TSTP Solution File: LCL710^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL710^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n020.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 0.12s 0.38s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL710^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.06/0.14 % 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
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon May 20 03:00:08 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 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
% 0.12/0.37 % (16895)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37 % (16897)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)
% 0.12/0.37 % (16898)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.37 % (16899)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)
% 0.12/0.37 % (16895)Instruction limit reached!
% 0.12/0.37 % (16895)------------------------------
% 0.12/0.37 % (16895)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (16895)Termination reason: Unknown
% 0.12/0.37 % (16895)Termination phase: shuffling
% 0.12/0.37
% 0.12/0.37 % (16895)Memory used [KB]: 1023
% 0.12/0.37 % (16895)Time elapsed: 0.003 s
% 0.12/0.37 % (16895)Instructions burned: 2 (million)
% 0.12/0.37 % (16895)------------------------------
% 0.12/0.37 % (16895)------------------------------
% 0.12/0.37 % (16899)Instruction limit reached!
% 0.12/0.37 % (16899)------------------------------
% 0.12/0.37 % (16899)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (16899)Termination reason: Unknown
% 0.12/0.37 % (16899)Termination phase: shuffling
% 0.12/0.37
% 0.12/0.37 % (16899)Memory used [KB]: 1023
% 0.12/0.37 % (16899)Time elapsed: 0.003 s
% 0.12/0.37 % (16899)Instructions burned: 3 (million)
% 0.12/0.37 % (16899)------------------------------
% 0.12/0.37 % (16899)------------------------------
% 0.12/0.37 % (16893)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)
% 0.12/0.37 % (16894)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)
% 0.12/0.37 % (16893)Instruction limit reached!
% 0.12/0.37 % (16893)------------------------------
% 0.12/0.37 % (16893)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (16893)Termination reason: Unknown
% 0.12/0.37 % (16893)Termination phase: shuffling
% 0.12/0.37
% 0.12/0.37 % (16893)Memory used [KB]: 1023
% 0.12/0.37 % (16893)Time elapsed: 0.004 s
% 0.12/0.37 % (16893)Instructions burned: 5 (million)
% 0.12/0.37 % (16893)------------------------------
% 0.12/0.37 % (16893)------------------------------
% 0.12/0.38 % (16894)Refutation not found, incomplete strategy
% 0.12/0.38 % (16894)------------------------------
% 0.12/0.38 % (16894)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.38 % (16894)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.38
% 0.12/0.38
% 0.12/0.38 % (16894)Memory used [KB]: 5628
% 0.12/0.38 % (16894)Time elapsed: 0.009 s
% 0.12/0.38 % (16894)Instructions burned: 12 (million)
% 0.12/0.38 % (16894)------------------------------
% 0.12/0.38 % (16894)------------------------------
% 0.12/0.38 % (16897)First to succeed.
% 0.12/0.38 % (16898)Instruction limit reached!
% 0.12/0.38 % (16898)------------------------------
% 0.12/0.38 % (16898)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.38 % (16898)Termination reason: Unknown
% 0.12/0.38 % (16898)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (16898)Memory used [KB]: 5756
% 0.12/0.38 % (16898)Time elapsed: 0.011 s
% 0.12/0.38 % (16898)Instructions burned: 19 (million)
% 0.12/0.38 % (16898)------------------------------
% 0.12/0.38 % (16898)------------------------------
% 0.12/0.38 % (16896)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)
% 0.12/0.38 % (16896)Instruction limit reached!
% 0.12/0.38 % (16896)------------------------------
% 0.12/0.38 % (16896)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.38 % (16896)Termination reason: Unknown
% 0.12/0.38 % (16896)Termination phase: shuffling
% 0.12/0.38
% 0.12/0.38 % (16896)Memory used [KB]: 1023
% 0.12/0.38 % (16896)Time elapsed: 0.003 s
% 0.12/0.38 % (16896)Instructions burned: 2 (million)
% 0.12/0.38 % (16896)------------------------------
% 0.12/0.38 % (16896)------------------------------
% 0.12/0.38 % (16897)Refutation found. Thanks to Tanya!
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38 % SZS output start Proof for theBenchmark
% 0.12/0.38 thf(type_def_5, type, mu: $tType).
% 0.12/0.38 thf(func_def_0, type, mu: $tType).
% 0.12/0.38 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.12/0.38 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_15, type, mtrue: $i > $o).
% 0.12/0.38 thf(func_def_16, type, mfalse: $i > $o).
% 0.12/0.38 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.12/0.38 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.12/0.38 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.12/0.38 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.12/0.38 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.12/0.38 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.12/0.38 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.12/0.38 thf(func_def_52, type, sK4: $i > ($i > $o) > $i).
% 0.12/0.38 thf(func_def_53, type, ph5: !>[X0: $tType]:(X0)).
% 0.12/0.38 thf(f213,plain,(
% 0.12/0.38 $false),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f212])).
% 0.12/0.38 thf(f212,plain,(
% 0.12/0.38 ($false = $true)),
% 0.12/0.38 inference(forward_demodulation,[],[f209,f117])).
% 0.12/0.38 thf(f117,plain,(
% 0.12/0.38 ($false = (sK0 @ sK3 @ sK2))),
% 0.12/0.38 inference(binary_proxy_clausification,[],[f116])).
% 0.12/0.38 thf(f116,plain,(
% 0.12/0.38 ($false = ((sK0 @ sK2 @ sK3) => (sK0 @ sK3 @ sK2)))),
% 0.12/0.38 inference(beta_eta_normalization,[],[f115])).
% 0.12/0.38 thf(f115,plain,(
% 0.12/0.38 ($false = ((^[Y0 : $i]: ((sK0 @ sK2 @ Y0) => (sK0 @ Y0 @ sK2))) @ sK3))),
% 0.12/0.38 inference(sigma_clausification,[],[f114])).
% 0.12/0.38 thf(f114,plain,(
% 0.12/0.38 ($false = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ sK2 @ Y0) => (sK0 @ Y0 @ sK2)))))),
% 0.12/0.38 inference(beta_eta_normalization,[],[f113])).
% 0.12/0.38 thf(f113,plain,(
% 0.12/0.38 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ Y1 @ Y0))))) @ sK2))),
% 0.12/0.38 inference(sigma_clausification,[],[f112])).
% 0.12/0.38 thf(f112,plain,(
% 0.12/0.38 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y0 @ Y1) => (sK0 @ Y1 @ Y0)))))))),
% 0.12/0.38 inference(beta_eta_normalization,[],[f111])).
% 0.12/0.38 thf(f111,plain,(
% 0.12/0.38 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ sK0) != $true)),
% 0.12/0.38 inference(definition_unfolding,[],[f99,f107])).
% 0.12/0.38 thf(f107,plain,(
% 0.12/0.38 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.12/0.38 inference(cnf_transformation,[],[f84])).
% 0.12/0.38 thf(f84,plain,(
% 0.12/0.38 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.12/0.38 inference(fool_elimination,[],[f83])).
% 0.12/0.38 thf(f83,plain,(
% 0.12/0.38 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))))),
% 0.12/0.38 inference(rectify,[],[f19])).
% 0.12/0.38 thf(f19,axiom,(
% 0.12/0.38 (msymmetric = (^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.12/0.38 thf(f99,plain,(
% 0.12/0.38 ((msymmetric @ sK0) != $true)),
% 0.12/0.38 inference(cnf_transformation,[],[f97])).
% 0.12/0.38 thf(f97,plain,(
% 0.12/0.38 ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ Y0 @ (mbox @ sK0 @ (mdia @ sK0 @ Y0))))))) & ((msymmetric @ sK0) != $true)),
% 0.12/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.12/0.38 thf(f96,plain,(
% 0.12/0.38 ? [X0 : $i > $i > $o] : (((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ Y0 @ (mbox @ X0 @ (mdia @ X0 @ Y0)))))) = $true) & ($true != (msymmetric @ X0))) => (($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ Y0 @ (mbox @ sK0 @ (mdia @ sK0 @ Y0))))))) & ((msymmetric @ sK0) != $true))),
% 0.12/0.38 introduced(choice_axiom,[])).
% 0.12/0.38 thf(f95,plain,(
% 0.12/0.38 ? [X0 : $i > $i > $o] : (((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ Y0 @ (mbox @ X0 @ (mdia @ X0 @ Y0)))))) = $true) & ($true != (msymmetric @ X0)))),
% 0.12/0.38 inference(ennf_transformation,[],[f90])).
% 0.12/0.38 thf(f90,plain,(
% 0.12/0.38 ~! [X0 : $i > $i > $o] : (((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ Y0 @ (mbox @ X0 @ (mdia @ X0 @ Y0)))))) = $true) => ($true = (msymmetric @ X0)))),
% 0.12/0.38 inference(fool_elimination,[],[f89])).
% 0.12/0.38 thf(f89,plain,(
% 0.12/0.38 ~! [X0 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mimplies @ X1 @ (mbox @ X0 @ (mdia @ X0 @ X1)))))) => (msymmetric @ X0))),
% 0.12/0.38 inference(rectify,[],[f33])).
% 0.12/0.38 thf(f33,negated_conjecture,(
% 0.12/0.38 ~! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ X11 @ (mbox @ X6 @ (mdia @ X6 @ X11)))))) => (msymmetric @ X6))),
% 0.12/0.38 inference(negated_conjecture,[],[f32])).
% 0.12/0.38 thf(f32,conjecture,(
% 0.12/0.38 ! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ X11 @ (mbox @ X6 @ (mdia @ X6 @ X11)))))) => (msymmetric @ X6))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.12/0.38 thf(f209,plain,(
% 0.12/0.38 ((sK0 @ sK3 @ sK2) = $true)),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f202])).
% 0.12/0.38 thf(f202,plain,(
% 0.12/0.38 ((sK0 @ sK3 @ sK2) = $true) | ($false = $true)),
% 0.12/0.38 inference(superposition,[],[f118,f169])).
% 0.12/0.38 thf(f169,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (($false = (sK0 @ X0 @ X1)) | ((sK0 @ X1 @ X0) = $true)) )),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f166])).
% 0.12/0.38 thf(f166,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (((sK0 @ X1 @ X0) = $true) | ($false != $false) | (X0 != X0) | ($false = (sK0 @ X0 @ X1))) )),
% 0.12/0.38 inference(equality_factoring,[],[f158])).
% 0.12/0.38 thf(f158,plain,(
% 0.12/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (sK0 @ X2 @ X0)) | ($false = (sK0 @ X1 @ X0)) | ((sK0 @ X0 @ X1) = $true) | (X1 != X2)) )),
% 0.12/0.38 inference(equality_proxy_clausification,[],[f156])).
% 0.12/0.38 thf(f156,plain,(
% 0.12/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (sK0 @ X1 @ X0)) | ((sK0 @ X0 @ X1) = $true) | ($false = (X1 = X2)) | ($false = (sK0 @ X2 @ X0))) )),
% 0.12/0.38 inference(superposition,[],[f135,f137])).
% 0.12/0.38 thf(f137,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (((sK4 @ X0 @ (= @ X1)) = X1) | ($false = (sK0 @ X1 @ X0))) )),
% 0.12/0.38 inference(leibniz_equality_elimination,[],[f136])).
% 0.12/0.38 thf(f136,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((X2 @ (sK4 @ X3 @ X2)) = $true) | ($false = (sK0 @ X1 @ X3)) | ($false = (X2 @ X1))) )),
% 0.12/0.38 inference(not_proxy_clausification,[],[f133])).
% 0.12/0.38 thf(f133,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (X2 @ X1)) | ($false = (sK0 @ X1 @ X3)) | ($false = (~ (X2 @ (sK4 @ X3 @ X2))))) )),
% 0.12/0.38 inference(binary_proxy_clausification,[],[f132])).
% 0.12/0.38 thf(f132,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (sK0 @ X1 @ X3)) | ($false = (X2 @ X1)) | ($false = ((~ (sK0 @ X3 @ (sK4 @ X3 @ X2))) | (~ (X2 @ (sK4 @ X3 @ X2)))))) )),
% 0.12/0.38 inference(beta_eta_normalization,[],[f131])).
% 0.12/0.38 thf(f131,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (sK0 @ X1 @ X3)) | ($false = (X2 @ X1)) | ($false = ((^[Y0 : $i]: ((~ (sK0 @ X3 @ Y0)) | (~ (X2 @ Y0)))) @ (sK4 @ X3 @ X2)))) )),
% 0.12/0.38 inference(sigma_clausification,[],[f130])).
% 0.12/0.38 thf(f130,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X3 @ Y0)) | (~ (X2 @ Y0)))))) | ($false = (X2 @ X1)) | ($false = (sK0 @ X1 @ X3))) )),
% 0.12/0.38 inference(not_proxy_clausification,[],[f129])).
% 0.12/0.38 thf(f129,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (X2 @ X1)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X3 @ Y0)) | (~ (X2 @ Y0))))))) | ($false = (sK0 @ X1 @ X3))) )),
% 0.12/0.38 inference(not_proxy_clausification,[],[f128])).
% 0.12/0.38 thf(f128,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((~ (sK0 @ X1 @ X3)) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X3 @ Y0)) | (~ (X2 @ Y0))))))) | ($false = (X2 @ X1))) )),
% 0.12/0.38 inference(binary_proxy_clausification,[],[f127])).
% 0.12/0.38 thf(f127,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (X2 @ X1)) | ($true = ((~ (sK0 @ X1 @ X3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X3 @ Y0)) | (~ (X2 @ Y0))))))))) )),
% 0.12/0.38 inference(not_proxy_clausification,[],[f126])).
% 0.12/0.38 thf(f126,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (~ (X2 @ X1))) | ($true = ((~ (sK0 @ X1 @ X3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X3 @ Y0)) | (~ (X2 @ Y0))))))))) )),
% 0.12/0.38 inference(beta_eta_normalization,[],[f125])).
% 0.12/0.38 thf(f125,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (~ (X2 @ X1))) | (((^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (~ (X2 @ Y1)))))))) @ X3) = $true)) )),
% 0.12/0.38 inference(pi_clausification,[],[f124])).
% 0.12/0.38 thf(f124,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (~ (X2 @ Y1)))))))))) | ($true = (~ (X2 @ X1)))) )),
% 0.12/0.38 inference(binary_proxy_clausification,[],[f123])).
% 0.12/0.38 thf(f123,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (~ (X2 @ Y1))))))))) | (~ (X2 @ X1))) = $true)) )),
% 0.12/0.38 inference(beta_eta_normalization,[],[f122])).
% 0.12/0.38 thf(f122,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y1 @ Y2)) | (~ (Y0 @ Y2))))))))) | (~ (Y0 @ X1)))) @ X2))) )),
% 0.12/0.38 inference(pi_clausification,[],[f121])).
% 0.12/0.38 thf(f121,plain,(
% 0.12/0.38 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y1 @ Y2)) | (~ (Y0 @ Y2))))))))) | (~ (Y0 @ X1))))))) )),
% 0.12/0.38 inference(beta_eta_normalization,[],[f120])).
% 0.12/0.38 thf(f120,plain,(
% 0.12/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (sK0 @ Y2 @ Y3)) | (~ (Y1 @ Y3))))))))) | (~ (Y1 @ Y0)))))) @ X1))) )),
% 0.12/0.38 inference(pi_clausification,[],[f119])).
% 0.12/0.38 thf(f119,plain,(
% 0.12/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (sK0 @ Y2 @ Y3)) | (~ (Y1 @ Y3))))))))) | (~ (Y1 @ Y0))))))) = $true)),
% 0.12/0.38 inference(beta_eta_normalization,[],[f110])).
% 0.12/0.38 thf(f110,plain,(
% 0.12/0.38 ($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]: ((Y4 @ Y5) | (Y3 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ Y0 @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK0 @ ((^[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)))))))),
% 0.12/0.38 inference(definition_unfolding,[],[f100,f105,f106,f109,f102,f108])).
% 0.12/0.38 thf(f108,plain,(
% 0.12/0.38 (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)))))))),
% 0.12/0.38 inference(definition_unfolding,[],[f101,f98,f102,f98])).
% 0.12/0.38 thf(f98,plain,(
% 0.12/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.12/0.38 inference(cnf_transformation,[],[f66])).
% 0.12/0.38 thf(f66,plain,(
% 0.12/0.38 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.12/0.38 inference(fool_elimination,[],[f65])).
% 0.12/0.38 thf(f65,plain,(
% 0.12/0.38 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.12/0.38 inference(rectify,[],[f3])).
% 0.12/0.38 thf(f3,axiom,(
% 0.12/0.38 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.12/0.38 thf(f101,plain,(
% 0.12/0.38 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.12/0.38 inference(cnf_transformation,[],[f86])).
% 0.12/0.38 thf(f86,plain,(
% 0.12/0.38 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.12/0.38 inference(fool_elimination,[],[f85])).
% 0.12/0.38 thf(f85,plain,(
% 0.12/0.38 ((^[X0 : $i > $i > $o, X1 : $i > $o] : (mnot @ (mbox @ X0 @ (mnot @ X1)))) = mdia)),
% 0.12/0.38 inference(rectify,[],[f17])).
% 0.12/0.38 thf(f17,axiom,(
% 0.12/0.38 ((^[X6 : $i > $i > $o, X3 : $i > $o] : (mnot @ (mbox @ X6 @ (mnot @ X3)))) = mdia)),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia)).
% 0.12/0.38 thf(f102,plain,(
% 0.12/0.38 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.12/0.38 inference(cnf_transformation,[],[f62])).
% 0.12/0.38 thf(f62,plain,(
% 0.12/0.38 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.12/0.38 inference(fool_elimination,[],[f61])).
% 0.12/0.38 thf(f61,plain,(
% 0.12/0.38 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))) = mbox)),
% 0.12/0.38 inference(rectify,[],[f16])).
% 0.12/0.38 thf(f16,axiom,(
% 0.12/0.38 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))) = mbox)),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.12/0.38 thf(f109,plain,(
% 0.12/0.38 (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)))))),
% 0.12/0.38 inference(definition_unfolding,[],[f104,f103,f98])).
% 0.12/0.38 thf(f103,plain,(
% 0.12/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.12/0.38 inference(cnf_transformation,[],[f78])).
% 0.12/0.38 thf(f78,plain,(
% 0.12/0.38 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.12/0.38 inference(fool_elimination,[],[f77])).
% 0.12/0.38 thf(f77,plain,(
% 0.12/0.38 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.12/0.38 inference(rectify,[],[f4])).
% 0.12/0.38 thf(f4,axiom,(
% 0.12/0.38 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.12/0.38 thf(f104,plain,(
% 0.12/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.12/0.38 inference(cnf_transformation,[],[f60])).
% 0.12/0.38 thf(f60,plain,(
% 0.12/0.38 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.12/0.38 inference(fool_elimination,[],[f59])).
% 0.12/0.38 thf(f59,plain,(
% 0.12/0.38 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.12/0.38 inference(rectify,[],[f6])).
% 0.12/0.38 thf(f6,axiom,(
% 0.12/0.38 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.12/0.38 thf(f106,plain,(
% 0.12/0.38 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.12/0.38 inference(cnf_transformation,[],[f56])).
% 0.12/0.38 thf(f56,plain,(
% 0.12/0.38 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.12/0.38 inference(fool_elimination,[],[f55])).
% 0.12/0.38 thf(f55,plain,(
% 0.12/0.38 ((^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))) = mforall_prop)),
% 0.12/0.38 inference(rectify,[],[f11])).
% 0.12/0.38 thf(f11,axiom,(
% 0.12/0.38 ((^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))) = mforall_prop)),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop)).
% 0.12/0.38 thf(f105,plain,(
% 0.12/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.12/0.38 inference(cnf_transformation,[],[f53])).
% 0.12/0.38 thf(f53,plain,(
% 0.12/0.38 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.12/0.38 inference(fool_elimination,[],[f52])).
% 0.12/0.38 thf(f52,plain,(
% 0.12/0.38 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.12/0.38 inference(rectify,[],[f28])).
% 0.12/0.38 thf(f28,axiom,(
% 0.12/0.38 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.12/0.38 thf(f100,plain,(
% 0.12/0.38 ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ Y0 @ (mbox @ sK0 @ (mdia @ sK0 @ Y0)))))))),
% 0.12/0.38 inference(cnf_transformation,[],[f97])).
% 0.12/0.38 thf(f135,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((sK0 @ X3 @ (sK4 @ X3 @ X2)) = $true) | ($false = (sK0 @ X1 @ X3)) | ($false = (X2 @ X1))) )),
% 0.12/0.38 inference(not_proxy_clausification,[],[f134])).
% 0.12/0.38 thf(f134,plain,(
% 0.12/0.38 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (X2 @ X1)) | ($false = (~ (sK0 @ X3 @ (sK4 @ X3 @ X2)))) | ($false = (sK0 @ X1 @ X3))) )),
% 0.12/0.38 inference(binary_proxy_clausification,[],[f132])).
% 0.12/0.38 thf(f118,plain,(
% 0.12/0.38 ($true = (sK0 @ sK2 @ sK3))),
% 0.12/0.38 inference(binary_proxy_clausification,[],[f116])).
% 0.12/0.38 % SZS output end Proof for theBenchmark
% 0.12/0.38 % (16897)------------------------------
% 0.12/0.38 % (16897)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.38 % (16897)Termination reason: Refutation
% 0.12/0.38
% 0.12/0.38 % (16897)Memory used [KB]: 5756
% 0.12/0.38 % (16897)Time elapsed: 0.013 s
% 0.12/0.38 % (16897)Instructions burned: 16 (million)
% 0.12/0.38 % (16897)------------------------------
% 0.12/0.38 % (16897)------------------------------
% 0.12/0.38 % (16891)Success in time 0.025 s
% 0.12/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------