%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU281+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p 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 : Fri Sep 25 02:56:28 PM UTC 2026
% Result : Theorem 1.61s 1.74s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 6
% Syntax : Number of formulae : 151 ( 11 unt; 3 def)
% Number of atoms : 592 ( 241 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 598 ( 202 ~; 262 |; 122 &)
% ( 7 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 2 con; 0-3 aty)
% Number of variables : 358 ( 0 sgn 261 !; 97 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4,X5] :
( X5 = singleton(X4)
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e16_22__wellord2__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
? [X2] :
! [X3] :
( in(X3,X2)
<=> ( ? [X4,X5] :
( X5 = singleton(X4)
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f16,axiom,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 )
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3 )
=> X3 = X4 )
=> ? [X2] :
! [X3] :
( in(X3,X2)
<=> ? [X4] :
( ? [X9,X10] :
( X10 = singleton(X9)
& in(X9,X0)
& ordered_pair(X9,X10) = X3 )
& X4 = X3
& in(X4,cartesian_product2(X0,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e16_22__wellord2__2) ).
fof(f17,plain,
! [X0,X1] :
( ! [X2,X3,X4] :
( ( ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 )
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3 )
=> X3 = X4 )
=> ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) ) ),
inference(rectify,[],[f16]) ).
fof(f19,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( in(X3,X2)
<~> ( ? [X4,X5] :
( X5 = singleton(X4)
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 )
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3
& X3 != X4 )
| ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 )
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3
& X3 != X4 )
| ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) ) ),
inference(flattening,[],[f25]) ).
fof(f30,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( in(X3,X2)
| ( ? [X4,X5] :
( X5 = singleton(X4)
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1)) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f31,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( in(X3,X2)
| ( ? [X4,X5] :
( X5 = singleton(X4)
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1)) ) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
? [X0,X1] :
! [X2] :
? [X3] :
( ( in(X3,X2)
| ( ? [X6,X7] :
( singleton(X6) = X7
& in(X6,X0)
& ordered_pair(X6,X7) = X3 )
& in(X3,cartesian_product2(X0,X1)) ) )
& ( ~ in(X3,X2)
| ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,X0)
| ordered_pair(X4,X5) != X3 )
| ~ in(X3,cartesian_product2(X0,X1)) ) ),
inference(rectify,[],[f31]) ).
fof(f33,plain,
! [X2] :
( ( in(sK4(X2),X2)
| ( sK6(X2) = singleton(sK5(X2))
& in(sK5(X2),sK2)
& sK4(X2) = ordered_pair(sK5(X2),sK6(X2))
& in(sK4(X2),cartesian_product2(sK2,sK3)) ) )
& ( ~ in(sK4(X2),X2)
| ! [X4,X5] :
( singleton(X4) != X5
| ~ in(X4,sK2)
| ordered_pair(X4,X5) != sK4(X2) )
| ~ in(sK4(X2),cartesian_product2(sK2,sK3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X3,sK4(X2)),skolemize(X6,sK5(X2)),skolemize(X7,sK6(X2))],[f32]) ).
fof(f38,plain,
! [X0] :
( ~ sP1(X0)
| ? [X2,X3,X4] :
( sP0(X4,X0)
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3
& X3 != X4 ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f39,plain,
! [X0] :
( ~ sP1(X0)
| ? [X1,X2,X3] :
( sP0(X3,X0)
& X1 = X3
& ? [X4,X5] :
( singleton(X4) = X5
& in(X4,X0)
& ordered_pair(X4,X5) = X2 )
& X1 = X2
& X2 != X3 ) ),
inference(rectify,[],[f38]) ).
fof(f40,plain,
! [X0] :
( ~ sP1(X0)
| ( sP0(sK13(X0),X0)
& sK11(X0) = sK13(X0)
& sK15(X0) = singleton(sK14(X0))
& in(sK14(X0),X0)
& sK12(X0) = ordered_pair(sK14(X0),sK15(X0))
& sK11(X0) = sK12(X0)
& sK12(X0) != sK13(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15]),skolemize(X1,sK11(X0)),skolemize(X2,sK12(X0)),skolemize(X3,sK13(X0)),skolemize(X4,sK14(X0)),skolemize(X5,sK15(X0))],[f39]) ).
fof(f44,plain,
! [X0,X1] :
( sP1(X0)
| ? [X9] :
! [X10] :
( ( ~ in(X10,X9)
| ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) )
& ( ! [X11] :
( ! [X12,X13] :
( singleton(X12) != X13
| ~ in(X12,X0)
| ordered_pair(X12,X13) != X10 )
| X10 != X11
| ~ in(X11,cartesian_product2(X0,X1)) )
| in(X10,X9) ) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X0,X1] :
( sP1(X0)
| ? [X2] :
! [X3] :
( ( ~ in(X3,X2)
| ? [X7] :
( ? [X8,X9] :
( singleton(X8) = X9
& in(X8,X0)
& ordered_pair(X8,X9) = X3 )
& X3 = X7
& in(X7,cartesian_product2(X0,X1)) ) )
& ( ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) )
| in(X3,X2) ) ) ),
inference(rectify,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( sP1(X0)
| ! [X3] :
( ( ~ in(X3,sK18(X0,X1))
| ( sK21(X0,X3) = singleton(sK20(X0,X3))
& in(sK20(X0,X3),X0)
& ordered_pair(sK20(X0,X3),sK21(X0,X3)) = X3
& sK19(X0,X1,X3) = X3
& in(sK19(X0,X1,X3),cartesian_product2(X0,X1)) ) )
& ( ! [X4] :
( ! [X5,X6] :
( singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3 )
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1)) )
| in(X3,sK18(X0,X1)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21]),skolemize(X2,sK18(X0,X1)),skolemize(X7,sK19(X0,X1,X3)),skolemize(X8,sK20(X0,X3)),skolemize(X9,sK21(X0,X3))],[f45]) ).
fof(f47,plain,
! [X2] :
( in(sK4(X2),X2)
| sK6(X2) = singleton(sK5(X2)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f48,plain,
! [X2] :
( in(sK4(X2),X2)
| in(sK5(X2),sK2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f49,plain,
! [X2] :
( in(sK4(X2),X2)
| sK4(X2) = ordered_pair(sK5(X2),sK6(X2)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f50,plain,
! [X2] :
( in(sK4(X2),X2)
| in(sK4(X2),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f51,plain,
! [X2,X4,X5] :
( ~ in(sK4(X2),X2)
| singleton(X4) != X5
| ~ in(X4,sK2)
| ordered_pair(X4,X5) != sK4(X2)
| ~ in(sK4(X2),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f69,plain,
! [X0] :
( ~ sP1(X0)
| sP0(sK13(X0),X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f70,plain,
! [X0] :
( ~ sP1(X0)
| sK11(X0) = sK13(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f74,plain,
! [X0] :
( ~ sP1(X0)
| sK11(X0) = sK12(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f75,plain,
! [X0] :
( ~ sP1(X0)
| sK12(X0) != sK13(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f79,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK18(X0,X1))
| sK21(X0,X3) = singleton(sK20(X0,X3)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f80,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK18(X0,X1))
| in(sK20(X0,X3),X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f81,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK18(X0,X1))
| ordered_pair(sK20(X0,X3),sK21(X0,X3)) = X3 ),
inference(cnf_transformation,[],[f46]) ).
fof(f82,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK18(X0,X1))
| sK19(X0,X1,X3) = X3 ),
inference(cnf_transformation,[],[f46]) ).
fof(f83,plain,
! [X3,X0,X1] :
( sP1(X0)
| ~ in(X3,sK18(X0,X1))
| in(sK19(X0,X1,X3),cartesian_product2(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f84,plain,
! [X3,X0,X1,X6,X4,X5] :
( sP1(X0)
| singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X3
| X3 != X4
| ~ in(X4,cartesian_product2(X0,X1))
| in(X3,sK18(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f85,plain,
! [X2,X4] :
( ~ in(sK4(X2),X2)
| ~ in(X4,sK2)
| sK4(X2) != ordered_pair(X4,singleton(X4))
| ~ in(sK4(X2),cartesian_product2(sK2,sK3)) ),
inference(equality_resolution,[],[f51]) ).
fof(f86,plain,
! [X0,X1,X6,X4,X5] :
( sP1(X0)
| singleton(X5) != X6
| ~ in(X5,X0)
| ordered_pair(X5,X6) != X4
| ~ in(X4,cartesian_product2(X0,X1))
| in(X4,sK18(X0,X1)) ),
inference(equality_resolution,[],[f84]) ).
fof(f87,plain,
! [X0,X1,X6,X5] :
( sP1(X0)
| singleton(X5) != X6
| ~ in(X5,X0)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X0,X1))
| in(ordered_pair(X5,X6),sK18(X0,X1)) ),
inference(equality_resolution,[],[f86]) ).
fof(f88,plain,
! [X0,X1,X5] :
( sP1(X0)
| ~ in(X5,X0)
| ~ in(ordered_pair(X5,singleton(X5)),cartesian_product2(X0,X1))
| in(ordered_pair(X5,singleton(X5)),sK18(X0,X1)) ),
inference(equality_resolution,[],[f87]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ in(X0,sK2)
| ~ in(sK4(X1),X1)
| ~ in(sK4(X1),cartesian_product2(sK2,sK3))
| ( ordered_pair(X0,singleton(X0)) != sK4(X1) ) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_50,negated_conjecture,
! [X0: $i] :
( in(sK4(X0),X0)
| in(sK4(X0),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_51,negated_conjecture,
! [X0: $i] :
( in(sK4(X0),X0)
| ( ordered_pair(sK5(X0),sK6(X0)) = sK4(X0) ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( in(sK5(X0),sK2)
| in(sK4(X0),X0) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( in(sK4(X0),X0)
| ( singleton(sK5(X0)) = sK6(X0) ) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_71,plain,
! [X0: $i] :
( ~ sP1(X0)
| ( sK12(X0) != sK13(X0) ) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_72,plain,
! [X0: $i] :
( ( sK12(X0) = sK11(X0) )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_76,plain,
! [X0: $i] :
( ( sK13(X0) = sK11(X0) )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_77,plain,
! [X0: $i] :
( sP0(sK13(X0),X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X1)
| in(ordered_pair(X0,singleton(X0)),sK18(X1,X2))
| ~ in(X0,X1)
| ~ in(ordered_pair(X0,singleton(X0)),cartesian_product2(X1,X2)) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X1)
| in(sK19(X1,X2,X0),cartesian_product2(X1,X2))
| ~ in(X0,sK18(X1,X2)) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X1)
| ( sK19(X1,X2,X0) = X0 )
| ~ in(X0,sK18(X1,X2)) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X1)
| ( ordered_pair(sK20(X1,X0),sK21(X1,X0)) = X0 )
| ~ in(X0,sK18(X1,X2)) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X1)
| in(sK20(X1,X0),X1)
| ~ in(X0,sK18(X1,X2)) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X1)
| ( singleton(sK20(X1,X0)) = sK21(X1,X0) )
| ~ in(X0,sK18(X1,X2)) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_99,plain,
( ( sK13(sK2) = sK11(sK2) )
| ~ sP1(sK2) ),
inference(instantiation,[status(thm)],[c_76]) ).
tcf(c_100,plain,
( ( sK12(sK2) = sK11(sK2) )
| ~ sP1(sK2) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_103,plain,
( ~ sP1(sK2)
| ( sK12(sK2) != sK13(sK2) ) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_2321,definition,
iPr_def_10 = cartesian_product2(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2322,negated_conjecture,
! [X0: $i] :
( in(sK4(X0),X0)
| ( singleton(sK5(X0)) = sK6(X0) ) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_2323,negated_conjecture,
! [X0: $i] :
( in(sK5(X0),sK2)
| in(sK4(X0),X0) ),
inference(demodulation,[status(thm)],[c_52]) ).
tcf(c_2324,negated_conjecture,
! [X0: $i] :
( in(sK4(X0),X0)
| ( ordered_pair(sK5(X0),sK6(X0)) = sK4(X0) ) ),
inference(demodulation,[status(thm)],[c_51]) ).
tcf(c_2325,negated_conjecture,
! [X0: $i] :
( in(sK4(X0),iPr_def_10)
| in(sK4(X0),X0) ),
inference(demodulation,[status(thm)],[c_50,c_2321]) ).
tcf(c_2326,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ in(X0,sK2)
| ~ in(sK4(X1),iPr_def_10)
| ~ in(sK4(X1),X1)
| ( ordered_pair(X0,singleton(X0)) != sK4(X1) ) ),
inference(demodulation,[status(thm)],[c_49]) ).
tcf(c_2329,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2780,plain,
! [X0: $i] :
( sP1(sK2)
| in(ordered_pair(X0,singleton(X0)),sK18(sK2,sK3))
| ~ in(X0,sK2)
| ~ in(ordered_pair(X0,singleton(X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2321,c_81]) ).
tcf(c_2799,plain,
! [X0: $i,X1: $i] :
( sP1(X0)
| in(sK20(X0,sK4(sK18(X0,X1))),X0)
| ( ordered_pair(sK5(sK18(X0,X1)),sK6(sK18(X0,X1))) = sK4(sK18(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2324,c_85]) ).
tcf(c_2800,plain,
! [X0: $i,X1: $i] :
( sP1(X0)
| in(sK20(X0,sK4(sK18(X0,X1))),X0)
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2322,c_85]) ).
tcf(c_2835,plain,
! [X0: $i,X1: $i] :
( sP1(X0)
| ( sK19(X0,X1,sK4(sK18(X0,X1))) = sK4(sK18(X0,X1)) )
| ( ordered_pair(sK5(sK18(X0,X1)),sK6(sK18(X0,X1))) = sK4(sK18(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2324,c_83]) ).
tcf(c_2836,plain,
! [X0: $i,X1: $i] :
( sP1(X0)
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ( sK19(X0,X1,sK4(sK18(X0,X1))) = sK4(sK18(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2322,c_83]) ).
tcf(c_2837,plain,
! [X0: $i,X1: $i] :
( sP1(X0)
| in(sK4(sK18(X0,X1)),iPr_def_10)
| ( sK19(X0,X1,sK4(sK18(X0,X1))) = sK4(sK18(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2325,c_83]) ).
tcf(c_2902,plain,
! [X0: $i] :
( sP1(sK2)
| in(sK19(sK2,sK3,X0),iPr_def_10)
| ~ in(X0,sK18(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_2321,c_82]) ).
tcf(c_3106,plain,
! [X0: $i,X1: $i] :
( ( sK12(X0) = sK13(X0) )
| ( sK13(X0) != X1 )
| ( sK12(X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_2329]) ).
tcf(c_3129,plain,
! [X0: $i,X1: $i] :
( sP1(X0)
| ( singleton(sK20(X0,sK4(sK18(X0,X1)))) = sK21(X0,sK4(sK18(X0,X1))) )
| ( ordered_pair(sK5(sK18(X0,X1)),sK6(sK18(X0,X1))) = sK4(sK18(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2324,c_86]) ).
tcf(c_3130,plain,
! [X0: $i,X1: $i] :
( sP1(X0)
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ( singleton(sK20(X0,sK4(sK18(X0,X1)))) = sK21(X0,sK4(sK18(X0,X1))) ) ),
inference(superposition,[status(thm)],[c_2322,c_86]) ).
tcf(c_3131,plain,
! [X0: $i,X1: $i] :
( sP1(X0)
| in(sK4(sK18(X0,X1)),iPr_def_10)
| ( singleton(sK20(X0,sK4(sK18(X0,X1)))) = sK21(X0,sK4(sK18(X0,X1))) ) ),
inference(superposition,[status(thm)],[c_2325,c_86]) ).
tcf(c_3239,plain,
! [X0: $i,X1: $i] :
( sP1(X0)
| ( ordered_pair(sK5(sK18(X0,X1)),sK6(sK18(X0,X1))) = sK4(sK18(X0,X1)) )
| ( ordered_pair(sK20(X0,sK4(sK18(X0,X1))),sK21(X0,sK4(sK18(X0,X1)))) = sK4(sK18(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2324,c_84]) ).
tcf(c_3240,plain,
! [X0: $i,X1: $i] :
( sP1(X0)
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ( ordered_pair(sK20(X0,sK4(sK18(X0,X1))),sK21(X0,sK4(sK18(X0,X1)))) = sK4(sK18(X0,X1)) ) ),
inference(superposition,[status(thm)],[c_2322,c_84]) ).
tcf(c_3302,plain,
! [X0: $i] :
( ( sK12(X0) = sK13(X0) )
| ( sK13(X0) != sK11(X0) )
| ( sK12(X0) != sK11(X0) ) ),
inference(instantiation,[status(thm)],[c_3106]) ).
tcf(c_3303,plain,
( ( sK12(sK2) = sK13(sK2) )
| ( sK13(sK2) != sK11(sK2) )
| ( sK12(sK2) != sK11(sK2) ) ),
inference(instantiation,[status(thm)],[c_3302]) ).
tcf(c_3314,plain,
! [X0: $i] :
( ~ in(X0,sK18(sK2,sK3))
| in(sK19(sK2,sK3,X0),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_2902,c_99,c_100,c_103,c_2902,c_3303]) ).
tcf(c_3315,plain,
! [X0: $i] :
( in(sK19(sK2,sK3,X0),iPr_def_10)
| ~ in(X0,sK18(sK2,sK3)) ),
inference(renaming,[status(thm)],[c_3314]) ).
tcf(c_3441,plain,
! [X0: $i,X1: $i] :
( ( singleton(sK20(X0,sK4(sK18(X0,X1)))) = sK21(X0,sK4(sK18(X0,X1))) )
| in(sK4(sK18(X0,X1)),iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_3131,c_76,c_72,c_71,c_3131,c_3302]) ).
tcf(c_3442,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK18(X0,X1)),iPr_def_10)
| ( singleton(sK20(X0,sK4(sK18(X0,X1)))) = sK21(X0,sK4(sK18(X0,X1))) ) ),
inference(renaming,[status(thm)],[c_3441]) ).
tcf(c_3485,plain,
! [X0: $i,X1: $i] :
( ( singleton(sK20(X0,sK4(sK18(X0,X1)))) = sK21(X0,sK4(sK18(X0,X1))) )
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_3130,c_76,c_72,c_71,c_3130,c_3302]) ).
tcf(c_3486,plain,
! [X0: $i,X1: $i] :
( ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ( singleton(sK20(X0,sK4(sK18(X0,X1)))) = sK21(X0,sK4(sK18(X0,X1))) ) ),
inference(renaming,[status(thm)],[c_3485]) ).
tcf(c_3492,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ~ in(sK4(X2),iPr_def_10)
| ~ in(sK4(X2),X2)
| ~ in(sK20(X0,sK4(sK18(X0,X1))),sK2)
| ( ordered_pair(sK20(X0,sK4(sK18(X0,X1))),sK21(X0,sK4(sK18(X0,X1)))) != sK4(X2) ) ),
inference(superposition,[status(thm)],[c_3486,c_2326]) ).
tcf(c_3510,plain,
! [X0: $i,X1: $i] :
( ( ordered_pair(sK20(X0,sK4(sK18(X0,X1))),sK21(X0,sK4(sK18(X0,X1)))) = sK4(sK18(X0,X1)) )
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_3240,c_76,c_72,c_71,c_3240,c_3302]) ).
tcf(c_3511,plain,
! [X0: $i,X1: $i] :
( ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ( ordered_pair(sK20(X0,sK4(sK18(X0,X1))),sK21(X0,sK4(sK18(X0,X1)))) = sK4(sK18(X0,X1)) ) ),
inference(renaming,[status(thm)],[c_3510]) ).
tcf(c_3521,plain,
! [X0: $i,X1: $i] :
( ( ordered_pair(sK20(X0,sK4(sK18(X0,X1))),sK21(X0,sK4(sK18(X0,X1)))) = sK4(sK18(X0,X1)) )
| ( ordered_pair(sK5(sK18(X0,X1)),sK6(sK18(X0,X1))) = sK4(sK18(X0,X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_3239,c_76,c_72,c_71,c_3239,c_3302]) ).
tcf(c_3522,plain,
! [X0: $i,X1: $i] :
( ( ordered_pair(sK5(sK18(X0,X1)),sK6(sK18(X0,X1))) = sK4(sK18(X0,X1)) )
| ( ordered_pair(sK20(X0,sK4(sK18(X0,X1))),sK21(X0,sK4(sK18(X0,X1)))) = sK4(sK18(X0,X1)) ) ),
inference(renaming,[status(thm)],[c_3521]) ).
tcf(c_3616,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ~ in(sK4(X2),iPr_def_10)
| ~ in(sK4(X2),X2)
| ~ in(sK20(X0,sK4(sK18(X0,X1))),sK2)
| ( sK4(sK18(X0,X1)) != sK4(X2) ) ),
inference(superposition,[status(thm)],[c_3511,c_3492]) ).
tcf(c_3696,plain,
! [X0: $i] :
( ~ in(ordered_pair(X0,singleton(X0)),iPr_def_10)
| ~ in(X0,sK2)
| in(ordered_pair(X0,singleton(X0)),sK18(sK2,sK3)) ),
inference(global_subsumption_just,[status(thm)],[c_2780,c_99,c_100,c_103,c_2780,c_3303]) ).
tcf(c_3697,plain,
! [X0: $i] :
( in(ordered_pair(X0,singleton(X0)),sK18(sK2,sK3))
| ~ in(X0,sK2)
| ~ in(ordered_pair(X0,singleton(X0)),iPr_def_10) ),
inference(renaming,[status(thm)],[c_3696]) ).
tcf(c_3704,plain,
! [X0: $i,X1: $i] :
( in(ordered_pair(sK20(X0,sK4(sK18(X0,X1))),sK21(X0,sK4(sK18(X0,X1)))),sK18(sK2,sK3))
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ~ in(sK20(X0,sK4(sK18(X0,X1))),sK2)
| ~ in(ordered_pair(sK20(X0,sK4(sK18(X0,X1))),singleton(sK20(X0,sK4(sK18(X0,X1))))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3486,c_3697]) ).
tcf(c_4112,plain,
! [X0: $i,X1: $i] :
( ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ~ in(sK4(sK18(X0,X1)),iPr_def_10)
| ~ in(sK20(X0,sK4(sK18(X0,X1))),sK2)
| ~ in(sK4(sK18(X0,X1)),sK18(X0,X1)) ),
inference(equality_resolution,[status(thm)],[c_3616]) ).
tcf(c_4376,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK18(X0,X1)),sK18(X0,X1))
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) ) ),
inference(instantiation,[status(thm)],[c_2322]) ).
tcf(c_4424,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK18(X0,X1)),sK18(sK2,sK3))
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ~ in(sK20(X0,sK4(sK18(X0,X1))),sK2)
| ~ in(ordered_pair(sK20(X0,sK4(sK18(X0,X1))),singleton(sK20(X0,sK4(sK18(X0,X1))))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3511,c_3704]) ).
tcf(c_4464,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK18(X0,X1)),sK18(sK2,sK3))
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ~ in(sK20(X0,sK4(sK18(X0,X1))),sK2)
| ~ in(ordered_pair(sK20(X0,sK4(sK18(X0,X1))),sK21(X0,sK4(sK18(X0,X1)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3486,c_4424]) ).
tcf(c_4479,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK18(X0,X1)),sK18(sK2,sK3))
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ~ in(sK4(sK18(X0,X1)),iPr_def_10)
| ~ in(sK20(X0,sK4(sK18(X0,X1))),sK2) ),
inference(superposition,[status(thm)],[c_3511,c_4464]) ).
tcf(c_4498,plain,
! [X0: $i,X1: $i] :
( ~ in(sK20(X0,sK4(sK18(X0,X1))),sK2)
| ~ in(sK4(sK18(X0,X1)),iPr_def_10)
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) ) ),
inference(global_subsumption_just,[status(thm)],[c_4479,c_4112,c_4376]) ).
tcf(c_4499,plain,
! [X0: $i,X1: $i] :
( ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ~ in(sK4(sK18(X0,X1)),iPr_def_10)
| ~ in(sK20(X0,sK4(sK18(X0,X1))),sK2) ),
inference(renaming,[status(thm)],[c_4498]) ).
fof(f27,definition,
! [X4,X0] :
( ~ sP0(X4,X0)
| ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f28,definition,
! [X0] :
( ~ sP1(X0)
| ? [X2,X3,X4] :
( sP0(X4,X0)
& X2 = X4
& ? [X5,X6] :
( X6 = singleton(X5)
& in(X5,X0)
& ordered_pair(X5,X6) = X3 )
& X2 = X3
& X3 != X4 ) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
fof(f29,plain,
! [X0,X1] :
( sP1(X0)
| ? [X9] :
! [X10] :
( in(X10,X9)
<=> ? [X11] :
( ? [X12,X13] :
( singleton(X12) = X13
& in(X12,X0)
& ordered_pair(X12,X13) = X10 )
& X10 = X11
& in(X11,cartesian_product2(X0,X1)) ) ) ),
inference(definition_folding,[],[f26,f28,f27]) ).
fof(f41,plain,
! [X4,X0] :
( ~ sP0(X4,X0)
| ? [X7,X8] :
( X8 = singleton(X7)
& in(X7,X0)
& ordered_pair(X7,X8) = X4 ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f42,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2,X3] :
( singleton(X2) = X3
& in(X2,X1)
& ordered_pair(X2,X3) = X0 ) ),
inference(rectify,[],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( sK17(X0,X1) = singleton(sK16(X0,X1))
& in(sK16(X0,X1),X1)
& ordered_pair(sK16(X0,X1),sK17(X0,X1)) = X0 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X2,sK16(X0,X1)),skolemize(X3,sK17(X0,X1))],[f42]) ).
fof(f78,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ordered_pair(sK16(X0,X1),sK17(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( ordered_pair(sK16(X0,X1),sK17(X0,X1)) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_442,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ordered_pair(sK16(X1,X2),sK17(X1,X2)) = X1 )
| ~ sP1(X0)
| ( X0 != X2 )
| ( sK13(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_78]) ).
tcf(c_443,plain,
! [X0: $i] :
( ( ordered_pair(sK16(sK13(X0),X0),sK17(sK13(X0),X0)) = sK13(X0) )
| ~ sP1(X0) ),
inference(unflattening,[status(thm)],[c_442]) ).
tcf(c_3341,plain,
! [X0: $i] : ~ sP1(X0),
inference(global_subsumption_just,[status(thm)],[c_443,c_76,c_72,c_71,c_3302]) ).
tcf(c_3345,plain,
! [X0: $i,X1: $i] :
( in(sK4(sK18(X0,X1)),iPr_def_10)
| ( sK19(X0,X1,sK4(sK18(X0,X1))) = sK4(sK18(X0,X1)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2837,c_3341]) ).
tcf(c_3346,plain,
! [X0: $i,X1: $i] :
( ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) )
| ( sK19(X0,X1,sK4(sK18(X0,X1))) = sK4(sK18(X0,X1)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2836,c_3341]) ).
tcf(c_3347,plain,
! [X0: $i,X1: $i] :
( ( sK19(X0,X1,sK4(sK18(X0,X1))) = sK4(sK18(X0,X1)) )
| ( ordered_pair(sK5(sK18(X0,X1)),sK6(sK18(X0,X1))) = sK4(sK18(X0,X1)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2835,c_3341]) ).
tcf(c_3350,plain,
! [X0: $i,X1: $i] :
( in(sK20(X0,sK4(sK18(X0,X1))),X0)
| ( singleton(sK5(sK18(X0,X1))) = sK6(sK18(X0,X1)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2800,c_3341]) ).
tcf(c_3351,plain,
! [X0: $i,X1: $i] :
( in(sK20(X0,sK4(sK18(X0,X1))),X0)
| ( ordered_pair(sK5(sK18(X0,X1)),sK6(sK18(X0,X1))) = sK4(sK18(X0,X1)) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_2799,c_3341]) ).
tcf(c_3352,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( singleton(sK20(X1,X0)) = sK21(X1,X0) )
| ~ in(X0,sK18(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_86,c_3341]) ).
tcf(c_3353,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK20(X1,X0),X1)
| ~ in(X0,sK18(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_85,c_3341]) ).
tcf(c_3354,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ordered_pair(sK20(X1,X0),sK21(X1,X0)) = X0 )
| ~ in(X0,sK18(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_84,c_3341]) ).
tcf(c_3355,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( sK19(X1,X2,X0) = X0 )
| ~ in(X0,sK18(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_83,c_3341]) ).
tcf(c_3499,plain,
! [X0: $i,X1: $i] :
( ( ordered_pair(sK5(sK18(X0,X1)),sK6(sK18(X0,X1))) = sK4(sK18(X0,X1)) )
| ( singleton(sK20(X0,sK4(sK18(X0,X1)))) = sK21(X0,sK4(sK18(X0,X1))) ) ),
inference(global_subsumption_just,[status(thm)],[c_3129,c_3129,c_3341]) ).
tcf(c_3500,plain,
! [X0: $i,X1: $i] :
( ( singleton(sK20(X0,sK4(sK18(X0,X1)))) = sK21(X0,sK4(sK18(X0,X1))) )
| ( ordered_pair(sK5(sK18(X0,X1)),sK6(sK18(X0,X1))) = sK4(sK18(X0,X1)) ) ),
inference(renaming,[status(thm)],[c_3499]) ).
tcf(c_3788,plain,
( in(sK4(sK18(sK2,sK3)),iPr_def_10)
| ( singleton(sK5(sK18(sK2,sK3))) = sK6(sK18(sK2,sK3)) )
| ~ in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_3346,c_3315]) ).
tcf(c_4088,plain,
( in(sK4(sK18(sK2,sK3)),iPr_def_10)
| ( singleton(sK5(sK18(sK2,sK3))) = sK6(sK18(sK2,sK3)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3788,c_2325]) ).
tcf(c_4508,plain,
! [X0: $i] :
( ( singleton(sK5(sK18(sK2,X0))) = sK6(sK18(sK2,X0)) )
| ~ in(sK4(sK18(sK2,X0)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3350,c_4499]) ).
tcf(c_4641,plain,
singleton(sK5(sK18(sK2,sK3))) = sK6(sK18(sK2,sK3)),
inference(backward_subsumption_resolution,[status(thm)],[c_4088,c_4508]) ).
tcf(c_4661,plain,
( in(ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))),sK18(sK2,sK3))
| ~ in(sK5(sK18(sK2,sK3)),sK2)
| ~ in(ordered_pair(sK5(sK18(sK2,sK3)),singleton(sK5(sK18(sK2,sK3)))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_4641,c_3697]) ).
tcf(c_4667,plain,
( in(ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))),sK18(sK2,sK3))
| ~ in(sK5(sK18(sK2,sK3)),sK2)
| ~ in(ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))),iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_4661,c_4641]) ).
tcf(c_4861,plain,
( in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3))
| ( sK19(sK2,sK3,sK4(sK18(sK2,sK3))) = sK4(sK18(sK2,sK3)) )
| ~ in(sK5(sK18(sK2,sK3)),sK2)
| ~ in(ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3347,c_4667]) ).
tcf(c_4862,plain,
( in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3))
| ( singleton(sK20(sK2,sK4(sK18(sK2,sK3)))) = sK21(sK2,sK4(sK18(sK2,sK3))) )
| ~ in(sK5(sK18(sK2,sK3)),sK2)
| ~ in(ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3500,c_4667]) ).
tcf(c_4897,plain,
( ( singleton(sK20(sK2,sK4(sK18(sK2,sK3)))) = sK21(sK2,sK4(sK18(sK2,sK3))) )
| ~ in(ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4862,c_3352,c_2323]) ).
tcf(c_4905,plain,
( ( singleton(sK20(sK2,sK4(sK18(sK2,sK3)))) = sK21(sK2,sK4(sK18(sK2,sK3))) )
| ~ in(sK4(sK18(sK2,sK3)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3500,c_4897]) ).
tcf(c_4910,plain,
singleton(sK20(sK2,sK4(sK18(sK2,sK3)))) = sK21(sK2,sK4(sK18(sK2,sK3))),
inference(forward_subsumption_resolution,[status(thm)],[c_4905,c_3442]) ).
tcf(c_4921,plain,
! [X0: $i] :
( ~ in(sK4(X0),iPr_def_10)
| ~ in(sK4(X0),X0)
| ~ in(sK20(sK2,sK4(sK18(sK2,sK3))),sK2)
| ( ordered_pair(sK20(sK2,sK4(sK18(sK2,sK3))),sK21(sK2,sK4(sK18(sK2,sK3)))) != sK4(X0) ) ),
inference(superposition,[status(thm)],[c_4910,c_2326]) ).
tcf(c_4997,plain,
! [X0: $i] :
( ( ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))) = sK4(sK18(sK2,sK3)) )
| ~ in(sK4(X0),iPr_def_10)
| ~ in(sK4(X0),X0)
| ~ in(sK20(sK2,sK4(sK18(sK2,sK3))),sK2)
| ( sK4(sK18(sK2,sK3)) != sK4(X0) ) ),
inference(superposition,[status(thm)],[c_3522,c_4921]) ).
tcf(c_5035,plain,
! [X0: $i] :
( ( ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))) = sK4(sK18(sK2,sK3)) )
| ~ in(sK4(X0),iPr_def_10)
| ~ in(sK4(X0),X0)
| ( sK4(sK18(sK2,sK3)) != sK4(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4997,c_3351]) ).
tcf(c_5048,plain,
( ( ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))) = sK4(sK18(sK2,sK3)) )
| ~ in(sK4(sK18(sK2,sK3)),iPr_def_10)
| ~ in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3)) ),
inference(equality_resolution,[status(thm)],[c_5035]) ).
tcf(c_5243,plain,
( ( ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))) = sK4(sK18(sK2,sK3)) )
| ~ in(sK4(sK18(sK2,sK3)),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_5048,c_2324]) ).
tcf(c_6101,plain,
( ( sK19(sK2,sK3,sK4(sK18(sK2,sK3))) = sK4(sK18(sK2,sK3)) )
| ~ in(ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4861,c_3355,c_2323]) ).
tcf(c_6108,plain,
( ( sK19(sK2,sK3,sK4(sK18(sK2,sK3))) = sK4(sK18(sK2,sK3)) )
| ~ in(sK4(sK18(sK2,sK3)),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3347,c_6101]) ).
tcf(c_6131,plain,
sK19(sK2,sK3,sK4(sK18(sK2,sK3))) = sK4(sK18(sK2,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_6108,c_3345]) ).
tcf(c_6136,plain,
( in(sK4(sK18(sK2,sK3)),iPr_def_10)
| ~ in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_6131,c_3315]) ).
tcf(c_6249,plain,
in(sK4(sK18(sK2,sK3)),iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_6136,c_2325]) ).
tcf(c_6250,plain,
ordered_pair(sK5(sK18(sK2,sK3)),sK6(sK18(sK2,sK3))) = sK4(sK18(sK2,sK3)),
inference(backward_subsumption_resolution,[status(thm)],[c_5243,c_6249]) ).
tcf(c_6255,plain,
( in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3))
| ~ in(sK5(sK18(sK2,sK3)),sK2)
| ~ in(sK4(sK18(sK2,sK3)),iPr_def_10) ),
inference(demodulation,[status(thm)],[c_4667,c_6250]) ).
tcf(c_6261,plain,
( in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3))
| ~ in(sK5(sK18(sK2,sK3)),sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6255,c_6249]) ).
tcf(c_6283,plain,
in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_6261,c_2323]) ).
tcf(c_6285,plain,
ordered_pair(sK20(sK2,sK4(sK18(sK2,sK3))),sK21(sK2,sK4(sK18(sK2,sK3)))) = sK4(sK18(sK2,sK3)),
inference(superposition,[status(thm)],[c_6283,c_3354]) ).
tcf(c_6288,plain,
in(sK20(sK2,sK4(sK18(sK2,sK3))),sK2),
inference(superposition,[status(thm)],[c_6283,c_3353]) ).
tcf(c_6289,plain,
! [X0: $i] :
( ~ in(sK4(X0),iPr_def_10)
| ~ in(sK4(X0),X0)
| ~ in(sK20(sK2,sK4(sK18(sK2,sK3))),sK2)
| ( sK4(sK18(sK2,sK3)) != sK4(X0) ) ),
inference(demodulation,[status(thm)],[c_4921,c_6285]) ).
tcf(c_6290,plain,
! [X0: $i] :
( ~ in(sK4(X0),iPr_def_10)
| ~ in(sK4(X0),X0)
| ( sK4(sK18(sK2,sK3)) != sK4(X0) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6289,c_6288]) ).
tcf(c_6367,plain,
( ~ in(sK4(sK18(sK2,sK3)),iPr_def_10)
| ~ in(sK4(sK18(sK2,sK3)),sK18(sK2,sK3)) ),
inference(equality_resolution,[status(thm)],[c_6290]) ).
tcf(c_6368,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_6367,c_6249,c_6283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU281+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 13:31:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 1.61/1.74 % SZS status Started for theBenchmark.p
% 1.61/1.74 % SZS status Theorem for theBenchmark.p
% 1.61/1.74
% 1.61/1.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.61/1.74
% 1.61/1.74 % ------ iProver source info
% 1.61/1.74
% 1.61/1.74 % git: date: 2026-07-19 20:42:38 +0200
% 1.61/1.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.61/1.74 % git: non_committed_changes: false
% 1.61/1.74
% 1.61/1.74 % ------ Parsing...
% 1.61/1.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.61/1.74
% 1.61/1.74 % ------ Preprocessing... sup_sim: 0 sf_s rm: 16 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 1.61/1.74
% 1.61/1.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.61/1.74
% 1.61/1.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.61/1.74 % ------ Proving...
% 1.61/1.74 % ------ Problem Properties
% 1.61/1.74
% 1.61/1.74 %
% 1.61/1.74 % clauses 26
% 1.61/1.74 % conjectures 5
% 1.61/1.74 % EPR 4
% 1.61/1.74 % Horn 16
% 1.61/1.74 % unary 5
% 1.61/1.74 % binary 14
% 1.61/1.74 % lits 56
% 1.61/1.74 % lits eq 14
% 1.61/1.74 % fd_pure 0
% 1.61/1.74 % fd_pseudo 0
% 1.61/1.74 % fd_cond 0
% 1.61/1.74 % fd_pseudo_cond 0
% 1.61/1.74 % AC symbols 0
% 1.61/1.74
% 1.61/1.74 % ------ Schedule dynamic 5 is on
% 1.61/1.74
% 1.61/1.74 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.61/1.74
% 1.61/1.74
% 1.61/1.74 % ------
% 1.61/1.74 % Current options:
% 1.61/1.74 % ------
% 1.61/1.74
% 1.61/1.74
% 1.61/1.74 %
% 1.61/1.74
% 1.61/1.74 % ------ Proving...
% 1.61/1.74 %
% 1.61/1.74
% 1.61/1.74 % SZS status Theorem for theBenchmark.p
% 1.61/1.74
% 1.61/1.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.61/1.75
% 1.61/1.75
%------------------------------------------------------------------------------