TSTP Solution File: NUM812^5 by Vampire---4.9
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%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : NUM812^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n018.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 13:18:01 EDT 2024
% Result : Theorem 0.12s 0.39s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM812^5 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.07/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jun 23 04:03:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 Running higher-order theorem proving
% 0.12/0.35 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.12/0.37 % (27028)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37 % (27030)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)
% 0.12/0.37 % (27029)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)
% 0.12/0.37 % (27026)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)
% 0.12/0.37 % (27031)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.37 % (27027)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)
% 0.12/0.37 % (27025)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.37 % (27028)Instruction limit reached!
% 0.12/0.37 % (27028)------------------------------
% 0.12/0.37 % (27028)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (27030)Refutation not found, incomplete strategy
% 0.12/0.37 % (27030)------------------------------
% 0.12/0.37 % (27030)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (27030)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.37
% 0.12/0.37
% 0.12/0.37 % (27030)Memory used [KB]: 5373
% 0.12/0.37 % (27030)Time elapsed: 0.003 s
% 0.12/0.37 % (27030)Instructions burned: 1 (million)
% 0.12/0.37 % (27030)------------------------------
% 0.12/0.37 % (27030)------------------------------
% 0.12/0.37 % (27029)Instruction limit reached!
% 0.12/0.37 % (27029)------------------------------
% 0.12/0.37 % (27029)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.37 % (27029)Termination reason: Unknown
% 0.12/0.37 % (27029)Termination phase: Saturation
% 0.12/0.37
% 0.12/0.37 % (27029)Memory used [KB]: 5500
% 0.12/0.37 % (27029)Time elapsed: 0.004 s
% 0.12/0.37 % (27029)Instructions burned: 2 (million)
% 0.12/0.37 % (27029)------------------------------
% 0.12/0.37 % (27029)------------------------------
% 0.12/0.37 % (27028)Termination reason: Unknown
% 0.12/0.37 % (27028)Termination phase: Saturation
% 0.12/0.37
% 0.12/0.37 % (27028)Memory used [KB]: 5500
% 0.12/0.37 % (27028)Time elapsed: 0.004 s
% 0.12/0.37 % (27028)Instructions burned: 2 (million)
% 0.12/0.37 % (27028)------------------------------
% 0.12/0.37 % (27028)------------------------------
% 0.12/0.38 % (27027)Refutation not found, incomplete strategy
% 0.12/0.38 % (27027)------------------------------
% 0.12/0.38 % (27027)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (27027)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.38
% 0.12/0.38
% 0.12/0.38 % (27027)Memory used [KB]: 5500
% 0.12/0.38 % (27027)Time elapsed: 0.005 s
% 0.12/0.38 % (27027)Instructions burned: 3 (million)
% 0.12/0.38 % (27027)------------------------------
% 0.12/0.38 % (27027)------------------------------
% 0.12/0.38 % (27026)Instruction limit reached!
% 0.12/0.38 % (27026)------------------------------
% 0.12/0.38 % (27026)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.38 % (27026)Termination reason: Unknown
% 0.12/0.38 % (27026)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (27026)Memory used [KB]: 5500
% 0.12/0.38 % (27026)Time elapsed: 0.006 s
% 0.12/0.38 % (27026)Instructions burned: 4 (million)
% 0.12/0.38 % (27026)------------------------------
% 0.12/0.38 % (27026)------------------------------
% 0.12/0.38 % (27025)First to succeed.
% 0.12/0.39 % (27025)Refutation found. Thanks to Tanya!
% 0.12/0.39 % SZS status Theorem for theBenchmark
% 0.12/0.39 % SZS output start Proof for theBenchmark
% 0.12/0.39 thf(func_def_1, type, cS: $i > $i).
% 0.12/0.39 thf(func_def_14, type, sK2: ($i > $o) > $i).
% 0.12/0.39 thf(func_def_16, type, ph3: !>[X0: $tType]:(X0)).
% 0.12/0.39 thf(f237,plain,(
% 0.12/0.39 $false),
% 0.12/0.39 inference(trivial_inequality_removal,[],[f233])).
% 0.12/0.39 thf(f233,plain,(
% 0.12/0.39 (sK0 != sK0) | (c0 != c0)),
% 0.12/0.39 inference(superposition,[],[f13,f174])).
% 0.12/0.39 thf(f174,plain,(
% 0.12/0.39 ( ! [X0 : $i] : ((c0 = X0) | (sK0 != X0)) )),
% 0.12/0.39 inference(superposition,[],[f14,f112])).
% 0.12/0.39 thf(f112,plain,(
% 0.12/0.39 ( ! [X0 : $i] : (((cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0) | (c0 = X0)) )),
% 0.12/0.39 inference(equality_proxy_clausification,[],[f111])).
% 0.12/0.39 thf(f111,plain,(
% 0.12/0.39 ( ! [X0 : $i] : (($true = (X0 = c0)) | ((cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0)) )),
% 0.12/0.39 inference(not_proxy_clausification,[],[f110])).
% 0.12/0.39 thf(f110,plain,(
% 0.12/0.39 ( ! [X0 : $i] : (($false = (~ (X0 = c0))) | ((cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0)) )),
% 0.12/0.39 inference(beta_eta_normalization,[],[f70])).
% 0.12/0.39 thf(f70,plain,(
% 0.12/0.39 ( ! [X0 : $i] : (((cS @ (sK2 @ (^[Y0 : $i]: (~ (X0 = Y0))))) = X0) | ($false = ((^[Y0 : $i]: (~ (X0 = Y0))) @ c0))) )),
% 0.12/0.39 inference(leibniz_equality_elimination,[],[f25])).
% 0.12/0.39 thf(f25,plain,(
% 0.12/0.39 ( ! [X2 : $i,X1 : $i > $o] : (((X1 @ (cS @ (sK2 @ X1))) = $false) | ($true = (X1 @ X2)) | ((X1 @ c0) = $false)) )),
% 0.12/0.39 inference(binary_proxy_clausification,[],[f24])).
% 0.12/0.39 thf(f24,plain,(
% 0.12/0.39 ( ! [X2 : $i,X1 : $i > $o] : (($false = ((X1 @ (sK2 @ X1)) => (X1 @ (cS @ (sK2 @ X1))))) | ($true = (X1 @ X2)) | ((X1 @ c0) = $false)) )),
% 0.12/0.39 inference(pi_clausification,[],[f23])).
% 0.12/0.39 thf(f23,plain,(
% 0.12/0.39 ( ! [X1 : $i > $o] : (($true = (!! @ $i @ X1)) | ((X1 @ c0) = $false) | ($false = ((X1 @ (sK2 @ X1)) => (X1 @ (cS @ (sK2 @ X1)))))) )),
% 0.12/0.39 inference(beta_eta_normalization,[],[f22])).
% 0.12/0.39 thf(f22,plain,(
% 0.12/0.39 ( ! [X1 : $i > $o] : (($true = (!! @ $i @ X1)) | ((X1 @ c0) = $false) | (((^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))) @ (sK2 @ X1)) = $false)) )),
% 0.12/0.39 inference(sigma_clausification,[],[f21])).
% 0.12/0.39 thf(f21,plain,(
% 0.12/0.39 ( ! [X1 : $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))))) | ($true = (!! @ $i @ X1)) | ((X1 @ c0) = $false)) )),
% 0.12/0.39 inference(binary_proxy_clausification,[],[f20])).
% 0.12/0.39 thf(f20,plain,(
% 0.12/0.39 ( ! [X1 : $i > $o] : ((((X1 @ c0) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))))) = $false) | ($true = (!! @ $i @ X1))) )),
% 0.12/0.39 inference(binary_proxy_clausification,[],[f19])).
% 0.12/0.39 thf(f19,plain,(
% 0.12/0.39 ( ! [X1 : $i > $o] : (($true = (((X1 @ c0) & (!! @ $i @ (^[Y0 : $i]: ((X1 @ Y0) => (X1 @ (cS @ Y0)))))) => (!! @ $i @ X1)))) )),
% 0.12/0.39 inference(beta_eta_normalization,[],[f18])).
% 0.12/0.39 thf(f18,plain,(
% 0.12/0.39 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ Y0))) @ X1))) )),
% 0.12/0.39 inference(pi_clausification,[],[f17])).
% 0.12/0.39 thf(f17,plain,(
% 0.12/0.39 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ Y0)))))),
% 0.12/0.39 inference(beta_eta_normalization,[],[f16])).
% 0.12/0.39 thf(f16,plain,(
% 0.12/0.39 ($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.12/0.39 inference(definition_unfolding,[],[f15,f12])).
% 0.12/0.39 thf(f12,plain,(
% 0.12/0.39 (cIND = $true)),
% 0.12/0.39 inference(cnf_transformation,[],[f11])).
% 0.12/0.39 thf(f11,plain,(
% 0.12/0.39 (! [X1] : ((cS @ X1) != sK0) & (c0 != sK0)) & (cIND = $true)),
% 0.12/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f9,f10])).
% 0.12/0.39 thf(f10,plain,(
% 0.12/0.39 ? [X0] : (! [X1] : ((cS @ X1) != X0) & (c0 != X0)) => (! [X1] : ((cS @ X1) != sK0) & (c0 != sK0))),
% 0.12/0.39 introduced(choice_axiom,[])).
% 0.12/0.39 thf(f9,plain,(
% 0.12/0.39 ? [X0] : (! [X1] : ((cS @ X1) != X0) & (c0 != X0)) & (cIND = $true)),
% 0.12/0.39 inference(ennf_transformation,[],[f8])).
% 0.12/0.39 thf(f8,plain,(
% 0.12/0.39 ~((cIND = $true) => ! [X0] : ((c0 = X0) | ? [X1] : ((cS @ X1) = X0)))),
% 0.12/0.39 inference(fool_elimination,[],[f7])).
% 0.12/0.39 thf(f7,plain,(
% 0.12/0.39 ~(cIND => ! [X0] : (? [X1] : ((cS @ X1) = X0) | (c0 = X0)))),
% 0.12/0.39 inference(rectify,[],[f3])).
% 0.12/0.39 thf(f3,negated_conjecture,(
% 0.12/0.39 ~(cIND => ! [X2] : (? [X3] : ((cS @ X3) = X2) | (c0 = X2)))),
% 0.12/0.39 inference(negated_conjecture,[],[f2])).
% 0.12/0.39 thf(f2,conjecture,(
% 0.12/0.39 cIND => ! [X2] : (? [X3] : ((cS @ X3) = X2) | (c0 = X2))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM578)).
% 0.12/0.39 thf(f15,plain,(
% 0.12/0.39 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.12/0.39 inference(cnf_transformation,[],[f6])).
% 0.12/0.39 thf(f6,plain,(
% 0.12/0.39 (cIND = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (((Y0 @ c0) & (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) => (Y0 @ (cS @ Y1)))))) => (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))))),
% 0.12/0.39 inference(fool_elimination,[],[f5])).
% 0.12/0.39 thf(f5,plain,(
% 0.12/0.39 (cIND = ! [X0 : $i > $o] : ((! [X1] : ((X0 @ X1) => (X0 @ (cS @ X1))) & (X0 @ c0)) => ! [X2] : (X0 @ X2)))),
% 0.12/0.39 inference(rectify,[],[f1])).
% 0.12/0.39 thf(f1,axiom,(
% 0.12/0.39 (cIND = ! [X0 : $i > $o] : ((! [X1] : ((X0 @ X1) => (X0 @ (cS @ X1))) & (X0 @ c0)) => ! [X1] : (X0 @ X1)))),
% 0.12/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cIND_def)).
% 0.12/0.39 thf(f14,plain,(
% 0.12/0.39 ( ! [X1 : $i] : (((cS @ X1) != sK0)) )),
% 0.12/0.39 inference(cnf_transformation,[],[f11])).
% 0.12/0.39 thf(f13,plain,(
% 0.12/0.39 (c0 != sK0)),
% 0.12/0.39 inference(cnf_transformation,[],[f11])).
% 0.12/0.39 % SZS output end Proof for theBenchmark
% 0.12/0.39 % (27025)------------------------------
% 0.12/0.39 % (27025)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.12/0.39 % (27025)Termination reason: Refutation
% 0.12/0.39
% 0.12/0.39 % (27025)Memory used [KB]: 5628
% 0.12/0.39 % (27025)Time elapsed: 0.013 s
% 0.12/0.39 % (27025)Instructions burned: 14 (million)
% 0.12/0.39 % (27025)------------------------------
% 0.12/0.39 % (27025)------------------------------
% 0.12/0.39 % (27024)Success in time 0.038 s
%------------------------------------------------------------------------------