%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN014-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 13.30s 2.41s
% Output : Proof 13.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 15
% Syntax : Number of formulae : 176 ( 8 unt; 0 def)
% Number of atoms : 594 ( 465 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 544 ( 126 ~; 418 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 62 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,negated_conjecture,
( m = k
| n = k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_2) ).
fof(f1_nnf,plain,
( m = k
| n = k ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
( m = k
| n = k ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( m = k
| n = k ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f12,negated_conjecture,
( element(g(Y),Y)
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).
fof(f12_nnf,plain,
! [Y] :
( element(g(Y),Y)
| element(Y,n)
| Y = n ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [Y] :
( element(g(Y),Y)
| element(Y,n)
| Y = n ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( element(g(X0),X0)
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(f3,negated_conjecture,
( ~ element(Y,j)
| Y = k
| Y = j ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_4) ).
fof(f3_nnf,plain,
! [Y] :
( ~ element(Y,j)
| Y = k
| Y = j ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [Y] :
( ~ element(Y,j)
| Y = k
| Y = j ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ element(X0,j)
| X0 = k
| X0 = j ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p39,plain,
( g(j) = k
| g(j) = j
| element(j,n)
| j = n ),
inference(resolution,[status(thm)],[c12,c3]) ).
cnf(f10,negated_conjecture,
( g(Y) != Y
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).
fof(f10_nnf,plain,
! [Y] :
( g(Y) != Y
| element(Y,n)
| Y = n ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Y] :
( g(Y) != Y
| element(Y,n)
| Y = n ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( g(X0) != X0
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p112,plain,
( element(j,n)
| j = n
| g(j) = k
| element(j,n)
| j = n ),
inference(resolution,[status(thm)],[p39,c10]) ).
cnf(p132,plain,
( element(j,n)
| g(j) = k
| element(j,n)
| j = n ),
inference(factoring,[status(thm)],[p112]) ).
cnf(p134,plain,
( g(j) = k
| element(j,n)
| j = n ),
inference(factoring,[status(thm)],[p132]) ).
cnf(f9,negated_conjecture,
( g(Y) != n
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).
fof(f9_nnf,plain,
! [Y] :
( g(Y) != n
| element(Y,n)
| Y = n ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Y] :
( g(Y) != n
| element(Y,n)
| Y = n ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( g(X0) != n
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p136,plain,
( k != n
| element(j,n)
| j = n
| element(j,n)
| j = n ),
inference(superposition,[status(thm)],[p134,c9]) ).
cnf(p141,plain,
( k != n
| element(j,n)
| element(j,n)
| j = n ),
inference(factoring,[status(thm)],[p136]) ).
cnf(p143,plain,
( k != n
| element(j,n)
| j = n ),
inference(factoring,[status(thm)],[p141]) ).
cnf(p144,plain,
( n != n
| element(j,n)
| j = n
| m = k ),
inference(superposition,[status(thm)],[c1,p143]) ).
cnf(p145,plain,
( element(j,n)
| j = n
| m = k ),
inference(equality_resolution,[status(thm)],[p144]) ).
cnf(f16,negated_conjecture,
( ~ element(Y,k)
| Y = n
| Y = m
| Y = k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_17) ).
fof(f16_nnf,plain,
! [Y] :
( ~ element(Y,k)
| Y = n
| Y = m
| Y = k ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [Y] :
( ~ element(Y,k)
| Y = n
| Y = m
| Y = k ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ element(X0,k)
| X0 = n
| X0 = m
| X0 = k ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p52,plain,
( ~ element(X0,n)
| X0 = n
| X0 = m
| X0 = k
| m = k ),
inference(superposition,[status(thm)],[c1,c16]) ).
cnf(p152,plain,
( j = n
| j = m
| j = k
| m = k
| j = n
| m = k ),
inference(resolution,[status(thm)],[p145,p52]) ).
cnf(p267,plain,
( j = n
| j = m
| j = k
| j = n
| m = k ),
inference(factoring,[status(thm)],[p152]) ).
cnf(p269,plain,
( j = m
| j = k
| j = n
| m = k ),
inference(factoring,[status(thm)],[p267]) ).
cnf(p270,plain,
( n != k
| j = m
| j = n
| m = k ),
inference(equality_factoring,[status(thm)],[p269]) ).
cnf(p286,plain,
( m = k
| j = m
| j = n
| m = k ),
inference(resolution,[status(thm)],[p270,c1]) ).
cnf(p306,plain,
( j = m
| j = n
| m = k ),
inference(factoring,[status(thm)],[p286]) ).
cnf(p309,plain,
( ~ element(X0,n)
| X0 = k
| X0 = j
| j = m
| m = k ),
inference(superposition,[status(thm)],[p306,c3]) ).
cnf(p433,plain,
( ~ element(m,n)
| m = j
| j = m
| m = k ),
inference(factoring,[status(thm)],[p309]) ).
cnf(f14,negated_conjecture,
( element(Y,k)
| Y != m
| Y = k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).
fof(f14_nnf,plain,
! [Y] :
( element(Y,k)
| Y != m
| Y = k ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Y] :
( element(Y,k)
| Y != m
| Y = k ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( element(X0,k)
| X0 != m
| X0 = k ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p23,plain,
( element(m,k)
| m = k ),
inference(equality_resolution,[status(thm)],[c14]) ).
cnf(p24,plain,
( element(m,n)
| m = k
| m = k ),
inference(superposition,[status(thm)],[c1,p23]) ).
cnf(p29,plain,
( element(m,n)
| m = k ),
inference(factoring,[status(thm)],[p24]) ).
cnf(p437,plain,
( m = k
| m = j
| j = m
| m = k ),
inference(resolution,[status(thm)],[p433,p29]) ).
cnf(p442,plain,
( m = j
| j = m
| m = k ),
inference(factoring,[status(thm)],[p437]) ).
cnf(p443,plain,
( k != j
| j = m
| m = k ),
inference(equality_factoring,[status(thm)],[p442]) ).
cnf(p457,plain,
( k != n
| j = m
| m = k
| j = m
| m = k ),
inference(superposition,[status(thm)],[p306,p443]) ).
cnf(p552,plain,
( k != n
| j = m
| j = m
| m = k ),
inference(factoring,[status(thm)],[p457]) ).
cnf(p554,plain,
( k != n
| j = m
| m = k ),
inference(factoring,[status(thm)],[p552]) ).
cnf(p555,plain,
( n != n
| j = m
| m = k
| m = k ),
inference(superposition,[status(thm)],[c1,p554]) ).
cnf(p557,plain,
( n != n
| j = m
| m = k ),
inference(factoring,[status(thm)],[p555]) ).
cnf(p558,plain,
( j = m
| m = k ),
inference(equality_resolution,[status(thm)],[p557]) ).
cnf(p21,plain,
( j != k
| ~ element(X0,j)
| X0 = j ),
inference(equality_factoring,[status(thm)],[c3]) ).
cnf(f2,negated_conjecture,
( element(Y,j)
| Y != k
| Y = j ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_3) ).
fof(f2_nnf,plain,
! [Y] :
( element(Y,j)
| Y != k
| Y = j ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Y] :
( element(Y,j)
| Y != k
| Y = j ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( element(X0,j)
| X0 != k
| X0 = j ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p17,plain,
( element(k,j)
| k = j ),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p26,plain,
( k = j
| j != k
| k = j ),
inference(resolution,[status(thm)],[p21,p17]) ).
cnf(p30,plain,
( j != k
| k = j ),
inference(factoring,[status(thm)],[p26]) ).
cnf(p31,plain,
( j != n
| k = j
| m = k ),
inference(superposition,[status(thm)],[c1,p30]) ).
cnf(p316,plain,
( k = j
| m = k
| j = m
| m = k ),
inference(resolution,[status(thm)],[p306,p31]) ).
cnf(p333,plain,
( k = j
| j = m
| m = k ),
inference(factoring,[status(thm)],[p316]) ).
cnf(p334,plain,
( element(k,m)
| k = j
| k = j
| m = k ),
inference(superposition,[status(thm)],[p333,p17]) ).
cnf(p349,plain,
( element(k,m)
| k = j
| m = k ),
inference(factoring,[status(thm)],[p334]) ).
cnf(f7,negated_conjecture,
( element(f(Y),Y)
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_8) ).
fof(f7_nnf,plain,
! [Y] :
( element(f(Y),Y)
| ~ element(Y,m)
| Y = m ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Y] :
( element(f(Y),Y)
| ~ element(Y,m)
| Y = m ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( element(f(X0),X0)
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p354,plain,
( element(f(k),k)
| k = m
| k = j
| m = k ),
inference(resolution,[status(thm)],[p349,c7]) ).
cnf(p378,plain,
( j != m
| element(f(k),k)
| k = j
| m = k ),
inference(equality_factoring,[status(thm)],[p354]) ).
cnf(p569,plain,
( element(f(k),k)
| k = j
| m = k
| m = k ),
inference(resolution,[status(thm)],[p558,p378]) ).
cnf(p583,plain,
( element(f(k),k)
| k = j
| m = k ),
inference(factoring,[status(thm)],[p569]) ).
cnf(p50,plain,
( n != k
| ~ element(X0,k)
| X0 = n
| X0 = m ),
inference(equality_factoring,[status(thm)],[c16]) ).
cnf(p592,plain,
( n != k
| f(k) = n
| f(k) = m
| k = j
| m = k ),
inference(resolution,[status(thm)],[p583,p50]) ).
cnf(p903,plain,
( m = k
| f(k) = n
| f(k) = m
| k = j
| m = k ),
inference(resolution,[status(thm)],[p592,c1]) ).
cnf(p930,plain,
( f(k) = n
| f(k) = m
| k = j
| m = k ),
inference(factoring,[status(thm)],[p903]) ).
cnf(f5,negated_conjecture,
( f(Y) != Y
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_6) ).
fof(f5_nnf,plain,
! [Y] :
( f(Y) != Y
| ~ element(Y,m)
| Y = m ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [Y] :
( f(Y) != Y
| ~ element(Y,m)
| Y = m ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( f(X0) != X0
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p352,plain,
( f(k) != k
| k = m
| k = j
| m = k ),
inference(resolution,[status(thm)],[p349,c5]) ).
cnf(p373,plain,
( f(k) != n
| k = m
| k = j
| m = k
| m = k ),
inference(superposition,[status(thm)],[c1,p352]) ).
cnf(p682,plain,
( f(k) != n
| k = m
| k = j
| m = k ),
inference(factoring,[status(thm)],[p373]) ).
cnf(p950,plain,
( k = m
| k = j
| m = k
| f(k) = m
| k = j
| m = k ),
inference(resolution,[status(thm)],[p930,p682]) ).
cnf(p2370,plain,
( k = m
| k = j
| f(k) = m
| k = j
| m = k ),
inference(factoring,[status(thm)],[p950]) ).
cnf(p2377,plain,
( k = m
| f(k) = m
| k = j
| m = k ),
inference(factoring,[status(thm)],[p2370]) ).
cnf(p2378,plain,
( j != m
| f(k) = m
| k = j
| m = k ),
inference(equality_factoring,[status(thm)],[p2377]) ).
cnf(p2399,plain,
( m = k
| f(k) = m
| k = j
| m = k ),
inference(resolution,[status(thm)],[p2378,p558]) ).
cnf(p2403,plain,
( f(k) = m
| k = j
| m = k ),
inference(factoring,[status(thm)],[p2399]) ).
cnf(f4,negated_conjecture,
( f(Y) != m
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_5) ).
fof(f4_nnf,plain,
! [Y] :
( f(Y) != m
| ~ element(Y,m)
| Y = m ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [Y] :
( f(Y) != m
| ~ element(Y,m)
| Y = m ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( f(X0) != m
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p351,plain,
( f(k) != m
| k = m
| k = j
| m = k ),
inference(resolution,[status(thm)],[p349,c4]) ).
cnf(p2405,plain,
( k = m
| k = j
| m = k
| k = j
| m = k ),
inference(resolution,[status(thm)],[p2403,p351]) ).
cnf(p2466,plain,
( k = m
| k = j
| k = j
| m = k ),
inference(factoring,[status(thm)],[p2405]) ).
cnf(p2468,plain,
( k = m
| k = j
| m = k ),
inference(factoring,[status(thm)],[p2466]) ).
cnf(p2469,plain,
( j != m
| k = j
| m = k ),
inference(equality_factoring,[status(thm)],[p2468]) ).
cnf(p2491,plain,
( m = k
| k = j
| m = k ),
inference(resolution,[status(thm)],[p2469,p558]) ).
cnf(p2493,plain,
( k = j
| m = k ),
inference(factoring,[status(thm)],[p2491]) ).
cnf(p2494,plain,
( n = j
| m = k
| m = k ),
inference(superposition,[status(thm)],[c1,p2493]) ).
cnf(p2518,plain,
( n = j
| m = k ),
inference(factoring,[status(thm)],[p2494]) ).
cnf(p2528,plain,
( n = m
| m = k
| m = k ),
inference(superposition,[status(thm)],[p2518,p558]) ).
cnf(p2553,plain,
( n = m
| m = k ),
inference(factoring,[status(thm)],[p2528]) ).
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(p2554,plain,
( m != m
| m = k ),
inference(superposition,[status(thm)],[p2553,c0]) ).
cnf(p2563,plain,
m = k,
inference(equality_resolution,[status(thm)],[p2554]) ).
cnf(f15,negated_conjecture,
( element(Y,k)
| Y != n
| Y = k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
fof(f15_nnf,plain,
! [Y] :
( element(Y,k)
| Y != n
| Y = k ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [Y] :
( element(Y,k)
| Y != n
| Y = k ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( element(X0,k)
| X0 != n
| X0 = k ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p25,plain,
( element(n,k)
| n = k ),
inference(equality_resolution,[status(thm)],[c15]) ).
cnf(p2567,plain,
( element(n,m)
| n = k ),
inference(superposition,[status(thm)],[p2563,p25]) ).
cnf(p2631,plain,
( element(f(n),n)
| n = m
| n = k ),
inference(resolution,[status(thm)],[p2567,c7]) ).
cnf(p2669,plain,
( m != k
| element(f(n),n)
| n = m ),
inference(equality_factoring,[status(thm)],[p2631]) ).
cnf(p2680,plain,
( element(f(n),n)
| n = m ),
inference(resolution,[status(thm)],[p2669,p2563]) ).
cnf(f8,negated_conjecture,
( ~ element(V1,Y)
| ~ element(Y,V1)
| V1 = Y
| V1 = m
| element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_9) ).
fof(f8_nnf,plain,
! [Y,V1] :
( ~ element(V1,Y)
| ~ element(Y,V1)
| V1 = Y
| V1 = m
| element(Y,m)
| Y = m ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Y,V1] :
( ~ element(V1,Y)
| ~ element(Y,V1)
| V1 = Y
| V1 = m
| element(Y,m)
| Y = m ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = m
| element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p2693,plain,
( ~ element(n,f(n))
| n = f(n)
| n = m
| element(f(n),m)
| f(n) = m
| n = m ),
inference(resolution,[status(thm)],[p2680,c8]) ).
cnf(p2992,plain,
( ~ element(n,f(n))
| n = f(n)
| element(f(n),m)
| f(n) = m
| n = m ),
inference(factoring,[status(thm)],[p2693]) ).
cnf(f6,negated_conjecture,
( element(Y,f(Y))
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_7) ).
fof(f6_nnf,plain,
! [Y] :
( element(Y,f(Y))
| ~ element(Y,m)
| Y = m ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Y] :
( element(Y,f(Y))
| ~ element(Y,m)
| Y = m ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( element(X0,f(X0))
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p2630,plain,
( element(n,f(n))
| n = m
| n = k ),
inference(resolution,[status(thm)],[p2567,c6]) ).
cnf(p2667,plain,
( m != k
| element(n,f(n))
| n = m ),
inference(equality_factoring,[status(thm)],[p2630]) ).
cnf(p2677,plain,
( element(n,f(n))
| n = m ),
inference(resolution,[status(thm)],[p2667,p2563]) ).
cnf(p2994,plain,
( n = m
| n = f(n)
| element(f(n),m)
| f(n) = m
| n = m ),
inference(resolution,[status(thm)],[p2992,p2677]) ).
cnf(p2996,plain,
( n = f(n)
| element(f(n),m)
| f(n) = m
| n = m ),
inference(factoring,[status(thm)],[p2994]) ).
cnf(p47,plain,
( k != m
| ~ element(X0,k)
| X0 = n
| X0 = k ),
inference(equality_factoring,[status(thm)],[c16]) ).
cnf(p2570,plain,
( k != m
| ~ element(X0,m)
| X0 = n
| X0 = k ),
inference(superposition,[status(thm)],[p2563,p47]) ).
cnf(p3005,plain,
( k != m
| f(n) = n
| f(n) = k
| n = f(n)
| f(n) = m
| n = m ),
inference(resolution,[status(thm)],[p2996,p2570]) ).
cnf(p3105,plain,
( k != m
| k != m
| f(n) = n
| f(n) = k
| n = f(n)
| n = m ),
inference(equality_factoring,[status(thm)],[p3005]) ).
cnf(p3111,plain,
( k != m
| f(n) = n
| f(n) = k
| n = f(n)
| n = m ),
inference(factoring,[status(thm)],[p3105]) ).
cnf(p3121,plain,
( m != m
| f(n) = n
| f(n) = k
| n = f(n)
| n = m ),
inference(superposition,[status(thm)],[p2563,p3111]) ).
cnf(p3137,plain,
( f(n) = n
| f(n) = k
| n = f(n)
| n = m ),
inference(equality_resolution,[status(thm)],[p3121]) ).
cnf(p3141,plain,
( f(n) = n
| f(n) = m
| n = f(n)
| n = m ),
inference(superposition,[status(thm)],[p2563,p3137]) ).
cnf(p2678,plain,
( ~ element(f(n),n)
| f(n) = n
| f(n) = m
| element(n,m)
| n = m
| n = m ),
inference(resolution,[status(thm)],[p2677,c8]) ).
cnf(p2955,plain,
( ~ element(f(n),n)
| f(n) = n
| f(n) = m
| element(n,m)
| n = m ),
inference(factoring,[status(thm)],[p2678]) ).
cnf(p2957,plain,
( n = m
| f(n) = n
| f(n) = m
| element(n,m)
| n = m ),
inference(resolution,[status(thm)],[p2955,p2680]) ).
cnf(p2958,plain,
( f(n) = n
| f(n) = m
| element(n,m)
| n = m ),
inference(factoring,[status(thm)],[p2957]) ).
cnf(p2629,plain,
( f(n) != n
| n = m
| n = k ),
inference(resolution,[status(thm)],[p2567,c5]) ).
cnf(p2665,plain,
( m != k
| f(n) != n
| n = m ),
inference(equality_factoring,[status(thm)],[p2629]) ).
cnf(p2960,plain,
( m != k
| n = m
| f(n) = m
| element(n,m)
| n = m ),
inference(resolution,[status(thm)],[p2958,p2665]) ).
cnf(p2962,plain,
( m != k
| f(n) = m
| element(n,m)
| n = m ),
inference(factoring,[status(thm)],[p2960]) ).
cnf(p2964,plain,
( f(n) = m
| element(n,m)
| n = m ),
inference(resolution,[status(thm)],[p2962,p2563]) ).
cnf(p2628,plain,
( f(n) != m
| n = m
| n = k ),
inference(resolution,[status(thm)],[p2567,c4]) ).
cnf(p2662,plain,
( m != k
| f(n) != m
| n = m ),
inference(equality_factoring,[status(thm)],[p2628]) ).
cnf(p2969,plain,
( m != k
| n = m
| element(n,m)
| n = m ),
inference(resolution,[status(thm)],[p2964,p2662]) ).
cnf(p2975,plain,
( m != k
| element(n,m)
| n = m ),
inference(factoring,[status(thm)],[p2969]) ).
cnf(p2976,plain,
( element(n,m)
| n = m ),
inference(resolution,[status(thm)],[p2975,p2563]) ).
cnf(p2979,plain,
( f(n) != n
| n = m
| n = m ),
inference(resolution,[status(thm)],[p2976,c5]) ).
cnf(p2981,plain,
( f(n) != n
| n = m ),
inference(factoring,[status(thm)],[p2979]) ).
cnf(p3158,plain,
( n = m
| f(n) = m
| n = f(n)
| n = m ),
inference(resolution,[status(thm)],[p3141,p2981]) ).
cnf(p3159,plain,
( f(n) = m
| n = f(n)
| n = m ),
inference(factoring,[status(thm)],[p3158]) ).
cnf(p2978,plain,
( f(n) != m
| n = m
| n = m ),
inference(resolution,[status(thm)],[p2976,c4]) ).
cnf(p2980,plain,
( f(n) != m
| n = m ),
inference(factoring,[status(thm)],[p2978]) ).
cnf(p3168,plain,
( n = m
| n = f(n)
| n = m ),
inference(resolution,[status(thm)],[p3159,p2980]) ).
cnf(p3170,plain,
( n = f(n)
| n = m ),
inference(factoring,[status(thm)],[p3168]) ).
cnf(p3183,plain,
( n != n
| n = m
| n = m ),
inference(superposition,[status(thm)],[p3170,p2981]) ).
cnf(p3190,plain,
( n != n
| n = m ),
inference(factoring,[status(thm)],[p3183]) ).
cnf(p3191,plain,
n = m,
inference(equality_resolution,[status(thm)],[p3190]) ).
cnf(p3192,plain,
m != m,
inference(demodulation,[status(thm)],[p3191,c0]) ).
cnf(p3299,plain,
$false,
inference(equality_resolution,[status(thm)],[p3192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 23:50:06 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.30/2.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.30/2.41 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------