%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SYN015-1 : 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 : n003.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 2.63s 1.16s
% Output : CNFRefutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 59
% Number of leaves : 18
% Syntax : Number of formulae : 182 ( 16 unt; 0 def)
% Number of atoms : 649 ( 426 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 638 ( 171 ~; 467 |; 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 : 91 ( 0 sgn 91 !; 0 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
m != n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_1) ).
fof(f2,negated_conjecture,
! [X0] :
( element(X0,j)
| X0 != k
| X0 = j ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_2) ).
fof(f3,plain,
! [X0] :
( element(X0,j)
| k != X0
| j = X0 ),
inference(reorient_equations,[],[f2]) ).
fof(f4,negated_conjecture,
! [X0] :
( ~ element(X0,j)
| X0 = k
| X0 = j ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_3) ).
fof(f5,plain,
! [X0] :
( ~ element(X0,j)
| k = X0
| j = X0 ),
inference(reorient_equations,[],[f4]) ).
fof(f6,negated_conjecture,
! [X0] :
( f(X0) != m
| ~ element(X0,m)
| X0 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_4) ).
fof(f7,plain,
! [X0] :
( m != f(X0)
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
! [X0] :
( f(X0) != X0
| ~ element(X0,m)
| X0 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).
fof(f9,plain,
! [X0] :
( f(X0) != X0
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
! [X0] :
( element(X0,f(X0))
| ~ element(X0,m)
| X0 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_6) ).
fof(f11,plain,
! [X0] :
( element(X0,f(X0))
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
! [X0] :
( element(f(X0),X0)
| ~ element(X0,m)
| X0 = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).
fof(f13,plain,
! [X0] :
( element(f(X0),X0)
| ~ element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,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_8) ).
fof(f15,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X0 = X1
| m = X1
| element(X0,m)
| m = X0 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,negated_conjecture,
! [X0] :
( g(X0) != n
| element(X0,n)
| X0 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_9) ).
fof(f17,plain,
! [X0] :
( n != g(X0)
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f16]) ).
fof(f18,negated_conjecture,
! [X0] :
( g(X0) != X0
| element(X0,n)
| X0 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_10) ).
fof(f19,plain,
! [X0] :
( g(X0) != X0
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f18]) ).
fof(f20,negated_conjecture,
! [X0] :
( element(X0,g(X0))
| element(X0,n)
| X0 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_11) ).
fof(f21,plain,
! [X0] :
( element(X0,g(X0))
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f20]) ).
fof(f22,negated_conjecture,
! [X0] :
( element(g(X0),X0)
| element(X0,n)
| X0 = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_12) ).
fof(f23,plain,
! [X0] :
( element(g(X0),X0)
| element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f22]) ).
fof(f24,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_13) ).
fof(f25,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X0 = X1
| n = X1
| ~ element(X0,n)
| n = X0 ),
inference(reorient_equations,[],[f24]) ).
fof(f26,negated_conjecture,
! [X0] :
( element(X0,k)
| X0 != m
| X0 = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_14) ).
fof(f27,plain,
! [X0] :
( element(X0,k)
| m != X0
| k = X0 ),
inference(reorient_equations,[],[f26]) ).
fof(f28,negated_conjecture,
! [X0] :
( element(X0,k)
| X0 != n
| X0 = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_15) ).
fof(f29,plain,
! [X0] :
( element(X0,k)
| n != X0
| k = X0 ),
inference(reorient_equations,[],[f28]) ).
fof(f30,negated_conjecture,
! [X0] :
( ~ element(X0,k)
| X0 = n
| X0 = m
| X0 = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
fof(f31,plain,
! [X0] :
( ~ element(X0,k)
| n = X0
| m = X0
| k = X0 ),
inference(reorient_equations,[],[f30]) ).
fof(f32,plain,
( element(k,j)
| j = k ),
inference(equality_resolution,[],[f3]) ).
fof(f33,plain,
( element(m,k)
| m = k ),
inference(equality_resolution,[],[f27]) ).
fof(f34,plain,
( element(n,k)
| n = k ),
inference(equality_resolution,[],[f29]) ).
tcf(c_65,negated_conjecture,
m != n,
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,negated_conjecture,
( element(k,j)
| ( j = k ) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_67,negated_conjecture,
! [X0: $i] :
( ( X0 = k )
| ( X0 = j )
| ~ element(X0,j) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_68,negated_conjecture,
! [X0: $i] :
( ( X0 = m )
| ~ element(X0,m)
| ( f(X0) != m ) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_69,negated_conjecture,
! [X0: $i] :
( ( X0 = m )
| ~ element(X0,m)
| ( f(X0) != X0 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_70,negated_conjecture,
! [X0: $i] :
( element(X0,f(X0))
| ( X0 = m )
| ~ element(X0,m) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_71,negated_conjecture,
! [X0: $i] :
( element(f(X0),X0)
| ( X0 = m )
| ~ element(X0,m) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_72,negated_conjecture,
! [X0: $i,X1: $i] :
( element(X0,m)
| ( X1 = m )
| ( X0 = m )
| ( X0 = X1 )
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_73,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| ( X0 = n )
| ( g(X0) != n ) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_74,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| ( X0 = n )
| ( g(X0) != X0 ) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_75,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| element(X0,g(X0))
| ( X0 = n ) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_76,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| element(g(X0),X0)
| ( X0 = n ) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_77,negated_conjecture,
! [X0: $i,X1: $i] :
( ( X1 = n )
| ( X0 = n )
| ( X0 = X1 )
| ~ element(X0,n)
| ~ element(X1,X0)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_78,negated_conjecture,
( element(m,k)
| ( m = k ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_79,negated_conjecture,
( element(n,k)
| ( n = k ) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_80,negated_conjecture,
! [X0: $i] :
( ( X0 = k )
| ( X0 = n )
| ( X0 = m )
| ~ element(X0,k) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_291,negated_conjecture,
( element(n,k)
| ( n = k ) ),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_292,negated_conjecture,
( element(m,k)
| ( m = k ) ),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_293,negated_conjecture,
( element(k,j)
| ( j = k ) ),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_294,negated_conjecture,
! [X0: $i] :
( ( X0 = k )
| ( X0 = n )
| ( X0 = m )
| ~ element(X0,k) ),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_295,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_77]) ).
tcf(c_296,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| element(g(X0),X0)
| ( X0 = n ) ),
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_297,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| element(X0,g(X0))
| ( X0 = n ) ),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_298,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| ( X0 = n )
| ( g(X0) != X0 ) ),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_299,negated_conjecture,
! [X0: $i] :
( element(X0,n)
| ( X0 = n )
| ( g(X0) != n ) ),
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_300,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_72]) ).
tcf(c_301,negated_conjecture,
! [X0: $i] :
( element(f(X0),X0)
| ( X0 = m )
| ~ element(X0,m) ),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_302,negated_conjecture,
! [X0: $i] :
( element(X0,f(X0))
| ( X0 = m )
| ~ element(X0,m) ),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_303,negated_conjecture,
! [X0: $i] :
( ( X0 = m )
| ~ element(X0,m)
| ( f(X0) != X0 ) ),
inference(demodulation,[status(thm)],[c_69]) ).
tcf(c_304,negated_conjecture,
! [X0: $i] :
( ( X0 = m )
| ~ element(X0,m)
| ( f(X0) != m ) ),
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_305,negated_conjecture,
! [X0: $i] :
( ( X0 = k )
| ( X0 = j )
| ~ element(X0,j) ),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_306,negated_conjecture,
m != n,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_307,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_309,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_311,plain,
m = m,
inference(instantiation,[status(thm)],[c_307]) ).
tcf(c_589,plain,
( ( m = k )
| ( f(k) = k )
| ( f(k) = n )
| ( f(k) = m )
| ~ element(k,m) ),
inference(superposition,[status(thm)],[c_301,c_294]) ).
tcf(c_590,plain,
( element(k,n)
| ( n = k )
| ( g(k) = k )
| ( g(k) = n )
| ( g(k) = m ) ),
inference(superposition,[status(thm)],[c_296,c_294]) ).
tcf(c_610,plain,
( element(j,n)
| ( n = j )
| ( g(j) = k )
| ( g(j) = j ) ),
inference(superposition,[status(thm)],[c_296,c_305]) ).
tcf(c_683,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_301,c_300]) ).
tcf(c_684,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_297,c_300]) ).
tcf(c_748,plain,
! [X0: $i] :
( ( X0 = n )
| ( X0 = m )
| ( f(X0) = n )
| ( f(X0) = X0 )
| ~ element(X0,n)
| ~ element(X0,m)
| ~ element(f(X0),X0) ),
inference(superposition,[status(thm)],[c_302,c_295]) ).
tcf(c_853,plain,
! [X0: $i] :
( element(f(X0),m)
| ( X0 = m )
| ~ element(X0,m) ),
inference(global_subsumption_just,[status(thm)],[c_683,c_70,c_69,c_68,c_683]) ).
tcf(c_861,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_853,c_295]) ).
tcf(c_863,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_861,c_306]) ).
tcf(c_871,plain,
! [X0: $i] :
( ( m = n )
| ( n != X0 )
| ( m != X0 ) ),
inference(instantiation,[status(thm)],[c_309]) ).
tcf(c_872,plain,
( ( m = n )
| ( n != m )
| ( m != m ) ),
inference(instantiation,[status(thm)],[c_871]) ).
tcf(c_884,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_863,c_68,c_863]) ).
tcf(c_885,plain,
! [X0: $i] :
( ( X0 = m )
| ( f(X0) = n )
| ~ element(X0,m)
| ~ element(m,f(X0))
| ~ element(f(X0),n) ),
inference(renaming,[status(thm)],[c_884]) ).
tcf(c_896,plain,
( ( m = n )
| ( f(n) = n )
| ~ element(n,m)
| ~ element(m,f(n)) ),
inference(superposition,[status(thm)],[c_301,c_885]) ).
tcf(c_897,plain,
( ( f(n) = n )
| ~ element(n,m)
| ~ element(m,f(n)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_896,c_306]) ).
tcf(c_905,plain,
( ( n = m )
| ~ element(n,m)
| ( f(n) != n ) ),
inference(instantiation,[status(thm)],[c_303]) ).
tcf(c_906,plain,
( element(n,f(n))
| ( n = m )
| ~ element(n,m) ),
inference(instantiation,[status(thm)],[c_302]) ).
tcf(c_907,plain,
( element(f(n),n)
| ( n = m )
| ~ element(n,m) ),
inference(instantiation,[status(thm)],[c_301]) ).
tcf(c_909,plain,
( ( n = m )
| ~ element(n,m)
| ( f(n) != m ) ),
inference(instantiation,[status(thm)],[c_304]) ).
tcf(c_912,plain,
! [X0: $i,X1: $i] :
( ( n = X0 )
| ( n != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_309]) ).
tcf(c_915,plain,
( ~ element(m,f(n))
| ~ element(n,m) ),
inference(global_subsumption_just,[status(thm)],[c_897,c_65,c_311,c_872,c_897,c_905]) ).
tcf(c_916,plain,
( ~ element(n,m)
| ~ element(m,f(n)) ),
inference(renaming,[status(thm)],[c_915]) ).
tcf(c_921,plain,
! [X0: $i] :
( element(X0,n)
| element(X0,m)
| ( X0 = n )
| ( X0 = m )
| ( g(X0) = m ) ),
inference(global_subsumption_just,[status(thm)],[c_684,c_76,c_74,c_684]) ).
tcf(c_934,plain,
! [X0: $i] :
( element(X0,m)
| ( m = n )
| ( X0 = n )
| ( X0 = m )
| ( g(X0) = m )
| ~ element(n,X0) ),
inference(superposition,[status(thm)],[c_921,c_300]) ).
tcf(c_943,plain,
! [X0: $i] :
( element(X0,m)
| ( X0 = n )
| ( X0 = m )
| ( g(X0) = m )
| ~ element(n,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_934,c_306]) ).
tcf(c_1008,plain,
( element(k,m)
| ( n = k )
| ( m = k )
| ( g(k) = m ) ),
inference(superposition,[status(thm)],[c_291,c_943]) ).
tcf(c_1027,plain,
( ( n = k )
| ( m = k )
| ( m = n )
| ( g(k) = m )
| ~ element(k,n)
| ~ element(m,k) ),
inference(superposition,[status(thm)],[c_1008,c_295]) ).
tcf(c_1029,plain,
( ( n = k )
| ( m = k )
| ( g(k) = m )
| ( f(k) = k )
| ( f(k) = n )
| ( f(k) = m ) ),
inference(superposition,[status(thm)],[c_1008,c_589]) ).
tcf(c_1035,plain,
( ( n = k )
| ( m = k )
| ( g(k) = m )
| ~ element(k,n)
| ~ element(m,k) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1027,c_306]) ).
tcf(c_1056,plain,
( ( n = k )
| ( m = k )
| ( g(k) = m )
| ~ element(k,n) ),
inference(global_subsumption_just,[status(thm)],[c_1035,c_78,c_1035]) ).
tcf(c_1067,plain,
( ( n = k )
| ( m = k )
| ( g(k) = k )
| ( g(k) = n )
| ( g(k) = m ) ),
inference(superposition,[status(thm)],[c_590,c_1056]) ).
tcf(c_1107,plain,
! [X0: $i] :
( ( X0 = n )
| ( X0 = m )
| ( f(X0) = n )
| ~ element(X0,m)
| ~ element(X0,n) ),
inference(global_subsumption_just,[status(thm)],[c_748,c_71,c_69,c_748]) ).
tcf(c_1108,plain,
! [X0: $i] :
( ( X0 = n )
| ( X0 = m )
| ( f(X0) = n )
| ~ element(X0,n)
| ~ element(X0,m) ),
inference(renaming,[status(thm)],[c_1107]) ).
tcf(c_1119,plain,
( ( m = n )
| ( f(n) = n )
| ( f(n) = m )
| ( f(f(n)) = n )
| ~ element(n,m)
| ~ element(f(n),m) ),
inference(superposition,[status(thm)],[c_301,c_1108]) ).
tcf(c_1130,plain,
( ( f(n) = n )
| ( f(n) = m )
| ( f(f(n)) = n )
| ~ element(n,m)
| ~ element(f(n),m) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1119,c_306]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i] :
( ( X0 = n )
| ( n != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_309]) ).
tcf(c_1140,plain,
( ( f(f(n)) = n )
| ~ element(n,m)
| ~ element(f(n),m) ),
inference(global_subsumption_just,[status(thm)],[c_1130,c_65,c_311,c_872,c_909,c_905,c_1130]) ).
tcf(c_1148,plain,
( ( m = n )
| ( f(f(n)) = n )
| ~ element(n,m) ),
inference(superposition,[status(thm)],[c_853,c_1140]) ).
tcf(c_1150,plain,
( ( f(f(n)) = n )
| ~ element(n,m) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1148,c_306]) ).
tcf(c_1175,plain,
( element(k,n)
| element(k,m)
| ( n = k )
| ( m = k )
| ( f(k) = k )
| ( f(k) = n )
| ( f(k) = m ) ),
inference(superposition,[status(thm)],[c_1029,c_297]) ).
tcf(c_1198,plain,
( element(k,n)
| ( f(k) = m )
| ( f(k) = n )
| ( f(k) = k )
| ( m = k )
| ( n = k ) ),
inference(global_subsumption_just,[status(thm)],[c_1175,c_589,c_1175]) ).
tcf(c_1199,plain,
( element(k,n)
| ( n = k )
| ( m = k )
| ( f(k) = k )
| ( f(k) = n )
| ( f(k) = m ) ),
inference(renaming,[status(thm)],[c_1198]) ).
tcf(c_1213,plain,
( element(k,m)
| ( n = k )
| ( m = k )
| ( m = n )
| ( f(k) = k )
| ( f(k) = n )
| ( f(k) = m )
| ~ element(n,k) ),
inference(superposition,[status(thm)],[c_1199,c_300]) ).
tcf(c_1223,plain,
( element(k,m)
| ( n = k )
| ( m = k )
| ( f(k) = k )
| ( f(k) = n )
| ( f(k) = m )
| ~ element(n,k) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1213,c_306]) ).
tcf(c_1233,plain,
( ( f(k) = m )
| ( f(k) = n )
| ( f(k) = k )
| ( m = k )
| ( n = k ) ),
inference(global_subsumption_just,[status(thm)],[c_1223,c_79,c_589,c_1223]) ).
tcf(c_1234,plain,
( ( n = k )
| ( m = k )
| ( f(k) = k )
| ( f(k) = n )
| ( f(k) = m ) ),
inference(renaming,[status(thm)],[c_1233]) ).
tcf(c_1248,plain,
( ( n = k )
| ( m = k )
| ( f(k) = n )
| ( f(k) = m )
| ~ element(k,m) ),
inference(superposition,[status(thm)],[c_1234,c_303]) ).
tcf(c_1292,plain,
( element(k,n)
| ( n = k )
| ( m = k )
| ( g(k) = n )
| ( g(k) = m ) ),
inference(superposition,[status(thm)],[c_1067,c_298]) ).
tcf(c_1309,plain,
( ( g(k) = m )
| ( g(k) = n )
| ( m = k )
| ( n = k ) ),
inference(global_subsumption_just,[status(thm)],[c_1292,c_78,c_1035,c_1292]) ).
tcf(c_1310,plain,
( ( n = k )
| ( m = k )
| ( g(k) = n )
| ( g(k) = m ) ),
inference(renaming,[status(thm)],[c_1309]) ).
tcf(c_1323,plain,
( element(k,n)
| ( n = k )
| ( m = k )
| ( g(k) = m ) ),
inference(superposition,[status(thm)],[c_1310,c_297]) ).
tcf(c_1334,plain,
( ( g(k) = m )
| ( m = k )
| ( n = k ) ),
inference(global_subsumption_just,[status(thm)],[c_1323,c_78,c_1035,c_1323]) ).
tcf(c_1335,plain,
( ( n = k )
| ( m = k )
| ( g(k) = m ) ),
inference(renaming,[status(thm)],[c_1334]) ).
tcf(c_1346,plain,
( element(k,n)
| element(k,m)
| ( n = k )
| ( m = k ) ),
inference(superposition,[status(thm)],[c_1335,c_297]) ).
tcf(c_1369,plain,
( element(k,m)
| ( n = k )
| ( m = k )
| ( m = n )
| ~ element(n,k) ),
inference(superposition,[status(thm)],[c_1346,c_300]) ).
tcf(c_1376,plain,
( element(k,m)
| ( n = k )
| ( m = k )
| ~ element(n,k) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1369,c_306]) ).
tcf(c_1383,plain,
( element(k,m)
| ( n = k )
| ( m = k ) ),
inference(global_subsumption_just,[status(thm)],[c_1376,c_79,c_1376]) ).
tcf(c_1392,plain,
( ( n = k )
| ( m = k )
| ( f(k) = n )
| ( f(k) = m ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_1248,c_1383]) ).
tcf(c_1400,plain,
( ( n = k )
| ( m = k )
| ( m = n )
| ~ element(k,n)
| ~ element(m,k) ),
inference(superposition,[status(thm)],[c_1383,c_295]) ).
tcf(c_1403,plain,
( ( n = k )
| ( m = k )
| ~ element(k,n)
| ~ element(m,k) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1400,c_306]) ).
tcf(c_1408,plain,
( ( n = k )
| ( m = k )
| ~ element(k,n) ),
inference(global_subsumption_just,[status(thm)],[c_1403,c_78,c_1403]) ).
tcf(c_1468,plain,
( element(k,n)
| ( n = k )
| ( m = k )
| ( f(k) = m )
| ~ element(k,m) ),
inference(superposition,[status(thm)],[c_1392,c_302]) ).
tcf(c_1480,plain,
( ( f(k) = m )
| ( m = k )
| ( n = k ) ),
inference(global_subsumption_just,[status(thm)],[c_1468,c_1383,c_1408,c_1468]) ).
tcf(c_1481,plain,
( ( n = k )
| ( m = k )
| ( f(k) = m ) ),
inference(renaming,[status(thm)],[c_1480]) ).
tcf(c_1491,plain,
( ( n = k )
| ( m = k )
| ~ element(k,m) ),
inference(superposition,[status(thm)],[c_1481,c_304]) ).
tcf(c_1588,plain,
! [X0: $i] :
( ( n = X0 )
| ( n != k )
| ( X0 != k ) ),
inference(instantiation,[status(thm)],[c_912]) ).
tcf(c_1593,plain,
( ( n = k )
| ( m = k ) ),
inference(global_subsumption_just,[status(thm)],[c_1491,c_1383,c_1491]) ).
tcf(c_1603,plain,
! [X0: $i] :
( ( m = k )
| ( X0 = k )
| ( X0 = n )
| ( X0 = m )
| ~ element(X0,n) ),
inference(superposition,[status(thm)],[c_1593,c_294]) ).
tcf(c_1604,plain,
( element(n,j)
| ( j = k )
| ( m = k ) ),
inference(superposition,[status(thm)],[c_1593,c_293]) ).
tcf(c_1605,plain,
( element(m,n)
| ( m = k ) ),
inference(superposition,[status(thm)],[c_1593,c_292]) ).
tcf(c_1648,plain,
( element(n,m)
| ( j = k )
| ( n = j )
| ( m = k )
| ( m = j )
| ( m = n )
| ~ element(j,n) ),
inference(superposition,[status(thm)],[c_1604,c_300]) ).
tcf(c_1661,plain,
( element(n,m)
| ( j = k )
| ( n = j )
| ( m = k )
| ( m = j )
| ~ element(j,n) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1648,c_306]) ).
tcf(c_1685,plain,
! [X0: $i] :
( ( X0 = n )
| ( n != k )
| ( X0 != k ) ),
inference(instantiation,[status(thm)],[c_1137]) ).
tcf(c_1691,plain,
( ( n = j )
| ( j != k )
| ( n != k ) ),
inference(instantiation,[status(thm)],[c_1588]) ).
tcf(c_1696,plain,
! [X0: $i] :
( ( m = k )
| ~ element(X0,n)
| ( X0 = m )
| ( X0 = n ) ),
inference(global_subsumption_just,[status(thm)],[c_1603,c_1593,c_1603,c_1685]) ).
tcf(c_1697,plain,
! [X0: $i] :
( ( m = k )
| ( X0 = n )
| ( X0 = m )
| ~ element(X0,n) ),
inference(renaming,[status(thm)],[c_1696]) ).
tcf(c_1706,plain,
( ( m = k )
| ( m = n )
| ( f(n) = n )
| ( f(n) = m )
| ~ element(n,m) ),
inference(superposition,[status(thm)],[c_301,c_1697]) ).
tcf(c_1711,plain,
( ( n = j )
| ( m = k )
| ( m = j )
| ( g(j) = k )
| ( g(j) = j ) ),
inference(superposition,[status(thm)],[c_610,c_1697]) ).
tcf(c_1722,plain,
( ( m = k )
| ( f(n) = n )
| ( f(n) = m )
| ~ element(n,m) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1706,c_306]) ).
tcf(c_1744,plain,
( ( m = k )
| ~ element(n,m) ),
inference(global_subsumption_just,[status(thm)],[c_1722,c_65,c_311,c_872,c_909,c_905,c_1722]) ).
tcf(c_1750,plain,
( ( n = j )
| ( m = k )
| ( m = j )
| ~ element(j,n) ),
inference(global_subsumption_just,[status(thm)],[c_1661,c_1383,c_1491,c_1661,c_1691,c_1744]) ).
tcf(c_1852,plain,
( element(j,n)
| ( n = j )
| ( m = k )
| ( m = j )
| ( g(j) = k ) ),
inference(superposition,[status(thm)],[c_1711,c_298]) ).
tcf(c_1881,plain,
( ( g(j) = k )
| ( m = j )
| ( m = k )
| ( n = j ) ),
inference(global_subsumption_just,[status(thm)],[c_1852,c_1750,c_1852]) ).
tcf(c_1882,plain,
( ( n = j )
| ( m = k )
| ( m = j )
| ( g(j) = k ) ),
inference(renaming,[status(thm)],[c_1881]) ).
tcf(c_1893,plain,
( element(j,n)
| ( n = j )
| ( m = k )
| ( m = j )
| ( n != k ) ),
inference(superposition,[status(thm)],[c_1882,c_299]) ).
tcf(c_1895,plain,
( element(j,k)
| element(j,n)
| ( n = j )
| ( m = k )
| ( m = j ) ),
inference(superposition,[status(thm)],[c_1882,c_297]) ).
tcf(c_1940,plain,
( ( n = j )
| ( m = k )
| ( m = j ) ),
inference(global_subsumption_just,[status(thm)],[c_1895,c_1593,c_1750,c_1893]) ).
tcf(c_1955,plain,
! [X0: $i] :
( ( m = k )
| ( m = j )
| ( X0 = k )
| ( X0 = j )
| ~ element(X0,n) ),
inference(superposition,[status(thm)],[c_1940,c_305]) ).
tcf(c_1956,plain,
( element(k,n)
| ( j = k )
| ( m = k )
| ( m = j ) ),
inference(superposition,[status(thm)],[c_1940,c_293]) ).
tcf(c_1985,plain,
( ( m = k )
| ( m = j )
| ~ element(m,n) ),
inference(instantiation,[status(thm)],[c_1955]) ).
tcf(c_1992,plain,
( ( m = k )
| ( m = j ) ),
inference(global_subsumption_just,[status(thm)],[c_1956,c_1605,c_1985]) ).
tcf(c_1998,plain,
( element(n,m)
| ( j = k )
| ( m = k ) ),
inference(superposition,[status(thm)],[c_1992,c_1604]) ).
tcf(c_2004,plain,
( element(k,m)
| ( j = k )
| ( m = k ) ),
inference(superposition,[status(thm)],[c_1992,c_293]) ).
tcf(c_2027,plain,
( ( m = k )
| ( j = k ) ),
inference(global_subsumption_just,[status(thm)],[c_2004,c_1744,c_1998]) ).
tcf(c_2028,plain,
( ( j = k )
| ( m = k ) ),
inference(renaming,[status(thm)],[c_2027]) ).
tcf(c_2033,plain,
m = k,
inference(superposition,[status(thm)],[c_1992,c_2028]) ).
tcf(c_2047,plain,
! [X0: $i] :
( ( X0 = n )
| ( X0 = m )
| ~ element(X0,m) ),
inference(demodulation,[status(thm)],[c_294,c_2033]) ).
tcf(c_2049,plain,
( element(n,m)
| ( m = n ) ),
inference(demodulation,[status(thm)],[c_291,c_2033]) ).
tcf(c_2050,plain,
element(n,m),
inference(forward_subsumption_resolution,[status(thm)],[c_2049,c_306]) ).
tcf(c_2051,plain,
f(f(n)) = n,
inference(backward_subsumption_resolution,[status(thm)],[c_1150,c_2050]) ).
tcf(c_2053,plain,
~ element(m,f(n)),
inference(backward_subsumption_resolution,[status(thm)],[c_916,c_2050]) ).
tcf(c_2094,plain,
( ( f(n) = m )
| ~ element(f(n),m)
| ( f(n) != n ) ),
inference(superposition,[status(thm)],[c_2051,c_303]) ).
tcf(c_2095,plain,
( element(f(n),n)
| ( f(n) = m )
| ~ element(f(n),m) ),
inference(superposition,[status(thm)],[c_2051,c_302]) ).
tcf(c_2155,plain,
element(f(n),n),
inference(global_subsumption_just,[status(thm)],[c_2095,c_65,c_311,c_872,c_907,c_2050]) ).
tcf(c_2158,plain,
( element(f(n),m)
| ( m = n )
| ( f(n) = n )
| ( f(n) = m )
| ~ element(n,f(n)) ),
inference(superposition,[status(thm)],[c_2155,c_300]) ).
tcf(c_2160,plain,
( element(f(n),m)
| ( f(n) = n )
| ( f(n) = m )
| ~ element(n,f(n)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2158,c_306]) ).
tcf(c_2181,plain,
f(n) != n,
inference(global_subsumption_just,[status(thm)],[c_2094,c_65,c_311,c_872,c_905,c_2050]) ).
tcf(c_2183,plain,
element(f(n),m),
inference(global_subsumption_just,[status(thm)],[c_2160,c_65,c_311,c_872,c_909,c_906,c_905,c_2050,c_2160]) ).
tcf(c_2185,plain,
( ( f(n) = n )
| ( f(n) = m ) ),
inference(superposition,[status(thm)],[c_2183,c_2047]) ).
tcf(c_2188,plain,
f(n) = m,
inference(forward_subsumption_resolution,[status(thm)],[c_2185,c_2181]) ).
tcf(c_2189,plain,
element(m,m),
inference(demodulation,[status(thm)],[c_2183,c_2188]) ).
tcf(c_2194,plain,
~ element(m,m),
inference(demodulation,[status(thm)],[c_2053,c_2188]) ).
tcf(c_2195,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2189,c_2194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN015-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 23:52:51 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 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...
% 2.63/1.16 % SZS status Started for theBenchmark.p
% 2.63/1.16 % SZS status Unsatisfiable for theBenchmark.p
% 2.63/1.16
% 2.63/1.16 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.63/1.16
% 2.63/1.16 % ------ iProver source info
% 2.63/1.16
% 2.63/1.16 % git: date: 2026-07-19 20:42:38 +0200
% 2.63/1.16 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.63/1.16 % git: non_committed_changes: false
% 2.63/1.16
% 2.63/1.16 % ------ Parsing...% successful
% 2.63/1.16
% 2.63/1.16
% 2.63/1.16 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.63/1.16
% 2.63/1.16 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.63/1.16
% 2.63/1.16 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.63/1.16
% 2.63/1.16 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.63/1.16 % ------ Proving...
% 2.63/1.16 % ------ Problem Properties
% 2.63/1.16
% 2.63/1.16 %
% 2.63/1.16 % clauses 16
% 2.63/1.16 % conjectures 16
% 2.63/1.16 % EPR 8
% 2.63/1.16 % Horn 3
% 2.63/1.16 % unary 1
% 2.63/1.16 % binary 3
% 2.63/1.16 % lits 50
% 2.63/1.16 % lits eq 27
% 2.63/1.16 % fd_pure 0
% 2.63/1.16 % fd_pseudo 0
% 2.63/1.16 % fd_cond 10
% 2.63/1.16 % fd_pseudo_cond 2
% 2.63/1.16 % AC symbols 0
% 2.63/1.16
% 2.63/1.16 % ------ Schedule dynamic 5 is on
% 2.63/1.16
% 2.63/1.16 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.63/1.16
% 2.63/1.16
% 2.63/1.16 % ------
% 2.63/1.16 % Current options:
% 2.63/1.16 % ------
% 2.63/1.16
% 2.63/1.16
% 2.63/1.16 %
% 2.63/1.16
% 2.63/1.16 % ------ Proving...
% 2.63/1.16 %
% 2.63/1.16
% 2.63/1.16 % SZS status Unsatisfiable for theBenchmark.p
% 2.63/1.16
% 2.63/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.63/1.16
% 2.63/1.16
%------------------------------------------------------------------------------