TSTP Solution File: PUZ113^5 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : PUZ113^5 : TPTP v8.1.2. Bugfixed 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 : n024.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 : Sun May 5 08:49:16 EDT 2024
% Result : Theorem 0.22s 0.40s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : PUZ113^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.15/0.16 % 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 : n024.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 : Fri May 3 18:04:53 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a TH0_THM_EQU_NAR problem
% 0.22/0.37 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/tmp/tmp.Wkn7HK6qUM/Vampire---4.8_25554
% 0.22/0.39 % (25812)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 Vampire---4 for (2999ds/27Mi)
% 0.22/0.39 % (25814)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.22/0.39 % (25810)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on Vampire---4 for (2999ds/183Mi)
% 0.22/0.39 % (25816)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.22/0.39 % (25811)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 Vampire---4 for (2999ds/4Mi)
% 0.22/0.39 % (25817)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (2999ds/3Mi)
% 0.22/0.39 % (25813)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.22/0.39 % (25815)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (2999ds/275Mi)
% 0.22/0.39 % (25813)Instruction limit reached!
% 0.22/0.39 % (25813)------------------------------
% 0.22/0.39 % (25813)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (25813)Termination reason: Unknown
% 0.22/0.39 % (25814)Instruction limit reached!
% 0.22/0.39 % (25814)------------------------------
% 0.22/0.39 % (25814)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (25814)Termination reason: Unknown
% 0.22/0.39 % (25814)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (25814)Memory used [KB]: 895
% 0.22/0.39 % (25814)Time elapsed: 0.004 s
% 0.22/0.39 % (25814)Instructions burned: 3 (million)
% 0.22/0.39 % (25814)------------------------------
% 0.22/0.39 % (25814)------------------------------
% 0.22/0.39 % (25813)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (25813)Memory used [KB]: 5373
% 0.22/0.39 % (25813)Time elapsed: 0.003 s
% 0.22/0.39 % (25813)Instructions burned: 2 (million)
% 0.22/0.39 % (25813)------------------------------
% 0.22/0.39 % (25813)------------------------------
% 0.22/0.39 % (25817)Instruction limit reached!
% 0.22/0.39 % (25817)------------------------------
% 0.22/0.39 % (25817)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (25817)Termination reason: Unknown
% 0.22/0.39 % (25817)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.39 % (25817)Memory used [KB]: 5500
% 0.22/0.39 % (25817)Time elapsed: 0.004 s
% 0.22/0.39 % (25817)Instructions burned: 3 (million)
% 0.22/0.39 % (25817)------------------------------
% 0.22/0.39 % (25817)------------------------------
% 0.22/0.39 % (25815)Refutation not found, incomplete strategy
% 0.22/0.39 % (25815)------------------------------
% 0.22/0.39 % (25815)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (25815)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.39
% 0.22/0.39
% 0.22/0.39 % (25815)Memory used [KB]: 5500
% 0.22/0.39 % (25815)Time elapsed: 0.003 s
% 0.22/0.39 % (25815)Instructions burned: 2 (million)
% 0.22/0.39 % (25815)------------------------------
% 0.22/0.39 % (25815)------------------------------
% 0.22/0.39 % (25811)Instruction limit reached!
% 0.22/0.39 % (25811)------------------------------
% 0.22/0.39 % (25811)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.39 % (25811)Termination reason: Unknown
% 0.22/0.39 % (25811)Termination phase: Saturation
% 0.22/0.39
% 0.22/0.40 % (25811)Memory used [KB]: 5500
% 0.22/0.40 % (25811)Time elapsed: 0.005 s
% 0.22/0.40 % (25811)Instructions burned: 5 (million)
% 0.22/0.40 % (25811)------------------------------
% 0.22/0.40 % (25811)------------------------------
% 0.22/0.40 % (25812)First to succeed.
% 0.22/0.40 % (25812)Refutation found. Thanks to Tanya!
% 0.22/0.40 % SZS status Theorem for Vampire---4
% 0.22/0.40 % SZS output start Proof for Vampire---4
% 0.22/0.40 thf(func_def_1, type, s: $i > $i).
% 0.22/0.40 thf(func_def_2, type, cCKB6_BLACK: $i > $i > $o).
% 0.22/0.40 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.22/0.40 thf(func_def_17, type, sK3: $i > $i > $o).
% 0.22/0.40 thf(func_def_18, type, sK4: ($i > $i > $o) > $i).
% 0.22/0.40 thf(func_def_19, type, sK5: ($i > $i > $o) > $i).
% 0.22/0.40 thf(func_def_20, type, ph6: !>[X0: $tType]:(X0)).
% 0.22/0.40 thf(f94,plain,(
% 0.22/0.40 $false),
% 0.22/0.40 inference(avatar_sat_refutation,[],[f76,f82,f93])).
% 0.22/0.40 thf(f93,plain,(
% 0.22/0.40 ~spl2_1),
% 0.22/0.40 inference(avatar_contradiction_clause,[],[f92])).
% 0.22/0.40 thf(f92,plain,(
% 0.22/0.40 $false | ~spl2_1),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f91])).
% 0.22/0.40 thf(f91,plain,(
% 0.22/0.40 ($true = $false) | ~spl2_1),
% 0.22/0.40 inference(forward_demodulation,[],[f90,f49])).
% 0.22/0.40 thf(f49,plain,(
% 0.22/0.40 ($false = (sK3 @ sK0 @ sK1))),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f48])).
% 0.22/0.40 thf(f48,plain,(
% 0.22/0.40 ($true = $false) | ($false = (sK3 @ sK0 @ sK1))),
% 0.22/0.40 inference(superposition,[],[f29,f45])).
% 0.22/0.40 thf(f45,plain,(
% 0.22/0.40 ($false = (sK3 @ (s @ sK0) @ (s @ sK1)))),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f43])).
% 0.22/0.40 thf(f43,plain,(
% 0.22/0.40 ($true = $false) | ($false = (sK3 @ (s @ sK0) @ (s @ sK1)))),
% 0.22/0.40 inference(superposition,[],[f29,f20])).
% 0.22/0.40 thf(f20,plain,(
% 0.22/0.40 ($false = (sK3 @ (s @ (s @ sK0)) @ (s @ (s @ sK1))))),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f19])).
% 0.22/0.40 thf(f19,plain,(
% 0.22/0.40 ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y0 @ Y1) => ((sK3 @ (s @ (s @ Y0)) @ Y1) & (sK3 @ (s @ Y0) @ (s @ Y1)))))))) & (sK3 @ c1 @ c1)) => (sK3 @ (s @ (s @ sK0)) @ (s @ (s @ sK1)))))),
% 0.22/0.40 inference(beta_eta_normalization,[],[f18])).
% 0.22/0.40 thf(f18,plain,(
% 0.22/0.40 ($false = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => ((Y0 @ (s @ (s @ Y1)) @ Y2) & (Y0 @ (s @ Y1) @ (s @ Y2)))))))) & (Y0 @ c1 @ c1)) => (Y0 @ (s @ (s @ sK0)) @ (s @ (s @ sK1))))) @ sK3))),
% 0.22/0.40 inference(sigma_clausification,[],[f17])).
% 0.22/0.40 thf(f17,plain,(
% 0.22/0.40 ($true != (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => ((Y0 @ (s @ (s @ Y1)) @ Y2) & (Y0 @ (s @ Y1) @ (s @ Y2)))))))) & (Y0 @ c1 @ c1)) => (Y0 @ (s @ (s @ sK0)) @ (s @ (s @ sK1)))))))),
% 0.22/0.40 inference(beta_eta_normalization,[],[f15])).
% 0.22/0.40 thf(f15,plain,(
% 0.22/0.40 ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) => ((Y2 @ (s @ (s @ Y3)) @ Y4) & (Y2 @ (s @ Y3) @ (s @ Y4)))))))) & (Y2 @ c1 @ c1)) => (Y2 @ Y0 @ Y1))))))) @ (s @ (s @ sK0)) @ (s @ (s @ sK1))))),
% 0.22/0.40 inference(definition_unfolding,[],[f14,f12])).
% 0.22/0.40 thf(f12,plain,(
% 0.22/0.40 (cCKB6_BLACK = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) => ((Y2 @ (s @ (s @ Y3)) @ Y4) & (Y2 @ (s @ Y3) @ (s @ Y4)))))))) & (Y2 @ c1 @ c1)) => (Y2 @ Y0 @ Y1))))))))),
% 0.22/0.40 inference(cnf_transformation,[],[f8])).
% 0.22/0.40 thf(f8,plain,(
% 0.22/0.40 (cCKB6_BLACK = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) => ((Y2 @ (s @ (s @ Y3)) @ Y4) & (Y2 @ (s @ Y3) @ (s @ Y4)))))))) & (Y2 @ c1 @ c1)) => (Y2 @ Y0 @ Y1))))))))),
% 0.22/0.40 inference(fool_elimination,[],[f7])).
% 0.22/0.40 thf(f7,plain,(
% 0.22/0.40 (cCKB6_BLACK = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $i > $o] : (((X2 @ c1 @ c1) & ! [X3,X4] : ((X2 @ X4 @ X3) => ((X2 @ (s @ X4) @ (s @ X3)) & (X2 @ (s @ (s @ X4)) @ X3)))) => (X2 @ X0 @ X1)))))),
% 0.22/0.40 inference(rectify,[],[f1])).
% 0.22/0.40 thf(f1,axiom,(
% 0.22/0.40 (cCKB6_BLACK = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $i > $o] : (((X2 @ c1 @ c1) & ! [X4,X3] : ((X2 @ X3 @ X4) => ((X2 @ (s @ X3) @ (s @ X4)) & (X2 @ (s @ (s @ X3)) @ X4)))) => (X2 @ X0 @ X1)))))),
% 0.22/0.40 file('/export/starexec/sandbox/tmp/tmp.Wkn7HK6qUM/Vampire---4.8_25554',cCKB6_BLACK_def)).
% 0.22/0.40 thf(f14,plain,(
% 0.22/0.40 ($true != (cCKB6_BLACK @ (s @ (s @ sK0)) @ (s @ (s @ sK1))))),
% 0.22/0.40 inference(cnf_transformation,[],[f11])).
% 0.22/0.40 thf(f11,plain,(
% 0.22/0.40 ($true != (cCKB6_BLACK @ (s @ (s @ sK0)) @ (s @ (s @ sK1)))) & ($true = (cCKB6_BLACK @ sK0 @ sK1))),
% 0.22/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 0.22/0.40 thf(f10,plain,(
% 0.22/0.40 ? [X0,X1] : (($true != (cCKB6_BLACK @ (s @ (s @ X0)) @ (s @ (s @ X1)))) & ($true = (cCKB6_BLACK @ X0 @ X1))) => (($true != (cCKB6_BLACK @ (s @ (s @ sK0)) @ (s @ (s @ sK1)))) & ($true = (cCKB6_BLACK @ sK0 @ sK1)))),
% 0.22/0.40 introduced(choice_axiom,[])).
% 0.22/0.40 thf(f9,plain,(
% 0.22/0.40 ? [X0,X1] : (($true != (cCKB6_BLACK @ (s @ (s @ X0)) @ (s @ (s @ X1)))) & ($true = (cCKB6_BLACK @ X0 @ X1)))),
% 0.22/0.40 inference(ennf_transformation,[],[f6])).
% 0.22/0.40 thf(f6,plain,(
% 0.22/0.40 ~! [X0,X1] : (($true = (cCKB6_BLACK @ X0 @ X1)) => ($true = (cCKB6_BLACK @ (s @ (s @ X0)) @ (s @ (s @ X1)))))),
% 0.22/0.40 inference(fool_elimination,[],[f5])).
% 0.22/0.40 thf(f5,plain,(
% 0.22/0.40 ~! [X0,X1] : ((cCKB6_BLACK @ X0 @ X1) => (cCKB6_BLACK @ (s @ (s @ X0)) @ (s @ (s @ X1))))),
% 0.22/0.40 inference(rectify,[],[f3])).
% 0.22/0.40 thf(f3,negated_conjecture,(
% 0.22/0.40 ~! [X3,X4] : ((cCKB6_BLACK @ X3 @ X4) => (cCKB6_BLACK @ (s @ (s @ X3)) @ (s @ (s @ X4))))),
% 0.22/0.40 inference(negated_conjecture,[],[f2])).
% 0.22/0.40 thf(f2,conjecture,(
% 0.22/0.40 ! [X3,X4] : ((cCKB6_BLACK @ X3 @ X4) => (cCKB6_BLACK @ (s @ (s @ X3)) @ (s @ (s @ X4))))),
% 0.22/0.40 file('/export/starexec/sandbox/tmp/tmp.Wkn7HK6qUM/Vampire---4.8_25554',cCKB6_L11000)).
% 0.22/0.40 thf(f29,plain,(
% 0.22/0.40 ( ! [X2 : $i,X1 : $i] : (((sK3 @ (s @ X1) @ (s @ X2)) = $true) | ($false = (sK3 @ X1 @ X2))) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f28])).
% 0.22/0.40 thf(f28,plain,(
% 0.22/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK3 @ X1 @ X2)) | ($true = ((sK3 @ (s @ (s @ X1)) @ X2) & (sK3 @ (s @ X1) @ (s @ X2))))) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f27])).
% 0.22/0.40 thf(f27,plain,(
% 0.22/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((sK3 @ X1 @ X2) => ((sK3 @ (s @ (s @ X1)) @ X2) & (sK3 @ (s @ X1) @ (s @ X2)))))) )),
% 0.22/0.40 inference(beta_eta_normalization,[],[f26])).
% 0.22/0.40 thf(f26,plain,(
% 0.22/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK3 @ X1 @ Y0) => ((sK3 @ (s @ (s @ X1)) @ Y0) & (sK3 @ (s @ X1) @ (s @ Y0))))) @ X2))) )),
% 0.22/0.40 inference(pi_clausification,[],[f25])).
% 0.22/0.40 thf(f25,plain,(
% 0.22/0.40 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK3 @ X1 @ Y0) => ((sK3 @ (s @ (s @ X1)) @ Y0) & (sK3 @ (s @ X1) @ (s @ Y0)))))))) )),
% 0.22/0.40 inference(beta_eta_normalization,[],[f24])).
% 0.22/0.40 thf(f24,plain,(
% 0.22/0.40 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y0 @ Y1) => ((sK3 @ (s @ (s @ Y0)) @ Y1) & (sK3 @ (s @ Y0) @ (s @ Y1))))))) @ X1))) )),
% 0.22/0.40 inference(pi_clausification,[],[f23])).
% 0.22/0.40 thf(f23,plain,(
% 0.22/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y0 @ Y1) => ((sK3 @ (s @ (s @ Y0)) @ Y1) & (sK3 @ (s @ Y0) @ (s @ Y1)))))))))),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f21])).
% 0.22/0.40 thf(f21,plain,(
% 0.22/0.40 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK3 @ Y0 @ Y1) => ((sK3 @ (s @ (s @ Y0)) @ Y1) & (sK3 @ (s @ Y0) @ (s @ Y1)))))))) & (sK3 @ c1 @ c1)) = $true)),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f19])).
% 0.22/0.40 thf(f90,plain,(
% 0.22/0.40 ($true = (sK3 @ sK0 @ sK1)) | ~spl2_1),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f89])).
% 0.22/0.40 thf(f89,plain,(
% 0.22/0.40 ($true = $false) | ($true = (sK3 @ sK0 @ sK1)) | ~spl2_1),
% 0.22/0.40 inference(forward_demodulation,[],[f85,f22])).
% 0.22/0.40 thf(f22,plain,(
% 0.22/0.40 ($true = (sK3 @ c1 @ c1))),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f21])).
% 0.22/0.40 thf(f85,plain,(
% 0.22/0.40 ($false = (sK3 @ c1 @ c1)) | ($true = (sK3 @ sK0 @ sK1)) | ~spl2_1),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f84])).
% 0.22/0.40 thf(f84,plain,(
% 0.22/0.40 ($false = (sK3 @ c1 @ c1)) | ($true = $false) | ($true = (sK3 @ sK0 @ sK1)) | ~spl2_1),
% 0.22/0.40 inference(superposition,[],[f41,f66])).
% 0.22/0.40 thf(f66,plain,(
% 0.22/0.40 ($false = (sK3 @ (sK4 @ sK3) @ (sK5 @ sK3))) | ~spl2_1),
% 0.22/0.40 inference(avatar_component_clause,[],[f64])).
% 0.22/0.40 thf(f64,plain,(
% 0.22/0.40 spl2_1 <=> ($false = (sK3 @ (sK4 @ sK3) @ (sK5 @ sK3)))),
% 0.22/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
% 0.22/0.40 thf(f41,plain,(
% 0.22/0.40 ( ! [X1 : $i > $i > $o] : (((X1 @ (sK4 @ X1) @ (sK5 @ X1)) = $true) | ($true = (X1 @ sK0 @ sK1)) | ($false = (X1 @ c1 @ c1))) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f39])).
% 0.22/0.40 thf(f39,plain,(
% 0.22/0.40 ( ! [X1 : $i > $i > $o] : (($false = ((X1 @ (sK4 @ X1) @ (sK5 @ X1)) => ((X1 @ (s @ (s @ (sK4 @ X1))) @ (sK5 @ X1)) & (X1 @ (s @ (sK4 @ X1)) @ (s @ (sK5 @ X1)))))) | ($true = (X1 @ sK0 @ sK1)) | ($false = (X1 @ c1 @ c1))) )),
% 0.22/0.40 inference(beta_eta_normalization,[],[f38])).
% 0.22/0.40 thf(f38,plain,(
% 0.22/0.40 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i]: ((X1 @ (sK4 @ X1) @ Y0) => ((X1 @ (s @ (s @ (sK4 @ X1))) @ Y0) & (X1 @ (s @ (sK4 @ X1)) @ (s @ Y0))))) @ (sK5 @ X1)) = $false) | ($true = (X1 @ sK0 @ sK1)) | ($false = (X1 @ c1 @ c1))) )),
% 0.22/0.40 inference(sigma_clausification,[],[f37])).
% 0.22/0.40 thf(f37,plain,(
% 0.22/0.40 ( ! [X1 : $i > $i > $o] : (($false = (X1 @ c1 @ c1)) | ($true = (X1 @ sK0 @ sK1)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ (sK4 @ X1) @ Y0) => ((X1 @ (s @ (s @ (sK4 @ X1))) @ Y0) & (X1 @ (s @ (sK4 @ X1)) @ (s @ Y0)))))))) )),
% 0.22/0.40 inference(beta_eta_normalization,[],[f36])).
% 0.22/0.40 thf(f36,plain,(
% 0.22/0.40 ( ! [X1 : $i > $i > $o] : (($true = (X1 @ sK0 @ sK1)) | ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) => ((X1 @ (s @ (s @ Y0)) @ Y1) & (X1 @ (s @ Y0) @ (s @ Y1))))))) @ (sK4 @ X1))) | ($false = (X1 @ c1 @ c1))) )),
% 0.22/0.40 inference(sigma_clausification,[],[f35])).
% 0.22/0.40 thf(f35,plain,(
% 0.22/0.40 ( ! [X1 : $i > $i > $o] : (($true = (X1 @ sK0 @ sK1)) | ($false = (X1 @ c1 @ c1)) | ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) => ((X1 @ (s @ (s @ Y0)) @ Y1) & (X1 @ (s @ Y0) @ (s @ Y1)))))))))) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f34])).
% 0.22/0.40 thf(f34,plain,(
% 0.22/0.40 ( ! [X1 : $i > $i > $o] : (($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) => ((X1 @ (s @ (s @ Y0)) @ Y1) & (X1 @ (s @ Y0) @ (s @ Y1)))))))) & (X1 @ c1 @ c1))) | ($true = (X1 @ sK0 @ sK1))) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f33])).
% 0.22/0.40 thf(f33,plain,(
% 0.22/0.40 ( ! [X1 : $i > $i > $o] : (($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y0 @ Y1) => ((X1 @ (s @ (s @ Y0)) @ Y1) & (X1 @ (s @ Y0) @ (s @ Y1)))))))) & (X1 @ c1 @ c1)) => (X1 @ sK0 @ sK1)))) )),
% 0.22/0.40 inference(beta_eta_normalization,[],[f32])).
% 0.22/0.40 thf(f32,plain,(
% 0.22/0.40 ( ! [X1 : $i > $i > $o] : (($true = ((^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => ((Y0 @ (s @ (s @ Y1)) @ Y2) & (Y0 @ (s @ Y1) @ (s @ Y2)))))))) & (Y0 @ c1 @ c1)) => (Y0 @ sK0 @ sK1))) @ X1))) )),
% 0.22/0.40 inference(pi_clausification,[],[f31])).
% 0.22/0.40 thf(f31,plain,(
% 0.22/0.40 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => ((Y0 @ (s @ (s @ Y1)) @ Y2) & (Y0 @ (s @ Y1) @ (s @ Y2)))))))) & (Y0 @ c1 @ c1)) => (Y0 @ sK0 @ sK1)))))),
% 0.22/0.40 inference(beta_eta_normalization,[],[f16])).
% 0.22/0.40 thf(f16,plain,(
% 0.22/0.40 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) => ((Y2 @ (s @ (s @ Y3)) @ Y4) & (Y2 @ (s @ Y3) @ (s @ Y4)))))))) & (Y2 @ c1 @ c1)) => (Y2 @ Y0 @ Y1))))))) @ sK0 @ sK1))),
% 0.22/0.40 inference(definition_unfolding,[],[f13,f12])).
% 0.22/0.40 thf(f13,plain,(
% 0.22/0.40 ($true = (cCKB6_BLACK @ sK0 @ sK1))),
% 0.22/0.40 inference(cnf_transformation,[],[f11])).
% 0.22/0.40 thf(f82,plain,(
% 0.22/0.40 spl2_1 | ~spl2_2),
% 0.22/0.40 inference(avatar_split_clause,[],[f79,f68,f64])).
% 0.22/0.40 thf(f68,plain,(
% 0.22/0.40 spl2_2 <=> ($false = (sK3 @ (s @ (s @ (sK4 @ sK3))) @ (sK5 @ sK3)))),
% 0.22/0.40 introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
% 0.22/0.40 thf(f79,plain,(
% 0.22/0.40 ($false = (sK3 @ (sK4 @ sK3) @ (sK5 @ sK3))) | ~spl2_2),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f77])).
% 0.22/0.40 thf(f77,plain,(
% 0.22/0.40 ($true = $false) | ($false = (sK3 @ (sK4 @ sK3) @ (sK5 @ sK3))) | ~spl2_2),
% 0.22/0.40 inference(superposition,[],[f70,f30])).
% 0.22/0.40 thf(f30,plain,(
% 0.22/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (sK3 @ (s @ (s @ X1)) @ X2)) | ($false = (sK3 @ X1 @ X2))) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f28])).
% 0.22/0.40 thf(f70,plain,(
% 0.22/0.40 ($false = (sK3 @ (s @ (s @ (sK4 @ sK3))) @ (sK5 @ sK3))) | ~spl2_2),
% 0.22/0.40 inference(avatar_component_clause,[],[f68])).
% 0.22/0.40 thf(f76,plain,(
% 0.22/0.40 spl2_2 | spl2_1),
% 0.22/0.40 inference(avatar_split_clause,[],[f75,f64,f68])).
% 0.22/0.40 thf(f75,plain,(
% 0.22/0.40 ($false = (sK3 @ (s @ (s @ (sK4 @ sK3))) @ (sK5 @ sK3))) | ($false = (sK3 @ (sK4 @ sK3) @ (sK5 @ sK3)))),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f74])).
% 0.22/0.40 thf(f74,plain,(
% 0.22/0.40 ($false = (sK3 @ (s @ (s @ (sK4 @ sK3))) @ (sK5 @ sK3))) | ($true = $false) | ($false = (sK3 @ (sK4 @ sK3) @ (sK5 @ sK3)))),
% 0.22/0.40 inference(forward_demodulation,[],[f73,f22])).
% 0.22/0.40 thf(f73,plain,(
% 0.22/0.40 ($false = (sK3 @ (sK4 @ sK3) @ (sK5 @ sK3))) | ($false = (sK3 @ c1 @ c1)) | ($false = (sK3 @ (s @ (s @ (sK4 @ sK3))) @ (sK5 @ sK3)))),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f72])).
% 0.22/0.40 thf(f72,plain,(
% 0.22/0.40 ($false = (sK3 @ (s @ (s @ (sK4 @ sK3))) @ (sK5 @ sK3))) | ($false = (sK3 @ c1 @ c1)) | ($false = (sK3 @ (sK4 @ sK3) @ (sK5 @ sK3))) | ($true = $false)),
% 0.22/0.40 inference(forward_demodulation,[],[f57,f49])).
% 0.22/0.40 thf(f57,plain,(
% 0.22/0.40 ($true = (sK3 @ sK0 @ sK1)) | ($false = (sK3 @ c1 @ c1)) | ($false = (sK3 @ (sK4 @ sK3) @ (sK5 @ sK3))) | ($false = (sK3 @ (s @ (s @ (sK4 @ sK3))) @ (sK5 @ sK3)))),
% 0.22/0.40 inference(trivial_inequality_removal,[],[f55])).
% 0.22/0.40 thf(f55,plain,(
% 0.22/0.40 ($true = $false) | ($false = (sK3 @ c1 @ c1)) | ($true = (sK3 @ sK0 @ sK1)) | ($false = (sK3 @ (sK4 @ sK3) @ (sK5 @ sK3))) | ($false = (sK3 @ (s @ (s @ (sK4 @ sK3))) @ (sK5 @ sK3)))),
% 0.22/0.40 inference(superposition,[],[f42,f29])).
% 0.22/0.40 thf(f42,plain,(
% 0.22/0.40 ( ! [X1 : $i > $i > $o] : (((X1 @ (s @ (sK4 @ X1)) @ (s @ (sK5 @ X1))) = $false) | ($false = (X1 @ c1 @ c1)) | ((X1 @ (s @ (s @ (sK4 @ X1))) @ (sK5 @ X1)) = $false) | ($true = (X1 @ sK0 @ sK1))) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f40])).
% 0.22/0.40 thf(f40,plain,(
% 0.22/0.40 ( ! [X1 : $i > $i > $o] : (($true = (X1 @ sK0 @ sK1)) | ($false = (X1 @ c1 @ c1)) | ($false = ((X1 @ (s @ (s @ (sK4 @ X1))) @ (sK5 @ X1)) & (X1 @ (s @ (sK4 @ X1)) @ (s @ (sK5 @ X1)))))) )),
% 0.22/0.40 inference(binary_proxy_clausification,[],[f39])).
% 0.22/0.40 % SZS output end Proof for Vampire---4
% 0.22/0.40 % (25812)------------------------------
% 0.22/0.40 % (25812)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.40 % (25812)Termination reason: Refutation
% 0.22/0.40
% 0.22/0.40 % (25812)Memory used [KB]: 5500
% 0.22/0.40 % (25812)Time elapsed: 0.012 s
% 0.22/0.40 % (25812)Instructions burned: 11 (million)
% 0.22/0.40 % (25812)------------------------------
% 0.22/0.40 % (25812)------------------------------
% 0.22/0.40 % (25809)Success in time 0.014 s
% 0.22/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------