TSTP Solution File: SEU332+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU332+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:06:02 EDT 2023
% Result : Theorem 75.40s 10.82s
% Output : CNFRefutation 75.40s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% 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)))
=> ( X5 = X7
=> subset_complement(the_carrier(X0),X7) = X6 ) )
& 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)))
=> ( X5 = X7
=> subset_complement(the_carrier(X0),X7) = X6 ) )
& in(X5,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) ) ),
inference(negated_conjecture,[],[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(f33,axiom,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) )
=> ! [X2] :
( ! [X3,X4,X5] :
( ( ? [X9,X10] :
( ! [X11] :
( element(X11,powerset(the_carrier(X0)))
=> ( X9 = X11
=> subset_complement(the_carrier(X0),X11) = X10 ) )
& in(X9,X1)
& ordered_pair(X9,X10) = X5 )
& X3 = X5
& ? [X6,X7] :
( ! [X8] :
( element(X8,powerset(the_carrier(X0)))
=> ( X6 = X8
=> subset_complement(the_carrier(X0),X8) = X7 ) )
& in(X6,X1)
& ordered_pair(X6,X7) = X4 )
& X3 = X4 )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( ? [X12,X13] :
( ! [X14] :
( element(X14,powerset(the_carrier(X0)))
=> ( X12 = X14
=> subset_complement(the_carrier(X0),X14) = X13 ) )
& in(X12,X1)
& ordered_pair(X12,X13) = X4 )
& X4 = X5
& in(X5,cartesian_product2(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_2__tops_2__2) ).
fof(f34,plain,
! [X0,X1] :
( ( element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) )
=> ! [X2] :
( ! [X3,X4,X5] :
( ( ? [X6,X7] :
( ! [X8] :
( element(X8,powerset(the_carrier(X0)))
=> ( X6 = X8
=> subset_complement(the_carrier(X0),X8) = X7 ) )
& in(X6,X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X9,X10] :
( ! [X11] :
( element(X11,powerset(the_carrier(X0)))
=> ( X9 = X11
=> subset_complement(the_carrier(X0),X11) = X10 ) )
& in(X9,X1)
& ordered_pair(X9,X10) = X4 )
& X3 = X4 )
=> X4 = X5 )
=> ? [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)) ) ) ) ),
inference(rectify,[],[f33]) ).
fof(f51,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( ? [X5,X6] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f52,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( in(X4,X3)
<~> ( ? [X5,X6] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(flattening,[],[f51]) ).
fof(f66,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f68,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f69,plain,
! [X0,X1] :
( ! [X2] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( ? [X15,X16] :
( ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) )
& in(X15,X1)
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(X1,X2)) ) )
| ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X9,X10] :
( ! [X11] :
( subset_complement(the_carrier(X0),X11) = X10
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) )
& in(X9,X1)
& ordered_pair(X9,X10) = X4 )
& X3 = X4 ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( ? [X15,X16] :
( ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) )
& in(X15,X1)
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(X1,X2)) ) )
| ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X9,X10] :
( ! [X11] :
( subset_complement(the_carrier(X0),X11) = X10
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) )
& in(X9,X1)
& ordered_pair(X9,X10) = X4 )
& X3 = X4 ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X4] :
( ? [X9,X10] :
( ! [X11] :
( subset_complement(the_carrier(X0),X11) = X10
| X9 != X11
| ~ element(X11,powerset(the_carrier(X0))) )
& in(X9,X1)
& ordered_pair(X9,X10) = X4 )
| ~ sP0(X0,X1,X4) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ? [X12] :
! [X13] :
( in(X13,X12)
<=> ? [X14] :
( ? [X15,X16] :
( ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) )
& in(X15,X1)
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(X1,X2)) ) )
| ~ sP1(X0,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f73,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X0,X1,X2)
| ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& sP0(X0,X1,X4)
& X3 = X4 ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(definition_folding,[],[f70,f72,f71]) ).
fof(f74,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) )
| ~ in(X5,X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X1,X2))
| ~ in(X4,X3) )
& ( ( ? [X5,X6] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(nnf_transformation,[],[f52]) ).
fof(f75,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) )
| ~ in(X5,X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X1,X2))
| ~ in(X4,X3) )
& ( ( ? [X5,X6] :
( ! [X7] :
( subset_complement(the_carrier(X0),X7) = X6
| X5 != X7
| ~ element(X7,powerset(the_carrier(X0))) )
& in(X5,X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X1,X2)) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) )
| ~ in(X5,X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X1,X2))
| ~ in(X4,X3) )
& ( ( ? [X8,X9] :
( ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) )
& in(X8,X1)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(X1,X2)) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) ),
inference(rectify,[],[f75]) ).
fof(f77,plain,
( ? [X0,X1] :
( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ? [X7] :
( subset_complement(the_carrier(X0),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(X0))) )
| ~ in(X5,X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X1,X2))
| ~ in(X4,X3) )
& ( ( ? [X8,X9] :
( ! [X10] :
( subset_complement(the_carrier(X0),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(X0))) )
& in(X8,X1)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(X1,X2)) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(the_carrier(X0))))
& one_sorted_str(X0) )
=> ( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(sK3,X2))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(sK3,X2)) )
| in(X4,X3) ) )
& element(sK3,powerset(powerset(the_carrier(sK2))))
& one_sorted_str(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
( ? [X2] :
! [X3] :
? [X4] :
( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(sK3,X2))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(sK3,X2)) )
| in(X4,X3) ) )
=> ! [X3] :
? [X4] :
( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(sK3,sK4))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(sK3,sK4)) )
| in(X4,X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X3] :
( ? [X4] :
( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(sK3,sK4))
| ~ in(X4,X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = X4 )
& in(X4,cartesian_product2(sK3,sK4)) )
| in(X4,X3) ) )
=> ( ( ! [X6,X5] :
( ? [X7] :
( subset_complement(the_carrier(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3) )
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(sK5(X3),X3) )
& ( ( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = sK5(X3) )
& in(sK5(X3),cartesian_product2(sK3,sK4)) )
| in(sK5(X3),X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X5,X6] :
( ? [X7] :
( subset_complement(the_carrier(sK2),X7) != X6
& X5 = X7
& element(X7,powerset(the_carrier(sK2))) )
=> ( subset_complement(the_carrier(sK2),sK6(X5,X6)) != X6
& sK6(X5,X6) = X5
& element(sK6(X5,X6),powerset(the_carrier(sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X3] :
( ? [X9,X8] :
( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = X9
| X8 != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(X8,sK3)
& ordered_pair(X8,X9) = sK5(X3) )
=> ( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = sK8(X3)
| sK7(X3) != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(sK7(X3),sK3)
& sK5(X3) = ordered_pair(sK7(X3),sK8(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
( ! [X3] :
( ( ! [X5,X6] :
( ( subset_complement(the_carrier(sK2),sK6(X5,X6)) != X6
& sK6(X5,X6) = X5
& element(sK6(X5,X6),powerset(the_carrier(sK2))) )
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3) )
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(sK5(X3),X3) )
& ( ( ! [X10] :
( subset_complement(the_carrier(sK2),X10) = sK8(X3)
| sK7(X3) != X10
| ~ element(X10,powerset(the_carrier(sK2))) )
& in(sK7(X3),sK3)
& sK5(X3) = ordered_pair(sK7(X3),sK8(X3))
& in(sK5(X3),cartesian_product2(sK3,sK4)) )
| in(sK5(X3),X3) ) )
& element(sK3,powerset(powerset(the_carrier(sK2))))
& one_sorted_str(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8])],[f76,f81,f80,f79,f78,f77]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ? [X12] :
! [X13] :
( ( in(X13,X12)
| ! [X14] :
( ! [X15,X16] :
( ? [X17] :
( subset_complement(the_carrier(X0),X17) != X16
& X15 = X17
& element(X17,powerset(the_carrier(X0))) )
| ~ in(X15,X1)
| ordered_pair(X15,X16) != X13 )
| X13 != X14
| ~ in(X14,cartesian_product2(X1,X2)) ) )
& ( ? [X14] :
( ? [X15,X16] :
( ! [X17] :
( subset_complement(the_carrier(X0),X17) = X16
| X15 != X17
| ~ element(X17,powerset(the_carrier(X0))) )
& in(X15,X1)
& ordered_pair(X15,X16) = X13 )
& X13 = X14
& in(X14,cartesian_product2(X1,X2)) )
| ~ in(X13,X12) ) )
| ~ sP1(X0,X1,X2) ),
inference(nnf_transformation,[],[f72]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ! [X6,X7] :
( ? [X8] :
( subset_complement(the_carrier(X0),X8) != X7
& X6 = X8
& element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2)) ) )
& ( ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(X1,X2)) )
| ~ in(X4,X3) ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ! [X6,X7] :
( ? [X8] :
( subset_complement(the_carrier(X0),X8) != X7
& X6 = X8
& element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2)) ) )
& ( ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(X1,X2)) )
| ~ in(X4,X3) ) )
=> ! [X4] :
( ( in(X4,sK12(X0,X1,X2))
| ! [X5] :
( ! [X6,X7] :
( ? [X8] :
( subset_complement(the_carrier(X0),X8) != X7
& X6 = X8
& element(X8,powerset(the_carrier(X0))) )
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2)) ) )
& ( ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(X1,X2)) )
| ~ in(X4,sK12(X0,X1,X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X6,X7] :
( ? [X8] :
( subset_complement(the_carrier(X0),X8) != X7
& X6 = X8
& element(X8,powerset(the_carrier(X0))) )
=> ( subset_complement(the_carrier(X0),sK13(X0,X6,X7)) != X7
& sK13(X0,X6,X7) = X6
& element(sK13(X0,X6,X7),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0,X1,X2,X4] :
( ? [X9] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
& X4 = X9
& in(X9,cartesian_product2(X1,X2)) )
=> ( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
& sK14(X0,X1,X2,X4) = X4
& in(sK14(X0,X1,X2,X4),cartesian_product2(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
! [X0,X1,X4] :
( ? [X10,X11] :
( ! [X12] :
( subset_complement(the_carrier(X0),X12) = X11
| X10 != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(X10,X1)
& ordered_pair(X10,X11) = X4 )
=> ( ! [X12] :
( subset_complement(the_carrier(X0),X12) = sK16(X0,X1,X4)
| sK15(X0,X1,X4) != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(sK15(X0,X1,X4),X1)
& ordered_pair(sK15(X0,X1,X4),sK16(X0,X1,X4)) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK12(X0,X1,X2))
| ! [X5] :
( ! [X6,X7] :
( ( subset_complement(the_carrier(X0),sK13(X0,X6,X7)) != X7
& sK13(X0,X6,X7) = X6
& element(sK13(X0,X6,X7),powerset(the_carrier(X0))) )
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4 )
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2)) ) )
& ( ( ! [X12] :
( subset_complement(the_carrier(X0),X12) = sK16(X0,X1,X4)
| sK15(X0,X1,X4) != X12
| ~ element(X12,powerset(the_carrier(X0))) )
& in(sK15(X0,X1,X4),X1)
& ordered_pair(sK15(X0,X1,X4),sK16(X0,X1,X4)) = X4
& sK14(X0,X1,X2,X4) = X4
& in(sK14(X0,X1,X2,X4),cartesian_product2(X1,X2)) )
| ~ in(X4,sK12(X0,X1,X2)) ) )
| ~ sP1(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14,sK15,sK16])],[f90,f94,f93,f92,f91]) ).
fof(f100,plain,
! [X0,X1] :
( ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& sP0(X0,X1,X4)
& X3 = X4 )
=> ( sK20(X0,X1) != sK21(X0,X1)
& ? [X7,X6] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,X1)
& ordered_pair(X6,X7) = sK21(X0,X1) )
& sK19(X0,X1) = sK21(X0,X1)
& sP0(X0,X1,sK20(X0,X1))
& sK19(X0,X1) = sK20(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X7,X6] :
( ! [X8] :
( subset_complement(the_carrier(X0),X8) = X7
| X6 != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(X6,X1)
& ordered_pair(X6,X7) = sK21(X0,X1) )
=> ( ! [X8] :
( subset_complement(the_carrier(X0),X8) = sK23(X0,X1)
| sK22(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(sK22(X0,X1),X1)
& sK21(X0,X1) = ordered_pair(sK22(X0,X1),sK23(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X2] :
( sP1(X0,X1,X2)
| ( sK20(X0,X1) != sK21(X0,X1)
& ! [X8] :
( subset_complement(the_carrier(X0),X8) = sK23(X0,X1)
| sK22(X0,X1) != X8
| ~ element(X8,powerset(the_carrier(X0))) )
& in(sK22(X0,X1),X1)
& sK21(X0,X1) = ordered_pair(sK22(X0,X1),sK23(X0,X1))
& sK19(X0,X1) = sK21(X0,X1)
& sP0(X0,X1,sK20(X0,X1))
& sK19(X0,X1) = sK20(X0,X1) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21,sK22,sK23])],[f73,f101,f100]) ).
fof(f103,plain,
one_sorted_str(sK2),
inference(cnf_transformation,[],[f82]) ).
fof(f104,plain,
element(sK3,powerset(powerset(the_carrier(sK2)))),
inference(cnf_transformation,[],[f82]) ).
fof(f105,plain,
! [X3] :
( in(sK5(X3),cartesian_product2(sK3,sK4))
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f106,plain,
! [X3] :
( sK5(X3) = ordered_pair(sK7(X3),sK8(X3))
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f107,plain,
! [X3] :
( in(sK7(X3),sK3)
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f108,plain,
! [X3,X10] :
( subset_complement(the_carrier(sK2),X10) = sK8(X3)
| sK7(X3) != X10
| ~ element(X10,powerset(the_carrier(sK2)))
| in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f109,plain,
! [X3,X6,X5] :
( element(sK6(X5,X6),powerset(the_carrier(sK2)))
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f110,plain,
! [X3,X6,X5] :
( sK6(X5,X6) = X5
| ~ in(X5,sK3)
| ordered_pair(X5,X6) != sK5(X3)
| ~ in(sK5(X3),cartesian_product2(sK3,sK4))
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f111,plain,
! [X3,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))
| ~ in(sK5(X3),X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f147,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f149,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f151,plain,
! [X2,X0,X1,X4] :
( in(sK14(X0,X1,X2,X4),cartesian_product2(X1,X2))
| ~ in(X4,sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f152,plain,
! [X2,X0,X1,X4] :
( sK14(X0,X1,X2,X4) = X4
| ~ in(X4,sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f153,plain,
! [X2,X0,X1,X4] :
( ordered_pair(sK15(X0,X1,X4),sK16(X0,X1,X4)) = X4
| ~ in(X4,sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f154,plain,
! [X2,X0,X1,X4] :
( in(sK15(X0,X1,X4),X1)
| ~ in(X4,sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f155,plain,
! [X2,X0,X1,X4,X12] :
( subset_complement(the_carrier(X0),X12) = sK16(X0,X1,X4)
| sK15(X0,X1,X4) != X12
| ~ element(X12,powerset(the_carrier(X0)))
| ~ in(X4,sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f156,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK12(X0,X1,X2))
| element(sK13(X0,X6,X7),powerset(the_carrier(X0)))
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f157,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK12(X0,X1,X2))
| sK13(X0,X6,X7) = X6
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f158,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( in(X4,sK12(X0,X1,X2))
| subset_complement(the_carrier(X0),sK13(X0,X6,X7)) != X7
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X4
| X4 != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f162,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| sK19(X0,X1) = sK20(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f164,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| sK19(X0,X1) = sK21(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f166,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| in(sK22(X0,X1),X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f168,plain,
! [X2,X0,X1] :
( sP1(X0,X1,X2)
| sK20(X0,X1) != sK21(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f169,plain,
! [X3] :
( sK8(X3) = subset_complement(the_carrier(sK2),sK7(X3))
| ~ element(sK7(X3),powerset(the_carrier(sK2)))
| in(sK5(X3),X3) ),
inference(equality_resolution,[],[f108]) ).
fof(f170,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(ordered_pair(X6,X7),sK12(X0,X1,X2))
| subset_complement(the_carrier(X0),sK13(X0,X6,X7)) != X7
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f158]) ).
fof(f171,plain,
! [X2,X0,X1,X6,X7] :
( in(ordered_pair(X6,X7),sK12(X0,X1,X2))
| subset_complement(the_carrier(X0),sK13(X0,X6,X7)) != X7
| ~ in(X6,X1)
| ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f170]) ).
fof(f172,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(ordered_pair(X6,X7),sK12(X0,X1,X2))
| sK13(X0,X6,X7) = X6
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f157]) ).
fof(f173,plain,
! [X2,X0,X1,X6,X7] :
( in(ordered_pair(X6,X7),sK12(X0,X1,X2))
| sK13(X0,X6,X7) = X6
| ~ in(X6,X1)
| ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f172]) ).
fof(f174,plain,
! [X2,X0,X1,X6,X7,X5] :
( in(ordered_pair(X6,X7),sK12(X0,X1,X2))
| element(sK13(X0,X6,X7),powerset(the_carrier(X0)))
| ~ in(X6,X1)
| ordered_pair(X6,X7) != X5
| ~ in(X5,cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f156]) ).
fof(f175,plain,
! [X2,X0,X1,X6,X7] :
( in(ordered_pair(X6,X7),sK12(X0,X1,X2))
| element(sK13(X0,X6,X7),powerset(the_carrier(X0)))
| ~ in(X6,X1)
| ~ in(ordered_pair(X6,X7),cartesian_product2(X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f174]) ).
fof(f176,plain,
! [X2,X0,X1,X4] :
( sK16(X0,X1,X4) = subset_complement(the_carrier(X0),sK15(X0,X1,X4))
| ~ element(sK15(X0,X1,X4),powerset(the_carrier(X0)))
| ~ in(X4,sK12(X0,X1,X2))
| ~ sP1(X0,X1,X2) ),
inference(equality_resolution,[],[f155]) ).
cnf(c_49,negated_conjecture,
( subset_complement(the_carrier(sK2),sK6(X0,X1)) != X1
| ordered_pair(X0,X1) != sK5(X2)
| ~ in(sK5(X2),cartesian_product2(sK3,sK4))
| ~ in(sK5(X2),X2)
| ~ in(X0,sK3) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_50,negated_conjecture,
( ordered_pair(X0,X1) != sK5(X2)
| ~ in(sK5(X2),cartesian_product2(sK3,sK4))
| ~ in(sK5(X2),X2)
| ~ in(X0,sK3)
| sK6(X0,X1) = X0 ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_51,negated_conjecture,
( ordered_pair(X0,X1) != sK5(X2)
| ~ in(sK5(X2),cartesian_product2(sK3,sK4))
| ~ in(sK5(X2),X2)
| ~ in(X0,sK3)
| element(sK6(X0,X1),powerset(the_carrier(sK2))) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_52,negated_conjecture,
( ~ element(sK7(X0),powerset(the_carrier(sK2)))
| subset_complement(the_carrier(sK2),sK7(X0)) = sK8(X0)
| in(sK5(X0),X0) ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_53,negated_conjecture,
( in(sK5(X0),X0)
| in(sK7(X0),sK3) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_54,negated_conjecture,
( ordered_pair(sK7(X0),sK8(X0)) = sK5(X0)
| in(sK5(X0),X0) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_55,negated_conjecture,
( in(sK5(X0),cartesian_product2(sK3,sK4))
| in(sK5(X0),X0) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_56,negated_conjecture,
element(sK3,powerset(powerset(the_carrier(sK2)))),
inference(cnf_transformation,[],[f104]) ).
cnf(c_57,negated_conjecture,
one_sorted_str(sK2),
inference(cnf_transformation,[],[f103]) ).
cnf(c_93,plain,
( ~ element(X0,powerset(X1))
| subset_complement(X1,subset_complement(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f147]) ).
cnf(c_95,plain,
( ~ element(X0,powerset(X1))
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_97,plain,
( subset_complement(the_carrier(X0),sK13(X0,X1,X2)) != X2
| ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
| ~ sP1(X0,X3,X4)
| ~ in(X1,X3)
| in(ordered_pair(X1,X2),sK12(X0,X3,X4)) ),
inference(cnf_transformation,[],[f171]) ).
cnf(c_98,plain,
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ sP1(X4,X2,X3)
| ~ in(X0,X2)
| sK13(X4,X0,X1) = X0
| in(ordered_pair(X0,X1),sK12(X4,X2,X3)) ),
inference(cnf_transformation,[],[f173]) ).
cnf(c_99,plain,
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ sP1(X4,X2,X3)
| ~ in(X0,X2)
| in(ordered_pair(X0,X1),sK12(X4,X2,X3))
| element(sK13(X4,X0,X1),powerset(the_carrier(X4))) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_100,plain,
( ~ element(sK15(X0,X1,X2),powerset(the_carrier(X0)))
| ~ in(X2,sK12(X0,X1,X3))
| ~ sP1(X0,X1,X3)
| subset_complement(the_carrier(X0),sK15(X0,X1,X2)) = sK16(X0,X1,X2) ),
inference(cnf_transformation,[],[f176]) ).
cnf(c_101,plain,
( ~ in(X0,sK12(X1,X2,X3))
| ~ sP1(X1,X2,X3)
| in(sK15(X1,X2,X0),X2) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_102,plain,
( ~ in(X0,sK12(X1,X2,X3))
| ~ sP1(X1,X2,X3)
| ordered_pair(sK15(X1,X2,X0),sK16(X1,X2,X0)) = X0 ),
inference(cnf_transformation,[],[f153]) ).
cnf(c_103,plain,
( ~ in(X0,sK12(X1,X2,X3))
| ~ sP1(X1,X2,X3)
| sK14(X1,X2,X3,X0) = X0 ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_104,plain,
( ~ in(X0,sK12(X1,X2,X3))
| ~ sP1(X1,X2,X3)
| in(sK14(X1,X2,X3,X0),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_108,plain,
( sK20(X0,X1) != sK21(X0,X1)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ one_sorted_str(X0)
| sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_110,plain,
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| in(sK22(X1,X0),X0)
| sP1(X1,X0,X2) ),
inference(cnf_transformation,[],[f166]) ).
cnf(c_112,plain,
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| sK21(X1,X0) = sK19(X1,X0)
| sP1(X1,X0,X2) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_114,plain,
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| sK20(X1,X0) = sK19(X1,X0)
| sP1(X1,X0,X2) ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_940,plain,
( sK20(X0,X1) != sK21(X0,X1)
| X0 != sK2
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| sP1(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_57,c_108]) ).
cnf(c_941,plain,
( sK20(sK2,X0) != sK21(sK2,X0)
| ~ element(X0,powerset(powerset(the_carrier(sK2))))
| sP1(sK2,X0,X1) ),
inference(unflattening,[status(thm)],[c_940]) ).
cnf(c_952,plain,
( X0 != sK2
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| sK20(X0,X1) = sK19(X0,X1)
| sP1(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_57,c_114]) ).
cnf(c_953,plain,
( ~ element(X0,powerset(powerset(the_carrier(sK2))))
| sK20(sK2,X0) = sK19(sK2,X0)
| sP1(sK2,X0,X1) ),
inference(unflattening,[status(thm)],[c_952]) ).
cnf(c_976,plain,
( X0 != sK2
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| sK21(X0,X1) = sK19(X0,X1)
| sP1(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_57,c_112]) ).
cnf(c_977,plain,
( ~ element(X0,powerset(powerset(the_carrier(sK2))))
| sK21(sK2,X0) = sK19(sK2,X0)
| sP1(sK2,X0,X1) ),
inference(unflattening,[status(thm)],[c_976]) ).
cnf(c_1000,plain,
( X0 != sK2
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| in(sK22(X0,X1),X1)
| sP1(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_57,c_110]) ).
cnf(c_1001,plain,
( ~ element(X0,powerset(powerset(the_carrier(sK2))))
| in(sK22(sK2,X0),X0)
| sP1(sK2,X0,X1) ),
inference(unflattening,[status(thm)],[c_1000]) ).
cnf(c_4770,plain,
( ~ element(X0_13,powerset(powerset(the_carrier(sK2))))
| in(sK22(sK2,X0_13),X0_13)
| sP1(sK2,X0_13,X1_13) ),
inference(subtyping,[status(esa)],[c_1001]) ).
cnf(c_4772,plain,
( ~ element(X0_13,powerset(powerset(the_carrier(sK2))))
| sK21(sK2,X0_13) = sK19(sK2,X0_13)
| sP1(sK2,X0_13,X1_13) ),
inference(subtyping,[status(esa)],[c_977]) ).
cnf(c_4773,plain,
( ~ element(X0_13,powerset(powerset(the_carrier(sK2))))
| sK20(sK2,X0_13) = sK19(sK2,X0_13)
| sP1(sK2,X0_13,X1_13) ),
inference(subtyping,[status(esa)],[c_953]) ).
cnf(c_4774,plain,
( sK20(sK2,X0_13) != sK21(sK2,X0_13)
| ~ element(X0_13,powerset(powerset(the_carrier(sK2))))
| sP1(sK2,X0_13,X1_13) ),
inference(subtyping,[status(esa)],[c_941]) ).
cnf(c_4776,plain,
( ~ in(X0_13,sK12(X0_14,X1_13,X2_13))
| ~ sP1(X0_14,X1_13,X2_13)
| in(sK14(X0_14,X1_13,X2_13,X0_13),cartesian_product2(X1_13,X2_13)) ),
inference(subtyping,[status(esa)],[c_104]) ).
cnf(c_4777,plain,
( ~ in(X0_13,sK12(X0_14,X1_13,X2_13))
| ~ sP1(X0_14,X1_13,X2_13)
| sK14(X0_14,X1_13,X2_13,X0_13) = X0_13 ),
inference(subtyping,[status(esa)],[c_103]) ).
cnf(c_4778,plain,
( ~ in(X0_13,sK12(X0_14,X1_13,X2_13))
| ~ sP1(X0_14,X1_13,X2_13)
| ordered_pair(sK15(X0_14,X1_13,X0_13),sK16(X0_14,X1_13,X0_13)) = X0_13 ),
inference(subtyping,[status(esa)],[c_102]) ).
cnf(c_4779,plain,
( ~ in(X0_13,sK12(X0_14,X1_13,X2_13))
| ~ sP1(X0_14,X1_13,X2_13)
| in(sK15(X0_14,X1_13,X0_13),X1_13) ),
inference(subtyping,[status(esa)],[c_101]) ).
cnf(c_4780,plain,
( ~ element(sK15(X0_14,X0_13,X1_13),powerset(the_carrier(X0_14)))
| ~ in(X1_13,sK12(X0_14,X0_13,X2_13))
| ~ sP1(X0_14,X0_13,X2_13)
| subset_complement(the_carrier(X0_14),sK15(X0_14,X0_13,X1_13)) = sK16(X0_14,X0_13,X1_13) ),
inference(subtyping,[status(esa)],[c_100]) ).
cnf(c_4781,plain,
( ~ in(ordered_pair(X0_13,X1_13),cartesian_product2(X2_13,X3_13))
| ~ sP1(X0_14,X2_13,X3_13)
| ~ in(X0_13,X2_13)
| in(ordered_pair(X0_13,X1_13),sK12(X0_14,X2_13,X3_13))
| element(sK13(X0_14,X0_13,X1_13),powerset(the_carrier(X0_14))) ),
inference(subtyping,[status(esa)],[c_99]) ).
cnf(c_4782,plain,
( ~ in(ordered_pair(X0_13,X1_13),cartesian_product2(X2_13,X3_13))
| ~ sP1(X0_14,X2_13,X3_13)
| ~ in(X0_13,X2_13)
| sK13(X0_14,X0_13,X1_13) = X0_13
| in(ordered_pair(X0_13,X1_13),sK12(X0_14,X2_13,X3_13)) ),
inference(subtyping,[status(esa)],[c_98]) ).
cnf(c_4783,plain,
( subset_complement(the_carrier(X0_14),sK13(X0_14,X0_13,X1_13)) != X1_13
| ~ in(ordered_pair(X0_13,X1_13),cartesian_product2(X2_13,X3_13))
| ~ sP1(X0_14,X2_13,X3_13)
| ~ in(X0_13,X2_13)
| in(ordered_pair(X0_13,X1_13),sK12(X0_14,X2_13,X3_13)) ),
inference(subtyping,[status(esa)],[c_97]) ).
cnf(c_4785,plain,
( ~ element(X0_13,powerset(X1_13))
| element(subset_complement(X1_13,X0_13),powerset(X1_13)) ),
inference(subtyping,[status(esa)],[c_95]) ).
cnf(c_4787,plain,
( ~ element(X0_13,powerset(X1_13))
| subset_complement(X1_13,subset_complement(X1_13,X0_13)) = X0_13 ),
inference(subtyping,[status(esa)],[c_93]) ).
cnf(c_4794,negated_conjecture,
element(sK3,powerset(powerset(the_carrier(sK2)))),
inference(subtyping,[status(esa)],[c_56]) ).
cnf(c_4795,negated_conjecture,
( in(sK5(X0_13),cartesian_product2(sK3,sK4))
| in(sK5(X0_13),X0_13) ),
inference(subtyping,[status(esa)],[c_55]) ).
cnf(c_4796,negated_conjecture,
( ordered_pair(sK7(X0_13),sK8(X0_13)) = sK5(X0_13)
| in(sK5(X0_13),X0_13) ),
inference(subtyping,[status(esa)],[c_54]) ).
cnf(c_4797,negated_conjecture,
( in(sK5(X0_13),X0_13)
| in(sK7(X0_13),sK3) ),
inference(subtyping,[status(esa)],[c_53]) ).
cnf(c_4798,negated_conjecture,
( ~ element(sK7(X0_13),powerset(the_carrier(sK2)))
| subset_complement(the_carrier(sK2),sK7(X0_13)) = sK8(X0_13)
| in(sK5(X0_13),X0_13) ),
inference(subtyping,[status(esa)],[c_52]) ).
cnf(c_4799,negated_conjecture,
( ordered_pair(X0_13,X1_13) != sK5(X2_13)
| ~ in(sK5(X2_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X2_13),X2_13)
| ~ in(X0_13,sK3)
| element(sK6(X0_13,X1_13),powerset(the_carrier(sK2))) ),
inference(subtyping,[status(esa)],[c_51]) ).
cnf(c_4800,negated_conjecture,
( ordered_pair(X0_13,X1_13) != sK5(X2_13)
| ~ in(sK5(X2_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X2_13),X2_13)
| ~ in(X0_13,sK3)
| sK6(X0_13,X1_13) = X0_13 ),
inference(subtyping,[status(esa)],[c_50]) ).
cnf(c_4801,negated_conjecture,
( subset_complement(the_carrier(sK2),sK6(X0_13,X1_13)) != X1_13
| ordered_pair(X0_13,X1_13) != sK5(X2_13)
| ~ in(sK5(X2_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X2_13),X2_13)
| ~ in(X0_13,sK3) ),
inference(subtyping,[status(esa)],[c_49]) ).
cnf(c_4804,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_5612,plain,
( sK20(sK2,X0_13) != X1_13
| sK21(sK2,X0_13) != X1_13
| sK20(sK2,X0_13) = sK21(sK2,X0_13) ),
inference(instantiation,[status(thm)],[c_4804]) ).
cnf(c_6014,plain,
( sK20(sK2,X0_13) != sK19(sK2,X0_13)
| sK21(sK2,X0_13) != sK19(sK2,X0_13)
| sK20(sK2,X0_13) = sK21(sK2,X0_13) ),
inference(instantiation,[status(thm)],[c_5612]) ).
cnf(c_6015,plain,
( sK20(sK2,sK3) != sK19(sK2,sK3)
| sK21(sK2,sK3) != sK19(sK2,sK3)
| sK20(sK2,sK3) = sK21(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_6014]) ).
cnf(c_6025,plain,
( ~ element(X0_13,powerset(powerset(the_carrier(sK2))))
| sP1(sK2,X0_13,X1_13) ),
inference(global_subsumption_just,[status(thm)],[c_4770,c_4772,c_4773,c_4774,c_6014]) ).
cnf(c_8380,plain,
( ~ element(X0_13,powerset(powerset(the_carrier(sK2))))
| sP1(sK2,X0_13,X1_13) ),
inference(global_subsumption_just,[status(thm)],[c_4770,c_6025]) ).
cnf(c_8384,plain,
sP1(sK2,sK3,X0_13),
inference(superposition,[status(thm)],[c_4794,c_8380]) ).
cnf(c_8461,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK15(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13))),X0_13) ),
inference(superposition,[status(thm)],[c_4796,c_4779]) ).
cnf(c_8467,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_4796,c_4777]) ).
cnf(c_8468,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK5(sK12(X0_14,X0_13,X1_13)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4795,c_4777]) ).
cnf(c_8469,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK7(sK12(X0_14,X0_13,X1_13)),sK3) ),
inference(superposition,[status(thm)],[c_4797,c_4777]) ).
cnf(c_8512,plain,
( ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8384,c_8467]) ).
cnf(c_8529,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK15(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13))),sK16(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13)))) = sK5(sK12(X0_14,X0_13,X1_13))
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_4796,c_4778]) ).
cnf(c_8581,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK5(sK12(sK2,sK3,X0_13))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8384,c_8529]) ).
cnf(c_8598,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_8512,c_4782]) ).
cnf(c_8600,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8512,c_4800]) ).
cnf(c_8644,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(equality_resolution,[status(thm)],[c_8600]) ).
cnf(c_8658,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8581,c_4800]) ).
cnf(c_8672,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(equality_resolution,[status(thm)],[c_8658]) ).
cnf(c_9083,plain,
( ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8672,c_4796]) ).
cnf(c_9084,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ sP1(sK2,sK3,X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8461,c_9083]) ).
cnf(c_9087,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9084,c_8384]) ).
cnf(c_11083,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_8512,c_8598]) ).
cnf(c_11453,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_11083,c_8644]) ).
cnf(c_11454,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11453,c_8384]) ).
cnf(c_11527,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8468,c_11454]) ).
cnf(c_11528,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11527,c_8384]) ).
cnf(c_11546,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_8468,c_11528]) ).
cnf(c_11547,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11546,c_8384]) ).
cnf(c_11573,plain,
( ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_8469,c_11547]) ).
cnf(c_11574,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11573,c_8384]) ).
cnf(c_11837,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK15(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13))),X0_13) ),
inference(superposition,[status(thm)],[c_4796,c_4779]) ).
cnf(c_11843,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_4796,c_4777]) ).
cnf(c_11844,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK5(sK12(X0_14,X0_13,X1_13)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4795,c_4777]) ).
cnf(c_11845,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK7(sK12(X0_14,X0_13,X1_13)),sK3) ),
inference(superposition,[status(thm)],[c_4797,c_4777]) ).
cnf(c_11887,plain,
( ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8384,c_11843]) ).
cnf(c_11905,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK15(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13))),sK16(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13)))) = sK5(sK12(X0_14,X0_13,X1_13))
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_4796,c_4778]) ).
cnf(c_11934,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(X0_14)))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_11887,c_4781]) ).
cnf(c_11935,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_11887,c_4782]) ).
cnf(c_11936,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_11887,c_4799]) ).
cnf(c_11937,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_11887,c_4800]) ).
cnf(c_11958,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK5(sK12(sK2,sK3,X0_13))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8384,c_11905]) ).
cnf(c_11968,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_11936]) ).
cnf(c_11975,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(equality_resolution,[status(thm)],[c_11937]) ).
cnf(c_12041,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_11958,c_4799]) ).
cnf(c_12042,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_11958,c_4800]) ).
cnf(c_12049,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_12041]) ).
cnf(c_12056,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(equality_resolution,[status(thm)],[c_12042]) ).
cnf(c_12208,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))) = sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_11968,c_4787]) ).
cnf(c_12314,plain,
( ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12049,c_4796]) ).
cnf(c_12399,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(global_subsumption_just,[status(thm)],[c_12056,c_9087]) ).
cnf(c_13354,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(X0_14)))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_11887,c_11934]) ).
cnf(c_13365,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_13354,c_11975]) ).
cnf(c_13371,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13365,c_8384]) ).
cnf(c_13391,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_11887,c_11935]) ).
cnf(c_13402,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_13391,c_11975]) ).
cnf(c_13403,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13402,c_8384]) ).
cnf(c_13416,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(global_subsumption_just,[status(thm)],[c_13403,c_11528]) ).
cnf(c_13425,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_11844,c_13416]) ).
cnf(c_13426,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13425,c_8384]) ).
cnf(c_13439,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_13426,c_11574]) ).
cnf(c_13447,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_13439,c_13371]) ).
cnf(c_13706,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_11844,c_13447]) ).
cnf(c_13707,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13706,c_8384]) ).
cnf(c_13742,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_13707,c_4798]) ).
cnf(c_13766,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13742,c_4797]) ).
cnf(c_13768,plain,
( ~ sP1(sK2,sK3,sK4)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_13766,c_4777]) ).
cnf(c_13772,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13768,c_8384]) ).
cnf(c_13786,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_13772,c_11968]) ).
cnf(c_14177,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_13391,c_13786]) ).
cnf(c_14178,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_13354,c_13786]) ).
cnf(c_14179,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14178,c_8384]) ).
cnf(c_14180,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14177,c_8384]) ).
cnf(c_14743,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_11844,c_14180]) ).
cnf(c_14744,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14743,c_8384]) ).
cnf(c_14798,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_14744,c_4798]) ).
cnf(c_14839,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14798,c_4797]) ).
cnf(c_14841,plain,
( ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_14839,c_4777]) ).
cnf(c_14846,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14841,c_8384]) ).
cnf(c_14854,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_14846,c_14179]) ).
cnf(c_14888,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_11844,c_14854]) ).
cnf(c_14889,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14888,c_8384]) ).
cnf(c_15201,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_14889,c_4798]) ).
cnf(c_15220,plain,
( sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15201,c_4797]) ).
cnf(c_15222,plain,
( ~ sP1(sK2,sK3,sK4)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_15220,c_4777]) ).
cnf(c_15227,plain,
( sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15222,c_8384]) ).
cnf(c_15257,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_15227,c_4776]) ).
cnf(c_15258,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15257,c_8384]) ).
cnf(c_15263,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15258,c_4795]) ).
cnf(c_15270,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_15263,c_12399]) ).
cnf(c_15345,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_15270,c_4801]) ).
cnf(c_15346,plain,
( ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_15270,c_12314]) ).
cnf(c_15448,plain,
( ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15346,c_15263]) ).
cnf(c_15449,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ sP1(sK2,sK3,X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_15448,c_4780]) ).
cnf(c_15455,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15449,c_8384]) ).
cnf(c_15537,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_11837,c_15455]) ).
cnf(c_15540,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15537,c_8384]) ).
cnf(c_15547,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4796,c_15540]) ).
cnf(c_15569,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_15547,c_15345]) ).
cnf(c_15593,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_11958,c_15569]) ).
cnf(c_16054,plain,
( ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_15593]) ).
cnf(c_19142,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))) = sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_13391,c_12208]) ).
cnf(c_19145,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))) = sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19142,c_8384]) ).
cnf(c_19219,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))) = sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_11844,c_19145]) ).
cnf(c_19221,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))) = sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19219,c_8384]) ).
cnf(c_19431,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))) = sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_11844,c_19221]) ).
cnf(c_19433,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))) = sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19431,c_8384]) ).
cnf(c_19451,plain,
( ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))) = sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_11845,c_19433]) ).
cnf(c_19452,plain,
( subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))) = sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19451,c_8384]) ).
cnf(c_19851,plain,
( ~ element(X0_13,powerset(X1_13))
| subset_complement(X1_13,subset_complement(X1_13,subset_complement(X1_13,X0_13))) = subset_complement(X1_13,X0_13) ),
inference(superposition,[status(thm)],[c_4785,c_4787]) ).
cnf(c_19857,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK15(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13))),X0_13) ),
inference(superposition,[status(thm)],[c_4796,c_4779]) ).
cnf(c_19863,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_4796,c_4777]) ).
cnf(c_19864,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK5(sK12(X0_14,X0_13,X1_13)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4795,c_4777]) ).
cnf(c_19865,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK7(sK12(X0_14,X0_13,X1_13)),sK3) ),
inference(superposition,[status(thm)],[c_4797,c_4777]) ).
cnf(c_19907,plain,
( ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8384,c_19863]) ).
cnf(c_19925,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK15(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13))),sK16(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13)))) = sK5(sK12(X0_14,X0_13,X1_13))
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_4796,c_4778]) ).
cnf(c_19927,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK15(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13))),sK16(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13)))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK7(sK12(X0_14,X0_13,X1_13)),sK3) ),
inference(superposition,[status(thm)],[c_4797,c_4778]) ).
cnf(c_19938,plain,
( ~ in(ordered_pair(X0_13,X1_13),cartesian_product2(X2_13,X3_13))
| ~ sP1(X0_14,X2_13,X3_13)
| ~ in(X0_13,X2_13)
| sK14(X0_14,X2_13,X3_13,ordered_pair(X0_13,X1_13)) = ordered_pair(X0_13,X1_13)
| sK13(X0_14,X0_13,X1_13) = X0_13 ),
inference(superposition,[status(thm)],[c_4782,c_4777]) ).
cnf(c_19975,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK5(sK12(sK2,sK3,X0_13))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8384,c_19925]) ).
cnf(c_19992,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(X0_14)))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_19907,c_4781]) ).
cnf(c_19993,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_19907,c_4782]) ).
cnf(c_19995,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_19907,c_4800]) ).
cnf(c_20033,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK14(X0_14,X1_13,X2_13,ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))) = ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_19907,c_19938]) ).
cnf(c_20042,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(equality_resolution,[status(thm)],[c_19995]) ).
cnf(c_20063,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_19975,c_4800]) ).
cnf(c_20077,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(equality_resolution,[status(thm)],[c_20063]) ).
cnf(c_20098,plain,
( ~ element(X0_13,powerset(X1_13))
| subset_complement(X1_13,subset_complement(X1_13,subset_complement(X1_13,subset_complement(X1_13,X0_13)))) = subset_complement(X1_13,subset_complement(X1_13,X0_13)) ),
inference(superposition,[status(thm)],[c_4785,c_19851]) ).
cnf(c_20421,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(global_subsumption_just,[status(thm)],[c_20077,c_9087]) ).
cnf(c_20993,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(X0_14)))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_19907,c_19992]) ).
cnf(c_21036,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_20993,c_20042]) ).
cnf(c_21041,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21036,c_8384]) ).
cnf(c_21058,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_19907,c_19993]) ).
cnf(c_21069,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_21058,c_20042]) ).
cnf(c_21070,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21069,c_8384]) ).
cnf(c_21071,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(global_subsumption_just,[status(thm)],[c_21070,c_11528]) ).
cnf(c_21080,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_19864,c_21071]) ).
cnf(c_21081,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21080,c_8384]) ).
cnf(c_21083,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_21081,c_11574]) ).
cnf(c_21088,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) != sK8(sK12(sK2,sK3,sK4))
| ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_21083,c_4783]) ).
cnf(c_21091,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_21083,c_21041]) ).
cnf(c_21094,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_21091,c_13707]) ).
cnf(c_21104,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_21094,c_4798]) ).
cnf(c_21135,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_21104,c_15227]) ).
cnf(c_21136,plain,
( sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(renaming,[status(thm)],[c_21135]) ).
cnf(c_21140,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_21136,c_4776]) ).
cnf(c_21141,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21140,c_8384]) ).
cnf(c_21146,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21141,c_4795]) ).
cnf(c_21152,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_21146,c_20421]) ).
cnf(c_21161,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_21152,c_4801]) ).
cnf(c_21163,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_21161,c_15569]) ).
cnf(c_21171,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_19975,c_21163]) ).
cnf(c_21190,plain,
( ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_21171]) ).
cnf(c_21313,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_21190,c_15258,c_16054]) ).
cnf(c_21314,plain,
( ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(renaming,[status(thm)],[c_21313]) ).
cnf(c_21319,plain,
( ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21314,c_4796]) ).
cnf(c_21320,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_19857,c_21319]) ).
cnf(c_21323,plain,
( ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21320,c_8384]) ).
cnf(c_21327,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(X0_14,X0_13,X1_13)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(X0_14,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(X0_14)))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_21323,c_4781]) ).
cnf(c_21328,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(X0_14,X0_13,X1_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_21323,c_4782]) ).
cnf(c_21329,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_21323,c_4799]) ).
cnf(c_21330,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_21323,c_4800]) ).
cnf(c_21344,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_21329]) ).
cnf(c_21351,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_21330]) ).
cnf(c_21352,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_21344,c_15258,c_21344]) ).
cnf(c_21359,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_21352,c_20098]) ).
cnf(c_21410,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_21351,c_15258,c_21351]) ).
cnf(c_21441,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(X0_14,X0_13,X1_13)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(X0_14,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(X0_14)))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_21323,c_21327]) ).
cnf(c_21456,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_21441,c_21410]) ).
cnf(c_21461,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21456,c_8384]) ).
cnf(c_21476,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21461,c_21146]) ).
cnf(c_21901,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(X0_14,X0_13,X1_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_21323,c_21328]) ).
cnf(c_21916,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_21901,c_21410]) ).
cnf(c_21917,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21916,c_8384]) ).
cnf(c_21929,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21917,c_21146]) ).
cnf(c_21930,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4797,c_21929]) ).
cnf(c_21931,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_19927,c_21929]) ).
cnf(c_21933,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21931,c_8384]) ).
cnf(c_21940,plain,
( ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_21930,c_4779]) ).
cnf(c_21946,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21940,c_8384]) ).
cnf(c_21965,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_21933,c_4799]) ).
cnf(c_21966,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_21933,c_4800]) ).
cnf(c_22047,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_21965,c_21946,c_21965]) ).
cnf(c_22057,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_22047]) ).
cnf(c_22058,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_21966,c_21946,c_21966]) ).
cnf(c_22068,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_22058]) ).
cnf(c_22204,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_22057,c_15258,c_21930,c_22057]) ).
cnf(c_22224,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_22068,c_15258,c_21930,c_22068]) ).
cnf(c_22230,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22224,c_4801]) ).
cnf(c_22232,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_22224,c_22204]) ).
cnf(c_22309,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_22230,c_21946,c_22230]) ).
cnf(c_22310,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(renaming,[status(thm)],[c_22309]) ).
cnf(c_22330,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ sP1(sK2,sK3,X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22232,c_4780]) ).
cnf(c_22338,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22330,c_8384]) ).
cnf(c_22352,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_21930,c_22338]) ).
cnf(c_22365,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_22352,c_21476]) ).
cnf(c_22380,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22365,c_4798]) ).
cnf(c_22381,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_22380,c_15258,c_21351,c_22380]) ).
cnf(c_22382,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(renaming,[status(thm)],[c_22381]) ).
cnf(c_22387,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4797,c_22382]) ).
cnf(c_22388,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_19927,c_22382]) ).
cnf(c_22390,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22388,c_8384]) ).
cnf(c_22469,plain,
( ~ sP1(sK2,sK3,sK4)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_22387,c_4779]) ).
cnf(c_22476,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22469,c_8384]) ).
cnf(c_22495,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_22390,c_4799]) ).
cnf(c_22496,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22390,c_4800]) ).
cnf(c_22503,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_22495,c_22476,c_22495]) ).
cnf(c_22513,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_22503]) ).
cnf(c_22514,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_22496,c_22476,c_22496]) ).
cnf(c_22524,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_22514]) ).
cnf(c_22527,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_22513,c_15258,c_22387,c_22513]) ).
cnf(c_22585,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_22524,c_15258,c_22387,c_22524]) ).
cnf(c_22593,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_22585,c_22527]) ).
cnf(c_22607,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ sP1(sK2,sK3,X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22593,c_4780]) ).
cnf(c_22615,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22607,c_8384]) ).
cnf(c_22626,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22387,c_22615]) ).
cnf(c_22639,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_22626,c_21352]) ).
cnf(c_22653,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_21901,c_22639]) ).
cnf(c_22654,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_21441,c_22639]) ).
cnf(c_22655,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22654,c_8384]) ).
cnf(c_22656,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22653,c_8384]) ).
cnf(c_22663,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22655,c_21146]) ).
cnf(c_22735,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22656,c_21146]) ).
cnf(c_22742,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22735,c_4798]) ).
cnf(c_22748,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22742,c_4797]) ).
cnf(c_22749,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22748,c_4778]) ).
cnf(c_22751,plain,
( ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_22748,c_4779]) ).
cnf(c_22760,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22751,c_8384]) ).
cnf(c_22761,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22749,c_8384]) ).
cnf(c_22780,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_22761,c_4799]) ).
cnf(c_22781,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22761,c_4800]) ).
cnf(c_22788,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_22780,c_22760,c_22780]) ).
cnf(c_22798,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_22788]) ).
cnf(c_22799,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_22781,c_22760,c_22781]) ).
cnf(c_22809,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_22799]) ).
cnf(c_22866,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_22798,c_15258,c_22798]) ).
cnf(c_22873,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22866,c_22748]) ).
cnf(c_22885,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_22809,c_15258,c_22809]) ).
cnf(c_22892,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22885,c_22748]) ).
cnf(c_22895,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_22892,c_22873]) ).
cnf(c_22909,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ sP1(sK2,sK3,X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22895,c_4780]) ).
cnf(c_22917,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_22909,c_8384]) ).
cnf(c_22928,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22748,c_22917]) ).
cnf(c_22997,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_22928,c_22663]) ).
cnf(c_23014,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_22997,c_4798]) ).
cnf(c_23019,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23014,c_4797]) ).
cnf(c_23020,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_23019,c_4778]) ).
cnf(c_23022,plain,
( ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_23019,c_4779]) ).
cnf(c_23032,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23022,c_8384]) ).
cnf(c_23033,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23020,c_8384]) ).
cnf(c_23049,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_23033,c_4799]) ).
cnf(c_23050,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_23033,c_4800]) ).
cnf(c_23109,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_23049,c_23032,c_23049]) ).
cnf(c_23118,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_23109]) ).
cnf(c_23150,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_23050,c_23032,c_23050]) ).
cnf(c_23159,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_23150]) ).
cnf(c_23559,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_23118,c_15258,c_23118]) ).
cnf(c_23565,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23559,c_23019]) ).
cnf(c_23609,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_23159,c_15258,c_23159]) ).
cnf(c_23615,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23609,c_23019]) ).
cnf(c_23618,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_23615,c_23565]) ).
cnf(c_23631,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ sP1(sK2,sK3,X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_23618,c_4780]) ).
cnf(c_23639,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_23631,c_8384]) ).
cnf(c_23718,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_23019,c_23639]) ).
cnf(c_23727,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_23718,c_22310]) ).
cnf(c_23983,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_21933,c_23727]) ).
cnf(c_24275,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_23983]) ).
cnf(c_25753,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_21930,c_21359]) ).
cnf(c_25996,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_25753,c_15258,c_21930,c_24275]) ).
cnf(c_26011,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_25996,c_21476]) ).
cnf(c_26138,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_26011,c_4798]) ).
cnf(c_26206,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_26138,c_21410,c_26138]) ).
cnf(c_26207,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(renaming,[status(thm)],[c_26206]) ).
cnf(c_26211,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4797,c_26207]) ).
cnf(c_26212,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_19927,c_26207]) ).
cnf(c_26214,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26212,c_8384]) ).
cnf(c_26230,plain,
( ~ sP1(sK2,sK3,sK4)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_26211,c_4779]) ).
cnf(c_26234,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_26211,c_21359]) ).
cnf(c_26243,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_26230,c_8384]) ).
cnf(c_26762,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_26214,c_4800]) ).
cnf(c_26872,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_26762,c_26243,c_26762]) ).
cnf(c_26881,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_26872]) ).
cnf(c_26948,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_26881,c_15258,c_26211,c_26881]) ).
cnf(c_26953,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_26948,c_4801]) ).
cnf(c_26961,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_26953,c_23718,c_26243,c_26953]) ).
cnf(c_26970,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_26214,c_26961]) ).
cnf(c_26981,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_26970]) ).
cnf(c_27253,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_26234,c_15258,c_26211,c_26981]) ).
cnf(c_27264,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_27253,c_21352]) ).
cnf(c_27279,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_21901,c_27264]) ).
cnf(c_27280,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_21441,c_27264]) ).
cnf(c_27281,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27280,c_8384]) ).
cnf(c_27282,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27279,c_8384]) ).
cnf(c_27709,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27281,c_21146]) ).
cnf(c_27725,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27282,c_21146]) ).
cnf(c_27732,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_27725,c_4798]) ).
cnf(c_27737,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27732,c_4797]) ).
cnf(c_27738,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_27737,c_4778]) ).
cnf(c_27740,plain,
( ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_27737,c_4779]) ).
cnf(c_27754,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27740,c_8384]) ).
cnf(c_27755,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27738,c_8384]) ).
cnf(c_27773,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_27755,c_4800]) ).
cnf(c_27918,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_27773,c_27754,c_27773]) ).
cnf(c_27927,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_27918]) ).
cnf(c_27975,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_27927,c_15258,c_27927]) ).
cnf(c_27981,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_27975,c_27737]) ).
cnf(c_27982,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_27981,c_4801]) ).
cnf(c_27990,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_27982,c_23718,c_27754,c_27982]) ).
cnf(c_27999,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_27755,c_27990]) ).
cnf(c_28011,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_27999]) ).
cnf(c_28797,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_28011,c_15258,c_28011]) ).
cnf(c_28802,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28797,c_27737]) ).
cnf(c_28808,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_28802,c_27709]) ).
cnf(c_28824,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_28808,c_4798]) ).
cnf(c_28828,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28824,c_4797]) ).
cnf(c_28829,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_28828,c_4778]) ).
cnf(c_28831,plain,
( ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_28828,c_4779]) ).
cnf(c_28845,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28831,c_8384]) ).
cnf(c_28846,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28829,c_8384]) ).
cnf(c_28898,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_28846,c_4800]) ).
cnf(c_28918,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_28898,c_28845,c_28898]) ).
cnf(c_28926,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_28918]) ).
cnf(c_28958,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_28926,c_15258,c_28926]) ).
cnf(c_28963,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28958,c_28828]) ).
cnf(c_28964,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_28963,c_4801]) ).
cnf(c_28972,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_28964,c_23718,c_28845,c_28964]) ).
cnf(c_28980,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_28846,c_28972]) ).
cnf(c_29206,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_28980]) ).
cnf(c_29225,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_29206,c_15258,c_29206]) ).
cnf(c_29229,plain,
subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) = sK8(sK12(sK2,sK3,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_29225,c_28828]) ).
cnf(c_29355,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_21088,c_29229]) ).
cnf(c_29875,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_19907,c_29355]) ).
cnf(c_29891,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_19907,c_29875]) ).
cnf(c_29904,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_29891,c_20042]) ).
cnf(c_29905,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29904,c_8384]) ).
cnf(c_29917,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_19864,c_29905]) ).
cnf(c_29918,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29917,c_8384]) ).
cnf(c_29925,plain,
( ~ sP1(sK2,sK3,sK4)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_19865,c_29918]) ).
cnf(c_29926,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29925,c_8384]) ).
cnf(c_29929,plain,
( ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) != sK8(sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_29926,c_4801]) ).
cnf(c_29933,plain,
( ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) != sK5(X0_13)
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29929,c_29229]) ).
cnf(c_29940,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_19907,c_29933]) ).
cnf(c_30041,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_29940]) ).
cnf(c_33758,plain,
( ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(X0_14,sK3,sK4)
| ~ sP1(sK2,sK3,X0_13)
| sK14(X0_14,sK3,sK4,ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))) = ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_19864,c_20033]) ).
cnf(c_33760,plain,
( ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(X0_14,sK3,sK4)
| sK14(X0_14,sK3,sK4,ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))) = ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33758,c_8384]) ).
cnf(c_33771,plain,
( ~ sP1(X0_14,sK3,sK4)
| ~ sP1(sK2,sK3,X0_13)
| sK14(X0_14,sK3,sK4,ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))) = ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_19865,c_33760]) ).
cnf(c_33772,plain,
( ~ sP1(X0_14,sK3,sK4)
| sK14(X0_14,sK3,sK4,ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))) = ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33771,c_8384]) ).
cnf(c_33780,plain,
( sK14(sK2,sK3,sK4,ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))) = ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8384,c_33772]) ).
cnf(c_33954,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),sK12(sK2,sK3,sK4))
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_33780,c_4776]) ).
cnf(c_33955,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_33954,c_8384]) ).
cnf(c_33968,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_19907,c_33955]) ).
cnf(c_35765,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_19907,c_33968]) ).
cnf(c_35787,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4795,c_35765]) ).
cnf(c_36122,plain,
( ~ element(X0_13,powerset(X1_13))
| subset_complement(X1_13,subset_complement(X1_13,subset_complement(X1_13,X0_13))) = subset_complement(X1_13,X0_13) ),
inference(superposition,[status(thm)],[c_4785,c_4787]) ).
cnf(c_36134,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_4796,c_4777]) ).
cnf(c_36135,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK5(sK12(X0_14,X0_13,X1_13)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4795,c_4777]) ).
cnf(c_36136,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK7(sK12(X0_14,X0_13,X1_13)),sK3) ),
inference(superposition,[status(thm)],[c_4797,c_4777]) ).
cnf(c_36178,plain,
( ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8384,c_36134]) ).
cnf(c_36264,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_36178,c_4782]) ).
cnf(c_36265,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_36178,c_4799]) ).
cnf(c_36266,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_36178,c_4800]) ).
cnf(c_36273,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_36265]) ).
cnf(c_36308,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(equality_resolution,[status(thm)],[c_36266]) ).
cnf(c_36365,plain,
( ~ element(X0_13,powerset(X1_13))
| subset_complement(X1_13,subset_complement(X1_13,subset_complement(X1_13,subset_complement(X1_13,X0_13)))) = subset_complement(X1_13,subset_complement(X1_13,X0_13)) ),
inference(superposition,[status(thm)],[c_4785,c_36122]) ).
cnf(c_36480,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))) = sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_36273,c_4787]) ).
cnf(c_36516,plain,
( ~ element(X0_13,powerset(X1_13))
| subset_complement(X1_13,subset_complement(X1_13,subset_complement(X1_13,subset_complement(X1_13,subset_complement(X1_13,X0_13))))) = subset_complement(X1_13,subset_complement(X1_13,subset_complement(X1_13,X0_13))) ),
inference(superposition,[status(thm)],[c_4785,c_36365]) ).
cnf(c_36848,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_36273,c_36516]) ).
cnf(c_37406,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_36178,c_36264]) ).
cnf(c_37417,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_37406,c_36308]) ).
cnf(c_37418,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37417,c_8384]) ).
cnf(c_37419,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(global_subsumption_just,[status(thm)],[c_37418,c_11528]) ).
cnf(c_37428,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_36135,c_37419]) ).
cnf(c_37429,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37428,c_8384]) ).
cnf(c_37431,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_37429,c_29926]) ).
cnf(c_37497,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))) = sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_37406,c_36480]) ).
cnf(c_37500,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))) = sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37497,c_8384]) ).
cnf(c_37511,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))) = sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(global_subsumption_just,[status(thm)],[c_37500,c_19221]) ).
cnf(c_37520,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))) = sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_36135,c_37511]) ).
cnf(c_37521,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))) = sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_37520,c_8384]) ).
cnf(c_37523,plain,
( subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))) = sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_37521,c_19452]) ).
cnf(c_41131,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_37406,c_36848]) ).
cnf(c_41152,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41131,c_8384]) ).
cnf(c_41181,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_36135,c_41152]) ).
cnf(c_41183,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13)))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))))))
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41181,c_8384]) ).
cnf(c_41260,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_36135,c_41183]) ).
cnf(c_41262,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41260,c_8384]) ).
cnf(c_41270,plain,
( ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_36136,c_41262]) ).
cnf(c_41271,plain,
( subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))))))) = subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41270,c_8384]) ).
cnf(c_41277,plain,
( ~ element(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))))))),powerset(the_carrier(sK2)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_41271,c_4785]) ).
cnf(c_42084,plain,
( ~ element(sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4)))))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_37523,c_41277]) ).
cnf(c_42097,plain,
( ~ element(sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_37431,c_42084]) ).
cnf(c_42106,plain,
( ~ element(sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK8(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(light_normalisation,[status(thm)],[c_42097,c_29229]) ).
cnf(c_42111,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK8(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_36273,c_42106]) ).
cnf(c_42128,plain,
( sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_42111,c_30041,c_35787]) ).
cnf(c_42129,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(renaming,[status(thm)],[c_42128]) ).
cnf(c_42134,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4796,c_42129]) ).
cnf(c_42137,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_37406,c_42129]) ).
cnf(c_42157,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42137,c_8384]) ).
cnf(c_42245,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_42134,c_35787,c_42157]) ).
cnf(c_42246,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(renaming,[status(thm)],[c_42245]) ).
cnf(c_42252,plain,
( ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_36136,c_42246]) ).
cnf(c_42253,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_42252,c_8384]) ).
cnf(c_47251,plain,
( ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| sK21(sK2,sK3) = sK19(sK2,sK3)
| sP1(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_4772]) ).
cnf(c_47253,plain,
( ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| sK20(sK2,sK3) = sK19(sK2,sK3)
| sP1(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_4773]) ).
cnf(c_47255,plain,
( sK20(sK2,sK3) != sK21(sK2,sK3)
| ~ element(sK3,powerset(powerset(the_carrier(sK2))))
| sP1(sK2,sK3,sK4) ),
inference(instantiation,[status(thm)],[c_4774]) ).
cnf(c_50961,plain,
( ~ in(sK5(sK12(X0_14,X0_13,X1_13)),sK12(X0_14,X0_13,X1_13))
| ~ sP1(X0_14,X0_13,X1_13)
| in(sK15(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13))),X0_13) ),
inference(instantiation,[status(thm)],[c_4779]) ).
cnf(c_50963,plain,
( ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK5(sK12(X0_14,X0_13,X1_13)),sK12(X0_14,X0_13,X1_13)) ),
inference(instantiation,[status(thm)],[c_4796]) ).
cnf(c_50964,plain,
( in(sK5(sK12(X0_14,X0_13,X1_13)),sK12(X0_14,X0_13,X1_13))
| in(sK7(sK12(X0_14,X0_13,X1_13)),sK3) ),
inference(instantiation,[status(thm)],[c_4797]) ).
cnf(c_51120,plain,
( ~ in(sK5(X0_13),sK12(X0_14,X1_13,X2_13))
| ~ sP1(X0_14,X1_13,X2_13)
| sK14(X0_14,X1_13,X2_13,sK5(X0_13)) = sK5(X0_13) ),
inference(instantiation,[status(thm)],[c_4777]) ).
cnf(c_65768,plain,
( in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| in(sK7(sK12(sK2,sK3,sK4)),sK3) ),
inference(instantiation,[status(thm)],[c_50964]) ).
cnf(c_73916,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ sP1(sK2,sK3,sK4)
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(instantiation,[status(thm)],[c_50961]) ).
cnf(c_73919,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ sP1(sK2,sK3,sK4)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_51120]) ).
cnf(c_80121,plain,
( ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_50963]) ).
cnf(c_82665,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_4796,c_4777]) ).
cnf(c_82666,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| sK14(X0_14,X0_13,X1_13,sK5(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK5(sK12(X0_14,X0_13,X1_13)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4795,c_4777]) ).
cnf(c_82705,plain,
( ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8384,c_82665]) ).
cnf(c_82731,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK15(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13))),sK16(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13)))) = sK5(sK12(X0_14,X0_13,X1_13))
| ordered_pair(sK7(sK12(X0_14,X0_13,X1_13)),sK8(sK12(X0_14,X0_13,X1_13))) = sK5(sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_4796,c_4778]) ).
cnf(c_82733,plain,
( ~ sP1(X0_14,X0_13,X1_13)
| ordered_pair(sK15(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13))),sK16(X0_14,X0_13,sK5(sK12(X0_14,X0_13,X1_13)))) = sK5(sK12(X0_14,X0_13,X1_13))
| in(sK7(sK12(X0_14,X0_13,X1_13)),sK3) ),
inference(superposition,[status(thm)],[c_4797,c_4778]) ).
cnf(c_82761,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_82705,c_4782]) ).
cnf(c_82762,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_82705,c_4799]) ).
cnf(c_82763,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_82705,c_4800]) ).
cnf(c_82784,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK5(sK12(sK2,sK3,X0_13))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_8384,c_82731]) ).
cnf(c_82793,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_82762]) ).
cnf(c_82800,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(equality_resolution,[status(thm)],[c_82763]) ).
cnf(c_82865,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_82784,c_4799]) ).
cnf(c_82866,plain,
( sK5(sK12(sK2,sK3,X0_13)) != sK5(X1_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(X1_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X1_13),X1_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_82784,c_4800]) ).
cnf(c_82873,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_82865]) ).
cnf(c_82880,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),sK12(sK2,sK3,X0_13))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(equality_resolution,[status(thm)],[c_82866]) ).
cnf(c_83117,plain,
( ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK3)
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_82873,c_4796]) ).
cnf(c_83190,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,X0_13)))
| ordered_pair(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(global_subsumption_just,[status(thm)],[c_82880,c_9087]) ).
cnf(c_84696,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(X1_13,X2_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),X1_13)
| ~ sP1(X0_14,X1_13,X2_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13))
| in(sK5(sK12(sK2,sK3,X0_13)),sK12(X0_14,X1_13,X2_13)) ),
inference(superposition,[status(thm)],[c_82705,c_82761]) ).
cnf(c_84707,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| ~ sP1(sK2,sK3,X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(superposition,[status(thm)],[c_84696,c_82800]) ).
cnf(c_84708,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_84707,c_8384]) ).
cnf(c_84774,plain,
( ~ in(sK5(sK12(sK2,sK3,X0_13)),cartesian_product2(sK3,X0_13))
| ~ in(sK7(sK12(sK2,sK3,X0_13)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,X0_13)),sK8(sK12(sK2,sK3,X0_13))) = sK7(sK12(sK2,sK3,X0_13))
| sK14(sK2,sK3,X0_13,sK5(sK12(sK2,sK3,X0_13))) = sK5(sK12(sK2,sK3,X0_13)) ),
inference(global_subsumption_just,[status(thm)],[c_84708,c_11528]) ).
cnf(c_84783,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_82666,c_84774]) ).
cnf(c_84784,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_84783,c_8384]) ).
cnf(c_84786,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_84784,c_29926]) ).
cnf(c_84791,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(sK7(sK12(sK2,sK3,sK4)),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_84786,c_82793]) ).
cnf(c_84809,plain,
( sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_84791,c_56,c_6015,c_47255,c_47253,c_47251,c_73919]) ).
cnf(c_84810,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(renaming,[status(thm)],[c_84809]) ).
cnf(c_84814,plain,
( sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4795,c_84810]) ).
cnf(c_84815,plain,
( sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(sK7(sK12(sK2,sK3,sK4)),sK3) ),
inference(superposition,[status(thm)],[c_4797,c_84810]) ).
cnf(c_84816,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_84696,c_84810]) ).
cnf(c_84819,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_84816,c_8384]) ).
cnf(c_84857,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_84819,c_42253]) ).
cnf(c_84861,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) != sK8(sK12(sK2,sK3,sK4))
| ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_84857,c_4783]) ).
cnf(c_84865,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_84861,c_29229]) ).
cnf(c_84920,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_82705,c_84865]) ).
cnf(c_84938,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_82705,c_84920]) ).
cnf(c_84949,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_84938,c_84810]) ).
cnf(c_84950,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_84949,c_8384]) ).
cnf(c_84951,plain,
sK14(sK2,sK3,sK4,sK5(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)),
inference(global_subsumption_just,[status(thm)],[c_84950,c_84815,c_84814,c_84950]) ).
cnf(c_84967,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ sP1(sK2,sK3,sK4)
| in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)) ),
inference(superposition,[status(thm)],[c_84951,c_4776]) ).
cnf(c_84968,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_84967,c_8384]) ).
cnf(c_84972,plain,
in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_84968,c_4795]) ).
cnf(c_84979,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_84972,c_83190]) ).
cnf(c_84983,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_84979,c_4801]) ).
cnf(c_84984,plain,
( ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_84979,c_83117]) ).
cnf(c_84985,plain,
( ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_84984,c_84972]) ).
cnf(c_84987,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_84983,c_56,c_6015,c_47255,c_47253,c_47251,c_73916,c_80121,c_84983]) ).
cnf(c_84988,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(renaming,[status(thm)],[c_84987]) ).
cnf(c_85012,plain,
( ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_84985,c_56,c_6015,c_47255,c_47253,c_47251,c_73916,c_80121,c_84985]) ).
cnf(c_85016,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ sP1(sK2,sK3,X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_85012,c_4780]) ).
cnf(c_85022,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85016,c_8384]) ).
cnf(c_85027,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4796,c_85022]) ).
cnf(c_85035,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_85027,c_84988]) ).
cnf(c_85050,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_82784,c_85035]) ).
cnf(c_85142,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_85050]) ).
cnf(c_85143,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85142,c_84972]) ).
cnf(c_85144,plain,
ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK5(sK12(sK2,sK3,sK4)),
inference(global_subsumption_just,[status(thm)],[c_85143,c_80121,c_85143]) ).
cnf(c_85160,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(X0_14,X0_13,X1_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(X0_14,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_85144,c_4782]) ).
cnf(c_85162,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_85144,c_4800]) ).
cnf(c_85183,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_85162]) ).
cnf(c_85184,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85183,c_84972]) ).
cnf(c_85505,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(X0_14,X0_13,X1_13)
| sK13(X0_14,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(X0_14,X0_13,X1_13)) ),
inference(light_normalisation,[status(thm)],[c_85160,c_85144]) ).
cnf(c_85518,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_85505,c_85184]) ).
cnf(c_85519,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85518,c_8384,c_84972]) ).
cnf(c_85528,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4797,c_85519]) ).
cnf(c_85529,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_82733,c_85519]) ).
cnf(c_85531,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85529,c_8384]) ).
cnf(c_85537,plain,
( ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_85528,c_4779]) ).
cnf(c_85543,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85537,c_8384]) ).
cnf(c_85652,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_85531,c_4799]) ).
cnf(c_85653,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_85531,c_4800]) ).
cnf(c_85660,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_85652,c_85543,c_85652]) ).
cnf(c_85669,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_85660]) ).
cnf(c_85670,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85669,c_84972]) ).
cnf(c_85671,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_85653,c_85543,c_85653]) ).
cnf(c_85680,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_85671]) ).
cnf(c_85681,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85680,c_84972]) ).
cnf(c_85742,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_85670,c_85528,c_85670]) ).
cnf(c_85756,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_85681,c_85528,c_85681]) ).
cnf(c_85761,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_85756,c_4801]) ).
cnf(c_85763,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_85756,c_85742]) ).
cnf(c_85765,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_85761,c_85543,c_85761]) ).
cnf(c_85766,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(renaming,[status(thm)],[c_85765]) ).
cnf(c_85786,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ sP1(sK2,sK3,X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_85763,c_4780]) ).
cnf(c_85792,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85786,c_8384]) ).
cnf(c_85868,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_85528,c_85792]) ).
cnf(c_85874,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) != sK8(sK12(sK2,sK3,sK4))
| ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_85868,c_4783]) ).
cnf(c_85882,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_85874,c_29229]) ).
cnf(c_88555,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,X0_13,X1_13)) ),
inference(light_normalisation,[status(thm)],[c_85882,c_85144]) ).
cnf(c_88575,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_88555,c_85184]) ).
cnf(c_88577,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88575,c_8384,c_84972]) ).
cnf(c_88591,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4797,c_88577]) ).
cnf(c_88592,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_82733,c_88577]) ).
cnf(c_88594,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88592,c_8384]) ).
cnf(c_88785,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_88594,c_4799]) ).
cnf(c_88786,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_88594,c_4800]) ).
cnf(c_88798,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_88785,c_56,c_6015,c_47255,c_47253,c_47251,c_65768,c_73916,c_85162,c_88785]) ).
cnf(c_88807,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_88798]) ).
cnf(c_88808,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88807,c_84972]) ).
cnf(c_88809,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(global_subsumption_just,[status(thm)],[c_88786,c_56,c_6015,c_47255,c_47253,c_47251,c_65768,c_73916,c_85162,c_88786]) ).
cnf(c_88818,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(equality_resolution,[status(thm)],[c_88809]) ).
cnf(c_88819,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88818,c_84972]) ).
cnf(c_88820,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_88808,c_88591,c_88808]) ).
cnf(c_88947,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(global_subsumption_just,[status(thm)],[c_88819,c_88591,c_88819]) ).
cnf(c_88954,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_88947,c_88820]) ).
cnf(c_88973,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ sP1(sK2,sK3,X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_88954,c_4780]) ).
cnf(c_88980,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88973,c_8384]) ).
cnf(c_89029,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_88591,c_88980]) ).
cnf(c_89053,plain,
( ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) != sK8(sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_89029,c_4801]) ).
cnf(c_89066,plain,
( ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) != sK5(X0_13)
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89053,c_29229]) ).
cnf(c_89068,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(light_normalisation,[status(thm)],[c_89066,c_85144]) ).
cnf(c_89074,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(equality_resolution,[status(thm)],[c_89068]) ).
cnf(c_89075,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89074,c_84972]) ).
cnf(c_89103,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_85505,c_89075]) ).
cnf(c_89106,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89103,c_8384,c_84972]) ).
cnf(c_89120,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4797,c_89106]) ).
cnf(c_89121,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_82733,c_89106]) ).
cnf(c_89123,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89121,c_8384]) ).
cnf(c_89129,plain,
( ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_89120,c_4779]) ).
cnf(c_89144,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89129,c_8384]) ).
cnf(c_89212,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_89123,c_4799]) ).
cnf(c_89213,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_89123,c_4800]) ).
cnf(c_89225,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_89212,c_89144,c_89212]) ).
cnf(c_89234,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_89225]) ).
cnf(c_89235,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89234,c_84972]) ).
cnf(c_89236,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(global_subsumption_just,[status(thm)],[c_89213,c_89144,c_89213]) ).
cnf(c_89245,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(equality_resolution,[status(thm)],[c_89236]) ).
cnf(c_89246,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89245,c_84972]) ).
cnf(c_89247,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_89235,c_89120,c_89235]) ).
cnf(c_89260,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(global_subsumption_just,[status(thm)],[c_89246,c_89120,c_89246]) ).
cnf(c_89267,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_89260,c_89247]) ).
cnf(c_89328,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ sP1(sK2,sK3,X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_89267,c_4780]) ).
cnf(c_89335,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89328,c_8384]) ).
cnf(c_89345,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_89120,c_89335]) ).
cnf(c_89369,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) != sK8(sK12(sK2,sK3,sK4))
| ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_89345,c_4783]) ).
cnf(c_89395,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89369,c_29229]) ).
cnf(c_89573,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,X0_13,X1_13)) ),
inference(light_normalisation,[status(thm)],[c_89395,c_85144]) ).
cnf(c_89586,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_89573,c_89075]) ).
cnf(c_89597,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89586,c_8384,c_84972]) ).
cnf(c_89610,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4797,c_89597]) ).
cnf(c_89611,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_82733,c_89597]) ).
cnf(c_89613,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89611,c_8384]) ).
cnf(c_89618,plain,
( ~ sP1(sK2,sK3,sK4)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_89610,c_4779]) ).
cnf(c_89634,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89618,c_8384]) ).
cnf(c_89702,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_89613,c_4799]) ).
cnf(c_89703,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_89613,c_4800]) ).
cnf(c_89715,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_89702,c_89634,c_89702]) ).
cnf(c_89723,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(equality_resolution,[status(thm)],[c_89715]) ).
cnf(c_89724,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89723,c_84972]) ).
cnf(c_89725,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(global_subsumption_just,[status(thm)],[c_89703,c_89634,c_89703]) ).
cnf(c_89733,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(equality_resolution,[status(thm)],[c_89725]) ).
cnf(c_89734,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89733,c_84972]) ).
cnf(c_89735,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))),powerset(the_carrier(sK2))) ),
inference(global_subsumption_just,[status(thm)],[c_89724,c_89610,c_89724]) ).
cnf(c_89750,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(global_subsumption_just,[status(thm)],[c_89734,c_89610,c_89734]) ).
cnf(c_89756,plain,
( subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| element(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),powerset(the_carrier(sK2))) ),
inference(superposition,[status(thm)],[c_89750,c_89735]) ).
cnf(c_89824,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| ~ sP1(sK2,sK3,X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_89756,c_4780]) ).
cnf(c_89831,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,X0_13))
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89824,c_8384]) ).
cnf(c_89840,plain,
subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),
inference(superposition,[status(thm)],[c_89610,c_89831]) ).
cnf(c_89864,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_85766,c_89840]) ).
cnf(c_89875,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_85531,c_89864]) ).
cnf(c_89977,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_89875]) ).
cnf(c_89978,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89977,c_84972]) ).
cnf(c_89979,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_89978,c_85528,c_89978]) ).
cnf(c_89983,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) != sK8(sK12(sK2,sK3,sK4))
| ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_89979,c_4783]) ).
cnf(c_90008,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_89983,c_29229]) ).
cnf(c_90060,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,X0_13,X1_13)) ),
inference(light_normalisation,[status(thm)],[c_90008,c_85144]) ).
cnf(c_90079,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_90060,c_85184]) ).
cnf(c_90080,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90079,c_8384,c_84972]) ).
cnf(c_90171,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4797,c_90080]) ).
cnf(c_90172,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_82733,c_90080]) ).
cnf(c_90174,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90172,c_8384]) ).
cnf(c_90179,plain,
( ~ sP1(sK2,sK3,sK4)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_90171,c_4779]) ).
cnf(c_90191,plain,
( sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90179,c_8384]) ).
cnf(c_90207,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_90174,c_4800]) ).
cnf(c_90232,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_90207,c_90191,c_90207]) ).
cnf(c_90240,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_90232]) ).
cnf(c_90241,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90240,c_84972]) ).
cnf(c_90386,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_90241,c_90171,c_90241]) ).
cnf(c_90390,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_90386,c_4801]) ).
cnf(c_90394,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90390,c_89840]) ).
cnf(c_90398,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_90394,c_90191,c_90394]) ).
cnf(c_90406,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_90174,c_90398]) ).
cnf(c_90538,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_90406]) ).
cnf(c_90539,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90538,c_84972]) ).
cnf(c_90540,plain,
sK6(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)),
inference(global_subsumption_just,[status(thm)],[c_90539,c_90171,c_90539]) ).
cnf(c_90675,plain,
( ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) != sK8(sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13) ),
inference(superposition,[status(thm)],[c_90540,c_4801]) ).
cnf(c_90677,plain,
( ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) != sK5(X0_13)
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90675,c_29229]) ).
cnf(c_90679,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13) ),
inference(light_normalisation,[status(thm)],[c_90677,c_85144]) ).
cnf(c_90684,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3) ),
inference(equality_resolution,[status(thm)],[c_90679]) ).
cnf(c_90685,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90684,c_84972]) ).
cnf(c_90693,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_85505,c_90685]) ).
cnf(c_90696,plain,
( ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90693,c_8384,c_84972]) ).
cnf(c_90707,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_4797,c_90696]) ).
cnf(c_90708,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_82733,c_90696]) ).
cnf(c_90710,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90708,c_8384]) ).
cnf(c_90715,plain,
( ~ sP1(sK2,sK3,sK4)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_90707,c_4779]) ).
cnf(c_90721,plain,
( sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4))
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90715,c_8384]) ).
cnf(c_90868,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_90710,c_4800]) ).
cnf(c_90892,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_90868,c_90721,c_90868]) ).
cnf(c_90900,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_90892]) ).
cnf(c_90901,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90900,c_84972]) ).
cnf(c_90916,plain,
( sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_90901,c_90707,c_90901]) ).
cnf(c_90920,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_90916,c_4801]) ).
cnf(c_90923,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_90920,c_89840]) ).
cnf(c_91035,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(global_subsumption_just,[status(thm)],[c_90923,c_90721,c_90923]) ).
cnf(c_91043,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_90710,c_91035]) ).
cnf(c_91288,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_91043]) ).
cnf(c_91289,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_91288,c_84972]) ).
cnf(c_91290,plain,
sK13(sK2,sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))) = sK7(sK12(sK2,sK3,sK4)),
inference(global_subsumption_just,[status(thm)],[c_91289,c_90707,c_91289]) ).
cnf(c_91311,plain,
( subset_complement(the_carrier(sK2),sK7(sK12(sK2,sK3,sK4))) != sK8(sK12(sK2,sK3,sK4))
| ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(superposition,[status(thm)],[c_91290,c_4783]) ).
cnf(c_91320,plain,
( ~ in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| in(ordered_pair(sK7(sK12(sK2,sK3,sK4)),sK8(sK12(sK2,sK3,sK4))),sK12(sK2,X0_13,X1_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_91311,c_29229]) ).
cnf(c_91533,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(X0_13,X1_13))
| ~ in(sK7(sK12(sK2,sK3,sK4)),X0_13)
| ~ sP1(sK2,X0_13,X1_13)
| in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,X0_13,X1_13)) ),
inference(light_normalisation,[status(thm)],[c_91320,c_85144]) ).
cnf(c_91545,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| ~ in(sK7(sK12(sK2,sK3,sK4)),sK3)
| ~ sP1(sK2,sK3,sK4) ),
inference(superposition,[status(thm)],[c_91533,c_90685]) ).
cnf(c_91546,plain,
~ in(sK7(sK12(sK2,sK3,sK4)),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_91545,c_8384,c_84972]) ).
cnf(c_91547,plain,
in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4)),
inference(superposition,[status(thm)],[c_4797,c_91546]) ).
cnf(c_91548,plain,
( ~ sP1(sK2,sK3,sK4)
| ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4)) ),
inference(superposition,[status(thm)],[c_82733,c_91546]) ).
cnf(c_91550,plain,
ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK5(sK12(sK2,sK3,sK4)),
inference(forward_subsumption_resolution,[status(thm)],[c_91548,c_8384]) ).
cnf(c_91553,plain,
( ~ sP1(sK2,sK3,sK4)
| in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3) ),
inference(superposition,[status(thm)],[c_91547,c_4779]) ).
cnf(c_91558,plain,
in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_91553,c_8384]) ).
cnf(c_91652,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(superposition,[status(thm)],[c_91550,c_4800]) ).
cnf(c_91656,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13)
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_91652,c_91558]) ).
cnf(c_91689,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4))
| sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))) ),
inference(equality_resolution,[status(thm)],[c_91656]) ).
cnf(c_91690,plain,
sK6(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) = sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),
inference(forward_subsumption_resolution,[status(thm)],[c_91689,c_84972,c_91547]) ).
cnf(c_91693,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| subset_complement(the_carrier(sK2),sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))
| ~ in(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK3)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13) ),
inference(superposition,[status(thm)],[c_91690,c_4801]) ).
cnf(c_91695,plain,
( ordered_pair(sK15(sK2,sK3,sK5(sK12(sK2,sK3,sK4))),sK16(sK2,sK3,sK5(sK12(sK2,sK3,sK4)))) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13) ),
inference(forward_subsumption_resolution,[status(thm)],[c_91693,c_91558,c_89840]) ).
cnf(c_91697,plain,
( sK5(sK12(sK2,sK3,sK4)) != sK5(X0_13)
| ~ in(sK5(X0_13),cartesian_product2(sK3,sK4))
| ~ in(sK5(X0_13),X0_13) ),
inference(light_normalisation,[status(thm)],[c_91695,c_91550]) ).
cnf(c_91701,plain,
( ~ in(sK5(sK12(sK2,sK3,sK4)),sK12(sK2,sK3,sK4))
| ~ in(sK5(sK12(sK2,sK3,sK4)),cartesian_product2(sK3,sK4)) ),
inference(equality_resolution,[status(thm)],[c_91697]) ).
cnf(c_91702,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_91701,c_84972,c_91547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU332+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 14:39:05 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 48.83/7.29 % SZS status Started for theBenchmark.p
% 48.83/7.29 ERROR - "ProverProcess:heur/379306:2.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Z3.Error("Sort mismatch at argument #1 for function (declare-fun k!98 (|16777216| |16777216|) |16777216|) supplied sort is |16777229|")
% 48.83/7.29 Fatal error: exception Z3.Error("Sort mismatch at argument #1 for function (declare-fun k!98 (|16777216| |16777216|) |16777216|) supplied sort is |16777229|")
% 48.83/7.29 ERROR - cmd was: ulimit -v 4096000; ./res/iproveropt_static_z3 --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 6 --comb_sup_mult 32 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground false --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs;Unflattening]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes;DemodLoopTriv;ACNormalisation]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;Demod;LightNorm;ACNormalisation]" --sup_immed_triv "[PropSubs]" --sup_indices_passive "[]" --sup_input_bw "[SubsumptionRes]" --sup_input_fw "[SMTSubs;]" --sup_input_triv "[]" --sup_iter_deepening 1 --sup_passive_queue_type priority_queues --sup_passive_queues "[[+min_def_symb;-score;+epr];[-next_state;-conj_dist;+conj_symb]]" --sup_passive_queues_freq "[3;512]" --sup_prop_simpl_given false --sup_prop_simpl_new true --sup_restarts_mult 16 --sup_score sim_d_gen --sup_share_max_num_cl 320 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering arity_rev --sup_to_prop_solver none --superposition_flag true --time_out_prep_mult 0.1 --proof_out true --sat_out_model small --clausifier res/vclausify_rel --clausifier_options "--mode clausify -t 2.00" --time_out_real 2.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_9lia65fr/l10gan5n 2>> /export/starexec/sandbox/tmp/iprover_out_9lia65fr/l10gan5n_error
% 75.40/10.82 % SZS status Theorem for theBenchmark.p
% 75.40/10.82
% 75.40/10.82 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 75.40/10.82
% 75.40/10.82 ------ iProver source info
% 75.40/10.82
% 75.40/10.82 git: date: 2023-05-31 18:12:56 +0000
% 75.40/10.82 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 75.40/10.82 git: non_committed_changes: false
% 75.40/10.82 git: last_make_outside_of_git: false
% 75.40/10.82
% 75.40/10.82 ------ Parsing...
% 75.40/10.82 ------ Clausification by vclausify_rel & Parsing by iProver...
% 75.40/10.82
% 75.40/10.82 ------ 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
% 75.40/10.82
% 75.40/10.82 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 75.40/10.82
% 75.40/10.82 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 75.40/10.82 ------ Proving...
% 75.40/10.82 ------ Problem Properties
% 75.40/10.82
% 75.40/10.82
% 75.40/10.82 clauses 35
% 75.40/10.82 conjectures 8
% 75.40/10.82 EPR 2
% 75.40/10.82 Horn 19
% 75.40/10.82 unary 5
% 75.40/10.82 binary 8
% 75.40/10.82 lits 102
% 75.40/10.82 lits eq 20
% 75.40/10.82 fd_pure 0
% 75.40/10.82 fd_pseudo 0
% 75.40/10.82 fd_cond 0
% 75.40/10.82 fd_pseudo_cond 0
% 75.40/10.82 AC symbols 0
% 75.40/10.82
% 75.40/10.82 ------ Input Options Time Limit: Unbounded
% 75.40/10.82
% 75.40/10.82
% 75.40/10.82 ------
% 75.40/10.82 Current options:
% 75.40/10.82 ------
% 75.40/10.82
% 75.40/10.82
% 75.40/10.82
% 75.40/10.82
% 75.40/10.82 ------ Proving...
% 75.40/10.82
% 75.40/10.82
% 75.40/10.82 % SZS status Theorem for theBenchmark.p
% 75.40/10.82
% 75.40/10.82 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 75.40/10.83
% 75.40/10.84
%------------------------------------------------------------------------------