%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN014-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 03:38:53 PM UTC 2026
% Result : Unsatisfiable 0.19s 1.26s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 19
% Syntax : Number of formulae : 138 ( 11 unt; 0 def)
% Number of atoms : 471 ( 292 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 459 ( 126 ~; 333 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 81 ( 0 sgn 81 !; 0 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
m != n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_1) ).
fof(f2,negated_conjecture,
( m = k
| n = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_2) ).
fof(f3,negated_conjecture,
! [X0] :
( element(X0,j)
| X0 != k
| X0 = j ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_3) ).
fof(f4,plain,
! [X0] :
( element(X0,j)
| k != X0
| j = X0 ),
inference(reorient_equations,[],[f3]) ).
fof(f5,negated_conjecture,
! [X0] :
( ~ element(X0,j)
| X0 = k
| X0 = j ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_4) ).
fof(f6,plain,
! [X0] :
( ~ element(X0,j)
| k = X0
| j = X0 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,negated_conjecture,
! [X0] :
( f(X0) != m
| ~ element(X0,m)
| X0 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).
fof(f8,plain,
! [X0] :
( m != f(X0)
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f7]) ).
fof(f9,negated_conjecture,
! [X0] :
( f(X0) != X0
| ~ element(X0,m)
| X0 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_6) ).
fof(f10,plain,
! [X0] :
( f(X0) != X0
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f9]) ).
fof(f11,negated_conjecture,
! [X0] :
( element(X0,f(X0))
| ~ element(X0,m)
| X0 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).
fof(f12,plain,
! [X0] :
( element(X0,f(X0))
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
! [X0] :
( element(f(X0),X0)
| ~ element(X0,m)
| X0 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_8) ).
fof(f14,plain,
! [X0] :
( element(f(X0),X0)
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = m
| element(X0,m)
| X0 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_9) ).
fof(f16,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X0 = X1
| m = X1
| element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
! [X0] :
( g(X0) != n
| element(X0,n)
| X0 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_10) ).
fof(f18,plain,
! [X0] :
( n != g(X0)
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f17]) ).
fof(f19,negated_conjecture,
! [X0] :
( g(X0) != X0
| element(X0,n)
| X0 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_11) ).
fof(f20,plain,
! [X0] :
( g(X0) != X0
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f19]) ).
fof(f21,negated_conjecture,
! [X0] :
( element(X0,g(X0))
| element(X0,n)
| X0 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_12) ).
fof(f22,plain,
! [X0] :
( element(X0,g(X0))
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f21]) ).
fof(f23,negated_conjecture,
! [X0] :
( element(g(X0),X0)
| element(X0,n)
| X0 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_13) ).
fof(f24,plain,
! [X0] :
( element(g(X0),X0)
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f23]) ).
fof(f25,negated_conjecture,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = n
| ~ element(X0,n)
| X0 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_14) ).
fof(f26,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X0 = X1
| n = X1
| ~ element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f25]) ).
fof(f27,negated_conjecture,
! [X0] :
( element(X0,k)
| X0 != m
| X0 = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_15) ).
fof(f28,plain,
! [X0] :
( element(X0,k)
| m != X0
| k = X0 ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
! [X0] :
( element(X0,k)
| X0 != n
| X0 = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
fof(f30,plain,
! [X0] :
( element(X0,k)
| n != X0
| k = X0 ),
inference(reorient_equations,[],[f29]) ).
fof(f31,negated_conjecture,
! [X0] :
( ~ element(X0,k)
| X0 = n
| X0 = m
| X0 = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_17) ).
fof(f32,plain,
! [X0] :
( ~ element(X0,k)
| n = X0
| m = X0
| k = X0 ),
inference(reorient_equations,[],[f31]) ).
fof(f33,plain,
( element(k,j)
| k = j ),
inference(equality_resolution,[],[f4]) ).
fof(f34,plain,
( element(m,k)
| m = k ),
inference(equality_resolution,[],[f28]) ).
fof(f35,plain,
( element(n,k)
| n = k ),
inference(equality_resolution,[],[f30]) ).
tcf(c_66,negated_conjecture,
m != n,
inference(cnf_transformation,[],[f1]) ).
tcf(c_67,negated_conjecture,
( ( n = k )
| ( m = k ) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_68,negated_conjecture,
( element(k,j)
| ( k = j ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_69,negated_conjecture,
! [X0: $i] :
( ( X0 = j )
| ( X0 = k )
| ~ element(X0,j) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_70,negated_conjecture,
! [X0: $i] :
( ( X0 = m )
| ~ element(X0,m)
| ( f(X0) != m ) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,negated_conjecture,
! [X0: $i] :
( ( X0 = m )
| ~ element(X0,m)
| ( f(X0) != X0 ) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_72,negated_conjecture,
! [X0: $i] :
( element(X0,f(X0))
| ( X0 = m )
| ~ element(X0,m) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_73,negated_conjecture,
! [X0: $i] :
( element(f(X0),X0)
| ( X0 = m )
| ~ element(X0,m) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_74,negated_conjecture,
! [X0: $i,X1: $i] :
( element(X0,m)
| ( X1 = m )
| ( X0 = m )
| ( X0 = X1 )
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_75,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| ( X0 = n )
| ( g(X0) != n ) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_76,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| ( X0 = n )
| ( g(X0) != X0 ) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_77,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| element(X0,g(X0))
| ( X0 = n ) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_78,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| element(g(X0),X0)
| ( X0 = n ) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_79,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X1 = n )
| ( X0 = n )
| ( X0 = X1 )
| ~ element(X0,n)
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_80,negated_conjecture,
( element(m,k)
| ( m = k ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_81,negated_conjecture,
( element(n,k)
| ( n = k ) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_82,negated_conjecture,
! [X0: $i] :
( ( X0 = k )
| ( X0 = n )
| ( X0 = m )
| ~ element(X0,k) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_301,negated_conjecture,
( element(n,k)
| ( n = k ) ),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_302,negated_conjecture,
( element(m,k)
| ( m = k ) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_303,negated_conjecture,
( element(k,j)
| ( k = j ) ),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_304,negated_conjecture,
! [X0: $i] :
( ( X0 = k )
| ( X0 = n )
| ( X0 = m )
| ~ element(X0,k) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_305,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X1 = n )
| ( X0 = n )
| ( X0 = X1 )
| ~ element(X0,n)
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_306,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| element(g(X0),X0)
| ( X0 = n ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_307,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| element(X0,g(X0))
| ( X0 = n ) ),
inference(demodulation,[status(thm)],[c_77]) ).
tcf(c_308,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| ( X0 = n )
| ( g(X0) != X0 ) ),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_309,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| ( X0 = n )
| ( g(X0) != n ) ),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_310,negated_conjecture,
! [X0: $i,X1: $i] :
( element(X0,m)
| ( X1 = m )
| ( X0 = m )
| ( X0 = X1 )
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_311,negated_conjecture,
! [X0: $i] :
( element(f(X0),X0)
| ( X0 = m )
| ~ element(X0,m) ),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_312,negated_conjecture,
! [X0: $i] :
( element(X0,f(X0))
| ( X0 = m )
| ~ element(X0,m) ),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_313,negated_conjecture,
! [X0: $i] :
( ( X0 = m )
| ~ element(X0,m)
| ( f(X0) != X0 ) ),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_314,negated_conjecture,
! [X0: $i] :
( ( X0 = m )
| ~ element(X0,m)
| ( f(X0) != m ) ),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_315,negated_conjecture,
! [X0: $i] :
( ( X0 = j )
| ( X0 = k )
| ~ element(X0,j) ),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_316,negated_conjecture,
( ( n = k )
| ( m = k ) ),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_317,negated_conjecture,
m != n,
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_318,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_320,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_322,plain,
m = m,
inference(instantiation,[status(thm)],[c_318]) ).
tcf(c_580,plain,
( element(n,j)
| ( k = j )
| ( m = k ) ),
inference(superposition,[status(thm)],[c_316,c_303]) ).
tcf(c_581,plain,
( element(m,n)
| ( m = k ) ),
inference(superposition,[status(thm)],[c_316,c_302]) ).
tcf(c_625,plain,
( element(j,n)
| ( n = j )
| ( g(j) = j )
| ( g(j) = k ) ),
inference(superposition,[status(thm)],[c_306,c_315]) ).
tcf(c_676,plain,
! [X0: $i] :
( ( m = k )
| ( X0 = k )
| ( X0 = n )
| ( X0 = m )
| ~ element(X0,n) ),
inference(superposition,[status(thm)],[c_316,c_304]) ).
tcf(c_705,plain,
! [X0: $i] :
( element(f(X0),m)
| ( X0 = m )
| ( f(X0) = m )
| ( f(X0) = X0 )
| ~ element(X0,m)
| ~ element(X0,f(X0)) ),
inference(superposition,[status(thm)],[c_311,c_310]) ).
tcf(c_706,plain,
! [X0: $i] :
( element(X0,n)
| element(X0,m)
| ( X0 = n )
| ( X0 = m )
| ( g(X0) = m )
| ( g(X0) = X0 )
| ~ element(g(X0),X0) ),
inference(superposition,[status(thm)],[c_307,c_310]) ).
tcf(c_862,plain,
( ( m = k )
| ( m = n )
| ( f(n) = k )
| ( f(n) = n )
| ( f(n) = m )
| ~ element(n,m) ),
inference(superposition,[status(thm)],[c_311,c_676]) ).
tcf(c_865,plain,
( ( k = j )
| ( n = j )
| ( m = j )
| ( m = k )
| ( g(j) = j )
| ( g(j) = k ) ),
inference(superposition,[status(thm)],[c_625,c_676]) ).
tcf(c_872,plain,
( ( m = k )
| ( f(n) = k )
| ( f(n) = n )
| ( f(n) = m )
| ~ element(n,m) ),
inference(forward_subsumption_resolution,[status(thm)],[c_862,c_317]) ).
tcf(c_878,plain,
! [X0: $i] :
( ( m = n )
| ( n != X0 )
| ( m != X0 ) ),
inference(instantiation,[status(thm)],[c_320]) ).
tcf(c_879,plain,
( ( m = n )
| ( n != m )
| ( m != m ) ),
inference(instantiation,[status(thm)],[c_878]) ).
tcf(c_905,plain,
( element(j,n)
| ( k = j )
| ( n = j )
| ( m = j )
| ( m = k )
| ( g(j) = k ) ),
inference(superposition,[status(thm)],[c_865,c_308]) ).
tcf(c_961,plain,
( ( n = m )
| ~ element(n,m)
| ( f(n) != n ) ),
inference(instantiation,[status(thm)],[c_313]) ).
tcf(c_962,plain,
( element(n,f(n))
| ( n = m )
| ~ element(n,m) ),
inference(instantiation,[status(thm)],[c_312]) ).
tcf(c_963,plain,
( element(f(n),n)
| ( n = m )
| ~ element(n,m) ),
inference(instantiation,[status(thm)],[c_311]) ).
tcf(c_965,plain,
( ( n = m )
| ~ element(n,m)
| ( f(n) != m ) ),
inference(instantiation,[status(thm)],[c_314]) ).
tcf(c_970,plain,
( ( m = k )
| ( f(n) = k )
| ~ element(n,m) ),
inference(global_subsumption_just,[status(thm)],[c_872,c_66,c_322,c_872,c_879,c_965,c_961]) ).
tcf(c_1002,plain,
( ( k = j )
| ( n = j )
| ( m = j )
| ( m = k )
| ( g(j) = k ) ),
inference(superposition,[status(thm)],[c_905,c_676]) ).
tcf(c_1020,plain,
( element(j,n)
| ( k = j )
| ( n = j )
| ( m = j )
| ( m = k )
| ( n != k ) ),
inference(superposition,[status(thm)],[c_1002,c_309]) ).
tcf(c_1022,plain,
( element(j,k)
| element(j,n)
| ( k = j )
| ( n = j )
| ( m = j )
| ( m = k ) ),
inference(superposition,[status(thm)],[c_1002,c_307]) ).
tcf(c_1036,plain,
( ( m = k )
| ( m = j )
| ( n = j )
| ( k = j )
| element(j,n) ),
inference(global_subsumption_just,[status(thm)],[c_1022,c_67,c_1020]) ).
tcf(c_1037,plain,
( element(j,n)
| ( k = j )
| ( n = j )
| ( m = j )
| ( m = k ) ),
inference(renaming,[status(thm)],[c_1036]) ).
tcf(c_1056,plain,
( ( k = j )
| ( n = j )
| ( m = j )
| ( m = k ) ),
inference(superposition,[status(thm)],[c_1037,c_676]) ).
tcf(c_1077,plain,
! [X0: $i] :
( element(f(X0),m)
| ( X0 = m )
| ~ element(X0,m) ),
inference(global_subsumption_just,[status(thm)],[c_705,c_72,c_71,c_70,c_705]) ).
tcf(c_1085,plain,
! [X0: $i] :
( ( m = n )
| ( X0 = m )
| ( f(X0) = n )
| ( f(X0) = m )
| ~ element(X0,m)
| ~ element(m,f(X0))
| ~ element(f(X0),n) ),
inference(superposition,[status(thm)],[c_1077,c_305]) ).
tcf(c_1087,plain,
! [X0: $i] :
( ( X0 = m )
| ( f(X0) = n )
| ( f(X0) = m )
| ~ element(X0,m)
| ~ element(m,f(X0))
| ~ element(f(X0),n) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1085,c_317]) ).
tcf(c_1105,plain,
! [X0: $i] :
( ( X0 = m )
| ( f(X0) = n )
| ~ element(f(X0),n)
| ~ element(m,f(X0))
| ~ element(X0,m) ),
inference(global_subsumption_just,[status(thm)],[c_1087,c_70,c_1087]) ).
tcf(c_1106,plain,
! [X0: $i] :
( ( X0 = m )
| ( f(X0) = n )
| ~ element(X0,m)
| ~ element(m,f(X0))
| ~ element(f(X0),n) ),
inference(renaming,[status(thm)],[c_1105]) ).
tcf(c_1117,plain,
( ( m = n )
| ( f(n) = n )
| ~ element(n,m)
| ~ element(m,f(n)) ),
inference(superposition,[status(thm)],[c_311,c_1106]) ).
tcf(c_1118,plain,
( ( f(n) = n )
| ~ element(n,m)
| ~ element(m,f(n)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1117,c_317]) ).
tcf(c_1122,plain,
( ~ element(m,f(n))
| ~ element(n,m) ),
inference(global_subsumption_just,[status(thm)],[c_1118,c_66,c_322,c_879,c_961,c_1118]) ).
tcf(c_1123,plain,
( ~ element(n,m)
| ~ element(m,f(n)) ),
inference(renaming,[status(thm)],[c_1122]) ).
tcf(c_1128,plain,
! [X0: $i] :
( element(X0,n)
| element(X0,m)
| ( X0 = n )
| ( X0 = m )
| ( g(X0) = m ) ),
inference(global_subsumption_just,[status(thm)],[c_706,c_78,c_76,c_706]) ).
tcf(c_1141,plain,
! [X0: $i] :
( element(X0,m)
| ( m = n )
| ( X0 = n )
| ( X0 = m )
| ( g(X0) = m )
| ~ element(n,X0) ),
inference(superposition,[status(thm)],[c_1128,c_310]) ).
tcf(c_1152,plain,
! [X0: $i] :
( element(X0,m)
| ( X0 = n )
| ( X0 = m )
| ( g(X0) = m )
| ~ element(n,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1141,c_317]) ).
tcf(c_1181,plain,
( element(f(n),m)
| ( m = n )
| ( f(n) = n )
| ( f(n) = m )
| ( g(f(n)) = m )
| ~ element(n,m) ),
inference(superposition,[status(thm)],[c_312,c_1152]) ).
tcf(c_1186,plain,
( element(f(n),m)
| ( f(n) = n )
| ( f(n) = m )
| ( g(f(n)) = m )
| ~ element(n,m) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1181,c_317]) ).
tcf(c_1206,plain,
! [X0: $i] :
( ( n = j )
| ( m = j )
| ( m = k )
| ( X0 = j )
| ( X0 = k )
| ~ element(X0,k) ),
inference(superposition,[status(thm)],[c_1056,c_315]) ).
tcf(c_1241,plain,
( ( n = j )
| ( m = j )
| ( m = k )
| ~ element(m,k) ),
inference(instantiation,[status(thm)],[c_1206]) ).
tcf(c_1246,plain,
( element(f(n),m)
| ( g(f(n)) = m )
| ~ element(n,m) ),
inference(global_subsumption_just,[status(thm)],[c_1186,c_66,c_322,c_879,c_965,c_961,c_1186]) ).
tcf(c_1256,plain,
( ( n = j )
| ( m = j )
| ( m = k ) ),
inference(global_subsumption_just,[status(thm)],[c_1206,c_80,c_1241]) ).
tcf(c_1270,plain,
! [X0: $i] :
( ( m = j )
| ( m = k )
| ( X0 = j )
| ( X0 = k )
| ~ element(X0,n) ),
inference(superposition,[status(thm)],[c_1256,c_315]) ).
tcf(c_1272,plain,
( element(k,n)
| ( k = j )
| ( m = j )
| ( m = k ) ),
inference(superposition,[status(thm)],[c_1256,c_303]) ).
tcf(c_1308,plain,
( ( m = j )
| ( m = k )
| ~ element(m,n) ),
inference(instantiation,[status(thm)],[c_1270]) ).
tcf(c_1312,plain,
( ( m = j )
| ( m = k ) ),
inference(global_subsumption_just,[status(thm)],[c_1272,c_581,c_1308]) ).
tcf(c_1323,plain,
( element(n,m)
| ( k = j )
| ( m = k ) ),
inference(superposition,[status(thm)],[c_1312,c_580]) ).
tcf(c_1367,plain,
( ( k = j )
| ( m = k )
| ( f(n) = k ) ),
inference(superposition,[status(thm)],[c_1323,c_970]) ).
tcf(c_1384,plain,
( element(k,n)
| ( k = j )
| ( m = k )
| ( m = n )
| ~ element(n,m) ),
inference(superposition,[status(thm)],[c_1367,c_311]) ).
tcf(c_1386,plain,
( ( k = j )
| ( m = k )
| ~ element(n,m)
| ~ element(m,k) ),
inference(superposition,[status(thm)],[c_1367,c_1123]) ).
tcf(c_1391,plain,
( element(k,n)
| ( k = j )
| ( m = k )
| ~ element(n,m) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1384,c_317]) ).
tcf(c_1465,plain,
( ( m = k )
| ( k = j ) ),
inference(global_subsumption_just,[status(thm)],[c_1391,c_80,c_1323,c_1386]) ).
tcf(c_1466,plain,
( ( k = j )
| ( m = k ) ),
inference(renaming,[status(thm)],[c_1465]) ).
tcf(c_1471,plain,
m = k,
inference(superposition,[status(thm)],[c_1312,c_1466]) ).
tcf(c_1484,plain,
! [X0: $i] :
( ( X0 = n )
| ( X0 = m )
| ~ element(X0,m) ),
inference(demodulation,[status(thm)],[c_304,c_1471]) ).
tcf(c_1487,plain,
( element(n,m)
| ( m = n ) ),
inference(demodulation,[status(thm)],[c_301,c_1471]) ).
tcf(c_1488,plain,
element(n,m),
inference(forward_subsumption_resolution,[status(thm)],[c_1487,c_317]) ).
tcf(c_1489,plain,
( element(f(n),m)
| ( g(f(n)) = m ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1246,c_1488]) ).
tcf(c_1597,plain,
( ( f(n) = n )
| ( f(n) = m )
| ( g(f(n)) = m ) ),
inference(superposition,[status(thm)],[c_1489,c_1484]) ).
tcf(c_1630,plain,
g(f(n)) = m,
inference(global_subsumption_just,[status(thm)],[c_1597,c_66,c_322,c_879,c_965,c_961,c_1488,c_1597]) ).
tcf(c_1635,plain,
( element(f(n),n)
| element(f(n),m)
| ( f(n) = n ) ),
inference(superposition,[status(thm)],[c_1630,c_307]) ).
tcf(c_1643,plain,
element(f(n),n),
inference(global_subsumption_just,[status(thm)],[c_1635,c_66,c_322,c_879,c_963,c_1488]) ).
tcf(c_1646,plain,
( element(f(n),m)
| ( m = n )
| ( f(n) = n )
| ( f(n) = m )
| ~ element(n,f(n)) ),
inference(superposition,[status(thm)],[c_1643,c_310]) ).
tcf(c_1648,plain,
( element(f(n),m)
| ( f(n) = n )
| ( f(n) = m )
| ~ element(n,f(n)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1646,c_317]) ).
tcf(c_1653,plain,
element(f(n),m),
inference(global_subsumption_just,[status(thm)],[c_1648,c_66,c_322,c_879,c_965,c_962,c_961,c_1488,c_1648]) ).
tcf(c_1655,plain,
( ( f(n) = n )
| ( f(n) = m ) ),
inference(superposition,[status(thm)],[c_1653,c_1484]) ).
tcf(c_1660,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1655,c_1488,c_961,c_965,c_879,c_322,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.35 % Computer : n009.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Thu Sep 24 23:51:13 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 0.19/1.26 % SZS status Started for theBenchmark.p
% 0.19/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 0.19/1.26
% 0.19/1.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.19/1.26
% 0.19/1.26 % ------ iProver source info
% 0.19/1.26
% 0.19/1.26 % git: date: 2026-07-19 20:42:38 +0200
% 0.19/1.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.19/1.26 % git: non_committed_changes: false
% 0.19/1.26
% 0.19/1.26 % ------ Parsing...% successful
% 0.19/1.26
% 0.19/1.26
% 0.19/1.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.19/1.26
% 0.19/1.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 0.19/1.26
% 0.19/1.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.19/1.26
% 0.19/1.26 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.19/1.26 % ------ Proving...
% 0.19/1.26 % ------ Problem Properties
% 0.19/1.26
% 0.19/1.26 %
% 0.19/1.26 % clauses 17
% 0.19/1.26 % conjectures 17
% 0.19/1.26 % EPR 9
% 0.19/1.26 % Horn 3
% 0.19/1.26 % unary 1
% 0.19/1.26 % binary 4
% 0.19/1.26 % lits 52
% 0.19/1.26 % lits eq 29
% 0.19/1.26 % fd_pure 0
% 0.19/1.26 % fd_pseudo 0
% 0.19/1.26 % fd_cond 10
% 0.19/1.26 % fd_pseudo_cond 2
% 0.19/1.26 % AC symbols 0
% 0.19/1.26
% 0.19/1.26 % ------ Schedule dynamic 5 is on
% 0.19/1.26
% 0.19/1.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.19/1.26
% 0.19/1.26
% 0.19/1.26 % ------
% 0.19/1.26 % Current options:
% 0.19/1.26 % ------
% 0.19/1.26
% 0.19/1.26
% 0.19/1.26 %
% 0.19/1.26
% 0.19/1.26 % ------ Proving...
% 0.19/1.26 %
% 0.19/1.26
% 0.19/1.26 % SZS status Unsatisfiable for theBenchmark.p
% 0.19/1.26
% 0.19/1.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.19/1.27
% 0.19/1.27
%------------------------------------------------------------------------------