%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYN013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 02:06:26 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 19
% Syntax : Number of formulae : 89 ( 12 unt; 3 def)
% Number of atoms : 256 ( 108 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 259 ( 92 ~; 164 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
m != n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_1) ).
fof(f2,negated_conjecture,
n != k,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_2) ).
fof(f3,negated_conjecture,
k != m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_3) ).
fof(f4,plain,
m != k,
inference(reorient_equations,[],[f3]) ).
fof(f5,negated_conjecture,
! [X0] :
( X0 = m
| ~ element(X0,m)
| f(X0) != m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_4) ).
fof(f6,plain,
! [X0] :
( ~ element(X0,m)
| m = X0
| m != f(X0) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
! [X0] :
( X0 = m
| ~ element(X0,m)
| f(X0) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).
fof(f8,plain,
! [X0] :
( ~ element(X0,m)
| m = X0
| f(X0) != X0 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
! [X0] :
( X0 = m
| ~ element(X0,m)
| element(X0,f(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_6) ).
fof(f10,plain,
! [X0] :
( ~ element(X0,m)
| m = X0
| element(X0,f(X0)) ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
! [X0] :
( X0 = m
| ~ element(X0,m)
| element(f(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).
fof(f12,plain,
! [X0] :
( ~ element(X0,m)
| m = X0
| element(f(X0),X0) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
! [X0,X1] :
( X0 = m
| element(X0,m)
| X1 = m
| X1 = X0
| ~ element(X0,X1)
| ~ element(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_8) ).
fof(f14,plain,
! [X0,X1] :
( ~ element(X0,X1)
| element(X0,m)
| m = X1
| X0 = X1
| m = X0
| ~ element(X1,X0) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
! [X0] :
( X0 = n
| element(X0,n)
| g(X0) != n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_9) ).
fof(f16,plain,
! [X0] :
( n != g(X0)
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
! [X0] :
( X0 = n
| element(X0,n)
| g(X0) != X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_10) ).
fof(f18,plain,
! [X0] :
( g(X0) != X0
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
! [X0] :
( X0 = n
| element(X0,n)
| element(X0,g(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_11) ).
fof(f20,plain,
! [X0] :
( element(X0,n)
| element(X0,g(X0))
| n = X0 ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
! [X0] :
( X0 = n
| element(X0,n)
| element(g(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_12) ).
fof(f22,plain,
! [X0] :
( element(g(X0),X0)
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
! [X0,X1] :
( X0 = n
| ~ element(X0,n)
| X1 = n
| X1 = X0
| ~ element(X0,X1)
| ~ element(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_13) ).
fof(f24,plain,
! [X0,X1] :
( ~ element(X0,n)
| n = X0
| n = X1
| X0 = X1
| ~ element(X0,X1)
| ~ element(X1,X0) ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
! [X0] :
( X0 = k
| X0 != m
| element(X0,k) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_14) ).
fof(f26,plain,
! [X0] :
( m != X0
| k = X0
| element(X0,k) ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
! [X0] :
( X0 = k
| X0 != n
| element(X0,k) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_15) ).
fof(f28,plain,
! [X0] :
( n != X0
| k = X0
| element(X0,k) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
! [X0] :
( X0 = k
| X0 = m
| X0 = n
| ~ element(X0,k) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
fof(f30,plain,
! [X0] :
( ~ element(X0,k)
| m = X0
| n = X0
| k = X0 ),
inference(reorient_equations,[],[f29]) ).
fof(f31,plain,
( m = k
| element(m,k) ),
inference(equality_resolution,[],[f26]) ).
fof(f32,plain,
element(m,k),
inference(forward_subsumption_resolution,[],[f31,f4]) ).
fof(f33,plain,
( n = k
| element(n,k) ),
inference(equality_resolution,[],[f28]) ).
fof(f34,plain,
element(n,k),
inference(forward_subsumption_resolution,[],[f33,f2]) ).
fof(f73,plain,
( m = g(k)
| n = g(k)
| k = g(k)
| element(k,n)
| n = k ),
inference(resolution,[],[f30,f22]) ).
fof(f74,plain,
( m = g(k)
| k = g(k)
| element(k,n)
| n = k ),
inference(forward_subsumption_resolution,[],[f73,f16]) ).
fof(f75,plain,
( m = g(k)
| element(k,n)
| n = k ),
inference(forward_subsumption_resolution,[],[f74,f18]) ).
fof(f76,plain,
( m = g(k)
| element(k,n) ),
inference(forward_subsumption_resolution,[],[f75,f2]) ).
fof(f78,definition,
( spl0_6
<=> element(k,n) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f79,plain,
( ~ element(k,n)
| spl0_6 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f80,plain,
( element(k,n)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl0_7
<=> m = g(k) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f84,plain,
( m = g(k)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f85,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f76,f82,f78]) ).
fof(f87,plain,
! [X0] :
( element(X0,m)
| m = n
| n = X0
| m = X0
| ~ element(n,X0)
| element(X0,g(X0))
| n = X0 ),
inference(resolution,[],[f14,f20]) ).
fof(f94,plain,
! [X0] :
( element(X0,m)
| m = n
| n = X0
| m = X0
| ~ element(n,X0)
| element(X0,g(X0)) ),
inference(duplicate_literal_removal,[],[f87]) ).
fof(f97,plain,
! [X0] :
( ~ element(n,X0)
| n = X0
| m = X0
| element(X0,m)
| element(X0,g(X0)) ),
inference(forward_subsumption_resolution,[],[f94,f1]) ).
fof(f104,plain,
( element(k,m)
| m = n
| n = k
| m = k
| ~ element(n,k)
| ~ spl0_6 ),
inference(resolution,[],[f80,f14]) ).
fof(f105,plain,
( element(k,m)
| n = k
| m = k
| ~ element(n,k)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f104,f1]) ).
fof(f106,plain,
( element(k,m)
| m = k
| ~ element(n,k)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f105,f2]) ).
fof(f107,plain,
( element(k,m)
| ~ element(n,k)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f106,f4]) ).
fof(f108,plain,
( element(k,m)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f107,f34]) ).
fof(f111,plain,
( ! [X0] :
( n = k
| n = X0
| k = X0
| ~ element(k,X0)
| ~ element(X0,k) )
| ~ spl0_6 ),
inference(resolution,[],[f24,f80]) ).
fof(f114,plain,
( ! [X0] :
( ~ element(k,X0)
| k = X0
| n = X0
| ~ element(X0,k) )
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f111,f2]) ).
fof(f127,plain,
( n = k
| m = k
| element(k,m)
| element(k,g(k)) ),
inference(resolution,[],[f97,f34]) ).
fof(f207,plain,
( m = k
| m = n
| ~ element(m,k)
| ~ spl0_6 ),
inference(resolution,[],[f114,f108]) ).
fof(f213,plain,
( m = n
| ~ element(m,k)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f207,f4]) ).
fof(f215,plain,
( ~ element(m,k)
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f213,f1]) ).
fof(f216,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f215,f32]) ).
fof(f217,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f216]) ).
fof(f218,plain,
( m = k
| element(k,m)
| element(k,g(k)) ),
inference(forward_subsumption_resolution,[],[f127,f2]) ).
fof(f224,definition,
( spl0_12
<=> element(k,m) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f225,plain,
( element(k,m)
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f224]) ).
fof(f228,plain,
( element(k,m)
| element(k,g(k)) ),
inference(forward_subsumption_resolution,[],[f218,f4]) ).
fof(f229,plain,
( element(k,m)
| element(k,m)
| ~ spl0_7 ),
inference(forward_demodulation,[],[f228,f84]) ).
fof(f230,plain,
( element(k,m)
| ~ spl0_7 ),
inference(duplicate_literal_removal,[],[f229]) ).
fof(f231,plain,
( spl0_12
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f230,f82,f224]) ).
fof(f237,plain,
( m = k
| element(f(k),k)
| ~ spl0_12 ),
inference(resolution,[],[f225,f12]) ).
fof(f238,plain,
( m = k
| element(k,f(k))
| ~ spl0_12 ),
inference(resolution,[],[f225,f10]) ).
fof(f239,plain,
( m = k
| k != f(k)
| ~ spl0_12 ),
inference(resolution,[],[f225,f8]) ).
fof(f240,plain,
( m = k
| m != f(k)
| ~ spl0_12 ),
inference(resolution,[],[f225,f6]) ).
fof(f245,plain,
( m != f(k)
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f240,f4]) ).
fof(f246,plain,
( k != f(k)
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f239,f4]) ).
fof(f247,plain,
( element(k,f(k))
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f238,f4]) ).
fof(f248,plain,
( element(f(k),k)
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f237,f4]) ).
fof(f370,plain,
( m = f(k)
| n = f(k)
| k = f(k)
| ~ spl0_12 ),
inference(resolution,[],[f248,f30]) ).
fof(f375,plain,
( n = f(k)
| k = f(k)
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f370,f245]) ).
fof(f378,plain,
( n = f(k)
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f375,f246]) ).
fof(f490,plain,
( element(k,n)
| ~ spl0_12 ),
inference(superposition,[],[f247,f378]) ).
fof(f493,plain,
( $false
| spl0_6
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[],[f490,f79]) ).
fof(f494,plain,
( spl0_6
| ~ spl0_12 ),
inference(avatar_contradiction_clause,[],[f493]) ).
cnf(s5,plain,
( spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f85]) ).
cnf(s7,plain,
~ spl0_6,
inference(sat_conversion,[],[f217]) ).
cnf(s9,plain,
( ~ spl0_7
| spl0_12 ),
inference(sat_conversion,[],[f231]) ).
cnf(s17,plain,
( spl0_6
| ~ spl0_12 ),
inference(sat_conversion,[],[f494]) ).
cnf(s18,plain,
~ spl0_12,
inference(rat,[],[s17,s7]) ).
cnf(s19,plain,
~ spl0_7,
inference(rat,[],[s9,s18]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s5,s19,s7]) ).
fof(f495,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 15:20:30 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.26 % (3461403)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (3461413)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=882463628:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.26 % (3461409)% WARNING: option uhcvi not known.
% 0.09/0.26 % (3461413) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3461403-3461413"...
% 0.09/0.26 % (3461408)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=775487108_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.26 % (3461409)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2941940506:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.26 % (3461412)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=316231683:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.26 % (3461410)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1570644446:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.26 % (3461411)dis+10_1_sil=32000:sp=arity:random_seed=2190319675:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.26 % (3461413)...printing done.
% 0.09/0.26 % (3461414)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2363999623:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.26 % Detected minimum model sizes of [3]
% 0.09/0.26 % Detected maximum model sizes of [max]
% 0.09/0.26 % (3461413)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (3461413)------------------------------
% 0.09/0.26 % (3461413)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (3461413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (3461413)CaDiCaL version: 2.1.3
% 0.09/0.26 % (3461413)Termination reason: Refutation
% 0.09/0.26 % (3461413)Time elapsed: 0.007 s
% 0.09/0.26 % (3461413)Peak memory usage: 12 MB
% 0.09/0.26 % (3461413)Instructions burned: 18 (million)
% 0.09/0.26 % (3461403)Success in time 0.033 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------