%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU342+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 02:20:13 PM UTC 2026
% Result : Theorem 3.61s 1.01s
% Output : CNFRefutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 71
% Syntax : Number of formulae : 342 ( 23 unt; 52 def)
% Number of atoms : 1320 ( 83 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1686 ( 708 ~; 805 |; 90 &)
% ( 59 <=>; 22 =>; 0 <=; 2 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 71 ( 69 usr; 53 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-4 aty)
% Number of variables : 282 ( 264 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] :
( latt_str(A)
=> ( ( lattice(A)
& ~ empty_carrier(A) )
=> ( join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& ~ empty_carrier(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( latt_str(A)
=> ( ( join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> ( lattice(A)
& ~ empty_carrier(A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> relation_of_lattice(A) = a_1_0_filter_1(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( join_semilatt_str(A)
=> one_sorted_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] :
( latt_str(A)
=> ( join_semilatt_str(A)
& meet_semilatt_str(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [A,B] :
( ( latt_str(B)
& lattice(B)
& ~ empty_carrier(B) )
=> ( in(A,a_1_0_filter_1(B))
<=> ? [C,D] :
( below_refl(B,C,D)
& A = ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D)
& element(D,the_carrier(B))
& element(C,the_carrier(B)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A,B,C,D] :
( ( element(D,B)
& element(C,A)
& ~ empty(B)
& ~ empty(A) )
=> ordered_pair_as_product_element(A,B,C,D) = ordered_pair(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& latt_str(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> ( below_refl(A,B,C)
<=> below(A,B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& latt_str(A)
& join_absorbing(A)
& meet_absorbing(A)
& meet_commutative(A)
& ~ empty_carrier(A) )
=> below_refl(A,B,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,conjecture,
! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A))
<=> below_refl(A,B,C) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
~ ! [A] :
( ( latt_str(A)
& lattice(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A))
<=> below_refl(A,B,C) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f42,axiom,
! [A,B,C,D] :
( ordered_pair(A,B) = ordered_pair(C,D)
=> ( B = D
& A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [A] :
( ( join_absorbing(A)
& meet_absorbing(A)
& meet_associative(A)
& meet_commutative(A)
& join_associative(A)
& join_commutative(A)
& ~ empty_carrier(A) )
| ~ lattice(A)
| empty_carrier(A)
| ~ latt_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f50,plain,
! [X0] :
( join_commutative(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f51,plain,
! [X0] :
( join_associative(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f52,plain,
! [X0] :
( meet_commutative(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f53,plain,
! [X0] :
( meet_associative(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f54,plain,
! [X0] :
( meet_absorbing(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f55,plain,
! [X0] :
( join_absorbing(X0)
| ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f56,plain,
! [A] :
( ( lattice(A)
& ~ empty_carrier(A) )
| ~ join_absorbing(A)
| ~ meet_absorbing(A)
| ~ meet_associative(A)
| ~ meet_commutative(A)
| ~ join_associative(A)
| ~ join_commutative(A)
| empty_carrier(A)
| ~ latt_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f58,plain,
! [X0] :
( lattice(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_associative(X0)
| ~ meet_commutative(X0)
| ~ join_associative(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f61,plain,
! [A] :
( relation_of_lattice(A) = a_1_0_filter_1(A)
| ~ latt_str(A)
| ~ lattice(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f62,plain,
! [X0] :
( relation_of_lattice(X0) = a_1_0_filter_1(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f69,plain,
! [A] :
( one_sorted_str(A)
| ~ join_semilatt_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f70,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f71,plain,
! [A] :
( ( join_semilatt_str(A)
& meet_semilatt_str(A) )
| ~ latt_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f17]) ).
fof(f73,plain,
! [X0] :
( join_semilatt_str(X0)
| ~ latt_str(X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f82,plain,
! [A] : element(sK4_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(B,sK4_skl(A))],[f24]) ).
fof(f83,plain,
! [X0] : element(sK4_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f84,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f85,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f86,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f91,plain,
! [A,B] :
( ( in(A,a_1_0_filter_1(B))
<=> ? [C,D] :
( below_refl(B,C,D)
& A = ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D)
& element(D,the_carrier(B))
& element(C,the_carrier(B)) ) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f92,plain,
! [A,B] :
( ( ( ! [C,D] :
( ~ below_refl(B,C,D)
| A != ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D)
| ~ element(D,the_carrier(B))
| ~ element(C,the_carrier(B)) )
| in(A,a_1_0_filter_1(B)) )
& ( ? [C,D] :
( below_refl(B,C,D)
& A = ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D)
& element(D,the_carrier(B))
& element(C,the_carrier(B)) )
| ~ in(A,a_1_0_filter_1(B)) ) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(NNF_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [B] :
( ( ! [A] :
( ! [C,D] :
( ~ below_refl(B,C,D)
| A != ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D)
| ~ element(D,the_carrier(B))
| ~ element(C,the_carrier(B)) )
| in(A,a_1_0_filter_1(B)) )
& ! [A] :
( ? [C,D] :
( below_refl(B,C,D)
& A = ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D)
& element(D,the_carrier(B))
& element(C,the_carrier(B)) )
| ~ in(A,a_1_0_filter_1(B)) ) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
! [B] :
( ( ! [A] :
( ! [C,D] :
( ~ below_refl(B,C,D)
| A != ordered_pair_as_product_element(the_carrier(B),the_carrier(B),C,D)
| ~ element(D,the_carrier(B))
| ~ element(C,the_carrier(B)) )
| in(A,a_1_0_filter_1(B)) )
& ! [A] :
( ( below_refl(B,sK5_skl(A,B),sK6_skl(A,B))
& A = ordered_pair_as_product_element(the_carrier(B),the_carrier(B),sK5_skl(A,B),sK6_skl(A,B))
& element(sK6_skl(A,B),the_carrier(B))
& element(sK5_skl(A,B),the_carrier(B)) )
| ~ in(A,a_1_0_filter_1(B)) ) )
| ~ latt_str(B)
| ~ lattice(B)
| empty_carrier(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(C,sK5_skl(A,B)),skolemize(D,sK6_skl(A,B))],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( element(sK5_skl(X1,X0),the_carrier(X0))
| ~ in(X1,a_1_0_filter_1(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( element(sK6_skl(X1,X0),the_carrier(X0))
| ~ in(X1,a_1_0_filter_1(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f97,plain,
! [X0,X1] :
( X1 = ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),sK5_skl(X1,X0),sK6_skl(X1,X0))
| ~ in(X1,a_1_0_filter_1(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f98,plain,
! [X0,X1] :
( below_refl(X0,sK5_skl(X1,X0),sK6_skl(X1,X0))
| ~ in(X1,a_1_0_filter_1(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( ~ below_refl(X0,X2,X3)
| X1 != ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X2,X3)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| in(X1,a_1_0_filter_1(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f104,plain,
( ~ empty_carrier(sK9_skl)
& one_sorted_str(sK9_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl]),skolemize(A,sK9_skl)],[f33]) ).
fof(f105,plain,
one_sorted_str(sK9_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,plain,
~ empty_carrier(sK9_skl),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f107,plain,
! [A,B,C,D] :
( ordered_pair_as_product_element(A,B,C,D) = ordered_pair(C,D)
| ~ element(D,B)
| ~ element(C,A)
| empty(B)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( ordered_pair_as_product_element(X0,X1,X2,X3) = ordered_pair(X2,X3)
| ~ element(X3,X1)
| ~ element(X2,X0)
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [A,B,C] :
( ( below_refl(A,B,C)
<=> below(A,B,C) )
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ join_absorbing(A)
| ~ meet_absorbing(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f110,plain,
! [A,B,C] :
( ( ( ~ below(A,B,C)
| below_refl(A,B,C) )
& ( below(A,B,C)
| ~ below_refl(A,B,C) ) )
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ join_absorbing(A)
| ~ meet_absorbing(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f109]) ).
fof(f111,plain,
! [X0,X1,X2] :
( below(X0,X1,X2)
| ~ below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ~ below(X0,X1,X2)
| below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
! [A,B,C] :
( below_refl(A,B,B)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ join_absorbing(A)
| ~ meet_absorbing(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f114,plain,
! [A,B] :
( below_refl(A,B,B)
| ! [C] : ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ latt_str(A)
| ~ join_absorbing(A)
| ~ meet_absorbing(A)
| ~ meet_commutative(A)
| empty_carrier(A) ),
inference(miniscoping,[status(thm)],[f113]) ).
fof(f115,plain,
! [X0,X1,X2] :
( below_refl(X0,X1,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f118,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f119,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f120,plain,
! [A,B] :
( A = B
| ? [C] :
( in(C,A)
<~> in(C,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f121,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,B)
| ~ in(C,A) )
& ( in(C,B)
| in(C,A) ) ) ),
inference(NNF_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
! [A,B] :
( A = B
| ( ( ~ in(sK10_skl(B,A),B)
| ~ in(sK10_skl(B,A),A) )
& ( in(sK10_skl(B,A),B)
| in(sK10_skl(B,A),A) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(C,sK10_skl(B,A))],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( X1 = X0
| in(sK10_skl(X0,X1),X0)
| in(sK10_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f125,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A))
<~> below_refl(A,B,C) )
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
& latt_str(A)
& lattice(A)
& ~ empty_carrier(A) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f126,plain,
? [A] :
( ? [B] :
( ? [C] :
( ( ~ below_refl(A,B,C)
| ~ in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A)) )
& ( below_refl(A,B,C)
| in(ordered_pair_as_product_element(the_carrier(A),the_carrier(A),B,C),relation_of_lattice(A)) )
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
& latt_str(A)
& lattice(A)
& ~ empty_carrier(A) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
( ( ~ below_refl(sK11_skl,sK12_skl,sK13_skl)
| ~ in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) )
& ( below_refl(sK11_skl,sK12_skl,sK13_skl)
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) )
& element(sK13_skl,the_carrier(sK11_skl))
& element(sK12_skl,the_carrier(sK11_skl))
& latt_str(sK11_skl)
& lattice(sK11_skl)
& ~ empty_carrier(sK11_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl,sK12_skl,sK13_skl]),skolemize(A,sK11_skl),skolemize(B,sK12_skl),skolemize(C,sK13_skl)],[f126]) ).
fof(f128,plain,
~ empty_carrier(sK11_skl),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
lattice(sK11_skl),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
latt_str(sK11_skl),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
element(sK12_skl,the_carrier(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f132,plain,
element(sK13_skl,the_carrier(sK11_skl)),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f133,plain,
( below_refl(sK11_skl,sK12_skl,sK13_skl)
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f134,plain,
( ~ below_refl(sK11_skl,sK12_skl,sK13_skl)
| ~ in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f135,plain,
! [A,B,C,D] :
( ( B = D
& A = C )
| ordered_pair(A,B) != ordered_pair(C,D) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f136,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f140,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f141,plain,
! [B] :
( ~ empty(B)
| ! [A] : ~ in(A,B) ),
inference(miniscoping,[status(thm)],[f140]) ).
fof(f142,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f146,definition,
( sQ0_spl
<=> in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( ~ sQ0_spl
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f148,plain,
( sQ0_spl
| ~ in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,definition,
( sQ1_spl
<=> below_refl(sK11_skl,sK12_skl,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ1_spl
| below_refl(sK11_skl,sK12_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f151,plain,
( sQ1_spl
| ~ below_refl(sK11_skl,sK12_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f133,f146,f149]) ).
fof(f153,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f134,f146,f149]) ).
fof(f155,plain,
! [X0,X1,X2] :
( ~ below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| in(ordered_pair_as_product_element(the_carrier(X0),the_carrier(X0),X1,X2),a_1_0_filter_1(X0))
| ~ latt_str(X0)
| ~ lattice(X0)
| empty_carrier(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f99]) ).
fof(f163,plain,
! [X0,X1,X2] :
( ~ in(X2,X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(resolution,[status(thm)],[f119,f142]) ).
fof(f164,plain,
( relation_of_lattice(sK11_skl) = a_1_0_filter_1(sK11_skl)
| ~ latt_str(sK11_skl)
| empty_carrier(sK11_skl) ),
inference(resolution,[status(thm)],[f62,f129]) ).
fof(f165,definition,
( sQ2_spl
<=> empty_carrier(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ2_spl
| empty_carrier(sK11_skl) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,definition,
( sQ3_spl
<=> latt_str(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ3_spl
| ~ latt_str(sK11_skl) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ4_spl
<=> relation_of_lattice(sK11_skl) = a_1_0_filter_1(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ4_spl
| relation_of_lattice(sK11_skl) = a_1_0_filter_1(sK11_skl) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( sQ4_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f164,f165,f168,f171]) ).
fof(f182,plain,
! [X0] :
( relation_of_lattice(X0) = a_1_0_filter_1(X0)
| ~ latt_str(X0)
| empty_carrier(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_associative(X0)
| ~ meet_commutative(X0)
| ~ join_associative(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(resolution,[status(thm)],[f58,f62]) ).
fof(f183,definition,
( sQ5_spl
<=> join_commutative(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ5_spl
| ~ join_commutative(sK11_skl) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,definition,
( sQ6_spl
<=> join_associative(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( sQ6_spl
| ~ join_associative(sK11_skl) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ7_spl
<=> meet_commutative(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ7_spl
| ~ meet_commutative(sK11_skl) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
( sQ8_spl
<=> meet_associative(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( sQ8_spl
| ~ meet_associative(sK11_skl) ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,definition,
( sQ9_spl
<=> meet_absorbing(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( sQ9_spl
| ~ meet_absorbing(sK11_skl) ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,definition,
( sQ10_spl
<=> join_absorbing(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ10_spl
| ~ join_absorbing(sK11_skl) ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,definition,
( sQ11_spl
<=> lattice(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( sQ11_spl
| ~ lattice(sK11_skl) ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f205,plain,
! [X0] :
( relation_of_lattice(X0) = a_1_0_filter_1(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| ~ meet_associative(X0)
| ~ meet_commutative(X0)
| ~ join_associative(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ latt_str(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f182]) ).
fof(f206,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f130]) ).
fof(f207,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f208,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f166,f128]) ).
fof(f209,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f208]) ).
fof(f216,plain,
! [X0] :
( X0 = ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl))
| ~ in(X0,a_1_0_filter_1(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ lattice(sK11_skl) ),
inference(resolution,[status(thm)],[f97,f128]) ).
fof(f217,definition,
! [X0] :
( sQ12_spl
<=> ( X0 = ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl))
| ~ in(X0,a_1_0_filter_1(sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f218,plain,
! [X0] :
( ~ sQ12_spl
| X0 = ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl))
| ~ in(X0,a_1_0_filter_1(sK11_skl)) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( sQ12_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f216,f201,f168,f217]) ).
fof(f221,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ4_spl
| X0 = ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ),
inference(forward_demodulation,[status(thm)],[f172,f218]) ).
fof(f222,plain,
! [X0] :
( below_refl(sK11_skl,sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl))
| ~ in(X0,a_1_0_filter_1(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ lattice(sK11_skl) ),
inference(resolution,[status(thm)],[f98,f128]) ).
fof(f223,definition,
! [X0] :
( sQ13_spl
<=> ( below_refl(sK11_skl,sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl))
| ~ in(X0,a_1_0_filter_1(sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f224,plain,
! [X0] :
( ~ sQ13_spl
| below_refl(sK11_skl,sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl))
| ~ in(X0,a_1_0_filter_1(sK11_skl)) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f222,f201,f168,f223]) ).
fof(f227,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ4_spl
| below_refl(sK11_skl,sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ),
inference(forward_demodulation,[status(thm)],[f172,f224]) ).
fof(f228,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f203,f129]) ).
fof(f229,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f230,plain,
! [X0,X1,X2] :
( ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| ~ below(X0,X1,X2)
| below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f112,f52]) ).
fof(f233,plain,
! [X0,X1,X2] :
( ~ lattice(X0)
| ~ below(X0,X1,X2)
| below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| empty_carrier(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f230]) ).
fof(f234,plain,
! [X0,X1,X2] :
( ~ lattice(X0)
| ~ below(X0,X1,X2)
| below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f54]) ).
fof(f238,plain,
! [X0,X1,X2] :
( ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| below_refl(X0,X1,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f115,f52]) ).
fof(f241,plain,
! [X0,X1,X2] :
( ~ lattice(X0)
| below_refl(X0,X1,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| ~ meet_absorbing(X0)
| empty_carrier(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f238]) ).
fof(f242,plain,
! [X0,X1,X2] :
( ~ lattice(X0)
| below_refl(X0,X1,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| ~ join_absorbing(X0)
| empty_carrier(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f241,f54]) ).
fof(f246,plain,
! [X0,X1,X2] :
( ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| ~ below(X0,X1,X2)
| below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f234,f55]) ).
fof(f247,plain,
! [X0,X1,X2] :
( ~ lattice(X0)
| ~ below(X0,X1,X2)
| below_refl(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f246]) ).
fof(f248,plain,
! [X0,X1,X2] :
( ~ lattice(X0)
| empty_carrier(X0)
| ~ latt_str(X0)
| ~ lattice(X0)
| below_refl(X0,X1,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(resolution,[status(thm)],[f242,f55]) ).
fof(f249,plain,
! [X0,X1,X2] :
( ~ lattice(X0)
| below_refl(X0,X1,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ latt_str(X0)
| empty_carrier(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f248]) ).
fof(f250,plain,
! [X0,X1] :
( ~ lattice(sK11_skl)
| ~ below(sK11_skl,X0,X1)
| below_refl(sK11_skl,X0,X1)
| ~ element(X1,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl))
| ~ latt_str(sK11_skl) ),
inference(resolution,[status(thm)],[f247,f128]) ).
fof(f251,definition,
! [X0,X1] :
( sQ14_spl
<=> ( ~ below(sK11_skl,X0,X1)
| below_refl(sK11_skl,X0,X1)
| ~ element(X1,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f252,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ below(sK11_skl,X0,X1)
| below_refl(sK11_skl,X0,X1)
| ~ element(X1,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( ~ sQ11_spl
| sQ14_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f250,f168,f251,f201]) ).
fof(f255,plain,
! [X0,X1] :
( ~ lattice(sK11_skl)
| below_refl(sK11_skl,X0,X0)
| ~ element(X1,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl))
| ~ latt_str(sK11_skl) ),
inference(resolution,[status(thm)],[f249,f128]) ).
fof(f256,definition,
! [X0] :
( sQ15_spl
<=> ( below_refl(sK11_skl,X0,X0)
| ~ element(X0,the_carrier(sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f257,plain,
! [X0] :
( ~ sQ15_spl
| below_refl(sK11_skl,X0,X0)
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,definition,
! [X1] :
( sQ16_spl
<=> ~ element(X1,the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f260,plain,
! [X0] :
( ~ sQ16_spl
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( ~ sQ11_spl
| sQ16_spl
| sQ15_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f255,f168,f256,f259,f201]) ).
fof(f264,plain,
( ~ sQ4_spl
| relation_of_lattice(sK11_skl) = relation_of_lattice(sK11_skl)
| ~ join_absorbing(sK11_skl)
| ~ meet_absorbing(sK11_skl)
| ~ meet_associative(sK11_skl)
| ~ meet_commutative(sK11_skl)
| ~ join_associative(sK11_skl)
| ~ join_commutative(sK11_skl)
| empty_carrier(sK11_skl)
| ~ latt_str(sK11_skl) ),
inference(paramodulation,[status(thm)],[f172,f205]) ).
fof(f265,definition,
( sQ17_spl
<=> relation_of_lattice(sK11_skl) = relation_of_lattice(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( ~ sQ4_spl
| sQ17_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f264,f168,f165,f183,f186,f189,f192,f195,f198,f265,f171]) ).
fof(f269,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ4_spl
| ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) = ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl)) ),
inference(resolution,[status(thm)],[f221,f147]) ).
fof(f277,plain,
! [X0] :
( ~ sQ15_spl
| ~ element(X0,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),X0,X0),a_1_0_filter_1(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f257,f155]) ).
fof(f278,definition,
! [X0] :
( sQ19_spl
<=> ( ~ element(X0,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),X0,X0),a_1_0_filter_1(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f279,plain,
! [X0] :
( ~ sQ19_spl
| ~ element(X0,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),X0,X0),a_1_0_filter_1(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,plain,
( ~ sQ15_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f277,f278,f165,f201,f168,f256]) ).
fof(f282,plain,
( ~ sQ16_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f132,f260]) ).
fof(f284,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ4_spl
| ~ element(X0,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),X0,X0),relation_of_lattice(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(forward_demodulation,[status(thm)],[f172,f279]) ).
fof(f285,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ4_spl
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),X0,X0),relation_of_lattice(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f284]) ).
fof(f286,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f282]) ).
fof(f289,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ4_spl
| ~ element(sK6_skl(X0,sK11_skl),the_carrier(sK11_skl))
| ~ element(sK5_skl(X0,sK11_skl),the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),a_1_0_filter_1(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| ~ in(X0,relation_of_lattice(sK11_skl)) ),
inference(resolution,[status(thm)],[f227,f155]) ).
fof(f290,definition,
! [X0] :
( sQ20_spl
<=> ( ~ element(sK6_skl(X0,sK11_skl),the_carrier(sK11_skl))
| ~ element(sK5_skl(X0,sK11_skl),the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),a_1_0_filter_1(sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f291,plain,
! [X0] :
( ~ sQ20_spl
| ~ element(sK6_skl(X0,sK11_skl),the_carrier(sK11_skl))
| ~ element(sK5_skl(X0,sK11_skl),the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),a_1_0_filter_1(sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,plain,
( ~ sQ13_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f289,f290,f165,f201,f168,f171,f223]) ).
fof(f294,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ4_spl
| ~ element(sK6_skl(X0,sK11_skl),the_carrier(sK11_skl))
| ~ element(sK5_skl(X0,sK11_skl),the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),relation_of_lattice(sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ),
inference(forward_demodulation,[status(thm)],[f172,f291]) ).
fof(f295,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ19_spl
| ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),X0,X0) = ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),X0,X0),sK11_skl),sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),X0,X0),sK11_skl))
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f285,f221]) ).
fof(f297,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ below_refl(sK11_skl,X0,X1)
| ~ element(X1,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ join_absorbing(sK11_skl)
| ~ meet_absorbing(sK11_skl)
| ~ meet_commutative(sK11_skl)
| empty_carrier(sK11_skl)
| below_refl(sK11_skl,X0,X1)
| ~ element(X1,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f252,f111]) ).
fof(f298,definition,
! [X0,X1] :
( sQ21_spl
<=> ( ~ below_refl(sK11_skl,X0,X1)
| ~ element(X1,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl))
| below_refl(sK11_skl,X0,X1)
| ~ element(X1,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ2_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f297,f298,f165,f189,f195,f198,f168,f251]) ).
fof(f302,plain,
( sQ10_spl
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| ~ latt_str(sK11_skl) ),
inference(resolution,[status(thm)],[f200,f55]) ).
fof(f303,plain,
( sQ10_spl
| ~ sQ11_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f302,f168,f165,f201,f198]) ).
fof(f304,plain,
( sQ9_spl
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| ~ latt_str(sK11_skl) ),
inference(resolution,[status(thm)],[f197,f54]) ).
fof(f305,plain,
( sQ9_spl
| ~ sQ11_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f304,f168,f165,f201,f195]) ).
fof(f312,plain,
( sQ7_spl
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| ~ latt_str(sK11_skl) ),
inference(resolution,[status(thm)],[f191,f52]) ).
fof(f313,plain,
( sQ7_spl
| ~ sQ11_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f312,f168,f165,f201,f189]) ).
fof(f329,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ4_spl
| ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) = ordered_pair(sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl))
| ~ element(sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl))
| ~ element(sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl))
| empty(the_carrier(sK11_skl))
| empty(the_carrier(sK11_skl)) ),
inference(paramodulation,[status(thm)],[f269,f108]) ).
fof(f330,definition,
( sQ22_spl
<=> empty(the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( sQ22_spl
| ~ empty(the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,definition,
( sQ23_spl
<=> element(sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( ~ sQ23_spl
| element(sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f335,plain,
( sQ23_spl
| ~ element(sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f333]) ).
fof(f336,definition,
( sQ24_spl
<=> element(sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( ~ sQ24_spl
| element(sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f338,plain,
( sQ24_spl
| ~ element(sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f351,definition,
( sQ28_spl
<=> ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) = ordered_pair(sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( ~ sQ28_spl
| ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) = ordered_pair(sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl)) ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ4_spl
| sQ28_spl
| ~ sQ24_spl
| ~ sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f329,f330,f333,f336,f351,f171,f217,f146]) ).
fof(f355,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ4_spl
| ~ in(X0,a_1_0_filter_1(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| ~ element(sK5_skl(X0,sK11_skl),the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),relation_of_lattice(sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ),
inference(resolution,[status(thm)],[f294,f96]) ).
fof(f357,definition,
! [X0] :
( sQ29_spl
<=> ( ~ in(X0,a_1_0_filter_1(sK11_skl))
| ~ element(sK5_skl(X0,sK11_skl),the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),relation_of_lattice(sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f358,plain,
! [X0] :
( ~ sQ29_spl
| ~ in(X0,a_1_0_filter_1(sK11_skl))
| ~ element(sK5_skl(X0,sK11_skl),the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),relation_of_lattice(sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f360,plain,
( ~ sQ20_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f355,f357,f165,f201,f168,f171,f290]) ).
fof(f361,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ4_spl
| ~ in(X0,relation_of_lattice(sK11_skl))
| ~ element(sK5_skl(X0,sK11_skl),the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),relation_of_lattice(sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ),
inference(forward_demodulation,[status(thm)],[f172,f358]) ).
fof(f362,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ4_spl
| ~ element(sK5_skl(X0,sK11_skl),the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),relation_of_lattice(sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f361]) ).
fof(f363,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ4_spl
| ~ in(X0,a_1_0_filter_1(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),relation_of_lattice(sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ),
inference(resolution,[status(thm)],[f362,f95]) ).
fof(f365,definition,
! [X0] :
( sQ30_spl
<=> ( ~ in(X0,a_1_0_filter_1(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),relation_of_lattice(sK11_skl))
| ~ in(X0,relation_of_lattice(sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( ~ sQ29_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f363,f365,f165,f201,f168,f171,f357]) ).
fof(f371,plain,
( sQ24_spl
| ~ in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),a_1_0_filter_1(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl) ),
inference(resolution,[status(thm)],[f338,f96]) ).
fof(f373,definition,
( sQ31_spl
<=> in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),a_1_0_filter_1(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( ~ sQ31_spl
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),a_1_0_filter_1(sK11_skl)) ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f375,plain,
( sQ31_spl
| ~ in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),a_1_0_filter_1(sK11_skl)) ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f376,plain,
( sQ24_spl
| ~ sQ31_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f371,f165,f201,f168,f373,f336]) ).
fof(f381,plain,
( sQ23_spl
| ~ in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),a_1_0_filter_1(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl) ),
inference(resolution,[status(thm)],[f335,f95]) ).
fof(f383,plain,
( sQ23_spl
| ~ sQ31_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f381,f165,f201,f168,f373,f333]) ).
fof(f388,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ19_spl
| ~ in(X0,a_1_0_filter_1(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK6_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)) = ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK6_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),sK11_skl),sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK6_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),sK11_skl)) ),
inference(resolution,[status(thm)],[f295,f96]) ).
fof(f390,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ19_spl
| ~ in(X0,a_1_0_filter_1(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK5_skl(X0,sK11_skl)) = ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK5_skl(X0,sK11_skl)),sK11_skl),sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK5_skl(X0,sK11_skl)),sK11_skl)) ),
inference(resolution,[status(thm)],[f295,f95]) ).
fof(f392,definition,
! [X0] :
( sQ32_spl
<=> ( ~ in(X0,a_1_0_filter_1(sK11_skl))
| ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK6_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)) = ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK6_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),sK11_skl),sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK6_skl(X0,sK11_skl),sK6_skl(X0,sK11_skl)),sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ19_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f388,f392,f165,f201,f168,f278,f171,f217]) ).
fof(f396,definition,
! [X0] :
( sQ33_spl
<=> ( ~ in(X0,a_1_0_filter_1(sK11_skl))
| ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK5_skl(X0,sK11_skl)) = ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK5_skl(X0,sK11_skl)),sK11_skl),sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK5_skl(X0,sK11_skl),sK5_skl(X0,sK11_skl)),sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( ~ sQ12_spl
| ~ sQ4_spl
| ~ sQ19_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f390,f396,f165,f201,f168,f278,f171,f217]) ).
fof(f424,plain,
( ~ sQ1_spl
| ~ element(sK13_skl,the_carrier(sK11_skl))
| ~ element(sK12_skl,the_carrier(sK11_skl))
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),a_1_0_filter_1(sK11_skl))
| ~ latt_str(sK11_skl)
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl) ),
inference(resolution,[status(thm)],[f150,f155]) ).
fof(f425,definition,
( sQ36_spl
<=> element(sK12_skl,the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( sQ36_spl
| ~ element(sK12_skl,the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f425]) ).
fof(f428,definition,
( sQ37_spl
<=> element(sK13_skl,the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( sQ37_spl
| ~ element(sK13_skl,the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f431,plain,
( ~ sQ1_spl
| ~ sQ37_spl
| ~ sQ36_spl
| sQ31_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f424,f165,f201,f168,f373,f425,f428,f149]) ).
fof(f433,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f430,f132]) ).
fof(f434,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f433]) ).
fof(f435,plain,
( ~ sQ31_spl
| ~ sQ4_spl
| in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) ),
inference(forward_demodulation,[status(thm)],[f172,f374]) ).
fof(f436,plain,
( ~ sQ31_spl
| ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f148]) ).
fof(f437,plain,
( ~ sQ31_spl
| ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f436]) ).
fof(f438,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f131]) ).
fof(f439,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f438]) ).
fof(f514,plain,
( sQ31_spl
| ~ sQ4_spl
| ~ in(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) ),
inference(forward_demodulation,[status(thm)],[f172,f375]) ).
fof(f515,plain,
( ~ sQ0_spl
| sQ31_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f514]) ).
fof(f516,plain,
( ~ sQ0_spl
| sQ31_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f525,plain,
! [X0,X1,X2] :
( X1 = X2
| in(sK10_skl(X2,X1),X2)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(resolution,[status(thm)],[f163,f123]) ).
fof(f530,plain,
! [X0] : ~ in(X0,empty_set),
inference(resolution,[status(thm)],[f86,f142]) ).
fof(f533,plain,
( ~ empty(the_carrier(sK11_skl))
| ~ one_sorted_str(sK11_skl) ),
inference(resolution,[status(thm)],[f85,f128]) ).
fof(f534,definition,
( sQ41_spl
<=> one_sorted_str(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ41_spl
| ~ one_sorted_str(sK11_skl) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,plain,
( ~ sQ22_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f533,f534,f330]) ).
fof(f776,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ element(X3,X2)
| X1 = X2
| in(X0,X1)
| ~ element(X0,X1) ),
inference(resolution,[status(thm)],[f525,f163]) ).
fof(f781,plain,
! [X0,X1,X2] :
( in(sK4_skl(X2),X2)
| X1 = X2
| in(X0,X1)
| ~ element(X0,X1) ),
inference(resolution,[status(thm)],[f776,f83]) ).
fof(f790,definition,
( sQ53_spl
<=> in(sK12_skl,the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f791,plain,
( ~ sQ53_spl
| in(sK12_skl,the_carrier(sK11_skl)) ),
inference(component_clause,[status(thm)],[f790]) ).
fof(f819,definition,
( sQ56_spl
<=> sK12_skl = the_carrier(sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f820,plain,
( ~ sQ56_spl
| sK12_skl = the_carrier(sK11_skl) ),
inference(component_clause,[status(thm)],[f819]) ).
fof(f822,definition,
( sQ57_spl
<=> in(the_carrier(sK11_skl),sK12_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f823,plain,
( ~ sQ57_spl
| in(the_carrier(sK11_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f822]) ).
fof(f824,plain,
( sQ57_spl
| ~ in(the_carrier(sK11_skl),sK12_skl) ),
inference(component_clause,[status(thm)],[f822]) ).
fof(f827,plain,
( sQ57_spl
| ~ sQ56_spl
| ~ in(sK12_skl,sK12_skl) ),
inference(backward_demodulation,[status(thm)],[f820,f824]) ).
fof(f828,plain,
( ~ sQ53_spl
| ~ sQ56_spl
| in(sK12_skl,sK12_skl) ),
inference(backward_demodulation,[status(thm)],[f820,f791]) ).
fof(f1079,plain,
( ~ sQ53_spl
| ~ sQ56_spl
| sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f828,f827]) ).
fof(f1080,plain,
( ~ sQ53_spl
| ~ sQ56_spl
| sQ57_spl ),
inference(contradiction_clause,[status(thm)],[f1079]) ).
fof(f1476,definition,
( sQ62_spl
<=> in(sK13_skl,the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1506,plain,
( sQ41_spl
| ~ join_semilatt_str(sK11_skl) ),
inference(resolution,[status(thm)],[f536,f70]) ).
fof(f1508,plain,
( sQ8_spl
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| ~ latt_str(sK11_skl) ),
inference(resolution,[status(thm)],[f194,f53]) ).
fof(f1509,plain,
( sQ8_spl
| ~ sQ11_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1508,f168,f165,f201,f192]) ).
fof(f1510,plain,
( sQ6_spl
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| ~ latt_str(sK11_skl) ),
inference(resolution,[status(thm)],[f188,f51]) ).
fof(f1511,plain,
( sQ6_spl
| ~ sQ11_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1510,f168,f165,f201,f186]) ).
fof(f1512,plain,
( sQ5_spl
| ~ lattice(sK11_skl)
| empty_carrier(sK11_skl)
| ~ latt_str(sK11_skl) ),
inference(resolution,[status(thm)],[f185,f50]) ).
fof(f1513,plain,
( sQ5_spl
| ~ sQ11_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1512,f168,f165,f201,f183]) ).
fof(f1516,plain,
( sQ41_spl
| ~ latt_str(sK11_skl) ),
inference(resolution,[status(thm)],[f1506,f73]) ).
fof(f1517,plain,
( sQ41_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1516,f168,f534]) ).
fof(f2000,plain,
! [X0,X1] :
( X1 = empty_set
| in(X0,X1)
| ~ element(X0,X1) ),
inference(resolution,[status(thm)],[f530,f781]) ).
fof(f2010,plain,
( ~ empty(the_carrier(sK9_skl))
| ~ one_sorted_str(sK9_skl) ),
inference(resolution,[status(thm)],[f106,f85]) ).
fof(f2016,definition,
! [X0,X1] :
( sQ67_spl
<=> ( X1 = the_carrier(sK9_skl)
| in(X0,X1)
| ~ element(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f2017,plain,
! [X0,X1] :
( ~ sQ67_spl
| X1 = the_carrier(sK9_skl)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(component_clause,[status(thm)],[f2016]) ).
fof(f2033,definition,
( sQ72_spl
<=> one_sorted_str(sK9_skl) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f2035,plain,
( sQ72_spl
| ~ one_sorted_str(sK9_skl) ),
inference(component_clause,[status(thm)],[f2033]) ).
fof(f2036,definition,
( sQ73_spl
<=> empty(the_carrier(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f2038,plain,
( sQ73_spl
| ~ empty(the_carrier(sK9_skl)) ),
inference(component_clause,[status(thm)],[f2036]) ).
fof(f2039,plain,
( ~ sQ73_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f2010,f2033,f2036]) ).
fof(f2043,definition,
! [X1] :
( sQ75_spl
<=> ~ element(X1,the_carrier(sK9_skl)) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f2044,plain,
! [X0] :
( ~ sQ75_spl
| ~ element(X0,the_carrier(sK9_skl)) ),
inference(component_clause,[status(thm)],[f2043]) ).
fof(f2078,plain,
( sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2035,f105]) ).
fof(f2079,plain,
sQ72_spl,
inference(contradiction_clause,[status(thm)],[f2078]) ).
fof(f2360,plain,
! [X0] :
( ~ sQ67_spl
| X0 = the_carrier(sK9_skl)
| in(sK4_skl(X0),X0) ),
inference(resolution,[status(thm)],[f2017,f83]) ).
fof(f2365,plain,
( ~ sQ67_spl
| empty_set = the_carrier(sK9_skl) ),
inference(resolution,[status(thm)],[f2360,f530]) ).
fof(f2374,plain,
( sQ73_spl
| ~ sQ67_spl
| ~ empty(empty_set) ),
inference(backward_demodulation,[status(thm)],[f2365,f2038]) ).
fof(f2380,plain,
( sQ73_spl
| ~ sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2374,f86]) ).
fof(f2381,plain,
( sQ73_spl
| ~ sQ67_spl ),
inference(contradiction_clause,[status(thm)],[f2380]) ).
fof(f2422,plain,
! [X0] :
( sQ22_spl
| in(X0,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f332,f119]) ).
fof(f2426,plain,
( ~ sQ57_spl
| ~ in(sK12_skl,the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f823,f47]) ).
fof(f2427,plain,
( ~ sQ57_spl
| ~ sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2426,f791]) ).
fof(f2428,plain,
( ~ sQ57_spl
| ~ sQ53_spl ),
inference(contradiction_clause,[status(thm)],[f2427]) ).
fof(f2852,plain,
( the_carrier(sK11_skl) = empty_set
| in(sK12_skl,the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f131,f2000]) ).
fof(f2858,definition,
( sQ92_spl
<=> the_carrier(sK11_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f2859,plain,
( ~ sQ92_spl
| the_carrier(sK11_skl) = empty_set ),
inference(component_clause,[status(thm)],[f2858]) ).
fof(f2861,plain,
( sQ92_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f2852,f790,f2858]) ).
fof(f2867,plain,
( the_carrier(sK11_skl) = empty_set
| in(sK13_skl,the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f132,f2000]) ).
fof(f2873,plain,
( sQ92_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f2867,f1476,f2858]) ).
fof(f2891,plain,
! [X0] :
( sQ73_spl
| in(X0,the_carrier(sK9_skl))
| ~ element(X0,the_carrier(sK9_skl)) ),
inference(resolution,[status(thm)],[f2038,f119]) ).
fof(f3000,plain,
( sQ22_spl
| ~ sQ92_spl
| ~ empty(empty_set) ),
inference(backward_demodulation,[status(thm)],[f2859,f332]) ).
fof(f3097,plain,
( sQ22_spl
| ~ sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3000,f86]) ).
fof(f3098,plain,
( sQ22_spl
| ~ sQ92_spl ),
inference(contradiction_clause,[status(thm)],[f3097]) ).
fof(f3349,plain,
! [X0,X1] :
( ~ sQ28_spl
| X1 = sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl)
| ordered_pair(X0,X1) != ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) ),
inference(paramodulation,[status(thm)],[f352,f137]) ).
fof(f3351,plain,
! [X0,X1] :
( ~ sQ28_spl
| X0 = sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl)
| ordered_pair(X0,X1) != ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) ),
inference(paramodulation,[status(thm)],[f352,f136]) ).
fof(f3498,plain,
( ~ sQ24_spl
| the_carrier(sK11_skl) = empty_set
| in(sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f337,f2000]) ).
fof(f3500,definition,
( sQ126_spl
<=> in(sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f3520,plain,
( ~ sQ24_spl
| sQ92_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f3498,f3500,f2858,f336]) ).
fof(f3527,plain,
( ~ sQ23_spl
| the_carrier(sK11_skl) = empty_set
| in(sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f334,f2000]) ).
fof(f3529,definition,
( sQ131_spl
<=> in(sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f3549,plain,
( ~ sQ23_spl
| sQ92_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f3527,f3529,f2858,f333]) ).
fof(f3613,plain,
! [X0,X1] :
( sQ73_spl
| in(X1,the_carrier(sK9_skl))
| ~ element(X1,the_carrier(sK9_skl))
| ~ element(X0,the_carrier(sK9_skl)) ),
inference(resolution,[status(thm)],[f2891,f163]) ).
fof(f3615,definition,
! [X1] :
( sQ136_spl
<=> ( in(X1,the_carrier(sK9_skl))
| ~ element(X1,the_carrier(sK9_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f3618,plain,
( sQ73_spl
| sQ136_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f3613,f2043,f3615,f2036]) ).
fof(f3619,plain,
( ~ sQ75_spl
| $false ),
inference(resolution,[status(thm)],[f2044,f83]) ).
fof(f3623,plain,
~ sQ75_spl,
inference(contradiction_clause,[status(thm)],[f3619]) ).
fof(f3824,plain,
! [X0,X1] :
( sQ22_spl
| in(X1,the_carrier(sK11_skl))
| ~ element(X1,the_carrier(sK11_skl))
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f2422,f163]) ).
fof(f3825,plain,
! [X0] :
( sQ22_spl
| ~ in(the_carrier(sK11_skl),X0)
| ~ element(X0,the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f2422,f47]) ).
fof(f3826,definition,
! [X1] :
( sQ137_spl
<=> ( in(X1,the_carrier(sK11_skl))
| ~ element(X1,the_carrier(sK11_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f3829,plain,
( sQ22_spl
| sQ137_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f3824,f259,f3826,f330]) ).
fof(f3832,plain,
( sQ22_spl
| ~ element(the_carrier(sK11_skl),the_carrier(sK11_skl))
| ~ element(the_carrier(sK11_skl),the_carrier(sK11_skl)) ),
inference(resolution,[status(thm)],[f3825,f2422]) ).
fof(f3833,definition,
( sQ138_spl
<=> element(the_carrier(sK11_skl),the_carrier(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f3836,plain,
( sQ22_spl
| ~ sQ138_spl ),
inference(split_clause,[status(thm)],[f3832,f3833,f330]) ).
fof(f3839,plain,
( ~ sQ28_spl
| ~ element(sK13_skl,the_carrier(sK11_skl))
| ~ element(sK12_skl,the_carrier(sK11_skl))
| empty(the_carrier(sK11_skl))
| empty(the_carrier(sK11_skl))
| sK13_skl = sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl) ),
inference(resolution,[status(thm)],[f3349,f108]) ).
fof(f3844,definition,
( sQ139_spl
<=> sK13_skl = sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f3845,plain,
( ~ sQ139_spl
| sK13_skl = sK6_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl) ),
inference(component_clause,[status(thm)],[f3844]) ).
fof(f3847,plain,
( ~ sQ28_spl
| ~ sQ37_spl
| ~ sQ36_spl
| sQ22_spl
| sQ139_spl ),
inference(split_clause,[status(thm)],[f3839,f3844,f330,f425,f428,f351]) ).
fof(f3855,definition,
( sQ142_spl
<=> ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) = ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f3857,plain,
( sQ142_spl
| ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) != ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) ),
inference(component_clause,[status(thm)],[f3855]) ).
fof(f3865,plain,
( ~ sQ28_spl
| ~ sQ139_spl
| ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) = ordered_pair(sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl),sK13_skl) ),
inference(backward_demodulation,[status(thm)],[f3845,f352]) ).
fof(f3873,plain,
( sQ142_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3857]) ).
fof(f3874,plain,
sQ142_spl,
inference(contradiction_clause,[status(thm)],[f3873]) ).
fof(f3925,plain,
( ~ sQ28_spl
| ~ element(sK13_skl,the_carrier(sK11_skl))
| ~ element(sK12_skl,the_carrier(sK11_skl))
| empty(the_carrier(sK11_skl))
| empty(the_carrier(sK11_skl))
| sK12_skl = sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl) ),
inference(resolution,[status(thm)],[f3351,f108]) ).
fof(f3929,definition,
( sQ147_spl
<=> sK12_skl = sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f3930,plain,
( ~ sQ147_spl
| sK12_skl = sK5_skl(ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl),sK11_skl) ),
inference(component_clause,[status(thm)],[f3929]) ).
fof(f3932,plain,
( ~ sQ28_spl
| ~ sQ37_spl
| ~ sQ36_spl
| sQ22_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f3925,f3929,f330,f425,f428,f351]) ).
fof(f3938,plain,
( ~ sQ28_spl
| ~ sQ139_spl
| ~ sQ147_spl
| ordered_pair_as_product_element(the_carrier(sK11_skl),the_carrier(sK11_skl),sK12_skl,sK13_skl) = ordered_pair(sK12_skl,sK13_skl) ),
inference(backward_demodulation,[status(thm)],[f3930,f3865]) ).
fof(f3949,plain,
( ~ sQ0_spl
| ~ sQ28_spl
| ~ sQ139_spl
| ~ sQ147_spl
| in(ordered_pair(sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) ),
inference(backward_demodulation,[status(thm)],[f3938,f147]) ).
fof(f3953,plain,
( ~ sQ147_spl
| ~ sQ28_spl
| ~ sQ139_spl
| sK12_skl = sK5_skl(ordered_pair(sK12_skl,sK13_skl),sK11_skl) ),
inference(backward_demodulation,[status(thm)],[f3938,f3930]) ).
fof(f3957,plain,
( ~ sQ139_spl
| ~ sQ28_spl
| ~ sQ147_spl
| sK13_skl = sK6_skl(ordered_pair(sK12_skl,sK13_skl),sK11_skl) ),
inference(backward_demodulation,[status(thm)],[f3938,f3845]) ).
fof(f4053,plain,
( ~ sQ147_spl
| ~ sQ28_spl
| ~ sQ139_spl
| ~ sQ13_spl
| ~ sQ4_spl
| below_refl(sK11_skl,sK12_skl,sK6_skl(ordered_pair(sK12_skl,sK13_skl),sK11_skl))
| ~ in(ordered_pair(sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) ),
inference(paramodulation,[status(thm)],[f3953,f227]) ).
fof(f4064,definition,
( sQ156_spl
<=> in(ordered_pair(sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f4066,plain,
( sQ156_spl
| ~ in(ordered_pair(sK12_skl,sK13_skl),relation_of_lattice(sK11_skl)) ),
inference(component_clause,[status(thm)],[f4064]) ).
fof(f4067,definition,
( sQ157_spl
<=> below_refl(sK11_skl,sK12_skl,sK6_skl(ordered_pair(sK12_skl,sK13_skl),sK11_skl)) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f4068,plain,
( ~ sQ157_spl
| below_refl(sK11_skl,sK12_skl,sK6_skl(ordered_pair(sK12_skl,sK13_skl),sK11_skl)) ),
inference(component_clause,[status(thm)],[f4067]) ).
fof(f4070,plain,
( ~ sQ147_spl
| ~ sQ28_spl
| ~ sQ139_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sQ157_spl
| ~ sQ156_spl ),
inference(split_clause,[status(thm)],[f4053,f4064,f4067,f171,f223,f3844,f351,f3929]) ).
fof(f4093,plain,
( sQ156_spl
| ~ sQ0_spl
| ~ sQ28_spl
| ~ sQ139_spl
| ~ sQ147_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4066,f3949]) ).
fof(f4094,plain,
( sQ156_spl
| ~ sQ0_spl
| ~ sQ28_spl
| ~ sQ139_spl
| ~ sQ147_spl ),
inference(contradiction_clause,[status(thm)],[f4093]) ).
fof(f4096,plain,
( ~ sQ157_spl
| ~ sQ139_spl
| ~ sQ28_spl
| ~ sQ147_spl
| below_refl(sK11_skl,sK12_skl,sK13_skl) ),
inference(forward_demodulation,[status(thm)],[f3957,f4068]) ).
fof(f4097,plain,
( ~ sQ157_spl
| ~ sQ139_spl
| ~ sQ28_spl
| ~ sQ147_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4096,f151]) ).
fof(f4098,plain,
( ~ sQ157_spl
| ~ sQ139_spl
| ~ sQ28_spl
| ~ sQ147_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f4097]) ).
fof(f4099,plain,
$false,
inference(sat_refutation,[status(thm)],[f152,f153,f174,f207,f209,f220,f226,f229,f254,f262,f268,f281,f286,f293,f301,f303,f305,f313,f354,f360,f368,f376,f383,f395,f399,f431,f434,f437,f439,f516,f537,f1080,f1509,f1511,f1513,f1517,f2039,f2079,f2381,f2428,f2861,f2873,f3098,f3520,f3549,f3618,f3623,f3829,f3836,f3847,f3874,f3932,f4070,f4094,f4098]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU342+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 06:15:59 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 3.61/1.01 % Refutation found
% 3.61/1.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.61/1.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.61/1.03 % Elapsed time: 0.666292 seconds
% 3.61/1.03 % CPU time: 5.019422 seconds
% 3.61/1.03 % Total memory used: 170.491 MB
% 3.61/1.03 % Net memory used: 167.865 MB
%------------------------------------------------------------------------------