%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN117-1 : 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 : n026.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 01:49:42 PM UTC 2026
% Result : Unsatisfiable 2.74s 1.18s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 25
% Syntax : Number of formulae : 85 ( 22 unt; 10 def)
% Number of atoms : 184 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 202 ( 103 ~; 89 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 23 ( 22 usr; 11 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
n0(d,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f24,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
fof(f26,axiom,
n0(d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
fof(f28,axiom,
k0(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
fof(f39,axiom,
! [X0,X1] :
( k1(X0)
| ~ n0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_001) ).
fof(f40,axiom,
! [X0,X1] :
( l1(X0,X0)
| ~ n0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_002) ).
fof(f42,axiom,
! [X0,X1] :
( l1(X0,X0)
| ~ k1(X0)
| ~ l0(X1)
| ~ l1(X1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_004) ).
fof(f106,axiom,
! [X0] :
( p1(X0,X0,X0)
| ~ k0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_068) ).
fof(f175,axiom,
! [X2,X0,X1] :
( n2(X0)
| ~ p1(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_137) ).
fof(f197,axiom,
! [X0] :
( p2(X0,X0,X0)
| ~ k1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_159) ).
fof(f282,axiom,
! [X0] :
( p3(X0,X0,X0)
| ~ n2(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_244) ).
fof(f305,axiom,
! [X2,X0,X1] :
( r3(X0,X1,X0)
| ~ p2(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_267) ).
fof(f337,axiom,
! [X2,X3,X0,X1] :
( s4(X0)
| ~ p3(X1,X2,X3)
| ~ l1(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_299) ).
fof(f338,axiom,
! [X2,X0,X1] :
( k5(X0)
| ~ s4(X1)
| ~ r3(X2,X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_300) ).
fof(f369,negated_conjecture,
~ k5(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f453,definition,
( spl0_22
<=> ! [X1] : ~ s4(X1) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f454,plain,
( ! [X1] : ~ s4(X1)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f456,definition,
( spl0_23
<=> ! [X2,X0] :
( k5(X0)
| ~ r3(X2,X0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f457,plain,
( ! [X2,X0] :
( ~ r3(X2,X0,X0)
| k5(X0) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f458,plain,
( spl0_22
| spl0_23 ),
inference(avatar_split_clause,[],[f338,f456,f453]) ).
fof(f662,definition,
( spl0_75
<=> n2(e) ),
introduced(definition,[new_symbols(definition,[spl0_75])],[avatar_definition]) ).
fof(f663,plain,
( n2(e)
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f664,plain,
( ~ n2(e)
| spl0_75 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f900,definition,
( spl0_134
<=> l0(c) ),
introduced(definition,[new_symbols(definition,[spl0_134])],[avatar_definition]) ).
fof(f901,plain,
( l0(c)
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f900]) ).
fof(f925,definition,
( spl0_140
<=> k1(e) ),
introduced(definition,[new_symbols(definition,[spl0_140])],[avatar_definition]) ).
fof(f926,plain,
( k1(e)
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f925]) ).
fof(f927,plain,
( ~ k1(e)
| spl0_140 ),
inference(avatar_component_clause,[],[f925]) ).
fof(f1186,definition,
( spl0_205
<=> k0(e) ),
introduced(definition,[new_symbols(definition,[spl0_205])],[avatar_definition]) ).
fof(f1187,plain,
( k0(e)
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f1186]) ).
fof(f1340,definition,
( spl0_242
<=> ! [X0] :
( p1(X0,X0,X0)
| ~ k0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_242])],[avatar_definition]) ).
fof(f1341,plain,
( ! [X0] :
( p1(X0,X0,X0)
| ~ k0(X0) )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f1340]) ).
fof(f1360,plain,
spl0_242,
inference(avatar_split_clause,[],[f106,f1340]) ).
fof(f1528,definition,
( spl0_287
<=> l1(c,c) ),
introduced(definition,[new_symbols(definition,[spl0_287])],[avatar_definition]) ).
fof(f1529,plain,
( l1(c,c)
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f1528]) ).
fof(f1530,plain,
( ~ l1(c,c)
| spl0_287 ),
inference(avatar_component_clause,[],[f1528]) ).
fof(f1544,definition,
( spl0_291
<=> ! [X1] :
( ~ l0(X1)
| ~ l1(X1,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_291])],[avatar_definition]) ).
fof(f1545,plain,
( ! [X1] :
( ~ l1(X1,X1)
| ~ l0(X1) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f1547,definition,
( spl0_292
<=> ! [X0] :
( l1(X0,X0)
| ~ k1(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_292])],[avatar_definition]) ).
fof(f1548,plain,
( ! [X0] :
( l1(X0,X0)
| ~ k1(X0) )
| ~ spl0_292 ),
inference(avatar_component_clause,[],[f1547]) ).
fof(f1549,plain,
( spl0_291
| spl0_292 ),
inference(avatar_split_clause,[],[f42,f1547,f1544]) ).
fof(f1556,plain,
spl0_205,
inference(avatar_split_clause,[],[f28,f1186]) ).
fof(f1558,plain,
spl0_134,
inference(avatar_split_clause,[],[f24,f900]) ).
fof(f1629,plain,
( ! [X0] : ~ n0(X0,e)
| spl0_140 ),
inference(resolution,[],[f39,f927]) ).
fof(f1640,plain,
( $false
| spl0_140 ),
inference(resolution,[],[f1629,f3]) ).
fof(f1643,plain,
spl0_140,
inference(avatar_contradiction_clause,[],[f1640]) ).
fof(f1774,plain,
( ! [X0] : ~ n0(X0,c)
| spl0_287 ),
inference(resolution,[],[f40,f1530]) ).
fof(f1783,plain,
( $false
| spl0_287 ),
inference(resolution,[],[f1774,f26]) ).
fof(f1784,plain,
spl0_287,
inference(avatar_contradiction_clause,[],[f1783]) ).
fof(f1785,plain,
( ~ l0(c)
| ~ spl0_287
| ~ spl0_291 ),
inference(resolution,[],[f1529,f1545]) ).
fof(f1786,plain,
( $false
| ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(forward_subsumption_resolution,[],[f1785,f901]) ).
fof(f1787,plain,
( ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(avatar_contradiction_clause,[],[f1786]) ).
fof(f1808,plain,
( ! [X0,X1] : ~ p1(X0,X1,e)
| spl0_75 ),
inference(resolution,[],[f175,f664]) ).
fof(f1811,plain,
( ~ k0(e)
| spl0_75
| ~ spl0_242 ),
inference(resolution,[],[f1808,f1341]) ).
fof(f1814,plain,
( $false
| spl0_75
| ~ spl0_205
| ~ spl0_242 ),
inference(forward_subsumption_resolution,[],[f1811,f1187]) ).
fof(f1815,plain,
( spl0_75
| ~ spl0_205
| ~ spl0_242 ),
inference(avatar_contradiction_clause,[],[f1814]) ).
fof(f2080,plain,
( ! [X2,X3,X0,X1] :
( ~ p3(X1,X2,X3)
| ~ l1(X0,X2) )
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f337,f454]) ).
fof(f2082,plain,
( ! [X0,X1] :
( ~ n2(X1)
| ~ l1(X0,X1) )
| ~ spl0_22 ),
inference(resolution,[],[f2080,f282]) ).
fof(f2084,plain,
( ! [X0] : ~ l1(X0,e)
| ~ spl0_22
| ~ spl0_75 ),
inference(resolution,[],[f2082,f663]) ).
fof(f2085,plain,
( ~ k1(e)
| ~ spl0_22
| ~ spl0_75
| ~ spl0_292 ),
inference(resolution,[],[f2084,f1548]) ).
fof(f2089,plain,
( $false
| ~ spl0_22
| ~ spl0_75
| ~ spl0_140
| ~ spl0_292 ),
inference(forward_subsumption_resolution,[],[f2085,f926]) ).
fof(f2090,plain,
( ~ spl0_22
| ~ spl0_75
| ~ spl0_140
| ~ spl0_292 ),
inference(avatar_contradiction_clause,[],[f2089]) ).
fof(f2092,plain,
( ! [X0,X1] :
( k5(X0)
| ~ p2(X0,X1,X0) )
| ~ spl0_23 ),
inference(resolution,[],[f457,f305]) ).
fof(f2102,plain,
( ! [X0] : ~ p2(e,X0,e)
| ~ spl0_23 ),
inference(resolution,[],[f2092,f369]) ).
fof(f2108,plain,
( ~ k1(e)
| ~ spl0_23 ),
inference(resolution,[],[f2102,f197]) ).
fof(f2120,plain,
( $false
| ~ spl0_23
| ~ spl0_140 ),
inference(forward_subsumption_resolution,[],[f2108,f926]) ).
fof(f2121,plain,
( ~ spl0_23
| ~ spl0_140 ),
inference(avatar_contradiction_clause,[],[f2120]) ).
cnf(s10,plain,
( spl0_22
| spl0_23 ),
inference(sat_conversion,[],[f458]) ).
cnf(s124,plain,
spl0_242,
inference(sat_conversion,[],[f1360]) ).
cnf(s152,plain,
( spl0_291
| spl0_292 ),
inference(sat_conversion,[],[f1549]) ).
cnf(s156,plain,
spl0_205,
inference(sat_conversion,[],[f1556]) ).
cnf(s158,plain,
spl0_134,
inference(sat_conversion,[],[f1558]) ).
cnf(s197,plain,
spl0_140,
inference(sat_conversion,[],[f1643]) ).
cnf(s236,plain,
spl0_287,
inference(sat_conversion,[],[f1784]) ).
cnf(s237,plain,
( ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(sat_conversion,[],[f1787]) ).
cnf(s248,plain,
( spl0_75
| ~ spl0_205
| ~ spl0_242 ),
inference(sat_conversion,[],[f1815]) ).
cnf(s302,plain,
( ~ spl0_22
| ~ spl0_75
| ~ spl0_140
| ~ spl0_292 ),
inference(sat_conversion,[],[f2090]) ).
cnf(s309,plain,
( ~ spl0_23
| ~ spl0_140 ),
inference(sat_conversion,[],[f2121]) ).
cnf(s313,plain,
~ spl0_23,
inference(rat,[],[s309,s197]) ).
cnf(s323,plain,
~ spl0_291,
inference(rat,[],[s237,s236,s158]) ).
cnf(s327,plain,
spl0_292,
inference(rat,[],[s152,s323]) ).
cnf(s350,plain,
spl0_75,
inference(rat,[],[s248,s156,s124]) ).
cnf(s351,plain,
~ spl0_22,
inference(rat,[],[s302,s327,s197,s350]) ).
cnf(s440,plain,
$false,
inference(rat,[],[s10,s313,s351]) ).
fof(f2124,plain,
$false,
inference(avatar_sat_refutation,[],[s440]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN117-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n026.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 15:38:46 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.74/1.18 % (3947182)Input is clausal, will run a generic CNF schedule.
% 2.74/1.18 % (3947192)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=419168960:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.74/1.18 % (3947192)First to succeed.
% 2.74/1.18 % (3947192)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3947182"
% 2.74/1.18 % (3947191)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=257548394:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.74/1.18 % (3947188)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2892475066:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.74/1.18 % (3947187)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=3610361303:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.74/1.18 % (3947190)lrs+10_1_sil=8000:sp=occurrence:random_seed=1277571282:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.74/1.18 % (3947189)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1217765371:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.74/1.18 % (3947193)dis-21_1_sil=8000:lcm=predicate:random_seed=1316711790: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)
% 2.74/1.18 % (3947190)Also succeeded, but the first one will report.
% 2.74/1.18 % (3947191)Also succeeded, but the first one will report.
% 2.74/1.18 % (3947193)Instruction limit reached!
% 2.74/1.18 % (3947193)------------------------------
% 2.74/1.18 % (3947193)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.18 % (3947193)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.18 % (3947193)CaDiCaL version: 2.1.3
% 2.74/1.18 % (3947193)Termination reason: Instruction limit
% 2.74/1.18 % (3947193)Termination phase: Saturation
% 2.74/1.18 % (3947193)Time elapsed: 0.055 s
% 2.74/1.18 % (3947193)Peak memory usage: 89 MB
% 2.74/1.18 % (3947193)Instructions burned: 117 (million)
% 2.74/1.18 % (3947192)Refutation found. Thanks to Tanya!
% 2.74/1.18 % SZS status Unsatisfiable for theBenchmark
% 2.74/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.18 % (3947192)------------------------------
% 2.74/1.18 % (3947192)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.18 % (3947192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.18 % (3947192)CaDiCaL version: 2.1.3
% 2.74/1.18 % (3947192)Termination reason: Refutation
% 2.74/1.18 % (3947192)Time elapsed: 0.013 s
% 2.74/1.18 % (3947192)Peak memory usage: 90 MB
% 2.74/1.18 % (3947192)Instructions burned: 35 (million)
% 2.74/1.18 % (3947192)------------------------------
% 2.74/1.18 % (3947192)------------------------------
% 2.74/1.18 % (3947182)Success in time 0.304 s
% 2.74/1.18 % Vampire exiting
%------------------------------------------------------------------------------