%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 01:07:52 PM UTC 2026
% Result : Unsatisfiable 2.50s 0.93s
% Output : Refutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 10 unt; 2 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 16 ~; 14 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 7 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] : less_than(X0,successor(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_than_successor) ).
fof(f7,axiom,
! [X2,X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,X2)
| ~ less_than(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_than) ).
fof(f9,axiom,
! [X0] : ~ less_than(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_not_less_than_x) ).
fof(f17,negated_conjecture,
less_than(i,n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f19,negated_conjecture,
less_than(a(i),a(m)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f20,negated_conjecture,
! [X0] :
( ~ less_than(a(X0),a(m))
| ~ less_than(X0,successor(n))
| less_than(X0,i) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
fof(f40,plain,
( ~ less_than(i,successor(n))
| less_than(i,i) ),
inference(resolution,[],[f20,f19]) ).
fof(f42,definition,
( spl1_3
<=> less_than(i,i) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
fof(f43,plain,
( less_than(i,i)
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f42]) ).
fof(f45,definition,
( spl1_4
<=> less_than(i,successor(n)) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
fof(f46,plain,
( ~ less_than(i,successor(n))
| spl1_4 ),
inference(avatar_component_clause,[],[f45]) ).
fof(f47,plain,
( spl1_3
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f40,f45,f42]) ).
fof(f63,plain,
( ! [X0] :
( ~ less_than(X0,successor(n))
| ~ less_than(i,X0) )
| spl1_4 ),
inference(resolution,[],[f7,f46]) ).
fof(f71,plain,
( ~ less_than(i,n)
| spl1_4 ),
inference(resolution,[],[f63,f6]) ).
fof(f90,plain,
( $false
| spl1_4 ),
inference(resolution,[],[f71,f17]) ).
fof(f92,plain,
spl1_4,
inference(avatar_contradiction_clause,[],[f90]) ).
fof(f93,plain,
( $false
| ~ spl1_3 ),
inference(resolution,[],[f43,f9]) ).
fof(f94,plain,
~ spl1_3,
inference(avatar_contradiction_clause,[],[f93]) ).
cnf(s2,plain,
( spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s4,plain,
spl1_4,
inference(sat_conversion,[],[f92]) ).
cnf(s5,plain,
~ spl1_3,
inference(sat_conversion,[],[f94]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s2,s4,s5]) ).
fof(f95,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n009.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 09:42:00 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running first-order theorem proving
% 0.06/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.50/0.93 % (2920770)Input is clausal, will run a generic CNF schedule.
% 2.50/0.93 % (2920795)dis-21_1_sil=8000:lcm=predicate:random_seed=514572353:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 2.50/0.93 % (2920795)First to succeed.
% 2.50/0.93 % (2920795)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2920770"
% 2.50/0.93 % (2920791)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=752171754:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.50/0.93 % (2920790)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3224144513:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.50/0.93 % (2920793)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=294420043:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.50/0.93 % (2920792)lrs+10_1_sil=8000:sp=occurrence:random_seed=972855541:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.50/0.93 % (2920789)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=3298560103:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.50/0.93 % (2920794)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3503178057:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.50/0.93 % (2920792)Also succeeded, but the first one will report.
% 2.50/0.93 % (2920794)Also succeeded, but the first one will report.
% 2.50/0.93 % (2920793)Also succeeded, but the first one will report.
% 2.50/0.93 % (2920795)Refutation found. Thanks to Tanya!
% 2.50/0.93 % SZS status Unsatisfiable for theBenchmark
% 2.50/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.50/0.93 % (2920795)------------------------------
% 2.50/0.93 % (2920795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/0.93 % (2920795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/0.93 % (2920795)CaDiCaL version: 2.1.3
% 2.50/0.93 % (2920795)Termination reason: Refutation
% 2.50/0.93 % (2920795)Time elapsed: 0.002 s
% 2.50/0.93 % (2920795)Peak memory usage: 89 MB
% 2.50/0.93 % (2920795)Instructions burned: 2 (million)
% 2.50/0.93 % (2920795)------------------------------
% 2.50/0.93 % (2920795)------------------------------
% 2.50/0.93 % (2920770)Success in time 0.304 s
% 2.50/0.93 % Vampire exiting
%------------------------------------------------------------------------------