%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN273-1 : 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 : n017.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 01:50:04 PM UTC 2026
% Result : Unsatisfiable 3.80s 1.37s
% Output : Refutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 76 ( 21 unt; 9 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 176 ( 92 ~; 75 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 20 ( 19 usr; 10 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 53 ( 0 sgn 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13,axiom,
r0(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
fof(f24,axiom,
l0(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
fof(f26,axiom,
n0(d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
fof(f33,axiom,
q0(d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_33) ).
fof(f39,axiom,
! [X0,X1] :
( k1(X0)
| ~ n0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_001) ).
fof(f73,axiom,
! [X0,X1] :
( m1(X0,X1,X0)
| ~ r0(X0)
| ~ l0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_035) ).
fof(f131,axiom,
! [X0,X1] :
( q1(X0,X0,X0)
| ~ q0(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_093) ).
fof(f165,axiom,
! [X2,X3,X0,X1] :
( ~ k2(X3,X1)
| ~ m1(X2,X1,X0)
| ~ k1(X3)
| k2(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_127) ).
fof(f167,axiom,
! [X0,X1] :
( k2(X0,X0)
| ~ q1(X1,X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_129) ).
fof(f232,axiom,
! [X0,X1] :
( ~ k2(X1,X0)
| k3(X0,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_194) ).
fof(f240,axiom,
! [X2,X3,X0,X1,X4] :
( k3(X0,X0,X1)
| ~ q0(X2,X1)
| ~ k2(X0,X3)
| ~ k3(X1,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_202) ).
fof(f325,axiom,
! [X0,X1] :
( ~ k3(X0,X0,X1)
| p4(X0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_287) ).
fof(f369,negated_conjecture,
~ p4(e,c,e),
file('/export/starexec/sandbox2/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(f1116,definition,
( spl0_188
<=> k1(c) ),
introduced(definition,[new_symbols(definition,[spl0_188])],[avatar_definition]) ).
fof(f1117,plain,
( k1(c)
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1116]) ).
fof(f1118,plain,
( ~ k1(c)
| spl0_188 ),
inference(avatar_component_clause,[],[f1116]) ).
fof(f1558,plain,
spl0_134,
inference(avatar_split_clause,[],[f24,f900]) ).
fof(f1562,plain,
spl0_107,
inference(avatar_split_clause,[],[f13,f790]) ).
fof(f1863,plain,
( ! [X0] : ~ n0(X0,c)
| spl0_188 ),
inference(resolution,[],[f1118,f39]) ).
fof(f1866,plain,
( $false
| spl0_188 ),
inference(resolution,[],[f1863,f26]) ).
fof(f1867,plain,
spl0_188,
inference(avatar_contradiction_clause,[],[f1866]) ).
fof(f1922,definition,
( spl0_310
<=> ! [X0] : ~ q1(X0,c,c) ),
introduced(definition,[new_symbols(definition,[spl0_310])],[avatar_definition]) ).
fof(f1923,plain,
( ! [X0] : ~ q1(X0,c,c)
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f1922]) ).
fof(f1953,plain,
! [X0,X1] :
( k3(X0,X0,X0)
| ~ q1(X1,X0,X0) ),
inference(resolution,[],[f232,f167]) ).
fof(f2007,definition,
( spl0_311
<=> ! [X0] : ~ q0(X0,c) ),
introduced(definition,[new_symbols(definition,[spl0_311])],[avatar_definition]) ).
fof(f2008,plain,
( ! [X0] : ~ q0(X0,c)
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f2007]) ).
fof(f2325,definition,
( spl0_325
<=> k2(c,c) ),
introduced(definition,[new_symbols(definition,[spl0_325])],[avatar_definition]) ).
fof(f2326,plain,
( k2(c,c)
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f2325]) ).
fof(f2327,plain,
( ~ k2(c,c)
| spl0_325 ),
inference(avatar_component_clause,[],[f2325]) ).
fof(f2329,plain,
( ! [X0] : ~ q1(X0,c,c)
| spl0_325 ),
inference(resolution,[],[f2327,f167]) ).
fof(f2330,plain,
( spl0_310
| spl0_325 ),
inference(avatar_split_clause,[],[f2329,f2325,f1922]) ).
fof(f2331,plain,
( ! [X0] : ~ q0(X0,c)
| ~ spl0_310 ),
inference(resolution,[],[f1923,f131]) ).
fof(f2352,plain,
( spl0_311
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f2331,f1922,f2007]) ).
fof(f2466,plain,
( ! [X0,X1] :
( ~ m1(X0,c,X1)
| ~ k1(c)
| k2(X1,c) )
| ~ spl0_325 ),
inference(resolution,[],[f165,f2326]) ).
fof(f2467,plain,
( ! [X0,X1] :
( k2(X1,c)
| ~ m1(X0,c,X1) )
| ~ spl0_188
| ~ spl0_325 ),
inference(forward_subsumption_resolution,[],[f2466,f1117]) ).
fof(f2596,plain,
! [X2,X3,X0,X1,X4] :
( p4(X2,X1,X2)
| ~ k2(X2,X3)
| ~ k3(X1,X4,X3)
| ~ q0(X0,X1) ),
inference(resolution,[],[f240,f325]) ).
fof(f3060,plain,
! [X2,X0,X1] :
( ~ k2(e,X0)
| ~ k3(c,X1,X0)
| ~ q0(X2,c) ),
inference(resolution,[],[f2596,f369]) ).
fof(f3064,definition,
( spl0_375
<=> ! [X0,X1] :
( ~ k2(e,X0)
| ~ k3(c,X1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_375])],[avatar_definition]) ).
fof(f3065,plain,
( ! [X0,X1] :
( ~ k2(e,X0)
| ~ k3(c,X1,X0) )
| ~ spl0_375 ),
inference(avatar_component_clause,[],[f3064]) ).
fof(f3066,plain,
( spl0_311
| spl0_375 ),
inference(avatar_split_clause,[],[f3060,f3064,f2007]) ).
fof(f3067,plain,
( $false
| ~ spl0_311 ),
inference(resolution,[],[f2008,f33]) ).
fof(f3068,plain,
~ spl0_311,
inference(avatar_contradiction_clause,[],[f3067]) ).
fof(f3078,plain,
( ! [X0,X1] :
( ~ k3(c,X0,c)
| ~ m1(X1,c,e) )
| ~ spl0_188
| ~ spl0_325
| ~ spl0_375 ),
inference(resolution,[],[f3065,f2467]) ).
fof(f3080,definition,
( spl0_376
<=> ! [X1] : ~ m1(X1,c,e) ),
introduced(definition,[new_symbols(definition,[spl0_376])],[avatar_definition]) ).
fof(f3081,plain,
( ! [X1] : ~ m1(X1,c,e)
| ~ spl0_376 ),
inference(avatar_component_clause,[],[f3080]) ).
fof(f3083,definition,
( spl0_377
<=> ! [X0] : ~ k3(c,X0,c) ),
introduced(definition,[new_symbols(definition,[spl0_377])],[avatar_definition]) ).
fof(f3084,plain,
( ! [X0] : ~ k3(c,X0,c)
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f3083]) ).
fof(f3085,plain,
( spl0_376
| spl0_377
| ~ spl0_188
| ~ spl0_325
| ~ spl0_375 ),
inference(avatar_split_clause,[],[f3078,f3064,f2325,f1116,f3083,f3080]) ).
fof(f3176,plain,
( ~ r0(e)
| ~ l0(c)
| ~ spl0_376 ),
inference(resolution,[],[f3081,f73]) ).
fof(f3179,plain,
( ~ l0(c)
| ~ spl0_107
| ~ spl0_376 ),
inference(forward_subsumption_resolution,[],[f3176,f791]) ).
fof(f3181,plain,
( $false
| ~ spl0_107
| ~ spl0_134
| ~ spl0_376 ),
inference(forward_subsumption_resolution,[],[f3179,f901]) ).
fof(f3182,plain,
( ~ spl0_107
| ~ spl0_134
| ~ spl0_376 ),
inference(avatar_contradiction_clause,[],[f3181]) ).
fof(f3194,plain,
( ! [X0] : ~ q1(X0,c,c)
| ~ spl0_377 ),
inference(resolution,[],[f3084,f1953]) ).
fof(f3206,plain,
( spl0_310
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f3194,f3083,f1922]) ).
cnf(s158,plain,
spl0_134,
inference(sat_conversion,[],[f1558]) ).
cnf(s162,plain,
spl0_107,
inference(sat_conversion,[],[f1562]) ).
cnf(s258,plain,
spl0_188,
inference(sat_conversion,[],[f1867]) ).
cnf(s320,plain,
( spl0_310
| spl0_325 ),
inference(sat_conversion,[],[f2330]) ).
cnf(s326,plain,
( ~ spl0_310
| spl0_311 ),
inference(sat_conversion,[],[f2352]) ).
cnf(s432,plain,
( spl0_311
| spl0_375 ),
inference(sat_conversion,[],[f3066]) ).
cnf(s433,plain,
~ spl0_311,
inference(sat_conversion,[],[f3068]) ).
cnf(s434,plain,
( ~ spl0_188
| ~ spl0_325
| ~ spl0_375
| spl0_376
| spl0_377 ),
inference(sat_conversion,[],[f3085]) ).
cnf(s453,plain,
( ~ spl0_107
| ~ spl0_134
| ~ spl0_376 ),
inference(sat_conversion,[],[f3182]) ).
cnf(s460,plain,
( spl0_310
| ~ spl0_377 ),
inference(sat_conversion,[],[f3206]) ).
cnf(s464,plain,
spl0_375,
inference(rat,[],[s432,s433]) ).
cnf(s472,plain,
~ spl0_310,
inference(rat,[],[s326,s433]) ).
cnf(s473,plain,
~ spl0_377,
inference(rat,[],[s460,s472]) ).
cnf(s474,plain,
spl0_325,
inference(rat,[],[s320,s472]) ).
cnf(s480,plain,
spl0_376,
inference(rat,[],[s434,s473,s474,s464,s258]) ).
cnf(s493,plain,
~ spl0_134,
inference(rat,[],[s453,s480,s162]) ).
cnf(s497,plain,
$false,
inference(rat,[],[s158,s493]) ).
fof(f3212,plain,
$false,
inference(avatar_sat_refutation,[],[s497]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN273-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n017.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
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 15:35:41 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 3.80/1.37 % (3649834)Input is clausal, will run a generic CNF schedule.
% 3.80/1.37 % (3649859)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1218428772:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.80/1.37 % (3649854)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=1767731056:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.80/1.37 % (3649855)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3425129456:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.80/1.37 % (3649857)lrs+10_1_sil=8000:sp=occurrence:random_seed=4271495833:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.80/1.37 % (3649860)dis-21_1_sil=8000:lcm=predicate:random_seed=2408244679: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)
% 3.80/1.37 % (3649856)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=31926220:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.80/1.37 % (3649857)Refutation not found, incomplete strategy
% 3.80/1.37 % (3649857)------------------------------
% 3.80/1.37 % (3649857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.37 % (3649857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.37 % (3649857)CaDiCaL version: 2.1.3
% 3.80/1.37 % (3649857)Termination reason: Refutation not found, incomplete strategy
% 3.80/1.37 % (3649857)Time elapsed: 0.011 s
% 3.80/1.37 % (3649857)Peak memory usage: 88 MB
% 3.80/1.37 % (3649857)Instructions burned: 13 (million)
% 3.80/1.37 % (3649858)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1583275146:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.80/1.37 % (3649859)First to succeed.
% 3.80/1.37 % (3649859)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3649834"
% 3.80/1.37 % (3649858)Also succeeded, but the first one will report.
% 3.80/1.37 % (3649860)Instruction limit reached!
% 3.80/1.37 % (3649860)------------------------------
% 3.80/1.37 % (3649860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.37 % (3649860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.37 % (3649860)CaDiCaL version: 2.1.3
% 3.80/1.37 % (3649860)Termination reason: Instruction limit
% 3.80/1.37 % (3649860)Termination phase: Saturation
% 3.80/1.37 % (3649860)Time elapsed: 0.055 s
% 3.80/1.37 % (3649860)Peak memory usage: 89 MB
% 3.80/1.37 % (3649860)Instructions burned: 118 (million)
% 3.80/1.37 % (3649872)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=21173942:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.80/1.37 % (3649872)Refutation not found, incomplete strategy
% 3.80/1.37 % (3649872)------------------------------
% 3.80/1.37 % (3649872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.37 % (3649872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.37 % (3649872)CaDiCaL version: 2.1.3
% 3.80/1.37 % (3649872)Termination reason: Refutation not found, incomplete strategy
% 3.80/1.37 % (3649872)Time elapsed: 0.002 s
% 3.80/1.37 % (3649872)Peak memory usage: 88 MB
% 3.80/1.37 % (3649872)Instructions burned: 2 (million)
% 3.80/1.37 % (3649857)------------------------------
% 3.80/1.37 % (3649857)------------------------------
% 3.80/1.37 % (3649859)Refutation found. Thanks to Tanya!
% 3.80/1.37 % SZS status Unsatisfiable for theBenchmark
% 3.80/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 3.80/1.37 % (3649859)------------------------------
% 3.80/1.37 % (3649859)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.80/1.37 % (3649859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.80/1.37 % (3649859)CaDiCaL version: 2.1.3
% 3.80/1.37 % (3649859)Termination reason: Refutation
% 3.80/1.37 % (3649859)Time elapsed: 0.046 s
% 3.80/1.37 % (3649859)Peak memory usage: 90 MB
% 3.80/1.37 % (3649859)Instructions burned: 68 (million)
% 3.80/1.37 % (3649859)------------------------------
% 3.80/1.37 % (3649859)------------------------------
% 3.80/1.37 % (3649834)Success in time 0.439 s
% 3.80/1.37 % Vampire exiting
%------------------------------------------------------------------------------