%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV008-1 : 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 : n019.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 01:07:53 PM UTC 2026
% Result : Unsatisfiable 3.46s 1.25s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 43 ( 16 unt; 4 def)
% Number of atoms : 83 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 74 ( 34 ~; 36 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 11 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X2,X0,X1] :
( ~ less_than(X2,X1)
| ~ less_than(X0,X2)
| less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_than) ).
fof(f8,axiom,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_related) ).
fof(f9,axiom,
! [X0] : ~ less_than(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_not_less_than_x) ).
fof(f15,negated_conjecture,
~ less_than(n,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
fof(f16,negated_conjecture,
less_than(one,l),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
fof(f17,negated_conjecture,
less_than(a(l),a(predecessor(l))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
fof(f18,negated_conjecture,
! [X0] :
( less_than(X0,n)
| less_than(n,X0)
| ~ less_than(one,n)
| ~ less_than(a(X0),a(predecessor(n))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
fof(f19,negated_conjecture,
! [X0] :
( ~ less_than(a(X0),a(predecessor(X0)))
| ~ less_than(X0,n)
| ~ less_than(one,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
fof(f23,definition,
( spl0_1
<=> less_than(one,n) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f25,plain,
( ~ less_than(one,n)
| spl0_1 ),
inference(avatar_component_clause,[],[f23]) ).
fof(f27,definition,
( spl0_2
<=> ! [X0] :
( less_than(X0,n)
| ~ less_than(a(X0),a(predecessor(n)))
| less_than(n,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f28,plain,
( ! [X0] :
( ~ less_than(a(X0),a(predecessor(n)))
| less_than(X0,n)
| less_than(n,X0) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f29,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f18,f27,f23]) ).
fof(f30,plain,
( ~ less_than(l,n)
| ~ less_than(one,l) ),
inference(resolution,[],[f19,f17]) ).
fof(f31,plain,
~ less_than(l,n),
inference(forward_subsumption_resolution,[],[f30,f16]) ).
fof(f48,plain,
! [X0] :
( ~ less_than(X0,one)
| less_than(X0,l) ),
inference(resolution,[],[f7,f16]) ).
fof(f55,plain,
( less_than(n,one)
| n = one
| spl0_1 ),
inference(resolution,[],[f8,f25]) ).
fof(f61,plain,
( less_than(n,l)
| n = l ),
inference(resolution,[],[f8,f31]) ).
fof(f67,definition,
( spl0_3
<=> n = one ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f69,plain,
( n = one
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f71,definition,
( spl0_4
<=> less_than(n,one) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f73,plain,
( less_than(n,one)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f75,plain,
n = l,
inference(forward_subsumption_resolution,[],[f61,f15]) ).
fof(f76,plain,
( spl0_3
| spl0_4
| spl0_1 ),
inference(avatar_split_clause,[],[f55,f23,f71,f67]) ).
fof(f81,plain,
( less_than(n,l)
| ~ spl0_3 ),
inference(superposition,[],[f16,f69]) ).
fof(f82,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f81,f15]) ).
fof(f83,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f82]) ).
fof(f85,plain,
( less_than(n,l)
| ~ spl0_4 ),
inference(resolution,[],[f73,f48]) ).
fof(f88,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f85,f15]) ).
fof(f89,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f88]) ).
fof(f96,plain,
less_than(a(n),a(predecessor(n))),
inference(superposition,[],[f17,f75]) ).
fof(f152,plain,
( less_than(n,n)
| less_than(n,n)
| ~ spl0_2 ),
inference(resolution,[],[f96,f28]) ).
fof(f156,plain,
( less_than(n,n)
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f152]) ).
fof(f157,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f156,f9]) ).
fof(f158,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f157]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s3,plain,
( spl0_1
| spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f76]) ).
cnf(s4,plain,
~ spl0_3,
inference(sat_conversion,[],[f83]) ).
cnf(s5,plain,
~ spl0_4,
inference(sat_conversion,[],[f89]) ).
cnf(s7,plain,
~ spl0_2,
inference(sat_conversion,[],[f158]) ).
cnf(s8,plain,
spl0_1,
inference(rat,[],[s3,s5,s4]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s7,s8]) ).
fof(f159,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV008-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.16 % Computer : n019.cluster.edu
% 0.13/0.16 % Model : x86_64 x86_64
% 0.13/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.16 % Memory : 8046.5625MB
% 0.13/0.16 % OS : Linux 6.8.0-71-generic
% 0.13/0.16 % CPULimit : 300
% 0.13/0.16 % WCLimit : 300
% 0.13/0.16 % DateTime : Mon Sep 28 09:42:39 UTC 2026
% 0.13/0.16 % CPUTime :
% 0.13/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.20 Running first-order theorem proving
% 0.13/0.20 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
% 3.46/1.25 % (3884997)Input is clausal, will run a generic CNF schedule.
% 3.46/1.25 % (3885024)lrs+10_1_sil=8000:sp=occurrence:random_seed=1411558712:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 3.46/1.25 % (3885024)First to succeed.
% 3.46/1.25 % (3885024)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3884997"
% 3.46/1.25 % (3885025)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=734259872:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 3.46/1.25 % (3885025)Also succeeded, but the first one will report.
% 3.46/1.25 % (3885023)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=476651720:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 3.46/1.25 % (3885022)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=303412824:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 3.46/1.25 % (3885021)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=669382315:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 3.46/1.25 % (3885026)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1831992600:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 3.46/1.25 % (3885027)dis-21_1_sil=8000:lcm=predicate:random_seed=358203548:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 3.46/1.25 % (3885026)Also succeeded, but the first one will report.
% 3.46/1.25 % (3885027)Instruction limit reached!
% 3.46/1.25 % (3885027)------------------------------
% 3.46/1.25 % (3885027)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.25 % (3885027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.25 % (3885027)CaDiCaL version: 2.1.3
% 3.46/1.25 % (3885027)Termination reason: Instruction limit
% 3.46/1.25 % (3885027)Termination phase: Saturation
% 3.46/1.25 % (3885027)Time elapsed: 0.116 s
% 3.46/1.25 % (3885027)Peak memory usage: 88 MB
% 3.46/1.25 % (3885027)Instructions burned: 117 (million)
% 3.46/1.25 % (3885024)Refutation found. Thanks to Tanya!
% 3.46/1.25 % SZS status Unsatisfiable for theBenchmark
% 3.46/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.25 % (3885024)------------------------------
% 3.46/1.25 % (3885024)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.25 % (3885024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.25 % (3885024)CaDiCaL version: 2.1.3
% 3.46/1.25 % (3885024)Termination reason: Refutation
% 3.46/1.25 % (3885024)Time elapsed: 0.005 s
% 3.46/1.25 % (3885024)Peak memory usage: 89 MB
% 3.46/1.25 % (3885024)Instructions burned: 5 (million)
% 3.46/1.25 % (3885024)------------------------------
% 3.46/1.25 % (3885024)------------------------------
% 3.46/1.25 % (3884997)Success in time 0.4 s
% 3.46/1.25 % Vampire exiting
%------------------------------------------------------------------------------