%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 : Sun Sep 27 08:46:05 AM UTC 2026
% Result : Theorem 1.00s 0.71s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 96 ( 19 unt; 0 def)
% Number of atoms : 411 ( 0 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 529 ( 214 ~; 232 |; 61 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 140 ( 0 sgn 75 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d4_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ( lower_bounded_relstr(A)
<=> ? [B] :
( relstr_element_smaller(A,the_carrier(A),B)
& element(B,the_carrier(A)) ) ) ),
file('theBenchmark.p',d4_yellow_0) ).
fof(d8_lattice3,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( relstr_element_smaller(A,B,C)
<=> ! [D] :
( element(D,the_carrier(A))
=> ( in(D,B)
=> related(A,C,D) ) ) ) ) ),
file('theBenchmark.p',d8_lattice3) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_orders_2) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(t15_yellow_0,axiom,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( ex_sup_of_relstr_set(A,B)
<=> ? [C] :
( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,B,D)
=> related(A,C,D) ) )
& relstr_set_smaller(A,B,C)
& element(C,the_carrier(A)) ) ) ),
file('theBenchmark.p',t15_yellow_0) ).
fof(t16_yellow_0,axiom,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( ex_inf_of_relstr_set(A,B)
<=> ? [C] :
( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_element_smaller(A,B,D)
=> related(A,D,C) ) )
& relstr_element_smaller(A,B,C)
& element(C,the_carrier(A)) ) ) ),
file('theBenchmark.p',t16_yellow_0) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t6_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( element(B,the_carrier(A))
=> ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) ) ) ),
file('theBenchmark.p',t6_yellow_0) ).
fof(t42_yellow_0,conjecture,
! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) )
=> ( ex_inf_of_relstr_set(A,the_carrier(A))
& ex_sup_of_relstr_set(A,empty_set) ) ),
file('theBenchmark.p',t42_yellow_0) ).
fof(t42_yellow_0_neg,negated_conjecture,
~ ! [A] :
( ( rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) )
=> ( ex_inf_of_relstr_set(A,the_carrier(A))
& ex_sup_of_relstr_set(A,empty_set) ) ),
inference(assume_negation,[status(cth)],[t42_yellow_0]) ).
fof(nnf_26,plain,
? [A] :
( ( ~ ex_inf_of_relstr_set(A,the_carrier(A))
| ~ ex_sup_of_relstr_set(A,empty_set) )
& rel_str(A)
& lower_bounded_relstr(A)
& antisymmetric_relstr(A)
& ~ empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[t42_yellow_0_neg]) ).
fof(sk_t42_yellow_0_neg,plain,
( ( ~ ex_inf_of_relstr_set(sK0,the_carrier(sK0))
| ~ ex_sup_of_relstr_set(sK0,empty_set) )
& rel_str(sK0)
& lower_bounded_relstr(sK0)
& antisymmetric_relstr(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(A,sK0)],[nnf_26]) ).
cnf(c_28,negated_conjecture,
rel_str(sK0),
inference(split_conjunct,[status(thm)],[sk_t42_yellow_0_neg]) ).
cnf(c_29,plain,
( relstr_set_smaller(A,empty_set,B)
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[t6_yellow_0]) ).
fof(nnf_19,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ? [D] :
( ~ related(A,D,C)
& relstr_element_smaller(A,B,D)
& element(D,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C)
| ~ element(C,the_carrier(A)) )
| ex_inf_of_relstr_set(A,B) )
& ( ? [X0] :
( ! [X1] :
( related(A,X1,X0)
| ~ relstr_element_smaller(A,B,X1)
| ~ element(X1,the_carrier(A)) )
& relstr_element_smaller(A,B,X0)
& element(X0,the_carrier(A)) )
| ~ ex_inf_of_relstr_set(A,B) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(fof_nnf,[status(thm)],[t16_yellow_0]) ).
fof(sk_t16_yellow_0_sk,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ( ~ related(A,sK1(A,B,C),C)
& relstr_element_smaller(A,B,sK1(A,B,C))
& element(sK1(A,B,C),the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C)
| ~ element(C,the_carrier(A)) )
| ex_inf_of_relstr_set(A,B) )
& ( ( ! [X1] :
( related(A,X1,sK4(A,B))
| ~ relstr_element_smaller(A,B,X1)
| ~ element(X1,the_carrier(A)) )
& relstr_element_smaller(A,B,sK4(A,B))
& element(sK4(A,B),the_carrier(A)) )
| ~ ex_inf_of_relstr_set(A,B) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK1]),skolemize(X0,sK4(A,B)),skolemize(D,sK1(A,B,C))],[nnf_19]) ).
fof(sk_t16_yellow_0,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ related(VAR_0,sK1(VAR_0,VAR_1,VAR_2),VAR_2)
| ~ relstr_element_smaller(VAR_0,VAR_1,VAR_2)
| ~ element(VAR_2,the_carrier(VAR_0))
| ex_inf_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( relstr_element_smaller(VAR_0,VAR_1,sK1(VAR_0,VAR_1,VAR_2))
| ~ relstr_element_smaller(VAR_0,VAR_1,VAR_2)
| ~ element(VAR_2,the_carrier(VAR_0))
| ex_inf_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( element(sK1(VAR_0,VAR_1,VAR_2),the_carrier(VAR_0))
| ~ relstr_element_smaller(VAR_0,VAR_1,VAR_2)
| ~ element(VAR_2,the_carrier(VAR_0))
| ex_inf_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( related(VAR_0,VAR_2,sK4(VAR_0,VAR_1))
| ~ relstr_element_smaller(VAR_0,VAR_1,VAR_2)
| ~ element(VAR_2,the_carrier(VAR_0))
| ~ ex_inf_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) )
& ! [VAR_0,VAR_1] :
( relstr_element_smaller(VAR_0,VAR_1,sK4(VAR_0,VAR_1))
| ~ ex_inf_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) )
& ! [VAR_0,VAR_1] :
( element(sK4(VAR_0,VAR_1),the_carrier(VAR_0))
| ~ ex_inf_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t16_yellow_0_sk]) ).
cnf(c_30,plain,
( ~ related(A,sK1(A,B,C),C)
| ~ relstr_element_smaller(A,B,C)
| ~ element(C,the_carrier(A))
| ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(split_conjunct,[status(thm)],[sk_t16_yellow_0]) ).
cnf(c_31,plain,
( relstr_element_smaller(A,B,sK1(A,B,C))
| ~ relstr_element_smaller(A,B,C)
| ~ element(C,the_carrier(A))
| ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(split_conjunct,[status(thm)],[sk_t16_yellow_0]) ).
cnf(c_32,plain,
( element(sK1(A,B,C),the_carrier(A))
| ~ relstr_element_smaller(A,B,C)
| ~ element(C,the_carrier(A))
| ex_inf_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(split_conjunct,[status(thm)],[sk_t16_yellow_0]) ).
fof(nnf_18,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ? [D] :
( ~ related(A,C,D)
& relstr_set_smaller(A,B,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C)
| ~ element(C,the_carrier(A)) )
| ex_sup_of_relstr_set(A,B) )
& ( ? [X0] :
( ! [X1] :
( related(A,X0,X1)
| ~ relstr_set_smaller(A,B,X1)
| ~ element(X1,the_carrier(A)) )
& relstr_set_smaller(A,B,X0)
& element(X0,the_carrier(A)) )
| ~ ex_sup_of_relstr_set(A,B) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(fof_nnf,[status(thm)],[t15_yellow_0]) ).
fof(sk_t15_yellow_0_sk,plain,
! [A] :
( ! [B] :
( ( ! [C] :
( ( ~ related(A,C,sK2(A,B,C))
& relstr_set_smaller(A,B,sK2(A,B,C))
& element(sK2(A,B,C),the_carrier(A)) )
| ~ relstr_set_smaller(A,B,C)
| ~ element(C,the_carrier(A)) )
| ex_sup_of_relstr_set(A,B) )
& ( ( ! [X1] :
( related(A,sK5(A,B),X1)
| ~ relstr_set_smaller(A,B,X1)
| ~ element(X1,the_carrier(A)) )
& relstr_set_smaller(A,B,sK5(A,B))
& element(sK5(A,B),the_carrier(A)) )
| ~ ex_sup_of_relstr_set(A,B) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK2]),skolemize(X0,sK5(A,B)),skolemize(D,sK2(A,B,C))],[nnf_18]) ).
fof(sk_t15_yellow_0,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ related(VAR_0,VAR_2,sK2(VAR_0,VAR_1,VAR_2))
| ~ relstr_set_smaller(VAR_0,VAR_1,VAR_2)
| ~ element(VAR_2,the_carrier(VAR_0))
| ex_sup_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( relstr_set_smaller(VAR_0,VAR_1,sK2(VAR_0,VAR_1,VAR_2))
| ~ relstr_set_smaller(VAR_0,VAR_1,VAR_2)
| ~ element(VAR_2,the_carrier(VAR_0))
| ex_sup_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( element(sK2(VAR_0,VAR_1,VAR_2),the_carrier(VAR_0))
| ~ relstr_set_smaller(VAR_0,VAR_1,VAR_2)
| ~ element(VAR_2,the_carrier(VAR_0))
| ex_sup_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( related(VAR_0,sK5(VAR_0,VAR_1),VAR_2)
| ~ relstr_set_smaller(VAR_0,VAR_1,VAR_2)
| ~ element(VAR_2,the_carrier(VAR_0))
| ~ ex_sup_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) )
& ! [VAR_0,VAR_1] :
( relstr_set_smaller(VAR_0,VAR_1,sK5(VAR_0,VAR_1))
| ~ ex_sup_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) )
& ! [VAR_0,VAR_1] :
( element(sK5(VAR_0,VAR_1),the_carrier(VAR_0))
| ~ ex_sup_of_relstr_set(VAR_0,VAR_1)
| ~ rel_str(VAR_0)
| ~ antisymmetric_relstr(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_t15_yellow_0_sk]) ).
cnf(c_36,plain,
( ~ related(A,C,sK2(A,B,C))
| ~ relstr_set_smaller(A,B,C)
| ~ element(C,the_carrier(A))
| ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(split_conjunct,[status(thm)],[sk_t15_yellow_0]) ).
cnf(c_38,plain,
( element(sK2(A,B,C),the_carrier(A))
| ~ relstr_set_smaller(A,B,C)
| ~ element(C,the_carrier(A))
| ex_sup_of_relstr_set(A,B)
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(split_conjunct,[status(thm)],[sk_t15_yellow_0]) ).
cnf(c_43,plain,
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[dt_l1_orders_2]) ).
cnf(c_47,plain,
( related(A,B,D)
| ~ in(D,C)
| ~ element(D,the_carrier(A))
| ~ relstr_element_smaller(A,C,B)
| ~ element(B,the_carrier(A))
| ~ rel_str(A) ),
inference(clausify,[status(thm)],[d8_lattice3]) ).
fof(nnf_3,plain,
! [A] :
( ( ( ! [B] :
( ~ relstr_element_smaller(A,the_carrier(A),B)
| ~ element(B,the_carrier(A)) )
| lower_bounded_relstr(A) )
& ( ? [X0] :
( relstr_element_smaller(A,the_carrier(A),X0)
& element(X0,the_carrier(A)) )
| ~ lower_bounded_relstr(A) ) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d4_yellow_0]) ).
fof(sk_d4_yellow_0_sk,plain,
! [A] :
( ( ( ! [B] :
( ~ relstr_element_smaller(A,the_carrier(A),B)
| ~ element(B,the_carrier(A)) )
| lower_bounded_relstr(A) )
& ( ( relstr_element_smaller(A,the_carrier(A),sK3(A))
& element(sK3(A),the_carrier(A)) )
| ~ lower_bounded_relstr(A) ) )
| ~ rel_str(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X0,sK3(A))],[nnf_3]) ).
fof(sk_d4_yellow_0,plain,
( ! [VAR_0,VAR_1] :
( ~ relstr_element_smaller(VAR_0,the_carrier(VAR_0),VAR_1)
| ~ element(VAR_1,the_carrier(VAR_0))
| lower_bounded_relstr(VAR_0)
| ~ rel_str(VAR_0) )
& ! [VAR_0] :
( relstr_element_smaller(VAR_0,the_carrier(VAR_0),sK3(VAR_0))
| ~ lower_bounded_relstr(VAR_0)
| ~ rel_str(VAR_0) )
& ! [VAR_0] :
( element(sK3(VAR_0),the_carrier(VAR_0))
| ~ lower_bounded_relstr(VAR_0)
| ~ rel_str(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d4_yellow_0_sk]) ).
cnf(c_49,plain,
( relstr_element_smaller(A,the_carrier(A),sK3(A))
| ~ lower_bounded_relstr(A)
| ~ rel_str(A) ),
inference(split_conjunct,[status(thm)],[sk_d4_yellow_0]) ).
cnf(c_50,plain,
( element(sK3(A),the_carrier(A))
| ~ lower_bounded_relstr(A)
| ~ rel_str(A) ),
inference(split_conjunct,[status(thm)],[sk_d4_yellow_0]) ).
cnf(c_51,plain,
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(clausify,[status(thm)],[fc1_struct_0]) ).
cnf(c_54,negated_conjecture,
one_sorted_str(sK0),
inference(resolve,[status(thm)],[c_43,c_28]) ).
cnf(c_57,negated_conjecture,
( ~ empty(the_carrier(sK0))
| empty_carrier(sK0) ),
inference(resolve,[status(thm)],[c_51,c_54]) ).
cnf(c_60,negated_conjecture,
( ~ ex_inf_of_relstr_set(sK0,the_carrier(sK0))
| ~ ex_sup_of_relstr_set(sK0,empty_set) ),
inference(split_conjunct,[status(thm)],[sk_t42_yellow_0_neg]) ).
cnf(c_61,negated_conjecture,
lower_bounded_relstr(sK0),
inference(split_conjunct,[status(thm)],[sk_t42_yellow_0_neg]) ).
cnf(c_62,negated_conjecture,
antisymmetric_relstr(sK0),
inference(split_conjunct,[status(thm)],[sk_t42_yellow_0_neg]) ).
cnf(c_63,negated_conjecture,
~ empty_carrier(sK0),
inference(split_conjunct,[status(thm)],[sk_t42_yellow_0_neg]) ).
cnf(c_67,plain,
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(clausify,[status(thm)],[t2_subset]) ).
cnf(c_77,negated_conjecture,
( relstr_set_smaller(sK0,empty_set,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_29,c_28]) ).
cnf(c_78,negated_conjecture,
( ~ related(sK0,sK1(sK0,A,B),B)
| ~ relstr_element_smaller(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,A)
| ~ antisymmetric_relstr(sK0) ),
inference(resolve,[status(thm)],[c_30,c_28]) ).
cnf(c_79,negated_conjecture,
( ~ related(sK0,sK1(sK0,A,B),B)
| ~ relstr_element_smaller(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,A) ),
inference(resolve,[status(thm)],[c_62,c_78]) ).
cnf(c_80,negated_conjecture,
( relstr_element_smaller(sK0,A,sK1(sK0,A,B))
| ~ relstr_element_smaller(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,A)
| ~ antisymmetric_relstr(sK0) ),
inference(resolve,[status(thm)],[c_31,c_28]) ).
cnf(c_81,negated_conjecture,
( relstr_element_smaller(sK0,A,sK1(sK0,A,B))
| ~ relstr_element_smaller(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,A) ),
inference(resolve,[status(thm)],[c_62,c_80]) ).
cnf(c_82,negated_conjecture,
( element(sK1(sK0,A,B),the_carrier(sK0))
| ~ relstr_element_smaller(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,A)
| ~ antisymmetric_relstr(sK0) ),
inference(resolve,[status(thm)],[c_32,c_28]) ).
cnf(c_83,negated_conjecture,
( element(sK1(sK0,A,B),the_carrier(sK0))
| ~ relstr_element_smaller(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,A) ),
inference(resolve,[status(thm)],[c_62,c_82]) ).
cnf(c_90,negated_conjecture,
( ~ related(sK0,B,sK2(sK0,A,B))
| ~ relstr_set_smaller(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ex_sup_of_relstr_set(sK0,A)
| ~ antisymmetric_relstr(sK0) ),
inference(resolve,[status(thm)],[c_36,c_28]) ).
cnf(c_91,negated_conjecture,
( ~ related(sK0,B,sK2(sK0,A,B))
| ~ relstr_set_smaller(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ex_sup_of_relstr_set(sK0,A) ),
inference(resolve,[status(thm)],[c_62,c_90]) ).
cnf(c_94,negated_conjecture,
( element(sK2(sK0,A,B),the_carrier(sK0))
| ~ relstr_set_smaller(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ex_sup_of_relstr_set(sK0,A)
| ~ antisymmetric_relstr(sK0) ),
inference(resolve,[status(thm)],[c_38,c_28]) ).
cnf(c_95,negated_conjecture,
( element(sK2(sK0,A,B),the_carrier(sK0))
| ~ relstr_set_smaller(sK0,A,B)
| ~ element(B,the_carrier(sK0))
| ex_sup_of_relstr_set(sK0,A) ),
inference(resolve,[status(thm)],[c_62,c_94]) ).
cnf(c_123,negated_conjecture,
( related(sK0,A,C)
| ~ in(C,B)
| ~ element(C,the_carrier(sK0))
| ~ relstr_element_smaller(sK0,B,A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_47,c_28]) ).
cnf(c_126,negated_conjecture,
( relstr_element_smaller(sK0,the_carrier(sK0),sK3(sK0))
| ~ lower_bounded_relstr(sK0) ),
inference(resolve,[status(thm)],[c_49,c_28]) ).
cnf(c_127,negated_conjecture,
relstr_element_smaller(sK0,the_carrier(sK0),sK3(sK0)),
inference(resolve,[status(thm)],[c_61,c_126]) ).
cnf(c_129,negated_conjecture,
( element(sK3(sK0),the_carrier(sK0))
| ~ lower_bounded_relstr(sK0) ),
inference(resolve,[status(thm)],[c_50,c_28]) ).
cnf(c_130,negated_conjecture,
element(sK3(sK0),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_61,c_129]) ).
cnf(c_131,negated_conjecture,
~ empty(the_carrier(sK0)),
inference(resolve,[status(thm)],[c_63,c_57]) ).
cnf(c_1734,negated_conjecture,
( related(sK0,sK3(sK0),A)
| ~ in(A,the_carrier(sK0))
| ~ element(A,the_carrier(sK0))
| ~ element(sK3(sK0),the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_127,c_123]) ).
cnf(c_170,negated_conjecture,
( related(sK0,sK3(sK0),A)
| ~ in(A,the_carrier(sK0))
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_130,c_1734]) ).
cnf(c_1735,negated_conjecture,
( element(sK1(sK0,the_carrier(sK0),sK3(sK0)),the_carrier(sK0))
| ~ element(sK3(sK0),the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_127,c_83]) ).
cnf(c_172,negated_conjecture,
( element(sK1(sK0,the_carrier(sK0),sK3(sK0)),the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_130,c_1735]) ).
cnf(c_1736,negated_conjecture,
( relstr_element_smaller(sK0,the_carrier(sK0),sK1(sK0,the_carrier(sK0),sK3(sK0)))
| ~ element(sK3(sK0),the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_127,c_81]) ).
cnf(c_173,negated_conjecture,
( relstr_element_smaller(sK0,the_carrier(sK0),sK1(sK0,the_carrier(sK0),sK3(sK0)))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_130,c_1736]) ).
cnf(c_1737,negated_conjecture,
( ~ related(sK0,sK1(sK0,the_carrier(sK0),sK3(sK0)),sK3(sK0))
| ~ element(sK3(sK0),the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_127,c_79]) ).
cnf(c_174,negated_conjecture,
( ~ related(sK0,sK1(sK0,the_carrier(sK0),sK3(sK0)),sK3(sK0))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_130,c_1737]) ).
cnf(c_187,plain,
( ~ related(sK0,sK1(sK0,A,sK3(sK0)),sK3(sK0))
| ~ relstr_element_smaller(sK0,A,sK3(sK0))
| ex_inf_of_relstr_set(sK0,A) ),
inference(resolve,[status(thm)],[c_130,c_79]) ).
cnf(c_188,plain,
relstr_set_smaller(sK0,empty_set,sK3(sK0)),
inference(resolve,[status(thm)],[c_130,c_77]) ).
cnf(c_1738,negated_conjecture,
( in(sK3(sK0),the_carrier(sK0))
| empty(the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_130,c_67]) ).
cnf(c_190,negated_conjecture,
in(sK3(sK0),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_131,c_1738]) ).
cnf(c_1739,negated_conjecture,
( element(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0))
| ~ element(sK3(sK0),the_carrier(sK0))
| ex_sup_of_relstr_set(sK0,empty_set) ),
inference(resolve,[status(thm)],[c_188,c_95]) ).
cnf(c_205,negated_conjecture,
( element(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0))
| ex_sup_of_relstr_set(sK0,empty_set) ),
inference(resolve,[status(thm)],[c_130,c_1739]) ).
cnf(c_1740,negated_conjecture,
( ~ related(sK0,sK3(sK0),sK2(sK0,empty_set,sK3(sK0)))
| ~ element(sK3(sK0),the_carrier(sK0))
| ex_sup_of_relstr_set(sK0,empty_set) ),
inference(resolve,[status(thm)],[c_188,c_91]) ).
cnf(c_207,negated_conjecture,
( ~ related(sK0,sK3(sK0),sK2(sK0,empty_set,sK3(sK0)))
| ex_sup_of_relstr_set(sK0,empty_set) ),
inference(resolve,[status(thm)],[c_130,c_1740]) ).
cnf(c_1741,negated_conjecture,
( related(sK0,A,sK3(sK0))
| ~ element(sK3(sK0),the_carrier(sK0))
| ~ relstr_element_smaller(sK0,the_carrier(sK0),A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_190,c_123]) ).
cnf(c_213,negated_conjecture,
( related(sK0,A,sK3(sK0))
| ~ relstr_element_smaller(sK0,the_carrier(sK0),A)
| ~ element(A,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_130,c_1741]) ).
cnf(c_243,plain,
( ~ ex_inf_of_relstr_set(sK0,the_carrier(sK0))
| element(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_205,c_60]) ).
cnf(c_263,plain,
( element(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0))
| element(sK1(sK0,the_carrier(sK0),sK3(sK0)),the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_172,c_243]) ).
cnf(c_269,plain,
( ~ ex_sup_of_relstr_set(sK0,empty_set)
| element(sK1(sK0,the_carrier(sK0),sK3(sK0)),the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_172,c_60]) ).
cnf(c_279,plain,
( related(sK0,sK1(sK0,the_carrier(sK0),sK3(sK0)),sK3(sK0))
| ~ element(sK1(sK0,the_carrier(sK0),sK3(sK0)),the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_173,c_213]) ).
cnf(c_681,plain,
( element(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0))
| related(sK0,sK1(sK0,the_carrier(sK0),sK3(sK0)),sK3(sK0))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_279,c_263]) ).
cnf(c_1742,plain,
( ~ relstr_element_smaller(sK0,the_carrier(sK0),sK3(sK0))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0))
| element(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_681,c_187]) ).
cnf(c_1743,plain,
( ~ relstr_element_smaller(sK0,the_carrier(sK0),sK3(sK0))
| element(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0)) ),
inference(copy,[status(thm)],[c_1742]) ).
cnf(c_1608,negated_conjecture,
( element(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0))
| ex_inf_of_relstr_set(sK0,the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_127,c_1743]) ).
cnf(c_1744,plain,
( element(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0))
| element(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_1608,c_243]) ).
cnf(c_1612,plain,
element(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0)),
inference(copy,[status(thm)],[c_1744]) ).
cnf(c_1637,plain,
( related(sK0,sK3(sK0),sK2(sK0,empty_set,sK3(sK0)))
| ~ in(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_1612,c_170]) ).
cnf(c_1745,plain,
( in(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0))
| empty(the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_1612,c_67]) ).
cnf(c_1656,negated_conjecture,
in(sK2(sK0,empty_set,sK3(sK0)),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_131,c_1745]) ).
cnf(c_1659,plain,
related(sK0,sK3(sK0),sK2(sK0,empty_set,sK3(sK0))),
inference(resolve,[status(thm)],[c_1656,c_1637]) ).
cnf(c_1661,negated_conjecture,
ex_sup_of_relstr_set(sK0,empty_set),
inference(resolve,[status(thm)],[c_1659,c_207]) ).
cnf(c_1672,plain,
element(sK1(sK0,the_carrier(sK0),sK3(sK0)),the_carrier(sK0)),
inference(resolve,[status(thm)],[c_1661,c_269]) ).
cnf(c_1675,negated_conjecture,
~ ex_inf_of_relstr_set(sK0,the_carrier(sK0)),
inference(resolve,[status(thm)],[c_1661,c_60]) ).
cnf(c_1746,negated_conjecture,
( related(sK0,sK1(sK0,the_carrier(sK0),sK3(sK0)),sK3(sK0))
| ~ element(sK1(sK0,the_carrier(sK0),sK3(sK0)),the_carrier(sK0)) ),
inference(resolve,[status(thm)],[c_1675,c_279]) ).
cnf(c_1714,negated_conjecture,
related(sK0,sK1(sK0,the_carrier(sK0),sK3(sK0)),sK3(sK0)),
inference(resolve,[status(thm)],[c_1672,c_1746]) ).
cnf(c_1747,negated_conjecture,
~ related(sK0,sK1(sK0,the_carrier(sK0),sK3(sK0)),sK3(sK0)),
inference(resolve,[status(thm)],[c_1675,c_174]) ).
cnf(c_1733,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1714,c_1747]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n004.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 09:18:51 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 1368462 was started by sandbox2 on n004,
% 0.15/0.43 % Sat Sep 26 09:18:51 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 1.00/0.71
% 1.00/0.71 % SZS status Theorem for theBenchmark
% 1.00/0.71
% 1.00/0.71 % Proof 1 at 0.20 (+ 0.05) seconds.
% 1.00/0.71 % Length of proof is 70.
% 1.00/0.71 % Level of proof is 16.
% 1.00/0.71 % Maximum clause weight is 38.000.
% 1.00/0.71 % Given clauses 477.
% 1.00/0.71
% 1.00/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------