%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM636^3 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:18:19 AM UTC 2026
% Result : Theorem 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM636^3 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n008.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 12:08:09 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.32 % (3060384)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (3060389)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3814644449:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (3060392)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=239834575:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.32 % (3060392) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3060384-3060392"...
% 0.22/0.32 % (3060392)...printing done.
% 0.22/0.32 % (3060392)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% 0.22/0.32 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.32 thf(func_def_1, type, succ: ($i > $i)).
% 0.22/0.32 thf(func_def_3, type, m: ($i > $o)).
% 0.22/0.32 thf(func_def_6, type, db0: !>[X0: $tType]:(X0)).
% 0.22/0.32 thf(func_def_7, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.32 thf(func_def_8, type, vNOT: ($o > $o)).
% 0.22/0.32 thf(func_def_9, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.22/0.32 thf(func_def_11, type, sK1: (($i > $o) > $i)).
% 0.22/0.32 thf(func_def_13, type, inv_succ_3: ($i > $i)).
% 0.22/0.32 thf(f3,axiom,(
% 0.22/0.32 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1))) & (X0 @ one)) => ! [X2 : $i] : (X0 @ X2))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',induction)).
% 0.22/0.32 thf(f5,axiom,(
% 0.22/0.32 (m @ one)),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_is_one)).
% 0.22/0.32 thf(f6,axiom,(
% 0.22/0.32 ! [X0 : $i] : ((m @ X0) => (m @ (succ @ X0)))),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_is_next)).
% 0.22/0.32 thf(f7,conjecture,(
% 0.22/0.32 ! [X0 : $i] : (m @ X0)),
% 0.22/0.32 file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_is_all)).
% 0.22/0.32 thf(f8,negated_conjecture,(
% 0.22/0.32 ~ ! [X0 : $i] : (m @ X0)),
% 0.22/0.32 inference(negated_conjecture,[status(cth)],[f7])).
% 0.22/0.32 thf(f9,plain,(
% 0.22/0.32 (m @ one)),
% 0.22/0.32 inference(rectify,[],[f5])).
% 0.22/0.32 thf(f10,plain,(
% 0.22/0.32 (((m @ one)) = $true)),
% 0.22/0.32 inference(fool_elimination,[],[f9])).
% 0.22/0.32 thf(f11,plain,(
% 0.22/0.32 ! [X0 : $i] : ((m @ X0) => (m @ (succ @ X0)))),
% 0.22/0.32 inference(rectify,[],[f6])).
% 0.22/0.32 thf(f12,plain,(
% 0.22/0.32 ! [X0 : $i] : ((((m @ X0)) = $true) => (((m @ (succ @ X0))) = $true))),
% 0.22/0.32 inference(fool_elimination,[],[f11])).
% 0.22/0.32 thf(f13,plain,(
% 0.22/0.32 ~ ! [X0 : $i] : (m @ X0)),
% 0.22/0.32 inference(rectify,[],[f8])).
% 0.22/0.32 thf(f14,plain,(
% 0.22/0.32 ~ ! [X0 : $i] : (((m @ X0)) = $true)),
% 0.22/0.32 inference(fool_elimination,[],[f13])).
% 0.22/0.32 thf(f16,plain,(
% 0.22/0.32 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((X0 @ X1) => (X0 @ (succ @ X1))) & (X0 @ one)) => ! [X2 : $i] : (X0 @ X2))),
% 0.22/0.32 inference(rectify,[],[f3])).
% 0.22/0.32 thf(f17,plain,(
% 0.22/0.32 ! [X0 : ($i > $o)] : ((! [X1 : $i] : ((((X0 @ X1)) = $true) => (((X0 @ (succ @ X1))) = $true)) & (((X0 @ one)) = $true)) => ! [X2 : $i] : (((X0 @ X2)) = $true))),
% 0.22/0.32 inference(fool_elimination,[],[f16])).
% 0.22/0.32 thf(f19,plain,(
% 0.22/0.32 ! [X0 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) = $true) | (? [X1 : $i] : ((((X0 @ (succ @ X1))) != $true) & (((X0 @ X1)) = $true)) | (((X0 @ one)) != $true)))),
% 0.22/0.32 inference(ennf_transformation,[],[f17])).
% 0.22/0.32 thf(f20,plain,(
% 0.22/0.32 ! [X0 : ($i > $o)] : (! [X2 : $i] : (((X0 @ X2)) = $true) | ? [X1 : $i] : ((((X0 @ (succ @ X1))) != $true) & (((X0 @ X1)) = $true)) | (((X0 @ one)) != $true))),
% 0.22/0.32 inference(flattening,[],[f19])).
% 0.22/0.32 thf(f21,plain,(
% 0.22/0.32 ? [X0 : $i] : (((m @ X0)) != $true)),
% 0.22/0.32 inference(ennf_transformation,[],[f14])).
% 0.22/0.32 thf(f23,plain,(
% 0.22/0.32 ! [X0 : $i] : ((((m @ X0)) != $true) | (((m @ (succ @ X0))) = $true))),
% 0.22/0.32 inference(ennf_transformation,[],[f12])).
% 0.22/0.32 thf(f24,plain,(
% 0.22/0.32 ($true != ((m @ sK0)))),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f21])).
% 0.22/0.32 thf(f25,plain,(
% 0.22/0.32 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | ? [X2 : $i] : (($true != ((X0 @ (succ @ X2)))) & (((X0 @ X2)) = $true)) | (((X0 @ one)) != $true))),
% 0.22/0.32 inference(rectify,[],[f20])).
% 0.22/0.32 thf(f26,plain,(
% 0.22/0.32 ! [X0 : ($i > $o)] : (! [X1 : $i] : (((X0 @ X1)) = $true) | (($true != ((X0 @ (succ @ (sK1 @ X0))))) & ($true = ((X0 @ (sK1 @ X0))))) | (((X0 @ one)) != $true))),
% 0.22/0.32 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,sK1 @ X0)],[f25])).
% 0.22/0.32 thf(f28,plain,(
% 0.22/0.32 (((m @ one)) = $true)),
% 0.22/0.32 inference(cnf_transformation,[],[f10])).
% 0.22/0.32 thf(f29,plain,(
% 0.22/0.32 ($true != ((m @ sK0)))),
% 0.22/0.32 inference(cnf_transformation,[],[f24])).
% 0.22/0.32 thf(f30,plain,(
% 0.22/0.32 ( ! [X0 : ($i > $o),X1 : $i] : (($true = ((X0 @ (sK1 @ X0)))) | (((X0 @ one)) != $true) | (((X0 @ X1)) = $true)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f26])).
% 0.22/0.32 thf(f31,plain,(
% 0.22/0.32 ( ! [X0 : ($i > $o),X1 : $i] : (($true != ((X0 @ (succ @ (sK1 @ X0))))) | (((X0 @ X1)) = $true) | (((X0 @ one)) != $true)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f26])).
% 0.22/0.32 thf(f33,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((m @ (succ @ X0))) = $true) | (((m @ X0)) != $true)) )),
% 0.22/0.32 inference(cnf_transformation,[],[f23])).
% 0.22/0.32 thf(f38,definition,(
% 0.22/0.32 spl2_1 <=> ($true = ((m @ sK0)))),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition])).
% 0.22/0.32 thf(f40,plain,(
% 0.22/0.32 ($true != ((m @ sK0))) | spl2_1),
% 0.22/0.32 inference(avatar_component_clause,[],[f38])).
% 0.22/0.32 thf(f41,plain,(
% 0.22/0.32 ~spl2_1),
% 0.22/0.32 inference(avatar_split_clause,[],[f29,f38])).
% 0.22/0.32 thf(f48,definition,(
% 0.22/0.32 spl2_3 <=> (((m @ one)) = $true)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition])).
% 0.22/0.32 thf(f50,plain,(
% 0.22/0.32 (((m @ one)) = $true) | ~spl2_3),
% 0.22/0.32 inference(avatar_component_clause,[],[f48])).
% 0.22/0.32 thf(f51,plain,(
% 0.22/0.32 spl2_3),
% 0.22/0.32 inference(avatar_split_clause,[],[f28,f48])).
% 0.22/0.32 thf(f116,definition,(
% 0.22/0.32 spl2_7 <=> ! [X0 : $i] : (((m @ X0)) = $true)),
% 0.22/0.32 introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition])).
% 0.22/0.32 thf(f117,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((m @ X0)) = $true)) ) | ~spl2_7),
% 0.22/0.32 inference(avatar_component_clause,[],[f116])).
% 0.22/0.32 thf(f148,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($true != ((m @ (sK1 @ m)))) | (((m @ X0)) = $true) | ($true != $true) | (((m @ one)) != $true)) )),
% 0.22/0.32 inference(superposition,[],[f31,f33])).
% 0.22/0.32 thf(f165,plain,(
% 0.22/0.32 ( ! [X0 : $i] : (($true != ((m @ (sK1 @ m)))) | (((m @ one)) != $true) | (((m @ X0)) = $true)) )),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f148])).
% 0.22/0.32 thf(f170,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((m @ X0)) = $true) | (((m @ one)) != $true)) )),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f165,f30])).
% 0.22/0.32 thf(f172,plain,(
% 0.22/0.32 ( ! [X0 : $i] : ((((m @ X0)) = $true)) ) | ~spl2_3),
% 0.22/0.32 inference(forward_subsumption_resolution,[],[f170,f50])).
% 0.22/0.32 thf(f178,plain,(
% 0.22/0.32 spl2_7 | ~spl2_3),
% 0.22/0.32 inference(avatar_split_clause,[],[f172,f48,f116])).
% 0.22/0.32 thf(f181,plain,(
% 0.22/0.32 ($true != $true) | (spl2_1 | ~spl2_7)),
% 0.22/0.32 inference(superposition,[],[f40,f117])).
% 0.22/0.32 thf(f185,plain,(
% 0.22/0.32 $false | (spl2_1 | ~spl2_7)),
% 0.22/0.32 inference(trivial_inequality_removal,[],[f181])).
% 0.22/0.32 thf(f186,plain,(
% 0.22/0.32 spl2_1 | ~spl2_7),
% 0.22/0.32 inference(avatar_contradiction_clause,[],[f185])).
% 0.22/0.32 cnf(s1, plain, ~spl2_1, inference(sat_conversion,[],[f41])).
% 0.22/0.32 cnf(s3, plain, spl2_3, inference(sat_conversion,[],[f51])).
% 0.22/0.32 cnf(s13, plain, ~spl2_3 | spl2_7, inference(sat_conversion,[],[f178])).
% 0.22/0.32 cnf(s14, plain, spl2_1 | ~spl2_7, inference(sat_conversion,[],[f186])).
% 0.22/0.32 cnf(s15, plain, spl2_7, inference(rat,[],[s13,s3])).
% 0.22/0.32 cnf(s16, plain, spl2_1, inference(rat,[],[s14,s15])).
% 0.22/0.32 cnf(s18, plain, $false, inference(rat,[],[s1,s16])).
% 0.22/0.32 thf(f188,plain,(
% 0.22/0.32 $false),
% 0.22/0.32 inference(avatar_sat_refutation,[],[s18])).
% 0.22/0.32 % SZS output end Proof for theBenchmark
% 0.22/0.32 % (3060392)------------------------------
% 0.22/0.32 % (3060392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (3060392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (3060392)CaDiCaL version: 2.1.3
% 0.22/0.32 % (3060392)Termination reason: Refutation
% 0.22/0.32 % (3060392)Time elapsed: 0.005 s
% 0.22/0.32 % (3060392)Peak memory usage: 13 MB
% 0.22/0.32 % (3060392)Instructions burned: 7 (million)
% 0.22/0.32 % (3060384)Success in time 0.06 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------