%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX035+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 : Tue Sep 29 01:45:43 PM UTC 2026
% Result : Theorem 2.69s 1.19s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 8 unt; 0 def)
% Number of atoms : 172 ( 50 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 214 ( 93 ~; 75 |; 34 &)
% ( 6 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 120 ( 108 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0,X1,X2] :
( times_succeeds(X0,X1,X2)
<=> ( ? [X3,X4] :
( X0 = s(X3)
& times_succeeds(X3,X1,X4)
& plus_succeeds(X1,X4,X2) )
| ( X0 = '0'
& X2 = '0' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id15) ).
fof(f30,axiom,
! [X0,X1,X2] :
( nat_succeeds(X0)
=> ( '@+'(X0,X1) = X2
<=> plus_succeeds(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','(@+)/2') ).
fof(f31,axiom,
! [X0,X1,X2] :
( ( nat_succeeds(X0)
& nat_succeeds(X1) )
=> ( '@*'(X0,X1) = X2
<=> times_succeeds(X0,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','(@*)/2') ).
fof(f36,axiom,
! [X0,X1,X2] :
( plus_succeeds(X0,X1,X2)
=> nat_succeeds(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(plus:types:1)') ).
fof(f53,axiom,
! [X0,X1,X2] :
( times_succeeds(X0,X1,X2)
=> nat_succeeds(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lemma-(times:types:1)') ).
fof(f62,conjecture,
! [X0,X1] :
( ( nat_succeeds(X0)
& nat_succeeds(X1) )
=> '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','corollary-(times:successor)') ).
fof(f63,negated_conjecture,
~ ! [X0,X1] :
( ( nat_succeeds(X0)
& nat_succeeds(X1) )
=> '@*'(s(X0),X1) = '@+'(X1,'@*'(X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f62]) ).
fof(f65,plain,
? [X0,X1] :
( '@*'(s(X0),X1) != '@+'(X1,'@*'(X0,X1))
& nat_succeeds(X0)
& nat_succeeds(X1) ),
inference(ennf_transformation,[],[f63]) ).
fof(f66,plain,
? [X0,X1] :
( '@*'(s(X0),X1) != '@+'(X1,'@*'(X0,X1))
& nat_succeeds(X0)
& nat_succeeds(X1) ),
inference(flattening,[],[f65]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( '@+'(X0,X1) = X2
<=> plus_succeeds(X0,X1,X2) )
| ~ nat_succeeds(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( '@*'(X0,X1) = X2
<=> times_succeeds(X0,X1,X2) )
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( '@*'(X0,X1) = X2
<=> times_succeeds(X0,X1,X2) )
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(flattening,[],[f83]) ).
fof(f92,plain,
! [X0,X1,X2] :
( nat_succeeds(X0)
| ~ plus_succeeds(X0,X1,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f99,plain,
! [X0,X1,X2] :
( nat_succeeds(X0)
| ~ times_succeeds(X0,X1,X2) ),
inference(ennf_transformation,[],[f53]) ).
fof(f100,plain,
( '@*'(s(sK0),sK1) != '@+'(sK1,'@*'(sK0,sK1))
& nat_succeeds(sK0)
& nat_succeeds(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f66]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( ( '@+'(X0,X1) = X2
| ~ plus_succeeds(X0,X1,X2) )
& ( plus_succeeds(X0,X1,X2)
| '@+'(X0,X1) != X2 ) )
| ~ nat_succeeds(X0) ),
inference(nnf_transformation,[],[f80]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ( ( '@*'(X0,X1) = X2
| ~ times_succeeds(X0,X1,X2) )
& ( times_succeeds(X0,X1,X2)
| '@*'(X0,X1) != X2 ) )
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(nnf_transformation,[],[f84]) ).
fof(f115,plain,
! [X0,X1,X2] :
( ( times_succeeds(X0,X1,X2)
| ( ! [X3,X4] :
( s(X3) != X0
| ~ times_succeeds(X3,X1,X4)
| ~ plus_succeeds(X1,X4,X2) )
& ( '0' != X0
| '0' != X2 ) ) )
& ( ? [X3,X4] :
( X0 = s(X3)
& times_succeeds(X3,X1,X4)
& plus_succeeds(X1,X4,X2) )
| ( X0 = '0'
& X2 = '0' )
| ~ times_succeeds(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f116,plain,
! [X0,X1,X2] :
( ( times_succeeds(X0,X1,X2)
| ( ! [X3,X4] :
( s(X3) != X0
| ~ times_succeeds(X3,X1,X4)
| ~ plus_succeeds(X1,X4,X2) )
& ( '0' != X0
| '0' != X2 ) ) )
& ( ? [X3,X4] :
( X0 = s(X3)
& times_succeeds(X3,X1,X4)
& plus_succeeds(X1,X4,X2) )
| ( X0 = '0'
& X2 = '0' )
| ~ times_succeeds(X0,X1,X2) ) ),
inference(flattening,[],[f115]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ( times_succeeds(X0,X1,X2)
| ( ! [X3,X4] :
( s(X3) != X0
| ~ times_succeeds(X3,X1,X4)
| ~ plus_succeeds(X1,X4,X2) )
& ( '0' != X0
| '0' != X2 ) ) )
& ( ? [X5,X6] :
( s(X5) = X0
& times_succeeds(X5,X1,X6)
& plus_succeeds(X1,X6,X2) )
| ( X0 = '0'
& X2 = '0' )
| ~ times_succeeds(X0,X1,X2) ) ),
inference(rectify,[],[f116]) ).
fof(f118,plain,
! [X0,X1,X2] :
( ( times_succeeds(X0,X1,X2)
| ( ! [X3,X4] :
( s(X3) != X0
| ~ times_succeeds(X3,X1,X4)
| ~ plus_succeeds(X1,X4,X2) )
& ( '0' != X0
| '0' != X2 ) ) )
& ( ( s(sK10(X0,X1,X2)) = X0
& times_succeeds(sK10(X0,X1,X2),X1,sK11(X0,X1,X2))
& plus_succeeds(X1,sK11(X0,X1,X2),X2) )
| ( X0 = '0'
& X2 = '0' )
| ~ times_succeeds(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X5,sK10(X0,X1,X2)),skolemize(X6,sK11(X0,X1,X2))],[f117]) ).
fof(f119,plain,
nat_succeeds(sK1),
inference(cnf_transformation,[],[f100]) ).
fof(f120,plain,
nat_succeeds(sK0),
inference(cnf_transformation,[],[f100]) ).
fof(f121,plain,
'@*'(s(sK0),sK1) != '@+'(sK1,'@*'(sK0,sK1)),
inference(cnf_transformation,[],[f100]) ).
fof(f131,plain,
! [X2,X0,X1] :
( plus_succeeds(X0,X1,X2)
| '@+'(X0,X1) != X2
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f132,plain,
! [X2,X0,X1] :
( '@+'(X0,X1) = X2
| ~ plus_succeeds(X0,X1,X2)
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f139,plain,
! [X2,X0,X1] :
( times_succeeds(X0,X1,X2)
| '@*'(X0,X1) != X2
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f140,plain,
! [X2,X0,X1] :
( '@*'(X0,X1) = X2
| ~ times_succeeds(X0,X1,X2)
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ plus_succeeds(X0,X1,X2)
| nat_succeeds(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f162,plain,
! [X2,X0,X1] :
( ~ times_succeeds(X0,X1,X2)
| nat_succeeds(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f170,plain,
! [X2,X3,X0,X1,X4] :
( times_succeeds(X0,X1,X2)
| s(X3) != X0
| ~ times_succeeds(X3,X1,X4)
| ~ plus_succeeds(X1,X4,X2) ),
inference(cnf_transformation,[],[f118]) ).
fof(f171,plain,
! [X0,X1] :
( plus_succeeds(X0,X1,'@+'(X0,X1))
| ~ nat_succeeds(X0) ),
inference(equality_resolution,[],[f131]) ).
fof(f172,plain,
! [X0,X1] :
( times_succeeds(X0,X1,'@*'(X0,X1))
| ~ nat_succeeds(X0)
| ~ nat_succeeds(X1) ),
inference(equality_resolution,[],[f139]) ).
fof(f179,plain,
! [X2,X3,X1,X4] :
( times_succeeds(s(X3),X1,X2)
| ~ times_succeeds(X3,X1,X4)
| ~ plus_succeeds(X1,X4,X2) ),
inference(equality_resolution,[],[f170]) ).
fof(f291,plain,
! [X2,X0,X1] :
( '@+'(X0,X1) = X2
| ~ plus_succeeds(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f132,f150]) ).
fof(f313,plain,
! [X0] :
( '@*'(s(sK0),sK1) != X0
| ~ plus_succeeds(sK1,'@*'(sK0,sK1),X0) ),
inference(superposition,[],[f121,f291]) ).
fof(f323,plain,
~ plus_succeeds(sK1,'@*'(sK0,sK1),'@*'(s(sK0),sK1)),
inference(equality_resolution,[],[f313]) ).
fof(f420,plain,
! [X2,X0,X1] :
( '@*'(X0,X1) = X2
| ~ times_succeeds(X0,X1,X2)
| ~ nat_succeeds(X1) ),
inference(forward_subsumption_resolution,[],[f140,f162]) ).
fof(f425,plain,
! [X0] :
( ~ plus_succeeds(sK1,'@*'(sK0,sK1),X0)
| ~ times_succeeds(s(sK0),sK1,X0)
| ~ nat_succeeds(sK1) ),
inference(superposition,[],[f323,f420]) ).
fof(f436,plain,
! [X0] :
( ~ plus_succeeds(sK1,'@*'(sK0,sK1),X0)
| ~ times_succeeds(s(sK0),sK1,X0) ),
inference(forward_subsumption_resolution,[],[f425,f119]) ).
fof(f440,plain,
( ~ times_succeeds(s(sK0),sK1,'@+'(sK1,'@*'(sK0,sK1)))
| ~ nat_succeeds(sK1) ),
inference(resolution,[],[f436,f171]) ).
fof(f443,plain,
~ times_succeeds(s(sK0),sK1,'@+'(sK1,'@*'(sK0,sK1))),
inference(forward_subsumption_resolution,[],[f440,f119]) ).
fof(f452,plain,
! [X0] :
( ~ times_succeeds(s(sK0),sK1,'@+'(sK1,X0))
| ~ times_succeeds(sK0,sK1,X0)
| ~ nat_succeeds(sK1) ),
inference(superposition,[],[f443,f420]) ).
fof(f454,plain,
! [X0] :
( ~ times_succeeds(s(sK0),sK1,'@+'(sK1,X0))
| ~ times_succeeds(sK0,sK1,X0) ),
inference(forward_subsumption_resolution,[],[f452,f119]) ).
fof(f470,plain,
! [X0,X1] :
( ~ times_succeeds(s(sK0),sK1,X0)
| ~ times_succeeds(sK0,sK1,X1)
| ~ plus_succeeds(sK1,X1,X0) ),
inference(superposition,[],[f454,f291]) ).
fof(f475,plain,
! [X0,X1] :
( ~ plus_succeeds(sK1,X1,X0)
| ~ times_succeeds(sK0,sK1,X1) ),
inference(forward_subsumption_resolution,[],[f470,f179]) ).
fof(f488,plain,
! [X0] :
( ~ times_succeeds(sK0,sK1,X0)
| ~ nat_succeeds(sK1) ),
inference(resolution,[],[f475,f171]) ).
fof(f491,plain,
! [X0] : ~ times_succeeds(sK0,sK1,X0),
inference(forward_subsumption_resolution,[],[f488,f119]) ).
fof(f505,plain,
( ~ nat_succeeds(sK0)
| ~ nat_succeeds(sK1) ),
inference(resolution,[],[f491,f172]) ).
fof(f506,plain,
~ nat_succeeds(sK1),
inference(forward_subsumption_resolution,[],[f505,f120]) ).
fof(f508,plain,
$false,
inference(forward_subsumption_resolution,[],[f506,f119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX035+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n008.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 14:55:20 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running first-order theorem proving
% 0.09/0.25 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
% 2.69/1.19 % (2310538)Detected formulas, will run a generic FOF schedule.
% 2.69/1.19 % (2310547)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3444039150:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.19 % (2310547)First to succeed.
% 2.69/1.19 % (2310547)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2310538"
% 2.69/1.19 % (2310545)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=2132746746:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.19 % (2310543)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=2294209569:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.19 % (2310544)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=1414199848:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.19 % (2310546)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2180156846:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.19 % (2310549)dis-21_1_sil=8000:lcm=predicate:random_seed=1799919403:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.69/1.19 % (2310548)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=87854841:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.19 % (2310546)Refutation not found, incomplete strategy
% 2.69/1.19 % (2310546)------------------------------
% 2.69/1.19 % (2310546)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.19 % (2310546)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.19 % (2310546)CaDiCaL version: 2.1.3
% 2.69/1.19 % (2310546)Termination reason: Refutation not found, incomplete strategy
% 2.69/1.19 % (2310546)Time elapsed: 0.003 s
% 2.69/1.19 % (2310546)Peak memory usage: 88 MB
% 2.69/1.19 % (2310546)Instructions burned: 2 (million)
% 2.69/1.19 % (2310549)Also succeeded, but the first one will report.
% 2.69/1.19 % (2310548)Instruction limit reached!
% 2.69/1.19 % (2310548)------------------------------
% 2.69/1.19 % (2310548)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.19 % (2310548)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.19 % (2310548)CaDiCaL version: 2.1.3
% 2.69/1.19 % (2310548)Termination reason: Instruction limit
% 2.69/1.19 % (2310548)Termination phase: Saturation
% 2.69/1.19 % (2310548)Time elapsed: 0.094 s
% 2.69/1.19 % (2310548)Peak memory usage: 90 MB
% 2.69/1.19 % (2310548)Instructions burned: 140 (million)
% 2.69/1.19 % (2310547)Refutation found. Thanks to Tanya!
% 2.69/1.19 % SZS status Theorem for theBenchmark
% 2.69/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.19 % (2310547)------------------------------
% 2.69/1.19 % (2310547)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.19 % (2310547)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.19 % (2310547)CaDiCaL version: 2.1.3
% 2.69/1.19 % (2310547)Termination reason: Refutation
% 2.69/1.19 % (2310547)Time elapsed: 0.006 s
% 2.69/1.19 % (2310547)Peak memory usage: 88 MB
% 2.69/1.19 % (2310547)Instructions burned: 14 (million)
% 2.69/1.19 % (2310547)------------------------------
% 2.69/1.19 % (2310547)------------------------------
% 2.69/1.19 % (2310538)Success in time 0.291 s
% 2.69/1.19 % Vampire exiting
%------------------------------------------------------------------------------