_12, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_13, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_14, type, individuals: $tType).
% 0.15/0.32 thf(func_def_15, type, mall: (individuals > $i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_16, type, mexists: (individuals > $i > $o) > $i > $o).
% 0.15/0.32 thf(func_def_17, type, mvalid: ($i > $o) > $o).
% 0.15/0.32 thf(func_def_18, type, msatisfiable: ($i > $o) > $o).
% 0.15/0.32 thf(func_def_19, type, mcountersatisfiable: ($i > $o) > $o).
% 0.15/0.32 thf(func_def_20, type, minvalid: ($i > $o) > $o).
% 0.15/0.32 thf(func_def_21, type, a: $i > $o).
% 0.15/0.32 thf(func_def_22, type, b: $i > $o).
% 0.15/0.32 thf(func_def_23, type, r: $i > $i > $o).
% 0.15/0.32 thf(f117,plain,(
% 0.15/0.32 $false),
% 0.15/0.32 inference(avatar_sat_refutation,[],[f96,f106,f116])).
% 0.15/0.32 thf(f116,plain,(
% 0.15/0.32 ~spl0_1),
% 0.15/0.32 inference(avatar_contradiction_clause,[],[f115])).
% 0.15/0.32 thf(f115,plain,(
% 0.15/0.32 $false | ~spl0_1),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f111])).
% 0.15/0.32 thf(f111,plain,(
% 0.15/0.32 ($false = $true) | ~spl0_1),
% 0.15/0.32 inference(superposition,[],[f110,f89])).
% 0.15/0.32 thf(f89,plain,(
% 0.15/0.32 ((a @ sK2) = $true)),
% 0.15/0.32 inference(not_proxy_clausification,[],[f88])).
% 0.15/0.32 thf(f88,plain,(
% 0.15/0.32 ($false = (~ (a @ sK2)))),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f85])).
% 0.15/0.32 thf(f85,plain,(
% 0.15/0.32 (((~ (a @ sK2)) | (b @ sK2)) = $false)),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f84])).
% 0.15/0.32 thf(f84,plain,(
% 0.15/0.32 (((r @ sK1 @ sK2) => ((~ (a @ sK2)) | (b @ sK2))) = $false)),
% 0.15/0.32 inference(beta_eta_normalization,[],[f83])).
% 0.15/0.32 thf(f83,plain,(
% 0.15/0.32 ($false = ((^[Y0 : $i]: ((r @ sK1 @ Y0) => ((~ (a @ Y0)) | (b @ Y0)))) @ sK2))),
% 0.15/0.32 inference(sigma_clausification,[],[f72])).
% 0.15/0.32 thf(f72,plain,(
% 0.15/0.32 ($false = (!! @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) => ((~ (a @ Y0)) | (b @ Y0))))))),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f71])).
% 0.15/0.32 thf(f71,plain,(
% 0.15/0.32 ($false = ((~ ((~ (?? @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) & (a @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) => (b @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) => ((~ (a @ Y0)) | (b @ Y0)))))))),
% 0.15/0.32 inference(beta_eta_normalization,[],[f70])).
% 0.15/0.32 thf(f70,plain,(
% 0.15/0.32 ($false = ((^[Y0 : $i]: ((~ ((~ (?? @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) & (a @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (b @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => ((~ (a @ Y1)) | (b @ Y1))))))) @ sK1))),
% 0.15/0.32 inference(sigma_clausification,[],[f69])).
% 0.15/0.32 thf(f69,plain,(
% 0.15/0.32 ($true != (!! @ $i @ (^[Y0 : $i]: ((~ ((~ (?? @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) & (a @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => (b @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((r @ Y0 @ Y1) => ((~ (a @ Y1)) | (b @ Y1)))))))))),
% 0.15/0.32 inference(beta_eta_normalization,[],[f68])).
% 0.15/0.32 thf(f68,plain,(
% 0.15/0.32 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[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)))) @ ((^[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)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))) @ r @ a) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ r @ b)) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))) @ r @ ((^[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)))) @ a @ b)))) != $true)),
% 0.15/0.32 inference(definition_unfolding,[],[f65,f55,f66,f66,f53,f52,f52,f66])).
% 0.15/0.32 thf(f52,plain,(
% 0.15/0.32 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.15/0.32 inference(cnf_transformation,[],[f36])).
% 0.15/0.32 thf(f36,plain,(
% 0.15/0.32 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) => (Y1 @ Y3))))))))))),
% 0.15/0.32 inference(fool_elimination,[],[f35])).
% 0.15/0.32 thf(f35,plain,(
% 0.15/0.32 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X0 @ X2 @ X3) => (X1 @ X3)))) = mbox)),
% 0.15/0.32 inference(rectify,[],[f8])).
% 0.15/0.32 thf(f8,axiom,(
% 0.15/0.32 ((^[X4 : $i > $i > $o, X5 : $i > $o, X0 : $i] : (! [X2] : ((X4 @ X0 @ X2) => (X5 @ X2)))) = mbox)),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.15/0.32 thf(f53,plain,(
% 0.15/0.32 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 0.15/0.32 inference(cnf_transformation,[],[f32])).
% 0.15/0.32 thf(f32,plain,(
% 0.15/0.32 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y2 @ Y3) & (Y1 @ Y3))))))))))),
% 0.15/0.32 inference(fool_elimination,[],[f31])).
% 0.15/0.32 thf(f31,plain,(
% 0.15/0.32 (mdia = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (? [X3] : ((X1 @ X3) & (X0 @ X2 @ X3)))))),
% 0.15/0.32 inference(rectify,[],[f9])).
% 0.15/0.32 thf(f9,axiom,(
% 0.15/0.32 (mdia = (^[X4 : $i > $i > $o, X5 : $i > $o, X0 : $i] : (? [X2] : ((X5 @ X2) & (X4 @ X0 @ X2)))))),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia)).
% 0.15/0.32 thf(f66,plain,(
% 0.15/0.32 (mimpl = (^[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)))))),
% 0.15/0.32 inference(definition_unfolding,[],[f60,f63,f54])).
% 0.15/0.32 thf(f54,plain,(
% 0.15/0.32 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.32 inference(cnf_transformation,[],[f43])).
% 0.15/0.32 thf(f43,plain,(
% 0.15/0.32 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.15/0.32 inference(fool_elimination,[],[f42])).
% 0.15/0.32 thf(f42,plain,(
% 0.15/0.32 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.15/0.32 inference(rectify,[],[f3])).
% 0.15/0.32 thf(f3,axiom,(
% 0.15/0.32 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.15/0.32 thf(f63,plain,(
% 0.15/0.32 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.32 inference(cnf_transformation,[],[f34])).
% 0.15/0.32 thf(f34,plain,(
% 0.15/0.32 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.15/0.32 inference(fool_elimination,[],[f33])).
% 0.15/0.32 thf(f33,plain,(
% 0.15/0.32 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.15/0.32 inference(rectify,[],[f4])).
% 0.15/0.32 thf(f4,axiom,(
% 0.15/0.32 (mor = (^[X0 : $i > $o, X2 : $i > $o, X1 : $i] : ((X2 @ X1) | (X0 @ X1))))),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.15/0.32 thf(f60,plain,(
% 0.15/0.32 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.32 inference(cnf_transformation,[],[f20])).
% 0.15/0.32 thf(f20,plain,(
% 0.15/0.32 (mimpl = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.15/0.32 inference(fool_elimination,[],[f19])).
% 0.15/0.32 thf(f19,plain,(
% 0.15/0.32 (mimpl = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.15/0.32 inference(rectify,[],[f6])).
% 0.15/0.32 thf(f6,axiom,(
% 0.15/0.32 (mimpl = (^[X1 : $i > $o, X3 : $i > $o] : (mor @ (mnot @ X1) @ X3)))),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimpl)).
% 0.15/0.32 thf(f55,plain,(
% 0.15/0.32 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.32 inference(cnf_transformation,[],[f38])).
% 0.15/0.32 thf(f38,plain,(
% 0.15/0.32 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.15/0.32 inference(fool_elimination,[],[f37])).
% 0.15/0.32 thf(f37,plain,(
% 0.15/0.32 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.15/0.32 inference(rectify,[],[f12])).
% 0.15/0.32 thf(f12,axiom,(
% 0.15/0.32 (mvalid = (^[X5 : $i > $o] : (! [X6] : (X5 @ X6))))),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.15/0.32 thf(f65,plain,(
% 0.15/0.32 ((mvalid @ (mimpl @ (mimpl @ (mdia @ r @ a) @ (mbox @ r @ b)) @ (mbox @ r @ (mimpl @ a @ b)))) != $true)),
% 0.15/0.32 inference(cnf_transformation,[],[f49])).
% 0.15/0.32 thf(f49,plain,(
% 0.15/0.32 ((mvalid @ (mimpl @ (mimpl @ (mdia @ r @ a) @ (mbox @ r @ b)) @ (mbox @ r @ (mimpl @ a @ b)))) != $true)),
% 0.15/0.32 inference(flattening,[],[f28])).
% 0.15/0.32 thf(f28,plain,(
% 0.15/0.32 ~((mvalid @ (mimpl @ (mimpl @ (mdia @ r @ a) @ (mbox @ r @ b)) @ (mbox @ r @ (mimpl @ a @ b)))) = $true)),
% 0.15/0.32 inference(fool_elimination,[],[f27])).
% 0.15/0.32 thf(f27,plain,(
% 0.15/0.32 ~(mvalid @ (mimpl @ (mimpl @ (mdia @ r @ a) @ (mbox @ r @ b)) @ (mbox @ r @ (mimpl @ a @ b))))),
% 0.15/0.32 inference(rectify,[],[f17])).
% 0.15/0.32 thf(f17,negated_conjecture,(
% 0.15/0.32 ~(mvalid @ (mimpl @ (mimpl @ (mdia @ r @ a) @ (mbox @ r @ b)) @ (mbox @ r @ (mimpl @ a @ b))))),
% 0.15/0.32 inference(negated_conjecture,[],[f16])).
% 0.15/0.32 thf(f16,conjecture,(
% 0.15/0.32 (mvalid @ (mimpl @ (mimpl @ (mdia @ r @ a) @ (mbox @ r @ b)) @ (mbox @ r @ (mimpl @ a @ b))))),
% 0.15/0.32 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm)).
% 0.15/0.32 thf(f110,plain,(
% 0.15/0.32 ((a @ sK2) = $false) | ~spl0_1),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f107])).
% 0.15/0.32 thf(f107,plain,(
% 0.15/0.32 ($false = $true) | ((a @ sK2) = $false) | ~spl0_1),
% 0.15/0.32 inference(superposition,[],[f92,f86])).
% 0.15/0.32 thf(f86,plain,(
% 0.15/0.32 ($true = (r @ sK1 @ sK2))),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f84])).
% 0.15/0.32 thf(f92,plain,(
% 0.15/0.32 ( ! [X2 : $i] : (($false = (r @ sK1 @ X2)) | ($false = (a @ X2))) ) | ~spl0_1),
% 0.15/0.32 inference(avatar_component_clause,[],[f91])).
% 0.15/0.32 thf(f91,plain,(
% 0.15/0.32 spl0_1 <=> ! [X2] : (($false = (a @ X2)) | ($false = (r @ sK1 @ X2)))),
% 0.15/0.32 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.15/0.32 thf(f106,plain,(
% 0.15/0.32 ~spl0_2),
% 0.15/0.32 inference(avatar_contradiction_clause,[],[f105])).
% 0.15/0.32 thf(f105,plain,(
% 0.15/0.32 $false | ~spl0_2),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f101])).
% 0.15/0.32 thf(f101,plain,(
% 0.15/0.32 ($false = $true) | ~spl0_2),
% 0.15/0.32 inference(superposition,[],[f100,f87])).
% 0.15/0.32 thf(f87,plain,(
% 0.15/0.32 ($false = (b @ sK2))),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f85])).
% 0.15/0.32 thf(f100,plain,(
% 0.15/0.32 ($true = (b @ sK2)) | ~spl0_2),
% 0.15/0.32 inference(trivial_inequality_removal,[],[f98])).
% 0.15/0.32 thf(f98,plain,(
% 0.15/0.32 ($false = $true) | ($true = (b @ sK2)) | ~spl0_2),
% 0.15/0.32 inference(superposition,[],[f95,f86])).
% 0.15/0.32 thf(f95,plain,(
% 0.15/0.32 ( ! [X1 : $i] : (((r @ sK1 @ X1) = $false) | ($true = (b @ X1))) ) | ~spl0_2),
% 0.15/0.32 inference(avatar_component_clause,[],[f94])).
% 0.15/0.32 thf(f94,plain,(
% 0.15/0.32 spl0_2 <=> ! [X1] : (($true = (b @ X1)) | ((r @ sK1 @ X1) = $false))),
% 0.15/0.32 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.15/0.32 thf(f96,plain,(
% 0.15/0.32 spl0_1 | spl0_2),
% 0.15/0.32 inference(avatar_split_clause,[],[f82,f94,f91])).
% 0.15/0.32 thf(f82,plain,(
% 0.15/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (b @ X1)) | ($false = (a @ X2)) | ((r @ sK1 @ X1) = $false) | ($false = (r @ sK1 @ X2))) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f81])).
% 0.15/0.32 thf(f81,plain,(
% 0.15/0.32 ( ! [X2 : $i,X1 : $i] : (($false = (a @ X2)) | (((r @ sK1 @ X1) => (b @ X1)) = $true) | ($false = (r @ sK1 @ X2))) )),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f80])).
% 0.15/0.32 thf(f80,plain,(
% 0.15/0.32 ( ! [X2 : $i,X1 : $i] : (($false = ((r @ sK1 @ X2) & (a @ X2))) | (((r @ sK1 @ X1) => (b @ X1)) = $true)) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f79])).
% 0.15/0.32 thf(f79,plain,(
% 0.15/0.32 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((r @ sK1 @ Y0) & (a @ Y0))) @ X2)) | (((r @ sK1 @ X1) => (b @ X1)) = $true)) )),
% 0.15/0.32 inference(pi_clausification,[],[f78])).
% 0.15/0.32 thf(f78,plain,(
% 0.15/0.32 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) & (a @ Y0)))) = $false) | (((r @ sK1 @ X1) => (b @ X1)) = $true)) )),
% 0.15/0.32 inference(beta_eta_normalization,[],[f77])).
% 0.15/0.32 thf(f77,plain,(
% 0.15/0.32 ( ! [X1 : $i] : (((?? @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) & (a @ Y0)))) = $false) | ($true = ((^[Y0 : $i]: ((r @ sK1 @ Y0) => (b @ Y0))) @ X1))) )),
% 0.15/0.32 inference(pi_clausification,[],[f76])).
% 0.15/0.32 thf(f76,plain,(
% 0.15/0.32 ((!! @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) => (b @ Y0)))) = $true) | ((?? @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) & (a @ Y0)))) = $false)),
% 0.15/0.32 inference(not_proxy_clausification,[],[f75])).
% 0.15/0.32 thf(f75,plain,(
% 0.15/0.32 ($true = (~ (?? @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) & (a @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) => (b @ Y0)))) = $true)),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f74])).
% 0.15/0.32 thf(f74,plain,(
% 0.15/0.32 (((~ (?? @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) & (a @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) => (b @ Y0))))) = $true)),
% 0.15/0.32 inference(not_proxy_clausification,[],[f73])).
% 0.15/0.32 thf(f73,plain,(
% 0.15/0.32 ($false = (~ ((~ (?? @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) & (a @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((r @ sK1 @ Y0) => (b @ Y0)))))))),
% 0.15/0.32 inference(binary_proxy_clausification,[],[f71])).
% 0.15/0.32 % SZS output end Proof for theBenchmark
% 0.15/0.32 % (12292)------------------------------
% 0.15/0.32 % (12292)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.15/0.32 % (12292)Termination reason: Refutation
% 0.15/0.32
% 0.15/0.32 % (12292)Memory used [KB]: 5628
% 0.15/0.32 % (12292)Time elapsed: 0.006 s
% 0.15/0.32 % (12292)Instructions burned: 5 (million)
% 0.15/0.32 % (12292)------------------------------
% 0.15/0.32 % (12292)------------------------------
% 0.15/0.32 % (12291)Success in time 0.005 s
%------------------------------------------------------------------------------