TSTP Solution File: LCL711^1 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : LCL711^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 11:33:19 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL711^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.10/0.12 % Command : run_vampire %s %d THM
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Jun 22 16:57:54 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 Running higher-order theorem proving
% 0.13/0.35 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
% 0.13/0.37 % (19878)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (19881)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (19880)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.13/0.37 % (19882)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (19883)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.13/0.37 % (19884)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37 % (19879)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.13/0.37 % (19882)Instruction limit reached!
% 0.13/0.37 % (19882)------------------------------
% 0.13/0.37 % (19882)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.37 % (19882)Termination reason: Unknown
% 0.13/0.37 % (19882)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (19882)Memory used [KB]: 1023
% 0.13/0.37 % (19882)Time elapsed: 0.003 s
% 0.13/0.37 % (19882)Instructions burned: 2 (million)
% 0.13/0.38 % (19882)------------------------------
% 0.13/0.38 % (19882)------------------------------
% 0.13/0.38 % (19881)Instruction limit reached!
% 0.13/0.38 % (19881)------------------------------
% 0.13/0.38 % (19881)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.38 % (19881)Termination reason: Unknown
% 0.13/0.38 % (19881)Termination phase: shuffling
% 0.13/0.38
% 0.13/0.38 % (19881)Memory used [KB]: 1023
% 0.13/0.38 % (19881)Time elapsed: 0.004 s
% 0.13/0.38 % (19881)Instructions burned: 3 (million)
% 0.13/0.38 % (19881)------------------------------
% 0.13/0.38 % (19881)------------------------------
% 0.13/0.38 % (19879)Instruction limit reached!
% 0.13/0.38 % (19879)------------------------------
% 0.13/0.38 % (19879)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.38 % (19879)Termination reason: Unknown
% 0.13/0.38 % (19879)Termination phase: Property scanning
% 0.13/0.38
% 0.13/0.38 % (19879)Memory used [KB]: 1023
% 0.13/0.38 % (19879)Time elapsed: 0.004 s
% 0.13/0.38 % (19879)Instructions burned: 4 (million)
% 0.13/0.38 % (19879)------------------------------
% 0.13/0.38 % (19879)------------------------------
% 0.13/0.38 % (19880)First to succeed.
% 0.13/0.38 % (19883)Also succeeded, but the first one will report.
% 0.13/0.38 % (19880)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38 % SZS output start Proof for theBenchmark
% 0.13/0.38 thf(type_def_5, type, mu: $tType).
% 0.13/0.38 thf(func_def_0, type, mu: $tType).
% 0.13/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.13/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.13/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.13/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.13/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.13/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.13/0.38 thf(func_def_33, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.13/0.38 thf(func_def_49, type, sK0: $i > $i > $o).
% 0.13/0.38 thf(func_def_52, type, sK3: $i > ($i > $o) > $i).
% 0.13/0.38 thf(func_def_53, type, sK4: $i > ($i > $o) > $i).
% 0.13/0.38 thf(func_def_54, type, ph5: !>[X0: $tType]:(X0)).
% 0.13/0.38 thf(f178,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f177])).
% 0.13/0.38 thf(f177,plain,(
% 0.13/0.38 ($false = $true)),
% 0.13/0.38 inference(forward_demodulation,[],[f176,f145])).
% 0.13/0.38 thf(f145,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($false = (sK0 @ sK2 @ X1))) )),
% 0.13/0.38 inference(pi_clausification,[],[f144])).
% 0.13/0.38 thf(f144,plain,(
% 0.13/0.38 ($false = (?? @ $i @ (sK0 @ sK2)))),
% 0.13/0.38 inference(beta_eta_normalization,[],[f143])).
% 0.13/0.38 thf(f143,plain,(
% 0.13/0.38 ($false = ((^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0))) @ sK2))),
% 0.13/0.38 inference(sigma_clausification,[],[f142])).
% 0.13/0.38 thf(f142,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (sK0 @ Y0)))) != $true)),
% 0.13/0.38 inference(beta_eta_normalization,[],[f140])).
% 0.13/0.38 thf(f140,plain,(
% 0.13/0.38 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))) @ sK0) != $true)),
% 0.13/0.38 inference(definition_unfolding,[],[f100,f110])).
% 0.13/0.39 thf(f110,plain,(
% 0.13/0.39 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f48])).
% 0.13/0.39 thf(f48,plain,(
% 0.13/0.39 (mserial = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y1 @ Y2)))))))),
% 0.13/0.39 inference(fool_elimination,[],[f47])).
% 0.13/0.39 thf(f47,plain,(
% 0.13/0.39 ((^[X0 : $i > $i > $o] : (! [X1] : ? [X2] : (X0 @ X1 @ X2))) = mserial)),
% 0.13/0.39 inference(rectify,[],[f20])).
% 0.13/0.39 thf(f20,axiom,(
% 0.13/0.39 ((^[X6 : $i > $i > $o] : (! [X8] : ? [X9] : (X6 @ X8 @ X9))) = mserial)),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mserial)).
% 0.13/0.39 thf(f100,plain,(
% 0.13/0.39 ($true != (mserial @ sK0))),
% 0.13/0.39 inference(cnf_transformation,[],[f97])).
% 0.13/0.39 thf(f97,plain,(
% 0.13/0.39 ($true != (mserial @ sK0)) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ (mdia @ sK0 @ Y0))))) = $true)),
% 0.13/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.13/0.39 thf(f96,plain,(
% 0.13/0.39 ? [X0 : $i > $i > $o] : (($true != (mserial @ X0)) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mdia @ X0 @ Y0))))) = $true)) => (($true != (mserial @ sK0)) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ (mdia @ sK0 @ Y0))))) = $true))),
% 0.13/0.39 introduced(choice_axiom,[])).
% 0.13/0.39 thf(f95,plain,(
% 0.13/0.39 ? [X0 : $i > $i > $o] : (($true != (mserial @ X0)) & ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mdia @ X0 @ Y0))))) = $true))),
% 0.13/0.39 inference(ennf_transformation,[],[f40])).
% 0.13/0.39 thf(f40,plain,(
% 0.13/0.39 ~! [X0 : $i > $i > $o] : (((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ Y0) @ (mdia @ X0 @ Y0))))) = $true) => ($true = (mserial @ X0)))),
% 0.13/0.39 inference(fool_elimination,[],[f39])).
% 0.13/0.39 thf(f39,plain,(
% 0.13/0.39 ~! [X0 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mimplies @ (mbox @ X0 @ X1) @ (mdia @ X0 @ X1))))) => (mserial @ X0))),
% 0.13/0.39 inference(rectify,[],[f33])).
% 0.13/0.39 thf(f33,negated_conjecture,(
% 0.13/0.39 ~! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ X6 @ X11) @ (mdia @ X6 @ X11))))) => (mserial @ X6))),
% 0.13/0.39 inference(negated_conjecture,[],[f32])).
% 0.13/0.39 thf(f32,conjecture,(
% 0.13/0.39 ! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ X6 @ X11) @ (mdia @ X6 @ X11))))) => (mserial @ X6))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj)).
% 0.13/0.39 thf(f176,plain,(
% 0.13/0.39 ( ! [X0 : $i > $o] : (($true = (sK0 @ sK2 @ (sK3 @ sK2 @ X0)))) )),
% 0.13/0.39 inference(trivial_inequality_removal,[],[f173])).
% 0.13/0.39 thf(f173,plain,(
% 0.13/0.39 ( ! [X0 : $i > $o] : (($false = $true) | ($true = (sK0 @ sK2 @ (sK3 @ sK2 @ X0)))) )),
% 0.13/0.39 inference(superposition,[],[f163,f145])).
% 0.13/0.39 thf(f163,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($true = (sK0 @ X1 @ (sK4 @ X1 @ X2))) | ((sK0 @ X1 @ (sK3 @ X1 @ X2)) = $true)) )),
% 0.13/0.39 inference(not_proxy_clausification,[],[f162])).
% 0.13/0.39 thf(f162,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (((sK0 @ X1 @ (sK3 @ X1 @ X2)) = $true) | ($false = (~ (sK0 @ X1 @ (sK4 @ X1 @ X2))))) )),
% 0.13/0.39 inference(not_proxy_clausification,[],[f161])).
% 0.13/0.39 thf(f161,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($false = (~ (sK0 @ X1 @ (sK3 @ X1 @ X2)))) | ($false = (~ (sK0 @ X1 @ (sK4 @ X1 @ X2))))) )),
% 0.13/0.39 inference(binary_proxy_clausification,[],[f159])).
% 0.13/0.39 thf(f159,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($false = ((~ (sK0 @ X1 @ (sK3 @ X1 @ X2))) | (X2 @ (sK3 @ X1 @ X2)))) | ($false = (~ (sK0 @ X1 @ (sK4 @ X1 @ X2))))) )),
% 0.13/0.39 inference(binary_proxy_clausification,[],[f157])).
% 0.13/0.39 thf(f157,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($false = ((~ (sK0 @ X1 @ (sK4 @ X1 @ X2))) | (~ (X2 @ (sK4 @ X1 @ X2))))) | ($false = ((~ (sK0 @ X1 @ (sK3 @ X1 @ X2))) | (X2 @ (sK3 @ X1 @ X2))))) )),
% 0.13/0.39 inference(beta_eta_normalization,[],[f156])).
% 0.13/0.39 thf(f156,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($false = ((~ (sK0 @ X1 @ (sK3 @ X1 @ X2))) | (X2 @ (sK3 @ X1 @ X2)))) | ($false = ((^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (~ (X2 @ Y0)))) @ (sK4 @ X1 @ X2)))) )),
% 0.13/0.39 inference(sigma_clausification,[],[f155])).
% 0.13/0.39 thf(f155,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (~ (X2 @ Y0)))))) | ($false = ((~ (sK0 @ X1 @ (sK3 @ X1 @ X2))) | (X2 @ (sK3 @ X1 @ X2))))) )),
% 0.13/0.39 inference(not_proxy_clausification,[],[f154])).
% 0.13/0.39 thf(f154,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (~ (X2 @ Y0))))))) | ($false = ((~ (sK0 @ X1 @ (sK3 @ X1 @ X2))) | (X2 @ (sK3 @ X1 @ X2))))) )),
% 0.13/0.39 inference(beta_eta_normalization,[],[f153])).
% 0.13/0.39 thf(f153,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($false = ((^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (X2 @ Y0))) @ (sK3 @ X1 @ X2))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (~ (X2 @ Y0)))))))) )),
% 0.13/0.39 inference(sigma_clausification,[],[f152])).
% 0.13/0.39 thf(f152,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (X2 @ Y0))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (~ (X2 @ Y0)))))))) )),
% 0.13/0.39 inference(not_proxy_clausification,[],[f151])).
% 0.13/0.39 thf(f151,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (X2 @ Y0)))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (~ (X2 @ Y0)))))))) )),
% 0.13/0.39 inference(binary_proxy_clausification,[],[f150])).
% 0.13/0.39 thf(f150,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (X2 @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (~ (X2 @ Y0))))))) = $true)) )),
% 0.13/0.39 inference(beta_eta_normalization,[],[f149])).
% 0.13/0.39 thf(f149,plain,(
% 0.13/0.39 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (~ (Y0 @ Y1)))))))) @ X2))) )),
% 0.13/0.39 inference(pi_clausification,[],[f148])).
% 0.13/0.39 thf(f148,plain,(
% 0.13/0.39 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (Y0 @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (~ (Y0 @ Y1))))))))))) )),
% 0.13/0.39 inference(beta_eta_normalization,[],[f147])).
% 0.13/0.39 thf(f147,plain,(
% 0.13/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (~ (Y1 @ Y2)))))))))) @ X1))) )),
% 0.13/0.39 inference(pi_clausification,[],[f146])).
% 0.13/0.39 thf(f146,plain,(
% 0.13/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (~ (Y1 @ Y2))))))))))) = $true)),
% 0.13/0.39 inference(beta_eta_normalization,[],[f141])).
% 0.13/0.39 thf(f141,plain,(
% 0.13/0.39 ($true = ((^[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]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK0 @ Y0) @ ((^[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]: ((~ (Y3 @ Y5 @ Y6)) | (Y4 @ Y6))))))))) @ Y1 @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y2)))))) @ sK0 @ Y0))))))),
% 0.13/0.39 inference(definition_unfolding,[],[f99,f108,f125,f132,f107,f139])).
% 0.13/0.39 thf(f139,plain,(
% 0.13/0.39 (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]: ((~ (Y2 @ Y4 @ Y5)) | (Y3 @ Y5))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.13/0.39 inference(definition_unfolding,[],[f126,f104,f107,f104])).
% 0.13/0.39 thf(f104,plain,(
% 0.13/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f77])).
% 0.13/0.39 thf(f77,plain,(
% 0.13/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.13/0.39 inference(fool_elimination,[],[f76])).
% 0.13/0.39 thf(f76,plain,(
% 0.13/0.39 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.13/0.39 inference(rectify,[],[f3])).
% 0.13/0.39 thf(f3,axiom,(
% 0.13/0.39 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.13/0.39 thf(f126,plain,(
% 0.13/0.39 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f87])).
% 0.13/0.39 thf(f87,plain,(
% 0.13/0.39 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.13/0.39 inference(fool_elimination,[],[f86])).
% 0.13/0.39 thf(f86,plain,(
% 0.13/0.39 (mdia = (^[X0 : $i > $i > $o, X1 : $i > $o] : (mnot @ (mbox @ X0 @ (mnot @ X1)))))),
% 0.13/0.39 inference(rectify,[],[f17])).
% 0.13/0.39 thf(f17,axiom,(
% 0.13/0.39 (mdia = (^[X6 : $i > $i > $o, X3 : $i > $o] : (mnot @ (mbox @ X6 @ (mnot @ X3)))))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia)).
% 0.13/0.39 thf(f107,plain,(
% 0.13/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f68])).
% 0.13/0.39 thf(f68,plain,(
% 0.13/0.39 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.13/0.39 inference(fool_elimination,[],[f67])).
% 0.13/0.39 thf(f67,plain,(
% 0.13/0.39 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))) = mbox)),
% 0.13/0.39 inference(rectify,[],[f16])).
% 0.13/0.39 thf(f16,axiom,(
% 0.13/0.39 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))) = mbox)),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox)).
% 0.13/0.39 thf(f132,plain,(
% 0.13/0.39 (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)))))),
% 0.13/0.39 inference(definition_unfolding,[],[f128,f120,f104])).
% 0.13/0.39 thf(f120,plain,(
% 0.13/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f58])).
% 0.13/0.39 thf(f58,plain,(
% 0.13/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.13/0.39 inference(fool_elimination,[],[f57])).
% 0.13/0.39 thf(f57,plain,(
% 0.13/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.13/0.39 inference(rectify,[],[f4])).
% 0.13/0.39 thf(f4,axiom,(
% 0.13/0.39 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.13/0.39 thf(f128,plain,(
% 0.13/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.39 inference(cnf_transformation,[],[f74])).
% 0.13/0.39 thf(f74,plain,(
% 0.13/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.13/0.39 inference(fool_elimination,[],[f73])).
% 0.13/0.39 thf(f73,plain,(
% 0.13/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.13/0.39 inference(rectify,[],[f6])).
% 0.13/0.39 thf(f6,axiom,(
% 0.13/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.13/0.39 thf(f125,plain,(
% 0.13/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.13/0.39 inference(cnf_transformation,[],[f36])).
% 0.13/0.39 thf(f36,plain,(
% 0.13/0.39 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.13/0.39 inference(fool_elimination,[],[f35])).
% 0.13/0.39 thf(f35,plain,(
% 0.13/0.39 (mforall_prop = (^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))))),
% 0.13/0.39 inference(rectify,[],[f11])).
% 0.13/0.39 thf(f11,axiom,(
% 0.13/0.39 (mforall_prop = (^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_prop)).
% 0.13/0.39 thf(f108,plain,(
% 0.13/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.39 inference(cnf_transformation,[],[f46])).
% 0.13/0.39 thf(f46,plain,(
% 0.13/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.13/0.39 inference(fool_elimination,[],[f45])).
% 0.13/0.39 thf(f45,plain,(
% 0.13/0.39 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.13/0.39 inference(rectify,[],[f28])).
% 0.13/0.39 thf(f28,axiom,(
% 0.13/0.39 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.13/0.39 thf(f99,plain,(
% 0.13/0.39 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ Y0) @ (mdia @ sK0 @ Y0))))) = $true)),
% 0.13/0.39 inference(cnf_transformation,[],[f97])).
% 0.13/0.39 % SZS output end Proof for theBenchmark
% 0.13/0.39 % (19880)------------------------------
% 0.13/0.39 % (19880)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.13/0.39 % (19880)Termination reason: Refutation
% 0.13/0.39
% 0.13/0.39 % (19880)Memory used [KB]: 5628
% 0.13/0.39 % (19880)Time elapsed: 0.011 s
% 0.13/0.39 % (19880)Instructions burned: 11 (million)
% 0.13/0.39 % (19880)------------------------------
% 0.13/0.39 % (19880)------------------------------
% 0.13/0.39 % (19877)Success in time 0.014 s
%------------------------------------------------------------------------------