%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 : Fri Sep 25 03:33:19 PM UTC 2026
% Result : Unsatisfiable 4.91s 11.23s
% Output : Proof 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 16
% Syntax : Number of formulae : 122 ( 14 unt; 0 def)
% Number of atoms : 536 ( 400 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 508 ( 94 ~; 414 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 62 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,negated_conjecture,
( ~ element(Y,k)
| Y = n
| Y = m
| Y = k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
fof(f15_nnf,plain,
! [Y] :
( ~ element(Y,k)
| Y = n
| Y = m
| Y = k ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [Y] :
( ~ element(Y,k)
| Y = n
| Y = m
| Y = k ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( ~ element(X0,k)
| X0 = n
| X0 = m
| X0 = k ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(f11,negated_conjecture,
( element(g(Y),Y)
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).
fof(f11_nnf,plain,
! [Y] :
( element(g(Y),Y)
| element(Y,n)
| Y = n ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [Y] :
( element(g(Y),Y)
| element(Y,n)
| Y = n ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( element(g(X0),X0)
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p30,plain,
( element(k,n)
| k = n
| g(k) = n
| g(k) = m
| g(k) = k ),
inference(resolution,[status(thm)],[c15,c11]) ).
cnf(f9,negated_conjecture,
( g(Y) != Y
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).
fof(f9_nnf,plain,
! [Y] :
( g(Y) != Y
| element(Y,n)
| Y = n ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Y] :
( g(Y) != Y
| element(Y,n)
| Y = n ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( g(X0) != X0
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p63,plain,
( element(k,n)
| k = n
| element(k,n)
| k = n
| g(k) = n
| g(k) = m ),
inference(resolution,[status(thm)],[p30,c9]) ).
cnf(p69,plain,
( element(k,n)
| element(k,n)
| k = n
| g(k) = n
| g(k) = m ),
inference(factoring,[status(thm)],[p63]) ).
cnf(p71,plain,
( element(k,n)
| k = n
| g(k) = n
| g(k) = m ),
inference(factoring,[status(thm)],[p69]) ).
cnf(f8,negated_conjecture,
( g(Y) != n
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_9) ).
fof(f8_nnf,plain,
! [Y] :
( g(Y) != n
| element(Y,n)
| Y = n ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Y] :
( g(Y) != n
| element(Y,n)
| Y = n ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( g(X0) != n
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p73,plain,
( element(k,n)
| k = n
| element(k,n)
| k = n
| g(k) = m ),
inference(resolution,[status(thm)],[p71,c8]) ).
cnf(p76,plain,
( element(k,n)
| element(k,n)
| k = n
| g(k) = m ),
inference(factoring,[status(thm)],[p73]) ).
cnf(p78,plain,
( element(k,n)
| k = n
| g(k) = m ),
inference(factoring,[status(thm)],[p76]) ).
cnf(f10,negated_conjecture,
( element(Y,g(Y))
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).
fof(f10_nnf,plain,
! [Y] :
( element(Y,g(Y))
| element(Y,n)
| Y = n ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Y] :
( element(Y,g(Y))
| element(Y,n)
| Y = n ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( element(X0,g(X0))
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p80,plain,
( element(k,m)
| element(k,n)
| k = n
| element(k,n)
| k = n ),
inference(superposition,[status(thm)],[p78,c10]) ).
cnf(p88,plain,
( element(k,m)
| element(k,n)
| element(k,n)
| k = n ),
inference(factoring,[status(thm)],[p80]) ).
cnf(p92,plain,
( element(k,m)
| element(k,n)
| k = n ),
inference(factoring,[status(thm)],[p88]) ).
cnf(f7,negated_conjecture,
( ~ element(V,Y)
| ~ element(Y,V)
| V = Y
| V = m
| element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_8) ).
fof(f7_nnf,plain,
! [Y,V] :
( ~ element(V,Y)
| ~ element(Y,V)
| V = Y
| V = m
| element(Y,m)
| Y = m ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Y,V] :
( ~ element(V,Y)
| ~ element(Y,V)
| V = Y
| V = m
| element(Y,m)
| Y = m ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = m
| element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p93,plain,
( ~ element(n,k)
| n = k
| n = m
| element(k,m)
| k = m
| element(k,m)
| k = n ),
inference(resolution,[status(thm)],[p92,c7]) ).
cnf(p108,plain,
( ~ element(n,k)
| n = k
| n = m
| k = m
| element(k,m)
| k = n ),
inference(factoring,[status(thm)],[p93]) ).
cnf(f14,negated_conjecture,
( element(Y,k)
| Y != n
| Y = k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).
fof(f14_nnf,plain,
! [Y] :
( element(Y,k)
| Y != n
| Y = k ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y] :
( element(Y,k)
| Y != n
| Y = k ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( element(X0,k)
| X0 != n
| X0 = k ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p17,plain,
( element(n,k)
| n = k ),
inference(equality_resolution,[status(thm)],[c14]) ).
cnf(p110,plain,
( n = k
| n = k
| n = m
| k = m
| element(k,m)
| k = n ),
inference(resolution,[status(thm)],[p108,p17]) ).
cnf(p113,plain,
( n = k
| n = m
| k = m
| element(k,m)
| k = n ),
inference(factoring,[status(thm)],[p110]) ).
cnf(f6,negated_conjecture,
( element(f(Y),Y)
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_7) ).
fof(f6_nnf,plain,
! [Y] :
( element(f(Y),Y)
| ~ element(Y,m)
| Y = m ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Y] :
( element(f(Y),Y)
| ~ element(Y,m)
| Y = m ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( element(f(X0),X0)
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p118,plain,
( element(f(k),k)
| k = m
| n = k
| n = m
| k = m
| k = n ),
inference(resolution,[status(thm)],[p113,c6]) ).
cnf(p130,plain,
( element(f(k),k)
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p118]) ).
cnf(p133,plain,
( f(k) = n
| f(k) = m
| f(k) = k
| n = k
| n = m
| k = m
| k = n ),
inference(resolution,[status(thm)],[p130,c15]) ).
cnf(f4,negated_conjecture,
( f(Y) != Y
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_5) ).
fof(f4_nnf,plain,
! [Y] :
( f(Y) != Y
| ~ element(Y,m)
| Y = m ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [Y] :
( f(Y) != Y
| ~ element(Y,m)
| Y = m ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( f(X0) != X0
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p116,plain,
( f(k) != k
| k = m
| n = k
| n = m
| k = m
| k = n ),
inference(resolution,[status(thm)],[p113,c4]) ).
cnf(p124,plain,
( f(k) != k
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p116]) ).
cnf(p222,plain,
( n = k
| n = m
| k = m
| k = n
| f(k) = n
| f(k) = m
| n = k
| n = m
| k = m
| k = n ),
inference(resolution,[status(thm)],[p133,p124]) ).
cnf(p304,plain,
( n = k
| n = m
| k = m
| f(k) = n
| f(k) = m
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p222]) ).
cnf(p458,plain,
( n = k
| n = m
| f(k) = n
| f(k) = m
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p304]) ).
cnf(p468,plain,
( n = k
| f(k) = n
| f(k) = m
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p458]) ).
cnf(p470,plain,
( f(k) = n
| f(k) = m
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p468]) ).
cnf(f5,negated_conjecture,
( element(Y,f(Y))
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_6) ).
fof(f5_nnf,plain,
! [Y] :
( element(Y,f(Y))
| ~ element(Y,m)
| Y = m ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Y] :
( element(Y,f(Y))
| ~ element(Y,m)
| Y = m ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( element(X0,f(X0))
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p117,plain,
( element(k,f(k))
| k = m
| n = k
| n = m
| k = m
| k = n ),
inference(resolution,[status(thm)],[p113,c5]) ).
cnf(p127,plain,
( element(k,f(k))
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p117]) ).
cnf(p473,plain,
( element(k,n)
| n = k
| n = m
| k = m
| k = n
| f(k) = m
| n = k
| n = m
| k = m
| k = n ),
inference(superposition,[status(thm)],[p470,p127]) ).
cnf(p525,plain,
( element(k,n)
| n = k
| n = m
| k = m
| f(k) = m
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p473]) ).
cnf(p529,plain,
( element(k,n)
| n = k
| n = m
| f(k) = m
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p525]) ).
cnf(p532,plain,
( element(k,n)
| n = k
| f(k) = m
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p529]) ).
cnf(p538,plain,
( element(k,n)
| f(k) = m
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p532]) ).
cnf(f3,negated_conjecture,
( f(Y) != m
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_4) ).
fof(f3_nnf,plain,
! [Y] :
( f(Y) != m
| ~ element(Y,m)
| Y = m ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [Y] :
( f(Y) != m
| ~ element(Y,m)
| Y = m ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( f(X0) != m
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p115,plain,
( f(k) != m
| k = m
| n = k
| n = m
| k = m
| k = n ),
inference(resolution,[status(thm)],[p113,c3]) ).
cnf(p122,plain,
( f(k) != m
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p115]) ).
cnf(p539,plain,
( n = k
| n = m
| k = m
| k = n
| element(k,n)
| n = k
| n = m
| k = m
| k = n ),
inference(resolution,[status(thm)],[p538,p122]) ).
cnf(p540,plain,
( n = k
| n = m
| k = m
| element(k,n)
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p539]) ).
cnf(p544,plain,
( n = k
| n = m
| element(k,n)
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p540]) ).
cnf(p551,plain,
( n = k
| element(k,n)
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p544]) ).
cnf(p553,plain,
( element(k,n)
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p551]) ).
cnf(f12,negated_conjecture,
( ~ element(V,Y)
| ~ element(Y,V)
| V = Y
| V = n
| ~ element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).
fof(f12_nnf,plain,
! [Y,V] :
( ~ element(V,Y)
| ~ element(Y,V)
| V = Y
| V = n
| ~ element(Y,n)
| Y = n ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [Y,V] :
( ~ element(V,Y)
| ~ element(Y,V)
| V = Y
| V = n
| ~ element(Y,n)
| Y = n ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = n
| ~ element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p554,plain,
( ~ element(X0,k)
| ~ element(k,X0)
| X0 = k
| X0 = n
| k = n
| n = k
| n = m
| k = m
| k = n ),
inference(resolution,[status(thm)],[p553,c12]) ).
cnf(p557,plain,
( ~ element(X0,k)
| ~ element(k,X0)
| X0 = k
| X0 = n
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p554]) ).
cnf(p564,plain,
( n = k
| n = m
| k = m
| k = n
| ~ element(m,k)
| m = k
| m = n
| n = k
| n = m
| k = m
| k = n ),
inference(resolution,[status(thm)],[p557,p113]) ).
cnf(p813,plain,
( n = k
| n = m
| k = m
| ~ element(m,k)
| m = k
| m = n
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p564]) ).
cnf(p841,plain,
( n = k
| n = m
| ~ element(m,k)
| m = k
| m = n
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p813]) ).
cnf(p847,plain,
( n = k
| ~ element(m,k)
| m = k
| m = n
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p841]) ).
cnf(p849,plain,
( ~ element(m,k)
| m = k
| m = n
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p847]) ).
cnf(f13,negated_conjecture,
( element(Y,k)
| Y != m
| Y = k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).
fof(f13_nnf,plain,
! [Y] :
( element(Y,k)
| Y != m
| Y = k ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [Y] :
( element(Y,k)
| Y != m
| Y = k ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( element(X0,k)
| X0 != m
| X0 = k ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p16,plain,
( element(m,k)
| m = k ),
inference(equality_resolution,[status(thm)],[c13]) ).
cnf(p850,plain,
( m = k
| m = k
| m = n
| n = k
| n = m
| k = m
| k = n ),
inference(resolution,[status(thm)],[p849,p16]) ).
cnf(p851,plain,
( m = k
| m = n
| n = k
| n = m
| k = m
| k = n ),
inference(factoring,[status(thm)],[p850]) ).
cnf(f1,negated_conjecture,
n != k,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_2) ).
fof(f1_nnf,plain,
n != k,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
n != k,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
n != k,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p854,plain,
( n != n
| m = k
| m = n
| n = k
| n = m
| k = m ),
inference(superposition,[status(thm)],[p851,c1]) ).
cnf(p859,plain,
( m = k
| m = n
| n = k
| n = m
| k = m ),
inference(equality_resolution,[status(thm)],[p854]) ).
cnf(f2,negated_conjecture,
k != m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_3) ).
fof(f2_nnf,plain,
k != m,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
k != m,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
k != m,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p860,plain,
( m = k
| m = n
| n = k
| n = m ),
inference(resolution,[status(thm)],[p859,c2]) ).
cnf(p861,plain,
( m = k
| m = n
| n = m ),
inference(resolution,[status(thm)],[p860,c1]) ).
cnf(f0,negated_conjecture,
m != n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_1) ).
fof(f0_nnf,plain,
m != n,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
m != n,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
m != n,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p864,plain,
( m != m
| m = k
| m = n ),
inference(superposition,[status(thm)],[p861,c0]) ).
cnf(p885,plain,
( m = k
| m = n ),
inference(equality_resolution,[status(thm)],[p864]) ).
cnf(p888,plain,
( m != m
| m = n ),
inference(superposition,[status(thm)],[p885,c2]) ).
cnf(p995,plain,
m = n,
inference(equality_resolution,[status(thm)],[p888]) ).
cnf(p996,plain,
$false,
inference(resolution,[status(thm)],[p995,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/10.38 % Computer : n018.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Thu Sep 24 23:52:59 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.91/11.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.91/11.23 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------