TSTP Solution File: SEV299^5 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SEV299^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n029.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 : Mon Jun 24 16:02:41 EDT 2024
% Result : Theorem 0.11s 0.38s
% Output : Refutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEV299^5 : TPTP v8.2.0. Bugfixed v6.2.0.
% 0.06/0.12 % Command : run_vampire %s %d THM
% 0.11/0.33 % Computer : n029.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 21 19:07:24 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.35 This is a TH0_THM_EQU_NAR problem
% 0.11/0.35 Running higher-order theorem proving
% 0.11/0.35 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/benchmark/theBenchmark.p -m 16384 -t 300
% 0.11/0.37 % (15976)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)
% 0.11/0.37 % (15977)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)
% 0.11/0.37 % (15978)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.11/0.37 % (15979)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)
% 0.11/0.37 % (15975)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.11/0.37 % (15980)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)
% 0.11/0.37 % (15981)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.11/0.37 % (15979)Instruction limit reached!
% 0.11/0.37 % (15979)------------------------------
% 0.11/0.37 % (15979)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (15979)Termination reason: Unknown
% 0.11/0.37 % (15979)Termination phase: shuffling
% 0.11/0.37
% 0.11/0.37 % (15979)Memory used [KB]: 895
% 0.11/0.37 % (15979)Time elapsed: 0.003 s
% 0.11/0.37 % (15979)Instructions burned: 2 (million)
% 0.11/0.37 % (15979)------------------------------
% 0.11/0.37 % (15979)------------------------------
% 0.11/0.37 % (15978)Instruction limit reached!
% 0.11/0.37 % (15978)------------------------------
% 0.11/0.37 % (15978)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (15978)Termination reason: Unknown
% 0.11/0.37 % (15978)Termination phase: Saturation
% 0.11/0.37
% 0.11/0.37 % (15978)Memory used [KB]: 5500
% 0.11/0.37 % (15978)Time elapsed: 0.004 s
% 0.11/0.37 % (15978)Instructions burned: 2 (million)
% 0.11/0.37 % (15978)------------------------------
% 0.11/0.37 % (15978)------------------------------
% 0.11/0.37 % (15980)Refutation not found, incomplete strategy
% 0.11/0.37 % (15980)------------------------------
% 0.11/0.37 % (15980)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (15980)Termination reason: Refutation not found, incomplete strategy
% 0.11/0.37
% 0.11/0.37
% 0.11/0.37 % (15980)Memory used [KB]: 5500
% 0.11/0.37 % (15980)Time elapsed: 0.004 s
% 0.11/0.37 % (15980)Instructions burned: 2 (million)
% 0.11/0.37 % (15980)------------------------------
% 0.11/0.37 % (15980)------------------------------
% 0.11/0.37 % (15976)Instruction limit reached!
% 0.11/0.37 % (15976)------------------------------
% 0.11/0.37 % (15976)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.37 % (15976)Termination reason: Unknown
% 0.11/0.37 % (15976)Termination phase: Saturation
% 0.11/0.37
% 0.11/0.37 % (15976)Memory used [KB]: 5500
% 0.11/0.37 % (15976)Time elapsed: 0.005 s
% 0.11/0.37 % (15976)Instructions burned: 4 (million)
% 0.11/0.37 % (15976)------------------------------
% 0.11/0.37 % (15976)------------------------------
% 0.11/0.38 % (15977)First to succeed.
% 0.11/0.38 % (15977)Refutation found. Thanks to Tanya!
% 0.11/0.38 % SZS status Theorem for theBenchmark
% 0.11/0.38 % SZS output start Proof for theBenchmark
% 0.11/0.38 thf(func_def_0, type, cNAT: (($i > $o) > $o) > $o).
% 0.11/0.38 thf(func_def_1, type, cSUCC: (($i > $o) > $o) > ($i > $o) > $o).
% 0.11/0.38 thf(func_def_2, type, cZERO: ($i > $o) > $o).
% 0.11/0.38 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 0.11/0.38 thf(func_def_17, type, sK0: (($i > $o) > $o) > $o).
% 0.11/0.38 thf(func_def_18, type, sK1: ($i > $o) > $o).
% 0.11/0.38 thf(func_def_20, type, sK3: ((($i > $o) > $o) > $o) > ($i > $o) > $o).
% 0.11/0.38 thf(func_def_21, type, ph4: !>[X0: $tType]:(X0)).
% 0.11/0.38 thf(f91,plain,(
% 0.11/0.38 $false),
% 0.11/0.38 inference(avatar_sat_refutation,[],[f60,f65,f85,f90])).
% 0.11/0.38 thf(f90,plain,(
% 0.11/0.38 ~spl2_3),
% 0.11/0.38 inference(avatar_contradiction_clause,[],[f89])).
% 0.11/0.38 thf(f89,plain,(
% 0.11/0.38 $false | ~spl2_3),
% 0.11/0.38 inference(trivial_inequality_removal,[],[f86])).
% 0.11/0.38 thf(f86,plain,(
% 0.11/0.38 ($false = $true) | ~spl2_3),
% 0.11/0.38 inference(backward_demodulation,[],[f31,f83])).
% 0.11/0.38 thf(f83,plain,(
% 0.11/0.38 ($false = (sK0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ~spl2_3),
% 0.11/0.38 inference(avatar_component_clause,[],[f81])).
% 0.11/0.38 thf(f81,plain,(
% 0.11/0.38 spl2_3 <=> ($false = (sK0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
% 0.11/0.38 introduced(avatar_definition,[new_symbols(naming,[spl2_3])])).
% 0.11/0.38 thf(f31,plain,(
% 0.11/0.38 ($true = (sK0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))))),
% 0.11/0.38 inference(beta_eta_normalization,[],[f29])).
% 0.11/0.38 thf(f29,plain,(
% 0.11/0.38 ($true = (sK0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.11/0.38 inference(definition_unfolding,[],[f25,f20])).
% 0.11/0.38 thf(f20,plain,(
% 0.11/0.38 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.11/0.38 inference(cnf_transformation,[],[f8])).
% 0.11/0.38 thf(f8,plain,(
% 0.11/0.38 (cZERO = (^[Y0 : $i > $o]: (~ (?? @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
% 0.11/0.38 inference(fool_elimination,[],[f7])).
% 0.11/0.38 thf(f7,plain,(
% 0.11/0.38 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.11/0.38 inference(rectify,[],[f1])).
% 0.11/0.38 thf(f1,axiom,(
% 0.11/0.38 (cZERO = (^[X0 : $i > $o] : (~? [X1] : (X0 @ X1))))),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cZERO_def)).
% 0.11/0.38 thf(f25,plain,(
% 0.11/0.38 ($true = (sK0 @ cZERO))),
% 0.11/0.38 inference(cnf_transformation,[],[f19])).
% 0.11/0.38 thf(f19,plain,(
% 0.11/0.38 ! [X1 : ($i > $o) > $o] : (((sK0 @ (cSUCC @ X1)) = $true) | ($true != (sK0 @ X1))) & ($true = (sK0 @ cZERO)) & (($true = (cNAT @ sK1)) & ($true != (sK0 @ sK1)))),
% 0.11/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f18,f17])).
% 0.11/0.38 thf(f17,plain,(
% 0.11/0.38 ? [X0 : (($i > $o) > $o) > $o] : (! [X1 : ($i > $o) > $o] : (((X0 @ (cSUCC @ X1)) = $true) | ((X0 @ X1) != $true)) & ((X0 @ cZERO) = $true) & ? [X2 : ($i > $o) > $o] : (((cNAT @ X2) = $true) & ((X0 @ X2) != $true))) => (! [X1 : ($i > $o) > $o] : (((sK0 @ (cSUCC @ X1)) = $true) | ($true != (sK0 @ X1))) & ($true = (sK0 @ cZERO)) & ? [X2 : ($i > $o) > $o] : (((cNAT @ X2) = $true) & ((sK0 @ X2) != $true)))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f18,plain,(
% 0.11/0.38 ? [X2 : ($i > $o) > $o] : (((cNAT @ X2) = $true) & ((sK0 @ X2) != $true)) => (($true = (cNAT @ sK1)) & ($true != (sK0 @ sK1)))),
% 0.11/0.38 introduced(choice_axiom,[])).
% 0.11/0.38 thf(f16,plain,(
% 0.11/0.38 ? [X0 : (($i > $o) > $o) > $o] : (! [X1 : ($i > $o) > $o] : (((X0 @ (cSUCC @ X1)) = $true) | ((X0 @ X1) != $true)) & ((X0 @ cZERO) = $true) & ? [X2 : ($i > $o) > $o] : (((cNAT @ X2) = $true) & ((X0 @ X2) != $true)))),
% 0.11/0.38 inference(flattening,[],[f15])).
% 0.11/0.38 thf(f15,plain,(
% 0.11/0.38 ? [X0 : (($i > $o) > $o) > $o] : (? [X2 : ($i > $o) > $o] : (((cNAT @ X2) = $true) & ((X0 @ X2) != $true)) & (! [X1 : ($i > $o) > $o] : (((X0 @ (cSUCC @ X1)) = $true) | ((X0 @ X1) != $true)) & ((X0 @ cZERO) = $true)))),
% 0.11/0.38 inference(ennf_transformation,[],[f10])).
% 0.11/0.38 thf(f10,plain,(
% 0.11/0.38 ~! [X0 : (($i > $o) > $o) > $o] : ((! [X1 : ($i > $o) > $o] : (((X0 @ X1) = $true) => ((X0 @ (cSUCC @ X1)) = $true)) & ((X0 @ cZERO) = $true)) => ! [X2 : ($i > $o) > $o] : (((cNAT @ X2) = $true) => ((X0 @ X2) = $true)))),
% 0.11/0.38 inference(fool_elimination,[],[f9])).
% 0.11/0.38 thf(f9,plain,(
% 0.11/0.38 ~! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => ! [X2 : ($i > $o) > $o] : ((cNAT @ X2) => (X0 @ X2)))),
% 0.11/0.38 inference(rectify,[],[f5])).
% 0.11/0.38 thf(f5,negated_conjecture,(
% 0.11/0.38 ~! [X4 : (($i > $o) > $o) > $o] : (((X4 @ cZERO) & ! [X5 : ($i > $o) > $o] : ((X4 @ X5) => (X4 @ (cSUCC @ X5)))) => ! [X6 : ($i > $o) > $o] : ((cNAT @ X6) => (X4 @ X6)))),
% 0.11/0.38 inference(negated_conjecture,[],[f4])).
% 0.11/0.38 thf(f4,conjecture,(
% 0.11/0.38 ! [X4 : (($i > $o) > $o) > $o] : (((X4 @ cZERO) & ! [X5 : ($i > $o) > $o] : ((X4 @ X5) => (X4 @ (cSUCC @ X5)))) => ! [X6 : ($i > $o) > $o] : ((cNAT @ X6) => (X4 @ X6)))),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cINDUCTION)).
% 0.11/0.38 thf(f85,plain,(
% 0.11/0.38 spl2_3 | spl2_2 | ~spl2_1),
% 0.11/0.38 inference(avatar_split_clause,[],[f77,f52,f56,f81])).
% 0.11/0.38 thf(f56,plain,(
% 0.11/0.38 spl2_2 <=> ($true = (sK0 @ sK1))),
% 0.11/0.38 introduced(avatar_definition,[new_symbols(naming,[spl2_2])])).
% 0.11/0.38 thf(f52,plain,(
% 0.11/0.38 spl2_1 <=> ($true = (sK0 @ (sK3 @ sK0)))),
% 0.11/0.38 introduced(avatar_definition,[new_symbols(naming,[spl2_1])])).
% 0.11/0.38 thf(f77,plain,(
% 0.11/0.38 ($true = (sK0 @ sK1)) | ($false = (sK0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ~spl2_1),
% 0.11/0.38 inference(trivial_inequality_removal,[],[f75])).
% 0.11/0.38 thf(f75,plain,(
% 0.11/0.38 ($false = (sK0 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) | ($true = (sK0 @ sK1)) | ($false = $true) | ~spl2_1),
% 0.11/0.38 inference(superposition,[],[f67,f39])).
% 0.11/0.38 thf(f39,plain,(
% 0.11/0.38 ( ! [X1 : (($i > $o) > $o) > $o] : (($false = (X1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK3 @ X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1))))))) | ($true = (X1 @ sK1)) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false)) )),
% 0.11/0.38 inference(binary_proxy_clausification,[],[f38])).
% 0.11/0.38 thf(f38,plain,(
% 0.11/0.38 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = (X1 @ sK1)) | ((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($false = ((X1 @ (sK3 @ X1)) => (X1 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK3 @ X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1))))))))) )),
% 0.11/0.38 inference(beta_eta_normalization,[],[f37])).
% 0.11/0.38 thf(f37,plain,(
% 0.11/0.38 ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($true = (X1 @ sK1)) | ($false = ((^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2)))))))) @ (sK3 @ X1)))) )),
% 0.11/0.38 inference(sigma_clausification,[],[f36])).
% 0.11/0.38 thf(f36,plain,(
% 0.11/0.38 ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($true = (X1 @ sK1)) | ($false = (!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))))) )),
% 0.11/0.38 inference(binary_proxy_clausification,[],[f35])).
% 0.11/0.38 thf(f35,plain,(
% 0.11/0.38 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = (X1 @ sK1)) | ($false = ((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))))) )),
% 0.11/0.38 inference(binary_proxy_clausification,[],[f34])).
% 0.11/0.38 thf(f34,plain,(
% 0.11/0.38 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = (((!! @ (($i > $o) > $o) @ (^[Y0 : ($i > $o) > $o]: ((X1 @ Y0) => (X1 @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))) & (X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0))))) => (X1 @ sK1)))) )),
% 0.11/0.38 inference(beta_eta_normalization,[],[f33])).
% 0.11/0.38 thf(f33,plain,(
% 0.11/0.38 ( ! [X1 : (($i > $o) > $o) > $o] : (($true = ((^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK1))) @ X1))) )),
% 0.11/0.38 inference(pi_clausification,[],[f32])).
% 0.11/0.38 thf(f32,plain,(
% 0.11/0.38 ($true = (!! @ ((($i > $o) > $o) > $o) @ (^[Y0 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y1 : ($i > $o) > $o]: ((Y0 @ Y1) => (Y0 @ (^[Y2 : $i > $o]: (?? @ $i @ (^[Y3 : $i]: ((Y1 @ (^[Y4 : $i]: ((Y2 @ Y4) & (~ (Y3 = Y4))))) & (Y2 @ Y3))))))))) & (Y0 @ (^[Y1 : $i > $o]: (~ (?? @ $i @ Y1))))) => (Y0 @ sK1)))))),
% 0.11/0.38 inference(beta_eta_normalization,[],[f30])).
% 0.11/0.38 thf(f30,plain,(
% 0.11/0.38 (((^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))) @ sK1) = $true)),
% 0.11/0.38 inference(definition_unfolding,[],[f24,f27])).
% 0.11/0.38 thf(f27,plain,(
% 0.11/0.38 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ ((^[Y3 : ($i > $o) > $o]: ((^[Y4 : $i > $o]: (?? @ $i @ (^[Y5 : $i]: ((Y3 @ (^[Y6 : $i]: ((Y4 @ Y6) & (~ (Y5 = Y6))))) & (Y4 @ Y5))))))) @ Y2))))) & (Y1 @ (^[Y2 : $i > $o]: (~ (?? @ $i @ (^[Y3 : $i]: (Y2 @ Y3))))))) => (Y1 @ Y0))))))),
% 0.11/0.38 inference(definition_unfolding,[],[f21,f22,f20])).
% 0.11/0.38 thf(f22,plain,(
% 0.11/0.38 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))),
% 0.11/0.38 inference(cnf_transformation,[],[f14])).
% 0.11/0.38 thf(f14,plain,(
% 0.11/0.38 (cSUCC = (^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))))),
% 0.11/0.38 inference(fool_elimination,[],[f13])).
% 0.11/0.38 thf(f13,plain,(
% 0.11/0.38 ((^[X0 : ($i > $o) > $o, X1 : $i > $o] : (? [X2] : ((X1 @ X2) & (X0 @ (^[X3 : $i] : ((X2 != X3) & (X1 @ X3))))))) = cSUCC)),
% 0.11/0.38 inference(rectify,[],[f2])).
% 0.11/0.38 thf(f2,axiom,(
% 0.11/0.38 ((^[X2 : ($i > $o) > $o, X0 : $i > $o] : (? [X1] : ((X0 @ X1) & (X2 @ (^[X3 : $i] : ((X1 != X3) & (X0 @ X3))))))) = cSUCC)),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSUCC_def)).
% 0.11/0.38 thf(f21,plain,(
% 0.11/0.38 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 0.11/0.38 inference(cnf_transformation,[],[f12])).
% 0.11/0.38 thf(f12,plain,(
% 0.11/0.38 (cNAT = (^[Y0 : ($i > $o) > $o]: (!! @ ((($i > $o) > $o) > $o) @ (^[Y1 : (($i > $o) > $o) > $o]: (((!! @ (($i > $o) > $o) @ (^[Y2 : ($i > $o) > $o]: ((Y1 @ Y2) => (Y1 @ (cSUCC @ Y2))))) & (Y1 @ cZERO)) => (Y1 @ Y0))))))),
% 0.11/0.38 inference(fool_elimination,[],[f11])).
% 0.11/0.38 thf(f11,plain,(
% 0.11/0.38 (cNAT = (^[X0 : ($i > $o) > $o] : (! [X1 : (($i > $o) > $o) > $o] : (((X1 @ cZERO) & ! [X2 : ($i > $o) > $o] : ((X1 @ X2) => (X1 @ (cSUCC @ X2)))) => (X1 @ X0)))))),
% 0.11/0.38 inference(rectify,[],[f3])).
% 0.11/0.38 thf(f3,axiom,(
% 0.11/0.38 (cNAT = (^[X2 : ($i > $o) > $o] : (! [X0 : (($i > $o) > $o) > $o] : (((X0 @ cZERO) & ! [X1 : ($i > $o) > $o] : ((X0 @ X1) => (X0 @ (cSUCC @ X1)))) => (X0 @ X2)))))),
% 0.11/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cNAT_def)).
% 0.11/0.38 thf(f24,plain,(
% 0.11/0.38 ($true = (cNAT @ sK1))),
% 0.11/0.38 inference(cnf_transformation,[],[f19])).
% 0.11/0.38 thf(f67,plain,(
% 0.11/0.38 ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK3 @ sK0 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1)))))) = $true) | ~spl2_1),
% 0.11/0.38 inference(trivial_inequality_removal,[],[f66])).
% 0.11/0.38 thf(f66,plain,(
% 0.11/0.38 ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK3 @ sK0 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1)))))) = $true) | ($true != $true) | ~spl2_1),
% 0.11/0.38 inference(superposition,[],[f41,f54])).
% 0.11/0.38 thf(f54,plain,(
% 0.11/0.38 ($true = (sK0 @ (sK3 @ sK0))) | ~spl2_1),
% 0.11/0.38 inference(avatar_component_clause,[],[f52])).
% 0.11/0.38 thf(f41,plain,(
% 0.11/0.38 ( ! [X1 : ($i > $o) > $o] : (($true != (sK0 @ X1)) | ((sK0 @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((X1 @ (^[Y2 : $i]: ((Y0 @ Y2) & (~ (Y1 = Y2))))) & (Y0 @ Y1)))))) = $true)) )),
% 0.11/0.38 inference(beta_eta_normalization,[],[f28])).
% 0.11/0.38 thf(f28,plain,(
% 0.11/0.38 ( ! [X1 : ($i > $o) > $o] : (($true = (sK0 @ ((^[Y0 : ($i > $o) > $o]: ((^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ (^[Y3 : $i]: ((Y1 @ Y3) & (~ (Y2 = Y3))))) & (Y1 @ Y2))))))) @ X1))) | ($true != (sK0 @ X1))) )),
% 0.11/0.38 inference(definition_unfolding,[],[f26,f22])).
% 0.11/0.38 thf(f26,plain,(
% 0.11/0.38 ( ! [X1 : ($i > $o) > $o] : (((sK0 @ (cSUCC @ X1)) = $true) | ($true != (sK0 @ X1))) )),
% 0.11/0.38 inference(cnf_transformation,[],[f19])).
% 0.11/0.38 thf(f65,plain,(
% 0.11/0.38 ~spl2_2),
% 0.11/0.38 inference(avatar_contradiction_clause,[],[f64])).
% 0.11/0.38 thf(f64,plain,(
% 0.11/0.38 $false | ~spl2_2),
% 0.11/0.38 inference(trivial_inequality_removal,[],[f61])).
% 0.11/0.38 thf(f61,plain,(
% 0.11/0.38 ($true != $true) | ~spl2_2),
% 0.11/0.38 inference(superposition,[],[f23,f58])).
% 0.11/0.38 thf(f58,plain,(
% 0.11/0.38 ($true = (sK0 @ sK1)) | ~spl2_2),
% 0.11/0.38 inference(avatar_component_clause,[],[f56])).
% 0.11/0.38 thf(f23,plain,(
% 0.11/0.38 ($true != (sK0 @ sK1))),
% 0.11/0.38 inference(cnf_transformation,[],[f19])).
% 0.11/0.38 thf(f60,plain,(
% 0.11/0.38 spl2_1 | spl2_2),
% 0.11/0.38 inference(avatar_split_clause,[],[f49,f56,f52])).
% 0.11/0.38 thf(f49,plain,(
% 0.11/0.38 ($true = (sK0 @ (sK3 @ sK0))) | ($true = (sK0 @ sK1))),
% 0.11/0.38 inference(trivial_inequality_removal,[],[f45])).
% 0.11/0.38 thf(f45,plain,(
% 0.11/0.38 ($false = $true) | ($true = (sK0 @ (sK3 @ sK0))) | ($true = (sK0 @ sK1))),
% 0.11/0.38 inference(superposition,[],[f40,f31])).
% 0.11/0.38 thf(f40,plain,(
% 0.11/0.38 ( ! [X1 : (($i > $o) > $o) > $o] : (((X1 @ (^[Y0 : $i > $o]: (~ (?? @ $i @ Y0)))) = $false) | ($true = (X1 @ (sK3 @ X1))) | ($true = (X1 @ sK1))) )),
% 0.11/0.38 inference(binary_proxy_clausification,[],[f38])).
% 0.11/0.38 % SZS output end Proof for theBenchmark
% 0.11/0.38 % (15977)------------------------------
% 0.11/0.38 % (15977)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.11/0.38 % (15977)Termination reason: Refutation
% 0.11/0.38
% 0.11/0.38 % (15977)Memory used [KB]: 5628
% 0.11/0.38 % (15977)Time elapsed: 0.011 s
% 0.11/0.38 % (15977)Instructions burned: 9 (million)
% 0.11/0.38 % (15977)------------------------------
% 0.11/0.38 % (15977)------------------------------
% 0.11/0.38 % (15974)Success in time 0.012 s
%------------------------------------------------------------------------------