%------------------------------------------------------------------------------
% File : Vampire---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 THM
% 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 01:49:00 PM UTC 2026
% Result : Unsatisfiable 0.66s 1.00s
% Output : Refutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 24
% Syntax : Number of formulae : 104 ( 14 unt; 8 def)
% Number of atoms : 328 ( 109 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 338 ( 114 ~; 216 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 30 ( 0 sgn 30 !; 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] :
( m != f(X0)
| ~ element(X0,m)
| m = 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] :
( f(X0) != X0
| ~ element(X0,m)
| m = 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,f(X0))
| ~ element(X0,m)
| m = 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(f(X0),X0)
| ~ element(X0,m)
| m = 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(X1,X0)
| element(X0,m)
| m = X1
| X0 = X1
| ~ element(X0,X1)
| m = 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,g(X0))
| element(X0,n)
| 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(X1,X0)
| ~ element(X0,n)
| n = X1
| X0 = X1
| ~ element(X0,X1)
| n = 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] :
( k = X0
| m != 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] :
( k = X0
| n != 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,
( n = k
| element(n,k) ),
inference(equality_resolution,[],[f28]) ).
fof(f34,definition,
( spl0_1
<=> element(n,k) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f36,plain,
( element(n,k)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f38,definition,
( spl0_2
<=> n = k ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f39,plain,
( n != k
| spl0_2 ),
inference(avatar_component_clause,[],[f38]) ).
fof(f41,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f32,f38,f34]) ).
fof(f43,definition,
( spl0_3
<=> element(m,k) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f45,plain,
( element(m,k)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl0_4
<=> m = k ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f48,plain,
( m != k
| spl0_4 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f50,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f31,f47,f43]) ).
fof(f51,plain,
~ spl0_4,
inference(avatar_split_clause,[],[f4,f47]) ).
fof(f52,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f2,f38]) ).
fof(f55,plain,
( m = f(k)
| n = f(k)
| k = f(k)
| ~ element(k,m)
| m = k ),
inference(resolution,[],[f30,f12]) ).
fof(f56,plain,
( m = g(k)
| n = g(k)
| k = g(k)
| element(k,n)
| n = k ),
inference(resolution,[],[f30,f22]) ).
fof(f57,plain,
( m = g(k)
| k = g(k)
| element(k,n)
| n = k ),
inference(forward_subsumption_resolution,[],[f56,f16]) ).
fof(f58,plain,
( n = f(k)
| k = f(k)
| ~ element(k,m)
| m = k ),
inference(forward_subsumption_resolution,[],[f55,f6]) ).
fof(f59,plain,
( m = g(k)
| element(k,n)
| n = k ),
inference(forward_subsumption_resolution,[],[f57,f18]) ).
fof(f60,plain,
( n = f(k)
| ~ element(k,m)
| m = k ),
inference(forward_subsumption_resolution,[],[f58,f8]) ).
fof(f61,plain,
( m = g(k)
| element(k,n)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f59,f39]) ).
fof(f62,plain,
( n = f(k)
| ~ element(k,m)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f60,f48]) ).
fof(f64,definition,
( spl0_5
<=> element(k,n) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f65,plain,
( ~ element(k,n)
| spl0_5 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f66,plain,
( element(k,n)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl0_6
<=> m = g(k) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f70,plain,
( m = g(k)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( spl0_5
| spl0_6
| spl0_2 ),
inference(avatar_split_clause,[],[f61,f38,f68,f64]) ).
fof(f73,definition,
( spl0_7
<=> element(k,m) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f74,plain,
( element(k,m)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f75,plain,
( ~ element(k,m)
| spl0_7 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f77,definition,
( spl0_8
<=> n = f(k) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f79,plain,
( n = f(k)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f80,plain,
( ~ spl0_7
| spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f62,f47,f77,f73]) ).
fof(f83,plain,
( element(k,m)
| m = n
| n = k
| ~ element(k,n)
| m = k
| ~ spl0_1 ),
inference(resolution,[],[f14,f36]) ).
fof(f92,plain,
( m = n
| n = k
| ~ element(k,n)
| m = k
| ~ spl0_1
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f83,f75]) ).
fof(f96,plain,
( n = k
| ~ element(k,n)
| m = k
| ~ spl0_1
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f92,f1]) ).
fof(f99,plain,
( ~ element(k,n)
| m = k
| ~ spl0_1
| spl0_2
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f96,f39]) ).
fof(f100,plain,
( ~ element(k,n)
| ~ spl0_1
| spl0_2
| spl0_4
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f99,f48]) ).
fof(f101,plain,
( ~ spl0_5
| ~ spl0_1
| spl0_2
| spl0_4
| spl0_7 ),
inference(avatar_split_clause,[],[f100,f73,f47,f38,f34,f64]) ).
fof(f105,plain,
( ~ element(k,n)
| m = n
| m = k
| ~ element(k,m)
| n = k
| ~ spl0_3 ),
inference(resolution,[],[f24,f45]) ).
fof(f119,plain,
( element(k,m)
| element(k,n)
| n = k
| ~ spl0_6 ),
inference(superposition,[],[f20,f70]) ).
fof(f122,plain,
( element(k,n)
| n = k
| ~ spl0_6
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f119,f75]) ).
fof(f123,plain,
( n = k
| spl0_5
| ~ spl0_6
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f122,f65]) ).
fof(f124,plain,
( $false
| spl0_2
| spl0_5
| ~ spl0_6
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f123,f39]) ).
fof(f125,plain,
( spl0_2
| spl0_5
| ~ spl0_6
| spl0_7 ),
inference(avatar_contradiction_clause,[],[f124]) ).
fof(f134,plain,
( element(k,n)
| ~ element(k,m)
| m = k
| ~ spl0_8 ),
inference(superposition,[],[f10,f79]) ).
fof(f137,plain,
( ~ element(k,m)
| m = k
| spl0_5
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f134,f65]) ).
fof(f138,plain,
( m = k
| spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f137,f74]) ).
fof(f139,plain,
( $false
| spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f138,f48]) ).
fof(f140,plain,
( spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f139]) ).
fof(f141,plain,
( m = n
| m = k
| ~ element(k,m)
| n = k
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f105,f66]) ).
fof(f142,plain,
( m = k
| ~ element(k,m)
| n = k
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f141,f1]) ).
fof(f143,plain,
( ~ element(k,m)
| n = k
| ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f142,f48]) ).
fof(f144,plain,
( n = k
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f143,f74]) ).
fof(f145,plain,
( $false
| spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[],[f144,f39]) ).
fof(f146,plain,
( spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f145]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f41]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f50]) ).
cnf(s3,plain,
~ spl0_4,
inference(sat_conversion,[],[f51]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f52]) ).
cnf(s5,plain,
( spl0_2
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f71]) ).
cnf(s6,plain,
( spl0_4
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f80]) ).
cnf(s7,plain,
( ~ spl0_1
| spl0_2
| spl0_4
| ~ spl0_5
| spl0_7 ),
inference(sat_conversion,[],[f101]) ).
cnf(s8,plain,
( spl0_2
| spl0_5
| ~ spl0_6
| spl0_7 ),
inference(sat_conversion,[],[f125]) ).
cnf(s9,plain,
( spl0_4
| spl0_5
| ~ spl0_7
| ~ spl0_8 ),
inference(sat_conversion,[],[f140]) ).
cnf(s10,plain,
( spl0_2
| ~ spl0_3
| spl0_4
| ~ spl0_5
| ~ spl0_7 ),
inference(sat_conversion,[],[f146]) ).
cnf(s11,plain,
spl0_3,
inference(rat,[],[s2,s3]) ).
cnf(s12,plain,
spl0_1,
inference(rat,[],[s1,s4]) ).
cnf(s13,plain,
( ~ spl0_6
| spl0_5 ),
inference(rat,[],[s9,s6,s8,s4,s3]) ).
cnf(s14,plain,
spl0_5,
inference(rat,[],[s13,s5,s4]) ).
cnf(s15,plain,
~ spl0_7,
inference(rat,[],[s10,s11,s3,s4,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s7,s12,s3,s4,s15,s14]) ).
fof(f147,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.08/0.19 % Computer : n011.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 15:20:16 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.66/1.00 % (3460416)Input is clausal, will run a generic CNF schedule.
% 0.66/1.00 % (3460518)lrs+10_1_sil=8000:sp=occurrence:random_seed=98451850:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.66/1.00 % (3460518)First to succeed.
% 0.66/1.00 % (3460518)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3460416"
% 0.66/1.00 % (3460522)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=405313427:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.66/1.00 % (3460517)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2368009932:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.66/1.00 % (3460519)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2494435419:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.66/1.00 % (3460513)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=1354190944:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.66/1.00 % (3460519)Also succeeded, but the first one will report.
% 0.66/1.00 % (3460522)Also succeeded, but the first one will report.
% 0.66/1.00 % (3460523)dis-21_1_sil=8000:lcm=predicate:random_seed=3144821580: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)
% 0.66/1.00 % (3460515)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2011521411:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.66/1.00 % (3460523)Instruction limit reached!
% 0.66/1.00 % (3460523)------------------------------
% 0.66/1.00 % (3460523)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/1.00 % (3460523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/1.00 % (3460523)CaDiCaL version: 2.1.3
% 0.66/1.00 % (3460523)Termination reason: Instruction limit
% 0.66/1.00 % (3460523)Termination phase: Saturation
% 0.66/1.00 % (3460523)Time elapsed: 0.060 s
% 0.66/1.00 % (3460523)Peak memory usage: 88 MB
% 0.66/1.00 % (3460523)Instructions burned: 119 (million)
% 0.66/1.00 % (3460518)Refutation found. Thanks to Tanya!
% 0.66/1.00 % SZS status Unsatisfiable for theBenchmark
% 0.66/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 2.72/1.18 % (3460518)------------------------------
% 2.72/1.18 % (3460518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.18 % (3460518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.18 % (3460518)CaDiCaL version: 2.1.3
% 2.72/1.18 % (3460518)Termination reason: Refutation
% 2.72/1.18 % (3460518)Time elapsed: 0.003 s
% 2.72/1.18 % (3460518)Peak memory usage: 89 MB
% 2.72/1.18 % (3460518)Instructions burned: 5 (million)
% 2.72/1.18 % (3460518)------------------------------
% 2.72/1.18 % (3460518)------------------------------
% 2.72/1.18 % (3460416)Success in time 0.315 s
% 2.72/1.18 % Vampire exiting
%------------------------------------------------------------------------------