TSTP Solution File: LCL716^1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : LCL716^1 : 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 : n010.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 00:22:21 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LCL716^1 : TPTP v8.2.0. Bugfixed v5.0.0.
% 0.07/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 20 01:42:38 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.37 This is a TH0_THM_EQU_NAR problem
% 0.14/0.37 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.39 % (22742)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.14/0.39 % (22739)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.14/0.39 % (22741)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.39 % (22744)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.14/0.39 % (22741)Instruction limit reached!
% 0.14/0.39 % (22741)------------------------------
% 0.14/0.39 % (22741)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (22741)Termination reason: Unknown
% 0.14/0.39 % (22741)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (22741)Memory used [KB]: 1023
% 0.14/0.39 % (22741)Time elapsed: 0.003 s
% 0.14/0.39 % (22741)Instructions burned: 3 (million)
% 0.14/0.39 % (22741)------------------------------
% 0.14/0.39 % (22741)------------------------------
% 0.14/0.39 % (22744)Instruction limit reached!
% 0.14/0.39 % (22744)------------------------------
% 0.14/0.39 % (22744)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (22744)Termination reason: Unknown
% 0.14/0.39 % (22744)Termination phase: shuffling
% 0.14/0.39
% 0.14/0.39 % (22744)Memory used [KB]: 1023
% 0.14/0.39 % (22744)Time elapsed: 0.004 s
% 0.14/0.39 % (22744)Instructions burned: 3 (million)
% 0.14/0.39 % (22744)------------------------------
% 0.14/0.39 % (22744)------------------------------
% 0.14/0.39 % (22737)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 % (22739)Refutation not found, incomplete strategy
% 0.14/0.40 % (22739)------------------------------
% 0.14/0.40 % (22739)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (22739)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.40
% 0.14/0.40
% 0.14/0.40 % (22739)Memory used [KB]: 5628
% 0.14/0.40 % (22739)Time elapsed: 0.011 s
% 0.14/0.40 % (22739)Instructions burned: 16 (million)
% 0.14/0.40 % (22739)------------------------------
% 0.14/0.40 % (22739)------------------------------
% 0.14/0.40 % (22742)First to succeed.
% 0.14/0.40 % (22740)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.40 % (22740)Instruction limit reached!
% 0.14/0.40 % (22740)------------------------------
% 0.14/0.40 % (22740)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (22740)Termination reason: Unknown
% 0.14/0.40 % (22740)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.40 % (22740)Memory used [KB]: 1023
% 0.14/0.40 % (22740)Time elapsed: 0.003 s
% 0.14/0.40 % (22740)Instructions burned: 2 (million)
% 0.14/0.40 % (22740)------------------------------
% 0.14/0.40 % (22740)------------------------------
% 0.14/0.40 % (22743)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 % (22738)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 % (22738)Instruction limit reached!
% 0.14/0.40 % (22738)------------------------------
% 0.14/0.40 % (22738)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (22738)Termination reason: Unknown
% 0.14/0.40 % (22738)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.40 % (22738)Memory used [KB]: 1023
% 0.14/0.40 % (22738)Time elapsed: 0.004 s
% 0.14/0.40 % (22738)Instructions burned: 4 (million)
% 0.14/0.40 % (22738)------------------------------
% 0.14/0.40 % (22738)------------------------------
% 0.14/0.40 % (22742)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% 0.14/0.40 thf(type_def_5, type, mu: $tType).
% 0.14/0.40 thf(func_def_0, type, mu: $tType).
% 0.14/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.14/0.40 thf(func_def_52, type, sK4: $i > ($i > $o) > $i).
% 0.14/0.40 thf(func_def_53, type, sK5: $i > ($i > $o) > $i).
% 0.14/0.40 thf(func_def_54, type, ph6: !>[X0: $tType]:(X0)).
% 0.14/0.40 thf(f267,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(avatar_sat_refutation,[],[f223,f240,f261])).
% 0.14/0.40 thf(f261,plain,(
% 0.14/0.40 ~spl1_4),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f260])).
% 0.14/0.40 thf(f260,plain,(
% 0.14/0.40 $false | ~spl1_4),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f247])).
% 0.14/0.40 thf(f247,plain,(
% 0.14/0.40 (sK2 != sK2) | ($false = $true) | ~spl1_4),
% 0.14/0.40 inference(superposition,[],[f221,f116])).
% 0.14/0.40 thf(f116,plain,(
% 0.14/0.40 ($true = (sK0 @ sK3 @ sK2))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f114])).
% 0.14/0.40 thf(f114,plain,(
% 0.14/0.40 ($false = ((sK0 @ sK3 @ sK2) => (?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0 @ sK2) & (sK0 @ sK3 @ Y0))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f113])).
% 0.14/0.40 thf(f113,plain,(
% 0.14/0.40 (((^[Y0 : $i]: ((sK0 @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ sK2) & (sK0 @ Y0 @ Y1)))))) @ sK3) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f112])).
% 0.14/0.40 thf(f112,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0 @ sK2) => (?? @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ sK2) & (sK0 @ Y0 @ Y1))))))) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f111])).
% 0.14/0.40 thf(f111,plain,(
% 0.14/0.40 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((sK0 @ Y2 @ Y0) & (sK0 @ Y1 @ Y2)))))))) @ sK2))),
% 0.14/0.40 inference(sigma_clausification,[],[f110])).
% 0.14/0.40 thf(f110,plain,(
% 0.14/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1 @ Y0) => (?? @ $i @ (^[Y2 : $i]: ((sK0 @ Y2 @ Y0) & (sK0 @ Y1 @ Y2))))))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f108])).
% 0.14/0.40 thf(f108,plain,(
% 0.14/0.40 ($true != ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)))))))))) @ sK0))),
% 0.14/0.40 inference(definition_unfolding,[],[f106,f100])).
% 0.14/0.40 thf(f100,plain,(
% 0.14/0.40 (mweakly_dense = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)))))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f70])).
% 0.14/0.40 thf(f70,plain,(
% 0.14/0.40 (mweakly_dense = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (?? @ $i @ (^[Y3 : $i]: ((Y0 @ Y3 @ Y1) & (Y0 @ Y2 @ Y3)))))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f69])).
% 0.14/0.40 thf(f69,plain,(
% 0.14/0.40 ((^[X0 : $i > $i > $o] : (! [X2,X3] : ((X0 @ X2 @ X3) => ? [X4] : ((X0 @ X2 @ X4) & (X0 @ X4 @ X3))))) = mweakly_dense)),
% 0.14/0.40 inference(rectify,[],[f25])).
% 0.14/0.40 thf(f25,axiom,(
% 0.14/0.40 ((^[X6 : $i > $i > $o] : (! [X10,X8,X9] : ((X6 @ X8 @ X9) => ? [X10] : ((X6 @ X8 @ X10) & (X6 @ X10 @ X9))))) = mweakly_dense)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mweakly_dense)).
% 0.14/0.40 thf(f106,plain,(
% 0.14/0.40 ($true != (mweakly_dense @ sK0))),
% 0.14/0.40 inference(cnf_transformation,[],[f97])).
% 0.14/0.40 thf(f97,plain,(
% 0.14/0.40 ($true != (mweakly_dense @ sK0)) & ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ (mbox @ sK0 @ Y0)) @ (mbox @ sK0 @ Y0))))))),
% 0.14/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.14/0.40 thf(f96,plain,(
% 0.14/0.40 ? [X0 : $i > $i > $o] : (($true != (mweakly_dense @ X0)) & ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ (mbox @ X0 @ Y0)) @ (mbox @ X0 @ Y0))))))) => (($true != (mweakly_dense @ sK0)) & ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ (mbox @ sK0 @ Y0)) @ (mbox @ sK0 @ Y0)))))))),
% 0.14/0.40 introduced(choice_axiom,[])).
% 0.14/0.40 thf(f95,plain,(
% 0.14/0.40 ? [X0 : $i > $i > $o] : (($true != (mweakly_dense @ X0)) & ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ (mbox @ X0 @ Y0)) @ (mbox @ X0 @ Y0)))))))),
% 0.14/0.40 inference(ennf_transformation,[],[f86])).
% 0.14/0.40 thf(f86,plain,(
% 0.14/0.40 ~! [X0 : $i > $i > $o] : (($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ X0 @ (mbox @ X0 @ Y0)) @ (mbox @ X0 @ Y0)))))) => ($true = (mweakly_dense @ X0)))),
% 0.14/0.40 inference(fool_elimination,[],[f85])).
% 0.14/0.40 thf(f85,plain,(
% 0.14/0.40 ~! [X0 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mimplies @ (mbox @ X0 @ (mbox @ X0 @ X1)) @ (mbox @ X0 @ X1))))) => (mweakly_dense @ X0))),
% 0.14/0.40 inference(rectify,[],[f33])).
% 0.14/0.40 thf(f33,negated_conjecture,(
% 0.14/0.40 ~! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ X6 @ (mbox @ X6 @ X11)) @ (mbox @ X6 @ X11))))) => (mweakly_dense @ X6))),
% 0.14/0.40 inference(negated_conjecture,[],[f32])).
% 0.14/0.40 thf(f32,conjecture,(
% 0.14/0.40 ! [X6 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mimplies @ (mbox @ X6 @ (mbox @ X6 @ X11)) @ (mbox @ X6 @ X11))))) => (mweakly_dense @ X6))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.14/0.40 thf(f221,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((sK0 @ sK3 @ X1) = $false) | (sK2 != X1)) ) | ~spl1_4),
% 0.14/0.40 inference(avatar_component_clause,[],[f220])).
% 0.14/0.40 thf(f220,plain,(
% 0.14/0.40 spl1_4 <=> ! [X1] : ((sK2 != X1) | ((sK0 @ sK3 @ X1) = $false))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.14/0.40 thf(f240,plain,(
% 0.14/0.40 ~spl1_3),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f239])).
% 0.14/0.40 thf(f239,plain,(
% 0.14/0.40 $false | ~spl1_3),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f236])).
% 0.14/0.40 thf(f236,plain,(
% 0.14/0.40 ($false = $true) | ~spl1_3),
% 0.14/0.40 inference(superposition,[],[f116,f218])).
% 0.14/0.40 thf(f218,plain,(
% 0.14/0.40 ($false = (sK0 @ sK3 @ sK2)) | ~spl1_3),
% 0.14/0.40 inference(avatar_component_clause,[],[f216])).
% 0.14/0.40 thf(f216,plain,(
% 0.14/0.40 spl1_3 <=> ($false = (sK0 @ sK3 @ sK2))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 0.14/0.40 thf(f223,plain,(
% 0.14/0.40 spl1_4 | spl1_3 | spl1_4),
% 0.14/0.40 inference(avatar_split_clause,[],[f210,f220,f216,f220])).
% 0.14/0.40 thf(f210,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : ((sK2 != X1) | ((sK0 @ sK3 @ X0) = $false) | (sK2 != X0) | ($false = (sK0 @ sK3 @ sK2)) | ((sK0 @ sK3 @ X1) = $false)) )),
% 0.14/0.40 inference(equality_proxy_clausification,[],[f209])).
% 0.14/0.40 thf(f209,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (((sK0 @ sK3 @ X0) = $false) | ((sK0 @ sK3 @ X1) = $false) | (sK2 != X1) | ($false = (sK2 = X0)) | ($false = (sK0 @ sK3 @ sK2))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f208])).
% 0.14/0.40 thf(f208,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (((sK0 @ sK3 @ X1) = $false) | ((sK0 @ sK3 @ X0) = $false) | ($false = (sK0 @ sK3 @ sK2)) | (sK2 != X1) | ($true = (~ (sK2 = X0)))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f207])).
% 0.14/0.40 thf(f207,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (((sK0 @ sK3 @ X0) = $false) | ($false = (sK0 @ sK3 @ sK2)) | ((sK0 @ sK3 @ X1) = $false) | ($true = ((^[Y0 : $i]: (~ (sK2 = Y0))) @ X0)) | (sK2 != X1)) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f204])).
% 0.14/0.40 thf(f204,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (($false = $true) | ($false = (sK0 @ sK3 @ sK2)) | ($true = ((^[Y0 : $i]: (~ (sK2 = Y0))) @ X0)) | ((sK0 @ sK3 @ X1) = $false) | ((sK0 @ sK3 @ X0) = $false) | (sK2 != X1)) )),
% 0.14/0.40 inference(superposition,[],[f135,f202])).
% 0.14/0.40 thf(f202,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (($false = (sK0 @ sK3 @ (sK4 @ X0 @ (^[Y0 : $i]: (~ (sK2 = Y0)))))) | ($false = (sK0 @ X0 @ sK2)) | (sK2 != X1) | ($false = (sK0 @ X0 @ X1))) )),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f200])).
% 0.14/0.40 thf(f200,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (($false = (sK0 @ sK3 @ (sK4 @ X0 @ (^[Y0 : $i]: (~ (sK2 = Y0)))))) | (sK2 != X1) | ($false = $true) | ($false = (sK0 @ X0 @ sK2)) | ($false = (sK0 @ X0 @ X1))) )),
% 0.14/0.40 inference(superposition,[],[f119,f177])).
% 0.14/0.40 thf(f177,plain,(
% 0.14/0.40 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = (sK0 @ (sK4 @ X0 @ (^[Y0 : $i]: (~ (X1 = Y0)))) @ X1)) | ($false = (sK0 @ X0 @ X1)) | ($false = (sK0 @ X0 @ X2)) | (X1 != X2)) )),
% 0.14/0.40 inference(equality_proxy_clausification,[],[f176])).
% 0.14/0.40 thf(f176,plain,(
% 0.14/0.40 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (sK0 @ X0 @ X2)) | ($true = (sK0 @ (sK4 @ X0 @ (^[Y0 : $i]: (~ (X1 = Y0)))) @ X1)) | ((X1 = X2) = $false) | ($false = (sK0 @ X0 @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f175])).
% 0.14/0.40 thf(f175,plain,(
% 0.14/0.40 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (sK0 @ X0 @ X1)) | ((~ (X1 = X2)) = $true) | ($true = (sK0 @ (sK4 @ X0 @ (^[Y0 : $i]: (~ (X1 = Y0)))) @ X1)) | ($false = (sK0 @ X0 @ X2))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f174])).
% 0.14/0.40 thf(f174,plain,(
% 0.14/0.40 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = (sK0 @ X0 @ X2)) | ($true = ((^[Y0 : $i]: (~ (X1 = Y0))) @ X2)) | ($true = (sK0 @ (sK4 @ X0 @ (^[Y0 : $i]: (~ (X1 = Y0)))) @ X1)) | ($false = (sK0 @ X0 @ X1))) )),
% 0.14/0.40 inference(superposition,[],[f142,f158])).
% 0.14/0.40 thf(f158,plain,(
% 0.14/0.40 ( ! [X0 : $i,X1 : $i] : (((sK5 @ X0 @ (^[Y0 : $i]: (~ (X1 = Y0)))) = X1) | ($false = (sK0 @ X0 @ X1))) )),
% 0.14/0.40 inference(leibniz_equality_elimination,[],[f140])).
% 0.14/0.40 thf(f140,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (X2 @ (sK5 @ X1 @ X2))) | ((sK0 @ X1 @ X3) = $false) | ($true = (X2 @ X3))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f139])).
% 0.14/0.40 thf(f139,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((sK0 @ X1 @ X3) = $false) | ($false = ((~ (sK0 @ (sK4 @ X1 @ X2) @ (sK5 @ X1 @ X2))) | (X2 @ (sK5 @ X1 @ X2)))) | ($true = (X2 @ X3))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f138])).
% 0.14/0.40 thf(f138,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (~ (sK0 @ X1 @ X3))) | ($false = ((~ (sK0 @ (sK4 @ X1 @ X2) @ (sK5 @ X1 @ X2))) | (X2 @ (sK5 @ X1 @ X2)))) | ($true = (X2 @ X3))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f137])).
% 0.14/0.40 thf(f137,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (X2 @ X3)) | ($false = ((^[Y0 : $i]: ((~ (sK0 @ (sK4 @ X1 @ X2) @ Y0)) | (X2 @ Y0))) @ (sK5 @ X1 @ X2))) | ($true = (~ (sK0 @ X1 @ X3)))) )),
% 0.14/0.40 inference(sigma_clausification,[],[f136])).
% 0.14/0.40 thf(f136,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ (sK4 @ X1 @ X2) @ Y0)) | (X2 @ Y0))))) | ($true = (~ (sK0 @ X1 @ X3))) | ($true = (X2 @ X3))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f131])).
% 0.14/0.40 thf(f131,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((~ (sK0 @ X1 @ X3)) | (X2 @ X3))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ (sK4 @ X1 @ X2) @ Y0)) | (X2 @ Y0)))))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f130])).
% 0.14/0.40 thf(f130,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = ((~ (sK0 @ X1 @ (sK4 @ X1 @ X2))) | (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ (sK4 @ X1 @ X2) @ Y0)) | (X2 @ Y0)))))) | ($true = ((~ (sK0 @ X1 @ X3)) | (X2 @ X3)))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f129])).
% 0.14/0.40 thf(f129,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((~ (sK0 @ X1 @ X3)) | (X2 @ X3))) | ($false = ((^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (X2 @ Y1)))))) @ (sK4 @ X1 @ X2)))) )),
% 0.14/0.40 inference(sigma_clausification,[],[f128])).
% 0.14/0.40 thf(f128,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (X2 @ Y1)))))))) | ($true = ((~ (sK0 @ X1 @ X3)) | (X2 @ X3)))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f127])).
% 0.14/0.40 thf(f127,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (X2 @ Y1)))))))) = $true) | ($true = ((~ (sK0 @ X1 @ X3)) | (X2 @ X3)))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f126])).
% 0.14/0.40 thf(f126,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (X2 @ Y1)))))))) = $true) | ($true = ((^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (X2 @ Y0))) @ X3))) )),
% 0.14/0.40 inference(pi_clausification,[],[f125])).
% 0.14/0.40 thf(f125,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (X2 @ Y0)))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (X2 @ Y1)))))))) = $true)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f124])).
% 0.14/0.40 thf(f124,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ Y0 @ Y1)) | (X2 @ Y1)))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (sK0 @ X1 @ Y0)) | (X2 @ Y0))))) = $true)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f123])).
% 0.14/0.40 thf(f123,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y1 @ Y2)) | (Y0 @ Y2)))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (Y0 @ Y1)))))) @ X2))) )),
% 0.14/0.40 inference(pi_clausification,[],[f122])).
% 0.14/0.40 thf(f122,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y1 @ Y2)) | (Y0 @ Y2)))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (sK0 @ X1 @ Y1)) | (Y0 @ Y1))))))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f121])).
% 0.14/0.40 thf(f121,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (sK0 @ Y2 @ Y3)) | (Y1 @ Y3)))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2)))))))) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f120])).
% 0.14/0.40 thf(f120,plain,(
% 0.14/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (!! @ $i @ (^[Y3 : $i]: ((~ (sK0 @ Y2 @ Y3)) | (Y1 @ Y3)))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (sK0 @ Y0 @ Y2)) | (Y1 @ Y2))))))))))),
% 0.14/0.40 inference(beta_eta_normalization,[],[f109])).
% 0.14/0.40 thf(f109,plain,(
% 0.14/0.40 ($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 @ ((^[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]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ sK0 @ Y0))))))),
% 0.14/0.40 inference(definition_unfolding,[],[f105,f98,f103,f107,f99,f99,f99])).
% 0.14/0.40 thf(f99,plain,(
% 0.14/0.40 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f55])).
% 0.14/0.40 thf(f55,plain,(
% 0.14/0.40 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f54])).
% 0.14/0.40 thf(f54,plain,(
% 0.14/0.40 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))) = mbox)),
% 0.14/0.40 inference(rectify,[],[f16])).
% 0.14/0.40 thf(f16,axiom,(
% 0.14/0.40 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))) = mbox)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.14/0.40 thf(f107,plain,(
% 0.14/0.40 (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)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f102,f104,f101])).
% 0.14/0.40 thf(f101,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f47])).
% 0.14/0.40 thf(f47,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(fool_elimination,[],[f46])).
% 0.14/0.40 thf(f46,plain,(
% 0.14/0.40 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f3])).
% 0.14/0.40 thf(f3,axiom,(
% 0.14/0.40 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.14/0.40 thf(f104,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f45])).
% 0.14/0.40 thf(f45,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f44])).
% 0.14/0.40 thf(f44,plain,(
% 0.14/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.14/0.40 inference(rectify,[],[f4])).
% 0.14/0.40 thf(f4,axiom,(
% 0.14/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.14/0.40 thf(f102,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f57])).
% 0.14/0.40 thf(f57,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f56])).
% 0.14/0.40 thf(f56,plain,(
% 0.14/0.40 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.40 inference(rectify,[],[f6])).
% 0.14/0.40 thf(f6,axiom,(
% 0.14/0.40 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.40 thf(f103,plain,(
% 0.14/0.40 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f84])).
% 0.14/0.40 thf(f84,plain,(
% 0.14/0.40 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.14/0.40 inference(fool_elimination,[],[f83])).
% 0.14/0.40 thf(f83,plain,(
% 0.14/0.40 ((^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))) = mforall_prop)),
% 0.14/0.40 inference(rectify,[],[f11])).
% 0.14/0.40 thf(f11,axiom,(
% 0.14/0.40 ((^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))) = mforall_prop)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop)).
% 0.14/0.40 thf(f98,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f80])).
% 0.14/0.40 thf(f80,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f79])).
% 0.14/0.40 thf(f79,plain,(
% 0.14/0.40 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.14/0.40 inference(rectify,[],[f28])).
% 0.14/0.40 thf(f28,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.40 thf(f105,plain,(
% 0.14/0.40 ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ sK0 @ (mbox @ sK0 @ Y0)) @ (mbox @ sK0 @ Y0))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f97])).
% 0.14/0.40 thf(f142,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((sK0 @ (sK4 @ X1 @ X2) @ (sK5 @ X1 @ X2)) = $true) | ($true = (X2 @ X3)) | ((sK0 @ X1 @ X3) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f141])).
% 0.14/0.40 thf(f141,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (~ (sK0 @ (sK4 @ X1 @ X2) @ (sK5 @ X1 @ X2)))) | ((sK0 @ X1 @ X3) = $false) | ($true = (X2 @ X3))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f139])).
% 0.14/0.40 thf(f119,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (sK0 @ X1 @ sK2)) | ((sK0 @ sK3 @ X1) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f118])).
% 0.14/0.40 thf(f118,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = ((sK0 @ X1 @ sK2) & (sK0 @ sK3 @ X1)))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f117])).
% 0.14/0.40 thf(f117,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((sK0 @ Y0 @ sK2) & (sK0 @ sK3 @ Y0))) @ X1))) )),
% 0.14/0.40 inference(pi_clausification,[],[f115])).
% 0.14/0.40 thf(f115,plain,(
% 0.14/0.40 ((?? @ $i @ (^[Y0 : $i]: ((sK0 @ Y0 @ sK2) & (sK0 @ sK3 @ Y0)))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f114])).
% 0.14/0.40 thf(f135,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (sK0 @ X1 @ (sK4 @ X1 @ X2))) | ($true = (X2 @ X3)) | ((sK0 @ X1 @ X3) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f134])).
% 0.14/0.40 thf(f134,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (X2 @ X3)) | ($true = (sK0 @ X1 @ (sK4 @ X1 @ X2))) | ($true = (~ (sK0 @ X1 @ X3)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f133])).
% 0.14/0.40 thf(f133,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (sK0 @ X1 @ (sK4 @ X1 @ X2))) | ($true = ((~ (sK0 @ X1 @ X3)) | (X2 @ X3)))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f132])).
% 0.14/0.40 thf(f132,plain,(
% 0.14/0.40 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($false = (~ (sK0 @ X1 @ (sK4 @ X1 @ X2)))) | ($true = ((~ (sK0 @ X1 @ X3)) | (X2 @ X3)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f130])).
% 0.14/0.40 % SZS output end Proof for theBenchmark
% 0.14/0.40 % (22742)------------------------------
% 0.14/0.40 % (22742)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (22742)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (22742)Memory used [KB]: 5756
% 0.14/0.40 % (22742)Time elapsed: 0.017 s
% 0.14/0.40 % (22742)Instructions burned: 20 (million)
% 0.14/0.40 % (22742)------------------------------
% 0.14/0.40 % (22742)------------------------------
% 0.14/0.40 % (22736)Success in time 0.029 s
% 0.14/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------