%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU356+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 08:59:06 AM UTC 2026
% Result : Theorem 102.95s 108.22s
% Output : Proof 102.95s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(d7_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ! [B] :
( ex_sup_of_relstr_set(A,B)
<=> ? [C] :
( ! [D] :
( element(D,the_carrier(A))
=> ( ( ! [E] :
( element(E,the_carrier(A))
=> ( relstr_set_smaller(A,B,E)
=> related(A,D,E) ) )
& relstr_set_smaller(A,B,D) )
=> D = 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',d7_yellow_0) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( rel_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_orders_2) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(existence_l1_orders_2,axiom,
? [A] : rel_str(A),
file('theBenchmark.p',existence_l1_orders_2) ).
fof(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(t15_yellow_0,conjecture,
! [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(t25_orders_2,axiom,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( related(A,C,B)
& related(A,B,C) )
=> B = C ) ) ) ),
file('theBenchmark.p',t25_orders_2) ).
fof(f_1_1,plain,
! [A] :
( ! [B] :
( ( ex_sup_of_relstr_set(A,B)
| ! [C] :
( ? [D] :
( D != C
& ! [E] :
( related(A,D,E)
| ~ relstr_set_smaller(A,B,E)
| ~ element(E,the_carrier(A)) )
& relstr_set_smaller(A,B,D)
& element(D,the_carrier(A)) )
| ? [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)) ) )
& ( ? [C] :
( ! [D] :
( D = C
| ? [E] :
( ~ related(A,D,E)
& relstr_set_smaller(A,B,E)
& element(E,the_carrier(A)) )
| ~ relstr_set_smaller(A,B,D)
| ~ element(D,the_carrier(A)) )
& ! [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) ) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d7_yellow_0]) ).
fof(f_1_2,plain,
! [U_9] :
( ! [U_8] :
( ( ex_sup_of_relstr_set(U_9,U_8)
| ! [U_7] :
( ? [U_6] :
( U_6 != U_7
& ! [U_5] :
( related(U_9,U_6,U_5)
| ~ relstr_set_smaller(U_9,U_8,U_5)
| ~ element(U_5,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_8,U_6)
& element(U_6,the_carrier(U_9)) )
| ? [U_4] :
( ~ related(U_9,U_7,U_4)
& relstr_set_smaller(U_9,U_8,U_4)
& element(U_4,the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_8,U_7)
| ~ element(U_7,the_carrier(U_9)) ) )
& ( ? [U_3] :
( ! [U_2] :
( U_2 = U_3
| ? [U_1] :
( ~ related(U_9,U_2,U_1)
& relstr_set_smaller(U_9,U_8,U_1)
& element(U_1,the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_8,U_2)
| ~ element(U_2,the_carrier(U_9)) )
& ! [U_0] :
( related(U_9,U_3,U_0)
| ~ relstr_set_smaller(U_9,U_8,U_0)
| ~ element(U_0,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_8,U_3)
& element(U_3,the_carrier(U_9)) )
| ~ ex_sup_of_relstr_set(U_9,U_8) ) )
| ~ rel_str(U_9) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_9] :
( ( ! [U_11] :
( ex_sup_of_relstr_set(U_9,U_11)
| ! [U_7] :
( ? [U_6] :
( U_6 != U_7
& ! [U_5] :
( related(U_9,U_6,U_5)
| ~ relstr_set_smaller(U_9,U_11,U_5)
| ~ element(U_5,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_11,U_6)
& element(U_6,the_carrier(U_9)) )
| ? [U_4] :
( ~ related(U_9,U_7,U_4)
& relstr_set_smaller(U_9,U_11,U_4)
& element(U_4,the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9)) ) )
& ! [U_10] :
( ? [U_3] :
( ! [U_2] :
( U_2 = U_3
| ? [U_1] :
( ~ related(U_9,U_2,U_1)
& relstr_set_smaller(U_9,U_10,U_1)
& element(U_1,the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_10,U_2)
| ~ element(U_2,the_carrier(U_9)) )
& ! [U_0] :
( related(U_9,U_3,U_0)
| ~ relstr_set_smaller(U_9,U_10,U_0)
| ~ element(U_0,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_10,U_3)
& element(U_3,the_carrier(U_9)) )
| ~ ex_sup_of_relstr_set(U_9,U_10) ) )
| ~ rel_str(U_9) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
! [U_9] :
( ( ! [U_11] :
( ex_sup_of_relstr_set(U_9,U_11)
| ! [U_7] :
( ? [U_6] :
( U_6 != U_7
& ! [U_5] :
( related(U_9,U_6,U_5)
| ~ relstr_set_smaller(U_9,U_11,U_5)
| ~ element(U_5,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_11,U_6)
& element(U_6,the_carrier(U_9)) )
| ? [U_4] :
( ~ related(U_9,U_7,U_4)
& relstr_set_smaller(U_9,U_11,U_4)
& element(U_4,the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9)) ) )
& ! [U_10] :
( ( ! [U_2] :
( U_2 = sK1(U_9,U_10)
| ? [U_1] :
( ~ related(U_9,U_2,U_1)
& relstr_set_smaller(U_9,U_10,U_1)
& element(U_1,the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_10,U_2)
| ~ element(U_2,the_carrier(U_9)) )
& ! [U_0] :
( related(U_9,sK1(U_9,U_10),U_0)
| ~ relstr_set_smaller(U_9,U_10,U_0)
| ~ element(U_0,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_10,sK1(U_9,U_10))
& element(sK1(U_9,U_10),the_carrier(U_9)) )
| ~ ex_sup_of_relstr_set(U_9,U_10) ) )
| ~ rel_str(U_9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1(U_9,U_10))],[f_1_3]) ).
fof(f_1_5,plain,
! [U_9] :
( ( ! [U_11] :
( ex_sup_of_relstr_set(U_9,U_11)
| ! [U_7] :
( ? [U_6] :
( U_6 != U_7
& ! [U_5] :
( related(U_9,U_6,U_5)
| ~ relstr_set_smaller(U_9,U_11,U_5)
| ~ element(U_5,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_11,U_6)
& element(U_6,the_carrier(U_9)) )
| ? [U_4] :
( ~ related(U_9,U_7,U_4)
& relstr_set_smaller(U_9,U_11,U_4)
& element(U_4,the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9)) ) )
& ! [U_10] :
( ( ! [U_2] :
( U_2 = sK1(U_9,U_10)
| ( ~ related(U_9,U_2,sK2(U_9,U_10,U_2))
& relstr_set_smaller(U_9,U_10,sK2(U_9,U_10,U_2))
& element(sK2(U_9,U_10,U_2),the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_10,U_2)
| ~ element(U_2,the_carrier(U_9)) )
& ! [U_0] :
( related(U_9,sK1(U_9,U_10),U_0)
| ~ relstr_set_smaller(U_9,U_10,U_0)
| ~ element(U_0,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_10,sK1(U_9,U_10))
& element(sK1(U_9,U_10),the_carrier(U_9)) )
| ~ ex_sup_of_relstr_set(U_9,U_10) ) )
| ~ rel_str(U_9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_1,sK2(U_9,U_10,U_2))],[f_1_4]) ).
fof(f_1_6,plain,
! [U_9] :
( ( ! [U_11] :
( ex_sup_of_relstr_set(U_9,U_11)
| ! [U_7] :
( ? [U_6] :
( U_6 != U_7
& ! [U_5] :
( related(U_9,U_6,U_5)
| ~ relstr_set_smaller(U_9,U_11,U_5)
| ~ element(U_5,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_11,U_6)
& element(U_6,the_carrier(U_9)) )
| ( ~ related(U_9,U_7,sK3(U_9,U_11,U_7))
& relstr_set_smaller(U_9,U_11,sK3(U_9,U_11,U_7))
& element(sK3(U_9,U_11,U_7),the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9)) ) )
& ! [U_10] :
( ( ! [U_2] :
( U_2 = sK1(U_9,U_10)
| ( ~ related(U_9,U_2,sK2(U_9,U_10,U_2))
& relstr_set_smaller(U_9,U_10,sK2(U_9,U_10,U_2))
& element(sK2(U_9,U_10,U_2),the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_10,U_2)
| ~ element(U_2,the_carrier(U_9)) )
& ! [U_0] :
( related(U_9,sK1(U_9,U_10),U_0)
| ~ relstr_set_smaller(U_9,U_10,U_0)
| ~ element(U_0,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_10,sK1(U_9,U_10))
& element(sK1(U_9,U_10),the_carrier(U_9)) )
| ~ ex_sup_of_relstr_set(U_9,U_10) ) )
| ~ rel_str(U_9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_4,sK3(U_9,U_11,U_7))],[f_1_5]) ).
fof(f_1_7,plain,
! [U_9] :
( ( ! [U_11] :
( ex_sup_of_relstr_set(U_9,U_11)
| ! [U_7] :
( ( sK4(U_9,U_11,U_7) != U_7
& ! [U_5] :
( related(U_9,sK4(U_9,U_11,U_7),U_5)
| ~ relstr_set_smaller(U_9,U_11,U_5)
| ~ element(U_5,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_11,sK4(U_9,U_11,U_7))
& element(sK4(U_9,U_11,U_7),the_carrier(U_9)) )
| ( ~ related(U_9,U_7,sK3(U_9,U_11,U_7))
& relstr_set_smaller(U_9,U_11,sK3(U_9,U_11,U_7))
& element(sK3(U_9,U_11,U_7),the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9)) ) )
& ! [U_10] :
( ( ! [U_2] :
( U_2 = sK1(U_9,U_10)
| ( ~ related(U_9,U_2,sK2(U_9,U_10,U_2))
& relstr_set_smaller(U_9,U_10,sK2(U_9,U_10,U_2))
& element(sK2(U_9,U_10,U_2),the_carrier(U_9)) )
| ~ relstr_set_smaller(U_9,U_10,U_2)
| ~ element(U_2,the_carrier(U_9)) )
& ! [U_0] :
( related(U_9,sK1(U_9,U_10),U_0)
| ~ relstr_set_smaller(U_9,U_10,U_0)
| ~ element(U_0,the_carrier(U_9)) )
& relstr_set_smaller(U_9,U_10,sK1(U_9,U_10))
& element(sK1(U_9,U_10),the_carrier(U_9)) )
| ~ ex_sup_of_relstr_set(U_9,U_10) ) )
| ~ rel_str(U_9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_6,sK4(U_9,U_11,U_7))],[f_1_6]) ).
cnf(f_1_8,plain,
( element(sK1(U_9,U_10),the_carrier(U_9))
| ~ ex_sup_of_relstr_set(U_9,U_10)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_9,plain,
( relstr_set_smaller(U_9,U_10,sK1(U_9,U_10))
| ~ ex_sup_of_relstr_set(U_9,U_10)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_10,plain,
( related(U_9,sK1(U_9,U_10),U_0)
| ~ relstr_set_smaller(U_9,U_10,U_0)
| ~ element(U_0,the_carrier(U_9))
| ~ ex_sup_of_relstr_set(U_9,U_10)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_11,plain,
( element(sK2(U_9,U_10,U_2),the_carrier(U_9))
| ~ relstr_set_smaller(U_9,U_10,U_2)
| U_2 = sK1(U_9,U_10)
| ~ element(U_2,the_carrier(U_9))
| ~ ex_sup_of_relstr_set(U_9,U_10)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_12,plain,
( relstr_set_smaller(U_9,U_10,sK2(U_9,U_10,U_2))
| ~ relstr_set_smaller(U_9,U_10,U_2)
| U_2 = sK1(U_9,U_10)
| ~ element(U_2,the_carrier(U_9))
| ~ ex_sup_of_relstr_set(U_9,U_10)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_13,plain,
( ~ related(U_9,U_2,sK2(U_9,U_10,U_2))
| ~ relstr_set_smaller(U_9,U_10,U_2)
| U_2 = sK1(U_9,U_10)
| ~ element(U_2,the_carrier(U_9))
| ~ ex_sup_of_relstr_set(U_9,U_10)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_14,plain,
( element(sK4(U_9,U_11,U_7),the_carrier(U_9))
| element(sK3(U_9,U_11,U_7),the_carrier(U_9))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_15,plain,
( relstr_set_smaller(U_9,U_11,sK4(U_9,U_11,U_7))
| element(sK3(U_9,U_11,U_7),the_carrier(U_9))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_16,plain,
( related(U_9,sK4(U_9,U_11,U_7),U_5)
| ~ relstr_set_smaller(U_9,U_11,U_5)
| ~ element(U_5,the_carrier(U_9))
| element(sK3(U_9,U_11,U_7),the_carrier(U_9))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_17,plain,
( sK4(U_9,U_11,U_7) != U_7
| element(sK3(U_9,U_11,U_7),the_carrier(U_9))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_18,plain,
( relstr_set_smaller(U_9,U_11,sK3(U_9,U_11,U_7))
| element(sK4(U_9,U_11,U_7),the_carrier(U_9))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_19,plain,
( ~ related(U_9,U_7,sK3(U_9,U_11,U_7))
| element(sK4(U_9,U_11,U_7),the_carrier(U_9))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_20,plain,
( relstr_set_smaller(U_9,U_11,sK4(U_9,U_11,U_7))
| relstr_set_smaller(U_9,U_11,sK3(U_9,U_11,U_7))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_21,plain,
( related(U_9,sK4(U_9,U_11,U_7),U_5)
| ~ relstr_set_smaller(U_9,U_11,U_5)
| ~ element(U_5,the_carrier(U_9))
| relstr_set_smaller(U_9,U_11,sK3(U_9,U_11,U_7))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_22,plain,
( sK4(U_9,U_11,U_7) != U_7
| relstr_set_smaller(U_9,U_11,sK3(U_9,U_11,U_7))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_23,plain,
( relstr_set_smaller(U_9,U_11,sK4(U_9,U_11,U_7))
| ~ related(U_9,U_7,sK3(U_9,U_11,U_7))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_24,plain,
( related(U_9,sK4(U_9,U_11,U_7),U_5)
| ~ relstr_set_smaller(U_9,U_11,U_5)
| ~ element(U_5,the_carrier(U_9))
| ~ related(U_9,U_7,sK3(U_9,U_11,U_7))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
cnf(f_1_25,plain,
( sK4(U_9,U_11,U_7) != U_7
| ~ related(U_9,U_7,sK3(U_9,U_11,U_7))
| ~ relstr_set_smaller(U_9,U_11,U_7)
| ~ element(U_7,the_carrier(U_9))
| ex_sup_of_relstr_set(U_9,U_11)
| ~ rel_str(U_9) ),
inference(clausify,[status(thm)],[f_1_7]) ).
fof(f_2_1,plain,
! [A] :
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_orders_2]) ).
fof(f_2_2,plain,
! [U_12] :
( one_sorted_str(U_12)
| ~ rel_str(U_12) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( one_sorted_str(U_12)
| ~ rel_str(U_12) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_3_2,plain,
$true,
inference(clausify,[status(thm)],[f_3_1]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_4_2,plain,
$true,
inference(clausify,[status(thm)],[f_4_1]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
? [A] : rel_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_orders_2]) ).
fof(f_6_2,plain,
? [U_13] : rel_str(U_13),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
rel_str(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_13,sK5)],[f_6_2]) ).
cnf(f_6_4,plain,
rel_str(sK5),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_7_2,plain,
? [U_14] : one_sorted_str(U_14),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
one_sorted_str(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_14,sK6)],[f_7_2]) ).
cnf(f_7_4,plain,
one_sorted_str(sK6),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_8_2,plain,
! [U_16] :
? [U_15] : element(U_15,U_16),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_16] : element(sK7(U_16),U_16),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_15,sK7(U_16))],[f_8_2]) ).
cnf(f_8_4,plain,
element(sK7(U_16),U_16),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,negated_conjecture,
~ ! [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)) ) ) ),
inference(negate,[status(cth)],[t15_yellow_0]) ).
fof(f_9_2,negated_conjecture,
? [A] :
( ? [B] :
( ( ~ ex_sup_of_relstr_set(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)) ) )
| ( ! [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) ) )
& rel_str(A)
& antisymmetric_relstr(A) ),
inference(fof_nnf,[status(thm)],[f_9_1]) ).
fof(f_9_3,negated_conjecture,
? [U_22] :
( ? [U_21] :
( ( ~ ex_sup_of_relstr_set(U_22,U_21)
& ? [U_20] :
( ! [U_19] :
( related(U_22,U_20,U_19)
| ~ relstr_set_smaller(U_22,U_21,U_19)
| ~ element(U_19,the_carrier(U_22)) )
& relstr_set_smaller(U_22,U_21,U_20)
& element(U_20,the_carrier(U_22)) ) )
| ( ! [U_18] :
( ? [U_17] :
( ~ related(U_22,U_18,U_17)
& relstr_set_smaller(U_22,U_21,U_17)
& element(U_17,the_carrier(U_22)) )
| ~ relstr_set_smaller(U_22,U_21,U_18)
| ~ element(U_18,the_carrier(U_22)) )
& ex_sup_of_relstr_set(U_22,U_21) ) )
& rel_str(U_22)
& antisymmetric_relstr(U_22) ),
inference(variable_rename,[status(thm)],[f_9_2]) ).
fof(f_9_4,negated_conjecture,
? [U_22] :
( ( ? [U_24] :
( ~ ex_sup_of_relstr_set(U_22,U_24)
& ? [U_20] :
( ! [U_19] :
( related(U_22,U_20,U_19)
| ~ relstr_set_smaller(U_22,U_24,U_19)
| ~ element(U_19,the_carrier(U_22)) )
& relstr_set_smaller(U_22,U_24,U_20)
& element(U_20,the_carrier(U_22)) ) )
| ? [U_23] :
( ! [U_18] :
( ? [U_17] :
( ~ related(U_22,U_18,U_17)
& relstr_set_smaller(U_22,U_23,U_17)
& element(U_17,the_carrier(U_22)) )
| ~ relstr_set_smaller(U_22,U_23,U_18)
| ~ element(U_18,the_carrier(U_22)) )
& ex_sup_of_relstr_set(U_22,U_23) ) )
& rel_str(U_22)
& antisymmetric_relstr(U_22) ),
inference(miniscope,[status(thm)],[f_9_3]) ).
fof(f_9_5,negated_conjecture,
( ( ? [U_24] :
( ~ ex_sup_of_relstr_set(sK8,U_24)
& ? [U_20] :
( ! [U_19] :
( related(sK8,U_20,U_19)
| ~ relstr_set_smaller(sK8,U_24,U_19)
| ~ element(U_19,the_carrier(sK8)) )
& relstr_set_smaller(sK8,U_24,U_20)
& element(U_20,the_carrier(sK8)) ) )
| ? [U_23] :
( ! [U_18] :
( ? [U_17] :
( ~ related(sK8,U_18,U_17)
& relstr_set_smaller(sK8,U_23,U_17)
& element(U_17,the_carrier(sK8)) )
| ~ relstr_set_smaller(sK8,U_23,U_18)
| ~ element(U_18,the_carrier(sK8)) )
& ex_sup_of_relstr_set(sK8,U_23) ) )
& rel_str(sK8)
& antisymmetric_relstr(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_22,sK8)],[f_9_4]) ).
fof(f_9_6,negated_conjecture,
( ( ? [U_24] :
( ~ ex_sup_of_relstr_set(sK8,U_24)
& ? [U_20] :
( ! [U_19] :
( related(sK8,U_20,U_19)
| ~ relstr_set_smaller(sK8,U_24,U_19)
| ~ element(U_19,the_carrier(sK8)) )
& relstr_set_smaller(sK8,U_24,U_20)
& element(U_20,the_carrier(sK8)) ) )
| ( ! [U_18] :
( ? [U_17] :
( ~ related(sK8,U_18,U_17)
& relstr_set_smaller(sK8,sK9,U_17)
& element(U_17,the_carrier(sK8)) )
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8)) )
& ex_sup_of_relstr_set(sK8,sK9) ) )
& rel_str(sK8)
& antisymmetric_relstr(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_23,sK9)],[f_9_5]) ).
fof(f_9_7,negated_conjecture,
( ( ? [U_24] :
( ~ ex_sup_of_relstr_set(sK8,U_24)
& ? [U_20] :
( ! [U_19] :
( related(sK8,U_20,U_19)
| ~ relstr_set_smaller(sK8,U_24,U_19)
| ~ element(U_19,the_carrier(sK8)) )
& relstr_set_smaller(sK8,U_24,U_20)
& element(U_20,the_carrier(sK8)) ) )
| ( ! [U_18] :
( ( ~ related(sK8,U_18,sK10(U_18))
& relstr_set_smaller(sK8,sK9,sK10(U_18))
& element(sK10(U_18),the_carrier(sK8)) )
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8)) )
& ex_sup_of_relstr_set(sK8,sK9) ) )
& rel_str(sK8)
& antisymmetric_relstr(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_17,sK10(U_18))],[f_9_6]) ).
fof(f_9_8,negated_conjecture,
( ( ( ~ ex_sup_of_relstr_set(sK8,sK11)
& ? [U_20] :
( ! [U_19] :
( related(sK8,U_20,U_19)
| ~ relstr_set_smaller(sK8,sK11,U_19)
| ~ element(U_19,the_carrier(sK8)) )
& relstr_set_smaller(sK8,sK11,U_20)
& element(U_20,the_carrier(sK8)) ) )
| ( ! [U_18] :
( ( ~ related(sK8,U_18,sK10(U_18))
& relstr_set_smaller(sK8,sK9,sK10(U_18))
& element(sK10(U_18),the_carrier(sK8)) )
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8)) )
& ex_sup_of_relstr_set(sK8,sK9) ) )
& rel_str(sK8)
& antisymmetric_relstr(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_24,sK11)],[f_9_7]) ).
fof(f_9_9,negated_conjecture,
( ( ( ~ ex_sup_of_relstr_set(sK8,sK11)
& ! [U_19] :
( related(sK8,sK12,U_19)
| ~ relstr_set_smaller(sK8,sK11,U_19)
| ~ element(U_19,the_carrier(sK8)) )
& relstr_set_smaller(sK8,sK11,sK12)
& element(sK12,the_carrier(sK8)) )
| ( ! [U_18] :
( ( ~ related(sK8,U_18,sK10(U_18))
& relstr_set_smaller(sK8,sK9,sK10(U_18))
& element(sK10(U_18),the_carrier(sK8)) )
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8)) )
& ex_sup_of_relstr_set(sK8,sK9) ) )
& rel_str(sK8)
& antisymmetric_relstr(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_20,sK12)],[f_9_8]) ).
cnf(f_9_10,negated_conjecture,
antisymmetric_relstr(sK8),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_11,negated_conjecture,
rel_str(sK8),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_12,negated_conjecture,
( element(sK12,the_carrier(sK8))
| ex_sup_of_relstr_set(sK8,sK9) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_13,negated_conjecture,
( relstr_set_smaller(sK8,sK11,sK12)
| ex_sup_of_relstr_set(sK8,sK9) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_14,negated_conjecture,
( related(sK8,sK12,U_19)
| ~ relstr_set_smaller(sK8,sK11,U_19)
| ~ element(U_19,the_carrier(sK8))
| ex_sup_of_relstr_set(sK8,sK9) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_15,negated_conjecture,
( ~ ex_sup_of_relstr_set(sK8,sK11)
| ex_sup_of_relstr_set(sK8,sK9) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_16,negated_conjecture,
( element(sK10(U_18),the_carrier(sK8))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| element(sK12,the_carrier(sK8)) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_17,negated_conjecture,
( relstr_set_smaller(sK8,sK9,sK10(U_18))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| element(sK12,the_carrier(sK8)) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_18,negated_conjecture,
( ~ related(sK8,U_18,sK10(U_18))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| element(sK12,the_carrier(sK8)) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_19,negated_conjecture,
( element(sK10(U_18),the_carrier(sK8))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| relstr_set_smaller(sK8,sK11,sK12) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_20,negated_conjecture,
( relstr_set_smaller(sK8,sK9,sK10(U_18))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| relstr_set_smaller(sK8,sK11,sK12) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_21,negated_conjecture,
( ~ related(sK8,U_18,sK10(U_18))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| relstr_set_smaller(sK8,sK11,sK12) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_22,negated_conjecture,
( element(sK10(U_18),the_carrier(sK8))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| related(sK8,sK12,U_19)
| ~ relstr_set_smaller(sK8,sK11,U_19)
| ~ element(U_19,the_carrier(sK8)) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_23,negated_conjecture,
( relstr_set_smaller(sK8,sK9,sK10(U_18))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| related(sK8,sK12,U_19)
| ~ relstr_set_smaller(sK8,sK11,U_19)
| ~ element(U_19,the_carrier(sK8)) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_24,negated_conjecture,
( ~ related(sK8,U_18,sK10(U_18))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| related(sK8,sK12,U_19)
| ~ relstr_set_smaller(sK8,sK11,U_19)
| ~ element(U_19,the_carrier(sK8)) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_25,negated_conjecture,
( element(sK10(U_18),the_carrier(sK8))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| ~ ex_sup_of_relstr_set(sK8,sK11) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_26,negated_conjecture,
( relstr_set_smaller(sK8,sK9,sK10(U_18))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| ~ ex_sup_of_relstr_set(sK8,sK11) ),
inference(clausify,[status(thm)],[f_9_9]) ).
cnf(f_9_27,negated_conjecture,
( ~ related(sK8,U_18,sK10(U_18))
| ~ relstr_set_smaller(sK8,sK9,U_18)
| ~ element(U_18,the_carrier(sK8))
| ~ ex_sup_of_relstr_set(sK8,sK11) ),
inference(clausify,[status(thm)],[f_9_9]) ).
fof(f_10_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( B = C
| ~ related(A,C,B)
| ~ related(A,B,C)
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(fof_nnf,[status(thm)],[t25_orders_2]) ).
fof(f_10_2,plain,
! [U_27] :
( ! [U_26] :
( ! [U_25] :
( U_26 = U_25
| ~ related(U_27,U_25,U_26)
| ~ related(U_27,U_26,U_25)
| ~ element(U_25,the_carrier(U_27)) )
| ~ element(U_26,the_carrier(U_27)) )
| ~ rel_str(U_27)
| ~ antisymmetric_relstr(U_27) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( U_26 = U_25
| ~ related(U_27,U_25,U_26)
| ~ related(U_27,U_26,U_25)
| ~ element(U_25,the_carrier(U_27))
| ~ element(U_26,the_carrier(U_27))
| ~ rel_str(U_27)
| ~ antisymmetric_relstr(U_27) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_3_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_3_2]) ).
cnf(f_4_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_2]) ).
cnf(f_5_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( rel_str(Eq_y_0)
| ~ rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( ex_sup_of_relstr_set(Eq_y_0,Eq_y_1)
| ~ ex_sup_of_relstr_set(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( relstr_set_smaller(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relstr_set_smaller(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( related(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ related(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( one_sorted_str(Eq_y_0)
| ~ one_sorted_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( antisymmetric_relstr(Eq_y_0)
| ~ antisymmetric_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU356+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.37 % Computer : n002.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Sun Sep 20 00:05:27 UTC 2026
% 0.11/5.38 % CPUTime :
% 102.95/108.22 % SZS status Theorem for theBenchmark
% 102.95/108.22 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------