%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU329+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:24:44 PM UTC 2026
% Result : Theorem 4.95s 1.20s
% Output : CNFRefutation 4.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 2
% Syntax : Number of formulae : 135 ( 7 unt; 0 def)
% Number of atoms : 1148 ( 408 equ)
% Maximal formula atoms : 518 ( 8 avg)
% Number of connectives : 1699 ( 686 ~; 896 |; 99 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 92 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 3 con; 0-6 aty)
% Number of variables : 372 ( 11 sgn 35 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_tarski__e4_7_1__tops_2__2,axiom,
! [X1,X2] :
( ( element(X2,powerset(powerset(the_carrier(X1))))
& one_sorted_str(X1) )
=> ! [X3] :
( ! [X4,X5,X6] :
( ( ? [X10,X11] :
( ! [X12] :
( element(X12,powerset(the_carrier(X1)))
=> ( X12 = X10
=> X11 = subset_complement(the_carrier(X1),X12) ) )
& in(X10,complements_of_subsets(the_carrier(X1),X2))
& ordered_pair(X10,X11) = X6 )
& X4 = X6
& ? [X7,X8] :
( ! [X9] :
( element(X9,powerset(the_carrier(X1)))
=> ( X9 = X7
=> X8 = subset_complement(the_carrier(X1),X9) ) )
& in(X7,complements_of_subsets(the_carrier(X1),X2))
& ordered_pair(X7,X8) = X5 )
& X4 = X5 )
=> X5 = X6 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( ? [X13,X14] :
( ! [X15] :
( element(X15,powerset(the_carrier(X1)))
=> ( X15 = X13
=> X14 = subset_complement(the_carrier(X1),X15) ) )
& in(X13,complements_of_subsets(the_carrier(X1),X2))
& ordered_pair(X13,X14) = X5 )
& X6 = X5
& in(X6,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_1__tops_2__2) ).
fof(s1_xboole_0__e4_7_1__tops_2__1,conjecture,
! [X1,X2] :
( ( element(X2,powerset(powerset(the_carrier(X1))))
& one_sorted_str(X1) )
=> ! [X3] :
? [X4] :
! [X5] :
( in(X5,X4)
<=> ( ? [X6,X7] :
( ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X6
=> X7 = subset_complement(the_carrier(X1),X8) ) )
& in(X6,complements_of_subsets(the_carrier(X1),X2))
& ordered_pair(X6,X7) = X5 )
& in(X5,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_7_1__tops_2__1) ).
fof(c_0_2,plain,
! [X73,X74,X80,X83,X84,X86,X90,X91,X92,X93,X94] :
( ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk12_2(X73,X74) != esk13_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| X94 != subset_complement(the_carrier(X73),esk22_6(X73,X74,X84,X91,X93,X94)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk12_2(X73,X74) != esk13_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| esk22_6(X73,X74,X84,X91,X93,X94) = X93 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk12_2(X73,X74) != esk13_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| element(esk22_6(X73,X74,X84,X91,X93,X94),powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk12_2(X73,X74) != esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| esk21_4(X73,X74,X84,X86) = subset_complement(the_carrier(X73),X90)
| X90 != esk20_4(X73,X74,X84,X86)
| ~ element(X90,powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk12_2(X73,X74) != esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk20_4(X73,X74,X84,X86),complements_of_subsets(the_carrier(X73),X74)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk12_2(X73,X74) != esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| ordered_pair(esk20_4(X73,X74,X84,X86),esk21_4(X73,X74,X84,X86)) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk12_2(X73,X74) != esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| esk19_4(X73,X74,X84,X86) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk12_2(X73,X74) != esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk19_4(X73,X74,X84,X86),cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk17_2(X73,X74) = subset_complement(the_carrier(X73),X83)
| X83 != esk16_2(X73,X74)
| ~ element(X83,powerset(the_carrier(X73)))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| X94 != subset_complement(the_carrier(X73),esk22_6(X73,X74,X84,X91,X93,X94)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk17_2(X73,X74) = subset_complement(the_carrier(X73),X83)
| X83 != esk16_2(X73,X74)
| ~ element(X83,powerset(the_carrier(X73)))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| esk22_6(X73,X74,X84,X91,X93,X94) = X93 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk17_2(X73,X74) = subset_complement(the_carrier(X73),X83)
| X83 != esk16_2(X73,X74)
| ~ element(X83,powerset(the_carrier(X73)))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| element(esk22_6(X73,X74,X84,X91,X93,X94),powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk17_2(X73,X74) = subset_complement(the_carrier(X73),X83)
| X83 != esk16_2(X73,X74)
| ~ element(X83,powerset(the_carrier(X73)))
| ~ in(X86,esk18_3(X73,X74,X84))
| esk21_4(X73,X74,X84,X86) = subset_complement(the_carrier(X73),X90)
| X90 != esk20_4(X73,X74,X84,X86)
| ~ element(X90,powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk17_2(X73,X74) = subset_complement(the_carrier(X73),X83)
| X83 != esk16_2(X73,X74)
| ~ element(X83,powerset(the_carrier(X73)))
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk20_4(X73,X74,X84,X86),complements_of_subsets(the_carrier(X73),X74)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk17_2(X73,X74) = subset_complement(the_carrier(X73),X83)
| X83 != esk16_2(X73,X74)
| ~ element(X83,powerset(the_carrier(X73)))
| ~ in(X86,esk18_3(X73,X74,X84))
| ordered_pair(esk20_4(X73,X74,X84,X86),esk21_4(X73,X74,X84,X86)) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk17_2(X73,X74) = subset_complement(the_carrier(X73),X83)
| X83 != esk16_2(X73,X74)
| ~ element(X83,powerset(the_carrier(X73)))
| ~ in(X86,esk18_3(X73,X74,X84))
| esk19_4(X73,X74,X84,X86) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk17_2(X73,X74) = subset_complement(the_carrier(X73),X83)
| X83 != esk16_2(X73,X74)
| ~ element(X83,powerset(the_carrier(X73)))
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk19_4(X73,X74,X84,X86),cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk16_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| X94 != subset_complement(the_carrier(X73),esk22_6(X73,X74,X84,X91,X93,X94)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk16_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| esk22_6(X73,X74,X84,X91,X93,X94) = X93 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk16_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| element(esk22_6(X73,X74,X84,X91,X93,X94),powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk16_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| ~ in(X86,esk18_3(X73,X74,X84))
| esk21_4(X73,X74,X84,X86) = subset_complement(the_carrier(X73),X90)
| X90 != esk20_4(X73,X74,X84,X86)
| ~ element(X90,powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk16_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk20_4(X73,X74,X84,X86),complements_of_subsets(the_carrier(X73),X74)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk16_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| ~ in(X86,esk18_3(X73,X74,X84))
| ordered_pair(esk20_4(X73,X74,X84,X86),esk21_4(X73,X74,X84,X86)) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk16_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| ~ in(X86,esk18_3(X73,X74,X84))
| esk19_4(X73,X74,X84,X86) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk16_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk19_4(X73,X74,X84,X86),cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk16_2(X73,X74),esk17_2(X73,X74)) = esk13_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| X94 != subset_complement(the_carrier(X73),esk22_6(X73,X74,X84,X91,X93,X94)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk16_2(X73,X74),esk17_2(X73,X74)) = esk13_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| esk22_6(X73,X74,X84,X91,X93,X94) = X93 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk16_2(X73,X74),esk17_2(X73,X74)) = esk13_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| element(esk22_6(X73,X74,X84,X91,X93,X94),powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk16_2(X73,X74),esk17_2(X73,X74)) = esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| esk21_4(X73,X74,X84,X86) = subset_complement(the_carrier(X73),X90)
| X90 != esk20_4(X73,X74,X84,X86)
| ~ element(X90,powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk16_2(X73,X74),esk17_2(X73,X74)) = esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk20_4(X73,X74,X84,X86),complements_of_subsets(the_carrier(X73),X74)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk16_2(X73,X74),esk17_2(X73,X74)) = esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| ordered_pair(esk20_4(X73,X74,X84,X86),esk21_4(X73,X74,X84,X86)) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk16_2(X73,X74),esk17_2(X73,X74)) = esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| esk19_4(X73,X74,X84,X86) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk16_2(X73,X74),esk17_2(X73,X74)) = esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk19_4(X73,X74,X84,X86),cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk13_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| X94 != subset_complement(the_carrier(X73),esk22_6(X73,X74,X84,X91,X93,X94)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk13_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| esk22_6(X73,X74,X84,X91,X93,X94) = X93 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk13_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| element(esk22_6(X73,X74,X84,X91,X93,X94),powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| esk21_4(X73,X74,X84,X86) = subset_complement(the_carrier(X73),X90)
| X90 != esk20_4(X73,X74,X84,X86)
| ~ element(X90,powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk20_4(X73,X74,X84,X86),complements_of_subsets(the_carrier(X73),X74)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| ordered_pair(esk20_4(X73,X74,X84,X86),esk21_4(X73,X74,X84,X86)) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| esk19_4(X73,X74,X84,X86) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk13_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk19_4(X73,X74,X84,X86),cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk15_2(X73,X74) = subset_complement(the_carrier(X73),X80)
| X80 != esk14_2(X73,X74)
| ~ element(X80,powerset(the_carrier(X73)))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| X94 != subset_complement(the_carrier(X73),esk22_6(X73,X74,X84,X91,X93,X94)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk15_2(X73,X74) = subset_complement(the_carrier(X73),X80)
| X80 != esk14_2(X73,X74)
| ~ element(X80,powerset(the_carrier(X73)))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| esk22_6(X73,X74,X84,X91,X93,X94) = X93 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk15_2(X73,X74) = subset_complement(the_carrier(X73),X80)
| X80 != esk14_2(X73,X74)
| ~ element(X80,powerset(the_carrier(X73)))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| element(esk22_6(X73,X74,X84,X91,X93,X94),powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk15_2(X73,X74) = subset_complement(the_carrier(X73),X80)
| X80 != esk14_2(X73,X74)
| ~ element(X80,powerset(the_carrier(X73)))
| ~ in(X86,esk18_3(X73,X74,X84))
| esk21_4(X73,X74,X84,X86) = subset_complement(the_carrier(X73),X90)
| X90 != esk20_4(X73,X74,X84,X86)
| ~ element(X90,powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk15_2(X73,X74) = subset_complement(the_carrier(X73),X80)
| X80 != esk14_2(X73,X74)
| ~ element(X80,powerset(the_carrier(X73)))
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk20_4(X73,X74,X84,X86),complements_of_subsets(the_carrier(X73),X74)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk15_2(X73,X74) = subset_complement(the_carrier(X73),X80)
| X80 != esk14_2(X73,X74)
| ~ element(X80,powerset(the_carrier(X73)))
| ~ in(X86,esk18_3(X73,X74,X84))
| ordered_pair(esk20_4(X73,X74,X84,X86),esk21_4(X73,X74,X84,X86)) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk15_2(X73,X74) = subset_complement(the_carrier(X73),X80)
| X80 != esk14_2(X73,X74)
| ~ element(X80,powerset(the_carrier(X73)))
| ~ in(X86,esk18_3(X73,X74,X84))
| esk19_4(X73,X74,X84,X86) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk15_2(X73,X74) = subset_complement(the_carrier(X73),X80)
| X80 != esk14_2(X73,X74)
| ~ element(X80,powerset(the_carrier(X73)))
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk19_4(X73,X74,X84,X86),cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk14_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| X94 != subset_complement(the_carrier(X73),esk22_6(X73,X74,X84,X91,X93,X94)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk14_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| esk22_6(X73,X74,X84,X91,X93,X94) = X93 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk14_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| element(esk22_6(X73,X74,X84,X91,X93,X94),powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk14_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| ~ in(X86,esk18_3(X73,X74,X84))
| esk21_4(X73,X74,X84,X86) = subset_complement(the_carrier(X73),X90)
| X90 != esk20_4(X73,X74,X84,X86)
| ~ element(X90,powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk14_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk20_4(X73,X74,X84,X86),complements_of_subsets(the_carrier(X73),X74)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk14_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| ~ in(X86,esk18_3(X73,X74,X84))
| ordered_pair(esk20_4(X73,X74,X84,X86),esk21_4(X73,X74,X84,X86)) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk14_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| ~ in(X86,esk18_3(X73,X74,X84))
| esk19_4(X73,X74,X84,X86) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| in(esk14_2(X73,X74),complements_of_subsets(the_carrier(X73),X74))
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk19_4(X73,X74,X84,X86),cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk14_2(X73,X74),esk15_2(X73,X74)) = esk12_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| X94 != subset_complement(the_carrier(X73),esk22_6(X73,X74,X84,X91,X93,X94)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk14_2(X73,X74),esk15_2(X73,X74)) = esk12_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| esk22_6(X73,X74,X84,X91,X93,X94) = X93 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk14_2(X73,X74),esk15_2(X73,X74)) = esk12_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| element(esk22_6(X73,X74,X84,X91,X93,X94),powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk14_2(X73,X74),esk15_2(X73,X74)) = esk12_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| esk21_4(X73,X74,X84,X86) = subset_complement(the_carrier(X73),X90)
| X90 != esk20_4(X73,X74,X84,X86)
| ~ element(X90,powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk14_2(X73,X74),esk15_2(X73,X74)) = esk12_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk20_4(X73,X74,X84,X86),complements_of_subsets(the_carrier(X73),X74)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk14_2(X73,X74),esk15_2(X73,X74)) = esk12_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| ordered_pair(esk20_4(X73,X74,X84,X86),esk21_4(X73,X74,X84,X86)) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk14_2(X73,X74),esk15_2(X73,X74)) = esk12_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| esk19_4(X73,X74,X84,X86) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| ordered_pair(esk14_2(X73,X74),esk15_2(X73,X74)) = esk12_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk19_4(X73,X74,X84,X86),cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk12_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| X94 != subset_complement(the_carrier(X73),esk22_6(X73,X74,X84,X91,X93,X94)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk12_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| esk22_6(X73,X74,X84,X91,X93,X94) = X93 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk12_2(X73,X74)
| in(X91,esk18_3(X73,X74,X84))
| X92 != X91
| ~ in(X92,cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84))
| ~ in(X93,complements_of_subsets(the_carrier(X73),X74))
| ordered_pair(X93,X94) != X91
| element(esk22_6(X73,X74,X84,X91,X93,X94),powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk12_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| esk21_4(X73,X74,X84,X86) = subset_complement(the_carrier(X73),X90)
| X90 != esk20_4(X73,X74,X84,X86)
| ~ element(X90,powerset(the_carrier(X73))) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk12_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk20_4(X73,X74,X84,X86),complements_of_subsets(the_carrier(X73),X74)) )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk12_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| ordered_pair(esk20_4(X73,X74,X84,X86),esk21_4(X73,X74,X84,X86)) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk12_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| esk19_4(X73,X74,X84,X86) = X86 )
& ( ~ element(X74,powerset(powerset(the_carrier(X73))))
| ~ one_sorted_str(X73)
| esk11_2(X73,X74) = esk12_2(X73,X74)
| ~ in(X86,esk18_3(X73,X74,X84))
| in(esk19_4(X73,X74,X84,X86),cartesian_product2(complements_of_subsets(the_carrier(X73),X74),X84)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[s1_tarski__e4_7_1__tops_2__2])])])])])])]) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2] :
( ( element(X2,powerset(powerset(the_carrier(X1))))
& one_sorted_str(X1) )
=> ! [X3] :
? [X4] :
! [X5] :
( in(X5,X4)
<=> ( ? [X6,X7] :
( ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X6
=> X7 = subset_complement(the_carrier(X1),X8) ) )
& in(X6,complements_of_subsets(the_carrier(X1),X2))
& ordered_pair(X6,X7) = X5 )
& in(X5,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ) ) ),
inference(assume_negation,[status(cth)],[s1_xboole_0__e4_7_1__tops_2__1]) ).
cnf(c_0_4,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| X7 != X4
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(X5,X6) != X4
| esk11_2(X1,X2) = esk12_2(X1,X2)
| in(X4,esk18_3(X1,X2,X3))
| element(esk22_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
fof(c_0_5,negated_conjecture,
! [X19,X21,X22,X26] :
( ( in(esk4_1(X19),X19)
| esk7_1(X19) = subset_complement(the_carrier(esk1_0),X26)
| X26 != esk6_1(X19)
| ~ element(X26,powerset(the_carrier(esk1_0))) )
& ( in(esk4_1(X19),X19)
| in(esk6_1(X19),complements_of_subsets(the_carrier(esk1_0),esk2_0)) )
& ( in(esk4_1(X19),X19)
| ordered_pair(esk6_1(X19),esk7_1(X19)) = esk4_1(X19) )
& ( in(esk4_1(X19),X19)
| in(esk4_1(X19),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0)) )
& ( ~ in(esk4_1(X19),X19)
| ~ in(esk4_1(X19),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(X21,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X21,X22) != esk4_1(X19)
| X22 != subset_complement(the_carrier(esk1_0),esk5_3(X19,X21,X22)) )
& ( ~ in(esk4_1(X19),X19)
| ~ in(esk4_1(X19),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(X21,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X21,X22) != esk4_1(X19)
| esk5_3(X19,X21,X22) = X21 )
& ( ~ in(esk4_1(X19),X19)
| ~ in(esk4_1(X19),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(X21,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X21,X22) != esk4_1(X19)
| element(esk5_3(X19,X21,X22),powerset(the_carrier(esk1_0))) )
& element(esk2_0,powerset(powerset(the_carrier(esk1_0))))
& one_sorted_str(esk1_0) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])])]) ).
cnf(c_0_6,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| X7 != X4
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(X5,X6) != X4
| esk11_2(X1,X2) = esk12_2(X1,X2)
| in(X4,esk18_3(X1,X2,X3))
| esk22_6(X1,X2,X3,X4,X5,X6) = X5 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ in(ordered_pair(X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X5))
| element(esk22_6(X1,X2,X5,ordered_pair(X3,X4),X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk18_3(X1,X2,X5))
| esk11_2(X1,X2) = esk12_2(X1,X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_4])]) ).
cnf(c_0_8,negated_conjecture,
( in(esk4_1(X1),X1)
| ordered_pair(esk6_1(X1),esk7_1(X1)) = esk4_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ in(ordered_pair(X4,X5),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| in(ordered_pair(X4,X5),esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| esk22_6(X1,X2,X3,ordered_pair(X4,X5),X4,X5) = X4 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_6])]) ).
cnf(c_0_10,plain,
( ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ one_sorted_str(X2)
| X7 != X5
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ordered_pair(X6,X1) != X5
| X1 != subset_complement(the_carrier(X2),esk22_6(X2,X3,X4,X5,X6,X1))
| esk11_2(X2,X3) = esk12_2(X2,X3)
| in(X5,esk18_3(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_11,negated_conjecture,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(esk6_1(X3),complements_of_subsets(the_carrier(X1),X2))
| ~ in(esk4_1(X3),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X4))
| element(esk22_6(X1,X2,X4,esk4_1(X3),esk6_1(X3),esk7_1(X3)),powerset(the_carrier(X1)))
| in(esk4_1(X3),X3)
| in(esk4_1(X3),esk18_3(X1,X2,X4))
| esk11_2(X1,X2) = esk12_2(X1,X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( in(esk4_1(X1),X1)
| in(esk4_1(X1),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
element(esk2_0,powerset(powerset(the_carrier(esk1_0)))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
one_sorted_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_15,negated_conjecture,
( in(esk4_1(X1),X1)
| in(esk6_1(X1),complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(esk6_1(X4),complements_of_subsets(the_carrier(X1),X2))
| ~ in(esk4_1(X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| in(esk4_1(X4),X4)
| in(esk4_1(X4),esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| esk22_6(X1,X2,X3,esk4_1(X4),esk6_1(X4),esk7_1(X4)) = esk6_1(X4) ),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_17,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ in(ordered_pair(X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X5))
| subset_complement(the_carrier(X1),esk22_6(X1,X2,X5,ordered_pair(X3,X4),X3,X4)) != X4
| in(ordered_pair(X3,X4),esk18_3(X1,X2,X5))
| esk11_2(X1,X2) = esk12_2(X1,X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_10])]) ).
cnf(c_0_18,negated_conjecture,
( X1 != esk6_1(X2)
| ~ element(X1,powerset(the_carrier(esk1_0)))
| in(esk4_1(X2),X2)
| esk7_1(X2) = subset_complement(the_carrier(esk1_0),X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,negated_conjecture,
( element(esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(X1),esk6_1(X1),esk7_1(X1)),powerset(the_carrier(esk1_0)))
| in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(X1),esk6_1(X1),esk7_1(X1)) = esk6_1(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_21,negated_conjecture,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(esk6_1(X3),complements_of_subsets(the_carrier(X1),X2))
| ~ in(esk4_1(X3),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X4))
| subset_complement(the_carrier(X1),esk22_6(X1,X2,X4,esk4_1(X3),esk6_1(X3),esk7_1(X3))) != esk7_1(X3)
| in(esk4_1(X3),X3)
| in(esk4_1(X3),esk18_3(X1,X2,X4))
| esk11_2(X1,X2) = esk12_2(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_8]) ).
cnf(c_0_22,negated_conjecture,
( ~ element(esk6_1(X1),powerset(the_carrier(esk1_0)))
| in(esk4_1(X1),X1)
| esk7_1(X1) = subset_complement(the_carrier(esk1_0),esk6_1(X1)) ),
inference(er,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( element(esk6_1(X1),powerset(the_carrier(esk1_0)))
| in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( esk7_1(X1) != subset_complement(the_carrier(esk1_0),esk6_1(X1))
| in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_20]),c_0_13]),c_0_14])]),c_0_15]),c_0_12]) ).
cnf(c_0_25,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| ~ in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| in(esk19_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_26,negated_conjecture,
( in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_27,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| ~ in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| esk19_4(X1,X2,X3,X4) = X4 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_28,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| in(esk19_4(esk1_0,esk2_0,X1,X2),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X1))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_13]),c_0_14])]) ).
cnf(c_0_29,negated_conjecture,
( in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(ef,[status(thm)],[c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| esk19_4(esk1_0,esk2_0,X1,X2) = X2
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_13]),c_0_14])]) ).
cnf(c_0_31,negated_conjecture,
( ~ in(esk4_1(X1),X1)
| ~ in(esk4_1(X1),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(X2,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X2,X3) != esk4_1(X1)
| element(esk5_3(X1,X2,X3),powerset(the_carrier(esk1_0))) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_32,negated_conjecture,
( ~ in(esk4_1(X1),X1)
| ~ in(esk4_1(X1),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(X2,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X2,X3) != esk4_1(X1)
| esk5_3(X1,X2,X3) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_33,negated_conjecture,
( in(esk19_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| esk19_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))) = esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_35,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| ~ in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| in(esk20_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_36,negated_conjecture,
( ~ in(esk4_1(X3),X3)
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(X3),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ordered_pair(X1,X2) != esk4_1(X3)
| element(X1,powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
( in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| in(esk20_4(esk1_0,esk2_0,X1,X2),complements_of_subsets(the_carrier(esk1_0),esk2_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_13]),c_0_14])]) ).
cnf(c_0_39,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| ~ in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| ordered_pair(esk20_4(X1,X2,X3,X4),esk21_4(X1,X2,X3,X4)) = X4 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_40,negated_conjecture,
( ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X1,X2) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| element(X1,powerset(the_carrier(esk1_0)))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_29]) ).
cnf(c_0_41,negated_conjecture,
( in(esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),complements_of_subsets(the_carrier(esk1_0),esk2_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_29]) ).
cnf(c_0_42,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),esk21_4(esk1_0,esk2_0,X1,X2)) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_13]),c_0_14])]) ).
cnf(c_0_43,negated_conjecture,
( ~ in(esk4_1(X2),X2)
| ~ in(esk4_1(X2),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(X3,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X3,X1) != esk4_1(X2)
| X1 != subset_complement(the_carrier(esk1_0),esk5_3(X2,X3,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_44,plain,
( ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ one_sorted_str(X2)
| ~ in(X5,esk18_3(X2,X3,X4))
| X1 != esk20_4(X2,X3,X4,X5)
| ~ element(X1,powerset(the_carrier(X2)))
| esk11_2(X2,X3) = esk12_2(X2,X3)
| esk21_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_45,negated_conjecture,
( ordered_pair(esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),X1) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| element(esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),powerset(the_carrier(esk1_0)))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| ordered_pair(esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),esk21_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)))) = esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_42,c_0_29]) ).
cnf(c_0_47,negated_conjecture,
( ~ in(esk4_1(X2),X2)
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(X2),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(X2) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_32])]) ).
cnf(c_0_48,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ element(esk20_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| ~ in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| esk21_4(X1,X2,X3,X4) = subset_complement(the_carrier(X1),esk20_4(X1,X2,X3,X4)) ),
inference(er,[status(thm)],[c_0_44]) ).
cnf(c_0_49,negated_conjecture,
( element(esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),powerset(the_carrier(esk1_0)))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
( ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_37]),c_0_29]) ).
cnf(c_0_51,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| ~ in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| in(esk19_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_52,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| esk21_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))) = subset_complement(the_carrier(esk1_0),esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_13]),c_0_14])]),c_0_29]) ).
cnf(c_0_53,negated_conjecture,
( ordered_pair(esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),subset_complement(the_carrier(esk1_0),esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))))) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_41]) ).
cnf(c_0_54,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| ~ in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| esk19_4(X1,X2,X3,X4) = X4 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_55,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| in(esk19_4(esk1_0,esk2_0,X1,X2),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X1))
| esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_13]),c_0_14])]) ).
cnf(c_0_56,negated_conjecture,
esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_52]),c_0_53]) ).
cnf(c_0_57,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| esk19_4(esk1_0,esk2_0,X1,X2) = X2
| esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_13]),c_0_14])]) ).
cnf(c_0_58,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| in(esk19_4(esk1_0,esk2_0,X1,X2),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X1))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| esk19_4(esk1_0,esk2_0,X1,X2) = X2
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(rw,[status(thm)],[c_0_57,c_0_56]) ).
cnf(c_0_60,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| X7 != X4
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(X5,X6) != X4
| esk11_2(X1,X2) = esk13_2(X1,X2)
| in(X4,esk18_3(X1,X2,X3))
| element(esk22_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_61,negated_conjecture,
( in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| in(esk19_4(esk1_0,esk2_0,X1,esk4_1(esk18_3(esk1_0,esk2_0,X1))),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X1))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_58,c_0_12]) ).
cnf(c_0_62,negated_conjecture,
( in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| esk19_4(esk1_0,esk2_0,X1,esk4_1(esk18_3(esk1_0,esk2_0,X1))) = esk4_1(esk18_3(esk1_0,esk2_0,X1)) ),
inference(spm,[status(thm)],[c_0_59,c_0_12]) ).
cnf(c_0_63,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| X7 != X4
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(X5,X6) != X4
| esk11_2(X1,X2) = esk13_2(X1,X2)
| in(X4,esk18_3(X1,X2,X3))
| esk22_6(X1,X2,X3,X4,X5,X6) = X5 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_64,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ in(ordered_pair(X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X5))
| element(esk22_6(X1,X2,X5,ordered_pair(X3,X4),X3,X4),powerset(the_carrier(X1)))
| in(ordered_pair(X3,X4),esk18_3(X1,X2,X5))
| esk11_2(X1,X2) = esk13_2(X1,X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_60])]) ).
cnf(c_0_65,negated_conjecture,
( in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X1))
| in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_66,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ in(ordered_pair(X4,X5),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| in(ordered_pair(X4,X5),esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| esk22_6(X1,X2,X3,ordered_pair(X4,X5),X4,X5) = X4 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_63])]) ).
cnf(c_0_67,negated_conjecture,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(esk6_1(X3),complements_of_subsets(the_carrier(X1),X2))
| ~ in(esk4_1(X3),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X4))
| element(esk22_6(X1,X2,X4,esk4_1(X3),esk6_1(X3),esk7_1(X3)),powerset(the_carrier(X1)))
| in(esk4_1(X3),X3)
| in(esk4_1(X3),esk18_3(X1,X2,X4))
| esk11_2(X1,X2) = esk13_2(X1,X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_8]) ).
cnf(c_0_68,negated_conjecture,
( in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(ef,[status(thm)],[c_0_65]) ).
cnf(c_0_69,negated_conjecture,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(esk6_1(X4),complements_of_subsets(the_carrier(X1),X2))
| ~ in(esk4_1(X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| in(esk4_1(X4),X4)
| in(esk4_1(X4),esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| esk22_6(X1,X2,X3,esk4_1(X4),esk6_1(X4),esk7_1(X4)) = esk6_1(X4) ),
inference(spm,[status(thm)],[c_0_66,c_0_8]) ).
cnf(c_0_70,plain,
( ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ one_sorted_str(X2)
| X7 != X5
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ordered_pair(X6,X1) != X5
| X1 != subset_complement(the_carrier(X2),esk22_6(X2,X3,X4,X5,X6,X1))
| esk11_2(X2,X3) = esk13_2(X2,X3)
| in(X5,esk18_3(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_71,negated_conjecture,
( element(esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk6_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk7_1(esk18_3(esk1_0,esk2_0,esk3_0))),powerset(the_carrier(esk1_0)))
| in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_56]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_72,negated_conjecture,
( in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk6_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk7_1(esk18_3(esk1_0,esk2_0,esk3_0))) = esk6_1(esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_68]),c_0_56]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_73,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ in(ordered_pair(X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X5))
| subset_complement(the_carrier(X1),esk22_6(X1,X2,X5,ordered_pair(X3,X4),X3,X4)) != X4
| in(ordered_pair(X3,X4),esk18_3(X1,X2,X5))
| esk11_2(X1,X2) = esk13_2(X1,X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_70])]) ).
cnf(c_0_74,negated_conjecture,
( element(esk6_1(esk18_3(esk1_0,esk2_0,esk3_0)),powerset(the_carrier(esk1_0)))
| in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_75,negated_conjecture,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(esk6_1(X3),complements_of_subsets(the_carrier(X1),X2))
| ~ in(esk4_1(X3),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X4))
| subset_complement(the_carrier(X1),esk22_6(X1,X2,X4,esk4_1(X3),esk6_1(X3),esk7_1(X3))) != esk7_1(X3)
| in(esk4_1(X3),X3)
| in(esk4_1(X3),esk18_3(X1,X2,X4))
| esk11_2(X1,X2) = esk13_2(X1,X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_8]) ).
cnf(c_0_76,negated_conjecture,
( in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| esk7_1(esk18_3(esk1_0,esk2_0,esk3_0)) = subset_complement(the_carrier(esk1_0),esk6_1(esk18_3(esk1_0,esk2_0,esk3_0))) ),
inference(spm,[status(thm)],[c_0_22,c_0_74]) ).
cnf(c_0_77,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| ~ in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| in(esk20_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_78,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| esk12_2(X1,X2) != esk13_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| in(esk20_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_79,negated_conjecture,
( ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| ordered_pair(X1,X2) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| element(X1,powerset(the_carrier(esk1_0)))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_68]) ).
cnf(c_0_80,negated_conjecture,
( in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_72]),c_0_56]),c_0_13]),c_0_14])]),c_0_15]),c_0_68]),c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| in(esk20_4(esk1_0,esk2_0,X1,X2),complements_of_subsets(the_carrier(esk1_0),esk2_0))
| esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_13]),c_0_14])]) ).
cnf(c_0_82,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| esk13_2(esk1_0,esk2_0) != esk12_2(esk1_0,esk2_0)
| in(esk20_4(esk1_0,esk2_0,X1,X2),complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_13]),c_0_14])]) ).
cnf(c_0_83,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| ~ in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| ordered_pair(esk20_4(X1,X2,X3,X4),esk21_4(X1,X2,X3,X4)) = X4 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_84,negated_conjecture,
( ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X1,X2) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| element(X1,powerset(the_carrier(esk1_0)))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| in(esk20_4(esk1_0,esk2_0,X1,X2),complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_56]),c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0)
| ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),esk21_4(esk1_0,esk2_0,X1,X2)) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_13]),c_0_14])]) ).
cnf(c_0_87,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),X3) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| element(esk20_4(esk1_0,esk2_0,X1,X2),powerset(the_carrier(esk1_0)))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),esk21_4(esk1_0,esk2_0,X1,X2)) = X2 ),
inference(rw,[status(thm)],[c_0_86,c_0_56]) ).
cnf(c_0_89,plain,
( ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ one_sorted_str(X2)
| ~ in(X5,esk18_3(X2,X3,X4))
| X1 != esk20_4(X2,X3,X4,X5)
| ~ element(X1,powerset(the_carrier(X2)))
| esk11_2(X2,X3) = esk13_2(X2,X3)
| esk21_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_90,negated_conjecture,
( ordered_pair(esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),X1) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| element(esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),powerset(the_carrier(esk1_0)))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_87,c_0_80]) ).
cnf(c_0_91,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| ordered_pair(esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),esk21_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)))) = esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_88,c_0_80]) ).
cnf(c_0_92,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| esk12_2(X1,X2) != esk13_2(X1,X2)
| X7 != X4
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(X5,X6) != X4
| in(X4,esk18_3(X1,X2,X3))
| element(esk22_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_93,negated_conjecture,
( ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_68]) ).
cnf(c_0_94,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ element(esk20_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| ~ in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| esk21_4(X1,X2,X3,X4) = subset_complement(the_carrier(X1),esk20_4(X1,X2,X3,X4)) ),
inference(er,[status(thm)],[c_0_89]) ).
cnf(c_0_95,negated_conjecture,
( element(esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),powerset(the_carrier(esk1_0)))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| esk12_2(X1,X2) != esk13_2(X1,X2)
| X7 != X4
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ordered_pair(X5,X6) != X4
| in(X4,esk18_3(X1,X2,X3))
| esk22_6(X1,X2,X3,X4,X5,X6) = X5 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_97,plain,
( ~ one_sorted_str(X3)
| ~ element(X4,powerset(powerset(the_carrier(X3))))
| ~ in(X1,complements_of_subsets(the_carrier(X3),X4))
| ~ in(ordered_pair(X1,X2),cartesian_product2(complements_of_subsets(the_carrier(X3),X4),X5))
| esk13_2(X3,X4) != esk12_2(X3,X4)
| element(esk22_6(X3,X4,X5,ordered_pair(X1,X2),X1,X2),powerset(the_carrier(X3)))
| in(ordered_pair(X1,X2),esk18_3(X3,X4,X5)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_92])]) ).
cnf(c_0_98,negated_conjecture,
( ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_93,c_0_80]) ).
cnf(c_0_99,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| esk21_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))) = subset_complement(the_carrier(esk1_0),esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_56]),c_0_13]),c_0_14])]),c_0_80]) ).
cnf(c_0_100,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ in(ordered_pair(X4,X5),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| esk13_2(X1,X2) != esk12_2(X1,X2)
| in(ordered_pair(X4,X5),esk18_3(X1,X2,X3))
| esk22_6(X1,X2,X3,ordered_pair(X4,X5),X4,X5) = X4 ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_96])]) ).
cnf(c_0_101,negated_conjecture,
( ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(esk6_1(X1),complements_of_subsets(the_carrier(X2),X3))
| ~ in(esk4_1(X1),cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| esk13_2(X2,X3) != esk12_2(X2,X3)
| element(esk22_6(X2,X3,X4,esk4_1(X1),esk6_1(X1),esk7_1(X1)),powerset(the_carrier(X2)))
| in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_97,c_0_8]) ).
cnf(c_0_102,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),subset_complement(the_carrier(esk1_0),esk20_4(esk1_0,esk2_0,X1,X2))) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_98,c_0_85]) ).
cnf(c_0_103,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| ordered_pair(esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),subset_complement(the_carrier(esk1_0),esk20_4(esk1_0,esk2_0,esk3_0,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))))) = esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_91,c_0_99]) ).
cnf(c_0_104,negated_conjecture,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ in(esk6_1(X4),complements_of_subsets(the_carrier(X1),X2))
| ~ in(esk4_1(X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| esk13_2(X1,X2) != esk12_2(X1,X2)
| in(esk4_1(X4),X4)
| in(esk4_1(X4),esk18_3(X1,X2,X3))
| esk22_6(X1,X2,X3,esk4_1(X4),esk6_1(X4),esk7_1(X4)) = esk6_1(X4) ),
inference(spm,[status(thm)],[c_0_100,c_0_8]) ).
cnf(c_0_105,plain,
( ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ one_sorted_str(X2)
| esk12_2(X2,X3) != esk13_2(X2,X3)
| X7 != X5
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ordered_pair(X6,X1) != X5
| X1 != subset_complement(the_carrier(X2),esk22_6(X2,X3,X4,X5,X6,X1))
| in(X5,esk18_3(X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_106,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| esk12_2(X1,X2) != esk13_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| in(esk19_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_107,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| esk12_2(X1,X2) != esk13_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| esk19_4(X1,X2,X3,X4) = X4 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_108,negated_conjecture,
( esk13_2(esk1_0,esk2_0) != esk12_2(esk1_0,esk2_0)
| element(esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(X1),esk6_1(X1),esk7_1(X1)),powerset(the_carrier(esk1_0)))
| in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_109,negated_conjecture,
esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_80]) ).
cnf(c_0_110,negated_conjecture,
( esk13_2(esk1_0,esk2_0) != esk12_2(esk1_0,esk2_0)
| in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(X1),esk6_1(X1),esk7_1(X1)) = esk6_1(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_12]),c_0_13]),c_0_14])]),c_0_15]) ).
cnf(c_0_111,plain,
( ~ one_sorted_str(X3)
| ~ element(X4,powerset(powerset(the_carrier(X3))))
| ~ in(X1,complements_of_subsets(the_carrier(X3),X4))
| ~ in(ordered_pair(X1,X2),cartesian_product2(complements_of_subsets(the_carrier(X3),X4),X5))
| esk13_2(X3,X4) != esk12_2(X3,X4)
| subset_complement(the_carrier(X3),esk22_6(X3,X4,X5,ordered_pair(X1,X2),X1,X2)) != X2
| in(ordered_pair(X1,X2),esk18_3(X3,X4,X5)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_105])]) ).
cnf(c_0_112,plain,
( ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(X1,esk18_3(X2,X3,X4))
| esk13_2(X2,X3) != esk12_2(X2,X3)
| in(X1,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4)) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,negated_conjecture,
( element(esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(X1),esk6_1(X1),esk7_1(X1)),powerset(the_carrier(esk1_0)))
| in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_108,c_0_109])]) ).
cnf(c_0_114,negated_conjecture,
( in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(X1),esk6_1(X1),esk7_1(X1)) = esk6_1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_109])]) ).
cnf(c_0_115,negated_conjecture,
( ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ in(esk6_1(X1),complements_of_subsets(the_carrier(X2),X3))
| ~ in(esk4_1(X1),cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| esk13_2(X2,X3) != esk12_2(X2,X3)
| subset_complement(the_carrier(X2),esk22_6(X2,X3,X4,esk4_1(X1),esk6_1(X1),esk7_1(X1))) != esk7_1(X1)
| in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(X2,X3,X4)) ),
inference(spm,[status(thm)],[c_0_111,c_0_8]) ).
cnf(c_0_116,negated_conjecture,
( ~ in(X1,esk18_3(esk1_0,esk2_0,X2))
| esk13_2(esk1_0,esk2_0) != esk12_2(esk1_0,esk2_0)
| in(X1,cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_13]),c_0_14])]) ).
cnf(c_0_117,negated_conjecture,
( element(esk6_1(X1),powerset(the_carrier(esk1_0)))
| in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_118,negated_conjecture,
( esk7_1(X1) != subset_complement(the_carrier(esk1_0),esk6_1(X1))
| in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_114]),c_0_109]),c_0_13]),c_0_14])]),c_0_15]),c_0_12]) ).
cnf(c_0_119,negated_conjecture,
( ~ in(X1,esk18_3(esk1_0,esk2_0,X2))
| in(X1,cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_109])]) ).
cnf(c_0_120,negated_conjecture,
( in(esk4_1(X1),X1)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_117]),c_0_118]) ).
cnf(c_0_121,negated_conjecture,
( ~ in(esk4_1(X3),X3)
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(X3),esk18_3(esk1_0,esk2_0,esk3_0))
| ordered_pair(X1,X2) != esk4_1(X3)
| element(X1,powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_36,c_0_119]) ).
cnf(c_0_122,negated_conjecture,
in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0)),
inference(ef,[status(thm)],[c_0_120]) ).
cnf(c_0_123,plain,
( ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ one_sorted_str(X2)
| esk12_2(X2,X3) != esk13_2(X2,X3)
| ~ in(X5,esk18_3(X2,X3,X4))
| X1 != esk20_4(X2,X3,X4,X5)
| ~ element(X1,powerset(the_carrier(X2)))
| esk21_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_124,negated_conjecture,
( ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X1,X2) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| element(X1,powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_122])]) ).
cnf(c_0_125,negated_conjecture,
( ~ in(esk4_1(X2),X2)
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(X2),esk18_3(esk1_0,esk2_0,esk3_0))
| ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_119]) ).
cnf(c_0_126,plain,
( ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1)
| esk12_2(X1,X2) != esk13_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ordered_pair(esk20_4(X1,X2,X3,X4),esk21_4(X1,X2,X3,X4)) = X4 ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_127,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ element(esk20_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| ~ in(X4,esk18_3(X1,X2,X3))
| esk13_2(X1,X2) != esk12_2(X1,X2)
| esk21_4(X1,X2,X3,X4) = subset_complement(the_carrier(X1),esk20_4(X1,X2,X3,X4)) ),
inference(er,[status(thm)],[c_0_123]) ).
cnf(c_0_128,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),X3) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| element(esk20_4(esk1_0,esk2_0,X1,X2),powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_124,c_0_85]) ).
cnf(c_0_129,negated_conjecture,
( ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_122]),c_0_122])]) ).
cnf(c_0_130,plain,
( ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ element(esk20_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| ~ in(X4,esk18_3(X1,X2,X3))
| esk13_2(X1,X2) != esk12_2(X1,X2)
| ordered_pair(esk20_4(X1,X2,X3,X4),subset_complement(the_carrier(X1),esk20_4(X1,X2,X3,X4))) = X4 ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_131,negated_conjecture,
( ~ in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,X1))
| element(esk20_4(esk1_0,esk2_0,X1,esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))),powerset(the_carrier(esk1_0))) ),
inference(er,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_126]),c_0_109]),c_0_13]),c_0_14])])]) ).
cnf(c_0_132,negated_conjecture,
( ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),subset_complement(the_carrier(esk1_0),esk20_4(esk1_0,esk2_0,X1,X2))) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(spm,[status(thm)],[c_0_129,c_0_85]) ).
cnf(c_0_133,negated_conjecture,
~ in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,X1)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_109]),c_0_13]),c_0_14])]),c_0_132]) ).
cnf(c_0_134,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_122,c_0_133]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU329+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.52 % Computer : n016.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Mon Sep 21 06:16:53 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.52 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.57 Running first-order theorem proving
% 0.10/0.57 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.95/1.20 % Version: 3.5.1
% 4.95/1.20 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.95/1.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.95/1.20 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.95/1.20 % Starting new_bool_3 with 300s (1) cores
% 4.95/1.20 % Starting new_bool_1 with 300s (1) cores
% 4.95/1.20 % Starting sh5l with 300s (1) cores
% 4.95/1.20 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1734218 completed with status 0
% 4.95/1.20 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 4.95/1.20 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.95/1.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.95/1.20 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.95/1.20 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.95/1.20 % No SInE strategy applied
% 4.95/1.20 % Search class: FGHSS-FSLM32-MFFFFFNN
% 4.95/1.20 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.95/1.20 % Starting SubtermCWHack with 136s (1) cores
% 4.95/1.20 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.95/1.20 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 4.95/1.20 % Starting new_bool_3 with 136s (1) cores
% 4.95/1.20 % Starting new_bool_1 with 136s (1) cores
% 4.95/1.20 % G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1734227 completed with status 0
% 4.95/1.20 % Result found by G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 4.95/1.20 % Preprocessing class: FSMSSMSSSSSNFFN.
% 4.95/1.20 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 4.95/1.20 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 4.95/1.20 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 4.95/1.20 % No SInE strategy applied
% 4.95/1.20 % Search class: FGHSS-FSLM32-MFFFFFNN
% 4.95/1.20 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 4.95/1.20 % Starting SubtermCWHack with 136s (1) cores
% 4.95/1.20 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 4.95/1.20 % Starting G-E--_208_B07_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 4.95/1.20 % Preprocessing time : 0.002 s
% 4.95/1.20 % Presaturation interreduction done
% 4.95/1.20
% 4.95/1.20 % Proof found!
% 4.95/1.20 % SZS status Theorem
% 4.95/1.20 % SZS output start CNFRefutation
% See solution above
% 4.95/1.20 % Parsed axioms : 34
% 4.95/1.20 % Removed by relevancy pruning/SinE : 0
% 4.95/1.20 % Initial clauses : 144
% 4.95/1.20 % Removed in clause preprocessing : 6
% 4.95/1.20 % Initial clauses in saturation : 138
% 4.95/1.20 % Processed clauses : 4357
% 4.95/1.20 % ...of these trivial : 6
% 4.95/1.20 % ...subsumed : 1886
% 4.95/1.20 % ...remaining for further processing : 2465
% 4.95/1.20 % Other redundant clauses eliminated : 83
% 4.95/1.20 % Clauses deleted for lack of memory : 0
% 4.95/1.20 % Backward-subsumed : 291
% 4.95/1.20 % Backward-rewritten : 479
% 4.95/1.20 % Generated clauses : 13988
% 4.95/1.20 % ...of the previous two non-redundant : 13648
% 4.95/1.20 % ...aggressively subsumed : 0
% 4.95/1.20 % Contextual simplify-reflections : 234
% 4.95/1.20 % Paramodulations : 13914
% 4.95/1.20 % Factorizations : 12
% 4.95/1.20 % NegExts : 0
% 4.95/1.20 % Equation resolutions : 96
% 4.95/1.20 % Disequality decompositions : 0
% 4.95/1.20 % Total rewrite steps : 2663
% 4.95/1.20 % ...of those cached : 2638
% 4.95/1.20 % Propositional unsat checks : 0
% 4.95/1.20 % Propositional check models : 0
% 4.95/1.20 % Propositional check unsatisfiable : 0
% 4.95/1.20 % Propositional clauses : 0
% 4.95/1.20 % Propositional clauses after purity: 0
% 4.95/1.20 % Propositional unsat core size : 0
% 4.95/1.20 % Propositional preprocessing time : 0.000
% 4.95/1.20 % Propositional encoding time : 0.000
% 4.95/1.20 % Propositional solver time : 0.000
% 4.95/1.20 % Success case prop preproc time : 0.000
% 4.95/1.20 % Success case prop encoding time : 0.000
% 4.95/1.20 % Success case prop solver time : 0.000
% 4.95/1.20 % Current number of processed clauses : 1511
% 4.95/1.20 % Positive orientable unit clauses : 24
% 4.95/1.20 % Positive unorientable unit clauses: 0
% 4.95/1.20 % Negative unit clauses : 12
% 4.95/1.20 % Non-unit-clauses : 1475
% 4.95/1.20 % Current number of unprocessed clauses: 8840
% 4.95/1.20 % ...number of literals in the above : 48233
% 4.95/1.20 % Current number of archived formulas : 0
% 4.95/1.20 % Current number of archived clauses : 909
% 4.95/1.20 % Clause-clause subsumption calls (NU) : 866170
% 4.95/1.20 % Rec. Clause-clause subsumption calls : 292515
% 4.95/1.20 % Non-unit clause-clause subsumptions : 2112
% 4.95/1.20 % Unit Clause-clause subsumption calls : 1770
% 4.95/1.20 % Rewrite failures with RHS unbound : 0
% 4.95/1.20 % BW rewrite match attempts : 6
% 4.95/1.20 % BW rewrite match successes : 6
% 4.95/1.20 % Condensation attempts : 0
% 4.95/1.20 % Condensation successes : 0
% 4.95/1.20 % Termbank termtop insertions : 766722
% 4.95/1.20 % Search garbage collected termcells : 1565
% 4.95/1.20
% 4.95/1.20 % -------------------------------------------------
% 4.95/1.20 % User time : 0.593 s
% 4.95/1.20 % System time : 0.010 s
% 4.95/1.20 % Total time : 0.603 s
% 4.95/1.20 % Maximum resident set size: 3936 pages
% 4.95/1.20
% 4.95/1.20 % -------------------------------------------------
% 4.95/1.20 % User time : 2.911 s
% 4.95/1.20 % System time : 0.055 s
% 4.95/1.20 % Total time : 2.966 s
% 4.95/1.20 % Maximum resident set size: 4864 pages
% 4.95/1.20 % E exiting
%------------------------------------------------------------------------------