%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 02:57:12 PM UTC 2026
% Result : Theorem 1.25s 1.19s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 163 ( 22 unt; 2 def)
% Number of atoms : 765 ( 14 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 903 ( 385 ~; 404 |; 84 &)
% ( 11 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 302 ( 0 sgn 280 !; 22 ?; 150 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( rel_str(X0)
=> ( lower_bounded_relstr(X0)
<=> ? [X1] :
( relstr_element_smaller(X0,the_carrier(X0),X1)
& element(X1,the_carrier(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_yellow_0) ).
fof(f4,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1,X2] :
( element(X2,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X1)
=> related(X0,X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_lattice3) ).
fof(f6,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f13,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f19,axiom,
! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0) )
=> ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_set_smaller(X0,X1,X3)
=> related(X0,X2,X3) ) )
& relstr_set_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t15_yellow_0) ).
fof(f20,axiom,
! [X0] :
( ( rel_str(X0)
& antisymmetric_relstr(X0) )
=> ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( element(X3,the_carrier(X0))
=> ( relstr_element_smaller(X0,X1,X3)
=> related(X0,X3,X2) ) )
& relstr_element_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_yellow_0) ).
fof(f21,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f22,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f23,conjecture,
! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& ~ empty_carrier(X0) )
=> ( ex_inf_of_relstr_set(X0,the_carrier(X0))
& ex_sup_of_relstr_set(X0,empty_set) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t42_yellow_0) ).
fof(f24,negated_conjecture,
~ ! [X0] :
( ( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& ~ empty_carrier(X0) )
=> ( ex_inf_of_relstr_set(X0,the_carrier(X0))
& ex_sup_of_relstr_set(X0,empty_set) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f26,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ( relstr_element_smaller(X0,empty_set,X1)
& relstr_set_smaller(X0,empty_set,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_yellow_0) ).
fof(f32,plain,
! [X0] :
( ~ rel_str(X0)
| ( lower_bounded_relstr(X0)
<=> ? [X1] :
( relstr_element_smaller(X0,the_carrier(X0),X1)
& element(X1,the_carrier(X0)) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ in(X3,X1)
| related(X0,X2,X3) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f34,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( relstr_element_smaller(X0,X1,X2)
<=> ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ in(X3,X1)
| related(X0,X2,X3) ) ) ) ),
inference(flattening,[],[f33]) ).
fof(f35,plain,
! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f36,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f37,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X3)
| related(X0,X2,X3) )
& relstr_set_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) ) ),
inference(ennf_transformation,[],[f19]) ).
fof(f39,plain,
! [X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ! [X1] :
( ex_sup_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X3)
| related(X0,X2,X3) )
& relstr_set_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X3)
| related(X0,X3,X2) )
& relstr_element_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) ) ),
inference(ennf_transformation,[],[f20]) ).
fof(f41,plain,
! [X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ! [X1] :
( ex_inf_of_relstr_set(X0,X1)
<=> ? [X2] :
( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X3)
| related(X0,X3,X2) )
& relstr_element_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) ) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f43,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f44,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(flattening,[],[f43]) ).
fof(f45,plain,
? [X0] :
( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& ~ empty_carrier(X0)
& ( ~ ex_inf_of_relstr_set(X0,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,empty_set) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f46,plain,
? [X0] :
( rel_str(X0)
& lower_bounded_relstr(X0)
& antisymmetric_relstr(X0)
& ~ empty_carrier(X0)
& ( ~ ex_inf_of_relstr_set(X0,the_carrier(X0))
| ~ ex_sup_of_relstr_set(X0,empty_set) ) ),
inference(flattening,[],[f45]) ).
fof(f48,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1] :
( ~ element(X1,the_carrier(X0))
| ( relstr_element_smaller(X0,empty_set,X1)
& relstr_set_smaller(X0,empty_set,X1) ) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f51,plain,
! [X0] :
( ~ rel_str(X0)
| ( ( ~ lower_bounded_relstr(X0)
| ? [X1] :
( relstr_element_smaller(X0,the_carrier(X0),X1)
& element(X1,the_carrier(X0)) ) )
& ( ! [X1] :
( ~ relstr_element_smaller(X0,the_carrier(X0),X1)
| ~ element(X1,the_carrier(X0)) )
| lower_bounded_relstr(X0) ) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f52,plain,
! [X0] :
( ~ rel_str(X0)
| ( ( ~ lower_bounded_relstr(X0)
| ? [X2] :
( relstr_element_smaller(X0,the_carrier(X0),X2)
& element(X2,the_carrier(X0)) ) )
& ( ! [X1] :
( ~ relstr_element_smaller(X0,the_carrier(X0),X1)
| ~ element(X1,the_carrier(X0)) )
| lower_bounded_relstr(X0) ) ) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
! [X0] :
( ~ rel_str(X0)
| ( ( ~ lower_bounded_relstr(X0)
| ( relstr_element_smaller(X0,the_carrier(X0),sK0(X0))
& element(sK0(X0),the_carrier(X0)) ) )
& ( ! [X1] :
( ~ relstr_element_smaller(X0,the_carrier(X0),X1)
| ~ element(X1,the_carrier(X0)) )
| lower_bounded_relstr(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0))],[f52]) ).
fof(f54,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ relstr_element_smaller(X0,X1,X2)
| ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ in(X3,X1)
| related(X0,X2,X3) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& in(X3,X1)
& ~ related(X0,X2,X3) )
| relstr_element_smaller(X0,X1,X2) ) ) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f55,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ relstr_element_smaller(X0,X1,X2)
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| ~ in(X4,X1)
| related(X0,X2,X4) ) )
& ( ? [X3] :
( element(X3,the_carrier(X0))
& in(X3,X1)
& ~ related(X0,X2,X3) )
| relstr_element_smaller(X0,X1,X2) ) ) ) ),
inference(rectify,[],[f54]) ).
fof(f56,plain,
! [X0] :
( ~ rel_str(X0)
| ! [X1,X2] :
( ~ element(X2,the_carrier(X0))
| ( ( ~ relstr_element_smaller(X0,X1,X2)
| ! [X4] :
( ~ element(X4,the_carrier(X0))
| ~ in(X4,X1)
| related(X0,X2,X4) ) )
& ( ( element(sK1(X0,X1,X2),the_carrier(X0))
& in(sK1(X0,X1,X2),X1)
& ~ related(X0,X2,sK1(X0,X1,X2)) )
| relstr_element_smaller(X0,X1,X2) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f55]) ).
fof(f64,plain,
! [X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ! [X1] :
( ( ~ ex_sup_of_relstr_set(X0,X1)
| ? [X2] :
( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X3)
| related(X0,X2,X3) )
& relstr_set_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) )
& ( ! [X2] :
( ? [X3] :
( element(X3,the_carrier(X0))
& relstr_set_smaller(X0,X1,X3)
& ~ related(X0,X2,X3) )
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ex_sup_of_relstr_set(X0,X1) ) ) ),
inference(nnf_transformation,[],[f39]) ).
fof(f65,plain,
! [X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ! [X1] :
( ( ~ ex_sup_of_relstr_set(X0,X1)
| ? [X4] :
( ! [X5] :
( ~ element(X5,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X5)
| related(X0,X4,X5) )
& relstr_set_smaller(X0,X1,X4)
& element(X4,the_carrier(X0)) ) )
& ( ! [X2] :
( ? [X3] :
( element(X3,the_carrier(X0))
& relstr_set_smaller(X0,X1,X3)
& ~ related(X0,X2,X3) )
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ex_sup_of_relstr_set(X0,X1) ) ) ),
inference(rectify,[],[f64]) ).
fof(f66,plain,
! [X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ! [X1] :
( ( ~ ex_sup_of_relstr_set(X0,X1)
| ( ! [X5] :
( ~ element(X5,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X5)
| related(X0,sK10(X0,X1),X5) )
& relstr_set_smaller(X0,X1,sK10(X0,X1))
& element(sK10(X0,X1),the_carrier(X0)) ) )
& ( ! [X2] :
( ( element(sK9(X0,X1,X2),the_carrier(X0))
& relstr_set_smaller(X0,X1,sK9(X0,X1,X2))
& ~ related(X0,X2,sK9(X0,X1,X2)) )
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ex_sup_of_relstr_set(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X3,sK9(X0,X1,X2)),skolemize(X4,sK10(X0,X1))],[f65]) ).
fof(f67,plain,
! [X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ! [X1] :
( ( ~ ex_inf_of_relstr_set(X0,X1)
| ? [X2] :
( ! [X3] :
( ~ element(X3,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X3)
| related(X0,X3,X2) )
& relstr_element_smaller(X0,X1,X2)
& element(X2,the_carrier(X0)) ) )
& ( ! [X2] :
( ? [X3] :
( element(X3,the_carrier(X0))
& relstr_element_smaller(X0,X1,X3)
& ~ related(X0,X3,X2) )
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ex_inf_of_relstr_set(X0,X1) ) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f68,plain,
! [X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ! [X1] :
( ( ~ ex_inf_of_relstr_set(X0,X1)
| ? [X4] :
( ! [X5] :
( ~ element(X5,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X5)
| related(X0,X5,X4) )
& relstr_element_smaller(X0,X1,X4)
& element(X4,the_carrier(X0)) ) )
& ( ! [X2] :
( ? [X3] :
( element(X3,the_carrier(X0))
& relstr_element_smaller(X0,X1,X3)
& ~ related(X0,X3,X2) )
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ex_inf_of_relstr_set(X0,X1) ) ) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ! [X1] :
( ( ~ ex_inf_of_relstr_set(X0,X1)
| ( ! [X5] :
( ~ element(X5,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X5)
| related(X0,X5,sK12(X0,X1)) )
& relstr_element_smaller(X0,X1,sK12(X0,X1))
& element(sK12(X0,X1),the_carrier(X0)) ) )
& ( ! [X2] :
( ( element(sK11(X0,X1,X2),the_carrier(X0))
& relstr_element_smaller(X0,X1,sK11(X0,X1,X2))
& ~ related(X0,sK11(X0,X1,X2),X2) )
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ex_inf_of_relstr_set(X0,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X3,sK11(X0,X1,X2)),skolemize(X4,sK12(X0,X1))],[f68]) ).
fof(f70,plain,
( rel_str(sK13)
& lower_bounded_relstr(sK13)
& antisymmetric_relstr(sK13)
& ~ empty_carrier(sK13)
& ( ~ ex_inf_of_relstr_set(sK13,the_carrier(sK13))
| ~ ex_sup_of_relstr_set(sK13,empty_set) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X0,sK13)],[f46]) ).
fof(f72,plain,
! [X0] :
( ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| relstr_element_smaller(X0,the_carrier(X0),sK0(X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f73,plain,
! [X0] :
( ~ rel_str(X0)
| ~ lower_bounded_relstr(X0)
| element(sK0(X0),the_carrier(X0)) ),
inference(cnf_transformation,[],[f53]) ).
fof(f75,plain,
! [X2,X0,X1,X4] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X4,the_carrier(X0))
| ~ in(X4,X1)
| related(X0,X2,X4) ),
inference(cnf_transformation,[],[f56]) ).
fof(f76,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| element(sK1(X0,X1,X2),the_carrier(X0))
| relstr_element_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ related(X0,X2,sK1(X0,X1,X2))
| relstr_element_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f56]) ).
fof(f79,plain,
! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f83,plain,
! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f37]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| element(sK9(X0,X1,X2),the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f95,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ related(X0,X2,sK9(X0,X1,X2))
| ~ relstr_set_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_sup_of_relstr_set(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| element(sK11(X0,X1,X2),the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_inf_of_relstr_set(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| relstr_element_smaller(X0,X1,sK11(X0,X1,X2))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_inf_of_relstr_set(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ rel_str(X0)
| ~ antisymmetric_relstr(X0)
| ~ related(X0,sK11(X0,X1,X2),X2)
| ~ relstr_element_smaller(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ex_inf_of_relstr_set(X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f102,plain,
! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f103,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f104,plain,
rel_str(sK13),
inference(cnf_transformation,[],[f70]) ).
fof(f105,plain,
lower_bounded_relstr(sK13),
inference(cnf_transformation,[],[f70]) ).
fof(f106,plain,
antisymmetric_relstr(sK13),
inference(cnf_transformation,[],[f70]) ).
fof(f107,plain,
~ empty_carrier(sK13),
inference(cnf_transformation,[],[f70]) ).
fof(f108,plain,
( ~ ex_inf_of_relstr_set(sK13,the_carrier(sK13))
| ~ ex_sup_of_relstr_set(sK13,empty_set) ),
inference(cnf_transformation,[],[f70]) ).
fof(f111,plain,
! [X0,X1] :
( ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| relstr_set_smaller(X0,empty_set,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_51,plain,
! [X0: $i] :
( element(sK0(X0),the_carrier(X0))
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_52,plain,
! [X0: $i] :
( relstr_element_smaller(X0,the_carrier(X0),sK0(X0))
| ~ rel_str(X0)
| ~ lower_bounded_relstr(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( relstr_element_smaller(X0,X2,X1)
| ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ related(X0,X1,sK1(X0,X2,X1)) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( relstr_element_smaller(X1,X2,X0)
| element(sK1(X1,X2,X0),the_carrier(X1))
| ~ rel_str(X1)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( related(X0,X2,X3)
| ~ rel_str(X0)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_57,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_61,plain,
! [X0: $i] :
( empty_carrier(X0)
| ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0)) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_sup_of_relstr_set(X0,X2)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ relstr_set_smaller(X0,X2,X1)
| ~ related(X0,X1,sK9(X0,X2,X1)) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_sup_of_relstr_set(X0,X1)
| element(sK9(X0,X1,X2),the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_inf_of_relstr_set(X0,X1)
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ related(X0,sK11(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_inf_of_relstr_set(X0,X1)
| relstr_element_smaller(X0,X1,sK11(X0,X1,X2))
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_inf_of_relstr_set(X0,X1)
| element(sK11(X0,X1,X2),the_carrier(X0))
| ~ antisymmetric_relstr(X0)
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_82,negated_conjecture,
( ~ ex_sup_of_relstr_set(sK13,empty_set)
| ~ ex_inf_of_relstr_set(sK13,the_carrier(sK13)) ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_83,negated_conjecture,
~ empty_carrier(sK13),
inference(cnf_transformation,[],[f107]) ).
tcf(c_84,negated_conjecture,
antisymmetric_relstr(sK13),
inference(cnf_transformation,[],[f106]) ).
tcf(c_85,negated_conjecture,
lower_bounded_relstr(sK13),
inference(cnf_transformation,[],[f105]) ).
tcf(c_86,negated_conjecture,
rel_str(sK13),
inference(cnf_transformation,[],[f104]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( relstr_set_smaller(X1,empty_set,X0)
| ~ rel_str(X1)
| ~ element(X0,the_carrier(X1)) ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_93,plain,
( one_sorted_str(sK13)
| ~ rel_str(sK13) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_99,plain,
( empty_carrier(sK13)
| ~ one_sorted_str(sK13)
| ~ empty(the_carrier(sK13)) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_101,plain,
( element(sK0(sK13),the_carrier(sK13))
| ~ rel_str(sK13)
| ~ lower_bounded_relstr(sK13) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_104,plain,
( relstr_element_smaller(sK13,the_carrier(sK13),sK0(sK13))
| ~ rel_str(sK13)
| ~ lower_bounded_relstr(sK13) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_644,plain,
! [X0: $i] :
( ~ one_sorted_str(X0)
| ~ empty(the_carrier(X0))
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_83]) ).
tcf(c_645,plain,
( ~ one_sorted_str(sK13)
| ~ empty(the_carrier(sK13)) ),
inference(unflattening,[status(thm)],[c_644]) ).
tcf(c_646,plain,
~ empty(the_carrier(sK13)),
inference(global_subsumption_just,[status(thm)],[c_645,c_86,c_83,c_93,c_99]) ).
tcf(c_749,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_inf_of_relstr_set(X0,X1)
| element(sK11(X0,X1,X2),the_carrier(X0))
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_84]) ).
tcf(c_750,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| element(sK11(sK13,X0,X1),the_carrier(sK13))
| ~ rel_str(sK13)
| ~ element(X1,the_carrier(sK13))
| ~ relstr_element_smaller(sK13,X0,X1) ),
inference(unflattening,[status(thm)],[c_749]) ).
tcf(c_752,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| element(sK11(sK13,X0,X1),the_carrier(sK13))
| ~ relstr_element_smaller(sK13,X0,X1)
| ~ element(X1,the_carrier(sK13)) ),
inference(global_subsumption_just,[status(thm)],[c_750,c_86,c_750]) ).
tcf(c_753,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| element(sK11(sK13,X0,X1),the_carrier(sK13))
| ~ element(X1,the_carrier(sK13))
| ~ relstr_element_smaller(sK13,X0,X1) ),
inference(renaming,[status(thm)],[c_752]) ).
tcf(c_767,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_inf_of_relstr_set(X0,X1)
| relstr_element_smaller(X0,X1,sK11(X0,X1,X2))
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_75,c_84]) ).
tcf(c_768,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| relstr_element_smaller(sK13,X0,sK11(sK13,X0,X1))
| ~ rel_str(sK13)
| ~ element(X1,the_carrier(sK13))
| ~ relstr_element_smaller(sK13,X0,X1) ),
inference(unflattening,[status(thm)],[c_767]) ).
tcf(c_770,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| relstr_element_smaller(sK13,X0,sK11(sK13,X0,X1))
| ~ relstr_element_smaller(sK13,X0,X1)
| ~ element(X1,the_carrier(sK13)) ),
inference(global_subsumption_just,[status(thm)],[c_768,c_86,c_768]) ).
tcf(c_771,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| relstr_element_smaller(sK13,X0,sK11(sK13,X0,X1))
| ~ element(X1,the_carrier(sK13))
| ~ relstr_element_smaller(sK13,X0,X1) ),
inference(renaming,[status(thm)],[c_770]) ).
tcf(c_785,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_inf_of_relstr_set(X0,X1)
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ~ related(X0,sK11(X0,X1,X2),X2)
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_74,c_84]) ).
tcf(c_786,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| ~ rel_str(sK13)
| ~ element(X1,the_carrier(sK13))
| ~ relstr_element_smaller(sK13,X0,X1)
| ~ related(sK13,sK11(sK13,X0,X1),X1) ),
inference(unflattening,[status(thm)],[c_785]) ).
tcf(c_788,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| ~ related(sK13,sK11(sK13,X0,X1),X1)
| ~ relstr_element_smaller(sK13,X0,X1)
| ~ element(X1,the_carrier(sK13)) ),
inference(global_subsumption_just,[status(thm)],[c_786,c_86,c_786]) ).
tcf(c_789,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| ~ element(X1,the_carrier(sK13))
| ~ relstr_element_smaller(sK13,X0,X1)
| ~ related(sK13,sK11(sK13,X0,X1),X1) ),
inference(renaming,[status(thm)],[c_788]) ).
tcf(c_845,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_sup_of_relstr_set(X0,X1)
| element(sK9(X0,X1,X2),the_carrier(X0))
| ~ rel_str(X0)
| ~ element(X2,the_carrier(X0))
| ~ relstr_set_smaller(X0,X1,X2)
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_70,c_84]) ).
tcf(c_846,plain,
! [X0: $i,X1: $i] :
( ex_sup_of_relstr_set(sK13,X0)
| element(sK9(sK13,X0,X1),the_carrier(sK13))
| ~ rel_str(sK13)
| ~ element(X1,the_carrier(sK13))
| ~ relstr_set_smaller(sK13,X0,X1) ),
inference(unflattening,[status(thm)],[c_845]) ).
tcf(c_848,plain,
! [X0: $i,X1: $i] :
( ex_sup_of_relstr_set(sK13,X0)
| element(sK9(sK13,X0,X1),the_carrier(sK13))
| ~ relstr_set_smaller(sK13,X0,X1)
| ~ element(X1,the_carrier(sK13)) ),
inference(global_subsumption_just,[status(thm)],[c_846,c_86,c_846]) ).
tcf(c_849,plain,
! [X0: $i,X1: $i] :
( ex_sup_of_relstr_set(sK13,X0)
| element(sK9(sK13,X0,X1),the_carrier(sK13))
| ~ element(X1,the_carrier(sK13))
| ~ relstr_set_smaller(sK13,X0,X1) ),
inference(renaming,[status(thm)],[c_848]) ).
tcf(c_881,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_sup_of_relstr_set(X0,X2)
| ~ rel_str(X0)
| ~ element(X1,the_carrier(X0))
| ~ relstr_set_smaller(X0,X2,X1)
| ~ related(X0,X1,sK9(X0,X2,X1))
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_84]) ).
tcf(c_882,plain,
! [X0: $i,X1: $i] :
( ex_sup_of_relstr_set(sK13,X1)
| ~ rel_str(sK13)
| ~ element(X0,the_carrier(sK13))
| ~ relstr_set_smaller(sK13,X1,X0)
| ~ related(sK13,X0,sK9(sK13,X1,X0)) ),
inference(unflattening,[status(thm)],[c_881]) ).
tcf(c_884,plain,
! [X0: $i,X1: $i] :
( ex_sup_of_relstr_set(sK13,X1)
| ~ related(sK13,X0,sK9(sK13,X1,X0))
| ~ relstr_set_smaller(sK13,X1,X0)
| ~ element(X0,the_carrier(sK13)) ),
inference(global_subsumption_just,[status(thm)],[c_882,c_86,c_882]) ).
tcf(c_885,plain,
! [X0: $i,X1: $i] :
( ex_sup_of_relstr_set(sK13,X1)
| ~ element(X0,the_carrier(sK13))
| ~ relstr_set_smaller(sK13,X1,X0)
| ~ related(sK13,X0,sK9(sK13,X1,X0)) ),
inference(renaming,[status(thm)],[c_884]) ).
tcf(c_990,plain,
! [X0: $i,X1: $i] :
( relstr_set_smaller(X0,empty_set,X1)
| ~ element(X1,the_carrier(X0))
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_88,c_86]) ).
tcf(c_991,plain,
! [X0: $i] :
( relstr_set_smaller(sK13,empty_set,X0)
| ~ element(X0,the_carrier(sK13)) ),
inference(unflattening,[status(thm)],[c_990]) ).
tcf(c_999,plain,
! [X0: $i,X1: $i,X2: $i] :
( relstr_element_smaller(X0,X2,X1)
| element(sK1(X0,X2,X1),the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_86]) ).
tcf(c_1000,plain,
! [X0: $i,X1: $i] :
( relstr_element_smaller(sK13,X1,X0)
| element(sK1(sK13,X1,X0),the_carrier(sK13))
| ~ element(X0,the_carrier(sK13)) ),
inference(unflattening,[status(thm)],[c_999]) ).
tcf(c_1080,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( related(X0,X2,X3)
| ~ in(X3,X1)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ relstr_element_smaller(X0,X1,X2)
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_86]) ).
tcf(c_1081,plain,
! [X0: $i,X1: $i,X2: $i] :
( related(sK13,X1,X2)
| ~ in(X2,X0)
| ~ element(X2,the_carrier(sK13))
| ~ element(X1,the_carrier(sK13))
| ~ relstr_element_smaller(sK13,X0,X1) ),
inference(unflattening,[status(thm)],[c_1080]) ).
tcf(c_1097,plain,
! [X0: $i,X1: $i,X2: $i] :
( relstr_element_smaller(X0,X2,X1)
| ~ element(X1,the_carrier(X0))
| ~ related(X0,X1,sK1(X0,X2,X1))
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_86]) ).
tcf(c_1098,plain,
! [X0: $i,X1: $i] :
( relstr_element_smaller(sK13,X1,X0)
| ~ element(X0,the_carrier(sK13))
| ~ related(sK13,X0,sK1(sK13,X1,X0)) ),
inference(unflattening,[status(thm)],[c_1097]) ).
tcf(c_1109,plain,
! [X0: $i] :
( relstr_element_smaller(X0,the_carrier(X0),sK0(X0))
| ~ lower_bounded_relstr(X0)
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_86]) ).
tcf(c_1110,plain,
( relstr_element_smaller(sK13,the_carrier(sK13),sK0(sK13))
| ~ lower_bounded_relstr(sK13) ),
inference(unflattening,[status(thm)],[c_1109]) ).
tcf(c_1111,plain,
relstr_element_smaller(sK13,the_carrier(sK13),sK0(sK13)),
inference(global_subsumption_just,[status(thm)],[c_1110,c_86,c_85,c_104]) ).
tcf(c_1116,plain,
! [X0: $i] :
( element(sK0(X0),the_carrier(X0))
| ~ lower_bounded_relstr(X0)
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_86]) ).
tcf(c_1117,plain,
( element(sK0(sK13),the_carrier(sK13))
| ~ lower_bounded_relstr(sK13) ),
inference(unflattening,[status(thm)],[c_1116]) ).
tcf(c_1118,plain,
element(sK0(sK13),the_carrier(sK13)),
inference(global_subsumption_just,[status(thm)],[c_1117,c_86,c_85,c_101]) ).
tcf(c_2145,definition,
iPr_def_10 = the_carrier(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2146,definition,
iPr_def_11 = sK0(sK13),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2147,plain,
! [X0: $i,X1: $i] :
( relstr_element_smaller(sK13,X1,X0)
| ~ element(X0,iPr_def_10)
| ~ related(sK13,X0,sK1(sK13,X1,X0)) ),
inference(demodulation,[status(thm)],[c_1098,c_2145]) ).
tcf(c_2148,plain,
! [X0: $i,X1: $i,X2: $i] :
( related(sK13,X1,X2)
| ~ element(X2,iPr_def_10)
| ~ element(X1,iPr_def_10)
| ~ in(X2,X0)
| ~ relstr_element_smaller(sK13,X0,X1) ),
inference(demodulation,[status(thm)],[c_1081]) ).
tcf(c_2150,plain,
! [X0: $i,X1: $i] :
( relstr_element_smaller(sK13,X1,X0)
| element(sK1(sK13,X1,X0),iPr_def_10)
| ~ element(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_1000]) ).
tcf(c_2151,plain,
! [X0: $i] :
( relstr_set_smaller(sK13,empty_set,X0)
| ~ element(X0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_991]) ).
tcf(c_2153,plain,
! [X0: $i,X1: $i] :
( ex_sup_of_relstr_set(sK13,X1)
| ~ element(X0,iPr_def_10)
| ~ relstr_set_smaller(sK13,X1,X0)
| ~ related(sK13,X0,sK9(sK13,X1,X0)) ),
inference(demodulation,[status(thm)],[c_885]) ).
tcf(c_2155,plain,
! [X0: $i,X1: $i] :
( ex_sup_of_relstr_set(sK13,X0)
| element(sK9(sK13,X0,X1),iPr_def_10)
| ~ element(X1,iPr_def_10)
| ~ relstr_set_smaller(sK13,X0,X1) ),
inference(demodulation,[status(thm)],[c_849]) ).
tcf(c_2159,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| ~ element(X1,iPr_def_10)
| ~ relstr_element_smaller(sK13,X0,X1)
| ~ related(sK13,sK11(sK13,X0,X1),X1) ),
inference(demodulation,[status(thm)],[c_789]) ).
tcf(c_2160,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| relstr_element_smaller(sK13,X0,sK11(sK13,X0,X1))
| ~ element(X1,iPr_def_10)
| ~ relstr_element_smaller(sK13,X0,X1) ),
inference(demodulation,[status(thm)],[c_771]) ).
tcf(c_2161,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| element(sK11(sK13,X0,X1),iPr_def_10)
| ~ element(X1,iPr_def_10)
| ~ relstr_element_smaller(sK13,X0,X1) ),
inference(demodulation,[status(thm)],[c_753]) ).
tcf(c_2165,plain,
element(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_1118,c_2146]) ).
tcf(c_2166,plain,
relstr_element_smaller(sK13,iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_1111]) ).
tcf(c_2167,plain,
~ empty(iPr_def_10),
inference(demodulation,[status(thm)],[c_646]) ).
tcf(c_2169,negated_conjecture,
( ~ ex_inf_of_relstr_set(sK13,iPr_def_10)
| ~ ex_sup_of_relstr_set(sK13,empty_set) ),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_2976,plain,
! [X0: $i,X1: $i] :
( empty(iPr_def_10)
| relstr_element_smaller(sK13,X1,X0)
| in(sK1(sK13,X1,X0),iPr_def_10)
| ~ element(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2150,c_81]) ).
tcf(c_2977,plain,
! [X0: $i,X1: $i] :
( empty(iPr_def_10)
| ex_sup_of_relstr_set(sK13,X0)
| in(sK9(sK13,X0,X1),iPr_def_10)
| ~ element(X1,iPr_def_10)
| ~ relstr_set_smaller(sK13,X0,X1) ),
inference(superposition,[status(thm)],[c_2155,c_81]) ).
tcf(c_2981,plain,
( empty(iPr_def_10)
| in(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2165,c_81]) ).
tcf(c_2982,plain,
in(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_2981,c_2167]) ).
tcf(c_2991,plain,
! [X0: $i,X1: $i] :
( relstr_element_smaller(sK13,X1,X0)
| in(sK1(sK13,X1,X0),iPr_def_10)
| ~ element(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2976,c_2167]) ).
tcf(c_3000,plain,
! [X0: $i,X1: $i] :
( ex_sup_of_relstr_set(sK13,X0)
| in(sK9(sK13,X0,X1),iPr_def_10)
| ~ element(X1,iPr_def_10)
| ~ relstr_set_smaller(sK13,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2977,c_2167]) ).
tcf(c_3111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| related(sK13,sK11(sK13,X0,X1),X2)
| ~ element(X2,iPr_def_10)
| ~ element(X1,iPr_def_10)
| ~ in(X2,X0)
| ~ relstr_element_smaller(sK13,X0,X1)
| ~ element(sK11(sK13,X0,X1),iPr_def_10) ),
inference(superposition,[status(thm)],[c_2160,c_2148]) ).
tcf(c_3113,plain,
! [X0: $i] :
( related(sK13,iPr_def_11,X0)
| ~ element(iPr_def_11,iPr_def_10)
| ~ element(X0,iPr_def_10)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2166,c_2148]) ).
tcf(c_3114,plain,
! [X0: $i] :
( related(sK13,iPr_def_11,X0)
| ~ element(X0,iPr_def_10)
| ~ in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3113,c_2165]) ).
tcf(c_3211,plain,
! [X0: $i] :
( related(sK13,iPr_def_11,X0)
| ~ in(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3114,c_80]) ).
tcf(c_3218,plain,
! [X0: $i] :
( ex_sup_of_relstr_set(sK13,X0)
| ~ element(iPr_def_11,iPr_def_10)
| ~ relstr_set_smaller(sK13,X0,iPr_def_11)
| ~ in(sK9(sK13,X0,iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3211,c_2153]) ).
tcf(c_3219,plain,
! [X0: $i] :
( relstr_element_smaller(sK13,X0,iPr_def_11)
| ~ element(iPr_def_11,iPr_def_10)
| ~ in(sK1(sK13,X0,iPr_def_11),iPr_def_10) ),
inference(superposition,[status(thm)],[c_3211,c_2147]) ).
tcf(c_3220,plain,
! [X0: $i] :
( relstr_element_smaller(sK13,X0,iPr_def_11)
| ~ in(sK1(sK13,X0,iPr_def_11),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3219,c_2165]) ).
tcf(c_3223,plain,
! [X0: $i] :
( ex_sup_of_relstr_set(sK13,X0)
| ~ relstr_set_smaller(sK13,X0,iPr_def_11)
| ~ in(sK9(sK13,X0,iPr_def_11),iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3218,c_2165]) ).
tcf(c_3260,plain,
! [X0: $i] :
( relstr_element_smaller(sK13,X0,iPr_def_11)
| ~ element(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2991,c_3220]) ).
tcf(c_3261,plain,
! [X0: $i] : relstr_element_smaller(sK13,X0,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_3260,c_2165]) ).
tcf(c_3469,plain,
! [X0: $i] :
( ex_sup_of_relstr_set(sK13,X0)
| ~ element(iPr_def_11,iPr_def_10)
| ~ relstr_set_smaller(sK13,X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3000,c_3223]) ).
tcf(c_3470,plain,
! [X0: $i] :
( ex_sup_of_relstr_set(sK13,X0)
| ~ relstr_set_smaller(sK13,X0,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3469,c_2165]) ).
tcf(c_3489,plain,
( ex_sup_of_relstr_set(sK13,empty_set)
| ~ element(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_2151,c_3470]) ).
tcf(c_3490,plain,
ex_sup_of_relstr_set(sK13,empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_3489,c_2165]) ).
tcf(c_3491,plain,
~ ex_inf_of_relstr_set(sK13,iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_2169,c_3490]) ).
tcf(c_4038,plain,
! [X0: $i,X1: $i,X2: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| related(sK13,sK11(sK13,X0,X1),X2)
| ~ element(X2,iPr_def_10)
| ~ element(X1,iPr_def_10)
| ~ in(X2,X0)
| ~ relstr_element_smaller(sK13,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_3111,c_2161,c_3111]) ).
tcf(c_4052,plain,
! [X0: $i,X1: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| ~ element(X1,iPr_def_10)
| ~ in(X1,X0)
| ~ relstr_element_smaller(sK13,X0,X1) ),
inference(superposition,[status(thm)],[c_4038,c_2159]) ).
tcf(c_4087,plain,
! [X0: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| ~ element(iPr_def_11,iPr_def_10)
| ~ in(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_3261,c_4052]) ).
tcf(c_4088,plain,
! [X0: $i] :
( ex_inf_of_relstr_set(sK13,X0)
| ~ in(iPr_def_11,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4087,c_2165]) ).
tcf(c_4106,plain,
ex_inf_of_relstr_set(sK13,iPr_def_10),
inference(superposition,[status(thm)],[c_2982,c_4088]) ).
tcf(c_4107,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4106,c_3491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 13:52:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.25/1.19 % SZS status Started for theBenchmark.p
% 1.25/1.19 % SZS status Theorem for theBenchmark.p
% 1.25/1.19
% 1.25/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.25/1.19
% 1.25/1.19 % ------ iProver source info
% 1.25/1.19
% 1.25/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 1.25/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.25/1.19 % git: non_committed_changes: false
% 1.25/1.19
% 1.25/1.19 % ------ Parsing...
% 1.25/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.25/1.19
% 1.25/1.19 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 1.25/1.19
% 1.25/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.25/1.19
% 1.25/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.25/1.19 % ------ Proving...
% 1.25/1.19 % ------ Problem Properties
% 1.25/1.19
% 1.25/1.19 %
% 1.25/1.19 % clauses 46
% 1.25/1.19 % conjectures 2
% 1.25/1.19 % EPR 18
% 1.25/1.19 % Horn 37
% 1.25/1.19 % unary 12
% 1.25/1.19 % binary 15
% 1.25/1.19 % lits 111
% 1.25/1.19 % lits eq 4
% 1.25/1.19 % fd_pure 0
% 1.25/1.19 % fd_pseudo 0
% 1.25/1.19 % fd_cond 1
% 1.25/1.19 % fd_pseudo_cond 1
% 1.25/1.19 % AC symbols 0
% 1.25/1.19
% 1.25/1.19 % ------ Schedule dynamic 5 is on
% 1.25/1.19
% 1.25/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.25/1.19
% 1.25/1.19
% 1.25/1.19 % ------
% 1.25/1.19 % Current options:
% 1.25/1.19 % ------
% 1.25/1.19
% 1.25/1.19
% 1.25/1.19 %
% 1.25/1.19
% 1.25/1.19 % ------ Proving...
% 1.25/1.19 %
% 1.25/1.19
% 1.25/1.19 % SZS status Theorem for theBenchmark.p
% 1.25/1.19
% 1.25/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.25/1.19
% 1.25/1.19
%------------------------------------------------------------------------------