%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN222-1 : 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 : n013.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 01:49:57 PM UTC 2026
% Result : Unsatisfiable 2.83s 1.19s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 28
% Syntax : Number of formulae : 98 ( 28 unt; 14 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 203 ( 102 ~; 87 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 25 ( 24 usr; 15 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 36 ( 0 sgn 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
s0(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f14,axiom,
! [X0] : p0(b,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
fof(f17,axiom,
! [X0] : q0(X0,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
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(f34,axiom,
n0(c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
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(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(f228,axiom,
( s2(d)
| ~ s1(a)
| ~ s0(d) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_190) ).
fof(f258,axiom,
! [X0,X1] :
( l3(X0,X0)
| ~ s2(X1)
| ~ l1(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_220) ).
fof(f369,negated_conjecture,
! [X0] : ~ l3(X0,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f559,definition,
( spl0_49
<=> n0(c,d) ),
introduced(definition,[new_symbols(definition,[spl0_49])],[avatar_definition]) ).
fof(f560,plain,
( n0(c,d)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f559]) ).
fof(f602,definition,
( spl0_60
<=> ! [X1] : ~ s1(X1) ),
introduced(definition,[new_symbols(definition,[spl0_60])],[avatar_definition]) ).
fof(f603,plain,
( ! [X1] : ~ s1(X1)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f602]) ).
fof(f725,definition,
( spl0_91
<=> s2(d) ),
introduced(definition,[new_symbols(definition,[spl0_91])],[avatar_definition]) ).
fof(f726,plain,
( s2(d)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f756,definition,
( spl0_98
<=> ! [X1] : ~ s2(X1) ),
introduced(definition,[new_symbols(definition,[spl0_98])],[avatar_definition]) ).
fof(f757,plain,
( ! [X1] : ~ s2(X1)
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f756]) ).
fof(f759,definition,
( spl0_99
<=> ! [X0] :
( l3(X0,X0)
| ~ l1(X0,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_99])],[avatar_definition]) ).
fof(f760,plain,
( ! [X0] :
( ~ l1(X0,X0)
| l3(X0,X0) )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f759]) ).
fof(f761,plain,
( spl0_98
| spl0_99 ),
inference(avatar_split_clause,[],[f258,f759,f756]) ).
fof(f876,definition,
( spl0_128
<=> s0(d) ),
introduced(definition,[new_symbols(definition,[spl0_128])],[avatar_definition]) ).
fof(f880,definition,
( spl0_129
<=> s1(a) ),
introduced(definition,[new_symbols(definition,[spl0_129])],[avatar_definition]) ).
fof(f882,plain,
( ~ s1(a)
| spl0_129 ),
inference(avatar_component_clause,[],[f880]) ).
fof(f883,plain,
( ~ spl0_128
| ~ spl0_129
| spl0_91 ),
inference(avatar_split_clause,[],[f228,f725,f880,f876]) ).
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(f1033,definition,
( spl0_168
<=> k1(d) ),
introduced(definition,[new_symbols(definition,[spl0_168])],[avatar_definition]) ).
fof(f1034,plain,
( k1(d)
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1033]) ).
fof(f1035,plain,
( ~ k1(d)
| spl0_168 ),
inference(avatar_component_clause,[],[f1033]) ).
fof(f1141,definition,
( spl0_194
<=> ! [X1] : ~ p0(X1,X1) ),
introduced(definition,[new_symbols(definition,[spl0_194])],[avatar_definition]) ).
fof(f1142,plain,
( ! [X1] : ~ p0(X1,X1)
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f1141]) ).
fof(f1157,definition,
( spl0_198
<=> ! [X0,X1] :
( s1(X0)
| ~ q0(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_198])],[avatar_definition]) ).
fof(f1158,plain,
( ! [X0,X1] :
( s1(X0)
| ~ q0(X0,X1) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f1157]) ).
fof(f1159,plain,
( spl0_60
| spl0_198 ),
inference(avatar_split_clause,[],[f164,f1157,f602]) ).
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(f1554,plain,
spl0_49,
inference(avatar_split_clause,[],[f34,f559]) ).
fof(f1558,plain,
spl0_134,
inference(avatar_split_clause,[],[f24,f900]) ).
fof(f1568,plain,
spl0_128,
inference(avatar_split_clause,[],[f1,f876]) ).
fof(f1584,plain,
( $false
| ~ spl0_194 ),
inference(resolution,[],[f1142,f14]) ).
fof(f1585,plain,
~ spl0_194,
inference(avatar_contradiction_clause,[],[f1584]) ).
fof(f1663,plain,
( ! [X0] : ~ n0(X0,d)
| spl0_168 ),
inference(resolution,[],[f39,f1035]) ).
fof(f1667,plain,
( $false
| ~ spl0_49
| spl0_168 ),
inference(resolution,[],[f1663,f560]) ).
fof(f1668,plain,
( ~ spl0_49
| spl0_168 ),
inference(avatar_contradiction_clause,[],[f1667]) ).
fof(f1674,plain,
( ! [X0] : ~ p0(X0,X0)
| ~ spl0_60 ),
inference(forward_subsumption_resolution,[],[f163,f603]) ).
fof(f1675,plain,
( spl0_194
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f1674,f602,f1141]) ).
fof(f1693,plain,
( ! [X0] : ~ q0(a,X0)
| spl0_129
| ~ spl0_198 ),
inference(resolution,[],[f1158,f882]) ).
fof(f1722,plain,
( $false
| spl0_129
| ~ spl0_198 ),
inference(resolution,[],[f1693,f17]) ).
fof(f1725,plain,
( spl0_129
| ~ spl0_198 ),
inference(avatar_contradiction_clause,[],[f1722]) ).
fof(f1726,plain,
( $false
| ~ spl0_91
| ~ spl0_98 ),
inference(forward_subsumption_resolution,[],[f726,f757]) ).
fof(f1727,plain,
( ~ spl0_91
| ~ spl0_98 ),
inference(avatar_contradiction_clause,[],[f1726]) ).
fof(f1739,plain,
( ! [X0] : ~ n0(X0,c)
| spl0_287 ),
inference(resolution,[],[f40,f1530]) ).
fof(f1763,plain,
( $false
| spl0_287 ),
inference(resolution,[],[f1739,f26]) ).
fof(f1764,plain,
spl0_287,
inference(avatar_contradiction_clause,[],[f1763]) ).
fof(f1765,plain,
( ~ l0(c)
| ~ spl0_287
| ~ spl0_291 ),
inference(resolution,[],[f1529,f1545]) ).
fof(f1776,plain,
( $false
| ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(forward_subsumption_resolution,[],[f1765,f901]) ).
fof(f1777,plain,
( ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(avatar_contradiction_clause,[],[f1776]) ).
fof(f1780,plain,
( ! [X0] :
( l3(X0,X0)
| ~ k1(X0) )
| ~ spl0_99
| ~ spl0_292 ),
inference(resolution,[],[f1548,f760]) ).
fof(f1790,plain,
( ~ k1(d)
| ~ spl0_99
| ~ spl0_292 ),
inference(resolution,[],[f1780,f369]) ).
fof(f1791,plain,
( $false
| ~ spl0_99
| ~ spl0_168
| ~ spl0_292 ),
inference(forward_subsumption_resolution,[],[f1790,f1034]) ).
fof(f1792,plain,
( ~ spl0_99
| ~ spl0_168
| ~ spl0_292 ),
inference(avatar_contradiction_clause,[],[f1791]) ).
cnf(s43,plain,
( spl0_98
| spl0_99 ),
inference(sat_conversion,[],[f761]) ).
cnf(s59,plain,
( spl0_91
| ~ spl0_128
| ~ spl0_129 ),
inference(sat_conversion,[],[f883]) ).
cnf(s91,plain,
( spl0_60
| spl0_198 ),
inference(sat_conversion,[],[f1159]) ).
cnf(s152,plain,
( spl0_291
| spl0_292 ),
inference(sat_conversion,[],[f1549]) ).
cnf(s154,plain,
spl0_49,
inference(sat_conversion,[],[f1554]) ).
cnf(s158,plain,
spl0_134,
inference(sat_conversion,[],[f1558]) ).
cnf(s168,plain,
spl0_128,
inference(sat_conversion,[],[f1568]) ).
cnf(s174,plain,
~ spl0_194,
inference(sat_conversion,[],[f1585]) ).
cnf(s199,plain,
( ~ spl0_49
| spl0_168 ),
inference(sat_conversion,[],[f1668]) ).
cnf(s202,plain,
( ~ spl0_60
| spl0_194 ),
inference(sat_conversion,[],[f1675]) ).
cnf(s223,plain,
( spl0_129
| ~ spl0_198 ),
inference(sat_conversion,[],[f1725]) ).
cnf(s224,plain,
( ~ spl0_91
| ~ spl0_98 ),
inference(sat_conversion,[],[f1727]) ).
cnf(s232,plain,
spl0_287,
inference(sat_conversion,[],[f1764]) ).
cnf(s235,plain,
( ~ spl0_134
| ~ spl0_287
| ~ spl0_291 ),
inference(sat_conversion,[],[f1777]) ).
cnf(s241,plain,
( ~ spl0_99
| ~ spl0_168
| ~ spl0_292 ),
inference(sat_conversion,[],[f1792]) ).
cnf(s242,plain,
~ spl0_60,
inference(rat,[],[s202,s174]) ).
cnf(s248,plain,
~ spl0_291,
inference(rat,[],[s235,s232,s158]) ).
cnf(s250,plain,
spl0_168,
inference(rat,[],[s199,s154]) ).
cnf(s252,plain,
spl0_292,
inference(rat,[],[s152,s248]) ).
cnf(s253,plain,
~ spl0_99,
inference(rat,[],[s241,s250,s252]) ).
cnf(s300,plain,
spl0_198,
inference(rat,[],[s91,s242]) ).
cnf(s302,plain,
spl0_129,
inference(rat,[],[s223,s300]) ).
cnf(s327,plain,
spl0_91,
inference(rat,[],[s59,s302,s168]) ).
cnf(s329,plain,
~ spl0_98,
inference(rat,[],[s224,s327]) ).
cnf(s335,plain,
$false,
inference(rat,[],[s43,s253,s329]) ).
fof(f1793,plain,
$false,
inference(avatar_sat_refutation,[],[s335]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN222-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 15:38:06 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 2.83/1.19 % (1281431)Input is clausal, will run a generic CNF schedule.
% 2.83/1.19 % (1281544)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3233155223:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.83/1.19 % (1281544)First to succeed.
% 2.83/1.19 % (1281544)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1281431"
% 2.83/1.19 % (1281545)dis-21_1_sil=8000:lcm=predicate:random_seed=1252713047: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)
% 2.83/1.19 % (1281542)lrs+10_1_sil=8000:sp=occurrence:random_seed=2990839147:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.83/1.19 % (1281540)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3995263387:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.83/1.19 % (1281539)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=81418733:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.83/1.19 % (1281543)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=10962889:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.83/1.19 % (1281542)Also succeeded, but the first one will report.
% 2.83/1.19 % (1281543)Also succeeded, but the first one will report.
% 2.83/1.19 % (1281545)Also succeeded, but the first one will report.
% 2.83/1.19 % (1281541)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=963534819:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.83/1.19 % (1281544)Refutation found. Thanks to Tanya!
% 2.83/1.19 % SZS status Unsatisfiable for theBenchmark
% 2.83/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 2.83/1.19 % (1281544)------------------------------
% 2.83/1.19 % (1281544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.83/1.19 % (1281544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.83/1.19 % (1281544)CaDiCaL version: 2.1.3
% 2.83/1.19 % (1281544)Termination reason: Refutation
% 2.83/1.19 % (1281544)Time elapsed: 0.010 s
% 2.83/1.19 % (1281544)Peak memory usage: 90 MB
% 2.83/1.19 % (1281544)Instructions burned: 23 (million)
% 2.83/1.19 % (1281544)------------------------------
% 2.83/1.19 % (1281544)------------------------------
% 2.83/1.19 % (1281431)Success in time 0.329 s
% 2.83/1.19 % Vampire exiting
%------------------------------------------------------------------------------