%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU359+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 : n014.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 08:59:07 AM UTC 2026
% Result : Theorem 0.33s 0.60s
% Output : Proof 0.33s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(d9_yellow_0,axiom,
! [A] :
( rel_str(A)
=> ! [B,C] :
( element(C,the_carrier(A))
=> ( ex_sup_of_relstr_set(A,B)
=> ( C = join_on_relstr(A,B)
<=> ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,B,D)
=> related(A,C,D) ) )
& relstr_set_smaller(A,B,C) ) ) ) ) ),
file('theBenchmark.p',d9_yellow_0) ).
fof(dt_k1_yellow_0,axiom,
! [A,B] :
( rel_str(A)
=> element(join_on_relstr(A,B),the_carrier(A)) ),
file('theBenchmark.p',dt_k1_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,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(t30_yellow_0,conjecture,
! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) )
=> ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) ) )
& ( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
=> ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) ) ) ) ) ),
file('theBenchmark.p',t30_yellow_0) ).
fof(f_1_1,plain,
! [A] :
( ! [B,C] :
( ( ( C = join_on_relstr(A,B)
| ? [D] :
( ~ related(A,C,D)
& relstr_set_smaller(A,B,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(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) )
| C != join_on_relstr(A,B) ) )
| ~ ex_sup_of_relstr_set(A,B)
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d9_yellow_0]) ).
fof(f_1_2,plain,
! [U_4] :
( ! [U_3,U_2] :
( ( ( U_2 = join_on_relstr(U_4,U_3)
| ? [U_1] :
( ~ related(U_4,U_2,U_1)
& relstr_set_smaller(U_4,U_3,U_1)
& element(U_1,the_carrier(U_4)) )
| ~ relstr_set_smaller(U_4,U_3,U_2) )
& ( ( ! [U_0] :
( related(U_4,U_2,U_0)
| ~ relstr_set_smaller(U_4,U_3,U_0)
| ~ element(U_0,the_carrier(U_4)) )
& relstr_set_smaller(U_4,U_3,U_2) )
| U_2 != join_on_relstr(U_4,U_3) ) )
| ~ ex_sup_of_relstr_set(U_4,U_3)
| ~ element(U_2,the_carrier(U_4)) )
| ~ rel_str(U_4) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_4] :
( ! [U_3,U_2] :
( ( ( U_2 = join_on_relstr(U_4,U_3)
| ( ~ related(U_4,U_2,sK1(U_4,U_3,U_2))
& relstr_set_smaller(U_4,U_3,sK1(U_4,U_3,U_2))
& element(sK1(U_4,U_3,U_2),the_carrier(U_4)) )
| ~ relstr_set_smaller(U_4,U_3,U_2) )
& ( ( ! [U_0] :
( related(U_4,U_2,U_0)
| ~ relstr_set_smaller(U_4,U_3,U_0)
| ~ element(U_0,the_carrier(U_4)) )
& relstr_set_smaller(U_4,U_3,U_2) )
| U_2 != join_on_relstr(U_4,U_3) ) )
| ~ ex_sup_of_relstr_set(U_4,U_3)
| ~ element(U_2,the_carrier(U_4)) )
| ~ rel_str(U_4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_1,sK1(U_4,U_3,U_2))],[f_1_2]) ).
cnf(f_1_4,plain,
( relstr_set_smaller(U_4,U_3,U_2)
| U_2 != join_on_relstr(U_4,U_3)
| ~ ex_sup_of_relstr_set(U_4,U_3)
| ~ element(U_2,the_carrier(U_4))
| ~ rel_str(U_4) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_5,plain,
( related(U_4,U_2,U_0)
| ~ relstr_set_smaller(U_4,U_3,U_0)
| ~ element(U_0,the_carrier(U_4))
| U_2 != join_on_relstr(U_4,U_3)
| ~ ex_sup_of_relstr_set(U_4,U_3)
| ~ element(U_2,the_carrier(U_4))
| ~ rel_str(U_4) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_6,plain,
( element(sK1(U_4,U_3,U_2),the_carrier(U_4))
| ~ relstr_set_smaller(U_4,U_3,U_2)
| U_2 = join_on_relstr(U_4,U_3)
| ~ ex_sup_of_relstr_set(U_4,U_3)
| ~ element(U_2,the_carrier(U_4))
| ~ rel_str(U_4) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_7,plain,
( relstr_set_smaller(U_4,U_3,sK1(U_4,U_3,U_2))
| ~ relstr_set_smaller(U_4,U_3,U_2)
| U_2 = join_on_relstr(U_4,U_3)
| ~ ex_sup_of_relstr_set(U_4,U_3)
| ~ element(U_2,the_carrier(U_4))
| ~ rel_str(U_4) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_8,plain,
( ~ related(U_4,U_2,sK1(U_4,U_3,U_2))
| ~ relstr_set_smaller(U_4,U_3,U_2)
| U_2 = join_on_relstr(U_4,U_3)
| ~ ex_sup_of_relstr_set(U_4,U_3)
| ~ element(U_2,the_carrier(U_4))
| ~ rel_str(U_4) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A,B] :
( element(join_on_relstr(A,B),the_carrier(A))
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_yellow_0]) ).
fof(f_2_2,plain,
! [U_6,U_5] :
( element(join_on_relstr(U_6,U_5),the_carrier(U_6))
| ~ rel_str(U_6) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_6] :
( ! [U_5] : element(join_on_relstr(U_6,U_5),the_carrier(U_6))
| ~ rel_str(U_6) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( element(join_on_relstr(U_6,U_5),the_carrier(U_6))
| ~ rel_str(U_6) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_orders_2]) ).
fof(f_3_2,plain,
! [U_7] :
( one_sorted_str(U_7)
| ~ rel_str(U_7) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( one_sorted_str(U_7)
| ~ rel_str(U_7) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
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_m1_subset_1]) ).
cnf(f_5_2,plain,
$true,
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_6_2,plain,
$true,
inference(clausify,[status(thm)],[f_6_1]) ).
fof(f_7_1,plain,
? [A] : rel_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_orders_2]) ).
fof(f_7_2,plain,
? [U_8] : rel_str(U_8),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
rel_str(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_8,sK2)],[f_7_2]) ).
cnf(f_7_4,plain,
rel_str(sK2),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_8_2,plain,
? [U_9] : one_sorted_str(U_9),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
one_sorted_str(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_9,sK3)],[f_8_2]) ).
cnf(f_8_4,plain,
one_sorted_str(sK3),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_9_2,plain,
! [U_11] :
? [U_10] : element(U_10,U_11),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_11] : element(sK4(U_11),U_11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_10,sK4(U_11))],[f_9_2]) ).
cnf(f_9_4,plain,
element(sK4(U_11),U_11),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [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)],[t15_yellow_0]) ).
fof(f_10_2,plain,
! [U_17] :
( ! [U_16] :
( ( ex_sup_of_relstr_set(U_17,U_16)
| ! [U_15] :
( ? [U_14] :
( ~ related(U_17,U_15,U_14)
& relstr_set_smaller(U_17,U_16,U_14)
& element(U_14,the_carrier(U_17)) )
| ~ relstr_set_smaller(U_17,U_16,U_15)
| ~ element(U_15,the_carrier(U_17)) ) )
& ( ? [U_13] :
( ! [U_12] :
( related(U_17,U_13,U_12)
| ~ relstr_set_smaller(U_17,U_16,U_12)
| ~ element(U_12,the_carrier(U_17)) )
& relstr_set_smaller(U_17,U_16,U_13)
& element(U_13,the_carrier(U_17)) )
| ~ ex_sup_of_relstr_set(U_17,U_16) ) )
| ~ rel_str(U_17)
| ~ antisymmetric_relstr(U_17) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_17] :
( ( ! [U_19] :
( ex_sup_of_relstr_set(U_17,U_19)
| ! [U_15] :
( ? [U_14] :
( ~ related(U_17,U_15,U_14)
& relstr_set_smaller(U_17,U_19,U_14)
& element(U_14,the_carrier(U_17)) )
| ~ relstr_set_smaller(U_17,U_19,U_15)
| ~ element(U_15,the_carrier(U_17)) ) )
& ! [U_18] :
( ? [U_13] :
( ! [U_12] :
( related(U_17,U_13,U_12)
| ~ relstr_set_smaller(U_17,U_18,U_12)
| ~ element(U_12,the_carrier(U_17)) )
& relstr_set_smaller(U_17,U_18,U_13)
& element(U_13,the_carrier(U_17)) )
| ~ ex_sup_of_relstr_set(U_17,U_18) ) )
| ~ rel_str(U_17)
| ~ antisymmetric_relstr(U_17) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
! [U_17] :
( ( ! [U_19] :
( ex_sup_of_relstr_set(U_17,U_19)
| ! [U_15] :
( ? [U_14] :
( ~ related(U_17,U_15,U_14)
& relstr_set_smaller(U_17,U_19,U_14)
& element(U_14,the_carrier(U_17)) )
| ~ relstr_set_smaller(U_17,U_19,U_15)
| ~ element(U_15,the_carrier(U_17)) ) )
& ! [U_18] :
( ( ! [U_12] :
( related(U_17,sK5(U_17,U_18),U_12)
| ~ relstr_set_smaller(U_17,U_18,U_12)
| ~ element(U_12,the_carrier(U_17)) )
& relstr_set_smaller(U_17,U_18,sK5(U_17,U_18))
& element(sK5(U_17,U_18),the_carrier(U_17)) )
| ~ ex_sup_of_relstr_set(U_17,U_18) ) )
| ~ rel_str(U_17)
| ~ antisymmetric_relstr(U_17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_13,sK5(U_17,U_18))],[f_10_3]) ).
fof(f_10_5,plain,
! [U_17] :
( ( ! [U_19] :
( ex_sup_of_relstr_set(U_17,U_19)
| ! [U_15] :
( ( ~ related(U_17,U_15,sK6(U_17,U_19,U_15))
& relstr_set_smaller(U_17,U_19,sK6(U_17,U_19,U_15))
& element(sK6(U_17,U_19,U_15),the_carrier(U_17)) )
| ~ relstr_set_smaller(U_17,U_19,U_15)
| ~ element(U_15,the_carrier(U_17)) ) )
& ! [U_18] :
( ( ! [U_12] :
( related(U_17,sK5(U_17,U_18),U_12)
| ~ relstr_set_smaller(U_17,U_18,U_12)
| ~ element(U_12,the_carrier(U_17)) )
& relstr_set_smaller(U_17,U_18,sK5(U_17,U_18))
& element(sK5(U_17,U_18),the_carrier(U_17)) )
| ~ ex_sup_of_relstr_set(U_17,U_18) ) )
| ~ rel_str(U_17)
| ~ antisymmetric_relstr(U_17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_14,sK6(U_17,U_19,U_15))],[f_10_4]) ).
cnf(f_10_6,plain,
( element(sK5(U_17,U_18),the_carrier(U_17))
| ~ ex_sup_of_relstr_set(U_17,U_18)
| ~ rel_str(U_17)
| ~ antisymmetric_relstr(U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( relstr_set_smaller(U_17,U_18,sK5(U_17,U_18))
| ~ ex_sup_of_relstr_set(U_17,U_18)
| ~ rel_str(U_17)
| ~ antisymmetric_relstr(U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( related(U_17,sK5(U_17,U_18),U_12)
| ~ relstr_set_smaller(U_17,U_18,U_12)
| ~ element(U_12,the_carrier(U_17))
| ~ ex_sup_of_relstr_set(U_17,U_18)
| ~ rel_str(U_17)
| ~ antisymmetric_relstr(U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( element(sK6(U_17,U_19,U_15),the_carrier(U_17))
| ~ relstr_set_smaller(U_17,U_19,U_15)
| ~ element(U_15,the_carrier(U_17))
| ex_sup_of_relstr_set(U_17,U_19)
| ~ rel_str(U_17)
| ~ antisymmetric_relstr(U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_10,plain,
( relstr_set_smaller(U_17,U_19,sK6(U_17,U_19,U_15))
| ~ relstr_set_smaller(U_17,U_19,U_15)
| ~ element(U_15,the_carrier(U_17))
| ex_sup_of_relstr_set(U_17,U_19)
| ~ rel_str(U_17)
| ~ antisymmetric_relstr(U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_11,plain,
( ~ related(U_17,U_15,sK6(U_17,U_19,U_15))
| ~ relstr_set_smaller(U_17,U_19,U_15)
| ~ element(U_15,the_carrier(U_17))
| ex_sup_of_relstr_set(U_17,U_19)
| ~ rel_str(U_17)
| ~ antisymmetric_relstr(U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_1,negated_conjecture,
~ ! [A] :
( ( rel_str(A)
& antisymmetric_relstr(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( ( ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) )
=> ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) ) )
& ( ( ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) )
=> ( ! [D] :
( element(D,the_carrier(A))
=> ( relstr_set_smaller(A,C,D)
=> related(A,B,D) ) )
& relstr_set_smaller(A,C,B) ) ) ) ) ),
inference(negate,[status(cth)],[t30_yellow_0]) ).
fof(f_11_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ( ( ~ ex_sup_of_relstr_set(A,C)
| B != join_on_relstr(A,C) )
& ! [D] :
( related(A,B,D)
| ~ relstr_set_smaller(A,C,D)
| ~ element(D,the_carrier(A)) )
& relstr_set_smaller(A,C,B) )
| ( ( ? [D] :
( ~ related(A,B,D)
& relstr_set_smaller(A,C,D)
& element(D,the_carrier(A)) )
| ~ relstr_set_smaller(A,C,B) )
& ex_sup_of_relstr_set(A,C)
& B = join_on_relstr(A,C) ) )
& element(B,the_carrier(A)) )
& rel_str(A)
& antisymmetric_relstr(A) ),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_24] :
( ? [U_23] :
( ? [U_22] :
( ( ( ~ ex_sup_of_relstr_set(U_24,U_22)
| U_23 != join_on_relstr(U_24,U_22) )
& ! [U_21] :
( related(U_24,U_23,U_21)
| ~ relstr_set_smaller(U_24,U_22,U_21)
| ~ element(U_21,the_carrier(U_24)) )
& relstr_set_smaller(U_24,U_22,U_23) )
| ( ( ? [U_20] :
( ~ related(U_24,U_23,U_20)
& relstr_set_smaller(U_24,U_22,U_20)
& element(U_20,the_carrier(U_24)) )
| ~ relstr_set_smaller(U_24,U_22,U_23) )
& ex_sup_of_relstr_set(U_24,U_22)
& U_23 = join_on_relstr(U_24,U_22) ) )
& element(U_23,the_carrier(U_24)) )
& rel_str(U_24)
& antisymmetric_relstr(U_24) ),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
? [U_24] :
( ? [U_23] :
( ( ? [U_26] :
( ( ~ ex_sup_of_relstr_set(U_24,U_26)
| U_23 != join_on_relstr(U_24,U_26) )
& ! [U_21] :
( related(U_24,U_23,U_21)
| ~ relstr_set_smaller(U_24,U_26,U_21)
| ~ element(U_21,the_carrier(U_24)) )
& relstr_set_smaller(U_24,U_26,U_23) )
| ? [U_25] :
( ( ? [U_20] :
( ~ related(U_24,U_23,U_20)
& relstr_set_smaller(U_24,U_25,U_20)
& element(U_20,the_carrier(U_24)) )
| ~ relstr_set_smaller(U_24,U_25,U_23) )
& ex_sup_of_relstr_set(U_24,U_25)
& U_23 = join_on_relstr(U_24,U_25) ) )
& element(U_23,the_carrier(U_24)) )
& rel_str(U_24)
& antisymmetric_relstr(U_24) ),
inference(miniscope,[status(thm)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
( ? [U_23] :
( ( ? [U_26] :
( ( ~ ex_sup_of_relstr_set(sK7,U_26)
| U_23 != join_on_relstr(sK7,U_26) )
& ! [U_21] :
( related(sK7,U_23,U_21)
| ~ relstr_set_smaller(sK7,U_26,U_21)
| ~ element(U_21,the_carrier(sK7)) )
& relstr_set_smaller(sK7,U_26,U_23) )
| ? [U_25] :
( ( ? [U_20] :
( ~ related(sK7,U_23,U_20)
& relstr_set_smaller(sK7,U_25,U_20)
& element(U_20,the_carrier(sK7)) )
| ~ relstr_set_smaller(sK7,U_25,U_23) )
& ex_sup_of_relstr_set(sK7,U_25)
& U_23 = join_on_relstr(sK7,U_25) ) )
& element(U_23,the_carrier(sK7)) )
& rel_str(sK7)
& antisymmetric_relstr(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_24,sK7)],[f_11_4]) ).
fof(f_11_6,negated_conjecture,
( ( ? [U_26] :
( ( ~ ex_sup_of_relstr_set(sK7,U_26)
| sK8 != join_on_relstr(sK7,U_26) )
& ! [U_21] :
( related(sK7,sK8,U_21)
| ~ relstr_set_smaller(sK7,U_26,U_21)
| ~ element(U_21,the_carrier(sK7)) )
& relstr_set_smaller(sK7,U_26,sK8) )
| ? [U_25] :
( ( ? [U_20] :
( ~ related(sK7,sK8,U_20)
& relstr_set_smaller(sK7,U_25,U_20)
& element(U_20,the_carrier(sK7)) )
| ~ relstr_set_smaller(sK7,U_25,sK8) )
& ex_sup_of_relstr_set(sK7,U_25)
& sK8 = join_on_relstr(sK7,U_25) ) )
& element(sK8,the_carrier(sK7))
& rel_str(sK7)
& antisymmetric_relstr(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_23,sK8)],[f_11_5]) ).
fof(f_11_7,negated_conjecture,
( ( ? [U_26] :
( ( ~ ex_sup_of_relstr_set(sK7,U_26)
| sK8 != join_on_relstr(sK7,U_26) )
& ! [U_21] :
( related(sK7,sK8,U_21)
| ~ relstr_set_smaller(sK7,U_26,U_21)
| ~ element(U_21,the_carrier(sK7)) )
& relstr_set_smaller(sK7,U_26,sK8) )
| ( ( ? [U_20] :
( ~ related(sK7,sK8,U_20)
& relstr_set_smaller(sK7,sK9,U_20)
& element(U_20,the_carrier(sK7)) )
| ~ relstr_set_smaller(sK7,sK9,sK8) )
& ex_sup_of_relstr_set(sK7,sK9)
& sK8 = join_on_relstr(sK7,sK9) ) )
& element(sK8,the_carrier(sK7))
& rel_str(sK7)
& antisymmetric_relstr(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_25,sK9)],[f_11_6]) ).
fof(f_11_8,negated_conjecture,
( ( ? [U_26] :
( ( ~ ex_sup_of_relstr_set(sK7,U_26)
| sK8 != join_on_relstr(sK7,U_26) )
& ! [U_21] :
( related(sK7,sK8,U_21)
| ~ relstr_set_smaller(sK7,U_26,U_21)
| ~ element(U_21,the_carrier(sK7)) )
& relstr_set_smaller(sK7,U_26,sK8) )
| ( ( ( ~ related(sK7,sK8,sK10)
& relstr_set_smaller(sK7,sK9,sK10)
& element(sK10,the_carrier(sK7)) )
| ~ relstr_set_smaller(sK7,sK9,sK8) )
& ex_sup_of_relstr_set(sK7,sK9)
& sK8 = join_on_relstr(sK7,sK9) ) )
& element(sK8,the_carrier(sK7))
& rel_str(sK7)
& antisymmetric_relstr(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_20,sK10)],[f_11_7]) ).
fof(f_11_9,negated_conjecture,
( ( ( ( ~ ex_sup_of_relstr_set(sK7,sK11)
| sK8 != join_on_relstr(sK7,sK11) )
& ! [U_21] :
( related(sK7,sK8,U_21)
| ~ relstr_set_smaller(sK7,sK11,U_21)
| ~ element(U_21,the_carrier(sK7)) )
& relstr_set_smaller(sK7,sK11,sK8) )
| ( ( ( ~ related(sK7,sK8,sK10)
& relstr_set_smaller(sK7,sK9,sK10)
& element(sK10,the_carrier(sK7)) )
| ~ relstr_set_smaller(sK7,sK9,sK8) )
& ex_sup_of_relstr_set(sK7,sK9)
& sK8 = join_on_relstr(sK7,sK9) ) )
& element(sK8,the_carrier(sK7))
& rel_str(sK7)
& antisymmetric_relstr(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_26,sK11)],[f_11_8]) ).
fof(f_11_10,negated_conjecture,
( ! [U_21] :
( ~ ex_sup_of_relstr_set(sK7,sK11)
| sK8 != join_on_relstr(sK7,sK11)
| ~ sP2(U_21) )
& ! [U_21] :
( related(sK7,sK8,U_21)
| ~ relstr_set_smaller(sK7,sK11,U_21)
| ~ element(U_21,the_carrier(sK7))
| ~ sP2(U_21) )
& ! [U_21] :
( relstr_set_smaller(sK7,sK11,sK8)
| ~ sP2(U_21) )
& ( ~ related(sK7,sK8,sK10)
| ~ sP0 )
& ( relstr_set_smaller(sK7,sK9,sK10)
| ~ sP0 )
& ( element(sK10,the_carrier(sK7))
| ~ sP0 )
& ( sP0
| ~ relstr_set_smaller(sK7,sK9,sK8)
| ~ sP1 )
& ( ex_sup_of_relstr_set(sK7,sK9)
| ~ sP1 )
& ( sK8 = join_on_relstr(sK7,sK9)
| ~ sP1 )
& ! [U_21] :
( sP2(U_21)
| sP1 )
& element(sK8,the_carrier(sK7))
& rel_str(sK7)
& antisymmetric_relstr(sK7) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1,sP2])],[f_11_9]) ).
cnf(f_11_11,negated_conjecture,
antisymmetric_relstr(sK7),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_12,negated_conjecture,
rel_str(sK7),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_13,negated_conjecture,
element(sK8,the_carrier(sK7)),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_14,negated_conjecture,
( sP2(U_21)
| sP1 ),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_15,negated_conjecture,
( sK8 = join_on_relstr(sK7,sK9)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_16,negated_conjecture,
( ex_sup_of_relstr_set(sK7,sK9)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_17,negated_conjecture,
( sP0
| ~ relstr_set_smaller(sK7,sK9,sK8)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_18,negated_conjecture,
( element(sK10,the_carrier(sK7))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_19,negated_conjecture,
( relstr_set_smaller(sK7,sK9,sK10)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_20,negated_conjecture,
( ~ related(sK7,sK8,sK10)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_21,negated_conjecture,
( relstr_set_smaller(sK7,sK11,sK8)
| ~ sP2(U_21) ),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_22,negated_conjecture,
( related(sK7,sK8,U_21)
| ~ relstr_set_smaller(sK7,sK11,U_21)
| ~ element(U_21,the_carrier(sK7))
| ~ sP2(U_21) ),
inference(clausify,[status(thm)],[f_11_10]) ).
cnf(f_11_23,negated_conjecture,
( ~ ex_sup_of_relstr_set(sK7,sK11)
| sK8 != join_on_relstr(sK7,sK11)
| ~ sP2(U_21) ),
inference(clausify,[status(thm)],[f_11_10]) ).
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(f_6_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_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,
( join_on_relstr(Eq_x_0,Eq_x_1) = join_on_relstr(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,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(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,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(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_10,axiom,
( rel_str(Eq_y_0)
| ~ rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,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_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,
( 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_14,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_15,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_16,axiom,
( antisymmetric_relstr(Eq_y_0)
| ~ antisymmetric_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( sP2(Eq_y_0)
| ~ sP2(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 : SEU359+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
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 00:03:05 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.33/0.60 % SZS status Theorem for theBenchmark
% 0.33/0.60 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------