%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV678+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 12:59:39 PM UTC 2026
% Result : Theorem 3.37s 1.15s
% Output : Refutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 17 ( 5 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 62 ( 23 ~; 20 |; 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/sandbox/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/sandbox/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(f3276,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(f3277,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,[],[f3276]) ).
fof(f4441,plain,
( ~ p(cUseAuto_2emyFact)
& ! [X0] :
( cUseAuto_2eP___24a1(X0)
| ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0) ) ),
inference(ennf_transformation,[],[f2926]) ).
fof(f5946,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,[],[f3277]) ).
fof(f5947,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,[],[f5946]) ).
fof(f5948,plain,
( ( p(cUseAuto_2emyFact)
| ( ~ cUseAuto_2eP___24a1(sK892)
& cCoq_2eInit_2ePeano_2ele___24a2(sK892,cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eS___24a1(cCoq_2eInit_2eDatatypes_2eO))))
& cCoq_2eInit_2eDatatypes_2enat___24t(sK892) ) )
& ( ! [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,[sK892]),skolemize(X0,sK892)],[f5947]) ).
fof(f10367,plain,
( p(cUseAuto_2emyFact)
| cCoq_2eInit_2eDatatypes_2enat___24t(sK892) ),
inference(cnf_transformation,[],[f5948]) ).
fof(f10369,plain,
( p(cUseAuto_2emyFact)
| ~ cUseAuto_2eP___24a1(sK892) ),
inference(cnf_transformation,[],[f5948]) ).
fof(f16342,plain,
! [X0] :
( ~ cCoq_2eInit_2eDatatypes_2enat___24t(X0)
| cUseAuto_2eP___24a1(X0) ),
inference(cnf_transformation,[],[f4441]) ).
fof(f16343,plain,
~ p(cUseAuto_2emyFact),
inference(cnf_transformation,[],[f4441]) ).
fof(f19414,plain,
cCoq_2eInit_2eDatatypes_2enat___24t(sK892),
inference(global_subsumption,[],[f10367,f16343]) ).
fof(f19416,plain,
~ cUseAuto_2eP___24a1(sK892),
inference(global_subsumption,[],[f10369,f16343]) ).
fof(f19549,plain,
cUseAuto_2eP___24a1(sK892),
inference(resolution,[],[f19414,f16342]) ).
fof(f19550,plain,
$false,
inference(forward_subsumption_resolution,[],[f19549,f19416]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 06:55:25 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.37/1.14 % (3186259)Will run a generic schedule for satisfiability detection.
% 3.37/1.14 % (3186268)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2823236236:i=116_2997 on theBenchmark for (2997ds/116Mi)
% 3.37/1.14 % (3186265)% WARNING: option uhcvi not known.
% 3.37/1.14 % (3186264)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3987771416_2997 on theBenchmark for (2997ds/0Mi)
% 3.37/1.14 % (3186265)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4095575354:i=135531:add=off:rawr=on_2997 on theBenchmark for (2997ds/135531Mi)
% 3.37/1.14 % (3186266)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2700402069:i=88024:add=on:rawr=on_2997 on theBenchmark for (2997ds/88024Mi)
% 3.37/1.14 % (3186267)dis+10_1_sil=32000:sp=arity:random_seed=2144506134:i=103:fgj=on_2997 on theBenchmark for (2997ds/103Mi)
% 3.37/1.14 % (3186270)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3415043396:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2997 on theBenchmark for (2997ds/159Mi)
% 3.37/1.14 % (3186269)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2997394307:i=131_2997 on theBenchmark for (2997ds/131Mi)
% 3.37/1.14 % (3186268)Instruction limit reached!
% 3.37/1.14 % (3186268)------------------------------
% 3.37/1.14 % (3186268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/1.14 % (3186268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.14 % (3186268)CaDiCaL version: 2.1.3
% 3.37/1.14 % (3186268)Termination reason: Instruction limit
% 3.37/1.14 % (3186268)Termination phase: NewCNF
% 3.37/1.14 % (3186268)Time elapsed: 0.037 s
% 3.37/1.14 % (3186268)Peak memory usage: 19 MB
% 3.37/1.14 % (3186268)Instructions burned: 117 (million)
% 3.37/1.14 % (3186278)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3731267751:i=714:nm=2_2996 on theBenchmark for (2996ds/714Mi)
% 3.37/1.14 % (3186267)Instruction limit reached!
% 3.37/1.14 % (3186267)------------------------------
% 3.37/1.14 % (3186267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/1.14 % (3186267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.14 % (3186267)CaDiCaL version: 2.1.3
% 3.37/1.14 % (3186267)Termination reason: Instruction limit
% 3.37/1.14 % (3186267)Termination phase: Preprocessing 3
% 3.37/1.14 % (3186267)Time elapsed: 0.054 s
% 3.37/1.14 % (3186267)Peak memory usage: 18 MB
% 3.37/1.14 % (3186267)Instructions burned: 104 (million)
% 3.37/1.14 % (3186269)Instruction limit reached!
% 3.37/1.14 % (3186269)------------------------------
% 3.37/1.14 % (3186269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/1.14 % (3186269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.14 % (3186269)CaDiCaL version: 2.1.3
% 3.37/1.14 % (3186269)Termination reason: Instruction limit
% 3.37/1.14 % (3186269)Termination phase: Preprocessing 3
% 3.37/1.14 % (3186269)Time elapsed: 0.070 s
% 3.37/1.14 % (3186269)Peak memory usage: 19 MB
% 3.37/1.14 % (3186269)Instructions burned: 132 (million)
% 3.37/1.14 % (3186280)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=359165233:i=131:bd=preordered:fsd=on_2996 on theBenchmark for (2996ds/131Mi)
% 3.37/1.14 % (3186270)Instruction limit reached!
% 3.37/1.14 % (3186270)------------------------------
% 3.37/1.14 % (3186270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/1.14 % (3186270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.14 % (3186270)CaDiCaL version: 2.1.3
% 3.37/1.14 % (3186270)Termination reason: Instruction limit
% 3.37/1.14 % (3186270)Termination phase: Clausification
% 3.37/1.14 % (3186270)Time elapsed: 0.086 s
% 3.37/1.14 % (3186270)Peak memory usage: 21 MB
% 3.37/1.14 % (3186270)Instructions burned: 160 (million)
% 3.37/1.14 % (3186281)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4049369973:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2996 on theBenchmark for (2996ds/684Mi)
% 3.37/1.14 % (3186283)ott-21_1_sil=16000:fs=off:random_seed=2497856108:i=180:av=off:fsr=off_2996 on theBenchmark for (2996ds/180Mi)
% 3.37/1.14 % (3186280)Instruction limit reached!
% 3.37/1.14 % (3186280)------------------------------
% 3.37/1.14 % (3186280)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/1.14 % (3186280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.15 % (3186280)CaDiCaL version: 2.1.3
% 3.37/1.15 % (3186280)Termination reason: Instruction limit
% 3.37/1.15 % (3186280)Termination phase: Preprocessing 3
% 3.37/1.15 % (3186280)Time elapsed: 0.070 s
% 3.37/1.15 % (3186280)Peak memory usage: 19 MB
% 3.37/1.15 % (3186280)Instructions burned: 132 (million)
% 3.37/1.15 % (3186286)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2489408170:i=477:bd=all_2995 on theBenchmark for (2995ds/477Mi)
% 3.37/1.15 % (3186283)Instruction limit reached!
% 3.37/1.15 % (3186283)------------------------------
% 3.37/1.15 % (3186283)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/1.15 % (3186283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.15 % (3186283)CaDiCaL version: 2.1.3
% 3.37/1.15 % (3186283)Termination reason: Instruction limit
% 3.37/1.15 % (3186283)Termination phase: Property scanning
% 3.37/1.15 % (3186283)Time elapsed: 0.095 s
% 3.37/1.15 % (3186283)Peak memory usage: 22 MB
% 3.37/1.15 % (3186283)Instructions burned: 181 (million)
% 3.37/1.15 % (3186278)Instruction limit reached!
% 3.37/1.15 % (3186278)------------------------------
% 3.37/1.15 % (3186278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/1.15 % (3186278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.15 % (3186278)CaDiCaL version: 2.1.3
% 3.37/1.15 % (3186278)Termination reason: Instruction limit
% 3.37/1.15 % (3186278)Termination phase: Finite model building preprocessing
% 3.37/1.15 % (3186278)Time elapsed: 0.173 s
% 3.37/1.15 % (3186278)Peak memory usage: 28 MB
% 3.37/1.15 % (3186278)Instructions burned: 719 (million)
% 3.37/1.15 % (3186288)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3171197796:fmbsr=1.3:i=865:ins=25_2995 on theBenchmark for (2995ds/865Mi)
% 3.37/1.15 % (3186289)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=797618369:i=1179_2995 on theBenchmark for (2995ds/1179Mi)
% 3.37/1.15 % (3186286)Instruction limit reached!
% 3.37/1.15 % (3186286)------------------------------
% 3.37/1.15 % (3186286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/1.15 % (3186286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.15 % (3186286)CaDiCaL version: 2.1.3
% 3.37/1.15 % (3186286)Termination reason: Instruction limit
% 3.37/1.15 % (3186286)Termination phase: Property scanning
% 3.37/1.15 % (3186286)Time elapsed: 0.212 s
% 3.37/1.15 % (3186286)Peak memory usage: 23 MB
% 3.37/1.15 % (3186286)Instructions burned: 477 (million)
% 3.37/1.15 % (3186281)Instruction limit reached!
% 3.37/1.15 % (3186281)------------------------------
% 3.37/1.15 % (3186281)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/1.15 % (3186281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.15 % (3186281)CaDiCaL version: 2.1.3
% 3.37/1.15 % (3186281)Termination reason: Instruction limit
% 3.37/1.15 % (3186281)Termination phase: Property scanning
% 3.37/1.15 % (3186281)Time elapsed: 0.305 s
% 3.37/1.15 % (3186281)Peak memory usage: 24 MB
% 3.37/1.15 % (3186281)Instructions burned: 685 (million)
% 3.37/1.15 % (3186266) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3186259-3186266"...
% 3.37/1.15 % (3186292)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2406247478:i=889:ins=1_2993 on theBenchmark for (2993ds/889Mi)
% 3.37/1.15 % (3186266)...printing done.
% 3.37/1.15 % (3186293)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=4260932384:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2993 on theBenchmark for (2993ds/692Mi)
% 3.37/1.15 % (3186266)Refutation found. Thanks to Tanya!
% 3.37/1.15 % SZS status Theorem for theBenchmark
% 3.37/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 3.37/1.15 % (3186266)------------------------------
% 3.37/1.15 % (3186266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.37/1.15 % (3186266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.37/1.15 % (3186266)CaDiCaL version: 2.1.3
% 3.37/1.15 % (3186266)Termination reason: Refutation
% 3.37/1.15 % (3186266)Time elapsed: 0.417 s
% 3.37/1.15 % (3186266)Peak memory usage: 35 MB
% 3.37/1.15 % (3186266)Instructions burned: 941 (million)
% 3.37/1.15 % (3186259)Success in time 0.709 s
% 3.37/1.15 % Vampire exiting
%------------------------------------------------------------------------------