TSTP Solution File: SYO113^5 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO113^5 : TPTP v8.2.0. Released v4.0.0.
% 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 : n011.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 09:02:58 EDT 2024
% Result : Theorem 0.20s 0.38s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO113^5 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.13 % 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
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 10:22:08 EDT 2024
% 0.20/0.34 % CPUTime :
% 0.20/0.34 This is a TH0_THM_NEQ_NAR problem
% 0.20/0.35 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
% 0.20/0.36 % (7438)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)
% 0.20/0.37 % (7432)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)
% 0.20/0.37 % (7433)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)
% 0.20/0.37 % (7434)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.37 % (7435)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)
% 0.20/0.37 % (7436)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)
% 0.20/0.37 % (7438)Instruction limit reached!
% 0.20/0.37 % (7438)------------------------------
% 0.20/0.37 % (7438)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (7438)Termination reason: Unknown
% 0.20/0.37 % (7438)Termination phase: Saturation
% 0.20/0.37
% 0.20/0.37 % (7438)Memory used [KB]: 5500
% 0.20/0.37 % (7438)Time elapsed: 0.003 s
% 0.20/0.37 % (7438)Instructions burned: 3 (million)
% 0.20/0.37 % (7438)------------------------------
% 0.20/0.37 % (7438)------------------------------
% 0.20/0.37 % (7431)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.20/0.37 % (7434)Instruction limit reached!
% 0.20/0.37 % (7434)------------------------------
% 0.20/0.37 % (7434)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (7434)Termination reason: Unknown
% 0.20/0.37 % (7434)Termination phase: Property scanning
% 0.20/0.37 % (7435)Instruction limit reached!
% 0.20/0.37 % (7435)------------------------------
% 0.20/0.37 % (7435)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (7435)Termination reason: Unknown
% 0.20/0.37 % (7435)Termination phase: Property scanning
% 0.20/0.37
% 0.20/0.37 % (7435)Memory used [KB]: 895
% 0.20/0.37 % (7435)Time elapsed: 0.003 s
% 0.20/0.37 % (7435)Instructions burned: 2 (million)
% 0.20/0.37 % (7435)------------------------------
% 0.20/0.37 % (7435)------------------------------
% 0.20/0.37
% 0.20/0.37 % (7434)Memory used [KB]: 895
% 0.20/0.37 % (7434)Time elapsed: 0.003 s
% 0.20/0.37 % (7434)Instructions burned: 2 (million)
% 0.20/0.37 % (7434)------------------------------
% 0.20/0.37 % (7434)------------------------------
% 0.20/0.37 % (7437)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.20/0.37 % (7432)Instruction limit reached!
% 0.20/0.37 % (7432)------------------------------
% 0.20/0.37 % (7432)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.37 % (7432)Termination reason: Unknown
% 0.20/0.37 % (7432)Termination phase: Saturation
% 0.20/0.37
% 0.20/0.37 % (7432)Memory used [KB]: 5500
% 0.20/0.37 % (7432)Time elapsed: 0.005 s
% 0.20/0.37 % (7432)Instructions burned: 4 (million)
% 0.20/0.37 % (7432)------------------------------
% 0.20/0.37 % (7432)------------------------------
% 0.20/0.37 % (7431)First to succeed.
% 0.20/0.37 % (7436)Also succeeded, but the first one will report.
% 0.20/0.37 % (7433)Also succeeded, but the first one will report.
% 0.20/0.38 % (7431)Refutation found. Thanks to Tanya!
% 0.20/0.38 % SZS status Theorem for theBenchmark
% 0.20/0.38 % SZS output start Proof for theBenchmark
% 0.20/0.38 thf(func_def_0, type, cNUMBER: $i > $o).
% 0.20/0.38 thf(func_def_1, type, cODD: $i > $o).
% 0.20/0.38 thf(func_def_2, type, cEVEN: $i > $o).
% 0.20/0.38 thf(func_def_3, type, cS: $i > $i).
% 0.20/0.38 thf(f96,plain,(
% 0.20/0.38 $false),
% 0.20/0.38 inference(avatar_sat_refutation,[],[f47,f52,f58,f65,f73,f76,f95])).
% 0.20/0.38 thf(f95,plain,(
% 0.20/0.38 spl2_1 | ~spl2_7),
% 0.20/0.38 inference(avatar_contradiction_clause,[],[f94])).
% 0.20/0.38 thf(f94,plain,(
% 0.20/0.38 $false | (spl2_1 | ~spl2_7)),
% 0.20/0.38 inference(subsumption_resolution,[],[f93,f91])).
% 0.20/0.38 thf(f91,plain,(
% 0.20/0.38 ($true = (cODD @ sK0)) | (spl2_1 | ~spl2_7)),
% 0.20/0.38 inference(subsumption_resolution,[],[f90,f57])).
% 0.20/0.38 thf(f57,plain,(
% 0.20/0.38 ($true = (cNUMBER @ sK0)) | ~spl2_7),
% 0.20/0.38 inference(avatar_component_clause,[],[f55])).
% 0.20/0.38 thf(f55,plain,(
% 0.20/0.38 spl2_7 <=> ($true = (cNUMBER @ sK0))),
% 0.20/0.38 introduced(avatar_definition,[new_symbols(naming,[spl2_7])])).
% 0.20/0.38 thf(f90,plain,(
% 0.20/0.38 ($true != (cNUMBER @ sK0)) | ($true = (cODD @ sK0)) | spl2_1),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f89])).
% 0.20/0.38 thf(f89,plain,(
% 0.20/0.38 ($true != $true) | ($true != (cNUMBER @ sK0)) | ($true = (cODD @ sK0)) | spl2_1),
% 0.20/0.38 inference(superposition,[],[f88,f18])).
% 0.20/0.38 thf(f18,plain,(
% 0.20/0.38 ( ! [X4 : $i] : (($true = (cEVEN @ X4)) | ($true != (cNUMBER @ X4)) | ($true = (cODD @ X4))) )),
% 0.20/0.38 inference(cnf_transformation,[],[f13])).
% 0.20/0.38 thf(f13,plain,(
% 0.20/0.38 ! [X0] : (((cODD @ X0) != $true) | ((cODD @ (cS @ (cS @ X0))) = $true)) & (! [X1] : (((cNUMBER @ (cS @ X1)) = $true) & ((cNUMBER @ X1) = $true)) | ((($true != (cNUMBER @ (cS @ sK0))) | ($true != (cNUMBER @ (cS @ (cS @ sK0))))) & ($true = (cNUMBER @ (cS @ sK0))) & ($true = (cNUMBER @ sK0))) | ((cNUMBER @ c0) != $true) | ((cNUMBER @ (cS @ c0)) != $true)) & ($true != (cNUMBER @ sK1)) & ((cODD @ (cS @ c0)) = $true) & ! [X4] : ((($true = (cEVEN @ X4)) | ($true = (cODD @ X4)) | ($true != (cNUMBER @ X4))) & (($true = (cNUMBER @ X4)) | (($true != (cEVEN @ X4)) & ($true != (cODD @ X4))))) & ((cEVEN @ c0) = $true) & ! [X5] : (($true = (cEVEN @ (cS @ (cS @ X5)))) | ($true != (cEVEN @ X5)))),
% 0.20/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f10,f12,f11])).
% 0.20/0.38 thf(f11,plain,(
% 0.20/0.38 ? [X2] : ((($true != (cNUMBER @ (cS @ X2))) | ($true != (cNUMBER @ (cS @ (cS @ X2))))) & ($true = (cNUMBER @ (cS @ X2))) & ($true = (cNUMBER @ X2))) => ((($true != (cNUMBER @ (cS @ sK0))) | ($true != (cNUMBER @ (cS @ (cS @ sK0))))) & ($true = (cNUMBER @ (cS @ sK0))) & ($true = (cNUMBER @ sK0)))),
% 0.20/0.38 introduced(choice_axiom,[])).
% 0.20/0.38 thf(f12,plain,(
% 0.20/0.38 ? [X3] : ($true != (cNUMBER @ X3)) => ($true != (cNUMBER @ sK1))),
% 0.20/0.38 introduced(choice_axiom,[])).
% 0.20/0.38 thf(f10,plain,(
% 0.20/0.38 ! [X0] : (((cODD @ X0) != $true) | ((cODD @ (cS @ (cS @ X0))) = $true)) & (! [X1] : (((cNUMBER @ (cS @ X1)) = $true) & ((cNUMBER @ X1) = $true)) | ? [X2] : ((($true != (cNUMBER @ (cS @ X2))) | ($true != (cNUMBER @ (cS @ (cS @ X2))))) & ($true = (cNUMBER @ (cS @ X2))) & ($true = (cNUMBER @ X2))) | ((cNUMBER @ c0) != $true) | ((cNUMBER @ (cS @ c0)) != $true)) & ? [X3] : ($true != (cNUMBER @ X3)) & ((cODD @ (cS @ c0)) = $true) & ! [X4] : ((($true = (cEVEN @ X4)) | ($true = (cODD @ X4)) | ($true != (cNUMBER @ X4))) & (($true = (cNUMBER @ X4)) | (($true != (cEVEN @ X4)) & ($true != (cODD @ X4))))) & ((cEVEN @ c0) = $true) & ! [X5] : (($true = (cEVEN @ (cS @ (cS @ X5)))) | ($true != (cEVEN @ X5)))),
% 0.20/0.38 inference(rectify,[],[f9])).
% 0.20/0.38 thf(f9,plain,(
% 0.20/0.38 ! [X4] : (($true != (cODD @ X4)) | ($true = (cODD @ (cS @ (cS @ X4))))) & (! [X3] : (($true = (cNUMBER @ (cS @ X3))) & ($true = (cNUMBER @ X3))) | ? [X2] : ((($true != (cNUMBER @ (cS @ X2))) | ($true != (cNUMBER @ (cS @ (cS @ X2))))) & ($true = (cNUMBER @ (cS @ X2))) & ($true = (cNUMBER @ X2))) | ((cNUMBER @ c0) != $true) | ((cNUMBER @ (cS @ c0)) != $true)) & ? [X5] : ($true != (cNUMBER @ X5)) & ((cODD @ (cS @ c0)) = $true) & ! [X0] : ((((cEVEN @ X0) = $true) | ((cODD @ X0) = $true) | ((cNUMBER @ X0) != $true)) & (((cNUMBER @ X0) = $true) | (((cEVEN @ X0) != $true) & ((cODD @ X0) != $true)))) & ((cEVEN @ c0) = $true) & ! [X1] : (($true = (cEVEN @ (cS @ (cS @ X1)))) | ($true != (cEVEN @ X1)))),
% 0.20/0.38 inference(flattening,[],[f8])).
% 0.20/0.38 thf(f8,plain,(
% 0.20/0.38 ! [X4] : (($true != (cODD @ X4)) | ($true = (cODD @ (cS @ (cS @ X4))))) & (! [X3] : (($true = (cNUMBER @ (cS @ X3))) & ($true = (cNUMBER @ X3))) | ? [X2] : ((($true != (cNUMBER @ (cS @ X2))) | ($true != (cNUMBER @ (cS @ (cS @ X2))))) & ($true = (cNUMBER @ (cS @ X2))) & ($true = (cNUMBER @ X2))) | ((cNUMBER @ c0) != $true) | ((cNUMBER @ (cS @ c0)) != $true)) & ? [X5] : ($true != (cNUMBER @ X5)) & ((cODD @ (cS @ c0)) = $true) & ! [X0] : (((((cEVEN @ X0) = $true) | ((cODD @ X0) = $true)) | ((cNUMBER @ X0) != $true)) & (((cNUMBER @ X0) = $true) | (((cEVEN @ X0) != $true) & ((cODD @ X0) != $true)))) & ((cEVEN @ c0) = $true) & ! [X1] : (($true = (cEVEN @ (cS @ (cS @ X1)))) | ($true != (cEVEN @ X1)))),
% 0.20/0.38 inference(nnf_transformation,[],[f7])).
% 0.20/0.38 thf(f7,plain,(
% 0.20/0.38 ! [X4] : (($true != (cODD @ X4)) | ($true = (cODD @ (cS @ (cS @ X4))))) & (! [X3] : (($true = (cNUMBER @ (cS @ X3))) & ($true = (cNUMBER @ X3))) | ? [X2] : ((($true != (cNUMBER @ (cS @ X2))) | ($true != (cNUMBER @ (cS @ (cS @ X2))))) & ($true = (cNUMBER @ (cS @ X2))) & ($true = (cNUMBER @ X2))) | ((cNUMBER @ c0) != $true) | ((cNUMBER @ (cS @ c0)) != $true)) & ? [X5] : ($true != (cNUMBER @ X5)) & ((cODD @ (cS @ c0)) = $true) & ! [X0] : ((((cEVEN @ X0) = $true) | ((cODD @ X0) = $true)) <=> ((cNUMBER @ X0) = $true)) & ((cEVEN @ c0) = $true) & ! [X1] : (($true = (cEVEN @ (cS @ (cS @ X1)))) | ($true != (cEVEN @ X1)))),
% 0.20/0.38 inference(flattening,[],[f6])).
% 0.20/0.38 thf(f6,plain,(
% 0.20/0.38 ? [X5] : ($true != (cNUMBER @ X5)) & (! [X1] : (($true = (cEVEN @ (cS @ (cS @ X1)))) | ($true != (cEVEN @ X1))) & ! [X0] : ((((cEVEN @ X0) = $true) | ((cODD @ X0) = $true)) <=> ((cNUMBER @ X0) = $true)) & ((cEVEN @ c0) = $true) & (! [X3] : (($true = (cNUMBER @ (cS @ X3))) & ($true = (cNUMBER @ X3))) | (((cNUMBER @ (cS @ c0)) != $true) | ? [X2] : ((($true != (cNUMBER @ (cS @ X2))) | ($true != (cNUMBER @ (cS @ (cS @ X2))))) & (($true = (cNUMBER @ X2)) & ($true = (cNUMBER @ (cS @ X2))))) | ((cNUMBER @ c0) != $true))) & ! [X4] : (($true != (cODD @ X4)) | ($true = (cODD @ (cS @ (cS @ X4))))) & ((cODD @ (cS @ c0)) = $true))),
% 0.20/0.38 inference(ennf_transformation,[],[f5])).
% 0.20/0.38 thf(f5,plain,(
% 0.20/0.38 ~((! [X1] : (($true = (cEVEN @ X1)) => ($true = (cEVEN @ (cS @ (cS @ X1))))) & ! [X0] : ((((cEVEN @ X0) = $true) | ((cODD @ X0) = $true)) <=> ((cNUMBER @ X0) = $true)) & ((cEVEN @ c0) = $true) & ((((cNUMBER @ (cS @ c0)) = $true) & ! [X2] : ((($true = (cNUMBER @ X2)) & ($true = (cNUMBER @ (cS @ X2)))) => (($true = (cNUMBER @ (cS @ X2))) & ($true = (cNUMBER @ (cS @ (cS @ X2)))))) & ((cNUMBER @ c0) = $true)) => ! [X3] : (($true = (cNUMBER @ (cS @ X3))) & ($true = (cNUMBER @ X3)))) & ! [X4] : (($true = (cODD @ X4)) => ($true = (cODD @ (cS @ (cS @ X4))))) & ((cODD @ (cS @ c0)) = $true)) => ! [X5] : ($true = (cNUMBER @ X5)))),
% 0.20/0.38 inference(fool_elimination,[],[f4])).
% 0.20/0.38 thf(f4,plain,(
% 0.20/0.38 ~((! [X0] : (((cODD @ X0) | (cEVEN @ X0)) <=> (cNUMBER @ X0)) & ! [X1] : ((cEVEN @ X1) => (cEVEN @ (cS @ (cS @ X1)))) & (((cNUMBER @ (cS @ c0)) & ! [X2] : (((cNUMBER @ (cS @ X2)) & (cNUMBER @ X2)) => ((cNUMBER @ (cS @ X2)) & (cNUMBER @ (cS @ (cS @ X2))))) & (cNUMBER @ c0)) => ! [X3] : ((cNUMBER @ (cS @ X3)) & (cNUMBER @ X3))) & (cODD @ (cS @ c0)) & (cEVEN @ c0) & ! [X4] : ((cODD @ X4) => (cODD @ (cS @ (cS @ X4))))) => ! [X5] : (cNUMBER @ X5))),
% 0.20/0.38 inference(rectify,[],[f2])).
% 0.20/0.38 thf(f2,negated_conjecture,(
% 0.20/0.38 ~((! [X0] : (((cODD @ X0) | (cEVEN @ X0)) <=> (cNUMBER @ X0)) & ! [X0] : ((cEVEN @ X0) => (cEVEN @ (cS @ (cS @ X0)))) & (((cNUMBER @ (cS @ c0)) & ! [X1] : (((cNUMBER @ (cS @ X1)) & (cNUMBER @ X1)) => ((cNUMBER @ (cS @ X1)) & (cNUMBER @ (cS @ (cS @ X1))))) & (cNUMBER @ c0)) => ! [X1] : ((cNUMBER @ (cS @ X1)) & (cNUMBER @ X1))) & (cODD @ (cS @ c0)) & (cEVEN @ c0) & ! [X0] : ((cODD @ X0) => (cODD @ (cS @ (cS @ X0))))) => ! [X0] : (cNUMBER @ X0))),
% 0.20/0.38 inference(negated_conjecture,[],[f1])).
% 0.20/0.38 thf(f1,conjecture,(
% 0.20/0.38 (! [X0] : (((cODD @ X0) | (cEVEN @ X0)) <=> (cNUMBER @ X0)) & ! [X0] : ((cEVEN @ X0) => (cEVEN @ (cS @ (cS @ X0)))) & (((cNUMBER @ (cS @ c0)) & ! [X1] : (((cNUMBER @ (cS @ X1)) & (cNUMBER @ X1)) => ((cNUMBER @ (cS @ X1)) & (cNUMBER @ (cS @ (cS @ X1))))) & (cNUMBER @ c0)) => ! [X1] : ((cNUMBER @ (cS @ X1)) & (cNUMBER @ X1))) & (cODD @ (cS @ c0)) & (cEVEN @ c0) & ! [X0] : ((cODD @ X0) => (cODD @ (cS @ (cS @ X0))))) => ! [X0] : (cNUMBER @ X0)),
% 0.20/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM350)).
% 0.20/0.38 thf(f88,plain,(
% 0.20/0.38 ((cEVEN @ sK0) != $true) | spl2_1),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f87])).
% 0.20/0.38 thf(f87,plain,(
% 0.20/0.38 ($true != $true) | ((cEVEN @ sK0) != $true) | spl2_1),
% 0.20/0.38 inference(superposition,[],[f82,f14])).
% 0.20/0.38 thf(f14,plain,(
% 0.20/0.38 ( ! [X5 : $i] : (($true = (cEVEN @ (cS @ (cS @ X5)))) | ($true != (cEVEN @ X5))) )),
% 0.20/0.38 inference(cnf_transformation,[],[f13])).
% 0.20/0.38 thf(f82,plain,(
% 0.20/0.38 ($true != (cEVEN @ (cS @ (cS @ sK0)))) | spl2_1),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f79])).
% 0.20/0.38 thf(f79,plain,(
% 0.20/0.38 ($true != (cEVEN @ (cS @ (cS @ sK0)))) | ($true != $true) | spl2_1),
% 0.20/0.38 inference(superposition,[],[f31,f17])).
% 0.20/0.38 thf(f17,plain,(
% 0.20/0.38 ( ! [X4 : $i] : (($true = (cNUMBER @ X4)) | ($true != (cEVEN @ X4))) )),
% 0.20/0.38 inference(cnf_transformation,[],[f13])).
% 0.20/0.38 thf(f31,plain,(
% 0.20/0.38 ($true != (cNUMBER @ (cS @ (cS @ sK0)))) | spl2_1),
% 0.20/0.38 inference(avatar_component_clause,[],[f29])).
% 0.20/0.38 thf(f29,plain,(
% 0.20/0.38 spl2_1 <=> ($true = (cNUMBER @ (cS @ (cS @ sK0))))),
% 0.20/0.38 introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
% 0.20/0.38 thf(f93,plain,(
% 0.20/0.38 ($true != (cODD @ sK0)) | spl2_1),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f92])).
% 0.20/0.38 thf(f92,plain,(
% 0.20/0.38 ($true != (cODD @ sK0)) | ($true != $true) | spl2_1),
% 0.20/0.38 inference(superposition,[],[f81,f27])).
% 0.20/0.38 thf(f27,plain,(
% 0.20/0.38 ( ! [X0 : $i] : (((cODD @ (cS @ (cS @ X0))) = $true) | ((cODD @ X0) != $true)) )),
% 0.20/0.38 inference(cnf_transformation,[],[f13])).
% 0.20/0.38 thf(f81,plain,(
% 0.20/0.38 ((cODD @ (cS @ (cS @ sK0))) != $true) | spl2_1),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f80])).
% 0.20/0.38 thf(f80,plain,(
% 0.20/0.38 ((cODD @ (cS @ (cS @ sK0))) != $true) | ($true != $true) | spl2_1),
% 0.20/0.38 inference(superposition,[],[f31,f16])).
% 0.20/0.38 thf(f16,plain,(
% 0.20/0.38 ( ! [X4 : $i] : (($true = (cNUMBER @ X4)) | ($true != (cODD @ X4))) )),
% 0.20/0.38 inference(cnf_transformation,[],[f13])).
% 0.20/0.38 thf(f76,plain,(
% 0.20/0.38 ~spl2_4),
% 0.20/0.38 inference(avatar_contradiction_clause,[],[f75])).
% 0.20/0.38 thf(f75,plain,(
% 0.20/0.38 $false | ~spl2_4),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f74])).
% 0.20/0.38 thf(f74,plain,(
% 0.20/0.38 ($true != $true) | ~spl2_4),
% 0.20/0.38 inference(superposition,[],[f20,f42])).
% 0.20/0.38 thf(f42,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (((cNUMBER @ X1) = $true)) ) | ~spl2_4),
% 0.20/0.38 inference(avatar_component_clause,[],[f41])).
% 0.20/0.38 thf(f41,plain,(
% 0.20/0.38 spl2_4 <=> ! [X1] : ((cNUMBER @ X1) = $true)),
% 0.20/0.38 introduced(avatar_definition,[new_symbols(naming,[spl2_4])])).
% 0.20/0.38 thf(f20,plain,(
% 0.20/0.38 ($true != (cNUMBER @ sK1))),
% 0.20/0.38 inference(cnf_transformation,[],[f13])).
% 0.20/0.38 thf(f73,plain,(
% 0.20/0.38 spl2_5),
% 0.20/0.38 inference(avatar_contradiction_clause,[],[f72])).
% 0.20/0.38 thf(f72,plain,(
% 0.20/0.38 $false | spl2_5),
% 0.20/0.38 inference(subsumption_resolution,[],[f70,f15])).
% 0.20/0.38 thf(f15,plain,(
% 0.20/0.38 ((cEVEN @ c0) = $true)),
% 0.20/0.38 inference(cnf_transformation,[],[f13])).
% 0.20/0.38 thf(f70,plain,(
% 0.20/0.38 ((cEVEN @ c0) != $true) | spl2_5),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f68])).
% 0.20/0.38 thf(f68,plain,(
% 0.20/0.38 ((cEVEN @ c0) != $true) | ($true != $true) | spl2_5),
% 0.20/0.38 inference(superposition,[],[f46,f17])).
% 0.20/0.38 thf(f46,plain,(
% 0.20/0.38 ((cNUMBER @ c0) != $true) | spl2_5),
% 0.20/0.38 inference(avatar_component_clause,[],[f44])).
% 0.20/0.38 thf(f44,plain,(
% 0.20/0.38 spl2_5 <=> ((cNUMBER @ c0) = $true)),
% 0.20/0.38 introduced(avatar_definition,[new_symbols(naming,[spl2_5])])).
% 0.20/0.38 thf(f65,plain,(
% 0.20/0.38 spl2_2),
% 0.20/0.38 inference(avatar_contradiction_clause,[],[f64])).
% 0.20/0.38 thf(f64,plain,(
% 0.20/0.38 $false | spl2_2),
% 0.20/0.38 inference(subsumption_resolution,[],[f63,f19])).
% 0.20/0.38 thf(f19,plain,(
% 0.20/0.38 ((cODD @ (cS @ c0)) = $true)),
% 0.20/0.38 inference(cnf_transformation,[],[f13])).
% 0.20/0.38 thf(f63,plain,(
% 0.20/0.38 ((cODD @ (cS @ c0)) != $true) | spl2_2),
% 0.20/0.38 inference(trivial_inequality_removal,[],[f61])).
% 0.20/0.38 thf(f61,plain,(
% 0.20/0.38 ($true != $true) | ((cODD @ (cS @ c0)) != $true) | spl2_2),
% 0.20/0.38 inference(superposition,[],[f35,f16])).
% 0.20/0.38 thf(f35,plain,(
% 0.20/0.38 ((cNUMBER @ (cS @ c0)) != $true) | spl2_2),
% 0.20/0.38 inference(avatar_component_clause,[],[f33])).
% 0.20/0.38 thf(f33,plain,(
% 0.20/0.38 spl2_2 <=> ((cNUMBER @ (cS @ c0)) = $true)),
% 0.20/0.38 introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
% 0.20/0.38 thf(f58,plain,(
% 0.20/0.38 spl2_7 | spl2_4 | ~spl2_5 | ~spl2_2),
% 0.20/0.38 inference(avatar_split_clause,[],[f21,f33,f44,f41,f55])).
% 0.20/0.38 thf(f21,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (((cNUMBER @ X1) = $true) | ((cNUMBER @ (cS @ c0)) != $true) | ((cNUMBER @ c0) != $true) | ($true = (cNUMBER @ sK0))) )),
% 0.20/0.38 inference(cnf_transformation,[],[f13])).
% 0.20/0.38 thf(f52,plain,(
% 0.20/0.38 ~spl2_5 | ~spl2_2 | spl2_4 | spl2_3),
% 0.20/0.38 inference(avatar_split_clause,[],[f22,f37,f41,f33,f44])).
% 0.20/0.38 thf(f37,plain,(
% 0.20/0.38 spl2_3 <=> ($true = (cNUMBER @ (cS @ sK0)))),
% 0.20/0.38 introduced(avatar_definition,[new_symbols(naming,[spl2_3])])).
% 0.20/0.38 thf(f22,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (((cNUMBER @ c0) != $true) | ($true = (cNUMBER @ (cS @ sK0))) | ((cNUMBER @ (cS @ c0)) != $true) | ((cNUMBER @ X1) = $true)) )),
% 0.20/0.38 inference(cnf_transformation,[],[f13])).
% 0.20/0.38 thf(f47,plain,(
% 0.20/0.38 ~spl2_1 | ~spl2_2 | ~spl2_3 | spl2_4 | ~spl2_5),
% 0.20/0.38 inference(avatar_split_clause,[],[f23,f44,f41,f37,f33,f29])).
% 0.20/0.38 thf(f23,plain,(
% 0.20/0.38 ( ! [X1 : $i] : (($true != (cNUMBER @ (cS @ sK0))) | ($true != (cNUMBER @ (cS @ (cS @ sK0)))) | ((cNUMBER @ (cS @ c0)) != $true) | ((cNUMBER @ c0) != $true) | ((cNUMBER @ X1) = $true)) )),
% 0.20/0.38 inference(cnf_transformation,[],[f13])).
% 0.20/0.38 % SZS output end Proof for theBenchmark
% 0.20/0.38 % (7431)------------------------------
% 0.20/0.38 % (7431)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.38 % (7431)Termination reason: Refutation
% 0.20/0.38
% 0.20/0.38 % (7431)Memory used [KB]: 5628
% 0.20/0.38 % (7431)Time elapsed: 0.010 s
% 0.20/0.38 % (7431)Instructions burned: 7 (million)
% 0.20/0.38 % (7431)------------------------------
% 0.20/0.38 % (7431)------------------------------
% 0.20/0.38 % (7430)Success in time 0.01 s
% 0.20/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------