TSTP Solution File: NUM810^5 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM810^5 : TPTP v8.2.0. 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 : n002.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 01:46:14 EDT 2024
% Result : Theorem 0.19s 0.40s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM810^5 : TPTP v8.2.0. Bugfixed 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
% 0.13/0.35 % Computer : n002.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 : Mon May 20 05:46:38 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/benchmark/theBenchmark.p
% 0.13/0.37 % (10715)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)
% 0.13/0.37 % (10716)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (10718)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)
% 0.13/0.37 % (10717)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)
% 0.13/0.37 % (10719)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37 % (10714)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)
% 0.13/0.37 % (10720)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)
% 0.13/0.37 % (10716)Instruction limit reached!
% 0.13/0.37 % (10716)------------------------------
% 0.13/0.37 % (10716)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (10716)Termination reason: Unknown
% 0.13/0.37 % (10716)Termination phase: Saturation
% 0.13/0.37
% 0.13/0.37 % (10717)Instruction limit reached!
% 0.13/0.37 % (10717)------------------------------
% 0.13/0.37 % (10717)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (10716)Memory used [KB]: 5500
% 0.13/0.37 % (10716)Time elapsed: 0.003 s
% 0.13/0.37 % (10716)Instructions burned: 2 (million)
% 0.13/0.37 % (10716)------------------------------
% 0.13/0.37 % (10716)------------------------------
% 0.13/0.37 % (10717)Termination reason: Unknown
% 0.13/0.37 % (10717)Termination phase: Saturation
% 0.13/0.37
% 0.13/0.37 % (10717)Memory used [KB]: 5500
% 0.13/0.37 % (10717)Time elapsed: 0.003 s
% 0.13/0.37 % (10717)Instructions burned: 3 (million)
% 0.13/0.37 % (10717)------------------------------
% 0.13/0.37 % (10717)------------------------------
% 0.13/0.37 % (10720)Instruction limit reached!
% 0.13/0.37 % (10720)------------------------------
% 0.13/0.37 % (10720)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (10720)Termination reason: Unknown
% 0.13/0.37 % (10720)Termination phase: Saturation
% 0.13/0.37
% 0.13/0.37 % (10720)Memory used [KB]: 5500
% 0.13/0.37 % (10720)Time elapsed: 0.003 s
% 0.13/0.37 % (10720)Instructions burned: 3 (million)
% 0.13/0.37 % (10720)------------------------------
% 0.13/0.37 % (10720)------------------------------
% 0.13/0.37 % (10714)Instruction limit reached!
% 0.13/0.37 % (10714)------------------------------
% 0.13/0.37 % (10714)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (10714)Termination reason: Unknown
% 0.13/0.37 % (10714)Termination phase: Saturation
% 0.13/0.37
% 0.13/0.37 % (10714)Memory used [KB]: 5500
% 0.13/0.37 % (10714)Time elapsed: 0.004 s
% 0.13/0.37 % (10714)Instructions burned: 4 (million)
% 0.13/0.37 % (10714)------------------------------
% 0.13/0.37 % (10714)------------------------------
% 0.13/0.37 % (10713)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.38 % (10719)Instruction limit reached!
% 0.13/0.38 % (10719)------------------------------
% 0.13/0.38 % (10719)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (10719)Termination reason: Unknown
% 0.13/0.38 % (10719)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (10719)Memory used [KB]: 5628
% 0.13/0.38 % (10719)Time elapsed: 0.011 s
% 0.13/0.38 % (10719)Instructions burned: 18 (million)
% 0.13/0.38 % (10719)------------------------------
% 0.13/0.38 % (10719)------------------------------
% 0.19/0.38 % (10715)Instruction limit reached!
% 0.19/0.38 % (10715)------------------------------
% 0.19/0.38 % (10715)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.38 % (10715)Termination reason: Unknown
% 0.19/0.38 % (10715)Termination phase: Saturation
% 0.19/0.38
% 0.19/0.38 % (10715)Memory used [KB]: 5628
% 0.19/0.38 % (10721)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)
% 0.19/0.38 % (10715)Time elapsed: 0.016 s
% 0.19/0.38 % (10715)Instructions burned: 28 (million)
% 0.19/0.38 % (10715)------------------------------
% 0.19/0.38 % (10715)------------------------------
% 0.19/0.38 % (10722)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.38 % (10724)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on theBenchmark for (2999ds/1041Mi)
% 0.19/0.39 % (10725)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.39 % (10722)Instruction limit reached!
% 0.19/0.39 % (10722)------------------------------
% 0.19/0.39 % (10722)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.39 % (10722)Termination reason: Unknown
% 0.19/0.39 % (10722)Termination phase: Saturation
% 0.19/0.39
% 0.19/0.39 % (10722)Memory used [KB]: 5628
% 0.19/0.39 % (10722)Time elapsed: 0.010 s
% 0.19/0.39 % (10722)Instructions burned: 15 (million)
% 0.19/0.39 % (10722)------------------------------
% 0.19/0.39 % (10722)------------------------------
% 0.19/0.39 % (10723)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.39 % (10724)First to succeed.
% 0.19/0.39 % (10723)Instruction limit reached!
% 0.19/0.39 % (10723)------------------------------
% 0.19/0.39 % (10723)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.39 % (10723)Termination reason: Unknown
% 0.19/0.39 % (10723)Termination phase: Saturation
% 0.19/0.39
% 0.19/0.39 % (10723)Memory used [KB]: 5500
% 0.19/0.39 % (10723)Time elapsed: 0.003 s
% 0.19/0.39 % (10723)Instructions burned: 3 (million)
% 0.19/0.39 % (10723)------------------------------
% 0.19/0.39 % (10723)------------------------------
% 0.19/0.40 % (10724)Refutation found. Thanks to Tanya!
% 0.19/0.40 % SZS status Theorem for theBenchmark
% 0.19/0.40 % SZS output start Proof for theBenchmark
% 0.19/0.40 thf(func_def_1, type, cDOUBLE: $i > $i > $o).
% 0.19/0.40 thf(func_def_2, type, cS: $i > $i).
% 0.19/0.40 thf(func_def_16, type, ph1: !>[X0: $tType]:(X0)).
% 0.19/0.40 thf(f94,plain,(
% 0.19/0.40 $false),
% 0.19/0.40 inference(avatar_sat_refutation,[],[f46,f87,f93])).
% 0.19/0.40 thf(f93,plain,(
% 0.19/0.40 ~spl0_1),
% 0.19/0.40 inference(avatar_contradiction_clause,[],[f92])).
% 0.19/0.40 thf(f92,plain,(
% 0.19/0.40 $false | ~spl0_1),
% 0.19/0.40 inference(trivial_inequality_removal,[],[f91])).
% 0.19/0.40 thf(f91,plain,(
% 0.19/0.40 ($true = $false) | ~spl0_1),
% 0.19/0.40 inference(backward_demodulation,[],[f61,f90])).
% 0.19/0.40 thf(f90,plain,(
% 0.19/0.40 ( ! [X1 : $i] : (((cDOUBLE @ c0 @ X1) = $false)) ) | ~spl0_1),
% 0.19/0.40 inference(pi_clausification,[],[f42])).
% 0.19/0.40 thf(f42,plain,(
% 0.19/0.40 ((?? @ $i @ (cDOUBLE @ c0)) = $false) | ~spl0_1),
% 0.19/0.40 inference(avatar_component_clause,[],[f41])).
% 0.19/0.40 thf(f41,plain,(
% 0.19/0.40 spl0_1 <=> ((?? @ $i @ (cDOUBLE @ c0)) = $false)),
% 0.19/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.19/0.40 thf(f61,plain,(
% 0.19/0.40 ((cDOUBLE @ c0 @ c0) = $true)),
% 0.19/0.40 inference(binary_proxy_clausification,[],[f24])).
% 0.19/0.40 thf(f24,plain,(
% 0.19/0.40 ($true = ((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))))),
% 0.19/0.40 inference(binary_proxy_clausification,[],[f17])).
% 0.19/0.40 thf(f17,plain,(
% 0.19/0.40 ($true = (((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))))))),
% 0.19/0.40 inference(binary_proxy_clausification,[],[f13])).
% 0.19/0.40 thf(f13,plain,(
% 0.19/0.40 (((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))))) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cDOUBLE @ Y0))))) = $false)),
% 0.19/0.40 inference(not_proxy_clausification,[],[f12])).
% 0.19/0.40 thf(f12,plain,(
% 0.19/0.40 ((~ ((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))))) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cDOUBLE @ Y0)))))) = $true)),
% 0.19/0.40 inference(beta_eta_normalization,[],[f11])).
% 0.19/0.40 thf(f11,plain,(
% 0.19/0.40 ((~ ((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))) & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (cDOUBLE @ Y0 @ Y1))))))) = $true)),
% 0.19/0.40 inference(definition_unfolding,[],[f10,f9])).
% 0.19/0.40 thf(f9,plain,(
% 0.19/0.40 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.19/0.40 inference(cnf_transformation,[],[f8])).
% 0.19/0.40 thf(f8,plain,(
% 0.19/0.40 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.19/0.40 inference(fool_elimination,[],[f7])).
% 0.19/0.40 thf(f7,plain,(
% 0.19/0.40 (cIND = ! [X0 : $i > $o] : (((X0 @ c0) & ! [X1] : ((X0 @ X1) => (X0 @ (cS @ X1)))) => ! [X2] : (X0 @ X2)))),
% 0.19/0.40 inference(rectify,[],[f1])).
% 0.19/0.40 thf(f1,axiom,(
% 0.19/0.40 (cIND = ! [X0 : $i > $o] : (((X0 @ c0) & ! [X1] : ((X0 @ X1) => (X0 @ (cS @ X1)))) => ! [X1] : (X0 @ X1)))),
% 0.19/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cIND_def)).
% 0.19/0.40 thf(f10,plain,(
% 0.19/0.40 ((~ ((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))) & cIND) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (cDOUBLE @ Y0 @ Y1))))))) = $true)),
% 0.19/0.40 inference(cnf_transformation,[],[f6])).
% 0.19/0.40 thf(f6,plain,(
% 0.19/0.40 ((~ ((((cDOUBLE @ c0 @ c0) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))) & cIND) => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (^[Y1 : $i]: (cDOUBLE @ Y0 @ Y1))))))) = $true)),
% 0.19/0.40 inference(fool_elimination,[],[f5])).
% 0.19/0.40 thf(f5,plain,(
% 0.19/0.40 ~((cIND & ! [X0,X1] : ((cDOUBLE @ X1 @ X0) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ X0)))) & (cDOUBLE @ c0 @ c0)) => ! [X2] : ? [X3] : (cDOUBLE @ X2 @ X3))),
% 0.19/0.40 inference(rectify,[],[f3])).
% 0.19/0.40 thf(f3,negated_conjecture,(
% 0.19/0.40 ~((cIND & ! [X2,X1] : ((cDOUBLE @ X1 @ X2) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ X2)))) & (cDOUBLE @ c0 @ c0)) => ! [X1] : ? [X2] : (cDOUBLE @ X1 @ X2))),
% 0.19/0.40 inference(negated_conjecture,[],[f2])).
% 0.19/0.40 thf(f2,conjecture,(
% 0.19/0.40 (cIND & ! [X2,X1] : ((cDOUBLE @ X1 @ X2) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ X2)))) & (cDOUBLE @ c0 @ c0)) => ! [X1] : ? [X2] : (cDOUBLE @ X1 @ X2)),
% 0.19/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM140)).
% 0.19/0.40 thf(f87,plain,(
% 0.19/0.40 ~spl0_2),
% 0.19/0.40 inference(avatar_contradiction_clause,[],[f86])).
% 0.19/0.40 thf(f86,plain,(
% 0.19/0.40 $false | ~spl0_2),
% 0.19/0.40 inference(trivial_inequality_removal,[],[f85])).
% 0.19/0.40 thf(f85,plain,(
% 0.19/0.40 ($true = $false) | ~spl0_2),
% 0.19/0.40 inference(backward_demodulation,[],[f83,f84])).
% 0.19/0.40 thf(f84,plain,(
% 0.19/0.40 ( ! [X1 : $i] : (((cDOUBLE @ (cS @ sK3) @ X1) = $false)) ) | ~spl0_2),
% 0.19/0.40 inference(pi_clausification,[],[f54])).
% 0.19/0.40 thf(f54,plain,(
% 0.19/0.40 ((?? @ $i @ (cDOUBLE @ (cS @ sK3))) = $false) | ~spl0_2),
% 0.19/0.40 inference(binary_proxy_clausification,[],[f53])).
% 0.19/0.40 thf(f53,plain,(
% 0.19/0.40 (((?? @ $i @ (cDOUBLE @ sK3)) => (?? @ $i @ (cDOUBLE @ (cS @ sK3)))) = $false) | ~spl0_2),
% 0.19/0.40 inference(beta_eta_normalization,[],[f49])).
% 0.19/0.40 thf(f49,plain,(
% 0.19/0.40 (((^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0))))) @ sK3) = $false) | ~spl0_2),
% 0.19/0.40 inference(sigma_clausification,[],[f45])).
% 0.19/0.40 thf(f45,plain,(
% 0.19/0.40 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) = $false) | ~spl0_2),
% 0.19/0.40 inference(avatar_component_clause,[],[f44])).
% 0.19/0.40 thf(f44,plain,(
% 0.19/0.40 spl0_2 <=> ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) = $false)),
% 0.19/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.19/0.40 thf(f83,plain,(
% 0.19/0.40 ($true = (cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4)))) | ~spl0_2),
% 0.19/0.40 inference(boolean_simplification,[],[f80])).
% 0.19/0.40 thf(f80,plain,(
% 0.19/0.40 ($true = ($true => (cDOUBLE @ (cS @ sK3) @ (cS @ (cS @ sK4))))) | ~spl0_2),
% 0.19/0.40 inference(superposition,[],[f74,f71])).
% 0.19/0.40 thf(f71,plain,(
% 0.19/0.40 ($true = (cDOUBLE @ sK3 @ sK4)) | ~spl0_2),
% 0.19/0.40 inference(sigma_clausification,[],[f55])).
% 0.19/0.40 thf(f55,plain,(
% 0.19/0.40 ((?? @ $i @ (cDOUBLE @ sK3)) = $true) | ~spl0_2),
% 0.19/0.40 inference(binary_proxy_clausification,[],[f53])).
% 0.19/0.40 thf(f74,plain,(
% 0.19/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((cDOUBLE @ X1 @ X2) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ X2)))))) )),
% 0.19/0.40 inference(beta_eta_normalization,[],[f72])).
% 0.19/0.40 thf(f72,plain,(
% 0.19/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((cDOUBLE @ X1 @ Y0) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ Y0))))) @ X2))) )),
% 0.19/0.40 inference(pi_clausification,[],[f70])).
% 0.19/0.40 thf(f70,plain,(
% 0.19/0.40 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((cDOUBLE @ X1 @ Y0) => (cDOUBLE @ (cS @ X1) @ (cS @ (cS @ Y0)))))))) )),
% 0.19/0.40 inference(beta_eta_normalization,[],[f66])).
% 0.19/0.40 thf(f66,plain,(
% 0.19/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))) @ X1) = $true)) )),
% 0.19/0.40 inference(pi_clausification,[],[f63])).
% 0.19/0.40 thf(f63,plain,(
% 0.19/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1)))))))))),
% 0.19/0.40 inference(boolean_simplification,[],[f62])).
% 0.19/0.40 thf(f62,plain,(
% 0.19/0.40 (($true & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((cDOUBLE @ Y0 @ Y1) => (cDOUBLE @ (cS @ Y0) @ (cS @ (cS @ Y1))))))))) = $true)),
% 0.19/0.40 inference(backward_demodulation,[],[f24,f61])).
% 0.19/0.40 thf(f46,plain,(
% 0.19/0.40 spl0_1 | spl0_2),
% 0.19/0.40 inference(avatar_split_clause,[],[f39,f44,f41])).
% 0.19/0.40 thf(f39,plain,(
% 0.19/0.40 ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) = $false) | ((?? @ $i @ (cDOUBLE @ c0)) = $false)),
% 0.19/0.40 inference(binary_proxy_clausification,[],[f36])).
% 0.19/0.40 thf(f36,plain,(
% 0.19/0.40 (((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) & (?? @ $i @ (cDOUBLE @ c0))) = $false)),
% 0.19/0.40 inference(not_proxy_clausification,[],[f35])).
% 0.19/0.40 thf(f35,plain,(
% 0.19/0.40 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) & (?? @ $i @ (cDOUBLE @ c0)))))),
% 0.19/0.40 inference(boolean_simplification,[],[f34])).
% 0.19/0.40 thf(f34,plain,(
% 0.19/0.40 ((((!! @ $i @ (^[Y0 : $i]: ((?? @ $i @ (cDOUBLE @ Y0)) => (?? @ $i @ (cDOUBLE @ (cS @ Y0)))))) & (?? @ $i @ (cDOUBLE @ c0))) => $false) = $true)),
% 0.19/0.40 inference(beta_eta_normalization,[],[f30])).
% 0.19/0.40 thf(f30,plain,(
% 0.19/0.40 ($true = (((!! @ $i @ (^[Y0 : $i]: (((^[Y1 : $i]: (?? @ $i @ (cDOUBLE @ Y1))) @ Y0) => ((^[Y1 : $i]: (?? @ $i @ (cDOUBLE @ Y1))) @ (cS @ Y0))))) & ((^[Y0 : $i]: (?? @ $i @ (cDOUBLE @ Y0))) @ c0)) => $false))),
% 0.19/0.40 inference(superposition,[],[f28,f19])).
% 0.19/0.40 thf(f19,plain,(
% 0.19/0.40 ((!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cDOUBLE @ Y0)))) = $false)),
% 0.19/0.40 inference(boolean_simplification,[],[f18])).
% 0.19/0.40 thf(f18,plain,(
% 0.19/0.40 (($true => (!! @ $i @ (^[Y0 : $i]: (?? @ $i @ (cDOUBLE @ Y0))))) = $false)),
% 0.19/0.40 inference(backward_demodulation,[],[f13,f17])).
% 0.19/0.40 thf(f28,plain,(
% 0.19/0.40 ( ! [X1 : $i > $o] : (((((!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0))))) & (X1 @ c0)) => (!! @ $i @ X1)) = $true)) )),
% 0.19/0.40 inference(beta_eta_normalization,[],[f27])).
% 0.19/0.40 thf(f27,plain,(
% 0.19/0.40 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))) @ X1))) )),
% 0.19/0.40 inference(pi_clausification,[],[f26])).
% 0.19/0.40 thf(f26,plain,(
% 0.19/0.40 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0)))))),
% 0.19/0.40 inference(boolean_simplification,[],[f25])).
% 0.19/0.40 thf(f25,plain,(
% 0.19/0.40 (($true & (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1))))) & (Y0 @ c0)) => (!! @ $i @ Y0))))) = $true)),
% 0.19/0.40 inference(backward_demodulation,[],[f17,f24])).
% 0.19/0.40 % SZS output end Proof for theBenchmark
% 0.19/0.40 % (10724)------------------------------
% 0.19/0.40 % (10724)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.40 % (10724)Termination reason: Refutation
% 0.19/0.40
% 0.19/0.40 % (10724)Memory used [KB]: 5628
% 0.19/0.40 % (10724)Time elapsed: 0.012 s
% 0.19/0.40 % (10724)Instructions burned: 16 (million)
% 0.19/0.40 % (10724)------------------------------
% 0.19/0.40 % (10724)------------------------------
% 0.19/0.40 % (10712)Success in time 0.036 s
% 0.19/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------