%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM837+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 12:17:12 PM UTC 2026
% Result : Theorem 0.25s 1.70s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 8 unt; 0 def)
% Number of atoms : 24 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 21 ( 10 ~; 7 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 15 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X0] : vd269 = vplus(vd268,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','qe(171)') ).
fof(f2,negated_conjecture,
~ ? [X0] : vd269 = vplus(vd268,X0),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f4,axiom,
less(vd268,vd269),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conjunct1(170), 270, 0)') ).
fof(f15,axiom,
! [X0,X1] :
( less(X1,X0)
<=> ? [X2] : X0 = vplus(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof(f33,plain,
! [X0] : vd269 != vplus(vd268,X0),
inference(ennf_transformation,[],[f2]) ).
fof(f49,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X2] : X0 = vplus(X1,X2)
| ~ less(X1,X0) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f50,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( ? [X3] : vplus(X1,X3) = X0
| ~ less(X1,X0) ) ),
inference(rectify,[],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( ( less(X1,X0)
| ! [X2] : vplus(X1,X2) != X0 )
& ( vplus(X1,sK0(X0,X1)) = X0
| ~ less(X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f50]) ).
fof(f56,plain,
! [X0] : vd269 != vplus(vd268,X0),
inference(cnf_transformation,[],[f33]) ).
fof(f58,plain,
less(vd268,vd269),
inference(cnf_transformation,[],[f4]) ).
fof(f73,plain,
! [X0,X1] :
( ~ less(X1,X0)
| vplus(X1,sK0(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f51]) ).
fof(f191,plain,
vd269 = vplus(vd268,sK0(vd269,vd268)),
inference(resolution,[],[f73,f58]) ).
fof(f194,plain,
$false,
inference(forward_subsumption_resolution,[],[f191,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM837+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.42 % Computer : n018.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sun Sep 27 21:31:09 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 Running first-order theorem proving
% 0.23/0.48 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
% 0.25/1.70 % (2744103)Detected formulas, will run a generic FOF schedule.
% 0.25/1.70 % (2744113)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2861526703:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.25/1.70 % (2744113)First to succeed.
% 0.25/1.70 % (2744113)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2744103"
% 0.25/1.70 % (2744114)dis-21_1_sil=8000:lcm=predicate:random_seed=4043098996: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)
% 0.25/1.70 % (2744112)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3919503948:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.25/1.70 % (2744108)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=3937019207:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.25/1.70 % (2744110)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=1303685432:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.25/1.70 % (2744111)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1689032930:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.25/1.70 % (2744109)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=1682208657:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.25/1.70 % (2744112)Also succeeded, but the first one will report.
% 0.25/1.70 % (2744114)Also succeeded, but the first one will report.
% 0.25/1.70 % (2744111)Instruction limit reached!
% 0.25/1.70 % (2744111)------------------------------
% 0.25/1.70 % (2744111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.25/1.70 % (2744111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/1.70 % (2744111)CaDiCaL version: 2.1.3
% 0.25/1.70 % (2744111)Termination reason: Instruction limit
% 0.25/1.70 % (2744111)Termination phase: Saturation
% 0.25/1.70 % (2744111)Time elapsed: 0.107 s
% 0.25/1.70 % (2744111)Peak memory usage: 89 MB
% 0.25/1.70 % (2744111)Instructions burned: 109 (million)
% 0.25/1.70 % (2744113)Refutation found. Thanks to Tanya!
% 0.25/1.70 % SZS status Theorem for theBenchmark
% 0.25/1.70 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/1.70 % (2744113)------------------------------
% 0.25/1.70 % (2744113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.25/1.70 % (2744113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/1.70 % (2744113)CaDiCaL version: 2.1.3
% 0.25/1.70 % (2744113)Termination reason: Refutation
% 0.25/1.70 % (2744113)Time elapsed: 0.005 s
% 0.25/1.70 % (2744113)Peak memory usage: 89 MB
% 0.25/1.70 % (2744113)Instructions burned: 5 (million)
% 0.25/1.70 % (2744113)------------------------------
% 0.25/1.70 % (2744113)------------------------------
% 0.25/1.70 % (2744103)Success in time 0.448 s
% 0.25/1.70 % Vampire exiting
%------------------------------------------------------------------------------