TSTP Solution File: SEV289^5 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEV289^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 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 : n003.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 04:12:40 EDT 2024
% Result : Theorem 0.24s 0.42s
% Output : Refutation 0.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEV289^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.08/0.15 % 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
% 0.16/0.37 % Computer : n003.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sun May 19 19:17:37 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a TH0_THM_EQU_NAR problem
% 0.16/0.37 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
% 0.16/0.39 % (13935)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.40 % (13938)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.40 % (13940)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)
% 0.16/0.40 % (13938)Instruction limit reached!
% 0.16/0.40 % (13938)------------------------------
% 0.16/0.40 % (13938)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (13938)Termination reason: Unknown
% 0.16/0.40 % (13938)Termination phase: Preprocessing 3
% 0.16/0.40
% 0.16/0.40 % (13938)Memory used [KB]: 895
% 0.16/0.40 % (13938)Time elapsed: 0.003 s
% 0.16/0.40 % (13938)Instructions burned: 2 (million)
% 0.16/0.40 % (13938)------------------------------
% 0.16/0.40 % (13938)------------------------------
% 0.16/0.40 % (13939)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)
% 0.16/0.40 % (13940)Refutation not found, incomplete strategy
% 0.16/0.40 % (13940)------------------------------
% 0.16/0.40 % (13940)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (13940)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.40
% 0.16/0.40
% 0.16/0.40 % (13940)Memory used [KB]: 5500
% 0.16/0.40 % (13940)Time elapsed: 0.002 s
% 0.16/0.40 % (13940)Instructions burned: 2 (million)
% 0.16/0.40 % (13940)------------------------------
% 0.16/0.40 % (13940)------------------------------
% 0.16/0.40 % (13939)Instruction limit reached!
% 0.16/0.40 % (13939)------------------------------
% 0.16/0.40 % (13939)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (13939)Termination reason: Unknown
% 0.16/0.40 % (13939)Termination phase: Function definition elimination
% 0.16/0.40
% 0.16/0.40 % (13939)Memory used [KB]: 895
% 0.16/0.40 % (13939)Time elapsed: 0.003 s
% 0.16/0.40 % (13939)Instructions burned: 2 (million)
% 0.16/0.40 % (13939)------------------------------
% 0.16/0.40 % (13939)------------------------------
% 0.16/0.40 % (13942)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)
% 0.16/0.40 % (13936)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)
% 0.16/0.40 % (13937)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)
% 0.16/0.41 % (13942)Instruction limit reached!
% 0.16/0.41 % (13942)------------------------------
% 0.16/0.41 % (13942)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (13942)Termination reason: Unknown
% 0.16/0.41 % (13942)Termination phase: Saturation
% 0.16/0.41
% 0.16/0.41 % (13942)Memory used [KB]: 5500
% 0.16/0.41 % (13942)Time elapsed: 0.004 s
% 0.16/0.41 % (13942)Instructions burned: 3 (million)
% 0.16/0.41 % (13942)------------------------------
% 0.16/0.41 % (13942)------------------------------
% 0.16/0.41 % (13941)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.41 % (13936)Instruction limit reached!
% 0.16/0.41 % (13936)------------------------------
% 0.16/0.41 % (13936)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (13936)Termination reason: Unknown
% 0.16/0.41 % (13936)Termination phase: Saturation
% 0.16/0.41
% 0.16/0.41 % (13936)Memory used [KB]: 5500
% 0.16/0.41 % (13936)Time elapsed: 0.004 s
% 0.16/0.41 % (13936)Instructions burned: 4 (million)
% 0.16/0.41 % (13936)------------------------------
% 0.16/0.41 % (13936)------------------------------
% 0.24/0.41 % (13937)First to succeed.
% 0.24/0.42 % (13937)Refutation found. Thanks to Tanya!
% 0.24/0.42 % SZS status Theorem for theBenchmark
% 0.24/0.42 % SZS output start Proof for theBenchmark
% 0.24/0.42 thf(func_def_0, type, cNAT: (($i > $o) > $o) > $o).
% 0.24/0.42 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 0.24/0.42 thf(func_def_2, type, cZERO: ($i > $o) > $o).
% 0.24/0.42 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.24/0.42 thf(func_def_17, type, sK0: ($i > $o) > $o).
% 0.24/0.42 thf(func_def_19, type, sK2: ((($i > $o) > $o) > $o) > ($i > $o) > $o).
% 0.24/0.42 thf(func_def_20, type, sK3: (($i > $o) > $o) > $o).
% 0.24/0.42 thf(func_def_21, type, ph4: !>[X0: $tType]:(X0)).
% 0.24/0.42 thf(f95,plain,(
% 0.24/0.42 $false),
% 0.24/0.42 inference(avatar_sat_refutation,[],[f62,f77,f94])).
% 0.24/0.42 thf(f94,plain,(
% 0.24/0.42 ~spl1_1),
% 0.24/0.42 inference(avatar_contradiction_clause,[],[f93])).
% 0.24/0.42 thf(f93,plain,(
% 0.24/0.42 $false | ~spl1_1),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f92])).
% 0.24/0.42 thf(f92,plain,(
% 0.24/0.42 ($true = $false) | ~spl1_1),
% 0.24/0.42 inference(forward_demodulation,[],[f56,f47])).
% 0.24/0.42 thf(f47,plain,(
% 0.24/0.42 ((sK3 @ sK0) = $false)),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f45])).
% 0.24/0.42 thf(f45,plain,(
% 0.24/0.42 ($true = $false) | ((sK3 @ sK0) = $false)),
% 0.24/0.42 inference(superposition,[],[f44,f38])).
% 0.24/0.42 thf(f38,plain,(
% 0.24/0.42 ((sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) = $false)),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f37])).
% 0.24/0.42 thf(f37,plain,(
% 0.24/0.42 ($false = (((sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK0 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))),
% 0.24/0.42 inference(beta_eta_normalization,[],[f36])).
% 0.24/0.42 thf(f36,plain,(
% 0.24/0.42 (((^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ sK3) = $false)),
% 0.24/0.42 inference(sigma_clausification,[],[f35])).
% 0.24/0.42 thf(f35,plain,(
% 0.24/0.42 ($true != (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))))))) => (Y0 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (sK0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))),
% 0.24/0.42 inference(beta_eta_normalization,[],[f25])).
% 0.24/0.42 thf(f25,plain,(
% 0.24/0.42 ($true != ((^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3)))))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))))))))) @ Y2)))))) => (Y1 @ Y0))))) @ ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))) @ sK0)))),
% 0.24/0.42 inference(definition_unfolding,[],[f18,f23,f22])).
% 0.24/0.42 thf(f22,plain,(
% 0.24/0.42 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 0.24/0.42 inference(cnf_transformation,[],[f10])).
% 0.24/0.42 thf(f10,plain,(
% 0.24/0.42 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))),
% 0.24/0.42 inference(fool_elimination,[],[f9])).
% 0.24/0.42 thf(f9,plain,(
% 0.24/0.42 ((^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2] : ((X0 @ (^[X3 : $i] : ((X1 @ X3) & (X2 != X3)))) & (X1 @ X2)))) = cSUCC)),
% 0.24/0.42 inference(rectify,[],[f2])).
% 0.24/0.42 thf(f2,axiom,(
% 0.24/0.42 ((^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1] : ((X2 @ (^[X3 : $i] : ((X0 @ X3) & (X1 != X3)))) & (X0 @ X1)))) = cSUCC)),
% 0.24/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cSUCC_def)).
% 0.24/0.42 thf(f23,plain,(
% 0.24/0.42 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3)))))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))))))))) @ Y2)))))) => (Y1 @ Y0))))))),
% 0.24/0.42 inference(definition_unfolding,[],[f20,f21,f22])).
% 0.24/0.42 thf(f21,plain,(
% 0.24/0.42 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.24/0.42 inference(cnf_transformation,[],[f12])).
% 0.24/0.42 thf(f12,plain,(
% 0.24/0.42 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.24/0.42 inference(fool_elimination,[],[f11])).
% 0.24/0.42 thf(f11,plain,(
% 0.24/0.42 ((^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))) = cZERO)),
% 0.24/0.42 inference(rectify,[],[f1])).
% 0.24/0.42 thf(f1,axiom,(
% 0.24/0.42 ((^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))) = cZERO)),
% 0.24/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cZERO_def)).
% 0.24/0.42 thf(f20,plain,(
% 0.24/0.42 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2)))))) => (Y1 @ Y0))))))),
% 0.24/0.42 inference(cnf_transformation,[],[f8])).
% 0.24/0.42 thf(f8,plain,(
% 0.24/0.42 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ cZERO) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2)))))) => (Y1 @ Y0))))))),
% 0.24/0.42 inference(fool_elimination,[],[f7])).
% 0.24/0.42 thf(f7,plain,(
% 0.24/0.42 ((^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : ((! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2))) & (X1 @ cZERO)) => (X1 @ X0)))) = cNAT)),
% 0.24/0.42 inference(rectify,[],[f3])).
% 0.24/0.42 thf(f3,axiom,(
% 0.24/0.42 ((^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1))) & (X0 @ cZERO)) => (X0 @ X2)))) = cNAT)),
% 0.24/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cNAT_def)).
% 0.24/0.42 thf(f18,plain,(
% 0.24/0.42 ($true != (cNAT @ (cSUCC @ sK0)))),
% 0.24/0.42 inference(cnf_transformation,[],[f17])).
% 0.24/0.42 thf(f17,plain,(
% 0.24/0.42 ($true = (cNAT @ sK0)) & ($true != (cNAT @ (cSUCC @ sK0)))),
% 0.24/0.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16])).
% 0.24/0.42 thf(f16,plain,(
% 0.24/0.42 ? [X0 : ($i > $o) > $o] : (($true = (cNAT @ X0)) & ($true != (cNAT @ (cSUCC @ X0)))) => (($true = (cNAT @ sK0)) & ($true != (cNAT @ (cSUCC @ sK0))))),
% 0.24/0.42 introduced(choice_axiom,[])).
% 0.24/0.42 thf(f15,plain,(
% 0.24/0.42 ? [X0 : ($i > $o) > $o] : (($true = (cNAT @ X0)) & ($true != (cNAT @ (cSUCC @ X0))))),
% 0.24/0.42 inference(ennf_transformation,[],[f14])).
% 0.24/0.42 thf(f14,plain,(
% 0.24/0.42 ~! [X0 : ($i > $o) > $o] : (($true = (cNAT @ X0)) => ($true = (cNAT @ (cSUCC @ X0))))),
% 0.24/0.42 inference(fool_elimination,[],[f13])).
% 0.24/0.42 thf(f13,plain,(
% 0.24/0.42 ~! [X0 : ($i > $o) > $o] : ((cNAT @ X0) => (cNAT @ (cSUCC @ X0)))),
% 0.24/0.42 inference(rectify,[],[f5])).
% 0.24/0.42 thf(f5,negated_conjecture,(
% 0.24/0.42 ~! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => (cNAT @ (cSUCC @ X1)))),
% 0.24/0.42 inference(negated_conjecture,[],[f4])).
% 0.24/0.42 thf(f4,conjecture,(
% 0.24/0.42 ! [X1 : ($i > $o) > $o] : ((cNAT @ X1) => (cNAT @ (cSUCC @ X1)))),
% 0.24/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTTTP6101)).
% 0.24/0.42 thf(f44,plain,(
% 0.24/0.42 ( ! [X1 : ($i > $o) > $o] : (($true = (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))) | ($false = (sK3 @ X1))) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f43])).
% 0.24/0.42 thf(f43,plain,(
% 0.24/0.42 ( ! [X1 : ($i > $o) > $o] : (($true = ((sK3 @ X1) => (sK3 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2)))))))))))) )),
% 0.24/0.42 inference(beta_eta_normalization,[],[f42])).
% 0.24/0.42 thf(f42,plain,(
% 0.24/0.42 ( ! [X1 : ($i > $o) > $o] : (($true = ((^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ X1))) )),
% 0.24/0.42 inference(pi_clausification,[],[f40])).
% 0.24/0.42 thf(f40,plain,(
% 0.24/0.42 ($true = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3)))))))))))))),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f39])).
% 0.24/0.42 thf(f39,plain,(
% 0.24/0.42 (((sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((sK3 @ Y0) => (sK3 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) = $true)),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f37])).
% 0.24/0.42 thf(f56,plain,(
% 0.24/0.42 ((sK3 @ sK0) = $true) | ~spl1_1),
% 0.24/0.42 inference(avatar_component_clause,[],[f54])).
% 0.24/0.42 thf(f54,plain,(
% 0.24/0.42 spl1_1 <=> ((sK3 @ sK0) = $true)),
% 0.24/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.24/0.42 thf(f77,plain,(
% 0.24/0.42 ~spl1_2),
% 0.24/0.42 inference(avatar_contradiction_clause,[],[f76])).
% 0.24/0.42 thf(f76,plain,(
% 0.24/0.42 $false | ~spl1_2),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f75])).
% 0.24/0.42 thf(f75,plain,(
% 0.24/0.42 ($true = $false) | ~spl1_2),
% 0.24/0.42 inference(backward_demodulation,[],[f41,f70])).
% 0.24/0.42 thf(f70,plain,(
% 0.24/0.42 ($false = (sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ~spl1_2),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f69])).
% 0.24/0.42 thf(f69,plain,(
% 0.24/0.42 ($false = (sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ($true = $false) | ~spl1_2),
% 0.24/0.42 inference(forward_demodulation,[],[f68,f47])).
% 0.24/0.42 thf(f68,plain,(
% 0.24/0.42 ($false = (sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ((sK3 @ sK0) = $true) | ~spl1_2),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f67])).
% 0.24/0.42 thf(f67,plain,(
% 0.24/0.42 ($false = (sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ((sK3 @ sK0) = $true) | ($true = $false) | ~spl1_2),
% 0.24/0.42 inference(forward_demodulation,[],[f66,f60])).
% 0.24/0.42 thf(f60,plain,(
% 0.24/0.42 ($true = (sK3 @ (sK2 @ sK3))) | ~spl1_2),
% 0.24/0.42 inference(avatar_component_clause,[],[f58])).
% 0.24/0.42 thf(f58,plain,(
% 0.24/0.42 spl1_2 <=> ($true = (sK3 @ (sK2 @ sK3)))),
% 0.24/0.42 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.24/0.42 thf(f66,plain,(
% 0.24/0.42 ($false = (sK3 @ (sK2 @ sK3))) | ((sK3 @ sK0) = $true) | ($false = (sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f63])).
% 0.24/0.42 thf(f63,plain,(
% 0.24/0.42 ($true = $false) | ($false = (sK3 @ (sK2 @ sK3))) | ((sK3 @ sK0) = $true) | ($false = (sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
% 0.24/0.42 inference(superposition,[],[f33,f44])).
% 0.24/0.42 thf(f33,plain,(
% 0.24/0.42 ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK2 @ X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))) = $false) | ((X1 @ sK0) = $true) | ($false = (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f32])).
% 0.24/0.42 thf(f32,plain,(
% 0.24/0.42 ( ! [X1 : (($i > $o) > $o) > $o] : (($false = (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ($false = ((X1 @ (sK2 @ X1)) => (X1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) & (sK2 @ X1 @ (^[Y2 : $i]: ((~ (Y1 = Y2)) & (Y0 @ Y2))))))))))) | ((X1 @ sK0) = $true)) )),
% 0.24/0.42 inference(beta_eta_normalization,[],[f31])).
% 0.24/0.42 thf(f31,plain,(
% 0.24/0.42 ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ sK0) = $true) | ($false = (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | (((^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))) @ (sK2 @ X1)) = $false)) )),
% 0.24/0.42 inference(sigma_clausification,[],[f30])).
% 0.24/0.42 thf(f30,plain,(
% 0.24/0.42 ( ! [X1 : (($i > $o) > $o) > $o] : (($false = (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ($false = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) | ((X1 @ sK0) = $true)) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f29])).
% 0.24/0.42 thf(f29,plain,(
% 0.24/0.42 ( ! [X1 : (($i > $o) > $o) > $o] : ((((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) = $false) | ((X1 @ sK0) = $true)) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f28])).
% 0.24/0.42 thf(f28,plain,(
% 0.24/0.42 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = (((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) & (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ (^[Y3 : $i]: ((~ (Y2 = Y3)) & (Y1 @ Y3))))))))))))) => (X1 @ sK0)))) )),
% 0.24/0.42 inference(beta_eta_normalization,[],[f27])).
% 0.24/0.42 thf(f27,plain,(
% 0.24/0.42 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = ((^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))))))) => (Y0 @ sK0))) @ X1))) )),
% 0.24/0.42 inference(pi_clausification,[],[f26])).
% 0.24/0.42 thf(f26,plain,(
% 0.24/0.42 ($true = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1)))) & (!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y2 @ Y3) & (Y1 @ (^[Y4 : $i]: ((~ (Y3 = Y4)) & (Y2 @ Y4))))))))))))) => (Y0 @ sK0)))))),
% 0.24/0.42 inference(beta_eta_normalization,[],[f24])).
% 0.24/0.42 thf(f24,plain,(
% 0.24/0.42 ($true = ((^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3)))))) & (!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y4 @ Y5) & (Y3 @ (^[Y6 : $i]: ((~ (Y5 = Y6)) & (Y4 @ Y6)))))))))) @ Y2)))))) => (Y1 @ Y0))))) @ sK0))),
% 0.24/0.42 inference(definition_unfolding,[],[f19,f23])).
% 0.24/0.42 thf(f19,plain,(
% 0.24/0.42 ($true = (cNAT @ sK0))),
% 0.24/0.42 inference(cnf_transformation,[],[f17])).
% 0.24/0.42 thf(f41,plain,(
% 0.24/0.42 ($true = (sK3 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f39])).
% 0.24/0.42 thf(f62,plain,(
% 0.24/0.42 spl1_2 | spl1_1),
% 0.24/0.42 inference(avatar_split_clause,[],[f51,f54,f58])).
% 0.24/0.42 thf(f51,plain,(
% 0.24/0.42 ((sK3 @ sK0) = $true) | ($true = (sK3 @ (sK2 @ sK3)))),
% 0.24/0.42 inference(trivial_inequality_removal,[],[f49])).
% 0.24/0.42 thf(f49,plain,(
% 0.24/0.42 ($true = (sK3 @ (sK2 @ sK3))) | ((sK3 @ sK0) = $true) | ($true = $false)),
% 0.24/0.42 inference(superposition,[],[f34,f41])).
% 0.24/0.42 thf(f34,plain,(
% 0.24/0.42 ( ! [X1 : (($i > $o) > $o) > $o] : (($false = (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ($true = (X1 @ (sK2 @ X1))) | ((X1 @ sK0) = $true)) )),
% 0.24/0.42 inference(binary_proxy_clausification,[],[f32])).
% 0.24/0.42 % SZS output end Proof for theBenchmark
% 0.24/0.42 % (13937)------------------------------
% 0.24/0.42 % (13937)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.24/0.42 % (13937)Termination reason: Refutation
% 0.24/0.42
% 0.24/0.42 % (13937)Memory used [KB]: 5628
% 0.24/0.42 % (13937)Time elapsed: 0.032 s
% 0.24/0.42 % (13937)Instructions burned: 8 (million)
% 0.24/0.42 % (13937)------------------------------
% 0.24/0.42 % (13937)------------------------------
% 0.24/0.42 % (13934)Success in time 0.034 s
% 0.24/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------