%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU360+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 150.21s 150.54s
% Output : Proof 150.64s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('theBenchmark.p',cc1_finset_1) ).
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_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_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(fc1_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(rc1_finset_1,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_struct_0,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('theBenchmark.p',rc3_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(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
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(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
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(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_2_2,plain,
! [U_2] :
( finite(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_2] :
( finite(U_2)
| ~ empty(U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( finite(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( ( ( lower_bounded_relstr(A)
| ! [B] :
( ~ relstr_element_smaller(A,the_carrier(A),B)
| ~ element(B,the_carrier(A)) ) )
& ( ? [B] :
( relstr_element_smaller(A,the_carrier(A),B)
& element(B,the_carrier(A)) )
| ~ lower_bounded_relstr(A) ) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d4_yellow_0]) ).
fof(f_3_2,plain,
! [U_5] :
( ( ( lower_bounded_relstr(U_5)
| ! [U_4] :
( ~ relstr_element_smaller(U_5,the_carrier(U_5),U_4)
| ~ element(U_4,the_carrier(U_5)) ) )
& ( ? [U_3] :
( relstr_element_smaller(U_5,the_carrier(U_5),U_3)
& element(U_3,the_carrier(U_5)) )
| ~ lower_bounded_relstr(U_5) ) )
| ~ rel_str(U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_5] :
( ( ( lower_bounded_relstr(U_5)
| ! [U_4] :
( ~ relstr_element_smaller(U_5,the_carrier(U_5),U_4)
| ~ element(U_4,the_carrier(U_5)) ) )
& ( ( relstr_element_smaller(U_5,the_carrier(U_5),sK1(U_5))
& element(sK1(U_5),the_carrier(U_5)) )
| ~ lower_bounded_relstr(U_5) ) )
| ~ rel_str(U_5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1(U_5))],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_5] :
( relstr_element_smaller(U_5,the_carrier(U_5),sK1(U_5))
| ~ sP0(U_5) )
& ! [U_5] :
( element(sK1(U_5),the_carrier(U_5))
| ~ sP0(U_5) )
& ! [U_4,U_5] :
( lower_bounded_relstr(U_5)
| ~ relstr_element_smaller(U_5,the_carrier(U_5),U_4)
| ~ element(U_4,the_carrier(U_5))
| ~ sP1(U_4,U_5) )
& ! [U_4,U_5] :
( sP0(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ sP1(U_4,U_5) )
& ! [U_4,U_5] :
( sP1(U_4,U_5)
| ~ rel_str(U_5) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_3_3]) ).
cnf(f_3_5,plain,
( sP1(U_4,U_5)
| ~ rel_str(U_5) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( sP0(U_5)
| ~ lower_bounded_relstr(U_5)
| ~ sP1(U_4,U_5) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_7,plain,
( lower_bounded_relstr(U_5)
| ~ relstr_element_smaller(U_5,the_carrier(U_5),U_4)
| ~ element(U_4,the_carrier(U_5))
| ~ sP1(U_4,U_5) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_8,plain,
( element(sK1(U_5),the_carrier(U_5))
| ~ sP0(U_5) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_9,plain,
( relstr_element_smaller(U_5,the_carrier(U_5),sK1(U_5))
| ~ sP0(U_5) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
! [A] :
( ! [B,C] :
( ( ( relstr_element_smaller(A,B,C)
| ? [D] :
( ~ related(A,C,D)
& in(D,B)
& element(D,the_carrier(A)) ) )
& ( ! [D] :
( related(A,C,D)
| ~ in(D,B)
| ~ element(D,the_carrier(A)) )
| ~ relstr_element_smaller(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[d8_lattice3]) ).
fof(f_4_2,plain,
! [U_10] :
( ! [U_9,U_8] :
( ( ( relstr_element_smaller(U_10,U_9,U_8)
| ? [U_7] :
( ~ related(U_10,U_8,U_7)
& in(U_7,U_9)
& element(U_7,the_carrier(U_10)) ) )
& ( ! [U_6] :
( related(U_10,U_8,U_6)
| ~ in(U_6,U_9)
| ~ element(U_6,the_carrier(U_10)) )
| ~ relstr_element_smaller(U_10,U_9,U_8) ) )
| ~ element(U_8,the_carrier(U_10)) )
| ~ rel_str(U_10) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_10] :
( ! [U_9,U_8] :
( ( ( relstr_element_smaller(U_10,U_9,U_8)
| ( ~ related(U_10,U_8,sK2(U_10,U_9,U_8))
& in(sK2(U_10,U_9,U_8),U_9)
& element(sK2(U_10,U_9,U_8),the_carrier(U_10)) ) )
& ( ! [U_6] :
( related(U_10,U_8,U_6)
| ~ in(U_6,U_9)
| ~ element(U_6,the_carrier(U_10)) )
| ~ relstr_element_smaller(U_10,U_9,U_8) ) )
| ~ element(U_8,the_carrier(U_10)) )
| ~ rel_str(U_10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_7,sK2(U_10,U_9,U_8))],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_10,U_8,U_9] :
( ~ related(U_10,U_8,sK2(U_10,U_9,U_8))
| ~ sP2(U_10,U_8,U_9) )
& ! [U_10,U_8,U_9] :
( in(sK2(U_10,U_9,U_8),U_9)
| ~ sP2(U_10,U_8,U_9) )
& ! [U_10,U_8,U_9] :
( element(sK2(U_10,U_9,U_8),the_carrier(U_10))
| ~ sP2(U_10,U_8,U_9) )
& ! [U_10,U_8,U_6,U_9] :
( relstr_element_smaller(U_10,U_9,U_8)
| sP2(U_10,U_8,U_9)
| ~ sP3(U_10,U_8,U_6,U_9) )
& ! [U_10,U_8,U_6,U_9] :
( related(U_10,U_8,U_6)
| ~ in(U_6,U_9)
| ~ element(U_6,the_carrier(U_10))
| ~ relstr_element_smaller(U_10,U_9,U_8)
| ~ sP3(U_10,U_8,U_6,U_9) )
& ! [U_10,U_8,U_6,U_9] :
( sP3(U_10,U_8,U_6,U_9)
| ~ element(U_8,the_carrier(U_10))
| ~ rel_str(U_10) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2,sP3])],[f_4_3]) ).
cnf(f_4_5,plain,
( sP3(U_10,U_8,U_6,U_9)
| ~ element(U_8,the_carrier(U_10))
| ~ rel_str(U_10) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( related(U_10,U_8,U_6)
| ~ in(U_6,U_9)
| ~ element(U_6,the_carrier(U_10))
| ~ relstr_element_smaller(U_10,U_9,U_8)
| ~ sP3(U_10,U_8,U_6,U_9) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( relstr_element_smaller(U_10,U_9,U_8)
| sP2(U_10,U_8,U_9)
| ~ sP3(U_10,U_8,U_6,U_9) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_8,plain,
( element(sK2(U_10,U_9,U_8),the_carrier(U_10))
| ~ sP2(U_10,U_8,U_9) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_9,plain,
( in(sK2(U_10,U_9,U_8),U_9)
| ~ sP2(U_10,U_8,U_9) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_10,plain,
( ~ related(U_10,U_8,sK2(U_10,U_9,U_8))
| ~ sP2(U_10,U_8,U_9) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_5_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_5_1]) ).
cnf(f_5_3,plain,
$true,
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( one_sorted_str(A)
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_orders_2]) ).
fof(f_6_2,plain,
! [U_11] :
( one_sorted_str(U_11)
| ~ rel_str(U_11) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_11] :
( one_sorted_str(U_11)
| ~ rel_str(U_11) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( one_sorted_str(U_11)
| ~ rel_str(U_11) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
fof(f_7_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_7_1]) ).
cnf(f_7_3,plain,
$true,
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_8_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_8_1]) ).
cnf(f_8_3,plain,
$true,
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
fof(f_9_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
$true,
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
? [A] : rel_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_orders_2]) ).
fof(f_10_2,plain,
? [U_12] : rel_str(U_12),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
rel_str(sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_12,sK3)],[f_10_2]) ).
fof(f_10_4,plain,
rel_str(sK3),
inference(definitional_conversion,[status(esa)],[f_10_3]) ).
cnf(f_10_5,plain,
rel_str(sK3),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_11_2,plain,
? [U_13] : one_sorted_str(U_13),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
one_sorted_str(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_13,sK4)],[f_11_2]) ).
fof(f_11_4,plain,
one_sorted_str(sK4),
inference(definitional_conversion,[status(esa)],[f_11_3]) ).
cnf(f_11_5,plain,
one_sorted_str(sK4),
inference(clausify,[status(thm)],[f_11_4]) ).
fof(f_12_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_12_2,plain,
! [U_15] :
? [U_14] : element(U_14,U_15),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_15] : element(sK5(U_15),U_15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_14,sK5(U_15))],[f_12_2]) ).
fof(f_12_4,plain,
! [U_15] : element(sK5(U_15),U_15),
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,plain,
element(sK5(U_15),U_15),
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_1,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_13_2,plain,
! [U_16] :
( ~ empty(the_carrier(U_16))
| ~ one_sorted_str(U_16)
| empty_carrier(U_16) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_16] :
( ~ empty(the_carrier(U_16))
| ~ one_sorted_str(U_16)
| empty_carrier(U_16) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( ~ empty(the_carrier(U_16))
| ~ one_sorted_str(U_16)
| empty_carrier(U_16) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_14_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_14_1]) ).
cnf(f_14_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_15_2,plain,
? [U_17] :
( finite(U_17)
& ~ empty(U_17) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( finite(sK6)
& ~ empty(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_17,sK6)],[f_15_2]) ).
fof(f_15_4,plain,
( finite(sK6)
& ~ empty(sK6) ),
inference(definitional_conversion,[status(esa)],[f_15_3]) ).
cnf(f_15_5,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
finite(sK6),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_16_2,plain,
? [U_18] : empty(U_18),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_18,sK7)],[f_16_2]) ).
fof(f_16_4,plain,
empty(sK7),
inference(definitional_conversion,[status(esa)],[f_16_3]) ).
cnf(f_16_5,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_17_2,plain,
? [U_19] : ~ empty(U_19),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_19,sK8)],[f_17_2]) ).
fof(f_17_4,plain,
~ empty(sK8),
inference(definitional_conversion,[status(esa)],[f_17_3]) ).
cnf(f_17_5,plain,
~ empty(sK8),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_1,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_18_2,plain,
? [U_20] :
( ~ empty_carrier(U_20)
& one_sorted_str(U_20) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ~ empty_carrier(sK9)
& one_sorted_str(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_20,sK9)],[f_18_2]) ).
fof(f_18_4,plain,
( ~ empty_carrier(sK9)
& one_sorted_str(sK9) ),
inference(definitional_conversion,[status(esa)],[f_18_3]) ).
cnf(f_18_5,plain,
one_sorted_str(sK9),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
~ empty_carrier(sK9),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_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_19_2,plain,
! [U_26] :
( ! [U_25] :
( ( ex_sup_of_relstr_set(U_26,U_25)
| ! [U_24] :
( ? [U_23] :
( ~ related(U_26,U_24,U_23)
& relstr_set_smaller(U_26,U_25,U_23)
& element(U_23,the_carrier(U_26)) )
| ~ relstr_set_smaller(U_26,U_25,U_24)
| ~ element(U_24,the_carrier(U_26)) ) )
& ( ? [U_22] :
( ! [U_21] :
( related(U_26,U_22,U_21)
| ~ relstr_set_smaller(U_26,U_25,U_21)
| ~ element(U_21,the_carrier(U_26)) )
& relstr_set_smaller(U_26,U_25,U_22)
& element(U_22,the_carrier(U_26)) )
| ~ ex_sup_of_relstr_set(U_26,U_25) ) )
| ~ rel_str(U_26)
| ~ antisymmetric_relstr(U_26) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_26] :
( ( ! [U_28] :
( ex_sup_of_relstr_set(U_26,U_28)
| ! [U_24] :
( ? [U_23] :
( ~ related(U_26,U_24,U_23)
& relstr_set_smaller(U_26,U_28,U_23)
& element(U_23,the_carrier(U_26)) )
| ~ relstr_set_smaller(U_26,U_28,U_24)
| ~ element(U_24,the_carrier(U_26)) ) )
& ! [U_27] :
( ? [U_22] :
( ! [U_21] :
( related(U_26,U_22,U_21)
| ~ relstr_set_smaller(U_26,U_27,U_21)
| ~ element(U_21,the_carrier(U_26)) )
& relstr_set_smaller(U_26,U_27,U_22)
& element(U_22,the_carrier(U_26)) )
| ~ ex_sup_of_relstr_set(U_26,U_27) ) )
| ~ rel_str(U_26)
| ~ antisymmetric_relstr(U_26) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
! [U_26] :
( ( ! [U_28] :
( ex_sup_of_relstr_set(U_26,U_28)
| ! [U_24] :
( ? [U_23] :
( ~ related(U_26,U_24,U_23)
& relstr_set_smaller(U_26,U_28,U_23)
& element(U_23,the_carrier(U_26)) )
| ~ relstr_set_smaller(U_26,U_28,U_24)
| ~ element(U_24,the_carrier(U_26)) ) )
& ! [U_27] :
( ( ! [U_21] :
( related(U_26,sK10(U_26,U_27),U_21)
| ~ relstr_set_smaller(U_26,U_27,U_21)
| ~ element(U_21,the_carrier(U_26)) )
& relstr_set_smaller(U_26,U_27,sK10(U_26,U_27))
& element(sK10(U_26,U_27),the_carrier(U_26)) )
| ~ ex_sup_of_relstr_set(U_26,U_27) ) )
| ~ rel_str(U_26)
| ~ antisymmetric_relstr(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_22,sK10(U_26,U_27))],[f_19_3]) ).
fof(f_19_5,plain,
! [U_26] :
( ( ! [U_28] :
( ex_sup_of_relstr_set(U_26,U_28)
| ! [U_24] :
( ( ~ related(U_26,U_24,sK11(U_26,U_28,U_24))
& relstr_set_smaller(U_26,U_28,sK11(U_26,U_28,U_24))
& element(sK11(U_26,U_28,U_24),the_carrier(U_26)) )
| ~ relstr_set_smaller(U_26,U_28,U_24)
| ~ element(U_24,the_carrier(U_26)) ) )
& ! [U_27] :
( ( ! [U_21] :
( related(U_26,sK10(U_26,U_27),U_21)
| ~ relstr_set_smaller(U_26,U_27,U_21)
| ~ element(U_21,the_carrier(U_26)) )
& relstr_set_smaller(U_26,U_27,sK10(U_26,U_27))
& element(sK10(U_26,U_27),the_carrier(U_26)) )
| ~ ex_sup_of_relstr_set(U_26,U_27) ) )
| ~ rel_str(U_26)
| ~ antisymmetric_relstr(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_23,sK11(U_26,U_28,U_24))],[f_19_4]) ).
fof(f_19_6,plain,
( ! [U_24,U_26,U_28] :
( ~ related(U_26,U_24,sK11(U_26,U_28,U_24))
| ~ sP5(U_24,U_26,U_28) )
& ! [U_24,U_26,U_28] :
( relstr_set_smaller(U_26,U_28,sK11(U_26,U_28,U_24))
| ~ sP5(U_24,U_26,U_28) )
& ! [U_24,U_26,U_28] :
( element(sK11(U_26,U_28,U_24),the_carrier(U_26))
| ~ sP5(U_24,U_26,U_28) )
& ! [U_26,U_27,U_21] :
( related(U_26,sK10(U_26,U_27),U_21)
| ~ relstr_set_smaller(U_26,U_27,U_21)
| ~ element(U_21,the_carrier(U_26))
| ~ sP4(U_26,U_27,U_21) )
& ! [U_26,U_27,U_21] :
( relstr_set_smaller(U_26,U_27,sK10(U_26,U_27))
| ~ sP4(U_26,U_27,U_21) )
& ! [U_26,U_27,U_21] :
( element(sK10(U_26,U_27),the_carrier(U_26))
| ~ sP4(U_26,U_27,U_21) )
& ! [U_24,U_26,U_27,U_28,U_21] :
( ex_sup_of_relstr_set(U_26,U_28)
| sP5(U_24,U_26,U_28)
| ~ relstr_set_smaller(U_26,U_28,U_24)
| ~ element(U_24,the_carrier(U_26))
| ~ sP6(U_24,U_26,U_27,U_28,U_21) )
& ! [U_24,U_26,U_27,U_28,U_21] :
( sP4(U_26,U_27,U_21)
| ~ ex_sup_of_relstr_set(U_26,U_27)
| ~ sP6(U_24,U_26,U_27,U_28,U_21) )
& ! [U_24,U_26,U_27,U_28,U_21] :
( sP6(U_24,U_26,U_27,U_28,U_21)
| ~ rel_str(U_26)
| ~ antisymmetric_relstr(U_26) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4,sP5,sP6])],[f_19_5]) ).
cnf(f_19_7,plain,
( sP6(U_24,U_26,U_27,U_28,U_21)
| ~ rel_str(U_26)
| ~ antisymmetric_relstr(U_26) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_8,plain,
( sP4(U_26,U_27,U_21)
| ~ ex_sup_of_relstr_set(U_26,U_27)
| ~ sP6(U_24,U_26,U_27,U_28,U_21) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_9,plain,
( ex_sup_of_relstr_set(U_26,U_28)
| sP5(U_24,U_26,U_28)
| ~ relstr_set_smaller(U_26,U_28,U_24)
| ~ element(U_24,the_carrier(U_26))
| ~ sP6(U_24,U_26,U_27,U_28,U_21) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_10,plain,
( element(sK10(U_26,U_27),the_carrier(U_26))
| ~ sP4(U_26,U_27,U_21) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_11,plain,
( relstr_set_smaller(U_26,U_27,sK10(U_26,U_27))
| ~ sP4(U_26,U_27,U_21) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_12,plain,
( related(U_26,sK10(U_26,U_27),U_21)
| ~ relstr_set_smaller(U_26,U_27,U_21)
| ~ element(U_21,the_carrier(U_26))
| ~ sP4(U_26,U_27,U_21) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_13,plain,
( element(sK11(U_26,U_28,U_24),the_carrier(U_26))
| ~ sP5(U_24,U_26,U_28) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_14,plain,
( relstr_set_smaller(U_26,U_28,sK11(U_26,U_28,U_24))
| ~ sP5(U_24,U_26,U_28) ),
inference(clausify,[status(thm)],[f_19_6]) ).
cnf(f_19_15,plain,
( ~ related(U_26,U_24,sK11(U_26,U_28,U_24))
| ~ sP5(U_24,U_26,U_28) ),
inference(clausify,[status(thm)],[f_19_6]) ).
fof(f_20_1,plain,
! [A] :
( ! [B] :
( ( ex_inf_of_relstr_set(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)) ) )
& ( ? [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) ) )
| ~ rel_str(A)
| ~ antisymmetric_relstr(A) ),
inference(fof_nnf,[status(thm)],[t16_yellow_0]) ).
fof(f_20_2,plain,
! [U_34] :
( ! [U_33] :
( ( ex_inf_of_relstr_set(U_34,U_33)
| ! [U_32] :
( ? [U_31] :
( ~ related(U_34,U_31,U_32)
& relstr_element_smaller(U_34,U_33,U_31)
& element(U_31,the_carrier(U_34)) )
| ~ relstr_element_smaller(U_34,U_33,U_32)
| ~ element(U_32,the_carrier(U_34)) ) )
& ( ? [U_30] :
( ! [U_29] :
( related(U_34,U_29,U_30)
| ~ relstr_element_smaller(U_34,U_33,U_29)
| ~ element(U_29,the_carrier(U_34)) )
& relstr_element_smaller(U_34,U_33,U_30)
& element(U_30,the_carrier(U_34)) )
| ~ ex_inf_of_relstr_set(U_34,U_33) ) )
| ~ rel_str(U_34)
| ~ antisymmetric_relstr(U_34) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_34] :
( ( ! [U_36] :
( ex_inf_of_relstr_set(U_34,U_36)
| ! [U_32] :
( ? [U_31] :
( ~ related(U_34,U_31,U_32)
& relstr_element_smaller(U_34,U_36,U_31)
& element(U_31,the_carrier(U_34)) )
| ~ relstr_element_smaller(U_34,U_36,U_32)
| ~ element(U_32,the_carrier(U_34)) ) )
& ! [U_35] :
( ? [U_30] :
( ! [U_29] :
( related(U_34,U_29,U_30)
| ~ relstr_element_smaller(U_34,U_35,U_29)
| ~ element(U_29,the_carrier(U_34)) )
& relstr_element_smaller(U_34,U_35,U_30)
& element(U_30,the_carrier(U_34)) )
| ~ ex_inf_of_relstr_set(U_34,U_35) ) )
| ~ rel_str(U_34)
| ~ antisymmetric_relstr(U_34) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
! [U_34] :
( ( ! [U_36] :
( ex_inf_of_relstr_set(U_34,U_36)
| ! [U_32] :
( ? [U_31] :
( ~ related(U_34,U_31,U_32)
& relstr_element_smaller(U_34,U_36,U_31)
& element(U_31,the_carrier(U_34)) )
| ~ relstr_element_smaller(U_34,U_36,U_32)
| ~ element(U_32,the_carrier(U_34)) ) )
& ! [U_35] :
( ( ! [U_29] :
( related(U_34,U_29,sK12(U_34,U_35))
| ~ relstr_element_smaller(U_34,U_35,U_29)
| ~ element(U_29,the_carrier(U_34)) )
& relstr_element_smaller(U_34,U_35,sK12(U_34,U_35))
& element(sK12(U_34,U_35),the_carrier(U_34)) )
| ~ ex_inf_of_relstr_set(U_34,U_35) ) )
| ~ rel_str(U_34)
| ~ antisymmetric_relstr(U_34) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_30,sK12(U_34,U_35))],[f_20_3]) ).
fof(f_20_5,plain,
! [U_34] :
( ( ! [U_36] :
( ex_inf_of_relstr_set(U_34,U_36)
| ! [U_32] :
( ( ~ related(U_34,sK13(U_34,U_36,U_32),U_32)
& relstr_element_smaller(U_34,U_36,sK13(U_34,U_36,U_32))
& element(sK13(U_34,U_36,U_32),the_carrier(U_34)) )
| ~ relstr_element_smaller(U_34,U_36,U_32)
| ~ element(U_32,the_carrier(U_34)) ) )
& ! [U_35] :
( ( ! [U_29] :
( related(U_34,U_29,sK12(U_34,U_35))
| ~ relstr_element_smaller(U_34,U_35,U_29)
| ~ element(U_29,the_carrier(U_34)) )
& relstr_element_smaller(U_34,U_35,sK12(U_34,U_35))
& element(sK12(U_34,U_35),the_carrier(U_34)) )
| ~ ex_inf_of_relstr_set(U_34,U_35) ) )
| ~ rel_str(U_34)
| ~ antisymmetric_relstr(U_34) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_31,sK13(U_34,U_36,U_32))],[f_20_4]) ).
fof(f_20_6,plain,
( ! [U_32,U_36,U_34] :
( ~ related(U_34,sK13(U_34,U_36,U_32),U_32)
| ~ sP8(U_32,U_36,U_34) )
& ! [U_32,U_36,U_34] :
( relstr_element_smaller(U_34,U_36,sK13(U_34,U_36,U_32))
| ~ sP8(U_32,U_36,U_34) )
& ! [U_32,U_36,U_34] :
( element(sK13(U_34,U_36,U_32),the_carrier(U_34))
| ~ sP8(U_32,U_36,U_34) )
& ! [U_35,U_29,U_34] :
( related(U_34,U_29,sK12(U_34,U_35))
| ~ relstr_element_smaller(U_34,U_35,U_29)
| ~ element(U_29,the_carrier(U_34))
| ~ sP7(U_35,U_29,U_34) )
& ! [U_35,U_29,U_34] :
( relstr_element_smaller(U_34,U_35,sK12(U_34,U_35))
| ~ sP7(U_35,U_29,U_34) )
& ! [U_35,U_29,U_34] :
( element(sK12(U_34,U_35),the_carrier(U_34))
| ~ sP7(U_35,U_29,U_34) )
& ! [U_32,U_35,U_29,U_36,U_34] :
( ex_inf_of_relstr_set(U_34,U_36)
| sP8(U_32,U_36,U_34)
| ~ relstr_element_smaller(U_34,U_36,U_32)
| ~ element(U_32,the_carrier(U_34))
| ~ sP9(U_32,U_35,U_29,U_36,U_34) )
& ! [U_32,U_35,U_29,U_36,U_34] :
( sP7(U_35,U_29,U_34)
| ~ ex_inf_of_relstr_set(U_34,U_35)
| ~ sP9(U_32,U_35,U_29,U_36,U_34) )
& ! [U_32,U_35,U_29,U_36,U_34] :
( sP9(U_32,U_35,U_29,U_36,U_34)
| ~ rel_str(U_34)
| ~ antisymmetric_relstr(U_34) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7,sP8,sP9])],[f_20_5]) ).
cnf(f_20_7,plain,
( sP9(U_32,U_35,U_29,U_36,U_34)
| ~ rel_str(U_34)
| ~ antisymmetric_relstr(U_34) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_8,plain,
( sP7(U_35,U_29,U_34)
| ~ ex_inf_of_relstr_set(U_34,U_35)
| ~ sP9(U_32,U_35,U_29,U_36,U_34) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_9,plain,
( ex_inf_of_relstr_set(U_34,U_36)
| sP8(U_32,U_36,U_34)
| ~ relstr_element_smaller(U_34,U_36,U_32)
| ~ element(U_32,the_carrier(U_34))
| ~ sP9(U_32,U_35,U_29,U_36,U_34) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_10,plain,
( element(sK12(U_34,U_35),the_carrier(U_34))
| ~ sP7(U_35,U_29,U_34) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_11,plain,
( relstr_element_smaller(U_34,U_35,sK12(U_34,U_35))
| ~ sP7(U_35,U_29,U_34) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_12,plain,
( related(U_34,U_29,sK12(U_34,U_35))
| ~ relstr_element_smaller(U_34,U_35,U_29)
| ~ element(U_29,the_carrier(U_34))
| ~ sP7(U_35,U_29,U_34) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_13,plain,
( element(sK13(U_34,U_36,U_32),the_carrier(U_34))
| ~ sP8(U_32,U_36,U_34) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_14,plain,
( relstr_element_smaller(U_34,U_36,sK13(U_34,U_36,U_32))
| ~ sP8(U_32,U_36,U_34) ),
inference(clausify,[status(thm)],[f_20_6]) ).
cnf(f_20_15,plain,
( ~ related(U_34,sK13(U_34,U_36,U_32),U_32)
| ~ sP8(U_32,U_36,U_34) ),
inference(clausify,[status(thm)],[f_20_6]) ).
fof(f_21_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_21_2,plain,
! [U_38,U_37] :
( element(U_38,U_37)
| ~ in(U_38,U_37) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_38,U_37] :
( element(U_38,U_37)
| ~ in(U_38,U_37) ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( element(U_38,U_37)
| ~ in(U_38,U_37) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_22_2,plain,
! [U_40,U_39] :
( in(U_40,U_39)
| empty(U_39)
| ~ element(U_40,U_39) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_39,U_40] :
( in(U_40,U_39)
| empty(U_39)
| ~ element(U_40,U_39) ),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
( in(U_40,U_39)
| empty(U_39)
| ~ element(U_40,U_39) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,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(negate,[status(cth)],[t42_yellow_0]) ).
fof(f_23_2,negated_conjecture,
? [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)],[f_23_1]) ).
fof(f_23_3,negated_conjecture,
? [U_41] :
( ( ~ ex_inf_of_relstr_set(U_41,the_carrier(U_41))
| ~ ex_sup_of_relstr_set(U_41,empty_set) )
& rel_str(U_41)
& lower_bounded_relstr(U_41)
& antisymmetric_relstr(U_41)
& ~ empty_carrier(U_41) ),
inference(variable_rename,[status(thm)],[f_23_2]) ).
fof(f_23_4,negated_conjecture,
( ( ~ ex_inf_of_relstr_set(sK14,the_carrier(sK14))
| ~ ex_sup_of_relstr_set(sK14,empty_set) )
& rel_str(sK14)
& lower_bounded_relstr(sK14)
& antisymmetric_relstr(sK14)
& ~ empty_carrier(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_41,sK14)],[f_23_3]) ).
fof(f_23_5,negated_conjecture,
( ( ~ ex_inf_of_relstr_set(sK14,the_carrier(sK14))
| ~ ex_sup_of_relstr_set(sK14,empty_set) )
& rel_str(sK14)
& lower_bounded_relstr(sK14)
& antisymmetric_relstr(sK14)
& ~ empty_carrier(sK14) ),
inference(definitional_conversion,[status(esa)],[f_23_4]) ).
cnf(f_23_6,negated_conjecture,
~ empty_carrier(sK14),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_7,negated_conjecture,
antisymmetric_relstr(sK14),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_8,negated_conjecture,
lower_bounded_relstr(sK14),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_9,negated_conjecture,
rel_str(sK14),
inference(clausify,[status(thm)],[f_23_5]) ).
cnf(f_23_10,negated_conjecture,
( ~ ex_inf_of_relstr_set(sK14,the_carrier(sK14))
| ~ ex_sup_of_relstr_set(sK14,empty_set) ),
inference(clausify,[status(thm)],[f_23_5]) ).
fof(f_24_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_24_2,plain,
! [U_42] :
( U_42 = empty_set
| ~ empty(U_42) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_42] :
( U_42 = empty_set
| ~ empty(U_42) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( U_42 = empty_set
| ~ empty(U_42) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A] :
( ! [B] :
( ( relstr_element_smaller(A,empty_set,B)
& relstr_set_smaller(A,empty_set,B) )
| ~ element(B,the_carrier(A)) )
| ~ rel_str(A) ),
inference(fof_nnf,[status(thm)],[t6_yellow_0]) ).
fof(f_25_2,plain,
! [U_44] :
( ! [U_43] :
( ( relstr_element_smaller(U_44,empty_set,U_43)
& relstr_set_smaller(U_44,empty_set,U_43) )
| ~ element(U_43,the_carrier(U_44)) )
| ~ rel_str(U_44) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_44,U_43] :
( relstr_element_smaller(U_44,empty_set,U_43)
| ~ sP10(U_44,U_43) )
& ! [U_44,U_43] :
( relstr_set_smaller(U_44,empty_set,U_43)
| ~ sP10(U_44,U_43) )
& ! [U_44,U_43] :
( sP10(U_44,U_43)
| ~ element(U_43,the_carrier(U_44))
| ~ rel_str(U_44) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_25_2]) ).
cnf(f_25_4,plain,
( sP10(U_44,U_43)
| ~ element(U_43,the_carrier(U_44))
| ~ rel_str(U_44) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
( relstr_set_smaller(U_44,empty_set,U_43)
| ~ sP10(U_44,U_43) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
( relstr_element_smaller(U_44,empty_set,U_43)
| ~ sP10(U_44,U_43) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_26_2,plain,
! [U_46,U_45] :
( ~ empty(U_45)
| ~ in(U_46,U_45) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_45,U_46] :
( ~ empty(U_45)
| ~ in(U_46,U_45) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( ~ empty(U_45)
| ~ in(U_46,U_45) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_27_2,plain,
! [U_48,U_47] :
( ~ empty(U_47)
| U_48 = U_47
| ~ empty(U_48) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_48] :
( ! [U_47] :
( ~ empty(U_47)
| U_48 = U_47 )
| ~ empty(U_48) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
! [U_48,U_47] :
( ~ empty(U_47)
| U_48 = U_47
| ~ empty(U_48) ),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
( ~ empty(U_47)
| U_48 = U_47
| ~ empty(U_48) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_8_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_3]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_3]) ).
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) = sK1(Eq_y_0)
| 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,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(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,
( sK11(Eq_x_0,Eq_x_1,Eq_x_2) = sK11(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,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(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_12,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( rel_str(Eq_y_0)
| ~ rel_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( lower_bounded_relstr(Eq_y_0)
| ~ lower_bounded_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,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_18,axiom,
( relstr_element_smaller(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relstr_element_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_19,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_20,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_21,axiom,
( empty_carrier(Eq_y_0)
| ~ empty_carrier(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( antisymmetric_relstr(Eq_y_0)
| ~ antisymmetric_relstr(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,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_24,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_25,axiom,
( ex_inf_of_relstr_set(Eq_y_0,Eq_y_1)
| ~ ex_inf_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_26,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( sP2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP2(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_29,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(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_31,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(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_32,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(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_34,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(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_35,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP10(Eq_y_0,Eq_y_1)
| ~ sP10(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU360+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % 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 00:03:07 UTC 2026
% 0.13/0.36 % CPUTime :
% 150.21/150.54 % SZS status Theorem for theBenchmark
% 150.21/150.54 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------