%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n014.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 02:06:27 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.28s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 89 ( 18 unt; 8 def)
% Number of atoms : 227 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 236 ( 98 ~; 130 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 29 ( 0 sgn 29 !; 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(X1,X0)
| ~ element(X0,X1)
| 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(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(f90,definition,
( spl0_12
<=> equalish(k,m) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f92,plain,
( equalish(k,m)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f114,plain,
! [X0] :
( ~ element(X0,f(X0))
| equalish(X0,f(X0))
| equalish(X0,m)
| element(f(X0),m)
| equalish(f(X0),m)
| ~ element(X0,m)
| equalish(X0,m) ),
inference(resolution,[],[f12,f11]) ).
fof(f118,plain,
! [X0] :
( ~ element(X0,f(X0))
| equalish(X0,f(X0))
| equalish(X0,m)
| element(f(X0),m)
| equalish(f(X0),m)
| ~ element(X0,m) ),
inference(duplicate_literal_removal,[],[f114]) ).
fof(f121,plain,
! [X0] :
( equalish(X0,f(X0))
| equalish(X0,m)
| element(f(X0),m)
| equalish(f(X0),m)
| ~ element(X0,m) ),
inference(forward_subsumption_resolution,[],[f118,f10]) ).
fof(f123,plain,
! [X0] :
( equalish(X0,f(X0))
| equalish(X0,m)
| element(f(X0),m)
| ~ element(X0,m) ),
inference(forward_subsumption_resolution,[],[f121,f8]) ).
fof(f152,definition,
( spl0_22
<=> equalish(n,m) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f153,plain,
( ~ equalish(n,m)
| spl0_22 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f154,plain,
( equalish(n,m)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f156,definition,
( spl0_23
<=> element(n,m) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
fof(f157,plain,
( element(n,m)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f165,plain,
( element(n,k)
| equalish(n,k) ),
inference(resolution,[],[f1,f19]) ).
fof(f166,plain,
element(n,k),
inference(forward_subsumption_resolution,[],[f165,f23]) ).
fof(f173,definition,
( spl0_25
<=> element(n,k) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
fof(f174,plain,
( element(n,k)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f177,plain,
equalish(k,m),
inference(resolution,[],[f2,f26]) ).
fof(f182,plain,
spl0_12,
inference(avatar_split_clause,[],[f177,f90]) ).
fof(f183,plain,
! [X0] :
( ~ equalish(X0,m)
| equalish(X0,k) ),
inference(resolution,[],[f3,f26]) ).
fof(f203,plain,
( ! [X0] :
( ~ equalish(X0,k)
| equalish(X0,m) )
| ~ spl0_12 ),
inference(resolution,[],[f92,f3]) ).
fof(f212,plain,
spl0_25,
inference(avatar_split_clause,[],[f166,f173]) ).
fof(f227,plain,
( ! [X0] :
( ~ equalish(k,X0)
| element(n,X0) )
| ~ spl0_25 ),
inference(resolution,[],[f174,f4]) ).
fof(f264,plain,
! [X0] :
( element(f(X0),m)
| equalish(X0,m)
| ~ element(X0,m) ),
inference(forward_subsumption_resolution,[],[f123,f5]) ).
fof(f292,plain,
( equalish(n,k)
| ~ spl0_22 ),
inference(resolution,[],[f154,f183]) ).
fof(f298,plain,
( $false
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f292,f23]) ).
fof(f299,plain,
~ spl0_22,
inference(avatar_contradiction_clause,[],[f298]) ).
fof(f320,plain,
( element(n,m)
| ~ spl0_12
| ~ spl0_25 ),
inference(resolution,[],[f227,f92]) ).
fof(f324,plain,
( spl0_23
| ~ spl0_12
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f320,f173,f90,f156]) ).
fof(f349,definition,
( spl0_28
<=> equalish(f(n),m) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f350,plain,
( ~ equalish(f(n),m)
| spl0_28 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f351,plain,
( equalish(f(n),m)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f353,definition,
( spl0_29
<=> element(f(n),m) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f354,plain,
( element(f(n),m)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f355,plain,
( ~ element(f(n),m)
| spl0_29 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f363,definition,
( spl0_31
<=> equalish(f(n),n) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f364,plain,
( ~ equalish(f(n),n)
| spl0_31 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f365,plain,
( equalish(f(n),n)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f380,plain,
( equalish(n,m)
| ~ element(n,m)
| spl0_29 ),
inference(resolution,[],[f355,f264]) ).
fof(f382,plain,
( ~ element(n,m)
| spl0_22
| spl0_29 ),
inference(forward_subsumption_resolution,[],[f380,f153]) ).
fof(f383,plain,
( $false
| spl0_22
| ~ spl0_23
| spl0_29 ),
inference(forward_subsumption_resolution,[],[f382,f157]) ).
fof(f384,plain,
( spl0_22
| ~ spl0_23
| spl0_29 ),
inference(avatar_contradiction_clause,[],[f383]) ).
fof(f385,plain,
( ~ element(n,m)
| equalish(n,m)
| ~ spl0_28 ),
inference(resolution,[],[f351,f8]) ).
fof(f394,definition,
( spl0_35
<=> equalish(f(n),k) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f396,plain,
( equalish(f(n),k)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f403,plain,
( equalish(n,m)
| ~ spl0_23
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f385,f157]) ).
fof(f404,plain,
( $false
| spl0_22
| ~ spl0_23
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[],[f403,f153]) ).
fof(f405,plain,
( spl0_22
| ~ spl0_23
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[],[f404]) ).
fof(f408,plain,
( ! [X0] :
( element(f(n),X0)
| ~ equalish(m,X0) )
| ~ spl0_29 ),
inference(resolution,[],[f354,f4]) ).
fof(f413,plain,
( ~ element(n,m)
| equalish(n,m)
| ~ spl0_31 ),
inference(resolution,[],[f365,f9]) ).
fof(f422,plain,
( equalish(n,m)
| ~ spl0_23
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f413,f157]) ).
fof(f425,plain,
( $false
| spl0_22
| ~ spl0_23
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f422,f153]) ).
fof(f426,plain,
( spl0_22
| ~ spl0_23
| ~ spl0_31 ),
inference(avatar_contradiction_clause,[],[f425]) ).
fof(f711,plain,
( ~ equalish(m,k)
| equalish(f(n),n)
| equalish(f(n),m)
| equalish(f(n),k)
| ~ spl0_29 ),
inference(resolution,[],[f408,f20]) ).
fof(f717,plain,
( ~ equalish(m,k)
| equalish(f(n),n)
| equalish(f(n),k)
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f711,f3]) ).
fof(f720,plain,
( equalish(f(n),n)
| equalish(f(n),k)
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f717,f26]) ).
fof(f721,plain,
( equalish(f(n),k)
| ~ spl0_29
| spl0_31 ),
inference(forward_subsumption_resolution,[],[f720,f364]) ).
fof(f722,plain,
( spl0_35
| ~ spl0_29
| spl0_31 ),
inference(avatar_split_clause,[],[f721,f363,f353,f394]) ).
fof(f735,plain,
( equalish(f(n),m)
| ~ spl0_12
| ~ spl0_35 ),
inference(resolution,[],[f396,f203]) ).
fof(f743,plain,
( $false
| ~ spl0_12
| spl0_28
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[],[f735,f350]) ).
fof(f744,plain,
( ~ spl0_12
| spl0_28
| ~ spl0_35 ),
inference(avatar_contradiction_clause,[],[f743]) ).
cnf(s12,plain,
spl0_12,
inference(sat_conversion,[],[f182]) ).
cnf(s14,plain,
spl0_25,
inference(sat_conversion,[],[f212]) ).
cnf(s18,plain,
~ spl0_22,
inference(sat_conversion,[],[f299]) ).
cnf(s22,plain,
( ~ spl0_12
| spl0_23
| ~ spl0_25 ),
inference(sat_conversion,[],[f324]) ).
cnf(s26,plain,
( spl0_22
| ~ spl0_23
| spl0_29 ),
inference(sat_conversion,[],[f384]) ).
cnf(s30,plain,
( spl0_22
| ~ spl0_23
| ~ spl0_28 ),
inference(sat_conversion,[],[f405]) ).
cnf(s33,plain,
( spl0_22
| ~ spl0_23
| ~ spl0_31 ),
inference(sat_conversion,[],[f426]) ).
cnf(s46,plain,
( ~ spl0_29
| spl0_31
| spl0_35 ),
inference(sat_conversion,[],[f722]) ).
cnf(s47,plain,
( ~ spl0_12
| spl0_28
| ~ spl0_35 ),
inference(sat_conversion,[],[f744]) ).
cnf(s52,plain,
spl0_23,
inference(rat,[],[s22,s14,s12]) ).
cnf(s53,plain,
~ spl0_31,
inference(rat,[],[s33,s18,s52]) ).
cnf(s54,plain,
~ spl0_28,
inference(rat,[],[s30,s18,s52]) ).
cnf(s55,plain,
spl0_29,
inference(rat,[],[s26,s18,s52]) ).
cnf(s56,plain,
~ spl0_35,
inference(rat,[],[s47,s12,s54]) ).
cnf(s57,plain,
$false,
inference(rat,[],[s46,s53,s56,s55]) ).
fof(f751,plain,
$false,
inference(avatar_sat_refutation,[],[s57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN015-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.18 % Computer : n014.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Mon Sep 28 15:20:01 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.21 Running first-order model finding
% 0.11/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.28 % (1849133)Will run a generic schedule for satisfiability detection.
% 0.11/0.28 % (1849139)% WARNING: option uhcvi not known.
% 0.11/0.28 % (1849139)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=561151455:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.11/0.28 % (1849143)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3431337637:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.28 % (1849140)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3123511899:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.28 % (1849141)dis+10_1_sil=32000:sp=arity:random_seed=2899758522:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.11/0.28 % (1849142)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1151815340:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.28 % (1849144)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2369939383:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.11/0.28 % (1849141) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1849133-1849141"...
% 0.11/0.28 % (1849138)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3671903267_2999 on theBenchmark for (2999ds/0Mi)
% 0.11/0.28 % (1849141)...printing done.
% 0.11/0.28 % (1849141)Refutation found. Thanks to Tanya!
% 0.11/0.28 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.28 % (1849141)------------------------------
% 0.11/0.28 % (1849141)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.28 % (1849141)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.28 % (1849141)CaDiCaL version: 2.1.3
% 0.11/0.28 % (1849141)Termination reason: Refutation
% 0.11/0.28 % (1849141)Time elapsed: 0.015 s
% 0.11/0.28 % (1849141)Peak memory usage: 12 MB
% 0.11/0.28 % (1849141)Instructions burned: 20 (million)
% 0.11/0.28 % (1849133)Success in time 0.053 s
% 0.11/0.28 % Vampire exiting
%------------------------------------------------------------------------------