%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN202-1 : 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 : n009.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 01:49:54 PM UTC 2026
% Result : Unsatisfiable 3.47s 1.23s
% Output : Refutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 71 ( 23 unt; 9 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 184 ( 90 ~; 85 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 10 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(f1,axiom,
s0(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
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(f28,axiom,
k0(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).
fof(f106,axiom,
! [X0] :
( p1(X0,X0,X0)
| ~ k0(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_068) ).
fof(f131,axiom,
! [X0,X1] :
( q1(X0,X0,X0)
| ~ q0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_093) ).
fof(f162,axiom,
! [X0,X1] :
( r1(X0)
| ~ q0(X0,X1)
| ~ s0(d)
| ~ q1(d,X1,d) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_124) ).
fof(f163,axiom,
! [X0] :
( ~ p0(X0,X0)
| s1(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_125) ).
fof(f215,axiom,
! [X0,X1] :
( q2(X0,X1,X1)
| ~ k0(X1)
| ~ p1(X0,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_177) ).
fof(f225,axiom,
! [X2,X3,X0,X1] :
( q2(X0,X1,X0)
| ~ r1(X1)
| ~ m0(X2,X3,X0)
| ~ k0(X1)
| ~ q2(X1,X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_187) ).
fof(f227,axiom,
! [X0] :
( s2(X0)
| ~ q2(b,X0,b)
| ~ s1(b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_189) ).
fof(f369,negated_conjecture,
~ s2(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f547,definition,
( spl0_52
<=> ! [X2,X1] : ~ m0(X1,X2,b) ),
introduced(definition,[new_symbols(definition,[spl0_52])],[avatar_definition]) ).
fof(f548,plain,
( ! [X2,X1] : ~ m0(X1,X2,b)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f589,definition,
( spl0_64
<=> ! [X0] :
( p1(X0,X0,X0)
| ~ k0(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_64])],[avatar_definition]) ).
fof(f590,plain,
( ! [X0] :
( p1(X0,X0,X0)
| ~ k0(X0) )
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f648,definition,
( spl0_81
<=> s0(d) ),
introduced(definition,[new_symbols(definition,[spl0_81])],[avatar_definition]) ).
fof(f649,plain,
( ~ s0(d)
| spl0_81 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f651,definition,
( spl0_82
<=> ! [X0,X1] :
( r1(X0)
| ~ q1(d,X1,d)
| ~ q0(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[spl0_82])],[avatar_definition]) ).
fof(f652,plain,
( ! [X0,X1] :
( ~ q1(d,X1,d)
| r1(X0)
| ~ q0(X0,X1) )
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f651]) ).
fof(f653,plain,
( ~ spl0_81
| spl0_82 ),
inference(avatar_split_clause,[],[f162,f651,f648]) ).
fof(f1294,definition,
( spl0_261
<=> s1(b) ),
introduced(definition,[new_symbols(definition,[spl0_261])],[avatar_definition]) ).
fof(f1295,plain,
( ~ s1(b)
| spl0_261 ),
inference(avatar_component_clause,[],[f1294]) ).
fof(f1297,definition,
( spl0_262
<=> ! [X0] :
( s2(X0)
| ~ q2(b,X0,b) ) ),
introduced(definition,[new_symbols(definition,[spl0_262])],[avatar_definition]) ).
fof(f1298,plain,
( ! [X0] :
( ~ q2(b,X0,b)
| s2(X0) )
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f1297]) ).
fof(f1299,plain,
( ~ spl0_261
| spl0_262 ),
inference(avatar_split_clause,[],[f227,f1297,f1294]) ).
fof(f1322,definition,
( spl0_269
<=> s2(e) ),
introduced(definition,[new_symbols(definition,[spl0_269])],[avatar_definition]) ).
fof(f1323,plain,
( ~ s2(e)
| spl0_269 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f1389,plain,
~ spl0_269,
inference(avatar_split_clause,[],[f369,f1322]) ).
fof(f1400,plain,
( $false
| spl0_81 ),
inference(forward_subsumption_resolution,[],[f649,f1]) ).
fof(f1401,plain,
spl0_81,
inference(avatar_contradiction_clause,[],[f1400]) ).
fof(f1438,plain,
( $false
| ~ spl0_52 ),
inference(resolution,[],[f548,f19]) ).
fof(f1439,plain,
~ spl0_52,
inference(avatar_contradiction_clause,[],[f1438]) ).
fof(f1506,plain,
s1(b),
inference(resolution,[],[f163,f14]) ).
fof(f1507,plain,
( $false
| spl0_261 ),
inference(forward_subsumption_resolution,[],[f1506,f1295]) ).
fof(f1508,plain,
spl0_261,
inference(avatar_contradiction_clause,[],[f1507]) ).
fof(f1570,plain,
spl0_64,
inference(avatar_split_clause,[],[f106,f589]) ).
fof(f2089,plain,
( ! [X0,X1] :
( r1(X0)
| ~ q0(X0,d)
| ~ q0(X1,d) )
| ~ spl0_82 ),
inference(resolution,[],[f652,f131]) ).
fof(f2111,plain,
( ! [X0,X1] :
( r1(X0)
| ~ q0(X1,d) )
| ~ spl0_82 ),
inference(forward_subsumption_resolution,[],[f2089,f17]) ).
fof(f2118,definition,
( spl0_300
<=> ! [X0] : r1(X0) ),
introduced(definition,[new_symbols(definition,[spl0_300])],[avatar_definition]) ).
fof(f2119,plain,
( ! [X0] : r1(X0)
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f2118]) ).
fof(f2143,plain,
( ! [X0] : r1(X0)
| ~ spl0_82 ),
inference(forward_subsumption_resolution,[],[f2111,f17]) ).
fof(f2148,plain,
( spl0_300
| ~ spl0_82 ),
inference(avatar_split_clause,[],[f2143,f651,f2118]) ).
fof(f3061,plain,
( ! [X2,X3,X0,X1] :
( q2(X0,X1,X0)
| ~ m0(X2,X3,X0)
| ~ k0(X1)
| ~ q2(X1,X1,X1) )
| ~ spl0_300 ),
inference(forward_subsumption_resolution,[],[f225,f2119]) ).
fof(f3088,plain,
( ! [X2,X0,X1] :
( ~ m0(X0,X1,b)
| ~ k0(X2)
| ~ q2(X2,X2,X2)
| s2(X2) )
| ~ spl0_262
| ~ spl0_300 ),
inference(resolution,[],[f3061,f1298]) ).
fof(f3095,definition,
( spl0_380
<=> ! [X2] :
( ~ k0(X2)
| s2(X2)
| ~ q2(X2,X2,X2) ) ),
introduced(definition,[new_symbols(definition,[spl0_380])],[avatar_definition]) ).
fof(f3096,plain,
( ! [X2] :
( ~ q2(X2,X2,X2)
| s2(X2)
| ~ k0(X2) )
| ~ spl0_380 ),
inference(avatar_component_clause,[],[f3095]) ).
fof(f3097,plain,
( spl0_380
| spl0_52
| ~ spl0_262
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f3088,f2118,f1297,f547,f3095]) ).
fof(f3158,plain,
( ! [X0] :
( s2(X0)
| ~ k0(X0)
| ~ k0(X0)
| ~ p1(X0,X0,X0) )
| ~ spl0_380 ),
inference(resolution,[],[f3096,f215]) ).
fof(f3162,plain,
( ! [X0] :
( s2(X0)
| ~ k0(X0)
| ~ p1(X0,X0,X0) )
| ~ spl0_380 ),
inference(duplicate_literal_removal,[],[f3158]) ).
fof(f3163,plain,
( ! [X0] :
( s2(X0)
| ~ k0(X0) )
| ~ spl0_64
| ~ spl0_380 ),
inference(forward_subsumption_resolution,[],[f3162,f590]) ).
fof(f3170,plain,
( ~ k0(e)
| ~ spl0_64
| spl0_269
| ~ spl0_380 ),
inference(resolution,[],[f3163,f1323]) ).
fof(f3171,plain,
( $false
| ~ spl0_64
| spl0_269
| ~ spl0_380 ),
inference(forward_subsumption_resolution,[],[f3170,f28]) ).
fof(f3172,plain,
( ~ spl0_64
| spl0_269
| ~ spl0_380 ),
inference(avatar_contradiction_clause,[],[f3171]) ).
cnf(s37,plain,
( ~ spl0_81
| spl0_82 ),
inference(sat_conversion,[],[f653]) ).
cnf(s139,plain,
( ~ spl0_261
| spl0_262 ),
inference(sat_conversion,[],[f1299]) ).
cnf(s153,plain,
~ spl0_269,
inference(sat_conversion,[],[f1389]) ).
cnf(s159,plain,
spl0_81,
inference(sat_conversion,[],[f1401]) ).
cnf(s178,plain,
~ spl0_52,
inference(sat_conversion,[],[f1439]) ).
cnf(s206,plain,
spl0_261,
inference(sat_conversion,[],[f1508]) ).
cnf(s226,plain,
spl0_64,
inference(sat_conversion,[],[f1570]) ).
cnf(s319,plain,
( ~ spl0_82
| spl0_300 ),
inference(sat_conversion,[],[f2148]) ).
cnf(s412,plain,
( spl0_52
| ~ spl0_262
| ~ spl0_300
| spl0_380 ),
inference(sat_conversion,[],[f3097]) ).
cnf(s420,plain,
( ~ spl0_64
| spl0_269
| ~ spl0_380 ),
inference(sat_conversion,[],[f3172]) ).
cnf(s430,plain,
~ spl0_380,
inference(rat,[],[s420,s226,s153]) ).
cnf(s434,plain,
spl0_262,
inference(rat,[],[s139,s206]) ).
cnf(s435,plain,
~ spl0_300,
inference(rat,[],[s412,s430,s178,s434]) ).
cnf(s436,plain,
~ spl0_82,
inference(rat,[],[s319,s435]) ).
cnf(s553,plain,
$false,
inference(rat,[],[s37,s436,s159]) ).
fof(f3173,plain,
$false,
inference(avatar_sat_refutation,[],[s553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN202-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.26 % Computer : n009.cluster.edu
% 0.14/0.26 % Model : x86_64 x86_64
% 0.14/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.26 % Memory : 8046.5625MB
% 0.14/0.26 % OS : Linux 6.8.0-71-generic
% 0.14/0.26 % CPULimit : 300
% 0.14/0.26 % WCLimit : 300
% 0.14/0.26 % DateTime : Mon Sep 28 15:38:30 UTC 2026
% 0.14/0.26 % CPUTime :
% 0.14/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.29 Running first-order theorem proving
% 0.26/0.29 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
% 3.47/1.23 % (3165044)Input is clausal, will run a generic CNF schedule.
% 3.47/1.23 % (3165196)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=985807787:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.47/1.23 % (3165199)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=372546460:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.47/1.23 % (3165197)lrs+10_1_sil=8000:sp=occurrence:random_seed=3564225939:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.47/1.23 % (3165195)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1162036937:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.47/1.23 % (3165198)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3017111478:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.47/1.23 % (3165194)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=1235742758:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.47/1.23 % (3165200)dis-21_1_sil=8000:lcm=predicate:random_seed=2509574562: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)
% 3.47/1.23 % (3165198)First to succeed.
% 3.47/1.23 % (3165199)Also succeeded, but the first one will report.
% 3.47/1.23 % (3165198)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3165044"
% 3.47/1.23 % (3165200)Instruction limit reached!
% 3.47/1.23 % (3165200)------------------------------
% 3.47/1.23 % (3165200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.23 % (3165200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.23 % (3165200)CaDiCaL version: 2.1.3
% 3.47/1.23 % (3165200)Termination reason: Instruction limit
% 3.47/1.23 % (3165200)Termination phase: Saturation
% 3.47/1.23 % (3165200)Time elapsed: 0.056 s
% 3.47/1.23 % (3165200)Peak memory usage: 88 MB
% 3.47/1.23 % (3165200)Instructions burned: 120 (million)
% 3.47/1.23 % (3165197)Instruction limit reached!
% 3.47/1.23 % (3165197)------------------------------
% 3.47/1.23 % (3165197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.23 % (3165197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.23 % (3165197)CaDiCaL version: 2.1.3
% 3.47/1.23 % (3165197)Termination reason: Instruction limit
% 3.47/1.23 % (3165197)Termination phase: Saturation
% 3.47/1.23 % (3165197)Time elapsed: 0.069 s
% 3.47/1.23 % (3165197)Peak memory usage: 89 MB
% 3.47/1.23 % (3165197)Instructions burned: 108 (million)
% 3.47/1.23 % (3165209)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1143494310:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 3.47/1.23 % (3165208)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=2514221228:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.47/1.23 % (3165208)Refutation not found, incomplete strategy
% 3.47/1.23 % (3165208)------------------------------
% 3.47/1.23 % (3165208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.23 % (3165208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.23 % (3165208)CaDiCaL version: 2.1.3
% 3.47/1.23 % (3165208)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.23 % (3165208)Time elapsed: 0.003 s
% 3.47/1.23 % (3165208)Peak memory usage: 87 MB
% 3.47/1.23 % (3165208)Instructions burned: 2 (million)
% 3.47/1.23 % (3165209)Refutation not found, incomplete strategy
% 3.47/1.23 % (3165209)------------------------------
% 3.47/1.23 % (3165209)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.23 % (3165209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.23 % (3165209)CaDiCaL version: 2.1.3
% 3.47/1.23 % (3165209)Termination reason: Refutation not found, incomplete strategy
% 3.47/1.23 % (3165209)Time elapsed: 0.013 s
% 3.47/1.23 % (3165209)Peak memory usage: 88 MB
% 3.47/1.23 % (3165209)Instructions burned: 22 (million)
% 3.47/1.23 % (3165198)Refutation found. Thanks to Tanya!
% 3.47/1.23 % SZS status Unsatisfiable for theBenchmark
% 3.47/1.23 % SZS output start Proof for theBenchmark
% See solution above
% 4.05/1.42 % (3165198)------------------------------
% 4.05/1.42 % (3165198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.05/1.42 % (3165198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.05/1.42 % (3165198)CaDiCaL version: 2.1.3
% 4.05/1.42 % (3165198)Termination reason: Refutation
% 4.05/1.42 % (3165198)Time elapsed: 0.035 s
% 4.05/1.42 % (3165198)Peak memory usage: 90 MB
% 4.05/1.42 % (3165198)Instructions burned: 53 (million)
% 4.05/1.42 % (3165198)------------------------------
% 4.05/1.42 % (3165198)------------------------------
% 4.05/1.42 % (3165044)Success in time 0.474 s
% 4.05/1.42 % Vampire exiting
%------------------------------------------------------------------------------