%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 01:49:00 PM UTC 2026
% Result : Unsatisfiable 3.03s 1.12s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 81 ( 16 unt; 6 def)
% Number of atoms : 211 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 221 ( 91 ~; 124 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : equalish(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivityish) ).
fof(f2,axiom,
! [X0,X1] :
( ~ equalish(X0,X1)
| equalish(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetryish) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ equalish(X1,X2)
| ~ equalish(X0,X1)
| equalish(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivityish) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ element(X2,X0)
| ~ equalish(X0,X1)
| element(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_substitutionish1) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ element(X0,X1)
| ~ equalish(X0,X2)
| element(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_substitutionish2) ).
fof(f8,negated_conjecture,
! [X0] :
( ~ equalish(f(X0),m)
| ~ element(X0,m)
| equalish(X0,m) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_5) ).
fof(f9,negated_conjecture,
! [X0] :
( ~ equalish(f(X0),X0)
| ~ element(X0,m)
| equalish(X0,m) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_6) ).
fof(f10,negated_conjecture,
! [X0] :
( element(X0,f(X0))
| ~ element(X0,m)
| equalish(X0,m) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_7) ).
fof(f11,negated_conjecture,
! [X0] :
( element(f(X0),X0)
| ~ element(X0,m)
| equalish(X0,m) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_8) ).
fof(f12,negated_conjecture,
! [X0,X1] :
( ~ element(X0,X1)
| ~ element(X1,X0)
| equalish(X0,X1)
| equalish(X0,m)
| element(X1,m)
| equalish(X1,m) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_9) ).
fof(f19,negated_conjecture,
! [X0] :
( ~ equalish(X0,n)
| element(X0,k)
| equalish(X0,k) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
fof(f20,negated_conjecture,
! [X0] :
( ~ element(X0,k)
| equalish(X0,n)
| equalish(X0,m)
| equalish(X0,k) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_17) ).
fof(f22,negated_conjecture,
~ equalish(m,n),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_19) ).
fof(f23,negated_conjecture,
~ equalish(n,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_20) ).
fof(f26,negated_conjecture,
equalish(m,k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_23) ).
fof(f27,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| equalish(X0,X1)
| element(X1,m)
| equalish(X1,m) ),
inference(forward_subsumption_resolution,[],[f12,f4]) ).
fof(f91,definition,
( spl0_12
<=> equalish(k,m) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f93,plain,
( equalish(k,m)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f115,plain,
! [X0] :
( ~ element(X0,f(X0))
| equalish(X0,f(X0))
| element(f(X0),m)
| equalish(f(X0),m)
| ~ element(X0,m)
| equalish(X0,m) ),
inference(resolution,[],[f27,f11]) ).
fof(f120,plain,
! [X0] :
( equalish(X0,f(X0))
| element(f(X0),m)
| equalish(f(X0),m)
| ~ element(X0,m)
| equalish(X0,m) ),
inference(forward_subsumption_resolution,[],[f115,f10]) ).
fof(f122,plain,
! [X0] :
( equalish(X0,f(X0))
| element(f(X0),m)
| ~ element(X0,m)
| equalish(X0,m) ),
inference(forward_subsumption_resolution,[],[f120,f8]) ).
fof(f124,plain,
! [X0] :
( element(f(X0),m)
| ~ element(X0,m)
| equalish(X0,m) ),
inference(forward_subsumption_resolution,[],[f122,f5]) ).
fof(f131,definition,
( spl0_17
<=> equalish(n,m) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f132,plain,
( ~ equalish(n,m)
| spl0_17 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f133,plain,
( equalish(n,m)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f135,definition,
( spl0_18
<=> element(n,m) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
fof(f136,plain,
( element(n,m)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f137,plain,
( ~ element(n,m)
| spl0_18 ),
inference(avatar_component_clause,[],[f135]) ).
fof(f144,plain,
( element(n,k)
| equalish(n,k) ),
inference(resolution,[],[f1,f19]) ).
fof(f145,plain,
element(n,k),
inference(forward_subsumption_resolution,[],[f144,f23]) ).
fof(f150,plain,
equalish(k,m),
inference(resolution,[],[f2,f26]) ).
fof(f151,plain,
spl0_12,
inference(avatar_split_clause,[],[f150,f91]) ).
fof(f186,plain,
( ! [X0] :
( ~ equalish(X0,k)
| equalish(X0,m) )
| ~ spl0_12 ),
inference(resolution,[],[f93,f3]) ).
fof(f190,plain,
! [X0] :
( ~ equalish(k,X0)
| element(n,X0) ),
inference(resolution,[],[f145,f4]) ).
fof(f224,plain,
( equalish(m,n)
| ~ spl0_17 ),
inference(resolution,[],[f133,f2]) ).
fof(f225,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f224,f22]) ).
fof(f226,plain,
~ spl0_17,
inference(avatar_contradiction_clause,[],[f225]) ).
fof(f234,plain,
! [X0,X1] :
( element(f(X0),X1)
| equalish(X0,m)
| ~ equalish(m,X1)
| ~ element(X0,m) ),
inference(resolution,[],[f124,f4]) ).
fof(f269,plain,
( element(n,m)
| ~ spl0_12 ),
inference(resolution,[],[f190,f93]) ).
fof(f310,definition,
( spl0_23
<=> equalish(f(n),m) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f311,plain,
( ~ equalish(f(n),m)
| spl0_23 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f312,plain,
( equalish(f(n),m)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f324,definition,
( spl0_26
<=> equalish(f(n),n) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
fof(f325,plain,
( ~ equalish(f(n),n)
| spl0_26 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f326,plain,
( equalish(f(n),n)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f341,plain,
( $false
| ~ spl0_12
| spl0_18 ),
inference(forward_subsumption_resolution,[],[f269,f137]) ).
fof(f342,plain,
( ~ spl0_12
| spl0_18 ),
inference(avatar_contradiction_clause,[],[f341]) ).
fof(f417,plain,
( ~ element(n,m)
| equalish(n,m)
| ~ spl0_23 ),
inference(resolution,[],[f312,f8]) ).
fof(f430,definition,
( spl0_31
<=> element(f(n),k) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f431,plain,
( ~ element(f(n),k)
| spl0_31 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f432,plain,
( element(f(n),k)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f435,plain,
( equalish(n,m)
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f417,f136]) ).
fof(f436,plain,
( $false
| spl0_17
| ~ spl0_18
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f435,f132]) ).
fof(f437,plain,
( spl0_17
| ~ spl0_18
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f436]) ).
fof(f442,plain,
( ~ element(n,m)
| equalish(n,m)
| ~ spl0_26 ),
inference(resolution,[],[f326,f9]) ).
fof(f451,plain,
( equalish(n,m)
| ~ spl0_18
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f442,f136]) ).
fof(f454,plain,
( $false
| spl0_17
| ~ spl0_18
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f451,f132]) ).
fof(f455,plain,
( spl0_17
| ~ spl0_18
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f454]) ).
fof(f586,plain,
( equalish(f(n),n)
| equalish(f(n),m)
| equalish(f(n),k)
| ~ spl0_31 ),
inference(resolution,[],[f432,f20]) ).
fof(f590,plain,
( equalish(f(n),n)
| equalish(f(n),m)
| ~ spl0_12
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f586,f186]) ).
fof(f592,plain,
( equalish(f(n),m)
| ~ spl0_12
| spl0_26
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f590,f325]) ).
fof(f594,plain,
( $false
| ~ spl0_12
| spl0_23
| spl0_26
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f592,f311]) ).
fof(f595,plain,
( ~ spl0_12
| spl0_23
| spl0_26
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f594]) ).
fof(f658,plain,
( equalish(n,m)
| ~ equalish(m,k)
| ~ element(n,m)
| spl0_31 ),
inference(resolution,[],[f234,f431]) ).
fof(f666,plain,
( ~ equalish(m,k)
| ~ element(n,m)
| spl0_17
| spl0_31 ),
inference(forward_subsumption_resolution,[],[f658,f132]) ).
fof(f669,plain,
( ~ element(n,m)
| spl0_17
| spl0_31 ),
inference(forward_subsumption_resolution,[],[f666,f26]) ).
fof(f671,plain,
( $false
| spl0_17
| ~ spl0_18
| spl0_31 ),
inference(forward_subsumption_resolution,[],[f669,f136]) ).
fof(f672,plain,
( spl0_17
| ~ spl0_18
| spl0_31 ),
inference(avatar_contradiction_clause,[],[f671]) ).
cnf(s8,plain,
spl0_12,
inference(sat_conversion,[],[f151]) ).
cnf(s16,plain,
~ spl0_17,
inference(sat_conversion,[],[f226]) ).
cnf(s20,plain,
( ~ spl0_12
| spl0_18 ),
inference(sat_conversion,[],[f342]) ).
cnf(s29,plain,
( spl0_17
| ~ spl0_18
| ~ spl0_23 ),
inference(sat_conversion,[],[f437]) ).
cnf(s31,plain,
( spl0_17
| ~ spl0_18
| ~ spl0_26 ),
inference(sat_conversion,[],[f455]) ).
cnf(s41,plain,
( ~ spl0_12
| spl0_23
| spl0_26
| ~ spl0_31 ),
inference(sat_conversion,[],[f595]) ).
cnf(s43,plain,
( spl0_17
| ~ spl0_18
| spl0_31 ),
inference(sat_conversion,[],[f672]) ).
cnf(s45,plain,
spl0_18,
inference(rat,[],[s20,s8]) ).
cnf(s46,plain,
spl0_31,
inference(rat,[],[s43,s16,s45]) ).
cnf(s47,plain,
~ spl0_26,
inference(rat,[],[s31,s16,s45]) ).
cnf(s48,plain,
~ spl0_23,
inference(rat,[],[s29,s16,s45]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s41,s46,s8,s47,s48]) ).
fof(f673,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n006.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 15:19:55 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.03/1.12 % (4047800)Input is clausal, will run a generic CNF schedule.
% 3.03/1.12 % (4047805)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=63718084:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.03/1.12 % (4047806)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2157995077:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.03/1.12 % (4047807)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1443218653:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.03/1.12 % (4047808)lrs+10_1_sil=8000:sp=occurrence:random_seed=1166030449:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.03/1.12 % (4047811)dis-21_1_sil=8000:lcm=predicate:random_seed=2930691743: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)
% 3.03/1.12 % (4047809)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1757839558:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.03/1.12 % (4047810)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1380999033:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.03/1.12 % (4047808)First to succeed.
% 3.03/1.12 % (4047808)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4047800"
% 3.03/1.12 % (4047809)Also succeeded, but the first one will report.
% 3.03/1.12 % (4047811)Instruction limit reached!
% 3.03/1.12 % (4047811)------------------------------
% 3.03/1.12 % (4047811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.03/1.12 % (4047811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.12 % (4047811)CaDiCaL version: 2.1.3
% 3.03/1.12 % (4047811)Termination reason: Instruction limit
% 3.03/1.12 % (4047811)Termination phase: Saturation
% 3.03/1.12 % (4047811)Time elapsed: 0.077 s
% 3.03/1.12 % (4047811)Peak memory usage: 89 MB
% 3.03/1.12 % (4047811)Instructions burned: 118 (million)
% 3.03/1.12 % (4047810)Instruction limit reached!
% 3.03/1.12 % (4047810)------------------------------
% 3.03/1.12 % (4047810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.03/1.12 % (4047810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.03/1.12 % (4047810)CaDiCaL version: 2.1.3
% 3.03/1.12 % (4047810)Termination reason: Instruction limit
% 3.03/1.12 % (4047810)Termination phase: Saturation
% 3.03/1.12 % (4047810)Time elapsed: 0.121 s
% 3.03/1.12 % (4047810)Peak memory usage: 89 MB
% 3.03/1.12 % (4047810)Instructions burned: 181 (million)
% 3.03/1.12 % (4047819)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=729002565:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.03/1.12 % (4047819)Also succeeded, but the first one will report.
% 3.03/1.12 % (4047808)Refutation found. Thanks to Tanya!
% 3.03/1.12 % SZS status Unsatisfiable for theBenchmark
% 3.03/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.21 % (4047808)------------------------------
% 3.75/1.21 % (4047808)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.21 % (4047808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.21 % (4047808)CaDiCaL version: 2.1.3
% 3.75/1.21 % (4047808)Termination reason: Refutation
% 3.75/1.21 % (4047808)Time elapsed: 0.013 s
% 3.75/1.21 % (4047808)Peak memory usage: 89 MB
% 3.75/1.21 % (4047808)Instructions burned: 17 (million)
% 3.75/1.21 % (4047808)------------------------------
% 3.75/1.21 % (4047808)------------------------------
% 3.75/1.21 % (4047800)Success in time 0.452 s
% 3.75/1.21 % Vampire exiting
%------------------------------------------------------------------------------