%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU294+3 : TPTP v9.3.1. Released v3.2.0.
% 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 : n006.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 08:58:53 AM UTC 2026
% Result : Theorem 0.21s 0.51s
% Output : Proof 0.21s
% 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_arytm_3,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( element(B,A)
=> ( ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B) ) ) ),
file('theBenchmark.p',cc1_arytm_3) ).
fof(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('theBenchmark.p',cc1_finset_1) ).
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc2_arytm_3,axiom,
! [A] :
( ( ordinal(A)
& empty(A) )
=> ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc2_arytm_3) ).
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(cc2_ordinal1,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('theBenchmark.p',cc2_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_ordinal1) ).
fof(cc4_arytm_3,axiom,
! [A] :
( element(A,positive_rationals)
=> ( ordinal(A)
=> ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ) ),
file('theBenchmark.p',cc4_arytm_3) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_ordinal1,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('theBenchmark.p',fc2_ordinal1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc8_arytm_3,axiom,
~ empty(positive_rationals),
file('theBenchmark.p',fc8_arytm_3) ).
fof(rc1_arytm_3,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_arytm_3) ).
fof(rc1_finset_1,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finset_1) ).
fof(rc1_funcop_1,axiom,
? [A] :
( function_yielding(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funcop_1) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal1) ).
fof(rc1_ordinal2,axiom,
? [A] :
( being_limit_ordinal(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal2) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_arytm_3,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A)
& element(A,positive_rationals) ),
file('theBenchmark.p',rc2_arytm_3) ).
fof(rc2_finset_1,axiom,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_finset_1) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc2_ordinal1) ).
fof(rc2_ordinal2,axiom,
? [A] :
( ordinal_yielding(A)
& transfinite_sequence(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc2_ordinal2) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_arytm_3,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& element(A,positive_rationals) ),
file('theBenchmark.p',rc3_arytm_3) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc3_finset_1) ).
fof(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc3_ordinal1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc4_funct_1,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc4_funct_1) ).
fof(rc4_ordinal1,axiom,
? [A] :
( transfinite_sequence(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc4_ordinal1) ).
fof(rc5_funct_1,axiom,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
file('theBenchmark.p',rc5_funct_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t13_finset_1,conjecture,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('theBenchmark.p',t13_finset_1) ).
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(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]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [A] :
( ! [B] :
( ( ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B) )
| ~ element(B,A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_arytm_3]) ).
fof(f_2_2,plain,
! [U_3] :
( ! [U_2] :
( ( ordinal(U_2)
& epsilon_connected(U_2)
& epsilon_transitive(U_2) )
| ~ element(U_2,U_3) )
| ~ ordinal(U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( epsilon_transitive(U_2)
| ~ element(U_2,U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( epsilon_connected(U_2)
| ~ element(U_2,U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_2_2]) ).
cnf(f_2_5,plain,
( ordinal(U_2)
| ~ element(U_2,U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_3_2,plain,
! [U_4] :
( finite(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( finite(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_4_2,plain,
! [U_5] :
( function(U_5)
| ~ empty(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( function(U_5)
| ~ empty(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_5_2,plain,
! [U_6] :
( ( epsilon_connected(U_6)
& epsilon_transitive(U_6) )
| ~ ordinal(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( epsilon_transitive(U_6)
| ~ ordinal(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( epsilon_connected(U_6)
| ~ ordinal(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_6_2,plain,
! [U_7] :
( relation(U_7)
| ~ empty(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( relation(U_7)
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc2_arytm_3]) ).
fof(f_7_2,plain,
! [U_8] :
( ( natural(U_8)
& ordinal(U_8)
& epsilon_connected(U_8)
& epsilon_transitive(U_8) )
| ~ ordinal(U_8)
| ~ empty(U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( epsilon_transitive(U_8)
| ~ ordinal(U_8)
| ~ empty(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( epsilon_connected(U_8)
| ~ ordinal(U_8)
| ~ empty(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_5,plain,
( ordinal(U_8)
| ~ ordinal(U_8)
| ~ empty(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_6,plain,
( natural(U_8)
| ~ ordinal(U_8)
| ~ empty(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_8_2,plain,
! [U_10] :
( ! [U_9] :
( finite(U_9)
| ~ element(U_9,powerset(U_10)) )
| ~ finite(U_10) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( finite(U_9)
| ~ element(U_9,powerset(U_10))
| ~ finite(U_10) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_9_2,plain,
! [U_11] :
( ( one_to_one(U_11)
& function(U_11)
& relation(U_11) )
| ~ function(U_11)
| ~ empty(U_11)
| ~ relation(U_11) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( relation(U_11)
| ~ function(U_11)
| ~ empty(U_11)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( function(U_11)
| ~ function(U_11)
| ~ empty(U_11)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_5,plain,
( one_to_one(U_11)
| ~ function(U_11)
| ~ empty(U_11)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_10_2,plain,
! [U_12] :
( ordinal(U_12)
| ~ epsilon_connected(U_12)
| ~ epsilon_transitive(U_12) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( ordinal(U_12)
| ~ epsilon_connected(U_12)
| ~ epsilon_transitive(U_12) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_11_2,plain,
! [U_13] :
( ( ordinal(U_13)
& epsilon_connected(U_13)
& epsilon_transitive(U_13) )
| ~ empty(U_13) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( epsilon_transitive(U_13)
| ~ empty(U_13) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( epsilon_connected(U_13)
| ~ empty(U_13) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_5,plain,
( ordinal(U_13)
| ~ empty(U_13) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] :
( ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A)
| ~ element(A,positive_rationals) ),
inference(fof_nnf,[status(thm)],[cc4_arytm_3]) ).
fof(f_12_2,plain,
! [U_14] :
( ( natural(U_14)
& ordinal(U_14)
& epsilon_connected(U_14)
& epsilon_transitive(U_14) )
| ~ ordinal(U_14)
| ~ element(U_14,positive_rationals) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( epsilon_transitive(U_14)
| ~ ordinal(U_14)
| ~ element(U_14,positive_rationals) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( epsilon_connected(U_14)
| ~ ordinal(U_14)
| ~ element(U_14,positive_rationals) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_5,plain,
( ordinal(U_14)
| ~ ordinal(U_14)
| ~ element(U_14,positive_rationals) ),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_6,plain,
( natural(U_14)
| ~ ordinal(U_14)
| ~ element(U_14,positive_rationals) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_13_2,plain,
! [U_16] :
? [U_15] : element(U_15,U_16),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_16] : element(sK1(U_16),U_16),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_15,sK1(U_16))],[f_13_2]) ).
cnf(f_13_4,plain,
element(sK1(U_16),U_16),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_14_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
cnf(f_14_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_15_2,plain,
! [U_17] : ~ empty(powerset(U_17)),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
~ empty(powerset(U_17)),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_16_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
inference(fof_nnf,[status(thm)],[fc2_ordinal1]) ).
cnf(f_17_2,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_4,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_5,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_6,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_7,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_8,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_9,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_18_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
~ empty(positive_rationals),
inference(fof_nnf,[status(thm)],[fc8_arytm_3]) ).
cnf(f_19_2,plain,
~ empty(positive_rationals),
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_arytm_3]) ).
fof(f_20_2,plain,
? [U_18] :
( natural(U_18)
& ordinal(U_18)
& epsilon_connected(U_18)
& epsilon_transitive(U_18)
& ~ empty(U_18) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( natural(sK2)
& ordinal(sK2)
& epsilon_connected(sK2)
& epsilon_transitive(sK2)
& ~ empty(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_18,sK2)],[f_20_2]) ).
cnf(f_20_4,plain,
~ empty(sK2),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
epsilon_transitive(sK2),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
epsilon_connected(sK2),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_7,plain,
ordinal(sK2),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_8,plain,
natural(sK2),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_21_2,plain,
? [U_19] :
( finite(U_19)
& ~ empty(U_19) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( finite(sK3)
& ~ empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3)],[f_21_2]) ).
cnf(f_21_4,plain,
~ empty(sK3),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
finite(sK3),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] :
( function_yielding(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funcop_1]) ).
fof(f_22_2,plain,
? [U_20] :
( function_yielding(U_20)
& function(U_20)
& relation(U_20) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( function_yielding(sK4)
& function(sK4)
& relation(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_20,sK4)],[f_22_2]) ).
cnf(f_22_4,plain,
relation(sK4),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
function(sK4),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
function_yielding(sK4),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_23_2,plain,
? [U_21] :
( function(U_21)
& relation(U_21) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( function(sK5)
& relation(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_21,sK5)],[f_23_2]) ).
cnf(f_23_4,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
function(sK5),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_24_2,plain,
? [U_22] :
( ordinal(U_22)
& epsilon_connected(U_22)
& epsilon_transitive(U_22) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ordinal(sK6)
& epsilon_connected(sK6)
& epsilon_transitive(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_22,sK6)],[f_24_2]) ).
cnf(f_24_4,plain,
epsilon_transitive(sK6),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
epsilon_connected(sK6),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
ordinal(sK6),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( being_limit_ordinal(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal2]) ).
fof(f_25_2,plain,
? [U_23] :
( being_limit_ordinal(U_23)
& ordinal(U_23)
& epsilon_connected(U_23)
& epsilon_transitive(U_23) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( being_limit_ordinal(sK7)
& ordinal(sK7)
& epsilon_connected(sK7)
& epsilon_transitive(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_23,sK7)],[f_25_2]) ).
cnf(f_25_4,plain,
epsilon_transitive(sK7),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
epsilon_connected(sK7),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
ordinal(sK7),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_7,plain,
being_limit_ordinal(sK7),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_26_2,plain,
? [U_24] :
( relation(U_24)
& empty(U_24) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( relation(sK8)
& empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_24,sK8)],[f_26_2]) ).
cnf(f_26_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_27_2,plain,
! [U_26] :
( ? [U_25] :
( ~ empty(U_25)
& element(U_25,powerset(U_26)) )
| empty(U_26) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_26] :
( ( ~ empty(sK9(U_26))
& element(sK9(U_26),powerset(U_26)) )
| empty(U_26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_25,sK9(U_26))],[f_27_2]) ).
cnf(f_27_4,plain,
( element(sK9(U_26),powerset(U_26))
| empty(U_26) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( ~ empty(sK9(U_26))
| empty(U_26) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_28_2,plain,
? [U_27] : empty(U_27),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
empty(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_27,sK10)],[f_28_2]) ).
cnf(f_28_4,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A)
& element(A,positive_rationals) ),
inference(fof_nnf,[status(thm)],[rc2_arytm_3]) ).
fof(f_29_2,plain,
? [U_28] :
( ordinal(U_28)
& epsilon_connected(U_28)
& epsilon_transitive(U_28)
& ~ empty(U_28)
& element(U_28,positive_rationals) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& ~ empty(sK11)
& element(sK11,positive_rationals) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_28,sK11)],[f_29_2]) ).
cnf(f_29_4,plain,
element(sK11,positive_rationals),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
~ empty(sK11),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_6,plain,
epsilon_transitive(sK11),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_7,plain,
epsilon_connected(sK11),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_8,plain,
ordinal(sK11),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_finset_1]) ).
fof(f_30_2,plain,
! [U_30] :
? [U_29] :
( finite(U_29)
& natural(U_29)
& ordinal(U_29)
& epsilon_connected(U_29)
& epsilon_transitive(U_29)
& one_to_one(U_29)
& function(U_29)
& relation(U_29)
& empty(U_29)
& element(U_29,powerset(U_30)) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_30] :
( finite(sK12(U_30))
& natural(sK12(U_30))
& ordinal(sK12(U_30))
& epsilon_connected(sK12(U_30))
& epsilon_transitive(sK12(U_30))
& one_to_one(sK12(U_30))
& function(sK12(U_30))
& relation(sK12(U_30))
& empty(sK12(U_30))
& element(sK12(U_30),powerset(U_30)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_29,sK12(U_30))],[f_30_2]) ).
cnf(f_30_4,plain,
element(sK12(U_30),powerset(U_30)),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
empty(sK12(U_30)),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
relation(sK12(U_30)),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_7,plain,
function(sK12(U_30)),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_8,plain,
one_to_one(sK12(U_30)),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_9,plain,
epsilon_transitive(sK12(U_30)),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_10,plain,
epsilon_connected(sK12(U_30)),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_11,plain,
ordinal(sK12(U_30)),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_12,plain,
natural(sK12(U_30)),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_13,plain,
finite(sK12(U_30)),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_31_2,plain,
? [U_31] :
( function(U_31)
& empty(U_31)
& relation(U_31) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( function(sK13)
& empty(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_31,sK13)],[f_31_2]) ).
cnf(f_31_4,plain,
relation(sK13),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
empty(sK13),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_6,plain,
function(sK13),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_ordinal1]) ).
fof(f_32_2,plain,
? [U_32] :
( ordinal(U_32)
& epsilon_connected(U_32)
& epsilon_transitive(U_32)
& empty(U_32)
& one_to_one(U_32)
& function(U_32)
& relation(U_32) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ordinal(sK14)
& epsilon_connected(sK14)
& epsilon_transitive(sK14)
& empty(sK14)
& one_to_one(sK14)
& function(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_32,sK14)],[f_32_2]) ).
cnf(f_32_4,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
function(sK14),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_6,plain,
one_to_one(sK14),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_7,plain,
empty(sK14),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_8,plain,
epsilon_transitive(sK14),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_9,plain,
epsilon_connected(sK14),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_10,plain,
ordinal(sK14),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] :
( ordinal_yielding(A)
& transfinite_sequence(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_ordinal2]) ).
fof(f_33_2,plain,
? [U_33] :
( ordinal_yielding(U_33)
& transfinite_sequence(U_33)
& function(U_33)
& relation(U_33) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ordinal_yielding(sK15)
& transfinite_sequence(sK15)
& function(sK15)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_33,sK15)],[f_33_2]) ).
cnf(f_33_4,plain,
relation(sK15),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
function(sK15),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_6,plain,
transfinite_sequence(sK15),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_7,plain,
ordinal_yielding(sK15),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_34_2,plain,
? [U_34] :
( relation(U_34)
& ~ empty(U_34) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( relation(sK16)
& ~ empty(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_34,sK16)],[f_34_2]) ).
cnf(f_34_4,plain,
~ empty(sK16),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
relation(sK16),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_35_2,plain,
! [U_36] :
? [U_35] :
( empty(U_35)
& element(U_35,powerset(U_36)) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_36] :
( empty(sK17(U_36))
& element(sK17(U_36),powerset(U_36)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_35,sK17(U_36))],[f_35_2]) ).
cnf(f_35_4,plain,
element(sK17(U_36),powerset(U_36)),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
empty(sK17(U_36)),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_36_2,plain,
? [U_37] : ~ empty(U_37),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
~ empty(sK18),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_37,sK18)],[f_36_2]) ).
cnf(f_36_4,plain,
~ empty(sK18),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& element(A,positive_rationals) ),
inference(fof_nnf,[status(thm)],[rc3_arytm_3]) ).
fof(f_37_2,plain,
? [U_38] :
( natural(U_38)
& ordinal(U_38)
& epsilon_connected(U_38)
& epsilon_transitive(U_38)
& empty(U_38)
& element(U_38,positive_rationals) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( natural(sK19)
& ordinal(sK19)
& epsilon_connected(sK19)
& epsilon_transitive(sK19)
& empty(sK19)
& element(sK19,positive_rationals) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_38,sK19)],[f_37_2]) ).
cnf(f_37_4,plain,
element(sK19,positive_rationals),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
empty(sK19),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
epsilon_transitive(sK19),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_7,plain,
epsilon_connected(sK19),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_8,plain,
ordinal(sK19),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_9,plain,
natural(sK19),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_38_2,plain,
! [U_40] :
( ? [U_39] :
( finite(U_39)
& ~ empty(U_39)
& element(U_39,powerset(U_40)) )
| empty(U_40) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_40] :
( ( finite(sK20(U_40))
& ~ empty(sK20(U_40))
& element(sK20(U_40),powerset(U_40)) )
| empty(U_40) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_39,sK20(U_40))],[f_38_2]) ).
cnf(f_38_4,plain,
( element(sK20(U_40),powerset(U_40))
| empty(U_40) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_5,plain,
( ~ empty(sK20(U_40))
| empty(U_40) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_38_6,plain,
( finite(sK20(U_40))
| empty(U_40) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_39_2,plain,
? [U_41] :
( one_to_one(U_41)
& function(U_41)
& relation(U_41) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( one_to_one(sK21)
& function(sK21)
& relation(sK21) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_41,sK21)],[f_39_2]) ).
cnf(f_39_4,plain,
relation(sK21),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
function(sK21),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_6,plain,
one_to_one(sK21),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_40_2,plain,
? [U_42] :
( ordinal(U_42)
& epsilon_connected(U_42)
& epsilon_transitive(U_42)
& ~ empty(U_42) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ordinal(sK22)
& epsilon_connected(sK22)
& epsilon_transitive(sK22)
& ~ empty(sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_42,sK22)],[f_40_2]) ).
cnf(f_40_4,plain,
~ empty(sK22),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
epsilon_transitive(sK22),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_6,plain,
epsilon_connected(sK22),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_7,plain,
ordinal(sK22),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_41_2,plain,
? [U_43] :
( relation_empty_yielding(U_43)
& relation(U_43) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( relation_empty_yielding(sK23)
& relation(sK23) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_43,sK23)],[f_41_2]) ).
cnf(f_41_4,plain,
relation(sK23),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
relation_empty_yielding(sK23),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_42_2,plain,
? [U_44] :
( function(U_44)
& relation_empty_yielding(U_44)
& relation(U_44) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( function(sK24)
& relation_empty_yielding(sK24)
& relation(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_44,sK24)],[f_42_2]) ).
cnf(f_42_4,plain,
relation(sK24),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_5,plain,
relation_empty_yielding(sK24),
inference(clausify,[status(thm)],[f_42_3]) ).
cnf(f_42_6,plain,
function(sK24),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
? [A] :
( transfinite_sequence(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_ordinal1]) ).
fof(f_43_2,plain,
? [U_45] :
( transfinite_sequence(U_45)
& function(U_45)
& relation(U_45) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( transfinite_sequence(sK25)
& function(sK25)
& relation(sK25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_45,sK25)],[f_43_2]) ).
cnf(f_43_4,plain,
relation(sK25),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
function(sK25),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_6,plain,
transfinite_sequence(sK25),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc5_funct_1]) ).
fof(f_44_2,plain,
? [U_46] :
( function(U_46)
& relation_non_empty(U_46)
& relation(U_46) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( function(sK26)
& relation_non_empty(sK26)
& relation(sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_46,sK26)],[f_44_2]) ).
cnf(f_44_4,plain,
relation(sK26),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_5,plain,
relation_non_empty(sK26),
inference(clausify,[status(thm)],[f_44_3]) ).
cnf(f_44_6,plain,
function(sK26),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_45_2,plain,
! [U_48,U_47] : subset(U_48,U_48),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_48] : subset(U_48,U_48),
inference(miniscope,[status(thm)],[f_45_2]) ).
cnf(f_45_4,plain,
subset(U_48,U_48),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,negated_conjecture,
~ ! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
inference(negate,[status(cth)],[t13_finset_1]) ).
fof(f_46_2,negated_conjecture,
? [A,B] :
( ~ finite(A)
& finite(B)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[f_46_1]) ).
fof(f_46_3,negated_conjecture,
? [U_50,U_49] :
( ~ finite(U_50)
& finite(U_49)
& subset(U_50,U_49) ),
inference(variable_rename,[status(thm)],[f_46_2]) ).
fof(f_46_4,negated_conjecture,
? [U_50] :
( ? [U_49] :
( finite(U_49)
& subset(U_50,U_49) )
& ~ finite(U_50) ),
inference(miniscope,[status(thm)],[f_46_3]) ).
fof(f_46_5,negated_conjecture,
( ? [U_49] :
( finite(U_49)
& subset(sK27,U_49) )
& ~ finite(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_50,sK27)],[f_46_4]) ).
fof(f_46_6,negated_conjecture,
( finite(sK28)
& subset(sK27,sK28)
& ~ finite(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_49,sK28)],[f_46_5]) ).
fof(f_46_7,negated_conjecture,
( finite(sK28)
& subset(sK27,sK28)
& ~ finite(sK27) ),
inference(definitional_conversion,[status(esa)],[f_46_6]) ).
cnf(f_46_8,negated_conjecture,
~ finite(sK27),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_9,negated_conjecture,
subset(sK27,sK28),
inference(clausify,[status(thm)],[f_46_7]) ).
cnf(f_46_10,negated_conjecture,
finite(sK28),
inference(clausify,[status(thm)],[f_46_7]) ).
fof(f_47_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_47_2,plain,
! [U_52,U_51] :
( element(U_52,U_51)
| ~ in(U_52,U_51) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( element(U_52,U_51)
| ~ in(U_52,U_51) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_48_2,plain,
! [U_54,U_53] :
( in(U_54,U_53)
| empty(U_53)
| ~ element(U_54,U_53) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( in(U_54,U_53)
| empty(U_53)
| ~ element(U_54,U_53) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_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_49_2,plain,
! [U_56,U_55] :
( ( element(U_56,powerset(U_55))
| ~ subset(U_56,U_55) )
& ( subset(U_56,U_55)
| ~ element(U_56,powerset(U_55)) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_60,U_58] :
( element(U_60,powerset(U_58))
| ~ subset(U_60,U_58) )
& ! [U_59,U_57] :
( subset(U_59,U_57)
| ~ element(U_59,powerset(U_57)) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
( subset(U_59,U_57)
| ~ element(U_59,powerset(U_57)) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
( element(U_60,powerset(U_58))
| ~ subset(U_60,U_58) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_50_2,plain,
! [U_63,U_62,U_61] :
( element(U_63,U_61)
| ~ element(U_62,powerset(U_61))
| ~ in(U_63,U_62) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( element(U_63,U_61)
| ~ element(U_62,powerset(U_61))
| ~ in(U_63,U_62) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_51_2,plain,
! [U_66,U_65,U_64] :
( ~ empty(U_64)
| ~ element(U_65,powerset(U_64))
| ~ in(U_66,U_65) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_66,U_65] :
( ! [U_64] :
( ~ empty(U_64)
| ~ element(U_65,powerset(U_64)) )
| ~ in(U_66,U_65) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
( ~ empty(U_64)
| ~ element(U_65,powerset(U_64))
| ~ in(U_66,U_65) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_52_2,plain,
! [U_67] :
( U_67 = empty_set
| ~ empty(U_67) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( U_67 = empty_set
| ~ empty(U_67) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_53_2,plain,
! [U_69,U_68] :
( ~ empty(U_68)
| ~ in(U_69,U_68) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( ~ empty(U_68)
| ~ in(U_69,U_68) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_54_2,plain,
! [U_71,U_70] :
( ~ empty(U_70)
| U_71 = U_70
| ~ empty(U_71) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_71] :
( ! [U_70] :
( ~ empty(U_70)
| U_71 = U_70 )
| ~ empty(U_71) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
( ~ empty(U_70)
| U_71 = U_70
| ~ empty(U_71) ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_7_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_5]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_3]) ).
cnf(f_9_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_4]) ).
cnf(f_12_5_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_5]) ).
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,
( powerset(Eq_x_0) = powerset(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,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK12(Eq_x_0) = sK12(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK17(Eq_x_0) = sK17(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK20(Eq_x_0) = sK20(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,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_11,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,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_13,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( function_yielding(Eq_y_0)
| ~ function_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( being_limit_ordinal(Eq_y_0)
| ~ being_limit_ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( transfinite_sequence(Eq_y_0)
| ~ transfinite_sequence(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( ordinal_yielding(Eq_y_0)
| ~ ordinal_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( relation_non_empty(Eq_y_0)
| ~ relation_non_empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU294+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 23:49:12 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.21/0.51 % SZS status Theorem for theBenchmark
% 0.21/0.51 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------