%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN250-1 : 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 : n011.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 01:50:01 PM UTC 2026
% Result : Unsatisfiable 3.78s 1.18s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 27
% Syntax : Number of formulae : 95 ( 30 unt; 13 def)
% Number of atoms : 201 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 215 ( 109 ~; 93 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 14 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 40 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
s0(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
fof(f12,axiom,
! [X0] : m0(a,X0,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
fof(f13,axiom,
r0(e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
fof(f14,axiom,
! [X0] : p0(b,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
fof(f20,axiom,
l0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
fof(f21,axiom,
q0(b,e),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
fof(f24,axiom,
l0(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
fof(f36,axiom,
q0(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
fof(f53,axiom,
! [X2,X0,X1] :
( m1(X0,X1,X1)
| ~ l0(X2)
| ~ m0(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_015) ).
fof(f54,axiom,
! [X2,X3,X0,X1] :
( m1(X0,X1,X1)
| ~ m1(X2,X1,X0)
| ~ m1(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_016) ).
fof(f62,axiom,
! [X2,X0,X1] :
( m1(X0,a,X1)
| ~ m0(a,X2,a)
| ~ q0(X0,X1)
| ~ m1(X1,c,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_024) ).
fof(f67,axiom,
! [X0,X1] :
( m1(X0,X1,X0)
| ~ p0(X0,X1)
| ~ s0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_029) ).
fof(f73,axiom,
! [X0,X1] :
( m1(X0,X1,X0)
| ~ r0(X0)
| ~ l0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_035) ).
fof(f369,negated_conjecture,
~ m1(e,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f790,definition,
( spl0_107
<=> r0(e) ),
introduced(definition,[new_symbols(definition,[spl0_107])],[avatar_definition]) ).
fof(f791,plain,
( r0(e)
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f790]) ).
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(f1120,definition,
( spl0_189
<=> m1(b,a,e) ),
introduced(definition,[new_symbols(definition,[spl0_189])],[avatar_definition]) ).
fof(f1121,plain,
( m1(b,a,e)
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1120]) ).
fof(f1122,plain,
( ~ m1(b,a,e)
| spl0_189 ),
inference(avatar_component_clause,[],[f1120]) ).
fof(f1170,definition,
( spl0_201
<=> s0(b) ),
introduced(definition,[new_symbols(definition,[spl0_201])],[avatar_definition]) ).
fof(f1171,plain,
( s0(b)
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f1170]) ).
fof(f1239,definition,
( spl0_218
<=> ! [X1] : ~ l0(X1) ),
introduced(definition,[new_symbols(definition,[spl0_218])],[avatar_definition]) ).
fof(f1240,plain,
( ! [X1] : ~ l0(X1)
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f1239]) ).
fof(f1276,definition,
( spl0_227
<=> l0(a) ),
introduced(definition,[new_symbols(definition,[spl0_227])],[avatar_definition]) ).
fof(f1277,plain,
( l0(a)
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f1276]) ).
fof(f1373,definition,
( spl0_250
<=> q0(b,e) ),
introduced(definition,[new_symbols(definition,[spl0_250])],[avatar_definition]) ).
fof(f1374,plain,
( q0(b,e)
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f1373]) ).
fof(f1490,definition,
( spl0_278
<=> ! [X2] : ~ m0(a,X2,a) ),
introduced(definition,[new_symbols(definition,[spl0_278])],[avatar_definition]) ).
fof(f1491,plain,
( ! [X2] : ~ m0(a,X2,a)
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f1490]) ).
fof(f1493,definition,
( spl0_279
<=> ! [X0,X1] :
( m1(X0,a,X1)
| ~ m1(X1,c,X1)
| ~ q0(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_279])],[avatar_definition]) ).
fof(f1494,plain,
( ! [X0,X1] :
( m1(X0,a,X1)
| ~ m1(X1,c,X1)
| ~ q0(X0,X1) )
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f1493]) ).
fof(f1495,plain,
( spl0_278
| spl0_279 ),
inference(avatar_split_clause,[],[f62,f1493,f1490]) ).
fof(f1523,definition,
( spl0_286
<=> ! [X0,X1] :
( m1(X0,X1,X1)
| ~ m0(X1,X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_286])],[avatar_definition]) ).
fof(f1524,plain,
( ! [X0,X1] :
( m1(X0,X1,X1)
| ~ m0(X1,X1,X0) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f1523]) ).
fof(f1525,plain,
( spl0_218
| spl0_286 ),
inference(avatar_split_clause,[],[f53,f1523,f1239]) ).
fof(f1558,plain,
spl0_134,
inference(avatar_split_clause,[],[f24,f900]) ).
fof(f1559,plain,
spl0_250,
inference(avatar_split_clause,[],[f21,f1373]) ).
fof(f1560,plain,
spl0_227,
inference(avatar_split_clause,[],[f20,f1276]) ).
fof(f1562,plain,
spl0_107,
inference(avatar_split_clause,[],[f13,f790]) ).
fof(f1567,plain,
spl0_201,
inference(avatar_split_clause,[],[f5,f1170]) ).
fof(f1575,plain,
( $false
| ~ spl0_218
| ~ spl0_227 ),
inference(resolution,[],[f1240,f1277]) ).
fof(f1578,plain,
( ~ spl0_218
| ~ spl0_227 ),
inference(avatar_contradiction_clause,[],[f1575]) ).
fof(f1587,plain,
( $false
| ~ spl0_278 ),
inference(forward_subsumption_resolution,[],[f1491,f12]) ).
fof(f1588,plain,
~ spl0_278,
inference(avatar_contradiction_clause,[],[f1587]) ).
fof(f1694,plain,
( ~ m1(e,c,e)
| ~ q0(b,e)
| spl0_189
| ~ spl0_279 ),
inference(resolution,[],[f1494,f1122]) ).
fof(f1697,plain,
( ~ m1(e,c,e)
| spl0_189
| ~ spl0_250
| ~ spl0_279 ),
inference(forward_subsumption_resolution,[],[f1694,f1374]) ).
fof(f1712,definition,
( spl0_299
<=> m1(e,c,e) ),
introduced(definition,[new_symbols(definition,[spl0_299])],[avatar_definition]) ).
fof(f1714,plain,
( ~ m1(e,c,e)
| spl0_299 ),
inference(avatar_component_clause,[],[f1712]) ).
fof(f1716,plain,
( ~ spl0_299
| spl0_189
| ~ spl0_250
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f1697,f1493,f1373,f1120,f1712]) ).
fof(f1719,plain,
! [X0,X1] :
( ~ m1(X0,a,e)
| ~ m1(X0,X1,a) ),
inference(resolution,[],[f54,f369]) ).
fof(f1753,plain,
( ~ r0(e)
| ~ l0(c)
| spl0_299 ),
inference(resolution,[],[f1714,f73]) ).
fof(f1761,plain,
( ~ l0(c)
| ~ spl0_107
| spl0_299 ),
inference(forward_subsumption_resolution,[],[f1753,f791]) ).
fof(f1763,plain,
( $false
| ~ spl0_107
| ~ spl0_134
| spl0_299 ),
inference(forward_subsumption_resolution,[],[f1761,f901]) ).
fof(f1764,plain,
( ~ spl0_107
| ~ spl0_134
| spl0_299 ),
inference(avatar_contradiction_clause,[],[f1763]) ).
fof(f1766,plain,
( ! [X0] : ~ m1(b,X0,a)
| ~ spl0_189 ),
inference(resolution,[],[f1121,f1719]) ).
fof(f1769,plain,
( ! [X0,X1] :
( ~ m1(X0,a,b)
| ~ m1(X0,X1,a) )
| ~ spl0_189 ),
inference(resolution,[],[f1766,f54]) ).
fof(f1800,plain,
( ! [X0,X1] :
( ~ m1(X0,X1,a)
| ~ m1(b,c,b)
| ~ q0(X0,b) )
| ~ spl0_189
| ~ spl0_279 ),
inference(resolution,[],[f1769,f1494]) ).
fof(f1802,definition,
( spl0_308
<=> m1(b,c,b) ),
introduced(definition,[new_symbols(definition,[spl0_308])],[avatar_definition]) ).
fof(f1804,plain,
( ~ m1(b,c,b)
| spl0_308 ),
inference(avatar_component_clause,[],[f1802]) ).
fof(f1806,definition,
( spl0_309
<=> ! [X0,X1] :
( ~ m1(X0,X1,a)
| ~ q0(X0,b) ) ),
introduced(definition,[new_symbols(definition,[spl0_309])],[avatar_definition]) ).
fof(f1807,plain,
( ! [X0,X1] :
( ~ q0(X0,b)
| ~ m1(X0,X1,a) )
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f1806]) ).
fof(f1808,plain,
( ~ spl0_308
| spl0_309
| ~ spl0_189
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f1800,f1493,f1120,f1806,f1802]) ).
fof(f1811,plain,
( ~ p0(b,c)
| ~ s0(b)
| spl0_308 ),
inference(resolution,[],[f1804,f67]) ).
fof(f1818,plain,
( ~ s0(b)
| spl0_308 ),
inference(forward_subsumption_resolution,[],[f1811,f14]) ).
fof(f1821,plain,
( $false
| ~ spl0_201
| spl0_308 ),
inference(forward_subsumption_resolution,[],[f1818,f1171]) ).
fof(f1822,plain,
( ~ spl0_201
| spl0_308 ),
inference(avatar_contradiction_clause,[],[f1821]) ).
fof(f1825,plain,
( ! [X0] : ~ m1(a,X0,a)
| ~ spl0_309 ),
inference(resolution,[],[f1807,f36]) ).
fof(f1843,plain,
( ~ m0(a,a,a)
| ~ spl0_286
| ~ spl0_309 ),
inference(resolution,[],[f1825,f1524]) ).
fof(f1846,plain,
( $false
| ~ spl0_286
| ~ spl0_309 ),
inference(forward_subsumption_resolution,[],[f1843,f12]) ).
fof(f1847,plain,
( ~ spl0_286
| ~ spl0_309 ),
inference(avatar_contradiction_clause,[],[f1846]) ).
cnf(s141,plain,
( spl0_278
| spl0_279 ),
inference(sat_conversion,[],[f1495]) ).
cnf(s147,plain,
( spl0_218
| spl0_286 ),
inference(sat_conversion,[],[f1525]) ).
cnf(s158,plain,
spl0_134,
inference(sat_conversion,[],[f1558]) ).
cnf(s159,plain,
spl0_250,
inference(sat_conversion,[],[f1559]) ).
cnf(s160,plain,
spl0_227,
inference(sat_conversion,[],[f1560]) ).
cnf(s162,plain,
spl0_107,
inference(sat_conversion,[],[f1562]) ).
cnf(s167,plain,
spl0_201,
inference(sat_conversion,[],[f1567]) ).
cnf(s173,plain,
( ~ spl0_218
| ~ spl0_227 ),
inference(sat_conversion,[],[f1578]) ).
cnf(s178,plain,
~ spl0_278,
inference(sat_conversion,[],[f1588]) ).
cnf(s214,plain,
( spl0_189
| ~ spl0_250
| ~ spl0_279
| ~ spl0_299 ),
inference(sat_conversion,[],[f1716]) ).
cnf(s220,plain,
( ~ spl0_107
| ~ spl0_134
| spl0_299 ),
inference(sat_conversion,[],[f1764]) ).
cnf(s225,plain,
( ~ spl0_189
| ~ spl0_279
| ~ spl0_308
| spl0_309 ),
inference(sat_conversion,[],[f1808]) ).
cnf(s227,plain,
( ~ spl0_201
| spl0_308 ),
inference(sat_conversion,[],[f1822]) ).
cnf(s229,plain,
( ~ spl0_286
| ~ spl0_309 ),
inference(sat_conversion,[],[f1847]) ).
cnf(s235,plain,
spl0_308,
inference(rat,[],[s227,s167]) ).
cnf(s239,plain,
~ spl0_218,
inference(rat,[],[s173,s160]) ).
cnf(s240,plain,
spl0_299,
inference(rat,[],[s220,s162,s158]) ).
cnf(s244,plain,
spl0_286,
inference(rat,[],[s147,s239]) ).
cnf(s245,plain,
~ spl0_309,
inference(rat,[],[s229,s244]) ).
cnf(s250,plain,
spl0_279,
inference(rat,[],[s141,s178]) ).
cnf(s251,plain,
~ spl0_189,
inference(rat,[],[s225,s245,s235,s250]) ).
cnf(s253,plain,
$false,
inference(rat,[],[s214,s240,s159,s250,s251]) ).
fof(f1858,plain,
$false,
inference(avatar_sat_refutation,[],[s253]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN250-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 15:39:16 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.78/1.18 % (3481731)Input is clausal, will run a generic CNF schedule.
% 3.78/1.18 % (3481846)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=986426840:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.78/1.18 % (3481849)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1087278255:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.78/1.18 % (3481845)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=2163951203:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.78/1.18 % (3481848)lrs+10_1_sil=8000:sp=occurrence:random_seed=4027332720:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.78/1.18 % (3481847)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3682757201:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.78/1.18 % (3481848)Refutation not found, incomplete strategy
% 3.78/1.18 % (3481848)------------------------------
% 3.78/1.18 % (3481848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.18 % (3481848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.18 % (3481848)CaDiCaL version: 2.1.3
% 3.78/1.18 % (3481848)Termination reason: Refutation not found, incomplete strategy
% 3.78/1.18 % (3481848)Time elapsed: 0.003 s
% 3.78/1.18 % (3481848)Peak memory usage: 88 MB
% 3.78/1.18 % (3481848)Instructions burned: 2 (million)
% 3.78/1.18 % (3481850)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=286606883:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.78/1.18 % (3481850)First to succeed.
% 3.78/1.18 % (3481850)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3481731"
% 3.78/1.18 % (3481849)Also succeeded, but the first one will report.
% 3.78/1.18 % (3481851)dis-21_1_sil=8000:lcm=predicate:random_seed=200822541: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)
% 3.78/1.18 % (3481851)Instruction limit reached!
% 3.78/1.18 % (3481851)------------------------------
% 3.78/1.18 % (3481851)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.78/1.18 % (3481851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.78/1.18 % (3481851)CaDiCaL version: 2.1.3
% 3.78/1.18 % (3481851)Termination reason: Instruction limit
% 3.78/1.18 % (3481851)Termination phase: Saturation
% 3.78/1.18 % (3481851)Time elapsed: 0.096 s
% 3.78/1.18 % (3481851)Peak memory usage: 89 MB
% 3.78/1.18 % (3481851)Instructions burned: 117 (million)
% 3.78/1.18 % (3481848)------------------------------
% 3.78/1.18 % (3481848)------------------------------
% 3.78/1.18 % (3481850)Refutation found. Thanks to Tanya!
% 3.78/1.18 % SZS status Unsatisfiable for theBenchmark
% 3.78/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.41 % (3481850)------------------------------
% 0.19/1.41 % (3481850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.41 % (3481850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.41 % (3481850)CaDiCaL version: 2.1.3
% 0.19/1.41 % (3481850)Termination reason: Refutation
% 0.19/1.41 % (3481850)Time elapsed: 0.017 s
% 0.19/1.41 % (3481850)Peak memory usage: 90 MB
% 0.19/1.41 % (3481850)Instructions burned: 24 (million)
% 0.19/1.41 % (3481850)------------------------------
% 0.19/1.41 % (3481850)------------------------------
% 0.19/1.41 % (3481731)Success in time 0.512 s
% 0.19/1.41 % Vampire exiting
%------------------------------------------------------------------------------