%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU305+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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:55 AM UTC 2026
% Result : Theorem 36.40s 36.78s
% Output : Proof 36.62s
% 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_finsub_1,axiom,
! [A] :
( preboolean(A)
=> ( diff_closed(A)
& cup_closed(A) ) ),
file('theBenchmark.p',cc1_finsub_1) ).
fof(cc2_finsub_1,axiom,
! [A] :
( ( diff_closed(A)
& cup_closed(A) )
=> preboolean(A) ),
file('theBenchmark.p',cc2_finsub_1) ).
fof(commutativity_k3_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> join_commut(A,B,C) = join_commut(A,C,B) ),
file('theBenchmark.p',commutativity_k3_lattices) ).
fof(d1_lattices,axiom,
! [A] :
( ( join_semilatt_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> join(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C) ) ) ),
file('theBenchmark.p',d1_lattices) ).
fof(d3_lattices,axiom,
! [A] :
( ( join_semilatt_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( below(A,B,C)
<=> join(A,B,C) = C ) ) ) ),
file('theBenchmark.p',d3_lattices) ).
fof(dt_k1_binop_1,axiom,
$true,
file('theBenchmark.p',dt_k1_binop_1) ).
fof(dt_k1_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& ~ empty_carrier(A) )
=> element(join(A,B,C),the_carrier(A)) ),
file('theBenchmark.p',dt_k1_lattices) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_k2_binop_1,axiom,
! [A,B,C,D,E,F] :
( ( element(F,B)
& element(E,A)
& relation_of2(D,cartesian_product2(A,B),C)
& quasi_total(D,cartesian_product2(A,B),C)
& function(D)
& ~ empty(B)
& ~ empty(A) )
=> element(apply_binary_as_element(A,B,C,D,E,F),C) ),
file('theBenchmark.p',dt_k2_binop_1) ).
fof(dt_k2_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k2_zfmisc_1) ).
fof(dt_k3_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> element(join_commut(A,B,C),the_carrier(A)) ),
file('theBenchmark.p',dt_k3_lattices) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(dt_l2_lattices,axiom,
! [A] :
( join_semilatt_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l2_lattices) ).
fof(dt_m1_relset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_relset_1) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('theBenchmark.p',dt_m2_relset_1) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(dt_u2_lattices,axiom,
! [A] :
( join_semilatt_str(A)
=> ( relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_join(A)) ) ),
file('theBenchmark.p',dt_u2_lattices) ).
fof(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_l2_lattices,axiom,
? [A] : join_semilatt_str(A),
file('theBenchmark.p',existence_l2_lattices) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : relation_of2(C,A,B),
file('theBenchmark.p',existence_m1_relset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
file('theBenchmark.p',existence_m2_relset_1) ).
fof(fc1_finsub_1,axiom,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
file('theBenchmark.p',fc1_finsub_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(rc3_struct_0,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ? [B] :
( ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc5_struct_0) ).
fof(redefinition_k2_binop_1,axiom,
! [A,B,C,D,E,F] :
( ( element(F,B)
& element(E,A)
& relation_of2(D,cartesian_product2(A,B),C)
& quasi_total(D,cartesian_product2(A,B),C)
& function(D)
& ~ empty(B)
& ~ empty(A) )
=> apply_binary_as_element(A,B,C,D,E,F) = apply_binary(D,E,F) ),
file('theBenchmark.p',redefinition_k2_binop_1) ).
fof(redefinition_k3_lattices,axiom,
! [A,B,C] :
( ( element(C,the_carrier(A))
& element(B,the_carrier(A))
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> join_commut(A,B,C) = join(A,B,C) ),
file('theBenchmark.p',redefinition_k3_lattices) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('theBenchmark.p',redefinition_m2_relset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t26_lattices,conjecture,
! [A] :
( ( join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( below(A,C,B)
& below(A,B,C) )
=> B = C ) ) ) ),
file('theBenchmark.p',t26_lattices) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
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] :
( ( diff_closed(A)
& cup_closed(A) )
| ~ preboolean(A) ),
inference(fof_nnf,[status(thm)],[cc1_finsub_1]) ).
fof(f_2_2,plain,
! [U_2] :
( ( diff_closed(U_2)
& cup_closed(U_2) )
| ~ preboolean(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_2] :
( diff_closed(U_2)
| ~ sP0(U_2) )
& ! [U_2] :
( cup_closed(U_2)
| ~ sP0(U_2) )
& ! [U_2] :
( sP0(U_2)
| ~ preboolean(U_2) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_2_2]) ).
cnf(f_2_4,plain,
( sP0(U_2)
| ~ preboolean(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( cup_closed(U_2)
| ~ sP0(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( diff_closed(U_2)
| ~ sP0(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( preboolean(A)
| ~ diff_closed(A)
| ~ cup_closed(A) ),
inference(fof_nnf,[status(thm)],[cc2_finsub_1]) ).
fof(f_3_2,plain,
! [U_3] :
( preboolean(U_3)
| ~ diff_closed(U_3)
| ~ cup_closed(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_3] :
( preboolean(U_3)
| ~ diff_closed(U_3)
| ~ cup_closed(U_3) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( preboolean(U_3)
| ~ diff_closed(U_3)
| ~ cup_closed(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A,B,C] :
( join_commut(A,B,C) = join_commut(A,C,B)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[commutativity_k3_lattices]) ).
fof(f_4_2,plain,
! [U_6,U_5,U_4] :
( join_commut(U_6,U_5,U_4) = join_commut(U_6,U_4,U_5)
| ~ element(U_4,the_carrier(U_6))
| ~ element(U_5,the_carrier(U_6))
| ~ join_semilatt_str(U_6)
| ~ join_commutative(U_6)
| empty_carrier(U_6) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5,U_6,U_4] :
( join_commut(U_6,U_5,U_4) = join_commut(U_6,U_4,U_5)
| ~ element(U_4,the_carrier(U_6))
| ~ element(U_5,the_carrier(U_6))
| ~ join_semilatt_str(U_6)
| ~ join_commutative(U_6)
| empty_carrier(U_6) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( join_commut(U_6,U_5,U_4) = join_commut(U_6,U_4,U_5)
| ~ element(U_4,the_carrier(U_6))
| ~ element(U_5,the_carrier(U_6))
| ~ join_semilatt_str(U_6)
| ~ join_commutative(U_6)
| empty_carrier(U_6) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( join(A,B,C) = apply_binary_as_element(the_carrier(A),the_carrier(A),the_carrier(A),the_L_join(A),B,C)
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d1_lattices]) ).
fof(f_5_2,plain,
! [U_9] :
( ! [U_8] :
( ! [U_7] :
( join(U_9,U_8,U_7) = apply_binary_as_element(the_carrier(U_9),the_carrier(U_9),the_carrier(U_9),the_L_join(U_9),U_8,U_7)
| ~ element(U_7,the_carrier(U_9)) )
| ~ element(U_8,the_carrier(U_9)) )
| ~ join_semilatt_str(U_9)
| empty_carrier(U_9) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_8,U_7,U_9] :
( join(U_9,U_8,U_7) = apply_binary_as_element(the_carrier(U_9),the_carrier(U_9),the_carrier(U_9),the_L_join(U_9),U_8,U_7)
| ~ element(U_7,the_carrier(U_9))
| ~ element(U_8,the_carrier(U_9))
| ~ join_semilatt_str(U_9)
| empty_carrier(U_9) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( join(U_9,U_8,U_7) = apply_binary_as_element(the_carrier(U_9),the_carrier(U_9),the_carrier(U_9),the_L_join(U_9),U_8,U_7)
| ~ element(U_7,the_carrier(U_9))
| ~ element(U_8,the_carrier(U_9))
| ~ join_semilatt_str(U_9)
| empty_carrier(U_9) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] :
( ! [B] :
( ! [C] :
( ( ( below(A,B,C)
| join(A,B,C) != C )
& ( join(A,B,C) = C
| ~ below(A,B,C) ) )
| ~ element(C,the_carrier(A)) )
| ~ element(B,the_carrier(A)) )
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[d3_lattices]) ).
fof(f_6_2,plain,
! [U_12] :
( ! [U_11] :
( ! [U_10] :
( ( ( below(U_12,U_11,U_10)
| join(U_12,U_11,U_10) != U_10 )
& ( join(U_12,U_11,U_10) = U_10
| ~ below(U_12,U_11,U_10) ) )
| ~ element(U_10,the_carrier(U_12)) )
| ~ element(U_11,the_carrier(U_12)) )
| ~ join_semilatt_str(U_12)
| empty_carrier(U_12) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_10,U_12,U_11] :
( below(U_12,U_11,U_10)
| join(U_12,U_11,U_10) != U_10
| ~ sP1(U_10,U_12,U_11) )
& ! [U_10,U_12,U_11] :
( join(U_12,U_11,U_10) = U_10
| ~ below(U_12,U_11,U_10)
| ~ sP1(U_10,U_12,U_11) )
& ! [U_10,U_12,U_11] :
( sP1(U_10,U_12,U_11)
| ~ element(U_10,the_carrier(U_12))
| ~ element(U_11,the_carrier(U_12))
| ~ join_semilatt_str(U_12)
| empty_carrier(U_12) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP1(U_10,U_12,U_11)
| ~ element(U_10,the_carrier(U_12))
| ~ element(U_11,the_carrier(U_12))
| ~ join_semilatt_str(U_12)
| empty_carrier(U_12) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( join(U_12,U_11,U_10) = U_10
| ~ below(U_12,U_11,U_10)
| ~ sP1(U_10,U_12,U_11) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( below(U_12,U_11,U_10)
| join(U_12,U_11,U_10) != U_10
| ~ sP1(U_10,U_12,U_11) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_binop_1]) ).
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,
! [A,B,C] :
( element(join(A,B,C),the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k1_lattices]) ).
fof(f_8_2,plain,
! [U_15,U_14,U_13] :
( element(join(U_15,U_14,U_13),the_carrier(U_15))
| ~ element(U_13,the_carrier(U_15))
| ~ element(U_14,the_carrier(U_15))
| ~ join_semilatt_str(U_15)
| empty_carrier(U_15) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_14,U_13,U_15] :
( element(join(U_15,U_14,U_13),the_carrier(U_15))
| ~ element(U_13,the_carrier(U_15))
| ~ element(U_14,the_carrier(U_15))
| ~ join_semilatt_str(U_15)
| empty_carrier(U_15) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( element(join(U_15,U_14,U_13),the_carrier(U_15))
| ~ element(U_13,the_carrier(U_15))
| ~ element(U_14,the_carrier(U_15))
| ~ join_semilatt_str(U_15)
| empty_carrier(U_15) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_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,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_10_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
$true,
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A,B,C,D,E,F] :
( element(apply_binary_as_element(A,B,C,D,E,F),C)
| ~ element(F,B)
| ~ element(E,A)
| ~ relation_of2(D,cartesian_product2(A,B),C)
| ~ quasi_total(D,cartesian_product2(A,B),C)
| ~ function(D)
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_binop_1]) ).
fof(f_11_2,plain,
! [U_21,U_20,U_19,U_18,U_17,U_16] :
( element(apply_binary_as_element(U_21,U_20,U_19,U_18,U_17,U_16),U_19)
| ~ element(U_16,U_20)
| ~ element(U_17,U_21)
| ~ relation_of2(U_18,cartesian_product2(U_21,U_20),U_19)
| ~ quasi_total(U_18,cartesian_product2(U_21,U_20),U_19)
| ~ function(U_18)
| empty(U_20)
| empty(U_21) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_18,U_20,U_21,U_17,U_19,U_16] :
( element(apply_binary_as_element(U_21,U_20,U_19,U_18,U_17,U_16),U_19)
| ~ element(U_16,U_20)
| ~ element(U_17,U_21)
| ~ relation_of2(U_18,cartesian_product2(U_21,U_20),U_19)
| ~ quasi_total(U_18,cartesian_product2(U_21,U_20),U_19)
| ~ function(U_18)
| empty(U_20)
| empty(U_21) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( element(apply_binary_as_element(U_21,U_20,U_19,U_18,U_17,U_16),U_19)
| ~ element(U_16,U_20)
| ~ element(U_17,U_21)
| ~ relation_of2(U_18,cartesian_product2(U_21,U_20),U_19)
| ~ quasi_total(U_18,cartesian_product2(U_21,U_20),U_19)
| ~ function(U_18)
| empty(U_20)
| empty(U_21) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_zfmisc_1]) ).
fof(f_12_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_12_1]) ).
cnf(f_12_3,plain,
$true,
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A,B,C] :
( element(join_commut(A,B,C),the_carrier(A))
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[dt_k3_lattices]) ).
fof(f_13_2,plain,
! [U_24,U_23,U_22] :
( element(join_commut(U_24,U_23,U_22),the_carrier(U_24))
| ~ element(U_22,the_carrier(U_24))
| ~ element(U_23,the_carrier(U_24))
| ~ join_semilatt_str(U_24)
| ~ join_commutative(U_24)
| empty_carrier(U_24) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_22,U_24,U_23] :
( element(join_commut(U_24,U_23,U_22),the_carrier(U_24))
| ~ element(U_22,the_carrier(U_24))
| ~ element(U_23,the_carrier(U_24))
| ~ join_semilatt_str(U_24)
| ~ join_commutative(U_24)
| empty_carrier(U_24) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( element(join_commut(U_24,U_23,U_22),the_carrier(U_24))
| ~ element(U_22,the_carrier(U_24))
| ~ element(U_23,the_carrier(U_24))
| ~ join_semilatt_str(U_24)
| ~ join_commutative(U_24)
| empty_carrier(U_24) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
fof(f_14_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_14_1]) ).
cnf(f_14_3,plain,
$true,
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( one_sorted_str(A)
| ~ join_semilatt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l2_lattices]) ).
fof(f_15_2,plain,
! [U_25] :
( one_sorted_str(U_25)
| ~ join_semilatt_str(U_25) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_25] :
( one_sorted_str(U_25)
| ~ join_semilatt_str(U_25) ),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
( one_sorted_str(U_25)
| ~ join_semilatt_str(U_25) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_relset_1]) ).
fof(f_16_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_16_1]) ).
cnf(f_16_3,plain,
$true,
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_17_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
$true,
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
| ~ relation_of2_as_subset(C,A,B) ),
inference(fof_nnf,[status(thm)],[dt_m2_relset_1]) ).
fof(f_18_2,plain,
! [U_28,U_27,U_26] :
( element(U_26,powerset(cartesian_product2(U_28,U_27)))
| ~ relation_of2_as_subset(U_26,U_28,U_27) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_27,U_26,U_28] :
( element(U_26,powerset(cartesian_product2(U_28,U_27)))
| ~ relation_of2_as_subset(U_26,U_28,U_27) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( element(U_26,powerset(cartesian_product2(U_28,U_27)))
| ~ relation_of2_as_subset(U_26,U_28,U_27) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
fof(f_19_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_19_1]) ).
cnf(f_19_3,plain,
$true,
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A] :
( ( relation_of2_as_subset(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& quasi_total(the_L_join(A),cartesian_product2(the_carrier(A),the_carrier(A)),the_carrier(A))
& function(the_L_join(A)) )
| ~ join_semilatt_str(A) ),
inference(fof_nnf,[status(thm)],[dt_u2_lattices]) ).
fof(f_20_2,plain,
! [U_29] :
( ( relation_of2_as_subset(the_L_join(U_29),cartesian_product2(the_carrier(U_29),the_carrier(U_29)),the_carrier(U_29))
& quasi_total(the_L_join(U_29),cartesian_product2(the_carrier(U_29),the_carrier(U_29)),the_carrier(U_29))
& function(the_L_join(U_29)) )
| ~ join_semilatt_str(U_29) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_29] :
( relation_of2_as_subset(the_L_join(U_29),cartesian_product2(the_carrier(U_29),the_carrier(U_29)),the_carrier(U_29))
| ~ sP2(U_29) )
& ! [U_29] :
( quasi_total(the_L_join(U_29),cartesian_product2(the_carrier(U_29),the_carrier(U_29)),the_carrier(U_29))
| ~ sP2(U_29) )
& ! [U_29] :
( function(the_L_join(U_29))
| ~ sP2(U_29) )
& ! [U_29] :
( sP2(U_29)
| ~ join_semilatt_str(U_29) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_20_2]) ).
cnf(f_20_4,plain,
( sP2(U_29)
| ~ join_semilatt_str(U_29) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( function(the_L_join(U_29))
| ~ sP2(U_29) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
( quasi_total(the_L_join(U_29),cartesian_product2(the_carrier(U_29),the_carrier(U_29)),the_carrier(U_29))
| ~ sP2(U_29) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_7,plain,
( relation_of2_as_subset(the_L_join(U_29),cartesian_product2(the_carrier(U_29),the_carrier(U_29)),the_carrier(U_29))
| ~ sP2(U_29) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_21_2,plain,
? [U_30] : one_sorted_str(U_30),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
one_sorted_str(sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_30,sK1)],[f_21_2]) ).
fof(f_21_4,plain,
one_sorted_str(sK1),
inference(definitional_conversion,[status(esa)],[f_21_3]) ).
cnf(f_21_5,plain,
one_sorted_str(sK1),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
? [A] : join_semilatt_str(A),
inference(fof_nnf,[status(thm)],[existence_l2_lattices]) ).
fof(f_22_2,plain,
? [U_31] : join_semilatt_str(U_31),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
join_semilatt_str(sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_31,sK2)],[f_22_2]) ).
fof(f_22_4,plain,
join_semilatt_str(sK2),
inference(definitional_conversion,[status(esa)],[f_22_3]) ).
cnf(f_22_5,plain,
join_semilatt_str(sK2),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,plain,
! [A,B] :
? [C] : relation_of2(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m1_relset_1]) ).
fof(f_23_2,plain,
! [U_34,U_33] :
? [U_32] : relation_of2(U_32,U_34,U_33),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_34,U_33] : relation_of2(sK3(U_34,U_33),U_34,U_33),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_32,sK3(U_34,U_33))],[f_23_2]) ).
fof(f_23_4,plain,
! [U_34,U_33] : relation_of2(sK3(U_34,U_33),U_34,U_33),
inference(definitional_conversion,[status(esa)],[f_23_3]) ).
cnf(f_23_5,plain,
relation_of2(sK3(U_34,U_33),U_34,U_33),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_24_2,plain,
! [U_36] :
? [U_35] : element(U_35,U_36),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_36] : element(sK4(U_36),U_36),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_35,sK4(U_36))],[f_24_2]) ).
fof(f_24_4,plain,
! [U_36] : element(sK4(U_36),U_36),
inference(definitional_conversion,[status(esa)],[f_24_3]) ).
cnf(f_24_5,plain,
element(sK4(U_36),U_36),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
! [A,B] :
? [C] : relation_of2_as_subset(C,A,B),
inference(fof_nnf,[status(thm)],[existence_m2_relset_1]) ).
fof(f_25_2,plain,
! [U_39,U_38] :
? [U_37] : relation_of2_as_subset(U_37,U_39,U_38),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_39,U_38] : relation_of2_as_subset(sK5(U_39,U_38),U_39,U_38),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_37,sK5(U_39,U_38))],[f_25_2]) ).
fof(f_25_4,plain,
! [U_38,U_39] : relation_of2_as_subset(sK5(U_39,U_38),U_39,U_38),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
relation_of2_as_subset(sK5(U_39,U_38),U_39,U_38),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
! [A] :
( preboolean(powerset(A))
& diff_closed(powerset(A))
& cup_closed(powerset(A))
& ~ empty(powerset(A)) ),
inference(fof_nnf,[status(thm)],[fc1_finsub_1]) ).
fof(f_26_2,plain,
! [U_40] :
( preboolean(powerset(U_40))
& diff_closed(powerset(U_40))
& cup_closed(powerset(U_40))
& ~ empty(powerset(U_40)) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ! [U_44] : preboolean(powerset(U_44))
& ! [U_43] : diff_closed(powerset(U_43))
& ! [U_42] : cup_closed(powerset(U_42))
& ! [U_41] : ~ empty(powerset(U_41)) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_44] : preboolean(powerset(U_44))
& ! [U_43] : diff_closed(powerset(U_43))
& ! [U_42] : cup_closed(powerset(U_42))
& ! [U_41] : ~ empty(powerset(U_41)) ),
inference(definitional_conversion,[status(esa)],[f_26_3]) ).
cnf(f_26_5,plain,
~ empty(powerset(U_41)),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_6,plain,
cup_closed(powerset(U_42)),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_7,plain,
diff_closed(powerset(U_43)),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_8,plain,
preboolean(powerset(U_44)),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_1,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_27_2,plain,
! [U_45] :
( ~ empty(the_carrier(U_45))
| ~ one_sorted_str(U_45)
| empty_carrier(U_45) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_45] :
( ~ empty(the_carrier(U_45))
| ~ one_sorted_str(U_45)
| empty_carrier(U_45) ),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,plain,
( ~ empty(the_carrier(U_45))
| ~ one_sorted_str(U_45)
| empty_carrier(U_45) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_28_2,plain,
? [U_46] :
( ~ empty_carrier(U_46)
& one_sorted_str(U_46) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ~ empty_carrier(sK6)
& one_sorted_str(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_46,sK6)],[f_28_2]) ).
fof(f_28_4,plain,
( ~ empty_carrier(sK6)
& one_sorted_str(sK6) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
one_sorted_str(sK6),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
~ empty_carrier(sK6),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc5_struct_0]) ).
fof(f_29_2,plain,
! [U_48] :
( ? [U_47] :
( ~ empty(U_47)
& element(U_47,powerset(the_carrier(U_48))) )
| ~ one_sorted_str(U_48)
| empty_carrier(U_48) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_48] :
( ( ~ empty(sK7(U_48))
& element(sK7(U_48),powerset(the_carrier(U_48))) )
| ~ one_sorted_str(U_48)
| empty_carrier(U_48) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_47,sK7(U_48))],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_48] :
( ~ empty(sK7(U_48))
| ~ sP3(U_48) )
& ! [U_48] :
( element(sK7(U_48),powerset(the_carrier(U_48)))
| ~ sP3(U_48) )
& ! [U_48] :
( sP3(U_48)
| ~ one_sorted_str(U_48)
| empty_carrier(U_48) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_29_3]) ).
cnf(f_29_5,plain,
( sP3(U_48)
| ~ one_sorted_str(U_48)
| empty_carrier(U_48) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
( element(sK7(U_48),powerset(the_carrier(U_48)))
| ~ sP3(U_48) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_7,plain,
( ~ empty(sK7(U_48))
| ~ sP3(U_48) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [A,B,C,D,E,F] :
( apply_binary_as_element(A,B,C,D,E,F) = apply_binary(D,E,F)
| ~ element(F,B)
| ~ element(E,A)
| ~ relation_of2(D,cartesian_product2(A,B),C)
| ~ quasi_total(D,cartesian_product2(A,B),C)
| ~ function(D)
| empty(B)
| empty(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k2_binop_1]) ).
fof(f_30_2,plain,
! [U_54,U_53,U_52,U_51,U_50,U_49] :
( apply_binary_as_element(U_54,U_53,U_52,U_51,U_50,U_49) = apply_binary(U_51,U_50,U_49)
| ~ element(U_49,U_53)
| ~ element(U_50,U_54)
| ~ relation_of2(U_51,cartesian_product2(U_54,U_53),U_52)
| ~ quasi_total(U_51,cartesian_product2(U_54,U_53),U_52)
| ~ function(U_51)
| empty(U_53)
| empty(U_54) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_50,U_51,U_52,U_49,U_53,U_54] :
( apply_binary_as_element(U_54,U_53,U_52,U_51,U_50,U_49) = apply_binary(U_51,U_50,U_49)
| ~ element(U_49,U_53)
| ~ element(U_50,U_54)
| ~ relation_of2(U_51,cartesian_product2(U_54,U_53),U_52)
| ~ quasi_total(U_51,cartesian_product2(U_54,U_53),U_52)
| ~ function(U_51)
| empty(U_53)
| empty(U_54) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( apply_binary_as_element(U_54,U_53,U_52,U_51,U_50,U_49) = apply_binary(U_51,U_50,U_49)
| ~ element(U_49,U_53)
| ~ element(U_50,U_54)
| ~ relation_of2(U_51,cartesian_product2(U_54,U_53),U_52)
| ~ quasi_total(U_51,cartesian_product2(U_54,U_53),U_52)
| ~ function(U_51)
| empty(U_53)
| empty(U_54) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A,B,C] :
( join_commut(A,B,C) = join(A,B,C)
| ~ element(C,the_carrier(A))
| ~ element(B,the_carrier(A))
| ~ join_semilatt_str(A)
| ~ join_commutative(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[redefinition_k3_lattices]) ).
fof(f_31_2,plain,
! [U_57,U_56,U_55] :
( join_commut(U_57,U_56,U_55) = join(U_57,U_56,U_55)
| ~ element(U_55,the_carrier(U_57))
| ~ element(U_56,the_carrier(U_57))
| ~ join_semilatt_str(U_57)
| ~ join_commutative(U_57)
| empty_carrier(U_57) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_57,U_55,U_56] :
( join_commut(U_57,U_56,U_55) = join(U_57,U_56,U_55)
| ~ element(U_55,the_carrier(U_57))
| ~ element(U_56,the_carrier(U_57))
| ~ join_semilatt_str(U_57)
| ~ join_commutative(U_57)
| empty_carrier(U_57) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( join_commut(U_57,U_56,U_55) = join(U_57,U_56,U_55)
| ~ element(U_55,the_carrier(U_57))
| ~ element(U_56,the_carrier(U_57))
| ~ join_semilatt_str(U_57)
| ~ join_commutative(U_57)
| empty_carrier(U_57) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B,C] :
( ( relation_of2_as_subset(C,A,B)
| ~ relation_of2(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1]) ).
fof(f_32_2,plain,
! [U_60,U_59,U_58] :
( ( relation_of2_as_subset(U_58,U_60,U_59)
| ~ relation_of2(U_58,U_60,U_59) )
& ( relation_of2(U_58,U_60,U_59)
| ~ relation_of2_as_subset(U_58,U_60,U_59) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_66,U_64,U_62] :
( relation_of2_as_subset(U_62,U_66,U_64)
| ~ relation_of2(U_62,U_66,U_64) )
& ! [U_65,U_63,U_61] :
( relation_of2(U_61,U_65,U_63)
| ~ relation_of2_as_subset(U_61,U_65,U_63) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_62,U_64,U_66] :
( relation_of2_as_subset(U_62,U_66,U_64)
| ~ relation_of2(U_62,U_66,U_64) )
& ! [U_65,U_61,U_63] :
( relation_of2(U_61,U_65,U_63)
| ~ relation_of2_as_subset(U_61,U_65,U_63) ) ),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
( relation_of2(U_61,U_65,U_63)
| ~ relation_of2_as_subset(U_61,U_65,U_63) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
( relation_of2_as_subset(U_62,U_66,U_64)
| ~ relation_of2(U_62,U_66,U_64) ),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_33_2,plain,
! [U_68,U_67] : subset(U_68,U_68),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_68] : subset(U_68,U_68),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_68] : subset(U_68,U_68),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
subset(U_68,U_68),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_34_2,plain,
! [U_70,U_69] :
( element(U_70,U_69)
| ~ in(U_70,U_69) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_70,U_69] :
( element(U_70,U_69)
| ~ in(U_70,U_69) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( element(U_70,U_69)
| ~ in(U_70,U_69) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,negated_conjecture,
~ ! [A] :
( ( join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,the_carrier(A))
=> ! [C] :
( element(C,the_carrier(A))
=> ( ( below(A,C,B)
& below(A,B,C) )
=> B = C ) ) ) ),
inference(negate,[status(cth)],[t26_lattices]) ).
fof(f_35_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( B != C
& below(A,C,B)
& below(A,B,C)
& element(C,the_carrier(A)) )
& element(B,the_carrier(A)) )
& join_semilatt_str(A)
& join_commutative(A)
& ~ empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[f_35_1]) ).
fof(f_35_3,negated_conjecture,
? [U_73] :
( ? [U_72] :
( ? [U_71] :
( U_72 != U_71
& below(U_73,U_71,U_72)
& below(U_73,U_72,U_71)
& element(U_71,the_carrier(U_73)) )
& element(U_72,the_carrier(U_73)) )
& join_semilatt_str(U_73)
& join_commutative(U_73)
& ~ empty_carrier(U_73) ),
inference(variable_rename,[status(thm)],[f_35_2]) ).
fof(f_35_4,negated_conjecture,
( ? [U_72] :
( ? [U_71] :
( U_72 != U_71
& below(sK8,U_71,U_72)
& below(sK8,U_72,U_71)
& element(U_71,the_carrier(sK8)) )
& element(U_72,the_carrier(sK8)) )
& join_semilatt_str(sK8)
& join_commutative(sK8)
& ~ empty_carrier(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_73,sK8)],[f_35_3]) ).
fof(f_35_5,negated_conjecture,
( ? [U_71] :
( sK9 != U_71
& below(sK8,U_71,sK9)
& below(sK8,sK9,U_71)
& element(U_71,the_carrier(sK8)) )
& element(sK9,the_carrier(sK8))
& join_semilatt_str(sK8)
& join_commutative(sK8)
& ~ empty_carrier(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_72,sK9)],[f_35_4]) ).
fof(f_35_6,negated_conjecture,
( sK9 != sK10
& below(sK8,sK10,sK9)
& below(sK8,sK9,sK10)
& element(sK10,the_carrier(sK8))
& element(sK9,the_carrier(sK8))
& join_semilatt_str(sK8)
& join_commutative(sK8)
& ~ empty_carrier(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_71,sK10)],[f_35_5]) ).
fof(f_35_7,negated_conjecture,
( sK9 != sK10
& below(sK8,sK10,sK9)
& below(sK8,sK9,sK10)
& element(sK10,the_carrier(sK8))
& element(sK9,the_carrier(sK8))
& join_semilatt_str(sK8)
& join_commutative(sK8)
& ~ empty_carrier(sK8) ),
inference(definitional_conversion,[status(esa)],[f_35_6]) ).
cnf(f_35_8,negated_conjecture,
~ empty_carrier(sK8),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_9,negated_conjecture,
join_commutative(sK8),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_10,negated_conjecture,
join_semilatt_str(sK8),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_11,negated_conjecture,
element(sK9,the_carrier(sK8)),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_12,negated_conjecture,
element(sK10,the_carrier(sK8)),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_13,negated_conjecture,
below(sK8,sK9,sK10),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_14,negated_conjecture,
below(sK8,sK10,sK9),
inference(clausify,[status(thm)],[f_35_7]) ).
cnf(f_35_15,negated_conjecture,
sK9 != sK10,
inference(clausify,[status(thm)],[f_35_7]) ).
fof(f_36_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_36_2,plain,
! [U_75,U_74] :
( in(U_75,U_74)
| empty(U_74)
| ~ element(U_75,U_74) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_74,U_75] :
( in(U_75,U_74)
| empty(U_74)
| ~ element(U_75,U_74) ),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
( in(U_75,U_74)
| empty(U_74)
| ~ element(U_75,U_74) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_37_2,plain,
! [U_77,U_76] :
( ( element(U_77,powerset(U_76))
| ~ subset(U_77,U_76) )
& ( subset(U_77,U_76)
| ~ element(U_77,powerset(U_76)) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_81,U_79] :
( element(U_81,powerset(U_79))
| ~ subset(U_81,U_79) )
& ! [U_80,U_78] :
( subset(U_80,U_78)
| ~ element(U_80,powerset(U_78)) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_79,U_81] :
( element(U_81,powerset(U_79))
| ~ subset(U_81,U_79) )
& ! [U_80,U_78] :
( subset(U_80,U_78)
| ~ element(U_80,powerset(U_78)) ) ),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
( subset(U_80,U_78)
| ~ element(U_80,powerset(U_78)) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
( element(U_81,powerset(U_79))
| ~ subset(U_81,U_79) ),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_38_2,plain,
! [U_84,U_83,U_82] :
( element(U_84,U_82)
| ~ element(U_83,powerset(U_82))
| ~ in(U_84,U_83) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_82,U_84,U_83] :
( element(U_84,U_82)
| ~ element(U_83,powerset(U_82))
| ~ in(U_84,U_83) ),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
( element(U_84,U_82)
| ~ element(U_83,powerset(U_82))
| ~ in(U_84,U_83) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_39_2,plain,
! [U_87,U_86,U_85] :
( ~ empty(U_85)
| ~ element(U_86,powerset(U_85))
| ~ in(U_87,U_86) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_87,U_86] :
( ! [U_85] :
( ~ empty(U_85)
| ~ element(U_86,powerset(U_85)) )
| ~ in(U_87,U_86) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
! [U_86,U_85,U_87] :
( ~ empty(U_85)
| ~ element(U_86,powerset(U_85))
| ~ in(U_87,U_86) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
( ~ empty(U_85)
| ~ element(U_86,powerset(U_85))
| ~ in(U_87,U_86) ),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_40_2,plain,
! [U_88] :
( U_88 = empty_set
| ~ empty(U_88) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_88] :
( U_88 = empty_set
| ~ empty(U_88) ),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
( U_88 = empty_set
| ~ empty(U_88) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_41_2,plain,
! [U_90,U_89] :
( ~ empty(U_89)
| ~ in(U_90,U_89) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_89,U_90] :
( ~ empty(U_89)
| ~ in(U_90,U_89) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( ~ empty(U_89)
| ~ in(U_90,U_89) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_42_2,plain,
! [U_92,U_91] :
( ~ empty(U_91)
| U_92 = U_91
| ~ empty(U_92) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_92] :
( ! [U_91] :
( ~ empty(U_91)
| U_92 = U_91 )
| ~ empty(U_92) ),
inference(miniscope,[status(thm)],[f_42_2]) ).
fof(f_42_4,plain,
! [U_91,U_92] :
( ~ empty(U_91)
| U_92 = U_91
| ~ empty(U_92) ),
inference(definitional_conversion,[status(esa)],[f_42_3]) ).
cnf(f_42_5,plain,
( ~ empty(U_91)
| U_92 = U_91
| ~ empty(U_92) ),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_7_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_3]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_3]) ).
cnf(f_10_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_3]) ).
cnf(f_12_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_3]) ).
cnf(f_14_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_3]) ).
cnf(f_16_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_3]) ).
cnf(f_17_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_3]) ).
cnf(f_19_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_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,
( join_commut(Eq_x_0,Eq_x_1,Eq_x_2) = join_commut(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_6,axiom,
( join(Eq_x_0,Eq_x_1,Eq_x_2) = join(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,
( the_L_join(Eq_x_0) = the_L_join(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( apply_binary_as_element(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = apply_binary_as_element(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| Eq_x_5 != Eq_y_5
| 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_functions]) ).
cnf(equality_9,axiom,
( cartesian_product2(Eq_x_0,Eq_x_1) = cartesian_product2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( apply_binary(Eq_x_0,Eq_x_1,Eq_x_2) = apply_binary(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,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,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_15,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( preboolean(Eq_y_0)
| ~ preboolean(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( cup_closed(Eq_y_0)
| ~ cup_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( diff_closed(Eq_y_0)
| ~ diff_closed(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( empty_carrier(Eq_y_0)
| ~ empty_carrier(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( join_commutative(Eq_y_0)
| ~ join_commutative(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( join_semilatt_str(Eq_y_0)
| ~ join_semilatt_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,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_24,axiom,
( below(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ below(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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( quasi_total(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ quasi_total(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_28,axiom,
( relation_of2(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2(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,
( one_sorted_str(Eq_y_0)
| ~ one_sorted_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( relation_of2_as_subset(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ relation_of2_as_subset(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,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP1(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,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP3(Eq_y_0)
| ~ sP3(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 : SEU305+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
% 0.09/0.42 % Computer : n004.cluster.edu
% 0.09/0.42 % Model : x86_64 x86_64
% 0.09/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.42 % Memory : 8046.5625MB
% 0.09/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/0.42 % CPULimit : 300
% 0.09/0.42 % WCLimit : 300
% 0.09/0.42 % DateTime : Sat Sep 19 23:51:34 UTC 2026
% 0.09/0.42 % CPUTime :
% 36.40/36.78 % SZS status Theorem for theBenchmark
% 36.40/36.78 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------