%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN268-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 01:50:03 PM UTC 2026
% Result : Unsatisfiable 2.73s 1.15s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 21
% Syntax : Number of formulae : 62 ( 16 unt; 6 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 155 ( 81 ~; 68 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 7 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 69 ( 0 sgn 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0] : p0(b,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
fof(f15,axiom,
n0(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
fof(f17,axiom,
! [X0] : q0(X0,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
fof(f19,axiom,
! [X0,X1] : m0(X0,d,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
fof(f123,axiom,
! [X0,X1] :
( p1(X0,X0,X0)
| ~ p0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_085) ).
fof(f163,axiom,
! [X0] :
( ~ p0(X0,X0)
| s1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_125) ).
fof(f164,axiom,
! [X2,X0,X1] :
( s1(X0)
| ~ q0(X0,X1)
| ~ s1(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_126) ).
fof(f171,axiom,
! [X2,X3,X0,X1] :
( l2(X0,X0)
| ~ p0(X1,X1)
| ~ s1(X2)
| ~ m0(X3,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_133) ).
fof(f175,axiom,
! [X2,X0,X1] :
( ~ p1(X1,X2,X0)
| n2(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_137) ).
fof(f248,axiom,
! [X0] :
( k3(X0,X0,X0)
| ~ n2(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_210) ).
fof(f284,axiom,
! [X0] :
( p3(X0,X0,X0)
| ~ l2(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_246) ).
fof(f315,axiom,
! [X2,X0,X1] :
( ~ p3(X1,X2,X0)
| l4(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_277) ).
fof(f325,axiom,
! [X0,X1] :
( p4(X0,X1,X0)
| ~ k3(X0,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_287) ).
fof(f327,axiom,
! [X2,X3,X0,X1] :
( p4(X0,X0,X0)
| ~ l4(X0)
| ~ n0(X0,X1)
| ~ p4(X2,X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_289) ).
fof(f369,negated_conjecture,
! [X0,X1] : ~ p4(a,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f413,definition,
( spl0_13
<=> ! [X2,X3] : ~ p4(X2,X3,X2) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f414,plain,
( ! [X2,X3] : ~ p4(X2,X3,X2)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f416,definition,
( spl0_14
<=> ! [X0,X1] :
( p4(X0,X0,X0)
| ~ n0(X0,X1)
| ~ l4(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f417,plain,
( ! [X0,X1] :
( p4(X0,X0,X0)
| ~ n0(X0,X1)
| ~ l4(X0) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f418,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f327,f416,f413]) ).
fof(f440,definition,
( spl0_21
<=> ! [X1] : ~ s1(X1) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f441,plain,
( ! [X1] : ~ s1(X1)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f1024,definition,
( spl0_187
<=> ! [X0,X1] :
( s1(X0)
| ~ q0(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_187])],[avatar_definition]) ).
fof(f1025,plain,
( ! [X0,X1] :
( ~ q0(X0,X1)
| s1(X0) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f1024]) ).
fof(f1026,plain,
( spl0_21
| spl0_187 ),
inference(avatar_split_clause,[],[f164,f1024,f440]) ).
fof(f1028,definition,
( spl0_188
<=> ! [X1] : ~ p0(X1,X1) ),
introduced(definition,[new_symbols(definition,[spl0_188])],[avatar_definition]) ).
fof(f1029,plain,
( ! [X1] : ~ p0(X1,X1)
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1028]) ).
fof(f1031,definition,
( spl0_189
<=> ! [X2,X0,X3] :
( l2(X0,X0)
| ~ s1(X2)
| ~ m0(X3,X2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_189])],[avatar_definition]) ).
fof(f1032,plain,
( ! [X2,X3,X0] :
( l2(X0,X0)
| ~ s1(X2)
| ~ m0(X3,X2,X0) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1033,plain,
( spl0_188
| spl0_189 ),
inference(avatar_split_clause,[],[f171,f1031,f1028]) ).
fof(f1417,plain,
( $false
| ~ spl0_188 ),
inference(resolution,[],[f1029,f14]) ).
fof(f1418,plain,
~ spl0_188,
inference(avatar_contradiction_clause,[],[f1417]) ).
fof(f1502,plain,
( ! [X0] : ~ p0(X0,X0)
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[],[f163,f441]) ).
fof(f1503,plain,
( spl0_188
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f1502,f440,f1028]) ).
fof(f1509,plain,
( ! [X0] : s1(X0)
| ~ spl0_187 ),
inference(resolution,[],[f1025,f17]) ).
fof(f1646,plain,
( ! [X2,X3,X0] :
( ~ m0(X3,X2,X0)
| l2(X0,X0) )
| ~ spl0_187
| ~ spl0_189 ),
inference(forward_subsumption_resolution,[],[f1032,f1509]) ).
fof(f1660,plain,
! [X0,X1] :
( ~ p0(X0,X1)
| n2(X1) ),
inference(resolution,[],[f123,f175]) ).
fof(f1708,plain,
! [X0] :
( ~ l2(X0,X0)
| l4(X0) ),
inference(resolution,[],[f284,f315]) ).
fof(f1711,plain,
! [X0] : n2(X0),
inference(resolution,[],[f1660,f14]) ).
fof(f1750,plain,
( ! [X0] : l2(X0,X0)
| ~ spl0_187
| ~ spl0_189 ),
inference(resolution,[],[f1646,f19]) ).
fof(f1769,plain,
( ! [X0] : l4(X0)
| ~ spl0_187
| ~ spl0_189 ),
inference(resolution,[],[f1750,f1708]) ).
fof(f1825,plain,
( ! [X0,X1] : ~ k3(X0,X0,X1)
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f325,f414]) ).
fof(f1828,plain,
( ! [X0] : ~ n2(X0)
| ~ spl0_13 ),
inference(resolution,[],[f1825,f248]) ).
fof(f1832,plain,
( $false
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f1828,f1711]) ).
fof(f1833,plain,
~ spl0_13,
inference(avatar_contradiction_clause,[],[f1832]) ).
fof(f1855,plain,
( ! [X0,X1] :
( p4(X0,X0,X0)
| ~ n0(X0,X1) )
| ~ spl0_14
| ~ spl0_187
| ~ spl0_189 ),
inference(forward_subsumption_resolution,[],[f417,f1769]) ).
fof(f1856,plain,
( ! [X0] : ~ n0(a,X0)
| ~ spl0_14
| ~ spl0_187
| ~ spl0_189 ),
inference(resolution,[],[f1855,f369]) ).
fof(f1858,plain,
( $false
| ~ spl0_14
| ~ spl0_187
| ~ spl0_189 ),
inference(resolution,[],[f1856,f15]) ).
fof(f1859,plain,
( ~ spl0_14
| ~ spl0_187
| ~ spl0_189 ),
inference(avatar_contradiction_clause,[],[f1858]) ).
cnf(s6,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f418]) ).
cnf(s92,plain,
( spl0_21
| spl0_187 ),
inference(sat_conversion,[],[f1026]) ).
cnf(s93,plain,
( spl0_188
| spl0_189 ),
inference(sat_conversion,[],[f1033]) ).
cnf(s167,plain,
~ spl0_188,
inference(sat_conversion,[],[f1418]) ).
cnf(s205,plain,
( ~ spl0_21
| spl0_188 ),
inference(sat_conversion,[],[f1503]) ).
cnf(s275,plain,
~ spl0_13,
inference(sat_conversion,[],[f1833]) ).
cnf(s286,plain,
( ~ spl0_14
| ~ spl0_187
| ~ spl0_189 ),
inference(sat_conversion,[],[f1859]) ).
cnf(s287,plain,
~ spl0_21,
inference(rat,[],[s205,s167]) ).
cnf(s331,plain,
spl0_189,
inference(rat,[],[s93,s167]) ).
cnf(s332,plain,
spl0_187,
inference(rat,[],[s92,s287]) ).
cnf(s333,plain,
~ spl0_14,
inference(rat,[],[s286,s331,s332]) ).
cnf(s397,plain,
$false,
inference(rat,[],[s6,s333,s275]) ).
fof(f1860,plain,
$false,
inference(avatar_sat_refutation,[],[s397]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN268-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n008.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 15:40:59 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 2.73/1.15 % (2356594)Input is clausal, will run a generic CNF schedule.
% 2.73/1.15 % (2356650)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2144949227:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.73/1.15 % (2356650)First to succeed.
% 2.73/1.15 % (2356650)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2356594"
% 2.73/1.15 % (2356652)dis-21_1_sil=8000:lcm=predicate:random_seed=4142461309: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)
% 2.73/1.15 % (2356648)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3213792370:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.73/1.15 % (2356646)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=3408792871:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.73/1.15 % (2356647)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1753303204:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.73/1.15 % (2356649)lrs+10_1_sil=8000:sp=occurrence:random_seed=331111143:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.73/1.15 % (2356649)Also succeeded, but the first one will report.
% 2.73/1.15 % (2356652)Also succeeded, but the first one will report.
% 2.73/1.15 % (2356651)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=122317737:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.73/1.15 % (2356651)Also succeeded, but the first one will report.
% 2.73/1.15 % (2356650)Refutation found. Thanks to Tanya!
% 2.73/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.73/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/1.15 % (2356650)------------------------------
% 2.73/1.15 % (2356650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.73/1.15 % (2356650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.73/1.15 % (2356650)CaDiCaL version: 2.1.3
% 2.73/1.15 % (2356650)Termination reason: Refutation
% 2.73/1.15 % (2356650)Time elapsed: 0.010 s
% 2.73/1.15 % (2356650)Peak memory usage: 90 MB
% 2.73/1.15 % (2356650)Instructions burned: 27 (million)
% 2.73/1.15 % (2356650)------------------------------
% 2.73/1.15 % (2356650)------------------------------
% 2.73/1.15 % (2356594)Success in time 0.295 s
% 2.73/1.15 % Vampire exiting
%------------------------------------------------------------------------------