TSTP Solution File: LCL714^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL714^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n017.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 00:22:20 EDT 2024
% Result : Theorem 0.14s 0.42s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL714^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.08/0.15 % 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
% 0.14/0.38 % Computer : n017.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8042.1875MB
% 0.14/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Mon May 20 01:18:38 EDT 2024
% 0.14/0.38 % CPUTime :
% 0.14/0.38 This is a TH0_THM_EQU_NAR problem
% 0.14/0.38 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
% 0.14/0.40 % (26452)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.40 % (26453)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)
% 0.14/0.40 % (26454)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)
% 0.14/0.40 % (26455)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.40 % (26456)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)
% 0.14/0.40 % (26457)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)
% 0.14/0.40 % (26458)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.40 % (26459)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)
% 0.14/0.40 % (26455)Instruction limit reached!
% 0.14/0.40 % (26455)------------------------------
% 0.14/0.40 % (26455)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (26455)Termination reason: Unknown
% 0.14/0.40 % (26455)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.40 % (26456)Instruction limit reached!
% 0.14/0.40 % (26456)------------------------------
% 0.14/0.40 % (26456)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (26456)Termination reason: Unknown
% 0.14/0.40 % (26456)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.40 % (26456)Memory used [KB]: 1023
% 0.14/0.40 % (26456)Time elapsed: 0.003 s
% 0.14/0.40 % (26456)Instructions burned: 2 (million)
% 0.14/0.40 % (26456)------------------------------
% 0.14/0.40 % (26456)------------------------------
% 0.14/0.40 % (26455)Memory used [KB]: 1023
% 0.14/0.40 % (26455)Time elapsed: 0.003 s
% 0.14/0.40 % (26455)Instructions burned: 2 (million)
% 0.14/0.40 % (26455)------------------------------
% 0.14/0.40 % (26455)------------------------------
% 0.14/0.41 % (26453)Instruction limit reached!
% 0.14/0.41 % (26453)------------------------------
% 0.14/0.41 % (26453)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (26453)Termination reason: Unknown
% 0.14/0.41 % (26453)Termination phase: Property scanning
% 0.14/0.41
% 0.14/0.41 % (26453)Memory used [KB]: 1023
% 0.14/0.41 % (26453)Time elapsed: 0.004 s
% 0.14/0.41 % (26453)Instructions burned: 4 (million)
% 0.14/0.41 % (26453)------------------------------
% 0.14/0.41 % (26453)------------------------------
% 0.14/0.41 % (26459)Instruction limit reached!
% 0.14/0.41 % (26459)------------------------------
% 0.14/0.41 % (26459)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (26459)Termination reason: Unknown
% 0.14/0.41 % (26459)Termination phase: shuffling
% 0.14/0.41
% 0.14/0.41 % (26459)Memory used [KB]: 1023
% 0.14/0.41 % (26459)Time elapsed: 0.003 s
% 0.14/0.41 % (26459)Instructions burned: 4 (million)
% 0.14/0.41 % (26459)------------------------------
% 0.14/0.41 % (26459)------------------------------
% 0.14/0.41 % (26457)First to succeed.
% 0.14/0.41 % (26458)Instruction limit reached!
% 0.14/0.41 % (26458)------------------------------
% 0.14/0.41 % (26458)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.41 % (26458)Termination reason: Unknown
% 0.14/0.41 % (26458)Termination phase: Saturation
% 0.14/0.41
% 0.14/0.41 % (26458)Memory used [KB]: 5756
% 0.14/0.41 % (26458)Time elapsed: 0.012 s
% 0.14/0.41 % (26458)Instructions burned: 18 (million)
% 0.14/0.41 % (26458)------------------------------
% 0.14/0.41 % (26458)------------------------------
% 0.14/0.42 % (26452)Also succeeded, but the first one will report.
% 0.14/0.42 % (26457)Refutation found. Thanks to Tanya!
% 0.14/0.42 % SZS status Theorem for theBenchmark
% 0.14/0.42 % SZS output start Proof for theBenchmark
% 0.14/0.42 thf(type_def_5, type, mu: $tType).
% 0.14/0.42 thf(func_def_0, type, mu: $tType).
% 0.14/0.42 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.42 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.42 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.42 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.42 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.42 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.42 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.42 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.42 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.42 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.14/0.42 thf(func_def_53, type, ph5: !>[X0: $tType]:(X0)).
% 0.14/0.42 thf(f251,plain,(
% 0.14/0.42 $false),
% 0.14/0.42 inference(subsumption_resolution,[],[f250,f123])).
% 0.14/0.42 thf(f123,plain,(
% 0.14/0.42 (sK4 != sK3)),
% 0.14/0.42 inference(equality_proxy_clausification,[],[f119])).
% 0.14/0.42 thf(f119,plain,(
% 0.14/0.42 ($false = (sK4 = sK3))),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f118])).
% 0.14/0.42 thf(f118,plain,(
% 0.14/0.42 ($false = (((sK0 @ sK2 @ sK4) & (sK0 @ sK2 @ sK3)) => (sK4 = sK3)))),
% 0.14/0.42 inference(beta_eta_normalization,[],[f117])).
% 0.14/0.42 thf(f117,plain,(
% 0.14/0.42 ($false = ((^[Y0 : $i]: (((sK0 @ sK2 @ Y0) & (sK0 @ sK2 @ sK3)) => (Y0 = sK3))) @ sK4))),
% 0.14/0.42 inference(sigma_clausification,[],[f116])).
% 0.14/0.42 thf(f116,plain,(
% 0.14/0.42 ((!! @ $i @ (^[Y0 : $i]: (((sK0 @ sK2 @ Y0) & (sK0 @ sK2 @ sK3)) => (Y0 = sK3)))) = $false)),
% 0.14/0.42 inference(beta_eta_normalization,[],[f115])).
% 0.14/0.42 thf(f115,plain,(
% 0.14/0.42 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ sK2 @ Y1) & (sK0 @ sK2 @ Y0)) => (Y1 = Y0))))) @ sK3) = $false)),
% 0.14/0.42 inference(sigma_clausification,[],[f114])).
% 0.14/0.42 thf(f114,plain,(
% 0.14/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK0 @ sK2 @ Y1) & (sK0 @ sK2 @ Y0)) => (Y1 = Y0)))))) = $false)),
% 0.14/0.42 inference(beta_eta_normalization,[],[f113])).
% 0.14/0.42 thf(f113,plain,(
% 0.14/0.42 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (Y2 = Y1))))))) @ sK2) = $false)),
% 0.14/0.42 inference(sigma_clausification,[],[f112])).
% 0.14/0.42 thf(f112,plain,(
% 0.14/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK0 @ Y0 @ Y2) & (sK0 @ Y0 @ Y1)) => (Y2 = Y1)))))))) != $true)),
% 0.14/0.42 inference(beta_eta_normalization,[],[f111])).
% 0.14/0.42 thf(f111,plain,(
% 0.14/0.42 ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y3 = Y2))))))))) @ sK0))),
% 0.14/0.42 inference(definition_unfolding,[],[f100,f107])).
% 0.14/0.42 thf(f107,plain,(
% 0.14/0.42 (mpartially_functional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y3 = Y2))))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f40])).
% 0.14/0.42 thf(f40,plain,(
% 0.14/0.42 (mpartially_functional = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y3) & (Y0 @ Y1 @ Y2)) => (Y3 = Y2))))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f39])).
% 0.14/0.42 thf(f39,plain,(
% 0.14/0.42 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X3 @ X2) & (X0 @ X3 @ X1)) => (X1 = X2)))) = mpartially_functional)),
% 0.14/0.42 inference(rectify,[],[f23])).
% 0.14/0.42 thf(f23,axiom,(
% 0.14/0.42 ((^[X6 : $i > $i > $o] : (! [X9,X10,X8] : (((X6 @ X8 @ X10) & (X6 @ X8 @ X9)) => (X9 = X10)))) = mpartially_functional)),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mpartially_functional)).
% 0.14/0.42 thf(f100,plain,(
% 0.14/0.42 ($true != (mpartially_functional @ sK0))),
% 0.14/0.42 inference(cnf_transformation,[],[f97])).
% 0.14/0.42 thf(f97,plain,(
% 0.14/0.42 ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ sK0 @ Y0) @ (mbox @ sK0 @ Y0)))))) & ($true != (mpartially_functional @ sK0))),
% 0.14/0.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.14/0.42 thf(f96,plain,(
% 0.14/0.42 ? [X0 : $i > $i > $o] : (((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ X0 @ Y0) @ (mbox @ X0 @ Y0))))) = $true) & ((mpartially_functional @ X0) != $true)) => (($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ sK0 @ Y0) @ (mbox @ sK0 @ Y0)))))) & ($true != (mpartially_functional @ sK0)))),
% 0.14/0.42 introduced(choice_axiom,[])).
% 0.14/0.42 thf(f95,plain,(
% 0.14/0.42 ? [X0 : $i > $i > $o] : (((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ X0 @ Y0) @ (mbox @ X0 @ Y0))))) = $true) & ((mpartially_functional @ X0) != $true))),
% 0.14/0.42 inference(ennf_transformation,[],[f69])).
% 0.14/0.42 thf(f69,plain,(
% 0.14/0.42 ~! [X0 : $i > $i > $o] : (((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ X0 @ Y0) @ (mbox @ X0 @ Y0))))) = $true) => ((mpartially_functional @ X0) = $true))),
% 0.14/0.42 inference(fool_elimination,[],[f68])).
% 0.14/0.42 thf(f68,plain,(
% 0.14/0.42 ~! [X0 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mimplies @ (mdia @ X0 @ X1) @ (mbox @ X0 @ X1))))) => (mpartially_functional @ X0))),
% 0.14/0.42 inference(rectify,[],[f33])).
% 0.14/0.42 thf(f33,negated_conjecture,(
% 0.14/0.42 ~! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mdia @ X6 @ X11) @ (mbox @ X6 @ X11))))) => (mpartially_functional @ X6))),
% 0.14/0.42 inference(negated_conjecture,[],[f32])).
% 0.14/0.42 thf(f32,conjecture,(
% 0.14/0.42 ! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mdia @ X6 @ X11) @ (mbox @ X6 @ X11))))) => (mpartially_functional @ X6))),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.14/0.42 thf(f250,plain,(
% 0.14/0.42 (sK4 = sK3)),
% 0.14/0.42 inference(trivial_inequality_removal,[],[f243])).
% 0.14/0.42 thf(f243,plain,(
% 0.14/0.42 ($false = $true) | (sK4 = sK3)),
% 0.14/0.42 inference(superposition,[],[f122,f195])).
% 0.14/0.42 thf(f195,plain,(
% 0.14/0.42 ( ! [X0 : $i] : (((sK0 @ sK2 @ X0) = $false) | (sK3 = X0)) )),
% 0.14/0.42 inference(trivial_inequality_removal,[],[f186])).
% 0.14/0.42 thf(f186,plain,(
% 0.14/0.42 ( ! [X0 : $i] : (($false = $true) | ((sK0 @ sK2 @ X0) = $false) | (sK3 = X0)) )),
% 0.14/0.42 inference(superposition,[],[f141,f121])).
% 0.14/0.42 thf(f121,plain,(
% 0.14/0.42 ((sK0 @ sK2 @ sK3) = $true)),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f120])).
% 0.14/0.42 thf(f120,plain,(
% 0.14/0.42 ($true = ((sK0 @ sK2 @ sK4) & (sK0 @ sK2 @ sK3)))),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f118])).
% 0.14/0.42 thf(f141,plain,(
% 0.14/0.42 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((sK0 @ X2 @ X1) = $false) | ((sK0 @ X2 @ X0) = $false) | (X0 = X1)) )),
% 0.14/0.42 inference(leibniz_equality_elimination,[],[f139])).
% 0.14/0.42 thf(f139,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : (($false = (sK0 @ X1 @ X4)) | ((sK0 @ X1 @ X3) = $false) | ((X2 @ X3) = $false) | ((X2 @ X4) = $true)) )),
% 0.14/0.42 inference(not_proxy_clausification,[],[f138])).
% 0.14/0.42 thf(f138,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : (((X2 @ X3) = $false) | ((sK0 @ X1 @ X3) = $false) | ((X2 @ X4) = $true) | ((~ (sK0 @ X1 @ X4)) = $true)) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f137])).
% 0.14/0.42 thf(f137,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : (((X2 @ X3) = $false) | ((sK0 @ X1 @ X3) = $false) | (((X2 @ X4) | (~ (sK0 @ X1 @ X4))) = $true)) )),
% 0.14/0.42 inference(not_proxy_clausification,[],[f136])).
% 0.14/0.42 thf(f136,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : (((~ (X2 @ X3)) = $true) | ((sK0 @ X1 @ X3) = $false) | (((X2 @ X4) | (~ (sK0 @ X1 @ X4))) = $true)) )),
% 0.14/0.42 inference(not_proxy_clausification,[],[f135])).
% 0.14/0.42 thf(f135,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : (((~ (sK0 @ X1 @ X3)) = $true) | ((~ (X2 @ X3)) = $true) | (((X2 @ X4) | (~ (sK0 @ X1 @ X4))) = $true)) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f134])).
% 0.14/0.42 thf(f134,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : ((((~ (X2 @ X3)) | (~ (sK0 @ X1 @ X3))) = $true) | (((X2 @ X4) | (~ (sK0 @ X1 @ X4))) = $true)) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f133])).
% 0.14/0.42 thf(f133,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i,X4 : $i] : ((((~ (X2 @ X3)) | (~ (sK0 @ X1 @ X3))) = $true) | (((^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0)))) @ X4) = $true)) )),
% 0.14/0.42 inference(pi_clausification,[],[f132])).
% 0.14/0.42 thf(f132,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0)))))) | (((~ (X2 @ X3)) | (~ (sK0 @ X1 @ X3))) = $true)) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f131])).
% 0.14/0.42 thf(f131,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0)))) @ X3) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0))))))) )),
% 0.14/0.42 inference(pi_clausification,[],[f130])).
% 0.14/0.42 thf(f130,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0))))))) )),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f129])).
% 0.14/0.42 thf(f129,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (sK0 @ X1 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (X2 @ Y0)) | (~ (sK0 @ X1 @ Y0)))))) = $true)) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f128])).
% 0.14/0.42 thf(f128,plain,(
% 0.14/0.42 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (sK0 @ X1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ X1 @ Y1))))))) @ X2) = $true)) )),
% 0.14/0.42 inference(pi_clausification,[],[f127])).
% 0.14/0.42 thf(f127,plain,(
% 0.14/0.42 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (sK0 @ X1 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ X1 @ Y1)))))))))) )),
% 0.14/0.42 inference(beta_eta_normalization,[],[f126])).
% 0.14/0.42 thf(f126,plain,(
% 0.14/0.42 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2))))))))) @ X1) = $true)) )),
% 0.14/0.42 inference(pi_clausification,[],[f125])).
% 0.14/0.42 thf(f125,plain,(
% 0.14/0.42 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ Y0 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2)))))))))) = $true)),
% 0.14/0.42 inference(boolean_simplification,[],[f124])).
% 0.14/0.42 thf(f124,plain,(
% 0.14/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (sK0 @ Y0 @ Y2))))) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ Y0 @ Y2)))))))))))))),
% 0.14/0.42 inference(beta_eta_normalization,[],[f110])).
% 0.14/0.42 thf(f110,plain,(
% 0.14/0.42 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y4 @ Y5) | (Y3 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ ((^[Y3 : $i > $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6) | (~ (Y3 @ Y5 @ Y6)))))))))) @ Y1 @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ sK0 @ Y0) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (Y1 @ Y3 @ Y4)))))))))) @ sK0 @ Y0))))) = $true)),
% 0.14/0.42 inference(definition_unfolding,[],[f101,f98,f105,f109,f108,f102])).
% 0.14/0.42 thf(f102,plain,(
% 0.14/0.42 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f65])).
% 0.14/0.42 thf(f65,plain,(
% 0.14/0.42 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f64])).
% 0.14/0.42 thf(f64,plain,(
% 0.14/0.42 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : (~(X0 @ X2 @ X3) | (X1 @ X3)))) = mbox)),
% 0.14/0.42 inference(rectify,[],[f16])).
% 0.14/0.42 thf(f16,axiom,(
% 0.14/0.42 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : (~(X6 @ X2 @ X7) | (X3 @ X7)))) = mbox)),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.14/0.42 thf(f108,plain,(
% 0.14/0.42 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.14/0.42 inference(definition_unfolding,[],[f99,f103,f102,f103])).
% 0.14/0.42 thf(f103,plain,(
% 0.14/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f67])).
% 0.14/0.42 thf(f67,plain,(
% 0.14/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.42 inference(fool_elimination,[],[f66])).
% 0.14/0.42 thf(f66,plain,(
% 0.14/0.42 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.14/0.42 inference(rectify,[],[f3])).
% 0.14/0.42 thf(f3,axiom,(
% 0.14/0.42 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.14/0.42 thf(f99,plain,(
% 0.14/0.42 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f83])).
% 0.14/0.42 thf(f83,plain,(
% 0.14/0.42 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.14/0.42 inference(fool_elimination,[],[f82])).
% 0.14/0.42 thf(f82,plain,(
% 0.14/0.42 (mdia = (^[X0 : $i > $i > $o, X1 : $i > $o] : (mnot @ (mbox @ X0 @ (mnot @ X1)))))),
% 0.14/0.42 inference(rectify,[],[f17])).
% 0.14/0.42 thf(f17,axiom,(
% 0.14/0.42 (mdia = (^[X6 : $i > $i > $o, X3 : $i > $o] : (mnot @ (mbox @ X6 @ (mnot @ X3)))))),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia)).
% 0.14/0.42 thf(f109,plain,(
% 0.14/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.14/0.42 inference(definition_unfolding,[],[f104,f106,f103])).
% 0.14/0.42 thf(f106,plain,(
% 0.14/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f47])).
% 0.14/0.42 thf(f47,plain,(
% 0.14/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.14/0.42 inference(fool_elimination,[],[f46])).
% 0.14/0.42 thf(f46,plain,(
% 0.14/0.42 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.14/0.42 inference(rectify,[],[f4])).
% 0.14/0.42 thf(f4,axiom,(
% 0.14/0.42 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.14/0.42 thf(f104,plain,(
% 0.14/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.42 inference(cnf_transformation,[],[f79])).
% 0.14/0.42 thf(f79,plain,(
% 0.14/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.42 inference(fool_elimination,[],[f78])).
% 0.14/0.42 thf(f78,plain,(
% 0.14/0.42 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.42 inference(rectify,[],[f6])).
% 0.14/0.42 thf(f6,axiom,(
% 0.14/0.42 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.42 thf(f105,plain,(
% 0.14/0.42 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f57])).
% 0.14/0.42 thf(f57,plain,(
% 0.14/0.42 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.42 inference(fool_elimination,[],[f56])).
% 0.14/0.42 thf(f56,plain,(
% 0.14/0.42 (mforall_prop = (^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))))),
% 0.14/0.42 inference(rectify,[],[f11])).
% 0.14/0.42 thf(f11,axiom,(
% 0.14/0.42 (mforall_prop = (^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))))),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop)).
% 0.14/0.42 thf(f98,plain,(
% 0.14/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.42 inference(cnf_transformation,[],[f77])).
% 0.14/0.42 thf(f77,plain,(
% 0.14/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.42 inference(fool_elimination,[],[f76])).
% 0.14/0.42 thf(f76,plain,(
% 0.14/0.42 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.14/0.42 inference(rectify,[],[f28])).
% 0.14/0.42 thf(f28,axiom,(
% 0.14/0.42 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.14/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.42 thf(f101,plain,(
% 0.14/0.42 ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mdia @ sK0 @ Y0) @ (mbox @ sK0 @ Y0))))))),
% 0.14/0.42 inference(cnf_transformation,[],[f97])).
% 0.14/0.42 thf(f122,plain,(
% 0.14/0.42 ((sK0 @ sK2 @ sK4) = $true)),
% 0.14/0.42 inference(binary_proxy_clausification,[],[f120])).
% 0.14/0.42 % SZS output end Proof for theBenchmark
% 0.14/0.42 % (26457)------------------------------
% 0.14/0.42 % (26457)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.42 % (26457)Termination reason: Refutation
% 0.14/0.42
% 0.14/0.42 % (26457)Memory used [KB]: 5628
% 0.14/0.42 % (26457)Time elapsed: 0.014 s
% 0.14/0.42 % (26457)Instructions burned: 16 (million)
% 0.14/0.42 % (26457)------------------------------
% 0.14/0.42 % (26457)------------------------------
% 0.14/0.42 % (26451)Success in time 0.023 s
% 0.14/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------