%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM390+1 : 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 08:52:09 AM UTC 2026
% Result : Theorem 1.36s 1.63s
% Output : Proof 1.36s
% 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(antisymmetry_r2_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('theBenchmark.p',antisymmetry_r2_xboole_0) ).
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_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(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
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_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
file('theBenchmark.p',irreflexivity_r2_xboole_0) ).
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_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
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(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(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t21_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('theBenchmark.p',t21_ordinal1) ).
fof(t22_ordinal1,conjecture,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( in(B,C)
& subset(A,B) )
=> in(A,C) ) ) ) ),
file('theBenchmark.p',t22_ordinal1) ).
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(t7_ordinal1,axiom,
! [A,B] :
~ ( subset(B,A)
& in(A,B) ),
file('theBenchmark.p',t7_ordinal1) ).
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] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_3_2,plain,
! [U_4] :
( function(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( function(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_4_2,plain,
! [U_5] :
( ( epsilon_connected(U_5)
& epsilon_transitive(U_5) )
| ~ ordinal(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( epsilon_transitive(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( epsilon_connected(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_5_2,plain,
! [U_6] :
( relation(U_6)
| ~ empty(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( relation(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_7] :
( ( one_to_one(U_7)
& function(U_7)
& relation(U_7) )
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( relation(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( function(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( one_to_one(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_7_2,plain,
! [U_8] :
( ordinal(U_8)
| ~ epsilon_connected(U_8)
| ~ epsilon_transitive(U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( ordinal(U_8)
| ~ epsilon_connected(U_8)
| ~ epsilon_transitive(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ( epsilon_transitive(A)
| ? [B] :
( ~ subset(B,A)
& in(B,A) ) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(fof_nnf,[status(thm)],[d2_ordinal1]) ).
fof(f_8_2,plain,
! [U_11] :
( ( epsilon_transitive(U_11)
| ? [U_10] :
( ~ subset(U_10,U_11)
& in(U_10,U_11) ) )
& ( ! [U_9] :
( subset(U_9,U_11)
| ~ in(U_9,U_11) )
| ~ epsilon_transitive(U_11) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_13] :
( epsilon_transitive(U_13)
| ? [U_10] :
( ~ subset(U_10,U_13)
& in(U_10,U_13) ) )
& ! [U_12] :
( ! [U_9] :
( subset(U_9,U_12)
| ~ in(U_9,U_12) )
| ~ epsilon_transitive(U_12) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_13] :
( epsilon_transitive(U_13)
| ( ~ subset(sK1(U_13),U_13)
& in(sK1(U_13),U_13) ) )
& ! [U_12] :
( ! [U_9] :
( subset(U_9,U_12)
| ~ in(U_9,U_12) )
| ~ epsilon_transitive(U_12) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_13))],[f_8_3]) ).
cnf(f_8_5,plain,
( subset(U_9,U_12)
| ~ in(U_9,U_12)
| ~ epsilon_transitive(U_12) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( in(sK1(U_13),U_13)
| epsilon_transitive(U_13) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
( ~ subset(sK1(U_13),U_13)
| epsilon_transitive(U_13) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [A,B] :
( ( proper_subset(A,B)
| A = B
| ~ subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d8_xboole_0]) ).
fof(f_9_2,plain,
! [U_15,U_14] :
( ( proper_subset(U_15,U_14)
| U_15 = U_14
| ~ subset(U_15,U_14) )
& ( ( U_15 != U_14
& subset(U_15,U_14) )
| ~ proper_subset(U_15,U_14) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_19,U_17] :
( proper_subset(U_19,U_17)
| U_19 = U_17
| ~ subset(U_19,U_17) )
& ! [U_18,U_16] :
( ( U_18 != U_16
& subset(U_18,U_16) )
| ~ proper_subset(U_18,U_16) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( subset(U_18,U_16)
| ~ proper_subset(U_18,U_16) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( U_18 != U_16
| ~ proper_subset(U_18,U_16) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( proper_subset(U_19,U_17)
| U_19 = U_17
| ~ subset(U_19,U_17) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_10_2,plain,
! [U_21] :
? [U_20] : element(U_20,U_21),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_21] : element(sK2(U_21),U_21),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_20,sK2(U_21))],[f_10_2]) ).
cnf(f_10_4,plain,
element(sK2(U_21),U_21),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_11_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_11_1]) ).
cnf(f_11_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_12_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_13_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_14_2,plain,
! [U_23,U_22] : ~ proper_subset(U_23,U_23),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_23] : ~ proper_subset(U_23,U_23),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
~ proper_subset(U_23,U_23),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_15_2,plain,
? [U_24] :
( function(U_24)
& relation(U_24) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( function(sK3)
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_24,sK3)],[f_15_2]) ).
cnf(f_15_4,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
function(sK3),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_16_2,plain,
? [U_25] :
( ordinal(U_25)
& epsilon_connected(U_25)
& epsilon_transitive(U_25) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ordinal(sK4)
& epsilon_connected(sK4)
& epsilon_transitive(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_25,sK4)],[f_16_2]) ).
cnf(f_16_4,plain,
epsilon_transitive(sK4),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
epsilon_connected(sK4),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_6,plain,
ordinal(sK4),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_17_2,plain,
? [U_26] :
( relation(U_26)
& empty(U_26) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( relation(sK5)
& empty(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_26,sK5)],[f_17_2]) ).
cnf(f_17_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_18_2,plain,
? [U_27] : empty(U_27),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_27,sK6)],[f_18_2]) ).
cnf(f_18_4,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_19_2,plain,
? [U_28] :
( function(U_28)
& empty(U_28)
& relation(U_28) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( function(sK7)
& empty(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_28,sK7)],[f_19_2]) ).
cnf(f_19_4,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
function(sK7),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_20_2,plain,
? [U_29] :
( relation(U_29)
& ~ empty(U_29) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( relation(sK8)
& ~ empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_29,sK8)],[f_20_2]) ).
cnf(f_20_4,plain,
~ empty(sK8),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_21_2,plain,
? [U_30] : ~ empty(U_30),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_30,sK9)],[f_21_2]) ).
cnf(f_21_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_22_2,plain,
? [U_31] :
( one_to_one(U_31)
& function(U_31)
& relation(U_31) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_31,sK10)],[f_22_2]) ).
cnf(f_22_4,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
function(sK10),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
one_to_one(sK10),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_23_2,plain,
? [U_32] :
( relation_empty_yielding(U_32)
& relation(U_32) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( relation_empty_yielding(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_32,sK11)],[f_23_2]) ).
cnf(f_23_4,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
relation_empty_yielding(sK11),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_24_2,plain,
? [U_33] :
( function(U_33)
& relation_empty_yielding(U_33)
& relation(U_33) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( function(sK12)
& relation_empty_yielding(sK12)
& relation(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_33,sK12)],[f_24_2]) ).
cnf(f_24_4,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
relation_empty_yielding(sK12),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
function(sK12),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc5_funct_1]) ).
fof(f_25_2,plain,
? [U_34] :
( function(U_34)
& relation_non_empty(U_34)
& relation(U_34) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( function(sK13)
& relation_non_empty(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_34,sK13)],[f_25_2]) ).
cnf(f_25_4,plain,
relation(sK13),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
relation_non_empty(sK13),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
function(sK13),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_26_2,plain,
! [U_36,U_35] : subset(U_36,U_36),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_36] : subset(U_36,U_36),
inference(miniscope,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
subset(U_36,U_36),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_27_2,plain,
! [U_38,U_37] :
( element(U_38,U_37)
| ~ in(U_38,U_37) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( element(U_38,U_37)
| ~ in(U_38,U_37) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_28_2,plain,
! [U_41,U_40,U_39] :
( subset(U_41,U_39)
| ~ subset(U_40,U_39)
| ~ subset(U_41,U_40) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( subset(U_41,U_39)
| ~ subset(U_40,U_39)
| ~ subset(U_41,U_40) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A] :
( ! [B] :
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B) )
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[t21_ordinal1]) ).
fof(f_29_2,plain,
! [U_43] :
( ! [U_42] :
( in(U_43,U_42)
| ~ proper_subset(U_43,U_42)
| ~ ordinal(U_42) )
| ~ epsilon_transitive(U_43) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( in(U_43,U_42)
| ~ proper_subset(U_43,U_42)
| ~ ordinal(U_42)
| ~ epsilon_transitive(U_43) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,negated_conjecture,
~ ! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ! [C] :
( ordinal(C)
=> ( ( in(B,C)
& subset(A,B) )
=> in(A,C) ) ) ) ),
inference(negate,[status(cth)],[t22_ordinal1]) ).
fof(f_30_2,negated_conjecture,
? [A] :
( ? [B] :
( ? [C] :
( ~ in(A,C)
& in(B,C)
& subset(A,B)
& ordinal(C) )
& ordinal(B) )
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[f_30_1]) ).
fof(f_30_3,negated_conjecture,
? [U_46] :
( ? [U_45] :
( ? [U_44] :
( ~ in(U_46,U_44)
& in(U_45,U_44)
& subset(U_46,U_45)
& ordinal(U_44) )
& ordinal(U_45) )
& epsilon_transitive(U_46) ),
inference(variable_rename,[status(thm)],[f_30_2]) ).
fof(f_30_4,negated_conjecture,
( ? [U_45] :
( ? [U_44] :
( ~ in(sK14,U_44)
& in(U_45,U_44)
& subset(sK14,U_45)
& ordinal(U_44) )
& ordinal(U_45) )
& epsilon_transitive(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_46,sK14)],[f_30_3]) ).
fof(f_30_5,negated_conjecture,
( ? [U_44] :
( ~ in(sK14,U_44)
& in(sK15,U_44)
& subset(sK14,sK15)
& ordinal(U_44) )
& ordinal(sK15)
& epsilon_transitive(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_45,sK15)],[f_30_4]) ).
fof(f_30_6,negated_conjecture,
( ~ in(sK14,sK16)
& in(sK15,sK16)
& subset(sK14,sK15)
& ordinal(sK16)
& ordinal(sK15)
& epsilon_transitive(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_44,sK16)],[f_30_5]) ).
fof(f_30_7,negated_conjecture,
( ~ in(sK14,sK16)
& in(sK15,sK16)
& subset(sK14,sK15)
& ordinal(sK16)
& ordinal(sK15)
& epsilon_transitive(sK14) ),
inference(definitional_conversion,[status(esa)],[f_30_6]) ).
cnf(f_30_8,negated_conjecture,
epsilon_transitive(sK14),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_9,negated_conjecture,
ordinal(sK15),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_10,negated_conjecture,
ordinal(sK16),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_11,negated_conjecture,
subset(sK14,sK15),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_12,negated_conjecture,
in(sK15,sK16),
inference(clausify,[status(thm)],[f_30_7]) ).
cnf(f_30_13,negated_conjecture,
~ in(sK14,sK16),
inference(clausify,[status(thm)],[f_30_7]) ).
fof(f_31_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_31_2,plain,
! [U_48,U_47] :
( in(U_48,U_47)
| empty(U_47)
| ~ element(U_48,U_47) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( in(U_48,U_47)
| empty(U_47)
| ~ element(U_48,U_47) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_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_32_2,plain,
! [U_50,U_49] :
( ( element(U_50,powerset(U_49))
| ~ subset(U_50,U_49) )
& ( subset(U_50,U_49)
| ~ element(U_50,powerset(U_49)) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_54,U_52] :
( element(U_54,powerset(U_52))
| ~ subset(U_54,U_52) )
& ! [U_53,U_51] :
( subset(U_53,U_51)
| ~ element(U_53,powerset(U_51)) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( subset(U_53,U_51)
| ~ element(U_53,powerset(U_51)) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
( element(U_54,powerset(U_52))
| ~ subset(U_54,U_52) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_33_2,plain,
! [U_57,U_56,U_55] :
( element(U_57,U_55)
| ~ element(U_56,powerset(U_55))
| ~ in(U_57,U_56) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( element(U_57,U_55)
| ~ element(U_56,powerset(U_55))
| ~ in(U_57,U_56) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_34_2,plain,
! [U_60,U_59,U_58] :
( ~ empty(U_58)
| ~ element(U_59,powerset(U_58))
| ~ in(U_60,U_59) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_60,U_59] :
( ! [U_58] :
( ~ empty(U_58)
| ~ element(U_59,powerset(U_58)) )
| ~ in(U_60,U_59) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( ~ empty(U_58)
| ~ element(U_59,powerset(U_58))
| ~ in(U_60,U_59) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_35_2,plain,
! [U_61] :
( U_61 = empty_set
| ~ empty(U_61) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( U_61 = empty_set
| ~ empty(U_61) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_36_2,plain,
! [U_63,U_62] :
( ~ empty(U_62)
| ~ in(U_63,U_62) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
cnf(f_36_3,plain,
( ~ empty(U_62)
| ~ in(U_63,U_62) ),
inference(clausify,[status(thm)],[f_36_2]) ).
fof(f_37_1,plain,
! [A,B] :
( ~ subset(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_ordinal1]) ).
fof(f_37_2,plain,
! [U_65,U_64] :
( ~ subset(U_64,U_65)
| ~ in(U_65,U_64) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( ~ subset(U_64,U_65)
| ~ in(U_65,U_64) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_38_2,plain,
! [U_67,U_66] :
( ~ empty(U_66)
| U_67 = U_66
| ~ empty(U_67) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_67] :
( ! [U_66] :
( ~ empty(U_66)
| U_67 = U_66 )
| ~ empty(U_67) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( ~ empty(U_66)
| U_67 = U_66
| ~ empty(U_67) ),
inference(clausify,[status(thm)],[f_38_3]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_6_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_4]) ).
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,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,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_8,axiom,
( proper_subset(Eq_y_0,Eq_y_1)
| ~ proper_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_9,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| 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,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,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_16,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_17,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( relation_non_empty(Eq_y_0)
| ~ relation_non_empty(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
% 0.00/0.02 % Problem : NUM390+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 18:21:14 UTC 2026
% 0.09/0.35 % CPUTime :
% 1.36/1.63 % SZS status Theorem for theBenchmark
% 1.36/1.63 % SZS output start Proof for theBenchmark
% See solution above
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