%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN207-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 01:49:55 PM UTC 2026
% Result : Unsatisfiable 2.78s 1.23s
% Output : Refutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 23
% Syntax : Number of formulae : 75 ( 24 unt; 8 def)
% Number of atoms : 188 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 225 ( 112 ~; 105 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 9 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
n0(d,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
fof(f14,axiom,
! [X0] : p0(b,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
fof(f17,axiom,
! [X0] : q0(X0,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
fof(f19,axiom,
! [X0,X1] : m0(X0,d,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
fof(f24,axiom,
l0(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
fof(f34,axiom,
n0(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).
fof(f35,axiom,
m0(d,e,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_35) ).
fof(f39,axiom,
! [X0,X1] :
( ~ n0(X1,X0)
| k1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_001) ).
fof(f163,axiom,
! [X0] :
( ~ p0(X0,X0)
| s1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_125) ).
fof(f164,axiom,
! [X2,X0,X1] :
( s1(X0)
| ~ q0(X0,X1)
| ~ s1(X2) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',rule_133) ).
fof(f221,axiom,
! [X0,X1] :
( q2(X0,c,X1)
| ~ k1(X1)
| ~ l0(c)
| ~ l2(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_183) ).
fof(f227,axiom,
! [X0] :
( s2(X0)
| ~ q2(b,X0,b)
| ~ s1(b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_189) ).
fof(f311,axiom,
! [X2,X3,X0,X1] :
( ~ q2(X2,X0,X2)
| s3(X0,X1)
| ~ s2(X0)
| ~ m0(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_273) ).
fof(f369,negated_conjecture,
~ s3(c,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f538,definition,
( spl0_50
<=> ! [X1] : ~ s1(X1) ),
introduced(definition,[new_symbols(definition,[spl0_50])],[avatar_definition]) ).
fof(f539,plain,
( ! [X1] : ~ s1(X1)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f625,definition,
( spl0_75
<=> ! [X0,X1] :
( s1(X0)
| ~ q0(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_75])],[avatar_definition]) ).
fof(f626,plain,
( ! [X0,X1] :
( ~ q0(X0,X1)
| s1(X0) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f625]) ).
fof(f627,plain,
( spl0_50
| spl0_75 ),
inference(avatar_split_clause,[],[f164,f625,f538]) ).
fof(f838,definition,
( spl0_135
<=> l0(c) ),
introduced(definition,[new_symbols(definition,[spl0_135])],[avatar_definition]) ).
fof(f839,plain,
( ~ l0(c)
| spl0_135 ),
inference(avatar_component_clause,[],[f838]) ).
fof(f1017,definition,
( spl0_184
<=> s1(b) ),
introduced(definition,[new_symbols(definition,[spl0_184])],[avatar_definition]) ).
fof(f1018,plain,
( ~ s1(b)
| spl0_184 ),
inference(avatar_component_clause,[],[f1017]) ).
fof(f1020,definition,
( spl0_185
<=> ! [X0] :
( s2(X0)
| ~ q2(b,X0,b) ) ),
introduced(definition,[new_symbols(definition,[spl0_185])],[avatar_definition]) ).
fof(f1021,plain,
( ! [X0] :
( ~ q2(b,X0,b)
| s2(X0) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1020]) ).
fof(f1022,plain,
( ~ spl0_184
| spl0_185 ),
inference(avatar_split_clause,[],[f227,f1020,f1017]) ).
fof(f1132,definition,
( spl0_217
<=> ! [X1] : ~ p0(X1,X1) ),
introduced(definition,[new_symbols(definition,[spl0_217])],[avatar_definition]) ).
fof(f1133,plain,
( ! [X1] : ~ p0(X1,X1)
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f1132]) ).
fof(f1135,definition,
( spl0_218
<=> ! [X2,X0,X3] :
( l2(X0,X0)
| ~ s1(X2)
| ~ m0(X3,X2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_218])],[avatar_definition]) ).
fof(f1136,plain,
( ! [X2,X3,X0] :
( l2(X0,X0)
| ~ s1(X2)
| ~ m0(X3,X2,X0) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f1135]) ).
fof(f1137,plain,
( spl0_217
| spl0_218 ),
inference(avatar_split_clause,[],[f171,f1135,f1132]) ).
fof(f1146,definition,
( spl0_221
<=> ! [X0,X1] :
( q2(X0,c,X1)
| ~ l2(X1,X0)
| ~ k1(X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_221])],[avatar_definition]) ).
fof(f1147,plain,
( ! [X0,X1] :
( q2(X0,c,X1)
| ~ l2(X1,X0)
| ~ k1(X1) )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f1146]) ).
fof(f1148,plain,
( ~ spl0_135
| spl0_221 ),
inference(avatar_split_clause,[],[f221,f1146,f838]) ).
fof(f1400,plain,
( $false
| spl0_135 ),
inference(forward_subsumption_resolution,[],[f839,f24]) ).
fof(f1401,plain,
spl0_135,
inference(avatar_contradiction_clause,[],[f1400]) ).
fof(f1422,plain,
( $false
| ~ spl0_217 ),
inference(resolution,[],[f1133,f14]) ).
fof(f1423,plain,
~ spl0_217,
inference(avatar_contradiction_clause,[],[f1422]) ).
fof(f1478,plain,
k1(b),
inference(resolution,[],[f39,f7]) ).
fof(f1484,plain,
k1(d),
inference(resolution,[],[f39,f34]) ).
fof(f1501,plain,
( ! [X0] : ~ p0(X0,X0)
| ~ spl0_50 ),
inference(forward_subsumption_resolution,[],[f163,f539]) ).
fof(f1502,plain,
( spl0_217
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f1501,f538,f1132]) ).
fof(f1504,plain,
s1(b),
inference(resolution,[],[f163,f14]) ).
fof(f1505,plain,
( $false
| spl0_184 ),
inference(forward_subsumption_resolution,[],[f1504,f1018]) ).
fof(f1506,plain,
spl0_184,
inference(avatar_contradiction_clause,[],[f1505]) ).
fof(f1508,plain,
( ! [X0] : s1(X0)
| ~ spl0_75 ),
inference(resolution,[],[f626,f17]) ).
fof(f1640,plain,
( ! [X2,X3,X0] :
( ~ m0(X3,X2,X0)
| l2(X0,X0) )
| ~ spl0_75
| ~ spl0_218 ),
inference(forward_subsumption_resolution,[],[f1136,f1508]) ).
fof(f1743,plain,
( ! [X0] : l2(X0,X0)
| ~ spl0_75
| ~ spl0_218 ),
inference(resolution,[],[f1640,f19]) ).
fof(f2194,plain,
( ~ l2(b,b)
| ~ k1(b)
| s2(c)
| ~ spl0_185
| ~ spl0_221 ),
inference(resolution,[],[f1147,f1021]) ).
fof(f2195,plain,
( ~ k1(b)
| s2(c)
| ~ spl0_75
| ~ spl0_185
| ~ spl0_218
| ~ spl0_221 ),
inference(forward_subsumption_resolution,[],[f2194,f1743]) ).
fof(f2197,plain,
( s2(c)
| ~ spl0_75
| ~ spl0_185
| ~ spl0_218
| ~ spl0_221 ),
inference(forward_subsumption_resolution,[],[f2195,f1478]) ).
fof(f2924,plain,
( ! [X2,X0,X1] :
( s3(c,X0)
| ~ s2(c)
| ~ m0(X1,X2,X0)
| ~ l2(X1,X1)
| ~ k1(X1) )
| ~ spl0_221 ),
inference(resolution,[],[f311,f1147]) ).
fof(f2927,plain,
( ! [X2,X0,X1] :
( s3(c,X0)
| ~ m0(X1,X2,X0)
| ~ l2(X1,X1)
| ~ k1(X1) )
| ~ spl0_75
| ~ spl0_185
| ~ spl0_218
| ~ spl0_221 ),
inference(forward_subsumption_resolution,[],[f2924,f2197]) ).
fof(f2928,plain,
( ! [X2,X0,X1] :
( ~ m0(X1,X2,X0)
| s3(c,X0)
| ~ k1(X1) )
| ~ spl0_75
| ~ spl0_185
| ~ spl0_218
| ~ spl0_221 ),
inference(forward_subsumption_resolution,[],[f2927,f1743]) ).
fof(f3287,plain,
( s3(c,c)
| ~ k1(d)
| ~ spl0_75
| ~ spl0_185
| ~ spl0_218
| ~ spl0_221 ),
inference(resolution,[],[f2928,f35]) ).
fof(f3304,plain,
( ~ k1(d)
| ~ spl0_75
| ~ spl0_185
| ~ spl0_218
| ~ spl0_221 ),
inference(forward_subsumption_resolution,[],[f3287,f369]) ).
fof(f3311,plain,
( $false
| ~ spl0_75
| ~ spl0_185
| ~ spl0_218
| ~ spl0_221 ),
inference(forward_subsumption_resolution,[],[f3304,f1484]) ).
fof(f3312,plain,
( ~ spl0_75
| ~ spl0_185
| ~ spl0_218
| ~ spl0_221 ),
inference(avatar_contradiction_clause,[],[f3311]) ).
cnf(s32,plain,
( spl0_50
| spl0_75 ),
inference(sat_conversion,[],[f627]) ).
cnf(s94,plain,
( ~ spl0_184
| spl0_185 ),
inference(sat_conversion,[],[f1022]) ).
cnf(s109,plain,
( spl0_217
| spl0_218 ),
inference(sat_conversion,[],[f1137]) ).
cnf(s111,plain,
( ~ spl0_135
| spl0_221 ),
inference(sat_conversion,[],[f1148]) ).
cnf(s159,plain,
spl0_135,
inference(sat_conversion,[],[f1401]) ).
cnf(s170,plain,
~ spl0_217,
inference(sat_conversion,[],[f1423]) ).
cnf(s204,plain,
( ~ spl0_50
| spl0_217 ),
inference(sat_conversion,[],[f1502]) ).
cnf(s205,plain,
spl0_184,
inference(sat_conversion,[],[f1506]) ).
cnf(s438,plain,
( ~ spl0_75
| ~ spl0_185
| ~ spl0_218
| ~ spl0_221 ),
inference(sat_conversion,[],[f3312]) ).
cnf(s450,plain,
~ spl0_50,
inference(rat,[],[s204,s170]) ).
cnf(s488,plain,
spl0_221,
inference(rat,[],[s111,s159]) ).
cnf(s489,plain,
spl0_218,
inference(rat,[],[s109,s170]) ).
cnf(s493,plain,
spl0_185,
inference(rat,[],[s94,s205]) ).
cnf(s494,plain,
~ spl0_75,
inference(rat,[],[s438,s488,s489,s493]) ).
cnf(s547,plain,
$false,
inference(rat,[],[s32,s494,s450]) ).
fof(f3313,plain,
$false,
inference(avatar_sat_refutation,[],[s547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN207-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.26 % Computer : n005.cluster.edu
% 0.12/0.26 % Model : x86_64 x86_64
% 0.12/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.26 % Memory : 8046.5625MB
% 0.12/0.26 % OS : Linux 6.8.0-71-generic
% 0.12/0.26 % CPULimit : 300
% 0.12/0.26 % WCLimit : 300
% 0.12/0.26 % DateTime : Mon Sep 28 15:38:17 UTC 2026
% 0.12/0.27 % CPUTime :
% 0.12/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.30 Running first-order theorem proving
% 0.27/0.30 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.78/1.23 % (882504)Input is clausal, will run a generic CNF schedule.
% 2.78/1.23 % (882646)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3076580349:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.78/1.23 % (882646)First to succeed.
% 2.78/1.23 % (882646)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-882504"
% 2.78/1.23 % (882643)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=689537716:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.78/1.23 % (882645)lrs+10_1_sil=8000:sp=occurrence:random_seed=257188513:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.78/1.23 % (882644)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2079371021:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.78/1.23 % (882642)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=1314894623:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.78/1.23 % (882647)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2612796796:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.78/1.23 % (882648)dis-21_1_sil=8000:lcm=predicate:random_seed=2672339032: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)
% 2.78/1.23 % (882647)Also succeeded, but the first one will report.
% 2.78/1.23 % (882645)Also succeeded, but the first one will report.
% 2.78/1.23 % (882648)Instruction limit reached!
% 2.78/1.23 % (882648)------------------------------
% 2.78/1.23 % (882648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.23 % (882648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.23 % (882648)CaDiCaL version: 2.1.3
% 2.78/1.23 % (882648)Termination reason: Instruction limit
% 2.78/1.23 % (882648)Termination phase: Saturation
% 2.78/1.23 % (882648)Time elapsed: 0.055 s
% 2.78/1.23 % (882648)Peak memory usage: 89 MB
% 2.78/1.23 % (882648)Instructions burned: 117 (million)
% 2.78/1.23 % (882646)Refutation found. Thanks to Tanya!
% 2.78/1.23 % SZS status Unsatisfiable for theBenchmark
% 2.78/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 2.78/1.23 % (882646)------------------------------
% 2.78/1.23 % (882646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.78/1.23 % (882646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.78/1.23 % (882646)CaDiCaL version: 2.1.3
% 2.78/1.23 % (882646)Termination reason: Refutation
% 2.78/1.23 % (882646)Time elapsed: 0.021 s
% 2.78/1.23 % (882646)Peak memory usage: 90 MB
% 2.78/1.23 % (882646)Instructions burned: 56 (million)
% 2.78/1.23 % (882646)------------------------------
% 2.78/1.23 % (882646)------------------------------
% 2.78/1.23 % (882504)Success in time 0.293 s
% 2.78/1.23 % Vampire exiting
%------------------------------------------------------------------------------