%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU332+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 : n007.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 02:56:57 PM UTC 2026
% Result : Theorem 135.56s 34.32s
% Output : CNFRefutation 135.56s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f72ERROR: Could not build tree for root c_211026ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) )
=> ! [X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X7 = X5
=> X6 = subset_complement(the_carrier(X0),X7) ) )
& in(X5,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_7_2__tops_2__1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) )
=> ! [X2] :
? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( ! [X7] :
( element(X7,powerset(the_carrier(X0)))
=> ( X7 = X5
=> X6 = subset_complement(the_carrier(X0),X7) ) )
& in(X5,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f22,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f26,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f51,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0)
& ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( ? [X5,X6] :
( ! [X7] :
( ~ element(X7,powerset(the_carrier(X0)))
| X5 != X7
| X6 = subset_complement(the_carrier(X0),X7) )
& in(X5,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f52,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0)
& ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( ? [X5,X6] :
( ! [X7] :
( ~ element(X7,powerset(the_carrier(X0)))
| X5 != X7
| X6 = subset_complement(the_carrier(X0),X7) )
& in(X5,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) ) ),
inference(flattening,[],[f51]) ).
fof(f66,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f22]) ).
fof(f68,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f74,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0)
& ? [X2] :
! [X3] :
? [X4] :
( ( in(X4,X3)
| ( ? [X5,X6] :
( ! [X7] :
( ~ element(X7,powerset(the_carrier(X0)))
| X5 != X7
| X6 = subset_complement(the_carrier(X0),X7) )
& in(X5,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) )
& ( ~ in(X4,X3)
| ! [X5,X6] :
( ? [X7] :
( element(X7,powerset(the_carrier(X0)))
& X5 = X7
& subset_complement(the_carrier(X0),X7) != X6 )
| ~ in(X5,X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X1,X2)) ) ) ),
inference(nnf_transformation,[],[f52]) ).
fof(f75,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0)
& ? [X2] :
! [X3] :
? [X4] :
( ( in(X4,X3)
| ( ? [X5,X6] :
( ! [X7] :
( ~ element(X7,powerset(the_carrier(X0)))
| X5 != X7
| X6 = subset_complement(the_carrier(X0),X7) )
& in(X5,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) )
& ( ~ in(X4,X3)
| ! [X5,X6] :
( ? [X7] :
( element(X7,powerset(the_carrier(X0)))
& X5 = X7
& subset_complement(the_carrier(X0),X7) != X6 )
| ~ in(X5,X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X1,X2)) ) ) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
? [X0,X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0)
& ? [X2] :
! [X3] :
? [X4] :
( ( in(X4,X3)
| ( ? [X8,X9] :
( ! [X10] :
( ~ element(X10,powerset(the_carrier(X0)))
| X8 != X10
| subset_complement(the_carrier(X0),X10) = X9 )
& in(X8,X1)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) )
& ( ~ in(X4,X3)
| ! [X5,X6] :
( ? [X7] :
( element(X7,powerset(the_carrier(X0)))
& X5 = X7
& subset_complement(the_carrier(X0),X7) != X6 )
| ~ in(X5,X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X1,X2)) ) ) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
( element(sK3,powerset(powerset(the_carrier(sK2))))
& one_sorted_str(sK2)
& ! [X3] :
( ( in(sK5(X3),X3)
| ( ! [X10] :
( ~ element(X10,powerset(the_carrier(sK2)))
| sK7(X3) != X10
| sK8(X3) = subset_complement(the_carrier(sK2),X10) )
& in(sK7(X3),sK3)
& sK5(X3) = ordered_pair(sK7(X3),sK8(X3))
& in(sK5(X3),cartesian_product2(sK3,sK4)) ) )
& ( ~ in(sK5(X3),X3)
| ! [X5,X6] :
( ( element(sK6(X5,X6),powerset(the_carrier(sK2)))
& sK6(X5,X6) = X5
& subset_complement(the_carrier(sK2),sK6(X5,X6)) != X6 )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3) )
| ~ in(sK5(X3),cartesian_product2(sK3,sK4)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X4,sK5(X3)),skolemize(X7,sK6(X5,X6)),skolemize(X8,sK7(X3)),skolemize(X9,sK8(X3))],[f76]) ).
fof(f81,plain,
! [X2,X1,X0] :
( ~ sP1(X2,X1,X0)
| ? [X12] :
! [X13] :
( ( ~ in(X13,X12)
| ? [X14] :
( ? [X15,X16] :
( ! [X17] :
( ~ element(X17,powerset(the_carrier(X0)))
| X15 != X17
| subset_complement(the_carrier(X0),X17) = X16 )
& in(X15,X1)
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(X1,X2)) ) )
& ( ! [X14] :
( ! [X15,X16] :
( ? [X17] :
( element(X17,powerset(the_carrier(X0)))
& X15 = X17
& subset_complement(the_carrier(X0),X17) != X16 )
| ~ in(X15,X1)
| ordered_pair(X15,X16) != X13 )
| X13 != X14
| ~ in(X14,cartesian_product2(X1,X2)) )
| in(X13,X12) ) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ sP1(X0,X1,X2)
| ? [X3] :
! [X4] :
( ( ~ in(X4,X3)
| ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( ~ element(X12,powerset(the_carrier(X2)))
| X10 != X12
| subset_complement(the_carrier(X2),X12) = X11 )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(X1,X0)) ) )
& ( ! [X5] :
( ! [X6,X7] :
( ? [X8] :
( element(X8,powerset(the_carrier(X2)))
& X6 = X8
& subset_complement(the_carrier(X2),X8) != X7 )
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X0)) )
| in(X4,X3) ) ) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ sP1(X0,X1,X2)
| ! [X4] :
( ( ~ in(X4,sK12(X0,X1,X2))
| ( ! [X12] :
( ~ element(X12,powerset(the_carrier(X2)))
| sK15(X1,X2,X4) != X12
| subset_complement(the_carrier(X2),X12) = sK16(X1,X2,X4) )
& in(sK15(X1,X2,X4),X1)
& ordered_pair(sK15(X1,X2,X4),sK16(X1,X2,X4)) = X4
& sK14(X0,X1,X2,X4) = X4
& in(sK14(X0,X1,X2,X4),cartesian_product2(X1,X0)) ) )
& ( ! [X5] :
( ! [X6,X7] :
( ( element(sK13(X2,X6,X7),powerset(the_carrier(X2)))
& sK13(X2,X6,X7) = X6
& subset_complement(the_carrier(X2),sK13(X2,X6,X7)) != X7 )
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X0)) )
| in(X4,sK12(X0,X1,X2)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15,sK16]),skolemize(X3,sK12(X0,X1,X2)),skolemize(X8,sK13(X2,X6,X7)),skolemize(X9,sK14(X0,X1,X2,X4)),skolemize(X10,sK15(X1,X2,X4)),skolemize(X11,sK16(X1,X2,X4))],[f82]) ).
fof(f87,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0)
| ! [X2] :
( ( sP0(sK21(X0,X1),X1,X0)
& sK19(X0,X1) = sK21(X0,X1)
& ! [X8] :
( ~ element(X8,powerset(the_carrier(X0)))
| sK22(X0,X1) != X8
| subset_complement(the_carrier(X0),X8) = sK23(X0,X1) )
& in(sK22(X0,X1),X1)
& sK20(X0,X1) = ordered_pair(sK22(X0,X1),sK23(X0,X1))
& sK19(X0,X1) = sK20(X0,X1)
& sK20(X0,X1) != sK21(X0,X1) )
| sP1(X2,X1,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19,sK20,sK21,sK22,sK23]),skolemize(X3,sK19(X0,X1)),skolemize(X4,sK20(X0,X1)),skolemize(X5,sK21(X0,X1)),skolemize(X6,sK22(X0,X1)),skolemize(X7,sK23(X0,X1))],[f73]) ).
fof(f88,plain,
element(sK3,powerset(powerset(the_carrier(sK2)))),
inference(cnf_transformation,[],[f77]) ).
fof(f89,plain,
one_sorted_str(sK2),
inference(cnf_transformation,[],[f77]) ).
fof(f90,plain,
! [X3,X10] :
( in(sK5(X3),X3)
| ~ element(X10,powerset(the_carrier(sK2)))
| sK7(X3) != X10
| sK8(X3) = subset_complement(the_carrier(sK2),X10) ),
inference(cnf_transformation,[],[f77]) ).
fof(f91,plain,
! [X3] :
( in(sK5(X3),X3)
| in(sK7(X3),sK3) ),
inference(cnf_transformation,[],[f77]) ).
fof(f92,plain,
! [X3] :
( in(sK5(X3),X3)
| sK5(X3) = ordered_pair(sK7(X3),sK8(X3)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f93,plain,
! [X3] :
( in(sK5(X3),X3)
| in(sK5(X3),cartesian_product2(sK3,sK4)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f94,plain,
! [X3,X6,X5] :
( ~ in(sK5(X3),X3)
| element(sK6(X5,X6),powerset(the_carrier(sK2)))
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(sK3,sK4)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f95,plain,
! [X3,X6,X5] :
( ~ in(sK5(X3),X3)
| sK6(X5,X6) = X5
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(sK3,sK4)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f96,plain,
! [X3,X6,X5] :
( ~ in(sK5(X3),X3)
| subset_complement(the_carrier(sK2),sK6(X5,X6)) != X6
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(sK3,sK4)) ),
inference(cnf_transformation,[],[f77]) ).
fof(f132,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f66]) ).
fof(f134,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f136,plain,
! [X2,X0,X1,X4,X12] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,sK12(X0,X1,X2))
| ~ element(X12,powerset(the_carrier(X2)))
| sK15(X1,X2,X4) != X12
| subset_complement(the_carrier(X2),X12) = sK16(X1,X2,X4) ),
inference(cnf_transformation,[],[f83]) ).
fof(f137,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,sK12(X0,X1,X2))
| in(sK15(X1,X2,X4),X1) ),
inference(cnf_transformation,[],[f83]) ).
fof(f138,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,sK12(X0,X1,X2))
| ordered_pair(sK15(X1,X2,X4),sK16(X1,X2,X4)) = X4 ),
inference(cnf_transformation,[],[f83]) ).
fof(f139,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,sK12(X0,X1,X2))
| sK14(X0,X1,X2,X4) = X4 ),
inference(cnf_transformation,[],[f83]) ).
fof(f140,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,sK12(X0,X1,X2))
| in(sK14(X0,X1,X2,X4),cartesian_product2(X1,X0)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f141,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ sP1(X0,X1,X2)
| element(sK13(X2,X6,X7),powerset(the_carrier(X2)))
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X0))
| in(X4,sK12(X0,X1,X2)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f142,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ sP1(X0,X1,X2)
| sK13(X2,X6,X7) = X6
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X0))
| in(X4,sK12(X0,X1,X2)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f143,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( ~ sP1(X0,X1,X2)
| subset_complement(the_carrier(X2),sK13(X2,X6,X7)) != X7
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X0))
| in(X4,sK12(X0,X1,X2)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0)
| sK19(X0,X1) = sK21(X0,X1)
| sP1(X2,X1,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0)
| in(sK22(X0,X1),X1)
| sP1(X2,X1,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0)
| sK19(X0,X1) = sK20(X0,X1)
| sP1(X2,X1,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0)
| sK20(X0,X1) != sK21(X0,X1)
| sP1(X2,X1,X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f154,plain,
! [X3] :
( in(sK5(X3),X3)
| ~ element(sK7(X3),powerset(the_carrier(sK2)))
| sK8(X3) = subset_complement(the_carrier(sK2),sK7(X3)) ),
inference(equality_resolution,[],[f90]) ).
fof(f155,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ sP1(X0,X1,X2)
| subset_complement(the_carrier(X2),sK13(X2,X6,X7)) != X7
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(X1,X0))
| in(X5,sK12(X0,X1,X2)) ),
inference(equality_resolution,[],[f143]) ).
fof(f156,plain,
! [X2,X0,X1,X6,X7] :
( ~ sP1(X0,X1,X2)
| subset_complement(the_carrier(X2),sK13(X2,X6,X7)) != X7
| ~ in(X6,X1)
| ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X0))
| in(ordered_pair(X6,X7),sK12(X0,X1,X2)) ),
inference(equality_resolution,[],[f155]) ).
fof(f157,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ sP1(X0,X1,X2)
| sK13(X2,X6,X7) = X6
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(X1,X0))
| in(X5,sK12(X0,X1,X2)) ),
inference(equality_resolution,[],[f142]) ).
fof(f158,plain,
! [X2,X0,X1,X6,X7] :
( ~ sP1(X0,X1,X2)
| sK13(X2,X6,X7) = X6
| ~ in(X6,X1)
| ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X0))
| in(ordered_pair(X6,X7),sK12(X0,X1,X2)) ),
inference(equality_resolution,[],[f157]) ).
fof(f159,plain,
! [X2,X0,X1,X6,X7,X5] :
( ~ sP1(X0,X1,X2)
| element(sK13(X2,X6,X7),powerset(the_carrier(X2)))
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(X1,X0))
| in(X5,sK12(X0,X1,X2)) ),
inference(equality_resolution,[],[f141]) ).
fof(f160,plain,
! [X2,X0,X1,X6,X7] :
( ~ sP1(X0,X1,X2)
| element(sK13(X2,X6,X7),powerset(the_carrier(X2)))
| ~ in(X6,X1)
| ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X0))
| in(ordered_pair(X6,X7),sK12(X0,X1,X2)) ),
inference(equality_resolution,[],[f159]) ).
fof(f161,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,sK12(X0,X1,X2))
| ~ element(sK15(X1,X2,X4),powerset(the_carrier(X2)))
| sK16(X1,X2,X4) = subset_complement(the_carrier(X2),sK15(X1,X2,X4)) ),
inference(equality_resolution,[],[f136]) ).
tcf(c_49,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,sK3)
| ~ in(sK5(X2),X2)
| ~ in(sK5(X2),cartesian_product2(sK3,sK4))
| ( ordered_pair(X0,X1) != sK5(X2) )
| ( subset_complement(the_carrier(sK2),sK6(X0,X1)) != X1 ) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_50,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ( sK6(X0,X1) = X0 )
| ~ in(X0,sK3)
| ~ in(sK5(X2),X2)
| ~ in(sK5(X2),cartesian_product2(sK3,sK4))
| ( ordered_pair(X0,X1) != sK5(X2) ) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( element(sK6(X0,X1),powerset(the_carrier(sK2)))
| ~ in(X0,sK3)
| ~ in(sK5(X2),X2)
| ~ in(sK5(X2),cartesian_product2(sK3,sK4))
| ( ordered_pair(X0,X1) != sK5(X2) ) ),
inference(cnf_transformation,[],[f94]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( in(sK5(X0),X0)
| in(sK5(X0),cartesian_product2(sK3,sK4)) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( in(sK5(X0),X0)
| ( ordered_pair(sK7(X0),sK8(X0)) = sK5(X0) ) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( in(sK7(X0),sK3)
| in(sK5(X0),X0) ),
inference(cnf_transformation,[],[f91]) ).
tcf(c_55,negated_conjecture,
! [X0: $i] :
( in(sK5(X0),X0)
| ( subset_complement(the_carrier(sK2),sK7(X0)) = sK8(X0) )
| ~ element(sK7(X0),powerset(the_carrier(sK2))) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_56,negated_conjecture,
one_sorted_str(sK2),
inference(cnf_transformation,[],[f89]) ).
tcf(c_57,negated_conjecture,
element(sK3,powerset(powerset(the_carrier(sK2)))),
inference(cnf_transformation,[],[f88]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(X1,X2),sK12(X4,X3,X0))
| ~ in(X1,X3)
| ~ sP1(X4,X3,X0)
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ( subset_complement(the_carrier(X0),sK13(X0,X1,X2)) != X2 ) ),
inference(cnf_transformation,[],[f156]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( in(ordered_pair(X0,X1),sK12(X3,X2,X4))
| ( sK13(X4,X0,X1) = X0 )
| ~ in(X0,X2)
| ~ sP1(X3,X2,X4)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f158]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( element(sK13(X4,X0,X1),powerset(the_carrier(X4)))
| in(ordered_pair(X0,X1),sK12(X3,X2,X4))
| ~ in(X0,X2)
| ~ sP1(X3,X2,X4)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK14(X1,X2,X3,X0),cartesian_product2(X2,X1))
| ~ sP1(X1,X2,X3)
| ~ in(X0,sK12(X1,X2,X3)) ),
inference(cnf_transformation,[],[f140]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( sK14(X1,X2,X3,X0) = X0 )
| ~ sP1(X1,X2,X3)
| ~ in(X0,sK12(X1,X2,X3)) ),
inference(cnf_transformation,[],[f139]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ordered_pair(sK15(X2,X3,X0),sK16(X2,X3,X0)) = X0 )
| ~ sP1(X1,X2,X3)
| ~ in(X0,sK12(X1,X2,X3)) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in(sK15(X2,X3,X0),X2)
| ~ sP1(X1,X2,X3)
| ~ in(X0,sK12(X1,X2,X3)) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( subset_complement(the_carrier(X1),sK15(X0,X1,X2)) = sK16(X0,X1,X2) )
| ~ sP1(X3,X0,X1)
| ~ in(X2,sK12(X3,X0,X1))
| ~ element(sK15(X0,X1,X2),powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f161]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X2,X1,X0)
| ~ one_sorted_str(X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( sK20(X0,X1) != sK21(X0,X1) ) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X2,X0,X1)
| ( sK20(X1,X0) = sK19(X1,X0) )
| ~ one_sorted_str(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X2,X0,X1)
| in(sK22(X1,X0),X0)
| ~ one_sorted_str(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_113,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X2,X0,X1)
| ( sK21(X1,X0) = sK19(X1,X0) )
| ~ one_sorted_str(X1)
| ~ element(X0,powerset(powerset(the_carrier(X1)))) ),
inference(cnf_transformation,[],[f148]) ).
tcf(c_940,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X2,X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK2 )
| ( sK20(X0,X1) != sK21(X0,X1) ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_108]) ).
tcf(c_941,plain,
! [X0: $i,X1: $i] :
( sP1(X1,X0,sK2)
| ~ element(X0,powerset(powerset(the_carrier(sK2))))
| ( sK20(sK2,X0) != sK21(sK2,X0) ) ),
inference(unflattening,[status(thm)],[c_940]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X2,X1,X0)
| ( sK21(X0,X1) = sK19(X0,X1) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_113]) ).
tcf(c_965,plain,
! [X0: $i,X1: $i] :
( sP1(X1,X0,sK2)
| ( sK21(sK2,X0) = sK19(sK2,X0) )
| ~ element(X0,powerset(powerset(the_carrier(sK2)))) ),
inference(unflattening,[status(thm)],[c_964]) ).
tcf(c_976,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X2,X1,X0)
| in(sK22(X0,X1),X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_111]) ).
tcf(c_977,plain,
! [X0: $i,X1: $i] :
( sP1(X1,X0,sK2)
| in(sK22(sK2,X0),X0)
| ~ element(X0,powerset(powerset(the_carrier(sK2)))) ),
inference(unflattening,[status(thm)],[c_976]) ).
tcf(c_1000,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP1(X2,X1,X0)
| ( sK20(X0,X1) = sK19(X0,X1) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_109]) ).
tcf(c_1001,plain,
! [X0: $i,X1: $i] :
( sP1(X1,X0,sK2)
| ( sK20(sK2,X0) = sK19(sK2,X0) )
| ~ element(X0,powerset(powerset(the_carrier(sK2)))) ),
inference(unflattening,[status(thm)],[c_1000]) ).
tcf(c_4770,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,sK2)
| ( sK20(sK2,X0_iProver_sK18_2) = sK19(sK2,X0_iProver_sK18_2) )
| ~ element(X0_iProver_sK18_2,powerset(powerset(the_carrier(sK2)))) ),
inference(subtyping,[status(esa)],[c_1001]) ).
tcf(c_4772,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,sK2)
| in(sK22(sK2,X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ element(X0_iProver_sK18_2,powerset(powerset(the_carrier(sK2)))) ),
inference(subtyping,[status(esa)],[c_977]) ).
tcf(c_4773,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,sK2)
| ( sK21(sK2,X0_iProver_sK18_2) = sK19(sK2,X0_iProver_sK18_2) )
| ~ element(X0_iProver_sK18_2,powerset(powerset(the_carrier(sK2)))) ),
inference(subtyping,[status(esa)],[c_965]) ).
tcf(c_4774,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,sK2)
| ~ element(X0_iProver_sK18_2,powerset(powerset(the_carrier(sK2))))
| ( sK20(sK2,X0_iProver_sK18_2) != sK21(sK2,X0_iProver_sK18_2) ) ),
inference(subtyping,[status(esa)],[c_941]) ).
tcf(c_4776,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(X0_iProver_the_carrier_1),sK15(X0_iProver_sK18_2,X0_iProver_the_carrier_1,X1_iProver_sK18_2)) = sK16(X0_iProver_sK18_2,X0_iProver_the_carrier_1,X1_iProver_sK18_2) )
| ~ sP1(X2_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(X1_iProver_sK18_2,sK12(X2_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1))
| ~ element(sK15(X0_iProver_sK18_2,X0_iProver_the_carrier_1,X1_iProver_sK18_2),powerset(the_carrier(X0_iProver_the_carrier_1))) ),
inference(subtyping,[status(esa)],[c_104]) ).
tcf(c_4777,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK15(X2_iProver_sK18_2,X0_iProver_the_carrier_1,X0_iProver_sK18_2),X2_iProver_sK18_2)
| ~ sP1(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(X0_iProver_sK18_2,sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)) ),
inference(subtyping,[status(esa)],[c_103]) ).
tcf(c_4778,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK15(X2_iProver_sK18_2,X0_iProver_the_carrier_1,X0_iProver_sK18_2),sK16(X2_iProver_sK18_2,X0_iProver_the_carrier_1,X0_iProver_sK18_2)) = X0_iProver_sK18_2 )
| ~ sP1(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(X0_iProver_sK18_2,sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)) ),
inference(subtyping,[status(esa)],[c_102]) ).
tcf(c_4779,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1,X0_iProver_sK18_2) = X0_iProver_sK18_2 )
| ~ sP1(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(X0_iProver_sK18_2,sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)) ),
inference(subtyping,[status(esa)],[c_101]) ).
tcf(c_4780,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK14(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1,X0_iProver_sK18_2),cartesian_product2(X2_iProver_sK18_2,X1_iProver_sK18_2))
| ~ sP1(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(X0_iProver_sK18_2,sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)) ),
inference(subtyping,[status(esa)],[c_100]) ).
tcf(c_4781,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2,X3_iProver_sK18_2: iProver_sK18_2] :
( element(sK13(X0_iProver_the_carrier_1,X0_iProver_sK18_2,X1_iProver_sK18_2),powerset(the_carrier(X0_iProver_the_carrier_1)))
| in(ordered_pair(X0_iProver_sK18_2,X1_iProver_sK18_2),sK12(X3_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1))
| ~ in(X0_iProver_sK18_2,X2_iProver_sK18_2)
| ~ sP1(X3_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(ordered_pair(X0_iProver_sK18_2,X1_iProver_sK18_2),cartesian_product2(X2_iProver_sK18_2,X3_iProver_sK18_2)) ),
inference(subtyping,[status(esa)],[c_99]) ).
tcf(c_4782,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2,X3_iProver_sK18_2: iProver_sK18_2] :
( in(ordered_pair(X0_iProver_sK18_2,X1_iProver_sK18_2),sK12(X3_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( sK13(X0_iProver_the_carrier_1,X0_iProver_sK18_2,X1_iProver_sK18_2) = X0_iProver_sK18_2 )
| ~ in(X0_iProver_sK18_2,X2_iProver_sK18_2)
| ~ sP1(X3_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(ordered_pair(X0_iProver_sK18_2,X1_iProver_sK18_2),cartesian_product2(X2_iProver_sK18_2,X3_iProver_sK18_2)) ),
inference(subtyping,[status(esa)],[c_98]) ).
tcf(c_4783,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2,X3_iProver_sK18_2: iProver_sK18_2] :
( in(ordered_pair(X0_iProver_sK18_2,X1_iProver_sK18_2),sK12(X3_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1))
| ~ in(X0_iProver_sK18_2,X2_iProver_sK18_2)
| ~ sP1(X3_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(ordered_pair(X0_iProver_sK18_2,X1_iProver_sK18_2),cartesian_product2(X2_iProver_sK18_2,X3_iProver_sK18_2))
| ( subset_complement(the_carrier(X0_iProver_the_carrier_1),sK13(X0_iProver_the_carrier_1,X0_iProver_sK18_2,X1_iProver_sK18_2)) != X1_iProver_sK18_2 ) ),
inference(subtyping,[status(esa)],[c_97]) ).
tcf(c_4785,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( element(subset_complement(X1_iProver_sK18_2,X0_iProver_sK18_2),powerset(X1_iProver_sK18_2))
| ~ element(X0_iProver_sK18_2,powerset(X1_iProver_sK18_2)) ),
inference(subtyping,[status(esa)],[c_95]) ).
tcf(c_4787,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(X1_iProver_sK18_2,subset_complement(X1_iProver_sK18_2,X0_iProver_sK18_2)) = X0_iProver_sK18_2 )
| ~ element(X0_iProver_sK18_2,powerset(X1_iProver_sK18_2)) ),
inference(subtyping,[status(esa)],[c_93]) ).
tcf(c_4794,negated_conjecture,
element(sK3,powerset(powerset(the_carrier(sK2)))),
inference(subtyping,[status(esa)],[c_57]) ).
tcf(c_4795,negated_conjecture,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ( subset_complement(the_carrier(sK2),sK7(X0_iProver_sK18_2)) = sK8(X0_iProver_sK18_2) )
| ~ element(sK7(X0_iProver_sK18_2),powerset(the_carrier(sK2))) ),
inference(subtyping,[status(esa)],[c_55]) ).
tcf(c_4796,negated_conjecture,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( in(sK7(X0_iProver_sK18_2),sK3)
| in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2) ),
inference(subtyping,[status(esa)],[c_54]) ).
tcf(c_4797,negated_conjecture,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ( ordered_pair(sK7(X0_iProver_sK18_2),sK8(X0_iProver_sK18_2)) = sK5(X0_iProver_sK18_2) ) ),
inference(subtyping,[status(esa)],[c_53]) ).
tcf(c_4798,negated_conjecture,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4)) ),
inference(subtyping,[status(esa)],[c_52]) ).
tcf(c_4799,negated_conjecture,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(X0_iProver_sK18_2,X1_iProver_sK18_2),powerset(the_carrier(sK2)))
| ~ in(X0_iProver_sK18_2,sK3)
| ~ in(sK5(X2_iProver_sK18_2),X2_iProver_sK18_2)
| ~ in(sK5(X2_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( ordered_pair(X0_iProver_sK18_2,X1_iProver_sK18_2) != sK5(X2_iProver_sK18_2) ) ),
inference(subtyping,[status(esa)],[c_51]) ).
tcf(c_4800,negated_conjecture,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( ( sK6(X0_iProver_sK18_2,X1_iProver_sK18_2) = X0_iProver_sK18_2 )
| ~ in(X0_iProver_sK18_2,sK3)
| ~ in(sK5(X2_iProver_sK18_2),X2_iProver_sK18_2)
| ~ in(sK5(X2_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( ordered_pair(X0_iProver_sK18_2,X1_iProver_sK18_2) != sK5(X2_iProver_sK18_2) ) ),
inference(subtyping,[status(esa)],[c_50]) ).
tcf(c_4801,negated_conjecture,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( ~ in(X0_iProver_sK18_2,sK3)
| ~ in(sK5(X2_iProver_sK18_2),X2_iProver_sK18_2)
| ~ in(sK5(X2_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( ordered_pair(X0_iProver_sK18_2,X1_iProver_sK18_2) != sK5(X2_iProver_sK18_2) )
| ( subset_complement(the_carrier(sK2),sK6(X0_iProver_sK18_2,X1_iProver_sK18_2)) != X1_iProver_sK18_2 ) ),
inference(subtyping,[status(esa)],[c_49]) ).
tcf(c_4803,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] : X0_iProver_sK18_2 = X0_iProver_sK18_2,
theory(equality) ).
tcf(c_4804,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( ( X2_iProver_sK18_2 = X0_iProver_sK18_2 )
| ( X2_iProver_sK18_2 != X1_iProver_sK18_2 )
| ( X0_iProver_sK18_2 != X1_iProver_sK18_2 ) ),
theory(equality) ).
tcf(c_4806,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2,X3_iProver_sK18_2: iProver_sK18_2] :
( in(X0_iProver_sK18_2,X2_iProver_sK18_2)
| ~ in(X1_iProver_sK18_2,X3_iProver_sK18_2)
| ( X2_iProver_sK18_2 != X3_iProver_sK18_2 )
| ( X0_iProver_sK18_2 != X1_iProver_sK18_2 ) ),
theory(equality) ).
tcf(c_4808,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2,X3_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(X0_iProver_sK18_2,X2_iProver_sK18_2) = subset_complement(X1_iProver_sK18_2,X3_iProver_sK18_2) )
| ( X2_iProver_sK18_2 != X3_iProver_sK18_2 )
| ( X0_iProver_sK18_2 != X1_iProver_sK18_2 ) ),
theory(equality) ).
tcf(c_5612,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( sK20(sK2,X0_iProver_sK18_2) = sK21(sK2,X0_iProver_sK18_2) )
| ( sK21(sK2,X0_iProver_sK18_2) != X1_iProver_sK18_2 )
| ( sK20(sK2,X0_iProver_sK18_2) != X1_iProver_sK18_2 ) ),
inference(instantiation,[status(thm)],[c_4804]) ).
tcf(c_6014,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK20(sK2,X0_iProver_sK18_2) = sK21(sK2,X0_iProver_sK18_2) )
| ( sK21(sK2,X0_iProver_sK18_2) != sK19(sK2,X0_iProver_sK18_2) )
| ( sK20(sK2,X0_iProver_sK18_2) != sK19(sK2,X0_iProver_sK18_2) ) ),
inference(instantiation,[status(thm)],[c_5612]) ).
tcf(c_6025,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,sK2)
| ~ element(X0_iProver_sK18_2,powerset(powerset(the_carrier(sK2)))) ),
inference(global_subsumption_just,[status(thm)],[c_4772,c_4770,c_4773,c_4774,c_6014]) ).
tcf(c_7409,plain,
the_carrier(sK2) = the_carrier(sK2),
inference(instantiation,[status(thm)],[c_4803]) ).
tcf(c_8410,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,sK2)
| ~ element(X0_iProver_sK18_2,powerset(powerset(the_carrier(sK2)))) ),
inference(global_subsumption_just,[status(thm)],[c_4772,c_6025]) ).
tcf(c_8414,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] : sP1(X0_iProver_sK18_2,sK3,sK2),
inference(superposition,[status(thm)],[c_4794,c_8410]) ).
tcf(c_8488,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK15(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),X1_iProver_sK18_2)
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4797,c_4777]) ).
tcf(c_8546,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( ordered_pair(sK15(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),sK16(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4797,c_4778]) ).
tcf(c_8604,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_8414,c_8546]) ).
tcf(c_8695,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(X1_iProver_sK18_2),X1_iProver_sK18_2)
| ~ in(sK5(X1_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ( sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) != sK5(X1_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_8604,c_4800]) ).
tcf(c_8709,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_8695]) ).
tcf(c_9060,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8709,c_4797]) ).
tcf(c_9069,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_8488,c_9060]) ).
tcf(c_9072,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9069,c_8414]) ).
tcf(c_11941,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK15(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),X1_iProver_sK18_2)
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4797,c_4777]) ).
tcf(c_11947,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4797,c_4779]) ).
tcf(c_11948,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ( sK14(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4798,c_4779]) ).
tcf(c_11949,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK3)
| ( sK14(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4796,c_4779]) ).
tcf(c_11985,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_8414,c_11947]) ).
tcf(c_12003,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( ordered_pair(sK15(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),sK16(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4797,c_4778]) ).
tcf(c_12032,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| element(sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),powerset(the_carrier(X0_iProver_the_carrier_1)))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),X1_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),cartesian_product2(X1_iProver_sK18_2,X2_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_11985,c_4781]) ).
tcf(c_12033,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),X1_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),cartesian_product2(X1_iProver_sK18_2,X2_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_11985,c_4782]) ).
tcf(c_12034,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),powerset(the_carrier(sK2)))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK5(X1_iProver_sK18_2),X1_iProver_sK18_2)
| ~ in(sK5(X1_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ( sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) != sK5(X1_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_11985,c_4799]) ).
tcf(c_12035,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK5(X1_iProver_sK18_2),X1_iProver_sK18_2)
| ~ in(sK5(X1_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ( sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) != sK5(X1_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_11985,c_4800]) ).
tcf(c_12056,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_8414,c_12003]) ).
tcf(c_12066,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),powerset(the_carrier(sK2)))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_12034]) ).
tcf(c_12073,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_12035]) ).
tcf(c_12140,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK5(X1_iProver_sK18_2),X1_iProver_sK18_2)
| ~ in(sK5(X1_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ( sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) != sK5(X1_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_12056,c_4799]) ).
tcf(c_12141,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(X1_iProver_sK18_2),X1_iProver_sK18_2)
| ~ in(sK5(X1_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ( sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) != sK5(X1_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_12056,c_4800]) ).
tcf(c_12149,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_12140]) ).
tcf(c_12156,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_12141]) ).
tcf(c_12428,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12149,c_4797]) ).
tcf(c_12477,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_12156,c_9072]) ).
tcf(c_15167,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| element(sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),powerset(the_carrier(X0_iProver_the_carrier_1)))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),X1_iProver_sK18_2)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(X1_iProver_sK18_2,X2_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_11985,c_12032]) ).
tcf(c_15178,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),powerset(the_carrier(sK2)))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_15167,c_12073]) ).
tcf(c_15184,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),powerset(the_carrier(sK2)))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15178,c_8414]) ).
tcf(c_15545,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),X1_iProver_sK18_2)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(X1_iProver_sK18_2,X2_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_11985,c_12033]) ).
tcf(c_15559,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_15545,c_12073]) ).
tcf(c_15560,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15559,c_8414]) ).
tcf(c_15635,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_11948,c_15560]) ).
tcf(c_15636,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15635,c_8414]) ).
tcf(c_15647,plain,
( ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_11948,c_15636]) ).
tcf(c_15648,plain,
( ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15647,c_8414]) ).
tcf(c_15659,plain,
( ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_11949,c_15648]) ).
tcf(c_15660,plain,
( ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15659,c_8414]) ).
tcf(c_15668,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_15660,c_15184]) ).
tcf(c_16083,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_11948,c_15668]) ).
tcf(c_16084,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16083,c_8414]) ).
tcf(c_16097,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_16084,c_4795]) ).
tcf(c_16103,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16097,c_4796]) ).
tcf(c_16113,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_16103,c_4779]) ).
tcf(c_16117,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16113,c_8414]) ).
tcf(c_16142,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_16117,c_12066]) ).
tcf(c_16318,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_15545,c_16142]) ).
tcf(c_16319,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| element(sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_15167,c_16142]) ).
tcf(c_16320,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| element(sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16319,c_8414]) ).
tcf(c_16321,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16318,c_8414]) ).
tcf(c_16362,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_11948,c_16321]) ).
tcf(c_16363,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16362,c_8414]) ).
tcf(c_17300,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_16363,c_4795]) ).
tcf(c_17363,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17300,c_4796]) ).
tcf(c_17373,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_17363,c_4779]) ).
tcf(c_17378,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17373,c_8414]) ).
tcf(c_17667,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_17378,c_16320]) ).
tcf(c_17711,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_11948,c_17667]) ).
tcf(c_17712,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17711,c_8414]) ).
tcf(c_17858,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_17712,c_4795]) ).
tcf(c_17996,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17858,c_4796]) ).
tcf(c_18004,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_17996,c_4779]) ).
tcf(c_18009,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18004,c_8414]) ).
tcf(c_18012,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_18009,c_4780]) ).
tcf(c_18014,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18012,c_8414]) ).
tcf(c_18019,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18014,c_4798]) ).
tcf(c_18031,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(superposition,[status(thm)],[c_18019,c_12477]) ).
tcf(c_18082,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_18031,c_4801]) ).
tcf(c_18083,plain,
( element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3) ),
inference(superposition,[status(thm)],[c_18031,c_12428]) ).
tcf(c_18522,plain,
( element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18083,c_18019]) ).
tcf(c_18531,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_18522,c_4776]) ).
tcf(c_18537,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18531,c_8414]) ).
tcf(c_18595,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_11941,c_18537]) ).
tcf(c_18598,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18595,c_8414]) ).
tcf(c_18672,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_4797,c_18598]) ).
tcf(c_18686,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_18672,c_18082]) ).
tcf(c_18708,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_12056,c_18686]) ).
tcf(c_19698,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3) ),
inference(equality_resolution,[status(thm)],[c_18708]) ).
tcf(c_20167,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(X1_iProver_sK18_2,subset_complement(X1_iProver_sK18_2,subset_complement(X1_iProver_sK18_2,X0_iProver_sK18_2))) = subset_complement(X1_iProver_sK18_2,X0_iProver_sK18_2) )
| ~ element(X0_iProver_sK18_2,powerset(X1_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_4785,c_4787]) ).
tcf(c_20173,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK15(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),X1_iProver_sK18_2)
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4797,c_4777]) ).
tcf(c_20179,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4797,c_4779]) ).
tcf(c_20180,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ( sK14(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4798,c_4779]) ).
tcf(c_20216,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_8414,c_20179]) ).
tcf(c_20237,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( ordered_pair(sK15(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),sK16(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4797,c_4778]) ).
tcf(c_20239,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK3)
| ( ordered_pair(sK15(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),sK16(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4796,c_4778]) ).
tcf(c_20291,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_8414,c_20237]) ).
tcf(c_20298,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| element(sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),powerset(the_carrier(X0_iProver_the_carrier_1)))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),X1_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),cartesian_product2(X1_iProver_sK18_2,X2_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_20216,c_4781]) ).
tcf(c_20299,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),X1_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),cartesian_product2(X1_iProver_sK18_2,X2_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_20216,c_4782]) ).
tcf(c_20301,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK5(X1_iProver_sK18_2),X1_iProver_sK18_2)
| ~ in(sK5(X1_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ( sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) != sK5(X1_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_20216,c_4800]) ).
tcf(c_20315,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_20301]) ).
tcf(c_20379,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(X1_iProver_sK18_2),X1_iProver_sK18_2)
| ~ in(sK5(X1_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ( sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) != sK5(X1_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_20291,c_4800]) ).
tcf(c_20393,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_20379]) ).
tcf(c_20439,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(X1_iProver_sK18_2,subset_complement(X1_iProver_sK18_2,subset_complement(X1_iProver_sK18_2,subset_complement(X1_iProver_sK18_2,X0_iProver_sK18_2)))) = subset_complement(X1_iProver_sK18_2,subset_complement(X1_iProver_sK18_2,X0_iProver_sK18_2)) )
| ~ element(X0_iProver_sK18_2,powerset(X1_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_4785,c_20167]) ).
tcf(c_20716,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_20393,c_9072]) ).
tcf(c_21983,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| element(sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),powerset(the_carrier(X0_iProver_the_carrier_1)))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),X1_iProver_sK18_2)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(X1_iProver_sK18_2,X2_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_20216,c_20298]) ).
tcf(c_21994,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),powerset(the_carrier(sK2)))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_21983,c_20315]) ).
tcf(c_21999,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),powerset(the_carrier(sK2)))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21994,c_8414]) ).
tcf(c_22400,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),X1_iProver_sK18_2)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(X1_iProver_sK18_2,X2_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_20216,c_20299]) ).
tcf(c_22411,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_22400,c_20315]) ).
tcf(c_22412,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22411,c_8414]) ).
tcf(c_22413,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(global_subsumption_just,[status(thm)],[c_22412,c_15636]) ).
tcf(c_22422,plain,
( ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_20180,c_22413]) ).
tcf(c_22423,plain,
( ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22422,c_8414]) ).
tcf(c_22425,plain,
( ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_22423,c_15660]) ).
tcf(c_22433,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22425,c_21999]) ).
tcf(c_22436,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_22433,c_16084]) ).
tcf(c_22448,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_22436,c_4795]) ).
tcf(c_22523,plain,
( ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_22448,c_18009]) ).
tcf(c_22524,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(renaming,[status(thm)],[c_22523]) ).
tcf(c_22527,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_22524,c_4780]) ).
tcf(c_22529,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22527,c_8414]) ).
tcf(c_22534,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22529,c_4798]) ).
tcf(c_22546,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(superposition,[status(thm)],[c_22534,c_20716]) ).
tcf(c_22555,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_22546,c_4801]) ).
tcf(c_22557,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_22555,c_18686]) ).
tcf(c_22565,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_20291,c_22557]) ).
tcf(c_22586,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3) ),
inference(equality_resolution,[status(thm)],[c_22565]) ).
tcf(c_22788,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_22586,c_18014,c_19698]) ).
tcf(c_22789,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3) ),
inference(renaming,[status(thm)],[c_22788]) ).
tcf(c_22794,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22789,c_4797]) ).
tcf(c_22801,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_20173,c_22794]) ).
tcf(c_22804,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22801,c_8414]) ).
tcf(c_22810,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(sK4,sK3,sK2)),sK12(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1))
| element(sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(X0_iProver_the_carrier_1)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),cartesian_product2(X0_iProver_sK18_2,X1_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_22804,c_4781]) ).
tcf(c_22811,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(sK4,sK3,sK2)),sK12(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),cartesian_product2(X0_iProver_sK18_2,X1_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_22804,c_4782]) ).
tcf(c_22812,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_22804,c_4799]) ).
tcf(c_22813,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_22804,c_4800]) ).
tcf(c_22829,plain,
( element(sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_22812]) ).
tcf(c_22908,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_22813]) ).
tcf(c_22909,plain,
( element(sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_22829,c_18014,c_22829]) ).
tcf(c_22918,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))))) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_22909,c_20439]) ).
tcf(c_22921,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_22908,c_18014,c_22908]) ).
tcf(c_22954,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(sK4,sK3,sK2)),sK12(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1))
| element(sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(X0_iProver_the_carrier_1)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0_iProver_sK18_2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(X0_iProver_sK18_2,X1_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_22804,c_22810]) ).
tcf(c_23011,plain,
( element(sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22954,c_22921]) ).
tcf(c_23018,plain,
( element(sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23011,c_8414]) ).
tcf(c_23035,plain,
( element(sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23018,c_22534]) ).
tcf(c_23111,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(sK4,sK3,sK2)),sK12(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0_iProver_sK18_2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(X0_iProver_sK18_2,X1_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_22804,c_22811]) ).
tcf(c_23126,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_23111,c_22921]) ).
tcf(c_23127,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23126,c_8414]) ).
tcf(c_23139,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23127,c_22534]) ).
tcf(c_23148,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_4796,c_23139]) ).
tcf(c_23149,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_20239,c_23139]) ).
tcf(c_23151,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23149,c_8414]) ).
tcf(c_23231,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_23148,c_4777]) ).
tcf(c_23237,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23231,c_8414]) ).
tcf(c_23260,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_23151,c_4799]) ).
tcf(c_23261,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_23151,c_4800]) ).
tcf(c_23270,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_23260,c_23237,c_23260]) ).
tcf(c_23280,plain,
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_23270]) ).
tcf(c_23281,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_23261,c_23237,c_23261]) ).
tcf(c_23291,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_23281]) ).
tcf(c_23488,plain,
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_23280,c_18014,c_23148,c_23280]) ).
tcf(c_23508,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(global_subsumption_just,[status(thm)],[c_23291,c_18014,c_23148,c_23291]) ).
tcf(c_23514,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_23508,c_4801]) ).
tcf(c_23516,plain,
( element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_23508,c_23488]) ).
tcf(c_23524,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(global_subsumption_just,[status(thm)],[c_23514,c_23237,c_23514]) ).
tcf(c_23525,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(renaming,[status(thm)],[c_23524]) ).
tcf(c_23727,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_23516,c_4776]) ).
tcf(c_23735,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23727,c_8414]) ).
tcf(c_23776,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_23148,c_23735]) ).
tcf(c_23816,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_23776,c_23035]) ).
tcf(c_24006,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_23816,c_4795]) ).
tcf(c_24062,plain,
( ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_24006,c_18014,c_22908,c_24006]) ).
tcf(c_24063,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(renaming,[status(thm)],[c_24062]) ).
tcf(c_24068,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_4796,c_24063]) ).
tcf(c_24069,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_20239,c_24063]) ).
tcf(c_24071,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24069,c_8414]) ).
tcf(c_24099,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_24068,c_4777]) ).
tcf(c_24106,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_24099,c_8414]) ).
tcf(c_24496,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_24071,c_4799]) ).
tcf(c_24497,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_24071,c_4800]) ).
tcf(c_24521,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_24496,c_24106,c_24496]) ).
tcf(c_24531,plain,
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_24521]) ).
tcf(c_24548,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_24497,c_24106,c_24497]) ).
tcf(c_24558,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_24548]) ).
tcf(c_24577,plain,
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_24531,c_18014,c_24068,c_24531]) ).
tcf(c_25039,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(global_subsumption_just,[status(thm)],[c_24558,c_18014,c_24068,c_24558]) ).
tcf(c_25047,plain,
( element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_25039,c_24577]) ).
tcf(c_25830,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_25047,c_4776]) ).
tcf(c_25838,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25830,c_8414]) ).
tcf(c_25849,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_24068,c_25838]) ).
tcf(c_25862,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_25849,c_22909]) ).
tcf(c_25876,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_23111,c_25862]) ).
tcf(c_25877,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| element(sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22954,c_25862]) ).
tcf(c_25878,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| element(sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25877,c_8414]) ).
tcf(c_25879,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25876,c_8414]) ).
tcf(c_25886,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| element(sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25878,c_22534]) ).
tcf(c_25954,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25879,c_22534]) ).
tcf(c_25971,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_25954,c_4795]) ).
tcf(c_26112,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25971,c_4796]) ).
tcf(c_26121,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_26112,c_4778]) ).
tcf(c_26123,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_26112,c_4777]) ).
tcf(c_26132,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26123,c_8414]) ).
tcf(c_26133,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26121,c_8414]) ).
tcf(c_26189,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_26133,c_4799]) ).
tcf(c_26190,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_26133,c_4800]) ).
tcf(c_26229,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_26189,c_26132,c_26189]) ).
tcf(c_26239,plain,
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_26229]) ).
tcf(c_26259,plain,
cartesian_product2(sK3,sK4) = cartesian_product2(sK3,sK4),
inference(instantiation,[status(thm)],[c_4803]) ).
tcf(c_26270,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_26190,c_26132,c_26190]) ).
tcf(c_26280,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_26270]) ).
tcf(c_26318,plain,
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_26239,c_18014,c_26239]) ).
tcf(c_26325,plain,
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26318,c_26112]) ).
tcf(c_26928,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_26280,c_18014,c_26280]) ).
tcf(c_26935,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26928,c_26112]) ).
tcf(c_26946,plain,
( element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_26935,c_26325]) ).
tcf(c_26962,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_26946,c_4776]) ).
tcf(c_26970,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26962,c_8414]) ).
tcf(c_27026,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_26112,c_26970]) ).
tcf(c_27039,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_27026,c_25886]) ).
tcf(c_27197,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_27039,c_4795]) ).
tcf(c_27202,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27197,c_4796]) ).
tcf(c_27209,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_27202,c_4778]) ).
tcf(c_27211,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_27202,c_4777]) ).
tcf(c_27221,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27211,c_8414]) ).
tcf(c_27222,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27209,c_8414]) ).
tcf(c_27259,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_27222,c_4799]) ).
tcf(c_27260,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_27222,c_4800]) ).
tcf(c_27377,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_27259,c_27221,c_27259]) ).
tcf(c_27386,plain,
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_27377]) ).
tcf(c_27387,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_27260,c_27221,c_27260]) ).
tcf(c_27396,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_27387]) ).
tcf(c_27910,plain,
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_27386,c_18014,c_27386]) ).
tcf(c_27916,plain,
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27910,c_27202]) ).
tcf(c_27966,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_27396,c_18014,c_27396]) ).
tcf(c_27972,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27966,c_27202]) ).
tcf(c_27981,plain,
( element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(superposition,[status(thm)],[c_27972,c_27916]) ).
tcf(c_28019,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_27981,c_4776]) ).
tcf(c_28027,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28019,c_8414]) ).
tcf(c_28037,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(superposition,[status(thm)],[c_27202,c_28027]) ).
tcf(c_28046,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_28037,c_23525]) ).
tcf(c_28238,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_23151,c_28046]) ).
tcf(c_29218,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_28238]) ).
tcf(c_30472,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))))) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_23148,c_22918]) ).
tcf(c_30789,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_30472,c_18014,c_23148,c_29218]) ).
tcf(c_30804,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_30789,c_23035]) ).
tcf(c_32650,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_30804,c_4795]) ).
tcf(c_32770,plain,
( ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_32650,c_22921,c_32650]) ).
tcf(c_32771,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(renaming,[status(thm)],[c_32770]) ).
tcf(c_32775,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_4796,c_32771]) ).
tcf(c_32776,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_20239,c_32771]) ).
tcf(c_32778,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32776,c_8414]) ).
tcf(c_32784,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_32775,c_4777]) ).
tcf(c_32788,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))))) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_32775,c_22918]) ).
tcf(c_32797,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_32784,c_8414]) ).
tcf(c_32820,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_32778,c_4800]) ).
tcf(c_33455,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_32820,c_32797,c_32820]) ).
tcf(c_33464,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_33455]) ).
tcf(c_33511,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(global_subsumption_just,[status(thm)],[c_33464,c_18014,c_32775,c_33464]) ).
tcf(c_33516,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_33511,c_4801]) ).
tcf(c_33526,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_33516,c_28037,c_32797,c_33516]) ).
tcf(c_33535,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_32778,c_33526]) ).
tcf(c_33546,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_33535]) ).
tcf(c_33547,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_32788,c_18014,c_32775,c_33546]) ).
tcf(c_33558,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_33547,c_22909]) ).
tcf(c_33792,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_23111,c_33558]) ).
tcf(c_33795,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33792,c_8414]) ).
tcf(c_33825,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33795,c_22534]) ).
tcf(c_33840,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_33825,c_4795]) ).
tcf(c_33845,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33840,c_4796]) ).
tcf(c_33852,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_33845,c_4778]) ).
tcf(c_33854,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_33845,c_4777]) ).
tcf(c_33868,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33854,c_8414]) ).
tcf(c_33869,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33852,c_8414]) ).
tcf(c_33890,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_33869,c_4800]) ).
tcf(c_34563,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_33890,c_33868,c_33890]) ).
tcf(c_34572,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_34563]) ).
tcf(c_34598,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_34572,c_18014,c_34572]) ).
tcf(c_34604,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34598,c_33845]) ).
tcf(c_34611,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_34604,c_4801]) ).
tcf(c_34621,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_34611,c_28037,c_33868,c_34611]) ).
tcf(c_34630,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_33869,c_34621]) ).
tcf(c_34642,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_34630]) ).
tcf(c_35048,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_22524,c_4780]) ).
tcf(c_35050,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35048,c_8414]) ).
tcf(c_35054,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( ordered_pair(sK15(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),sK16(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4797,c_4778]) ).
tcf(c_35093,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_35050,c_4798]) ).
tcf(c_35110,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_8414,c_35054]) ).
tcf(c_35180,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(X1_iProver_sK18_2),X1_iProver_sK18_2)
| ~ in(sK5(X1_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ( sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) != sK5(X1_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_35110,c_4800]) ).
tcf(c_35194,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_35180]) ).
tcf(c_35499,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_35194,c_9072]) ).
tcf(c_35507,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(superposition,[status(thm)],[c_35093,c_35499]) ).
tcf(c_35509,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_35507,c_22804]) ).
tcf(c_35513,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(sK4,sK3,sK2)),sK12(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1))
| element(sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(X0_iProver_the_carrier_1)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),cartesian_product2(X0_iProver_sK18_2,X1_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_35509,c_4781]) ).
tcf(c_35514,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(sK4,sK3,sK2)),sK12(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),cartesian_product2(X0_iProver_sK18_2,X1_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_35509,c_4782]) ).
tcf(c_35515,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_35509,c_4799]) ).
tcf(c_35516,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_35509,c_4800]) ).
tcf(c_35523,plain,
( element(sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_35515]) ).
tcf(c_35524,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_35516,c_33547]) ).
tcf(c_35530,plain,
( element(sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_35523,c_22909]) ).
tcf(c_35536,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_35524,c_35530]) ).
tcf(c_36385,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(sK4,sK3,sK2)),sK12(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1))
| element(sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(X0_iProver_the_carrier_1)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0_iProver_sK18_2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(X0_iProver_sK18_2,X1_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_35509,c_35513]) ).
tcf(c_36398,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| element(sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_36385,c_35536]) ).
tcf(c_36403,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| element(sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36398,c_8414]) ).
tcf(c_36447,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| element(sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36403,c_35093]) ).
tcf(c_36864,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(sK4,sK3,sK2)),sK12(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(X1_iProver_sK18_2,X0_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0_iProver_sK18_2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(X0_iProver_sK18_2,X1_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_35509,c_35514]) ).
tcf(c_36878,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_36864,c_35536]) ).
tcf(c_36879,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36878,c_8414]) ).
tcf(c_36882,plain,
( ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_36879,c_18014,c_33840,c_34642]) ).
tcf(c_36883,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(renaming,[status(thm)],[c_36882]) ).
tcf(c_36887,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_4796,c_36883]) ).
tcf(c_36891,plain,
( ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_36887,c_18014,c_34642,c_36887]) ).
tcf(c_36892,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) ) ),
inference(renaming,[status(thm)],[c_36891]) ).
tcf(c_36903,plain,
( element(sK7(sK12(sK4,sK3,sK2)),powerset(the_carrier(sK2)))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_36892,c_36447]) ).
tcf(c_36913,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_36903,c_4795]) ).
tcf(c_36961,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36913,c_4796]) ).
tcf(c_36966,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_36961,c_4778]) ).
tcf(c_36968,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_36961,c_4777]) ).
tcf(c_36974,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36968,c_8414]) ).
tcf(c_36975,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_36966,c_8414]) ).
tcf(c_36986,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_36975,c_4800]) ).
tcf(c_37000,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_36986,c_36974,c_36986]) ).
tcf(c_37008,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_37000]) ).
tcf(c_37098,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_37008,c_18014,c_37008]) ).
tcf(c_37103,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37098,c_36961]) ).
tcf(c_37108,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_37103,c_4801]) ).
tcf(c_37112,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(global_subsumption_just,[status(thm)],[c_37108,c_28037,c_36974,c_37108]) ).
tcf(c_37120,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_36975,c_37112]) ).
tcf(c_37182,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_37120]) ).
tcf(c_37288,plain,
( ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_37182,c_18014,c_37182]) ).
tcf(c_37292,plain,
subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) = sK8(sK12(sK4,sK3,sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_37288,c_36961]) ).
tcf(c_49771,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK15(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),X1_iProver_sK18_2)
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) ),
inference(instantiation,[status(thm)],[c_4777]) ).
tcf(c_49774,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) ),
inference(instantiation,[status(thm)],[c_4798]) ).
tcf(c_49775,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK3)
| in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) ),
inference(instantiation,[status(thm)],[c_4796]) ).
tcf(c_49812,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( ( sK5(X0_iProver_sK18_2) = X2_iProver_sK18_2 )
| ( X2_iProver_sK18_2 != X1_iProver_sK18_2 )
| ( sK5(X0_iProver_sK18_2) != X1_iProver_sK18_2 ) ),
inference(instantiation,[status(thm)],[c_4804]) ).
tcf(c_49814,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] : sK5(X0_iProver_sK18_2) = sK5(X0_iProver_sK18_2),
inference(instantiation,[status(thm)],[c_4803]) ).
tcf(c_49818,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2,X3_iProver_sK18_2: iProver_sK18_2] :
( in(X0_iProver_sK18_2,X3_iProver_sK18_2)
| ~ in(sK5(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ( X3_iProver_sK18_2 != cartesian_product2(sK3,sK4) )
| ( X0_iProver_sK18_2 != sK5(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_4806]) ).
tcf(c_49832,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( ~ in(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) != sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( subset_complement(the_carrier(sK2),sK6(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)))) != sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_4801]) ).
tcf(c_49833,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( ( sK6(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) != sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_4800]) ).
tcf(c_49867,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK6(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)))) = sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) != X2_iProver_sK18_2 )
| ( subset_complement(the_carrier(sK2),sK6(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)))) != X2_iProver_sK18_2 ) ),
inference(instantiation,[status(thm)],[c_4804]) ).
tcf(c_49923,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( sK5(X0_iProver_sK18_2) = X1_iProver_sK18_2 )
| ( X1_iProver_sK18_2 != sK5(X0_iProver_sK18_2) )
| ( sK5(X0_iProver_sK18_2) != sK5(X0_iProver_sK18_2) ) ),
inference(instantiation,[status(thm)],[c_49812]) ).
tcf(c_49928,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK15(X2_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(X0_iProver_sK18_2)),sK16(X2_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(X0_iProver_sK18_2))) = sK5(X0_iProver_sK18_2) )
| ~ sP1(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK5(X0_iProver_sK18_2),sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)) ),
inference(instantiation,[status(thm)],[c_4778]) ).
tcf(c_49929,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK14(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(X0_iProver_sK18_2)),cartesian_product2(X2_iProver_sK18_2,X1_iProver_sK18_2))
| ~ sP1(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK5(X0_iProver_sK18_2),sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)) ),
inference(instantiation,[status(thm)],[c_4780]) ).
tcf(c_49930,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(X0_iProver_sK18_2)) = sK5(X0_iProver_sK18_2) )
| ~ sP1(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK5(X0_iProver_sK18_2),sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)) ),
inference(instantiation,[status(thm)],[c_4779]) ).
tcf(c_49944,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(X0_iProver_sK18_2,cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ( X0_iProver_sK18_2 != sK5(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( cartesian_product2(sK3,sK4) != cartesian_product2(sK3,sK4) ) ),
inference(instantiation,[status(thm)],[c_49818]) ).
tcf(c_49955,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] : sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) = sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1),
inference(instantiation,[status(thm)],[c_4803]) ).
tcf(c_50099,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2,X3_iProver_sK18_2: iProver_sK18_2] :
( ( sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) = X3_iProver_sK18_2 )
| ( X3_iProver_sK18_2 != X2_iProver_sK18_2 )
| ( sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) != X2_iProver_sK18_2 ) ),
inference(instantiation,[status(thm)],[c_4804]) ).
tcf(c_50188,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( ( sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) = ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) )
| ( sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) != sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) != sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_49923]) ).
tcf(c_50210,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ( cartesian_product2(sK3,sK4) != cartesian_product2(sK3,sK4) )
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) != sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_49944]) ).
tcf(c_50934,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( ( sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) = X2_iProver_sK18_2 )
| ( X2_iProver_sK18_2 != sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) != sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_50099]) ).
tcf(c_50935,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] : sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) = sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),
inference(instantiation,[status(thm)],[c_4803]) ).
tcf(c_52162,plain,
sP1(sK4,sK3,sK2),
inference(instantiation,[status(thm)],[c_8414]) ).
tcf(c_52163,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X1_iProver_the_carrier_1: iProver_the_carrier_1,X2_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(X0_iProver_the_carrier_1),sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)))) = sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)) )
| ( sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)) != X2_iProver_sK18_2 )
| ( subset_complement(the_carrier(X0_iProver_the_carrier_1),sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)))) != X2_iProver_sK18_2 ) ),
inference(instantiation,[status(thm)],[c_4804]) ).
tcf(c_52440,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] : sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),
inference(instantiation,[status(thm)],[c_49814]) ).
tcf(c_52459,plain,
( ( sK8(sK12(sK4,sK3,sK2)) = subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) )
| ( sK8(sK12(sK4,sK3,sK2)) != sK8(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) != sK8(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_50934]) ).
tcf(c_55598,plain,
sK8(sK12(sK4,sK3,sK2)) = sK8(sK12(sK4,sK3,sK2)),
inference(instantiation,[status(thm)],[c_50935]) ).
tcf(c_55690,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X1_iProver_the_carrier_1: iProver_the_carrier_1,X2_iProver_sK18_2: iProver_sK18_2] :
( in(ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),sK12(sK4,X2_iProver_sK18_2,X1_iProver_the_carrier_1))
| ( sK13(X1_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(sK4,X2_iProver_sK18_2,X1_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),X2_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),cartesian_product2(X2_iProver_sK18_2,sK4)) ),
inference(instantiation,[status(thm)],[c_4782]) ).
tcf(c_60022,plain,
( ( sK5(sK12(sK4,sK3,sK2)) = sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(sK12(sK4,sK3,sK2)) )
| ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) != sK5(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_49923]) ).
tcf(c_60625,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X1_iProver_the_carrier_1: iProver_the_carrier_1,X2_iProver_sK18_2: iProver_sK18_2,X3_iProver_sK18_2: iProver_sK18_2] :
( in(X0_iProver_sK18_2,X3_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1))),sK12(sK4,sK3,X1_iProver_the_carrier_1))
| ( X3_iProver_sK18_2 != sK12(sK4,sK3,X1_iProver_the_carrier_1) )
| ( X0_iProver_sK18_2 != ordered_pair(sK7(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X0_iProver_the_carrier_1))) ) ),
inference(instantiation,[status(thm)],[c_4806]) ).
tcf(c_64158,plain,
( ( subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK8(sK12(sK4,sK3,sK2)) != subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) )
| ( subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) != subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) ) ),
inference(instantiation,[status(thm)],[c_49867]) ).
tcf(c_64161,plain,
! [X0_iProver_the_carrier_1: iProver_the_carrier_1] :
( ( subset_complement(the_carrier(X0_iProver_the_carrier_1),sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK8(sK12(sK4,sK3,sK2)) != subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) )
| ( subset_complement(the_carrier(X0_iProver_the_carrier_1),sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) != subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) ) ),
inference(instantiation,[status(thm)],[c_52163]) ).
tcf(c_64162,plain,
( ( subset_complement(the_carrier(sK2),sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) = sK8(sK12(sK4,sK3,sK2)) )
| ( sK8(sK12(sK4,sK3,sK2)) != subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) )
| ( subset_complement(the_carrier(sK2),sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) != subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) ) ),
inference(instantiation,[status(thm)],[c_64161]) ).
tcf(c_64173,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1] :
( in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),sK12(sK4,X0_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,X0_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(sK4,sK3,sK2)),X0_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),cartesian_product2(X0_iProver_sK18_2,sK4)) ),
inference(instantiation,[status(thm)],[c_55690]) ).
tcf(c_64175,plain,
( in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),sK12(sK4,sK3,sK2))
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),cartesian_product2(sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_64173]) ).
tcf(c_64279,plain,
sK12(sK4,sK3,sK2) = sK12(sK4,sK3,sK2),
inference(instantiation,[status(thm)],[c_49955]) ).
tcf(c_64881,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X1_iProver_the_carrier_1: iProver_the_carrier_1,X2_iProver_sK18_2: iProver_sK18_2] :
( in(X0_iProver_sK18_2,sK12(sK4,sK3,X0_iProver_the_carrier_1))
| ~ in(ordered_pair(sK7(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X1_iProver_the_carrier_1)),sK8(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X1_iProver_the_carrier_1))),sK12(sK4,sK3,X0_iProver_the_carrier_1))
| ( X0_iProver_sK18_2 != ordered_pair(sK7(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X1_iProver_the_carrier_1)),sK8(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X1_iProver_the_carrier_1))) )
| ( sK12(sK4,sK3,X0_iProver_the_carrier_1) != sK12(sK4,sK3,X0_iProver_the_carrier_1) ) ),
inference(instantiation,[status(thm)],[c_60625]) ).
tcf(c_70910,plain,
( ( subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) = subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) )
| ( the_carrier(sK2) != the_carrier(sK2) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) != sK7(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_4808]) ).
tcf(c_71059,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(X0_iProver_sK18_2,X1_iProver_sK18_2) = subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) )
| ( X1_iProver_sK18_2 != sK7(sK12(sK4,sK3,sK2)) )
| ( X0_iProver_sK18_2 != the_carrier(sK2) ) ),
inference(instantiation,[status(thm)],[c_4808]) ).
tcf(c_71359,plain,
( in(sK7(sK12(sK4,sK3,sK2)),sK3)
| in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_49775]) ).
tcf(c_72211,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X1_iProver_the_carrier_1: iProver_the_carrier_1] :
( in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK12(sK4,sK3,X1_iProver_the_carrier_1))
| ~ in(ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),sK12(sK4,sK3,X1_iProver_the_carrier_1))
| ( sK12(sK4,sK3,X1_iProver_the_carrier_1) != sK12(sK4,sK3,X1_iProver_the_carrier_1) )
| ( sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) != ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) ) ),
inference(instantiation,[status(thm)],[c_64881]) ).
tcf(c_77307,plain,
( in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ( cartesian_product2(sK3,sK4) != cartesian_product2(sK3,sK4) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) != sK5(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_50210]) ).
tcf(c_77427,plain,
( ( sK5(sK12(sK4,sK3,sK2)) = ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) )
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(sK12(sK4,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) != sK5(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_50188]) ).
tcf(c_77716,plain,
( ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) != sK5(sK12(sK4,sK3,sK2)) )
| ( subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) != sK8(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_49832]) ).
tcf(c_78214,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),X0_iProver_sK18_2) = subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) )
| ( X0_iProver_sK18_2 != sK7(sK12(sK4,sK3,sK2)) )
| ( the_carrier(sK2) != the_carrier(sK2) ) ),
inference(instantiation,[status(thm)],[c_71059]) ).
tcf(c_109187,plain,
( ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) != sK5(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_49833]) ).
tcf(c_109189,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_49771]) ).
tcf(c_109190,plain,
( ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_49928]) ).
tcf(c_109191,plain,
( in(sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))),cartesian_product2(sK3,sK4))
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_49929]) ).
tcf(c_109192,plain,
( ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_49930]) ).
tcf(c_109455,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(instantiation,[status(thm)],[c_49774]) ).
tcf(c_109466,plain,
sK5(sK12(sK4,sK3,sK2)) = sK5(sK12(sK4,sK3,sK2)),
inference(instantiation,[status(thm)],[c_52440]) ).
tcf(c_110050,plain,
! [X0_iProver_the_carrier_1: iProver_the_carrier_1] :
( in(sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1)),sK12(sK4,sK3,X0_iProver_the_carrier_1))
| ~ in(ordered_pair(sK7(sK12(sK4,sK3,X0_iProver_the_carrier_1)),sK8(sK12(sK4,sK3,X0_iProver_the_carrier_1))),sK12(sK4,sK3,X0_iProver_the_carrier_1))
| ( sK12(sK4,sK3,X0_iProver_the_carrier_1) != sK12(sK4,sK3,X0_iProver_the_carrier_1) )
| ( sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1)) != ordered_pair(sK7(sK12(sK4,sK3,X0_iProver_the_carrier_1)),sK8(sK12(sK4,sK3,X0_iProver_the_carrier_1))) ) ),
inference(instantiation,[status(thm)],[c_72211]) ).
tcf(c_110057,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),sK12(sK4,sK3,sK2))
| ( sK12(sK4,sK3,sK2) != sK12(sK4,sK3,sK2) )
| ( sK5(sK12(sK4,sK3,sK2)) != ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) ) ),
inference(instantiation,[status(thm)],[c_110050]) ).
tcf(c_122088,plain,
! [X0_iProver_the_carrier_1: iProver_the_carrier_1] :
( ( subset_complement(the_carrier(sK2),sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) = subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) )
| ( the_carrier(sK2) != the_carrier(sK2) )
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) != sK7(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_78214]) ).
tcf(c_122092,plain,
( ( subset_complement(the_carrier(sK2),sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) = subset_complement(the_carrier(sK2),sK7(sK12(sK4,sK3,sK2))) )
| ( the_carrier(sK2) != the_carrier(sK2) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) != sK7(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_122088]) ).
tcf(c_126321,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_4797]) ).
tcf(c_127468,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X1_iProver_the_carrier_1: iProver_the_carrier_1] :
( in(ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1))),sK12(sK4,sK3,X0_iProver_the_carrier_1))
| ~ sP1(sK4,sK3,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)),sK3)
| ~ in(ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1))),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(X0_iProver_the_carrier_1),sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)))) != sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_4783]) ).
tcf(c_138458,plain,
! [X0_iProver_the_carrier_1: iProver_the_carrier_1] :
( in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),sK12(sK4,sK3,X0_iProver_the_carrier_1))
| ~ sP1(sK4,sK3,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(X0_iProver_the_carrier_1),sK13(X0_iProver_the_carrier_1,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) != sK8(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_127468]) ).
tcf(c_138459,plain,
( in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),sK12(sK4,sK3,sK2))
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ~ in(ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2)))) != sK8(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_138458]) ).
tcf(c_143380,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X1_iProver_the_carrier_1: iProver_the_carrier_1,X2_iProver_sK18_2: iProver_sK18_2,X3_iProver_sK18_2: iProver_sK18_2] :
( in(X0_iProver_sK18_2,X3_iProver_sK18_2)
| ~ in(sK14(sK4,sK3,X0_iProver_the_carrier_1,sK5(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X1_iProver_the_carrier_1))),cartesian_product2(sK3,sK4))
| ( X3_iProver_sK18_2 != cartesian_product2(sK3,sK4) )
| ( X0_iProver_sK18_2 != sK14(sK4,sK3,X0_iProver_the_carrier_1,sK5(sK12(X1_iProver_sK18_2,X2_iProver_sK18_2,X1_iProver_the_carrier_1))) ) ),
inference(instantiation,[status(thm)],[c_4806]) ).
tcf(c_143399,plain,
! [X0_iProver_the_carrier_1: iProver_the_carrier_1] :
( in(sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1)),sK12(sK4,sK3,X0_iProver_the_carrier_1))
| ( ordered_pair(sK7(sK12(sK4,sK3,X0_iProver_the_carrier_1)),sK8(sK12(sK4,sK3,X0_iProver_the_carrier_1))) = sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_126321]) ).
tcf(c_143400,plain,
( in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_143399]) ).
tcf(c_144230,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X1_iProver_the_carrier_1: iProver_the_carrier_1] :
( ( sK6(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1))),sK16(sK3,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)))) = sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1))),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)),sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1))
| ( ordered_pair(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1))),sK16(sK3,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)))) != sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_4800]) ).
tcf(c_144231,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X1_iProver_the_carrier_1: iProver_the_carrier_1] :
( element(sK6(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1))),sK16(sK3,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)))),powerset(the_carrier(sK2)))
| ~ in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1))),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)),sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1))
| ( ordered_pair(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1))),sK16(sK3,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)))) != sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X1_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_4799]) ).
tcf(c_147268,plain,
! [X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_the_carrier_1: iProver_the_carrier_1] :
( ( sK6(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1))),sK16(sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1)))) = sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1))) )
| ~ in(sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1)),sK12(sK4,sK3,X1_iProver_the_carrier_1))
| ~ in(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1))),sK3)
| ( ordered_pair(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1))),sK16(sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1)))) != sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_144230]) ).
tcf(c_147269,plain,
! [X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_the_carrier_1: iProver_the_carrier_1] :
( element(sK6(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1))),sK16(sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1)))),powerset(the_carrier(sK2)))
| ~ in(sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1)),sK12(sK4,sK3,X1_iProver_the_carrier_1))
| ~ in(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1))),sK3)
| ( ordered_pair(sK15(sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1))),sK16(sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1)))) != sK5(sK12(sK4,sK3,X1_iProver_the_carrier_1)) ) ),
inference(instantiation,[status(thm)],[c_144231]) ).
tcf(c_147274,plain,
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_147269]) ).
tcf(c_147275,plain,
( ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(sK12(sK4,sK3,sK2)) ) ),
inference(instantiation,[status(thm)],[c_147268]) ).
tcf(c_158690,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1] :
( in(sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1)),X0_iProver_sK18_2)
| ~ in(sK14(sK4,sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1))),cartesian_product2(sK3,sK4))
| ( X0_iProver_sK18_2 != cartesian_product2(sK3,sK4) )
| ( sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1)) != sK14(sK4,sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1))) ) ),
inference(instantiation,[status(thm)],[c_143380]) ).
tcf(c_172994,plain,
! [X0_iProver_the_carrier_1: iProver_the_carrier_1] :
( in(sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ~ in(sK14(sK4,sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1))),cartesian_product2(sK3,sK4))
| ( cartesian_product2(sK3,sK4) != cartesian_product2(sK3,sK4) )
| ( sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1)) != sK14(sK4,sK3,X0_iProver_the_carrier_1,sK5(sK12(sK4,sK3,X0_iProver_the_carrier_1))) ) ),
inference(instantiation,[status(thm)],[c_158690]) ).
tcf(c_172995,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))),cartesian_product2(sK3,sK4))
| ( cartesian_product2(sK3,sK4) != cartesian_product2(sK3,sK4) )
| ( sK5(sK12(sK4,sK3,sK2)) != sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(instantiation,[status(thm)],[c_172994]) ).
tcf(c_209058,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4797,c_4779]) ).
tcf(c_209059,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),cartesian_product2(sK3,sK4))
| ( sK14(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4798,c_4779]) ).
tcf(c_209094,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_8414,c_209058]) ).
tcf(c_209115,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK8(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ( ordered_pair(sK15(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),sK16(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4797,c_4778]) ).
tcf(c_209117,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2] :
( in(sK7(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)),sK3)
| ( ordered_pair(sK15(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))),sK16(X1_iProver_sK18_2,X0_iProver_the_carrier_1,sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)))) = sK5(sK12(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)) )
| ~ sP1(X0_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1) ),
inference(superposition,[status(thm)],[c_4796,c_4778]) ).
tcf(c_209145,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),X1_iProver_sK18_2)
| ~ in(ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))),cartesian_product2(X1_iProver_sK18_2,X2_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_209094,c_4782]) ).
tcf(c_209147,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK5(X1_iProver_sK18_2),X1_iProver_sK18_2)
| ~ in(sK5(X1_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ( sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) != sK5(X1_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_209094,c_4800]) ).
tcf(c_209168,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_8414,c_209115]) ).
tcf(c_209185,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_209147]) ).
tcf(c_209238,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK5(X1_iProver_sK18_2),X1_iProver_sK18_2)
| ~ in(sK5(X1_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ( sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) != sK5(X1_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_209168,c_4799]) ).
tcf(c_209239,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X1_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(X1_iProver_sK18_2),X1_iProver_sK18_2)
| ~ in(sK5(X1_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ( sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) != sK5(X1_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_209168,c_4800]) ).
tcf(c_209246,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_209238]) ).
tcf(c_209253,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_209239]) ).
tcf(c_209492,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))),powerset(the_carrier(sK2)))
| ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_209246,c_4797]) ).
tcf(c_209518,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) )
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_209253,c_9072]) ).
tcf(c_210535,plain,
! [X0_iProver_sK18_2: iProver_sK18_2,X0_iProver_the_carrier_1: iProver_the_carrier_1,X1_iProver_sK18_2: iProver_sK18_2,X2_iProver_sK18_2: iProver_sK18_2] :
( in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),sK12(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1))
| ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(X0_iProver_the_carrier_1,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X2_iProver_sK18_2,X1_iProver_sK18_2,X0_iProver_the_carrier_1)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),X1_iProver_sK18_2)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(X1_iProver_sK18_2,X2_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_209094,c_209145]) ).
tcf(c_210546,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(superposition,[status(thm)],[c_210535,c_209185]) ).
tcf(c_210547,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210546,c_8414]) ).
tcf(c_210548,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK14(X0_iProver_sK18_2,sK3,sK2,sK5(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK5(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK6(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK8(sK12(X0_iProver_sK18_2,sK3,sK2))) = sK7(sK12(X0_iProver_sK18_2,sK3,sK2)) )
| ~ in(sK7(sK12(X0_iProver_sK18_2,sK3,sK2)),sK3)
| ~ in(sK5(sK12(X0_iProver_sK18_2,sK3,sK2)),cartesian_product2(sK3,X0_iProver_sK18_2)) ),
inference(global_subsumption_just,[status(thm)],[c_210547,c_15636]) ).
tcf(c_210557,plain,
( ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(superposition,[status(thm)],[c_209059,c_210548]) ).
tcf(c_210558,plain,
( ( sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ( sK13(sK2,sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210557,c_8414]) ).
tcf(c_210560,plain,
sK14(sK4,sK3,sK2,sK5(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)),
inference(global_subsumption_just,[status(thm)],[c_210558,c_7409,c_26259,c_52162,c_52459,c_55598,c_64158,c_64162,c_64175,c_64279,c_70910,c_71359,c_77307,c_77427,c_77716,c_37292,c_109187,c_109192,c_109455,c_109466,c_110057,c_122092,c_138459,c_143400]) ).
tcf(c_210562,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ sP1(sK4,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_210560,c_4780]) ).
tcf(c_210564,plain,
( in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210562,c_8414]) ).
tcf(c_210566,plain,
in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4)),
inference(global_subsumption_just,[status(thm)],[c_210564,c_109455,c_210564]) ).
tcf(c_210573,plain,
( ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(superposition,[status(thm)],[c_210566,c_209518]) ).
tcf(c_210739,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_210573,c_4801]) ).
tcf(c_210740,plain,
( element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3) ),
inference(superposition,[status(thm)],[c_210573,c_209492]) ).
tcf(c_210741,plain,
( element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210740,c_210566]) ).
tcf(c_210743,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(global_subsumption_just,[status(thm)],[c_210739,c_7409,c_26259,c_52162,c_52459,c_55598,c_64158,c_64162,c_64175,c_64279,c_70910,c_71359,c_77307,c_77427,c_77716,c_37292,c_109189,c_109187,c_109455,c_109466,c_110057,c_122092,c_138459,c_143400,c_210739]) ).
tcf(c_210744,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(renaming,[status(thm)],[c_210743]) ).
tcf(c_210751,plain,
( element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2)))
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(global_subsumption_just,[status(thm)],[c_210741,c_52162,c_109189,c_143400,c_210741]) ).
tcf(c_210755,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_210751,c_4776]) ).
tcf(c_210761,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210755,c_8414]) ).
tcf(c_210766,plain,
( ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) ) ),
inference(superposition,[status(thm)],[c_4797,c_210761]) ).
tcf(c_210774,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_210766,c_210744]) ).
tcf(c_210789,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_209168,c_210774]) ).
tcf(c_210795,plain,
( ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_210789]) ).
tcf(c_210796,plain,
( ( ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210795,c_210566]) ).
tcf(c_210837,plain,
ordered_pair(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK5(sK12(sK4,sK3,sK2)),
inference(global_subsumption_just,[status(thm)],[c_210796,c_143400,c_210796]) ).
tcf(c_210848,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_210837,c_4800]) ).
tcf(c_210865,plain,
( ( sK6(sK7(sK12(sK4,sK3,sK2)),sK8(sK12(sK4,sK3,sK2))) = sK7(sK12(sK4,sK3,sK2)) )
| ~ in(sK7(sK12(sK4,sK3,sK2)),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_210848,c_7409,c_26259,c_52162,c_52459,c_55598,c_64158,c_64162,c_64175,c_64279,c_70910,c_77307,c_77427,c_77716,c_37292,c_109187,c_109466,c_110057,c_122092,c_138459,c_210566,c_210837]) ).
tcf(c_210867,plain,
~ in(sK7(sK12(sK4,sK3,sK2)),sK3),
inference(global_subsumption_just,[status(thm)],[c_210865,c_7409,c_26259,c_52162,c_52459,c_55598,c_64158,c_64162,c_64175,c_64279,c_70910,c_77307,c_77427,c_77716,c_37292,c_109466,c_110057,c_122092,c_138459,c_210566,c_210837,c_210865]) ).
tcf(c_210869,plain,
in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)),
inference(superposition,[status(thm)],[c_4796,c_210867]) ).
tcf(c_210870,plain,
( ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)) )
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_209117,c_210867]) ).
tcf(c_210872,plain,
ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK5(sK12(sK4,sK3,sK2)),
inference(forward_subsumption_resolution,[status(thm)],[c_210870,c_8414]) ).
tcf(c_210875,plain,
( in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ~ sP1(sK4,sK3,sK2) ),
inference(superposition,[status(thm)],[c_210869,c_4777]) ).
tcf(c_210878,plain,
in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_210875,c_8414]) ).
tcf(c_210883,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_210872,c_4799]) ).
tcf(c_210884,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_210872,c_4800]) ).
tcf(c_210885,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2)))
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210883,c_210878]) ).
tcf(c_210886,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210884,c_210878]) ).
tcf(c_210926,plain,
element(sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))),powerset(the_carrier(sK2))),
inference(global_subsumption_just,[status(thm)],[c_210885,c_7409,c_26259,c_52162,c_52459,c_55598,c_60022,c_64158,c_64162,c_64175,c_64279,c_70910,c_71359,c_77307,c_77427,c_77716,c_37292,c_109189,c_109187,c_109192,c_109191,c_109190,c_109455,c_109466,c_110057,c_122092,c_138459,c_143400,c_147274,c_172995]) ).
tcf(c_210937,plain,
sK6(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),
inference(global_subsumption_just,[status(thm)],[c_210886,c_52162,c_71359,c_109189,c_109190,c_147275,c_210566,c_210867]) ).
tcf(c_210939,plain,
element(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),powerset(the_carrier(sK2))),
inference(demodulation,[status(thm)],[c_210926,c_210937]) ).
tcf(c_210940,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ~ in(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK3)
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(superposition,[status(thm)],[c_210937,c_4801]) ).
tcf(c_210942,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ( ordered_pair(sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK5(X0_iProver_sK18_2) ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210940,c_210878]) ).
tcf(c_210944,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) )
| ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) != sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) ) ),
inference(light_normalisation,[status(thm)],[c_210942,c_210872]) ).
tcf(c_210953,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ sP1(X0_iProver_sK18_2,sK3,sK2)
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(superposition,[status(thm)],[c_210939,c_4776]) ).
tcf(c_210961,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ( subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))) )
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(X0_iProver_sK18_2,sK3,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_210953,c_8414]) ).
tcf(c_211015,plain,
subset_complement(the_carrier(sK2),sK15(sK3,sK2,sK5(sK12(sK4,sK3,sK2)))) = sK16(sK3,sK2,sK5(sK12(sK4,sK3,sK2))),
inference(superposition,[status(thm)],[c_210869,c_210961]) ).
tcf(c_211016,plain,
! [X0_iProver_sK18_2: iProver_sK18_2] :
( ~ in(sK5(X0_iProver_sK18_2),X0_iProver_sK18_2)
| ~ in(sK5(X0_iProver_sK18_2),cartesian_product2(sK3,sK4))
| ( sK5(sK12(sK4,sK3,sK2)) != sK5(X0_iProver_sK18_2) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_210944,c_211015]) ).
tcf(c_211025,plain,
( ~ in(sK5(sK12(sK4,sK3,sK2)),cartesian_product2(sK3,sK4))
| ~ in(sK5(sK12(sK4,sK3,sK2)),sK12(sK4,sK3,sK2)) ),
inference(equality_resolution,[status(thm)],[c_211016]) ).
tcf(c_211026,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_211025,c_210566,c_210869]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU332+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.19/0.44 % Computer : n007.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Thu Sep 24 13:41:53 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.26/0.51 Running first-order theorem proving
% 0.26/0.51 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
% 0.26/0.53
% 0.26/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.53
% 0.26/0.53 % Detected problem language: tptp
% 0.26/0.54 % Proving...
% 135.56/34.32 % SZS status Started for theBenchmark.p
% 135.56/34.32 % SZS status Theorem for theBenchmark.p
% 135.56/34.32
% 135.56/34.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 135.56/34.32
% 135.56/34.32 % ------ iProver source info
% 135.56/34.32
% 135.56/34.32 % git: date: 2026-07-19 20:42:38 +0200
% 135.56/34.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 135.56/34.32 % git: non_committed_changes: false
% 135.56/34.32
% 135.56/34.32 % ------ Parsing...
% 135.56/34.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 135.56/34.32
% 135.56/34.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 35 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 8 0s sf_e pe_s pe_e %
% 135.56/34.32
% 135.56/34.32 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 135.56/34.32
% 135.56/34.32 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 135.56/34.32 % ------ Proving...
% 135.56/34.32 % ------ Problem Properties
% 135.56/34.32
% 135.56/34.32 %
% 135.56/34.32 % clauses 35
% 135.56/34.32 % conjectures 8
% 135.56/34.32 % EPR 2
% 135.56/34.32 % Horn 19
% 135.56/34.32 % unary 5
% 135.56/34.32 % binary 8
% 135.56/34.32 % lits 102
% 135.56/34.32 % lits eq 20
% 135.56/34.32 % fd_pure 0
% 135.56/34.32 % fd_pseudo 0
% 135.56/34.32 % fd_cond 0
% 135.56/34.32 % fd_pseudo_cond 0
% 135.56/34.32 % AC symbols 0
% 135.56/34.32
% 135.56/34.32 % ------ Input Options Time Limit: Unbounded
% 135.56/34.32
% 135.56/34.32
% 135.56/34.32 % ------
% 135.56/34.32 % Current options:
% 135.56/34.32 % ------
% 135.56/34.32
% 135.56/34.32
% 135.56/34.32 %
% 135.56/34.32
% 135.56/34.32 % ------ Proving...
% 135.56/34.32 %
% 135.56/34.32
% 135.56/34.32 % SZS status Theorem for theBenchmark.p
% 135.56/34.32
% 135.56/34.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 135.56/34.35
% 135.56/34.35
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