%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV678+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 : Tue Sep 29 12:58:33 PM UTC 2026
% Result : Theorem 3.40s 1.34s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 16 ( 3 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 62 ( 22 ~; 21 |; 10 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 12 ( 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f267,axiom,
( p(cUseAuto_2emyFact)
<=> ! [X0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X0)
=> ( cCoq_2eInit_2ePeano_2ele___24a2(X0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
=> cUseAuto_2eP___24a1(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_UseAuto.myFact') ).
fof(f2925,conjecture,
( ! [X0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X0)
=> cUseAuto_2eP___24a1(X0) )
=> p(cUseAuto_2emyFact) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof(f2926,negated_conjecture,
~ ( ! [X0] :
( cCoq_2eInit_2eDatatypes_2enat___24t(X0)
=> cUseAuto_2eP___24a1(X0) )
=> p(cUseAuto_2emyFact) ),
inference(negated_conjecture,[status(cth)],[f2925]) ).
fof(f2928,plain,
( ~ p(cUseAuto_2emyFact)
& ! [X0] :
( cUseAuto_2eP___24a1(X0)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0) ) ),
inference(ennf_transformation,[],[f2926]) ).
fof(f2956,plain,
( p(cUseAuto_2emyFact)
<=> ! [X0] :
( cUseAuto_2eP___24a1(X0)
| ~ cCoq_2eInit_2ePeano_2ele___24a2(X0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0) ) ),
inference(ennf_transformation,[],[f267]) ).
fof(f2957,plain,
( p(cUseAuto_2emyFact)
<=> ! [X0] :
( cUseAuto_2eP___24a1(X0)
| ~ cCoq_2eInit_2ePeano_2ele___24a2(X0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0) ) ),
inference(flattening,[],[f2956]) ).
fof(f2959,plain,
( ( p(cUseAuto_2emyFact)
| ? [X0] :
( ~ cUseAuto_2eP___24a1(X0)
& cCoq_2eInit_2ePeano_2ele___24a2(X0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
& cCoq_2eInit_2eDatatypes_2enat___24t(X0) ) )
& ( ! [X0] :
( cUseAuto_2eP___24a1(X0)
| ~ cCoq_2eInit_2ePeano_2ele___24a2(X0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0) )
| ~ p(cUseAuto_2emyFact) ) ),
inference(nnf_transformation,[],[f2957]) ).
fof(f2960,plain,
( ( p(cUseAuto_2emyFact)
| ? [X0] :
( ~ cUseAuto_2eP___24a1(X0)
& cCoq_2eInit_2ePeano_2ele___24a2(X0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
& cCoq_2eInit_2eDatatypes_2enat___24t(X0) ) )
& ( ! [X1] :
( cUseAuto_2eP___24a1(X1)
| ~ cCoq_2eInit_2ePeano_2ele___24a2(X1,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) )
| ~ p(cUseAuto_2emyFact) ) ),
inference(rectify,[],[f2959]) ).
fof(f2961,plain,
( ( p(cUseAuto_2emyFact)
| ( ~ cUseAuto_2eP___24a1(sK0)
& cCoq_2eInit_2ePeano_2ele___24a2(sK0,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
& cCoq_2eInit_2eDatatypes_2enat___24t(sK0) ) )
& ( ! [X1] :
( cUseAuto_2eP___24a1(X1)
| ~ cCoq_2eInit_2ePeano_2ele___24a2(X1,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X1) )
| ~ p(cUseAuto_2emyFact) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f2960]) ).
fof(f2962,plain,
! [X0] :
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0)
| cUseAuto_2eP___24a1(X0) ),
inference(cnf_transformation,[],[f2928]) ).
fof(f2963,plain,
~ p(cUseAuto_2emyFact),
inference(cnf_transformation,[],[f2928]) ).
fof(f2981,plain,
( cCoq_2eInit_2eDatatypes_2enat___24t(sK0)
| p(cUseAuto_2emyFact) ),
inference(cnf_transformation,[],[f2961]) ).
fof(f2983,plain,
( ~ cUseAuto_2eP___24a1(sK0)
| p(cUseAuto_2emyFact) ),
inference(cnf_transformation,[],[f2961]) ).
fof(f3003,plain,
( cUseAuto_2eP___24a1(sK0)
| p(cUseAuto_2emyFact) ),
inference(resolution,[],[f2962,f2981]) ).
fof(f3004,plain,
p(cUseAuto_2emyFact),
inference(forward_subsumption_resolution,[],[f3003,f2983]) ).
fof(f3005,plain,
$false,
inference(forward_subsumption_resolution,[],[f3004,f2963]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV678+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n004.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 06:53:08 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.40/1.34 % (160119)Detected formulas, will run a generic FOF schedule.
% 3.40/1.34 % (160129)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3979755727:s2a=on:i=139:gtg=position_2998 on theBenchmark for (2998ds/139Mi)
% 3.40/1.34 % (160130)dis-21_1_sil=8000:lcm=predicate:random_seed=4076266149:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2998 on theBenchmark for (2998ds/129Mi)
% 3.40/1.34 % (160128)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3314899389:i=119:av=off:ss=axioms_2998 on theBenchmark for (2998ds/119Mi)
% 3.40/1.34 % (160126)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=348615810:i=141695:sd=1:nm=32:gsp=on:ss=included_2998 on theBenchmark for (2998ds/141695Mi)
% 3.40/1.34 % (160127)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2047087897:i=109:sd=1:ins=1:gsp=on:ss=axioms_2998 on theBenchmark for (2998ds/109Mi)
% 3.40/1.34 % (160124)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1065286604:i=141193_2998 on theBenchmark for (2998ds/141193Mi)
% 3.40/1.34 % (160125)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1111530522:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2998 on theBenchmark for (2998ds/134677Mi)
% 3.40/1.34 % (160127)First to succeed.
% 3.40/1.34 % (160128)Also succeeded, but the first one will report.
% 3.40/1.34 % (160127)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-160119"
% 3.40/1.34 % (160129)Instruction limit reached!
% 3.40/1.34 % (160129)------------------------------
% 3.40/1.34 % (160129)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.34 % (160129)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.34 % (160129)CaDiCaL version: 2.1.3
% 3.40/1.34 % (160129)Termination reason: Instruction limit
% 3.40/1.34 % (160129)Termination phase: Naming
% 3.40/1.34 % (160129)Time elapsed: 0.057 s
% 3.40/1.34 % (160129)Peak memory usage: 90 MB
% 3.40/1.34 % (160129)Instructions burned: 140 (million)
% 3.40/1.34 % (160130)Instruction limit reached!
% 3.40/1.34 % (160130)------------------------------
% 3.40/1.34 % (160130)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.34 % (160130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.34 % (160130)CaDiCaL version: 2.1.3
% 3.40/1.34 % (160130)Termination reason: Instruction limit
% 3.40/1.34 % (160130)Termination phase: Preprocessing 3
% 3.40/1.34 % (160130)Time elapsed: 0.062 s
% 3.40/1.34 % (160130)Peak memory usage: 92 MB
% 3.40/1.34 % (160130)Instructions burned: 131 (million)
% 3.40/1.34 % (160138)lrs+10_1_sil=8000:sp=occurrence:random_seed=2283740312:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.40/1.34 % (160138)Also succeeded, but the first one will report.
% 3.40/1.34 % (160139)lrs+10_1_sil=32000:urr=on:br=off:random_seed=831484262:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.40/1.34 % (160139)Also succeeded, but the first one will report.
% 3.40/1.34 % (160127)Refutation found. Thanks to Tanya!
% 3.40/1.34 % SZS status Theorem for theBenchmark
% 3.40/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.34 % (160127)------------------------------
% 3.40/1.34 % (160127)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.34 % (160127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.34 % (160127)CaDiCaL version: 2.1.3
% 3.40/1.34 % (160127)Termination reason: Refutation
% 3.40/1.34 % (160127)Time elapsed: 0.017 s
% 3.40/1.34 % (160127)Peak memory usage: 93 MB
% 3.40/1.34 % (160127)Instructions burned: 38 (million)
% 3.40/1.34 % (160127)------------------------------
% 3.40/1.34 % (160127)------------------------------
% 3.40/1.34 % (160119)Success in time 0.514 s
% 3.40/1.34 % Vampire exiting
%------------------------------------------------------------------------------