%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU329+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n029.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 : Tue May 5 05:11:30 PM UTC 2026
% Result : Theorem 5.95s 4.44s
% Output : CNFRefutation 5.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 2
% Syntax : Number of formulae : 133 ( 8 unt; 0 def)
% Number of atoms : 1133 ( 397 equ)
% Maximal formula atoms : 518 ( 8 avg)
% Number of connectives : 1679 ( 679 ~; 883 |; 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 : 367 ( 10 sgn 35 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_xboole_0__e4_7_1__tops_2__1,conjecture,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ! [X3] :
? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(X5,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
& ? [X6,X7] :
( ordered_pair(X6,X7) = X5
& in(X6,complements_of_subsets(the_carrier(X1),X2))
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X6
=> X7 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e4_7_1__tops_2__1) ).
fof(s1_tarski__e4_7_1__tops_2__2,axiom,
! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ! [X3] :
( ! [X4,X5,X6] :
( ( X4 = X5
& ? [X7,X8] :
( ordered_pair(X7,X8) = X5
& in(X7,complements_of_subsets(the_carrier(X1),X2))
& ! [X9] :
( element(X9,powerset(the_carrier(X1)))
=> ( X9 = X7
=> X8 = subset_complement(the_carrier(X1),X9) ) ) )
& X4 = X6
& ? [X10,X11] :
( ordered_pair(X10,X11) = X6
& in(X10,complements_of_subsets(the_carrier(X1),X2))
& ! [X12] :
( element(X12,powerset(the_carrier(X1)))
=> ( X12 = X10
=> X11 = subset_complement(the_carrier(X1),X12) ) ) ) )
=> X5 = X6 )
=> ? [X4] :
! [X5] :
( in(X5,X4)
<=> ? [X6] :
( in(X6,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
& X6 = X5
& ? [X13,X14] :
( ordered_pair(X13,X14) = X5
& in(X13,complements_of_subsets(the_carrier(X1),X2))
& ! [X15] :
( element(X15,powerset(the_carrier(X1)))
=> ( X15 = X13
=> X14 = subset_complement(the_carrier(X1),X15) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e4_7_1__tops_2__2) ).
fof(c_0_2,negated_conjecture,
~ ! [X1,X2] :
( ( one_sorted_str(X1)
& element(X2,powerset(powerset(the_carrier(X1)))) )
=> ! [X3] :
? [X4] :
! [X5] :
( in(X5,X4)
<=> ( in(X5,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
& ? [X6,X7] :
( ordered_pair(X6,X7) = X5
& in(X6,complements_of_subsets(the_carrier(X1),X2))
& ! [X8] :
( element(X8,powerset(the_carrier(X1)))
=> ( X8 = X6
=> X7 = subset_complement(the_carrier(X1),X8) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[s1_xboole_0__e4_7_1__tops_2__1]) ).
fof(c_0_3,plain,
! [X145,X146,X152,X155,X156,X158,X162,X163,X164,X165,X166] :
( ( in(esk19_4(X145,X146,X156,X158),cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| ~ in(X158,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk19_4(X145,X146,X156,X158) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ordered_pair(esk20_4(X145,X146,X156,X158),esk21_4(X145,X146,X156,X158)) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk20_4(X145,X146,X156,X158),complements_of_subsets(the_carrier(X145),X146))
| ~ in(X158,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ~ element(X162,powerset(the_carrier(X145)))
| X162 != esk20_4(X145,X146,X156,X158)
| esk21_4(X145,X146,X156,X158) = subset_complement(the_carrier(X145),X162)
| ~ in(X158,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( element(esk22_6(X145,X146,X156,X163,X165,X166),powerset(the_carrier(X145)))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk22_6(X145,X146,X156,X163,X165,X166) = X165
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( X166 != subset_complement(the_carrier(X145),esk22_6(X145,X146,X156,X163,X165,X166))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk19_4(X145,X146,X156,X158),cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| ~ in(X158,esk18_3(X145,X146,X156))
| ordered_pair(esk14_2(X145,X146),esk15_2(X145,X146)) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk19_4(X145,X146,X156,X158) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| ordered_pair(esk14_2(X145,X146),esk15_2(X145,X146)) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ordered_pair(esk20_4(X145,X146,X156,X158),esk21_4(X145,X146,X156,X158)) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| ordered_pair(esk14_2(X145,X146),esk15_2(X145,X146)) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk20_4(X145,X146,X156,X158),complements_of_subsets(the_carrier(X145),X146))
| ~ in(X158,esk18_3(X145,X146,X156))
| ordered_pair(esk14_2(X145,X146),esk15_2(X145,X146)) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ~ element(X162,powerset(the_carrier(X145)))
| X162 != esk20_4(X145,X146,X156,X158)
| esk21_4(X145,X146,X156,X158) = subset_complement(the_carrier(X145),X162)
| ~ in(X158,esk18_3(X145,X146,X156))
| ordered_pair(esk14_2(X145,X146),esk15_2(X145,X146)) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( element(esk22_6(X145,X146,X156,X163,X165,X166),powerset(the_carrier(X145)))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ordered_pair(esk14_2(X145,X146),esk15_2(X145,X146)) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk22_6(X145,X146,X156,X163,X165,X166) = X165
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ordered_pair(esk14_2(X145,X146),esk15_2(X145,X146)) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( X166 != subset_complement(the_carrier(X145),esk22_6(X145,X146,X156,X163,X165,X166))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ordered_pair(esk14_2(X145,X146),esk15_2(X145,X146)) = esk12_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk19_4(X145,X146,X156,X158),cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| ~ in(X158,esk18_3(X145,X146,X156))
| in(esk14_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk19_4(X145,X146,X156,X158) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| in(esk14_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ordered_pair(esk20_4(X145,X146,X156,X158),esk21_4(X145,X146,X156,X158)) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| in(esk14_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk20_4(X145,X146,X156,X158),complements_of_subsets(the_carrier(X145),X146))
| ~ in(X158,esk18_3(X145,X146,X156))
| in(esk14_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ~ element(X162,powerset(the_carrier(X145)))
| X162 != esk20_4(X145,X146,X156,X158)
| esk21_4(X145,X146,X156,X158) = subset_complement(the_carrier(X145),X162)
| ~ in(X158,esk18_3(X145,X146,X156))
| in(esk14_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( element(esk22_6(X145,X146,X156,X163,X165,X166),powerset(the_carrier(X145)))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| in(esk14_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk22_6(X145,X146,X156,X163,X165,X166) = X165
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| in(esk14_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( X166 != subset_complement(the_carrier(X145),esk22_6(X145,X146,X156,X163,X165,X166))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| in(esk14_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk19_4(X145,X146,X156,X158),cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| ~ in(X158,esk18_3(X145,X146,X156))
| ~ element(X152,powerset(the_carrier(X145)))
| X152 != esk14_2(X145,X146)
| esk15_2(X145,X146) = subset_complement(the_carrier(X145),X152)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk19_4(X145,X146,X156,X158) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| ~ element(X152,powerset(the_carrier(X145)))
| X152 != esk14_2(X145,X146)
| esk15_2(X145,X146) = subset_complement(the_carrier(X145),X152)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ordered_pair(esk20_4(X145,X146,X156,X158),esk21_4(X145,X146,X156,X158)) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| ~ element(X152,powerset(the_carrier(X145)))
| X152 != esk14_2(X145,X146)
| esk15_2(X145,X146) = subset_complement(the_carrier(X145),X152)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk20_4(X145,X146,X156,X158),complements_of_subsets(the_carrier(X145),X146))
| ~ in(X158,esk18_3(X145,X146,X156))
| ~ element(X152,powerset(the_carrier(X145)))
| X152 != esk14_2(X145,X146)
| esk15_2(X145,X146) = subset_complement(the_carrier(X145),X152)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ~ element(X162,powerset(the_carrier(X145)))
| X162 != esk20_4(X145,X146,X156,X158)
| esk21_4(X145,X146,X156,X158) = subset_complement(the_carrier(X145),X162)
| ~ in(X158,esk18_3(X145,X146,X156))
| ~ element(X152,powerset(the_carrier(X145)))
| X152 != esk14_2(X145,X146)
| esk15_2(X145,X146) = subset_complement(the_carrier(X145),X152)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( element(esk22_6(X145,X146,X156,X163,X165,X166),powerset(the_carrier(X145)))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ~ element(X152,powerset(the_carrier(X145)))
| X152 != esk14_2(X145,X146)
| esk15_2(X145,X146) = subset_complement(the_carrier(X145),X152)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk22_6(X145,X146,X156,X163,X165,X166) = X165
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ~ element(X152,powerset(the_carrier(X145)))
| X152 != esk14_2(X145,X146)
| esk15_2(X145,X146) = subset_complement(the_carrier(X145),X152)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( X166 != subset_complement(the_carrier(X145),esk22_6(X145,X146,X156,X163,X165,X166))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ~ element(X152,powerset(the_carrier(X145)))
| X152 != esk14_2(X145,X146)
| esk15_2(X145,X146) = subset_complement(the_carrier(X145),X152)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk19_4(X145,X146,X156,X158),cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| ~ in(X158,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk19_4(X145,X146,X156,X158) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ordered_pair(esk20_4(X145,X146,X156,X158),esk21_4(X145,X146,X156,X158)) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk20_4(X145,X146,X156,X158),complements_of_subsets(the_carrier(X145),X146))
| ~ in(X158,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ~ element(X162,powerset(the_carrier(X145)))
| X162 != esk20_4(X145,X146,X156,X158)
| esk21_4(X145,X146,X156,X158) = subset_complement(the_carrier(X145),X162)
| ~ in(X158,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( element(esk22_6(X145,X146,X156,X163,X165,X166),powerset(the_carrier(X145)))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk22_6(X145,X146,X156,X163,X165,X166) = X165
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( X166 != subset_complement(the_carrier(X145),esk22_6(X145,X146,X156,X163,X165,X166))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| esk11_2(X145,X146) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk19_4(X145,X146,X156,X158),cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| ~ in(X158,esk18_3(X145,X146,X156))
| ordered_pair(esk16_2(X145,X146),esk17_2(X145,X146)) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk19_4(X145,X146,X156,X158) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| ordered_pair(esk16_2(X145,X146),esk17_2(X145,X146)) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ordered_pair(esk20_4(X145,X146,X156,X158),esk21_4(X145,X146,X156,X158)) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| ordered_pair(esk16_2(X145,X146),esk17_2(X145,X146)) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk20_4(X145,X146,X156,X158),complements_of_subsets(the_carrier(X145),X146))
| ~ in(X158,esk18_3(X145,X146,X156))
| ordered_pair(esk16_2(X145,X146),esk17_2(X145,X146)) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ~ element(X162,powerset(the_carrier(X145)))
| X162 != esk20_4(X145,X146,X156,X158)
| esk21_4(X145,X146,X156,X158) = subset_complement(the_carrier(X145),X162)
| ~ in(X158,esk18_3(X145,X146,X156))
| ordered_pair(esk16_2(X145,X146),esk17_2(X145,X146)) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( element(esk22_6(X145,X146,X156,X163,X165,X166),powerset(the_carrier(X145)))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ordered_pair(esk16_2(X145,X146),esk17_2(X145,X146)) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk22_6(X145,X146,X156,X163,X165,X166) = X165
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ordered_pair(esk16_2(X145,X146),esk17_2(X145,X146)) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( X166 != subset_complement(the_carrier(X145),esk22_6(X145,X146,X156,X163,X165,X166))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ordered_pair(esk16_2(X145,X146),esk17_2(X145,X146)) = esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk19_4(X145,X146,X156,X158),cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| ~ in(X158,esk18_3(X145,X146,X156))
| in(esk16_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk19_4(X145,X146,X156,X158) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| in(esk16_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ordered_pair(esk20_4(X145,X146,X156,X158),esk21_4(X145,X146,X156,X158)) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| in(esk16_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk20_4(X145,X146,X156,X158),complements_of_subsets(the_carrier(X145),X146))
| ~ in(X158,esk18_3(X145,X146,X156))
| in(esk16_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ~ element(X162,powerset(the_carrier(X145)))
| X162 != esk20_4(X145,X146,X156,X158)
| esk21_4(X145,X146,X156,X158) = subset_complement(the_carrier(X145),X162)
| ~ in(X158,esk18_3(X145,X146,X156))
| in(esk16_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( element(esk22_6(X145,X146,X156,X163,X165,X166),powerset(the_carrier(X145)))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| in(esk16_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk22_6(X145,X146,X156,X163,X165,X166) = X165
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| in(esk16_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( X166 != subset_complement(the_carrier(X145),esk22_6(X145,X146,X156,X163,X165,X166))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| in(esk16_2(X145,X146),complements_of_subsets(the_carrier(X145),X146))
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk19_4(X145,X146,X156,X158),cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| ~ in(X158,esk18_3(X145,X146,X156))
| ~ element(X155,powerset(the_carrier(X145)))
| X155 != esk16_2(X145,X146)
| esk17_2(X145,X146) = subset_complement(the_carrier(X145),X155)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk19_4(X145,X146,X156,X158) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| ~ element(X155,powerset(the_carrier(X145)))
| X155 != esk16_2(X145,X146)
| esk17_2(X145,X146) = subset_complement(the_carrier(X145),X155)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ordered_pair(esk20_4(X145,X146,X156,X158),esk21_4(X145,X146,X156,X158)) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| ~ element(X155,powerset(the_carrier(X145)))
| X155 != esk16_2(X145,X146)
| esk17_2(X145,X146) = subset_complement(the_carrier(X145),X155)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk20_4(X145,X146,X156,X158),complements_of_subsets(the_carrier(X145),X146))
| ~ in(X158,esk18_3(X145,X146,X156))
| ~ element(X155,powerset(the_carrier(X145)))
| X155 != esk16_2(X145,X146)
| esk17_2(X145,X146) = subset_complement(the_carrier(X145),X155)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ~ element(X162,powerset(the_carrier(X145)))
| X162 != esk20_4(X145,X146,X156,X158)
| esk21_4(X145,X146,X156,X158) = subset_complement(the_carrier(X145),X162)
| ~ in(X158,esk18_3(X145,X146,X156))
| ~ element(X155,powerset(the_carrier(X145)))
| X155 != esk16_2(X145,X146)
| esk17_2(X145,X146) = subset_complement(the_carrier(X145),X155)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( element(esk22_6(X145,X146,X156,X163,X165,X166),powerset(the_carrier(X145)))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ~ element(X155,powerset(the_carrier(X145)))
| X155 != esk16_2(X145,X146)
| esk17_2(X145,X146) = subset_complement(the_carrier(X145),X155)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk22_6(X145,X146,X156,X163,X165,X166) = X165
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ~ element(X155,powerset(the_carrier(X145)))
| X155 != esk16_2(X145,X146)
| esk17_2(X145,X146) = subset_complement(the_carrier(X145),X155)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( X166 != subset_complement(the_carrier(X145),esk22_6(X145,X146,X156,X163,X165,X166))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| ~ element(X155,powerset(the_carrier(X145)))
| X155 != esk16_2(X145,X146)
| esk17_2(X145,X146) = subset_complement(the_carrier(X145),X155)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk19_4(X145,X146,X156,X158),cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| ~ in(X158,esk18_3(X145,X146,X156))
| esk12_2(X145,X146) != esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk19_4(X145,X146,X156,X158) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| esk12_2(X145,X146) != esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ordered_pair(esk20_4(X145,X146,X156,X158),esk21_4(X145,X146,X156,X158)) = X158
| ~ in(X158,esk18_3(X145,X146,X156))
| esk12_2(X145,X146) != esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( in(esk20_4(X145,X146,X156,X158),complements_of_subsets(the_carrier(X145),X146))
| ~ in(X158,esk18_3(X145,X146,X156))
| esk12_2(X145,X146) != esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( ~ element(X162,powerset(the_carrier(X145)))
| X162 != esk20_4(X145,X146,X156,X158)
| esk21_4(X145,X146,X156,X158) = subset_complement(the_carrier(X145),X162)
| ~ in(X158,esk18_3(X145,X146,X156))
| esk12_2(X145,X146) != esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( element(esk22_6(X145,X146,X156,X163,X165,X166),powerset(the_carrier(X145)))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| esk12_2(X145,X146) != esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( esk22_6(X145,X146,X156,X163,X165,X166) = X165
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| esk12_2(X145,X146) != esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) )
& ( X166 != subset_complement(the_carrier(X145),esk22_6(X145,X146,X156,X163,X165,X166))
| ordered_pair(X165,X166) != X163
| ~ in(X165,complements_of_subsets(the_carrier(X145),X146))
| ~ in(X164,cartesian_product2(complements_of_subsets(the_carrier(X145),X146),X156))
| X164 != X163
| in(X163,esk18_3(X145,X146,X156))
| esk12_2(X145,X146) != esk13_2(X145,X146)
| ~ one_sorted_str(X145)
| ~ element(X146,powerset(powerset(the_carrier(X145)))) ) ),
inference(distribute,[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_4,negated_conjecture,
! [X91,X93,X94,X98] :
( one_sorted_str(esk1_0)
& element(esk2_0,powerset(powerset(the_carrier(esk1_0))))
& ( element(esk5_3(X91,X93,X94),powerset(the_carrier(esk1_0)))
| ordered_pair(X93,X94) != esk4_1(X91)
| ~ in(X93,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(X91),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(esk4_1(X91),X91) )
& ( esk5_3(X91,X93,X94) = X93
| ordered_pair(X93,X94) != esk4_1(X91)
| ~ in(X93,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(X91),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(esk4_1(X91),X91) )
& ( X94 != subset_complement(the_carrier(esk1_0),esk5_3(X91,X93,X94))
| ordered_pair(X93,X94) != esk4_1(X91)
| ~ in(X93,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(X91),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(esk4_1(X91),X91) )
& ( in(esk4_1(X91),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| in(esk4_1(X91),X91) )
& ( ordered_pair(esk6_1(X91),esk7_1(X91)) = esk4_1(X91)
| in(esk4_1(X91),X91) )
& ( in(esk6_1(X91),complements_of_subsets(the_carrier(esk1_0),esk2_0))
| in(esk4_1(X91),X91) )
& ( ~ element(X98,powerset(the_carrier(esk1_0)))
| X98 != esk6_1(X91)
| esk7_1(X91) = subset_complement(the_carrier(esk1_0),X98)
| in(esk4_1(X91),X91) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_2])])])])]) ).
cnf(c_0_5,plain,
( in(esk19_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,negated_conjecture,
element(esk2_0,powerset(powerset(the_carrier(esk1_0)))),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
one_sorted_str(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( esk19_4(X1,X2,X3,X4) = X4
| esk11_2(X1,X2) = esk12_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_9,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk19_4(esk1_0,esk2_0,X1,X2),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X1))
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_6]),c_0_7])]) ).
cnf(c_0_10,negated_conjecture,
( in(esk4_1(X1),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| in(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| esk19_4(esk1_0,esk2_0,X1,X2) = X2
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_6]),c_0_7])]) ).
cnf(c_0_12,plain,
( esk22_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_13,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_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))
| in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( 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))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_15,plain,
( in(X5,esk18_3(X2,X3,X4))
| esk11_2(X2,X3) = esk12_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk22_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_16,plain,
( esk22_6(X1,X2,X3,ordered_pair(X4,X5),X4,X5) = X4
| esk11_2(X1,X2) = esk12_2(X1,X2)
| in(ordered_pair(X4,X5),esk18_3(X1,X2,X3))
| ~ in(ordered_pair(X4,X5),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_12])]) ).
cnf(c_0_17,negated_conjecture,
( ordered_pair(esk6_1(X1),esk7_1(X1)) = esk4_1(X1)
| in(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_18,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
( element(esk22_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_20,plain,
( esk11_2(X1,X2) = esk12_2(X1,X2)
| in(ordered_pair(X3,X4),esk18_3(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),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X5))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_15])]) ).
cnf(c_0_21,negated_conjecture,
( esk22_6(X1,X2,X3,esk4_1(X4),esk6_1(X4),esk7_1(X4)) = esk6_1(X4)
| esk11_2(X1,X2) = esk12_2(X1,X2)
| in(esk4_1(X4),esk18_3(X1,X2,X3))
| in(esk4_1(X4),X4)
| ~ in(esk4_1(X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(esk6_1(X4),complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0)) ),
inference(ef,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( in(esk6_1(X1),complements_of_subsets(the_carrier(esk1_0),esk2_0))
| in(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_24,plain,
( esk11_2(X1,X2) = esk12_2(X1,X2)
| in(ordered_pair(X3,X4),esk18_3(X1,X2,X5))
| element(esk22_6(X1,X2,X5,ordered_pair(X3,X4),X3,X4),powerset(the_carrier(X1)))
| ~ in(ordered_pair(X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X5))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_19])]) ).
cnf(c_0_25,negated_conjecture,
( esk11_2(X1,X2) = esk12_2(X1,X2)
| in(esk4_1(X3),esk18_3(X1,X2,X4))
| in(esk4_1(X3),X3)
| 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),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X4))
| ~ in(esk6_1(X3),complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
( 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))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),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_21,c_0_22]),c_0_6]),c_0_7])]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( esk7_1(X2) = subset_complement(the_carrier(esk1_0),X1)
| in(esk4_1(X2),X2)
| ~ element(X1,powerset(the_carrier(esk1_0)))
| X1 != esk6_1(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_28,negated_conjecture,
( element(esk5_3(X1,X2,X3),powerset(the_carrier(esk1_0)))
| ordered_pair(X2,X3) != esk4_1(X1)
| ~ in(X2,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(X1),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_29,negated_conjecture,
( esk5_3(X1,X2,X3) = X2
| ordered_pair(X2,X3) != esk4_1(X1)
| ~ in(X2,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(X1),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(esk4_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_30,negated_conjecture,
( esk11_2(X1,X2) = esk12_2(X1,X2)
| in(esk4_1(X3),esk18_3(X1,X2,X4))
| in(esk4_1(X3),X3)
| element(esk22_6(X1,X2,X4,esk4_1(X3),esk6_1(X3),esk7_1(X3)),powerset(the_carrier(X1)))
| ~ in(esk4_1(X3),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X4))
| ~ in(esk6_1(X3),complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_17]) ).
cnf(c_0_31,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_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(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_25,c_0_26]),c_0_6]),c_0_7])]),c_0_23]),c_0_22]) ).
cnf(c_0_32,negated_conjecture,
( esk7_1(X1) = subset_complement(the_carrier(esk1_0),esk6_1(X1))
| in(esk4_1(X1),X1)
| ~ element(esk6_1(X1),powerset(the_carrier(esk1_0))) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_33,negated_conjecture,
( element(X1,powerset(the_carrier(esk1_0)))
| ordered_pair(X1,X2) != esk4_1(X3)
| ~ in(esk4_1(X3),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(X3),X3) ),
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)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| in(esk4_1(X1),X1)
| element(esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(X1),esk6_1(X1),esk7_1(X1)),powerset(the_carrier(esk1_0))) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_10]),c_0_6]),c_0_7])]),c_0_23]) ).
cnf(c_0_35,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| ~ element(esk6_1(esk18_3(esk1_0,esk2_0,esk3_0)),powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( in(esk20_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_37,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| element(X1,powerset(the_carrier(esk1_0)))
| ordered_pair(X1,X2) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_38,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_26]),c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( esk11_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))
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_6]),c_0_7])]) ).
cnf(c_0_40,plain,
( ordered_pair(esk20_4(X1,X2,X3,X4),esk21_4(X1,X2,X3,X4)) = X4
| esk11_2(X1,X2) = esk12_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_41,negated_conjecture,
( X1 != subset_complement(the_carrier(esk1_0),esk5_3(X2,X3,X1))
| ordered_pair(X3,X1) != esk4_1(X2)
| ~ in(X3,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))
| ~ in(esk4_1(X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_42,plain,
( esk22_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_43,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| element(X1,powerset(the_carrier(esk1_0)))
| ordered_pair(X1,X2) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| 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)) ),
inference(spm,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),esk21_4(esk1_0,esk2_0,X1,X2)) = X2
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_6]),c_0_7])]) ).
cnf(c_0_46,negated_conjecture,
( ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(X2)
| ~ in(esk4_1(X2),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(esk4_1(X2),X2) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_29])]) ).
cnf(c_0_47,plain,
( in(X5,esk18_3(X2,X3,X4))
| esk11_2(X2,X3) = esk13_2(X2,X3)
| X1 != subset_complement(the_carrier(X2),esk22_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_48,plain,
( esk22_6(X1,X2,X3,ordered_pair(X4,X5),X4,X5) = X4
| esk11_2(X1,X2) = esk13_2(X1,X2)
| in(ordered_pair(X4,X5),esk18_3(X1,X2,X3))
| ~ in(ordered_pair(X4,X5),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_42])]) ).
cnf(c_0_49,plain,
( in(esk19_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_50,plain,
( esk19_4(X1,X2,X3,X4) = X4
| esk11_2(X1,X2) = esk13_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_51,plain,
( esk21_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| esk11_2(X2,X3) = esk12_2(X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk20_4(X2,X3,X4,X5)
| ~ in(X5,esk18_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_52,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_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)))
| 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)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
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))),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))
| esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_38]) ).
cnf(c_0_54,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(spm,[status(thm)],[c_0_46,c_0_22]) ).
cnf(c_0_55,plain,
( in(esk19_4(X1,X2,X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(X4,esk18_3(X1,X2,X3))
| esk12_2(X1,X2) != esk13_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_56,plain,
( esk19_4(X1,X2,X3,X4) = X4
| ~ in(X4,esk18_3(X1,X2,X3))
| esk12_2(X1,X2) != esk13_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_57,plain,
( esk11_2(X1,X2) = esk13_2(X1,X2)
| in(ordered_pair(X3,X4),esk18_3(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),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X5))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_47])]) ).
cnf(c_0_58,negated_conjecture,
( esk22_6(X1,X2,X3,esk4_1(X4),esk6_1(X4),esk7_1(X4)) = esk6_1(X4)
| esk11_2(X1,X2) = esk13_2(X1,X2)
| in(esk4_1(X4),esk18_3(X1,X2,X3))
| in(esk4_1(X4),X4)
| ~ in(esk4_1(X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(esk6_1(X4),complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_17]) ).
cnf(c_0_59,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0)
| in(esk19_4(esk1_0,esk2_0,X1,X2),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X1))
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_6]),c_0_7])]) ).
cnf(c_0_60,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0)
| esk19_4(esk1_0,esk2_0,X1,X2) = X2
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_6]),c_0_7])]) ).
cnf(c_0_61,plain,
( esk21_4(X1,X2,X3,X4) = subset_complement(the_carrier(X1),esk20_4(X1,X2,X3,X4))
| esk11_2(X1,X2) = esk12_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ element(esk20_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_62,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_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))) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_63,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(spm,[status(thm)],[c_0_54,c_0_38]) ).
cnf(c_0_64,plain,
( in(X1,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| esk13_2(X2,X3) != esk12_2(X2,X3)
| ~ in(X1,esk18_3(X2,X3,X4))
| ~ element(X3,powerset(powerset(the_carrier(X2))))
| ~ one_sorted_str(X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_65,plain,
( element(esk22_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk18_3(X1,X2,X3))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_66,negated_conjecture,
( esk11_2(X1,X2) = esk13_2(X1,X2)
| in(esk4_1(X3),esk18_3(X1,X2,X4))
| in(esk4_1(X3),X3)
| 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),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X4))
| ~ in(esk6_1(X3),complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_17]) ).
cnf(c_0_67,negated_conjecture,
( esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(X1),esk6_1(X1),esk7_1(X1)) = esk6_1(X1)
| esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| in(esk4_1(X1),X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_10]),c_0_6]),c_0_7])]),c_0_23]) ).
cnf(c_0_68,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_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))
| in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_59,c_0_10]) ).
cnf(c_0_69,negated_conjecture,
( 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))
| esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0)
| in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0)) ),
inference(spm,[status(thm)],[c_0_60,c_0_10]) ).
cnf(c_0_70,negated_conjecture,
( 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))))
| 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_61,c_0_62]),c_0_6]),c_0_7])]),c_0_38]) ).
cnf(c_0_71,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))),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_63,c_0_44]) ).
cnf(c_0_72,negated_conjecture,
( in(esk4_1(esk18_3(X1,X2,X3)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| in(esk4_1(esk18_3(X1,X2,X3)),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| esk13_2(X1,X2) != esk12_2(X1,X2)
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_10]) ).
cnf(c_0_73,plain,
( esk11_2(X1,X2) = esk13_2(X1,X2)
| in(ordered_pair(X3,X4),esk18_3(X1,X2,X5))
| element(esk22_6(X1,X2,X5,ordered_pair(X3,X4),X3,X4),powerset(the_carrier(X1)))
| ~ in(ordered_pair(X3,X4),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X5))
| ~ in(X3,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_65])]) ).
cnf(c_0_74,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| in(esk4_1(X1),X1)
| esk7_1(X1) != subset_complement(the_carrier(esk1_0),esk6_1(X1)) ),
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_66,c_0_67]),c_0_6]),c_0_7])]),c_0_23]),c_0_10]) ).
cnf(c_0_75,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0)
| in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),esk3_0))
| in(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X1)) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_76,negated_conjecture,
esk11_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_70]),c_0_71]) ).
cnf(c_0_77,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(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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_6]),c_0_7])]) ).
cnf(c_0_78,negated_conjecture,
( esk11_2(X1,X2) = esk13_2(X1,X2)
| in(esk4_1(X3),esk18_3(X1,X2,X4))
| in(esk4_1(X3),X3)
| element(esk22_6(X1,X2,X4,esk4_1(X3),esk6_1(X3),esk7_1(X3)),powerset(the_carrier(X1)))
| ~ in(esk4_1(X3),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X4))
| ~ in(esk6_1(X3),complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_17]) ).
cnf(c_0_79,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| in(esk4_1(X1),X1)
| ~ element(esk6_1(X1),powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_74,c_0_32]) ).
cnf(c_0_80,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(esk4_1(esk18_3(esk1_0,esk2_0,X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X1)) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_81,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| in(esk4_1(X1),X1)
| element(esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(X1),esk6_1(X1),esk7_1(X1)),powerset(the_carrier(esk1_0))) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_10]),c_0_6]),c_0_7])]),c_0_76]),c_0_23]) ).
cnf(c_0_82,negated_conjecture,
( esk22_6(esk1_0,esk2_0,esk3_0,esk4_1(X1),esk6_1(X1),esk7_1(X1)) = esk6_1(X1)
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| in(esk4_1(X1),X1) ),
inference(rw,[status(thm)],[c_0_67,c_0_76]) ).
cnf(c_0_83,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| in(esk4_1(X1),X1)
| ~ element(esk6_1(X1),powerset(the_carrier(esk1_0))) ),
inference(rw,[status(thm)],[c_0_79,c_0_76]) ).
cnf(c_0_84,plain,
( in(esk20_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_85,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)),
inference(ef,[status(thm)],[c_0_80]) ).
cnf(c_0_86,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| in(esk4_1(X1),esk18_3(esk1_0,esk2_0,esk3_0))
| in(esk4_1(X1),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]) ).
cnf(c_0_87,negated_conjecture,
( esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0)
| in(esk20_4(esk1_0,esk2_0,X1,X2),complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_6]),c_0_7])]) ).
cnf(c_0_88,negated_conjecture,
( element(X1,powerset(the_carrier(esk1_0)))
| ordered_pair(X1,X2) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_85]) ).
cnf(c_0_89,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| 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_86]) ).
cnf(c_0_90,negated_conjecture,
( 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))
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(rw,[status(thm)],[c_0_87,c_0_76]) ).
cnf(c_0_91,plain,
( ordered_pair(esk20_4(X1,X2,X3,X4),esk21_4(X1,X2,X3,X4)) = X4
| esk11_2(X1,X2) = esk13_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_92,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| element(X1,powerset(the_carrier(esk1_0)))
| ordered_pair(X1,X2) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| 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)) ),
inference(spm,[status(thm)],[c_0_90,c_0_89]) ).
cnf(c_0_94,negated_conjecture,
( ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),esk21_4(esk1_0,esk2_0,X1,X2)) = X2
| esk11_2(esk1_0,esk2_0) = esk13_2(esk1_0,esk2_0)
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_6]),c_0_7])]) ).
cnf(c_0_95,plain,
( esk21_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| esk11_2(X2,X3) = esk13_2(X2,X3)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk20_4(X2,X3,X4,X5)
| ~ in(X5,esk18_3(X2,X3,X4))
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_96,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_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)))
| 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)) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_97,negated_conjecture,
( ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),esk21_4(esk1_0,esk2_0,X1,X2)) = X2
| esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(rw,[status(thm)],[c_0_94,c_0_76]) ).
cnf(c_0_98,negated_conjecture,
( ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(spm,[status(thm)],[c_0_46,c_0_85]) ).
cnf(c_0_99,plain,
( esk21_4(X1,X2,X3,X4) = subset_complement(the_carrier(X1),esk20_4(X1,X2,X3,X4))
| esk11_2(X1,X2) = esk13_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ element(esk20_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(er,[status(thm)],[c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_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))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_89]) ).
cnf(c_0_101,negated_conjecture,
( esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0)
| ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(spm,[status(thm)],[c_0_98,c_0_89]) ).
cnf(c_0_102,plain,
( esk22_6(X1,X2,X3,X4,X5,X6) = X5
| in(X4,esk18_3(X1,X2,X3))
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| esk12_2(X1,X2) != esk13_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_103,negated_conjecture,
( 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))))
| 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_99,c_0_100]),c_0_76]),c_0_6]),c_0_7])]),c_0_89]) ).
cnf(c_0_104,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_101,c_0_93]) ).
cnf(c_0_105,plain,
( element(esk22_6(X1,X2,X3,X4,X5,X6),powerset(the_carrier(X1)))
| in(X4,esk18_3(X1,X2,X3))
| ordered_pair(X5,X6) != X4
| ~ in(X5,complements_of_subsets(the_carrier(X1),X2))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| X7 != X4
| esk12_2(X1,X2) != esk13_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_106,plain,
( in(X5,esk18_3(X2,X3,X4))
| X1 != subset_complement(the_carrier(X2),esk22_6(X2,X3,X4,X5,X6,X1))
| ordered_pair(X6,X1) != X5
| ~ in(X6,complements_of_subsets(the_carrier(X2),X3))
| ~ in(X7,cartesian_product2(complements_of_subsets(the_carrier(X2),X3),X4))
| X7 != X5
| esk12_2(X2,X3) != esk13_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_107,plain,
( esk22_6(X1,X2,X3,ordered_pair(X4,X5),X4,X5) = X4
| in(ordered_pair(X4,X5),esk18_3(X1,X2,X3))
| esk13_2(X1,X2) != esk12_2(X1,X2)
| ~ in(ordered_pair(X4,X5),cartesian_product2(complements_of_subsets(the_carrier(X1),X2),X3))
| ~ in(X4,complements_of_subsets(the_carrier(X1),X2))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_102])]) ).
cnf(c_0_108,negated_conjecture,
esk13_2(esk1_0,esk2_0) = esk12_2(esk1_0,esk2_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_103]),c_0_89]),c_0_104]) ).
cnf(c_0_109,plain,
( in(ordered_pair(X1,X2),esk18_3(X3,X4,X5))
| element(esk22_6(X3,X4,X5,ordered_pair(X1,X2),X1,X2),powerset(the_carrier(X3)))
| esk13_2(X3,X4) != esk12_2(X3,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(complements_of_subsets(the_carrier(X3),X4),X5))
| ~ in(X1,complements_of_subsets(the_carrier(X3),X4))
| ~ element(X4,powerset(powerset(the_carrier(X3))))
| ~ one_sorted_str(X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_105])]) ).
cnf(c_0_110,plain,
( in(ordered_pair(X1,X2),esk18_3(X3,X4,X5))
| subset_complement(the_carrier(X3),esk22_6(X3,X4,X5,ordered_pair(X1,X2),X1,X2)) != X2
| esk13_2(X3,X4) != esk12_2(X3,X4)
| ~ in(ordered_pair(X1,X2),cartesian_product2(complements_of_subsets(the_carrier(X3),X4),X5))
| ~ in(X1,complements_of_subsets(the_carrier(X3),X4))
| ~ element(X4,powerset(powerset(the_carrier(X3))))
| ~ one_sorted_str(X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_106])]) ).
cnf(c_0_111,negated_conjecture,
( esk22_6(esk1_0,esk2_0,X1,ordered_pair(X2,X3),X2,X3) = X2
| in(ordered_pair(X2,X3),esk18_3(esk1_0,esk2_0,X1))
| ~ in(ordered_pair(X2,X3),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X1))
| ~ in(X2,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_6]),c_0_7])]) ).
cnf(c_0_112,negated_conjecture,
( in(ordered_pair(X1,X2),esk18_3(esk1_0,esk2_0,X3))
| element(esk22_6(esk1_0,esk2_0,X3,ordered_pair(X1,X2),X1,X2),powerset(the_carrier(esk1_0)))
| ~ in(ordered_pair(X1,X2),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X3))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_108]),c_0_6]),c_0_7])]) ).
cnf(c_0_113,negated_conjecture,
( in(ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)),esk18_3(esk1_0,esk2_0,X2))
| ~ in(ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X2))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_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_110,c_0_111]),c_0_108]),c_0_6]),c_0_7])])]) ).
cnf(c_0_114,negated_conjecture,
( ordered_pair(esk6_1(X1),subset_complement(the_carrier(esk1_0),esk6_1(X1))) = esk4_1(X1)
| in(esk4_1(X1),X1)
| ~ element(esk6_1(X1),powerset(the_carrier(esk1_0))) ),
inference(spm,[status(thm)],[c_0_17,c_0_32]) ).
cnf(c_0_115,negated_conjecture,
( in(ordered_pair(X1,X2),esk18_3(esk1_0,esk2_0,X3))
| element(X1,powerset(the_carrier(esk1_0)))
| ~ in(ordered_pair(X1,X2),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X3))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(spm,[status(thm)],[c_0_112,c_0_111]) ).
cnf(c_0_116,negated_conjecture,
( in(esk4_1(X1),esk18_3(esk1_0,esk2_0,X2))
| in(esk4_1(X1),X1)
| ~ in(esk4_1(X1),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X2))
| ~ element(esk6_1(X1),powerset(the_carrier(esk1_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_23]) ).
cnf(c_0_117,negated_conjecture,
( in(esk4_1(X1),esk18_3(esk1_0,esk2_0,X2))
| in(esk4_1(X1),X1)
| ~ in(esk4_1(X1),cartesian_product2(complements_of_subsets(the_carrier(esk1_0),esk2_0),X2)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_17]),c_0_23]),c_0_116]) ).
cnf(c_0_118,plain,
( esk21_4(X2,X3,X4,X5) = subset_complement(the_carrier(X2),X1)
| ~ element(X1,powerset(the_carrier(X2)))
| X1 != esk20_4(X2,X3,X4,X5)
| ~ in(X5,esk18_3(X2,X3,X4))
| esk12_2(X2,X3) != esk13_2(X2,X3)
| ~ one_sorted_str(X2)
| ~ element(X3,powerset(powerset(the_carrier(X2)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_119,negated_conjecture,
in(esk4_1(esk18_3(esk1_0,esk2_0,esk3_0)),esk18_3(esk1_0,esk2_0,esk3_0)),
inference(spm,[status(thm)],[c_0_117,c_0_85]) ).
cnf(c_0_120,plain,
( in(esk20_4(X1,X2,X3,X4),complements_of_subsets(the_carrier(X1),X2))
| ~ in(X4,esk18_3(X1,X2,X3))
| esk12_2(X1,X2) != esk13_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_121,plain,
( ordered_pair(esk20_4(X1,X2,X3,X4),esk21_4(X1,X2,X3,X4)) = X4
| ~ in(X4,esk18_3(X1,X2,X3))
| esk12_2(X1,X2) != esk13_2(X1,X2)
| ~ one_sorted_str(X1)
| ~ element(X2,powerset(powerset(the_carrier(X1)))) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_122,plain,
( esk21_4(X1,X2,X3,X4) = subset_complement(the_carrier(X1),esk20_4(X1,X2,X3,X4))
| esk13_2(X1,X2) != esk12_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ element(esk20_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(er,[status(thm)],[c_0_118]) ).
cnf(c_0_123,negated_conjecture,
( ordered_pair(X1,subset_complement(the_carrier(esk1_0),X1)) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_98,c_0_119])]) ).
cnf(c_0_124,negated_conjecture,
( in(esk20_4(esk1_0,esk2_0,X1,X2),complements_of_subsets(the_carrier(esk1_0),esk2_0))
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_108]),c_0_6]),c_0_7])]) ).
cnf(c_0_125,plain,
( ordered_pair(esk20_4(X1,X2,X3,X4),subset_complement(the_carrier(X1),esk20_4(X1,X2,X3,X4))) = X4
| esk13_2(X1,X2) != esk12_2(X1,X2)
| ~ in(X4,esk18_3(X1,X2,X3))
| ~ element(esk20_4(X1,X2,X3,X4),powerset(the_carrier(X1)))
| ~ element(X2,powerset(powerset(the_carrier(X1))))
| ~ one_sorted_str(X1) ),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_126,negated_conjecture,
( element(X1,powerset(the_carrier(esk1_0)))
| ordered_pair(X1,X2) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(X1,complements_of_subsets(the_carrier(esk1_0),esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_119])]) ).
cnf(c_0_127,negated_conjecture,
( 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))
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_128,negated_conjecture,
( ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),subset_complement(the_carrier(esk1_0),esk20_4(esk1_0,esk2_0,X1,X2))) = X2
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1))
| ~ element(esk20_4(esk1_0,esk2_0,X1,X2),powerset(the_carrier(esk1_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_108]),c_0_6]),c_0_7])]) ).
cnf(c_0_129,negated_conjecture,
( element(esk20_4(esk1_0,esk2_0,X1,X2),powerset(the_carrier(esk1_0)))
| ordered_pair(esk20_4(esk1_0,esk2_0,X1,X2),X3) != esk4_1(esk18_3(esk1_0,esk2_0,esk3_0))
| ~ in(X2,esk18_3(esk1_0,esk2_0,X1)) ),
inference(spm,[status(thm)],[c_0_126,c_0_124]) ).
cnf(c_0_130,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(spm,[status(thm)],[c_0_127,c_0_128])]) ).
cnf(c_0_131,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(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_129,c_0_121]),c_0_108]),c_0_6]),c_0_7])])]),c_0_130]) ).
cnf(c_0_132,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_119,c_0_131]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU329+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n029.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:57:44 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 5.95/4.44 % Version : CSE_E---1.7
% 5.95/4.44 % Problem : theBenchmark.p
% 5.95/4.44 % SZS status Theorem for theBenchmark.p
% 5.95/4.44 % SZS output start CNFRefutation
% See solution above
% 5.95/4.45 % Total time : 3.373s
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