TSTP Solution File: SYO540^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO540^1 : TPTP v8.2.0. Released v5.2.0.
% 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 : n006.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 09:06:09 EDT 2024
% Result : Theorem 0.14s 0.39s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO540^1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.14 % 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
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 10:40:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 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
% 0.14/0.37 % (32274)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 (3000ds/2Mi)
% 0.14/0.37 % (32274)Instruction limit reached!
% 0.14/0.37 % (32274)------------------------------
% 0.14/0.37 % (32274)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (32274)Termination reason: Unknown
% 0.14/0.37 % (32274)Termination phase: Unused predicate definition removal
% 0.14/0.37
% 0.14/0.37 % (32274)Memory used [KB]: 895
% 0.14/0.37 % (32274)Time elapsed: 0.002 s
% 0.14/0.37 % (32274)Instructions burned: 2 (million)
% 0.14/0.37 % (32274)------------------------------
% 0.14/0.37 % (32274)------------------------------
% 0.14/0.37 % (32273)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.14/0.37 % (32271)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 (3000ds/4Mi)
% 0.14/0.37 % (32273)Instruction limit reached!
% 0.14/0.37 % (32273)------------------------------
% 0.14/0.37 % (32273)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (32273)Termination reason: Unknown
% 0.14/0.38 % (32273)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (32273)Memory used [KB]: 5373
% 0.14/0.38 % (32273)Time elapsed: 0.003 s
% 0.14/0.38 % (32273)Instructions burned: 2 (million)
% 0.14/0.38 % (32273)------------------------------
% 0.14/0.38 % (32273)------------------------------
% 0.14/0.38 % (32271)Instruction limit reached!
% 0.14/0.38 % (32271)------------------------------
% 0.14/0.38 % (32271)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (32271)Termination reason: Unknown
% 0.14/0.38 % (32271)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (32271)Memory used [KB]: 5500
% 0.14/0.38 % (32271)Time elapsed: 0.005 s
% 0.14/0.38 % (32271)Instructions burned: 4 (million)
% 0.14/0.38 % (32271)------------------------------
% 0.14/0.38 % (32271)------------------------------
% 0.14/0.38 % (32272)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 (3000ds/27Mi)
% 0.14/0.38 % (32270)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (3000ds/183Mi)
% 0.14/0.38 % (32276)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (3000ds/18Mi)
% 0.14/0.38 % (32277)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (3000ds/3Mi)
% 0.14/0.38 % (32275)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 (3000ds/275Mi)
% 0.14/0.38 % (32272)First to succeed.
% 0.14/0.38 % (32275)Refutation not found, incomplete strategy
% 0.14/0.38 % (32275)------------------------------
% 0.14/0.38 % (32275)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (32275)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (32275)Memory used [KB]: 5373
% 0.14/0.38 % (32275)Time elapsed: 0.002 s
% 0.14/0.38 % (32275)Instructions burned: 1 (million)
% 0.14/0.38 % (32275)------------------------------
% 0.14/0.38 % (32275)------------------------------
% 0.14/0.38 % (32277)Instruction limit reached!
% 0.14/0.38 % (32277)------------------------------
% 0.14/0.38 % (32277)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (32277)Termination reason: Unknown
% 0.14/0.38 % (32277)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (32277)Memory used [KB]: 5500
% 0.14/0.38 % (32277)Time elapsed: 0.003 s
% 0.14/0.38 % (32277)Instructions burned: 3 (million)
% 0.14/0.38 % (32277)------------------------------
% 0.14/0.38 % (32277)------------------------------
% 0.14/0.39 % (32278)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.14/0.39 % (32272)Refutation found. Thanks to Tanya!
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39 % SZS output start Proof for theBenchmark
% 0.14/0.39 thf(func_def_0, type, eps: ($i > $o) > $i).
% 0.14/0.39 thf(func_def_2, type, if: $o > $i > $i > $i).
% 0.14/0.39 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.14/0.39 thf(func_def_18, type, ph3: !>[X0: $tType]:(X0)).
% 0.14/0.39 thf(f137,plain,(
% 0.14/0.39 $false),
% 0.14/0.39 inference(avatar_sat_refutation,[],[f87,f91,f95,f136])).
% 0.14/0.39 thf(f136,plain,(
% 0.14/0.39 spl2_1 | spl2_3 | ~spl2_4),
% 0.14/0.39 inference(avatar_split_clause,[],[f135,f79,f76,f68])).
% 0.14/0.39 thf(f68,plain,(
% 0.14/0.39 spl2_1 <=> ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0)),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
% 0.14/0.39 thf(f76,plain,(
% 0.14/0.39 spl2_3 <=> ! [X1] : (sK0 != X1)),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl2_3])])).
% 0.14/0.39 thf(f79,plain,(
% 0.14/0.39 spl2_4 <=> (sK1 = $true)),
% 0.14/0.39 introduced(avatar_definition,[new_symbols(naming,[spl2_4])])).
% 0.14/0.39 thf(f135,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((sK0 != X1) | ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0)) ) | ~spl2_4),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f134])).
% 0.14/0.39 thf(f134,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((sK0 != X1) | ($false = $true) | ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0)) ) | ~spl2_4),
% 0.14/0.39 inference(forward_demodulation,[],[f108,f81])).
% 0.14/0.39 thf(f81,plain,(
% 0.14/0.39 (sK1 = $true) | ~spl2_4),
% 0.14/0.39 inference(avatar_component_clause,[],[f79])).
% 0.14/0.39 thf(f108,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0) | ($false = sK1) | (sK0 != X1)) )),
% 0.14/0.39 inference(duplicate_literal_removal,[],[f107])).
% 0.14/0.39 thf(f107,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0) | ($false = sK1) | ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0) | (sK0 != X1)) )),
% 0.14/0.39 inference(equality_proxy_clausification,[],[f105])).
% 0.14/0.39 thf(f105,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0) | ($true = (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) | (sK0 != X1) | ($false = sK1)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f104])).
% 0.14/0.39 thf(f104,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((sK0 != X1) | ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) = $true) | ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0) | ($false = sK1)) )),
% 0.14/0.39 inference(equality_proxy_clausification,[],[f103])).
% 0.14/0.39 thf(f103,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) | ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) = $true) | (sK0 != X1) | ($false = sK1)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f101])).
% 0.14/0.39 thf(f101,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($false = sK1) | (((sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))))) & (~ sK1)) = $true) | ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) = $true) | (sK0 != X1)) )),
% 0.14/0.39 inference(equality_proxy_clausification,[],[f100])).
% 0.14/0.39 thf(f100,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($false = sK1) | ((sK0 = X1) = $false) | (((sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))))) & (~ sK1)) = $true) | ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) = $true)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f99])).
% 0.14/0.39 thf(f99,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) | ((sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))))) & (~ sK1)))) | ($false = sK1) | ((sK0 = X1) = $false)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f98])).
% 0.14/0.39 thf(f98,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($false = (sK1 & (sK0 = X1))) | ($true = ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) | ((sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))))) & (~ sK1))))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f96])).
% 0.14/0.39 thf(f96,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($false = ((sK1 & (sK0 = X1)) | ((sK0 = X1) & (~ sK1)))) | ($true = ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) | ((sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))))) & (~ sK1))))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f92])).
% 0.14/0.39 thf(f92,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))) @ X1) = $false) | (((^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))) @ (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))))) = $true)) )),
% 0.14/0.39 introduced(choice_axiom,[])).
% 0.14/0.39 thf(f95,plain,(
% 0.14/0.39 ~spl2_1),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f94])).
% 0.14/0.39 thf(f94,plain,(
% 0.14/0.39 $false | ~spl2_1),
% 0.14/0.39 inference(trivial_inequality_removal,[],[f93])).
% 0.14/0.39 thf(f93,plain,(
% 0.14/0.39 (sK0 != sK0) | ~spl2_1),
% 0.14/0.39 inference(superposition,[],[f19,f70])).
% 0.14/0.39 thf(f70,plain,(
% 0.14/0.39 ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0) | ~spl2_1),
% 0.14/0.39 inference(avatar_component_clause,[],[f68])).
% 0.14/0.39 thf(f19,plain,(
% 0.14/0.39 ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) != sK0)),
% 0.14/0.39 inference(beta_eta_normalization,[],[f18])).
% 0.14/0.39 thf(f18,plain,(
% 0.14/0.39 (((^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))) @ sK1 @ sK0 @ sK0) != sK0)),
% 0.14/0.39 inference(definition_unfolding,[],[f16,f15])).
% 0.14/0.39 thf(f15,plain,(
% 0.14/0.39 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))))),
% 0.14/0.39 inference(cnf_transformation,[],[f7])).
% 0.14/0.39 thf(f7,plain,(
% 0.14/0.39 (if = (^[Y0 : $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (eps @ (^[Y3 : $i]: ((Y0 & (Y1 = Y3)) | ((Y2 = Y3) & (~ Y0)))))))))))),
% 0.14/0.39 inference(fool_elimination,[],[f6])).
% 0.14/0.39 thf(f6,plain,(
% 0.14/0.39 (if = (^[X0 : $o, X1 : $i, X2 : $i] : (eps @ (^[X3 : $i] : ((~X0 & (X2 = X3)) | ((X1 = X3) & X0))))))),
% 0.14/0.39 inference(rectify,[],[f2])).
% 0.14/0.39 thf(f2,axiom,(
% 0.14/0.39 (if = (^[X2 : $o, X1 : $i, X3 : $i] : (eps @ (^[X4 : $i] : ((~X2 & (X3 = X4)) | ((X1 = X4) & X2))))))),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifd)).
% 0.14/0.39 thf(f16,plain,(
% 0.14/0.39 ((if @ sK1 @ sK0 @ sK0) != sK0)),
% 0.14/0.39 inference(cnf_transformation,[],[f14])).
% 0.14/0.39 thf(f14,plain,(
% 0.14/0.39 ((if @ sK1 @ sK0 @ sK0) != sK0)),
% 0.14/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13])).
% 0.14/0.39 thf(f13,plain,(
% 0.14/0.39 ? [X0,X1 : $o] : ((if @ X1 @ X0 @ X0) != X0) => ((if @ sK1 @ sK0 @ sK0) != sK0)),
% 0.14/0.39 introduced(choice_axiom,[])).
% 0.14/0.39 thf(f12,plain,(
% 0.14/0.39 ? [X0,X1 : $o] : ((if @ X1 @ X0 @ X0) != X0)),
% 0.14/0.39 inference(ennf_transformation,[],[f10])).
% 0.14/0.39 thf(f10,plain,(
% 0.14/0.39 ~! [X0,X1 : $o] : ((if @ X1 @ X0 @ X0) = X0)),
% 0.14/0.39 inference(rectify,[],[f4])).
% 0.14/0.39 thf(f4,negated_conjecture,(
% 0.14/0.39 ~! [X1,X2 : $o] : ((if @ X2 @ X1 @ X1) = X1)),
% 0.14/0.39 inference(negated_conjecture,[],[f3])).
% 0.14/0.39 thf(f3,conjecture,(
% 0.14/0.39 ! [X1,X2 : $o] : ((if @ X2 @ X1 @ X1) = X1)),
% 0.14/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.14/0.39 thf(f91,plain,(
% 0.14/0.39 ~spl2_3),
% 0.14/0.39 inference(avatar_contradiction_clause,[],[f90])).
% 0.14/0.39 thf(f90,plain,(
% 0.14/0.39 $false | ~spl2_3),
% 0.14/0.39 inference(equality_resolution,[],[f77])).
% 0.14/0.39 thf(f77,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((sK0 != X1)) ) | ~spl2_3),
% 0.14/0.39 inference(avatar_component_clause,[],[f76])).
% 0.14/0.39 thf(f87,plain,(
% 0.14/0.39 spl2_3 | spl2_1 | spl2_4),
% 0.14/0.39 inference(avatar_split_clause,[],[f40,f79,f68,f76])).
% 0.14/0.39 thf(f40,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((sK0 != X1) | (sK1 = $true) | ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0)) )),
% 0.14/0.39 inference(duplicate_literal_removal,[],[f39])).
% 0.14/0.39 thf(f39,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((sK1 = $true) | (sK0 != X1) | ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0) | (sK1 = $true)) )),
% 0.14/0.39 inference(not_proxy_clausification,[],[f38])).
% 0.14/0.39 thf(f38,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((sK0 != X1) | ((~ sK1) = $false) | ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0) | (sK1 = $true)) )),
% 0.14/0.39 inference(equality_proxy_clausification,[],[f37])).
% 0.14/0.39 thf(f37,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((sK1 = $true) | ((sK0 = X1) = $false) | ((~ sK1) = $false) | ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f36])).
% 0.14/0.39 thf(f36,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((sK1 = $true) | ($false = ((sK0 = X1) & (~ sK1))) | ((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f34])).
% 0.14/0.39 thf(f34,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (((eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))) = sK0) | ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) = $true) | ($false = ((sK0 = X1) & (~ sK1)))) )),
% 0.14/0.39 inference(equality_proxy_clausification,[],[f25])).
% 0.14/0.39 thf(f25,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) | ($false = ((sK0 = X1) & (~ sK1))) | ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) = $true)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f24])).
% 0.14/0.39 thf(f24,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($false = ((sK1 & (sK0 = X1)) | ((sK0 = X1) & (~ sK1)))) | ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) = $true) | ($true = (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))))))) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f22])).
% 0.14/0.39 thf(f22,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((((sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))))) & (~ sK1)) = $true) | ($false = ((sK1 & (sK0 = X1)) | ((sK0 = X1) & (~ sK1)))) | ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) = $true)) )),
% 0.14/0.39 inference(binary_proxy_clausification,[],[f21])).
% 0.14/0.39 thf(f21,plain,(
% 0.14/0.39 ( ! [X1 : $i] : (($true = ((sK1 & (sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1))))))) | ((sK0 = (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))))) & (~ sK1)))) | ($false = ((sK1 & (sK0 = X1)) | ((sK0 = X1) & (~ sK1))))) )),
% 0.14/0.39 inference(beta_eta_normalization,[],[f20])).
% 0.14/0.39 thf(f20,plain,(
% 0.14/0.39 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))) @ X1) = $false) | (((^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))) @ (eps @ (^[Y0 : $i]: ((sK1 & (sK0 = Y0)) | ((sK0 = Y0) & (~ sK1)))))) = $true)) )),
% 0.14/0.39 introduced(choice_axiom,[])).
% 0.14/0.39 % SZS output end Proof for theBenchmark
% 0.14/0.39 % (32272)------------------------------
% 0.14/0.39 % (32272)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (32272)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (32272)Memory used [KB]: 5500
% 0.14/0.39 % (32272)Time elapsed: 0.010 s
% 0.14/0.39 % (32272)Instructions burned: 7 (million)
% 0.14/0.39 % (32272)------------------------------
% 0.14/0.39 % (32272)------------------------------
% 0.14/0.39 % (32269)Success in time 0.015 s
% 0.14/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------