TSTP Solution File: PUZ110^5 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : PUZ110^5 : 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 : n015.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 08:49:14 EDT 2024
% Result : Theorem 0.13s 0.38s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ110^5 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.12/0.14 % 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
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 18:00:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.ITtaoSyBIx/Vampire---4.8_32001
% 0.13/0.37 % (32110)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)
% 0.13/0.37 % (32112)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on Vampire---4 for (2999ds/2Mi)
% 0.13/0.37 % (32111)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)
% 0.13/0.37 % (32109)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)
% 0.13/0.37 % (32114)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)
% 0.13/0.37 % (32115)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on Vampire---4 for (2999ds/18Mi)
% 0.13/0.37 % (32113)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)
% 0.13/0.37 % (32112)Instruction limit reached!
% 0.13/0.37 % (32112)------------------------------
% 0.13/0.37 % (32112)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (32112)Termination reason: Unknown
% 0.13/0.37 % (32112)Termination phase: Function definition elimination
% 0.13/0.37
% 0.13/0.37 % (32112)Memory used [KB]: 895
% 0.13/0.37 % (32112)Time elapsed: 0.003 s
% 0.13/0.37 % (32112)Instructions burned: 2 (million)
% 0.13/0.37 % (32112)------------------------------
% 0.13/0.37 % (32112)------------------------------
% 0.13/0.37 % (32114)Refutation not found, incomplete strategy
% 0.13/0.37 % (32114)------------------------------
% 0.13/0.37 % (32114)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (32114)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.37
% 0.13/0.37
% 0.13/0.37 % (32114)Memory used [KB]: 5500
% 0.13/0.37 % (32113)Instruction limit reached!
% 0.13/0.37 % (32113)------------------------------
% 0.13/0.37 % (32113)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (32113)Termination reason: Unknown
% 0.13/0.37 % (32113)Termination phase: Saturation
% 0.13/0.37
% 0.13/0.37 % (32113)Memory used [KB]: 5500
% 0.13/0.37 % (32113)Time elapsed: 0.003 s
% 0.13/0.37 % (32113)Instructions burned: 3 (million)
% 0.13/0.37 % (32113)------------------------------
% 0.13/0.37 % (32113)------------------------------
% 0.13/0.37 % (32114)Time elapsed: 0.003 s
% 0.13/0.37 % (32114)Instructions burned: 2 (million)
% 0.13/0.37 % (32114)------------------------------
% 0.13/0.37 % (32114)------------------------------
% 0.13/0.38 % (32110)Instruction limit reached!
% 0.13/0.38 % (32110)------------------------------
% 0.13/0.38 % (32110)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (32110)Termination reason: Unknown
% 0.13/0.38 % (32110)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (32110)Memory used [KB]: 5500
% 0.13/0.38 % (32110)Time elapsed: 0.005 s
% 0.13/0.38 % (32110)Instructions burned: 4 (million)
% 0.13/0.38 % (32110)------------------------------
% 0.13/0.38 % (32110)------------------------------
% 0.13/0.38 % (32111)First to succeed.
% 0.13/0.38 % (32111)Refutation found. Thanks to Tanya!
% 0.13/0.38 % SZS status Theorem for Vampire---4
% 0.13/0.38 % SZS output start Proof for Vampire---4
% 0.13/0.38 thf(func_def_1, type, s: $i > $i).
% 0.13/0.38 thf(func_def_2, type, cCKB6_BLACK: $i > $i > $o).
% 0.13/0.38 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.13/0.38 thf(func_def_17, type, sK3: ($i > $i > $o) > $i).
% 0.13/0.38 thf(func_def_18, type, sK4: ($i > $i > $o) > $i).
% 0.13/0.38 thf(func_def_19, type, sK5: $i > $i > $o).
% 0.13/0.38 thf(func_def_20, type, ph6: !>[X0: $tType]:(X0)).
% 0.13/0.38 thf(f86,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(avatar_sat_refutation,[],[f68,f74,f83])).
% 0.13/0.38 thf(f83,plain,(
% 0.13/0.38 ~spl2_1),
% 0.13/0.38 inference(avatar_contradiction_clause,[],[f82])).
% 0.13/0.38 thf(f82,plain,(
% 0.13/0.38 $false | ~spl2_1),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f81])).
% 0.13/0.38 thf(f81,plain,(
% 0.13/0.38 ($true = $false) | ~spl2_1),
% 0.13/0.38 inference(forward_demodulation,[],[f80,f45])).
% 0.13/0.38 thf(f45,plain,(
% 0.13/0.38 ((sK5 @ sK0 @ sK1) = $false)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f44])).
% 0.13/0.38 thf(f44,plain,(
% 0.13/0.38 ((sK5 @ sK0 @ sK1) = $false) | ($true = $false)),
% 0.13/0.38 inference(superposition,[],[f32,f41])).
% 0.13/0.38 thf(f41,plain,(
% 0.13/0.38 ( ! [X2 : $i,X1 : $i] : (((sK5 @ (s @ (s @ X2)) @ X1) = $true) | ((sK5 @ X2 @ X1) = $false)) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f40])).
% 0.13/0.38 thf(f40,plain,(
% 0.13/0.38 ( ! [X2 : $i,X1 : $i] : ((((sK5 @ (s @ X2) @ (s @ X1)) & (sK5 @ (s @ (s @ X2)) @ X1)) = $true) | ((sK5 @ X2 @ X1) = $false)) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f39])).
% 0.13/0.38 thf(f39,plain,(
% 0.13/0.38 ( ! [X2 : $i,X1 : $i] : ((((sK5 @ X2 @ X1) => ((sK5 @ (s @ X2) @ (s @ X1)) & (sK5 @ (s @ (s @ X2)) @ X1))) = $true)) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f38])).
% 0.13/0.38 thf(f38,plain,(
% 0.13/0.38 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((sK5 @ Y0 @ X1) => ((sK5 @ (s @ Y0) @ (s @ X1)) & (sK5 @ (s @ (s @ Y0)) @ X1)))) @ X2))) )),
% 0.13/0.38 inference(pi_clausification,[],[f37])).
% 0.13/0.38 thf(f37,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((sK5 @ Y0 @ X1) => ((sK5 @ (s @ Y0) @ (s @ X1)) & (sK5 @ (s @ (s @ Y0)) @ X1))))))) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f36])).
% 0.13/0.38 thf(f36,plain,(
% 0.13/0.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1 @ Y0) => ((sK5 @ (s @ Y1) @ (s @ Y0)) & (sK5 @ (s @ (s @ Y1)) @ Y0)))))) @ X1))) )),
% 0.13/0.38 inference(pi_clausification,[],[f34])).
% 0.13/0.38 thf(f34,plain,(
% 0.13/0.38 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1 @ Y0) => ((sK5 @ (s @ Y1) @ (s @ Y0)) & (sK5 @ (s @ (s @ Y1)) @ Y0))))))) = $true)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f33])).
% 0.13/0.38 thf(f33,plain,(
% 0.13/0.38 (((sK5 @ c1 @ c1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1 @ Y0) => ((sK5 @ (s @ Y1) @ (s @ Y0)) & (sK5 @ (s @ (s @ Y1)) @ Y0)))))))) = $true)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f31])).
% 0.13/0.38 thf(f31,plain,(
% 0.13/0.38 ((((sK5 @ c1 @ c1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK5 @ Y1 @ Y0) => ((sK5 @ (s @ Y1) @ (s @ Y0)) & (sK5 @ (s @ (s @ Y1)) @ Y0)))))))) => (sK5 @ (s @ (s @ sK0)) @ sK1)) = $false)),
% 0.13/0.38 inference(beta_eta_normalization,[],[f30])).
% 0.13/0.38 thf(f30,plain,(
% 0.13/0.38 (((^[Y0 : $i > $i > $o]: (((Y0 @ c1 @ c1) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => ((Y0 @ (s @ Y2) @ (s @ Y1)) & (Y0 @ (s @ (s @ Y2)) @ Y1)))))))) => (Y0 @ (s @ (s @ sK0)) @ sK1))) @ sK5) = $false)),
% 0.13/0.38 inference(sigma_clausification,[],[f29])).
% 0.13/0.38 thf(f29,plain,(
% 0.13/0.38 ($true != (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ c1 @ c1) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => ((Y0 @ (s @ Y2) @ (s @ Y1)) & (Y0 @ (s @ (s @ Y2)) @ Y1)))))))) => (Y0 @ (s @ (s @ sK0)) @ sK1)))))),
% 0.13/0.38 inference(beta_eta_normalization,[],[f15])).
% 0.13/0.38 thf(f15,plain,(
% 0.13/0.38 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ c1 @ c1) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => ((Y2 @ (s @ Y4) @ (s @ Y3)) & (Y2 @ (s @ (s @ Y4)) @ Y3)))))))) => (Y2 @ Y0 @ Y1))))))) @ (s @ (s @ sK0)) @ sK1) != $true)),
% 0.13/0.38 inference(definition_unfolding,[],[f13,f14])).
% 0.13/0.38 thf(f14,plain,(
% 0.13/0.38 (cCKB6_BLACK = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ c1 @ c1) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => ((Y2 @ (s @ Y4) @ (s @ Y3)) & (Y2 @ (s @ (s @ Y4)) @ Y3)))))))) => (Y2 @ Y0 @ Y1))))))))),
% 0.13/0.38 inference(cnf_transformation,[],[f6])).
% 0.13/0.38 thf(f6,plain,(
% 0.13/0.38 (cCKB6_BLACK = (^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ c1 @ c1) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => ((Y2 @ (s @ Y4) @ (s @ Y3)) & (Y2 @ (s @ (s @ Y4)) @ Y3)))))))) => (Y2 @ Y0 @ Y1))))))))),
% 0.13/0.38 inference(fool_elimination,[],[f5])).
% 0.13/0.38 thf(f5,plain,(
% 0.13/0.38 (cCKB6_BLACK = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $i > $o] : ((! [X3,X4] : ((X2 @ X3 @ X4) => ((X2 @ (s @ (s @ X3)) @ X4) & (X2 @ (s @ X3) @ (s @ X4)))) & (X2 @ c1 @ c1)) => (X2 @ X0 @ X1)))))),
% 0.13/0.38 inference(rectify,[],[f1])).
% 0.13/0.38 thf(f1,axiom,(
% 0.13/0.38 (cCKB6_BLACK = (^[X0 : $i, X1 : $i] : (! [X2 : $i > $i > $o] : ((! [X3,X4] : ((X2 @ X3 @ X4) => ((X2 @ (s @ (s @ X3)) @ X4) & (X2 @ (s @ X3) @ (s @ X4)))) & (X2 @ c1 @ c1)) => (X2 @ X0 @ X1)))))),
% 0.13/0.38 file('/export/starexec/sandbox/tmp/tmp.ITtaoSyBIx/Vampire---4.8_32001',cCKB6_BLACK_def)).
% 0.13/0.38 thf(f13,plain,(
% 0.13/0.38 ((cCKB6_BLACK @ (s @ (s @ sK0)) @ sK1) != $true)),
% 0.13/0.38 inference(cnf_transformation,[],[f11])).
% 0.13/0.38 thf(f11,plain,(
% 0.13/0.38 ((cCKB6_BLACK @ (s @ (s @ sK0)) @ sK1) != $true) & ($true = (cCKB6_BLACK @ sK0 @ sK1))),
% 0.13/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f10])).
% 0.13/0.38 thf(f10,plain,(
% 0.13/0.38 ? [X0,X1] : (((cCKB6_BLACK @ (s @ (s @ X0)) @ X1) != $true) & ($true = (cCKB6_BLACK @ X0 @ X1))) => (((cCKB6_BLACK @ (s @ (s @ sK0)) @ sK1) != $true) & ($true = (cCKB6_BLACK @ sK0 @ sK1)))),
% 0.13/0.38 introduced(choice_axiom,[])).
% 0.13/0.38 thf(f9,plain,(
% 0.13/0.38 ? [X0,X1] : (((cCKB6_BLACK @ (s @ (s @ X0)) @ X1) != $true) & ($true = (cCKB6_BLACK @ X0 @ X1)))),
% 0.13/0.38 inference(ennf_transformation,[],[f8])).
% 0.13/0.38 thf(f8,plain,(
% 0.13/0.38 ~! [X0,X1] : (($true = (cCKB6_BLACK @ X0 @ X1)) => ((cCKB6_BLACK @ (s @ (s @ X0)) @ X1) = $true))),
% 0.13/0.38 inference(fool_elimination,[],[f7])).
% 0.13/0.38 thf(f7,plain,(
% 0.13/0.38 ~! [X0,X1] : ((cCKB6_BLACK @ X0 @ X1) => (cCKB6_BLACK @ (s @ (s @ X0)) @ X1))),
% 0.13/0.38 inference(rectify,[],[f3])).
% 0.13/0.38 thf(f3,negated_conjecture,(
% 0.13/0.38 ~! [X3,X4] : ((cCKB6_BLACK @ X3 @ X4) => (cCKB6_BLACK @ (s @ (s @ X3)) @ X4))),
% 0.13/0.38 inference(negated_conjecture,[],[f2])).
% 0.13/0.38 thf(f2,conjecture,(
% 0.13/0.38 ! [X3,X4] : ((cCKB6_BLACK @ X3 @ X4) => (cCKB6_BLACK @ (s @ (s @ X3)) @ X4))),
% 0.13/0.38 file('/export/starexec/sandbox/tmp/tmp.ITtaoSyBIx/Vampire---4.8_32001',cCKB6_L8000)).
% 0.13/0.38 thf(f32,plain,(
% 0.13/0.38 ((sK5 @ (s @ (s @ sK0)) @ sK1) = $false)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f31])).
% 0.13/0.38 thf(f80,plain,(
% 0.13/0.38 ($true = (sK5 @ sK0 @ sK1)) | ~spl2_1),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f79])).
% 0.13/0.38 thf(f79,plain,(
% 0.13/0.38 ($true = (sK5 @ sK0 @ sK1)) | ($true = $false) | ~spl2_1),
% 0.13/0.38 inference(forward_demodulation,[],[f78,f35])).
% 0.13/0.38 thf(f35,plain,(
% 0.13/0.38 ((sK5 @ c1 @ c1) = $true)),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f33])).
% 0.13/0.38 thf(f78,plain,(
% 0.13/0.38 ((sK5 @ c1 @ c1) = $false) | ($true = (sK5 @ sK0 @ sK1)) | ~spl2_1),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f76])).
% 0.13/0.38 thf(f76,plain,(
% 0.13/0.38 ($true = (sK5 @ sK0 @ sK1)) | ($true = $false) | ((sK5 @ c1 @ c1) = $false) | ~spl2_1),
% 0.13/0.38 inference(superposition,[],[f27,f58])).
% 0.13/0.38 thf(f58,plain,(
% 0.13/0.38 ((sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)) = $false) | ~spl2_1),
% 0.13/0.38 inference(avatar_component_clause,[],[f56])).
% 0.13/0.38 thf(f56,plain,(
% 0.13/0.38 spl2_1 <=> ((sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)) = $false)),
% 0.13/0.38 introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
% 0.13/0.38 thf(f27,plain,(
% 0.13/0.38 ( ! [X1 : $i > $i > $o] : (((X1 @ (sK4 @ X1) @ (sK3 @ X1)) = $true) | ((X1 @ c1 @ c1) = $false) | ($true = (X1 @ sK0 @ sK1))) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f25])).
% 0.13/0.38 thf(f25,plain,(
% 0.13/0.38 ( ! [X1 : $i > $i > $o] : (((X1 @ c1 @ c1) = $false) | (((X1 @ (sK4 @ X1) @ (sK3 @ X1)) => ((X1 @ (s @ (sK4 @ X1)) @ (s @ (sK3 @ X1))) & (X1 @ (s @ (s @ (sK4 @ X1))) @ (sK3 @ X1)))) = $false) | ($true = (X1 @ sK0 @ sK1))) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f24])).
% 0.13/0.38 thf(f24,plain,(
% 0.13/0.38 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i]: ((X1 @ Y0 @ (sK3 @ X1)) => ((X1 @ (s @ Y0) @ (s @ (sK3 @ X1))) & (X1 @ (s @ (s @ Y0)) @ (sK3 @ X1))))) @ (sK4 @ X1)) = $false) | ($true = (X1 @ sK0 @ sK1)) | ((X1 @ c1 @ c1) = $false)) )),
% 0.13/0.38 inference(sigma_clausification,[],[f23])).
% 0.13/0.38 thf(f23,plain,(
% 0.13/0.38 ( ! [X1 : $i > $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0 @ (sK3 @ X1)) => ((X1 @ (s @ Y0) @ (s @ (sK3 @ X1))) & (X1 @ (s @ (s @ Y0)) @ (sK3 @ X1)))))) = $false) | ((X1 @ c1 @ c1) = $false) | ($true = (X1 @ sK0 @ sK1))) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f22])).
% 0.13/0.38 thf(f22,plain,(
% 0.13/0.38 ( ! [X1 : $i > $i > $o] : (($true = (X1 @ sK0 @ sK1)) | (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ Y1) @ (s @ Y0)) & (X1 @ (s @ (s @ Y1)) @ Y0)))))) @ (sK3 @ X1)) = $false) | ((X1 @ c1 @ c1) = $false)) )),
% 0.13/0.38 inference(sigma_clausification,[],[f21])).
% 0.13/0.38 thf(f21,plain,(
% 0.13/0.38 ( ! [X1 : $i > $i > $o] : (($true = (X1 @ sK0 @ sK1)) | ((X1 @ c1 @ c1) = $false) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ Y1) @ (s @ Y0)) & (X1 @ (s @ (s @ Y1)) @ Y0))))))) = $false)) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f20])).
% 0.13/0.38 thf(f20,plain,(
% 0.13/0.38 ( ! [X1 : $i > $i > $o] : (($true = (X1 @ sK0 @ sK1)) | (((X1 @ c1 @ c1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ Y1) @ (s @ Y0)) & (X1 @ (s @ (s @ Y1)) @ Y0)))))))) = $false)) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f19])).
% 0.13/0.38 thf(f19,plain,(
% 0.13/0.38 ( ! [X1 : $i > $i > $o] : (($true = (((X1 @ c1 @ c1) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((X1 @ Y1 @ Y0) => ((X1 @ (s @ Y1) @ (s @ Y0)) & (X1 @ (s @ (s @ Y1)) @ Y0)))))))) => (X1 @ sK0 @ sK1)))) )),
% 0.13/0.38 inference(beta_eta_normalization,[],[f18])).
% 0.13/0.38 thf(f18,plain,(
% 0.13/0.38 ( ! [X1 : $i > $i > $o] : ((((^[Y0 : $i > $i > $o]: (((Y0 @ c1 @ c1) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => ((Y0 @ (s @ Y2) @ (s @ Y1)) & (Y0 @ (s @ (s @ Y2)) @ Y1)))))))) => (Y0 @ sK0 @ sK1))) @ X1) = $true)) )),
% 0.13/0.38 inference(pi_clausification,[],[f17])).
% 0.13/0.38 thf(f17,plain,(
% 0.13/0.38 ($true = (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((Y0 @ c1 @ c1) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => ((Y0 @ (s @ Y2) @ (s @ Y1)) & (Y0 @ (s @ (s @ Y2)) @ Y1)))))))) => (Y0 @ sK0 @ sK1)))))),
% 0.13/0.38 inference(beta_eta_normalization,[],[f16])).
% 0.13/0.38 thf(f16,plain,(
% 0.13/0.38 (((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ c1 @ c1) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) => ((Y2 @ (s @ Y4) @ (s @ Y3)) & (Y2 @ (s @ (s @ Y4)) @ Y3)))))))) => (Y2 @ Y0 @ Y1))))))) @ sK0 @ sK1) = $true)),
% 0.13/0.38 inference(definition_unfolding,[],[f12,f14])).
% 0.13/0.38 thf(f12,plain,(
% 0.13/0.38 ($true = (cCKB6_BLACK @ sK0 @ sK1))),
% 0.13/0.38 inference(cnf_transformation,[],[f11])).
% 0.13/0.38 thf(f74,plain,(
% 0.13/0.38 spl2_1 | ~spl2_2),
% 0.13/0.38 inference(avatar_split_clause,[],[f71,f60,f56])).
% 0.13/0.38 thf(f60,plain,(
% 0.13/0.38 spl2_2 <=> ((sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5)) = $false)),
% 0.13/0.38 introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
% 0.13/0.38 thf(f71,plain,(
% 0.13/0.38 ((sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)) = $false) | ~spl2_2),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f69])).
% 0.13/0.38 thf(f69,plain,(
% 0.13/0.38 ((sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)) = $false) | ($true = $false) | ~spl2_2),
% 0.13/0.38 inference(superposition,[],[f62,f41])).
% 0.13/0.38 thf(f62,plain,(
% 0.13/0.38 ((sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5)) = $false) | ~spl2_2),
% 0.13/0.38 inference(avatar_component_clause,[],[f60])).
% 0.13/0.38 thf(f68,plain,(
% 0.13/0.38 spl2_1 | spl2_2),
% 0.13/0.38 inference(avatar_split_clause,[],[f67,f60,f56])).
% 0.13/0.38 thf(f67,plain,(
% 0.13/0.38 ((sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5)) = $false) | ((sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)) = $false)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f66])).
% 0.13/0.38 thf(f66,plain,(
% 0.13/0.38 ($true = $false) | ((sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)) = $false) | ((sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5)) = $false)),
% 0.13/0.38 inference(forward_demodulation,[],[f65,f35])).
% 0.13/0.38 thf(f65,plain,(
% 0.13/0.38 ((sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5)) = $false) | ((sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)) = $false) | ((sK5 @ c1 @ c1) = $false)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f64])).
% 0.13/0.38 thf(f64,plain,(
% 0.13/0.38 ((sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)) = $false) | ((sK5 @ c1 @ c1) = $false) | ((sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5)) = $false) | ($true = $false)),
% 0.13/0.38 inference(forward_demodulation,[],[f49,f45])).
% 0.13/0.38 thf(f49,plain,(
% 0.13/0.38 ((sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5)) = $false) | ($true = (sK5 @ sK0 @ sK1)) | ((sK5 @ c1 @ c1) = $false) | ((sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)) = $false)),
% 0.13/0.38 inference(trivial_inequality_removal,[],[f47])).
% 0.13/0.38 thf(f47,plain,(
% 0.13/0.38 ((sK5 @ (sK4 @ sK5) @ (sK3 @ sK5)) = $false) | ((sK5 @ c1 @ c1) = $false) | ((sK5 @ (s @ (s @ (sK4 @ sK5))) @ (sK3 @ sK5)) = $false) | ($true = $false) | ($true = (sK5 @ sK0 @ sK1))),
% 0.13/0.38 inference(superposition,[],[f28,f42])).
% 0.13/0.38 thf(f42,plain,(
% 0.13/0.38 ( ! [X2 : $i,X1 : $i] : (($true = (sK5 @ (s @ X2) @ (s @ X1))) | ((sK5 @ X2 @ X1) = $false)) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f40])).
% 0.13/0.38 thf(f28,plain,(
% 0.13/0.38 ( ! [X1 : $i > $i > $o] : (((X1 @ (s @ (sK4 @ X1)) @ (s @ (sK3 @ X1))) = $false) | ((X1 @ (s @ (s @ (sK4 @ X1))) @ (sK3 @ X1)) = $false) | ($true = (X1 @ sK0 @ sK1)) | ((X1 @ c1 @ c1) = $false)) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f26])).
% 0.13/0.38 thf(f26,plain,(
% 0.13/0.38 ( ! [X1 : $i > $i > $o] : (($true = (X1 @ sK0 @ sK1)) | (((X1 @ (s @ (sK4 @ X1)) @ (s @ (sK3 @ X1))) & (X1 @ (s @ (s @ (sK4 @ X1))) @ (sK3 @ X1))) = $false) | ((X1 @ c1 @ c1) = $false)) )),
% 0.13/0.38 inference(binary_proxy_clausification,[],[f25])).
% 0.13/0.38 % SZS output end Proof for Vampire---4
% 0.13/0.38 % (32111)------------------------------
% 0.13/0.38 % (32111)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (32111)Termination reason: Refutation
% 0.13/0.38
% 0.13/0.38 % (32111)Memory used [KB]: 5500
% 0.13/0.38 % (32111)Time elapsed: 0.011 s
% 0.13/0.38 % (32111)Instructions burned: 8 (million)
% 0.13/0.38 % (32111)------------------------------
% 0.13/0.38 % (32111)------------------------------
% 0.13/0.38 % (32108)Success in time 0.012 s
% 0.13/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------