%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM404+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:52:10 AM UTC 2026
% Result : Theorem 18.66s 18.90s
% Output : Proof 18.84s
% 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_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(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_ordinal1) ).
fof(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
fof(d3_ordinal1,axiom,
! [A] :
( epsilon_connected(A)
<=> ! [B,C] :
~ ( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) ),
file('theBenchmark.p',d3_ordinal1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d4_ordinal1,axiom,
! [A] :
( ordinal(A)
<=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',d4_ordinal1) ).
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(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(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_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_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_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(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(t23_ordinal1,axiom,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('theBenchmark.p',t23_ordinal1) ).
fof(t24_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ~ ( ~ in(B,A)
& A != B
& ~ in(A,B) ) ) ),
file('theBenchmark.p',t24_ordinal1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t37_ordinal1,conjecture,
! [A] :
~ ! [B] :
( in(B,A)
<=> ordinal(B) ),
file('theBenchmark.p',t37_ordinal1) ).
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] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_2_2,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_3_2,plain,
! [U_3] :
( ( epsilon_connected(U_3)
& epsilon_transitive(U_3) )
| ~ ordinal(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( epsilon_transitive(U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( epsilon_connected(U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_4_2,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_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_5_2,plain,
! [U_5] :
( ( one_to_one(U_5)
& function(U_5)
& relation(U_5) )
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( relation(U_5)
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( function(U_5)
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
cnf(f_5_5,plain,
( one_to_one(U_5)
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_6_2,plain,
! [U_6] :
( ordinal(U_6)
| ~ epsilon_connected(U_6)
| ~ epsilon_transitive(U_6) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( ordinal(U_6)
| ~ epsilon_connected(U_6)
| ~ epsilon_transitive(U_6) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_7_2,plain,
! [U_7] :
( ( ordinal(U_7)
& epsilon_connected(U_7)
& epsilon_transitive(U_7) )
| ~ empty(U_7) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( epsilon_transitive(U_7)
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( epsilon_connected(U_7)
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_7_2]) ).
cnf(f_7_5,plain,
( ordinal(U_7)
| ~ empty(U_7) ),
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_10] :
( ( epsilon_transitive(U_10)
| ? [U_9] :
( ~ subset(U_9,U_10)
& in(U_9,U_10) ) )
& ( ! [U_8] :
( subset(U_8,U_10)
| ~ in(U_8,U_10) )
| ~ epsilon_transitive(U_10) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_12] :
( epsilon_transitive(U_12)
| ? [U_9] :
( ~ subset(U_9,U_12)
& in(U_9,U_12) ) )
& ! [U_11] :
( ! [U_8] :
( subset(U_8,U_11)
| ~ in(U_8,U_11) )
| ~ epsilon_transitive(U_11) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_12] :
( epsilon_transitive(U_12)
| ( ~ subset(sK1(U_12),U_12)
& in(sK1(U_12),U_12) ) )
& ! [U_11] :
( ! [U_8] :
( subset(U_8,U_11)
| ~ in(U_8,U_11) )
| ~ epsilon_transitive(U_11) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_9,sK1(U_12))],[f_8_3]) ).
cnf(f_8_5,plain,
( subset(U_8,U_11)
| ~ in(U_8,U_11)
| ~ epsilon_transitive(U_11) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( in(sK1(U_12),U_12)
| epsilon_transitive(U_12) ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_7,plain,
( ~ subset(sK1(U_12),U_12)
| epsilon_transitive(U_12) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
! [A] :
( ( epsilon_connected(A)
| ? [B,C] :
( ~ in(C,B)
& B != C
& ~ in(B,C)
& in(C,A)
& in(B,A) ) )
& ( ! [B,C] :
( in(C,B)
| B = C
| in(B,C)
| ~ in(C,A)
| ~ in(B,A) )
| ~ epsilon_connected(A) ) ),
inference(fof_nnf,[status(thm)],[d3_ordinal1]) ).
fof(f_9_2,plain,
! [U_17] :
( ( epsilon_connected(U_17)
| ? [U_16,U_15] :
( ~ in(U_15,U_16)
& U_16 != U_15
& ~ in(U_16,U_15)
& in(U_15,U_17)
& in(U_16,U_17) ) )
& ( ! [U_14,U_13] :
( in(U_13,U_14)
| U_14 = U_13
| in(U_14,U_13)
| ~ in(U_13,U_17)
| ~ in(U_14,U_17) )
| ~ epsilon_connected(U_17) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_19] :
( epsilon_connected(U_19)
| ? [U_16] :
( ? [U_15] :
( ~ in(U_15,U_16)
& U_16 != U_15
& ~ in(U_16,U_15)
& in(U_15,U_19) )
& in(U_16,U_19) ) )
& ! [U_18] :
( ! [U_14] :
( ! [U_13] :
( in(U_13,U_14)
| U_14 = U_13
| in(U_14,U_13)
| ~ in(U_13,U_18) )
| ~ in(U_14,U_18) )
| ~ epsilon_connected(U_18) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
fof(f_9_4,plain,
( ! [U_19] :
( epsilon_connected(U_19)
| ( ? [U_15] :
( ~ in(U_15,sK2(U_19))
& sK2(U_19) != U_15
& ~ in(sK2(U_19),U_15)
& in(U_15,U_19) )
& in(sK2(U_19),U_19) ) )
& ! [U_18] :
( ! [U_14] :
( ! [U_13] :
( in(U_13,U_14)
| U_14 = U_13
| in(U_14,U_13)
| ~ in(U_13,U_18) )
| ~ in(U_14,U_18) )
| ~ epsilon_connected(U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2(U_19))],[f_9_3]) ).
fof(f_9_5,plain,
( ! [U_19] :
( epsilon_connected(U_19)
| ( ~ in(sK3(U_19),sK2(U_19))
& sK2(U_19) != sK3(U_19)
& ~ in(sK2(U_19),sK3(U_19))
& in(sK3(U_19),U_19)
& in(sK2(U_19),U_19) ) )
& ! [U_18] :
( ! [U_14] :
( ! [U_13] :
( in(U_13,U_14)
| U_14 = U_13
| in(U_14,U_13)
| ~ in(U_13,U_18) )
| ~ in(U_14,U_18) )
| ~ epsilon_connected(U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_15,sK3(U_19))],[f_9_4]) ).
cnf(f_9_6,plain,
( in(U_13,U_14)
| U_14 = U_13
| in(U_14,U_13)
| ~ in(U_13,U_18)
| ~ in(U_14,U_18)
| ~ epsilon_connected(U_18) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_7,plain,
( in(sK2(U_19),U_19)
| epsilon_connected(U_19) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_8,plain,
( in(sK3(U_19),U_19)
| epsilon_connected(U_19) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_9,plain,
( ~ in(sK2(U_19),sK3(U_19))
| epsilon_connected(U_19) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_10,plain,
( sK2(U_19) != sK3(U_19)
| epsilon_connected(U_19) ),
inference(clausify,[status(thm)],[f_9_5]) ).
cnf(f_9_11,plain,
( ~ in(sK3(U_19),sK2(U_19))
| epsilon_connected(U_19) ),
inference(clausify,[status(thm)],[f_9_5]) ).
fof(f_10_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_10_2,plain,
! [U_23,U_22] :
( ( subset(U_23,U_22)
| ? [U_21] :
( ~ in(U_21,U_22)
& in(U_21,U_23) ) )
& ( ! [U_20] :
( in(U_20,U_22)
| ~ in(U_20,U_23) )
| ~ subset(U_23,U_22) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_27,U_25] :
( subset(U_27,U_25)
| ? [U_21] :
( ~ in(U_21,U_25)
& in(U_21,U_27) ) )
& ! [U_26,U_24] :
( ! [U_20] :
( in(U_20,U_24)
| ~ in(U_20,U_26) )
| ~ subset(U_26,U_24) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
( ! [U_27,U_25] :
( subset(U_27,U_25)
| ( ~ in(sK4(U_27,U_25),U_25)
& in(sK4(U_27,U_25),U_27) ) )
& ! [U_26,U_24] :
( ! [U_20] :
( in(U_20,U_24)
| ~ in(U_20,U_26) )
| ~ subset(U_26,U_24) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_21,sK4(U_27,U_25))],[f_10_3]) ).
cnf(f_10_5,plain,
( in(U_20,U_24)
| ~ in(U_20,U_26)
| ~ subset(U_26,U_24) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_6,plain,
( in(sK4(U_27,U_25),U_27)
| subset(U_27,U_25) ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_7,plain,
( ~ in(sK4(U_27,U_25),U_25)
| subset(U_27,U_25) ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
! [A] :
( ( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) )
& ( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ) ),
inference(fof_nnf,[status(thm)],[d4_ordinal1]) ).
fof(f_11_2,plain,
! [U_28] :
( ( ordinal(U_28)
| ~ epsilon_connected(U_28)
| ~ epsilon_transitive(U_28) )
& ( ( epsilon_connected(U_28)
& epsilon_transitive(U_28) )
| ~ ordinal(U_28) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_30] :
( ordinal(U_30)
| ~ epsilon_connected(U_30)
| ~ epsilon_transitive(U_30) )
& ! [U_29] :
( ( epsilon_connected(U_29)
& epsilon_transitive(U_29) )
| ~ ordinal(U_29) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( epsilon_transitive(U_29)
| ~ ordinal(U_29) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( epsilon_connected(U_29)
| ~ ordinal(U_29) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( ordinal(U_30)
| ~ epsilon_connected(U_30)
| ~ epsilon_transitive(U_30) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_12_2,plain,
! [U_32] :
? [U_31] : element(U_31,U_32),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_32] : element(sK5(U_32),U_32),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_31,sK5(U_32))],[f_12_2]) ).
cnf(f_12_4,plain,
element(sK5(U_32),U_32),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_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]) ).
cnf(f_13_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_14_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_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_15_2,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
cnf(f_15_4,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
cnf(f_15_5,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
cnf(f_15_6,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
cnf(f_15_7,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
cnf(f_15_8,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
cnf(f_15_9,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_16_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_17_2,plain,
? [U_33] :
( function(U_33)
& relation(U_33) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_33,sK6)],[f_17_2]) ).
cnf(f_17_4,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
function(sK6),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_18_2,plain,
? [U_34] :
( ordinal(U_34)
& epsilon_connected(U_34)
& epsilon_transitive(U_34) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ordinal(sK7)
& epsilon_connected(sK7)
& epsilon_transitive(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_34,sK7)],[f_18_2]) ).
cnf(f_18_4,plain,
epsilon_transitive(sK7),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
epsilon_connected(sK7),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_6,plain,
ordinal(sK7),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_19_2,plain,
? [U_35] :
( relation(U_35)
& empty(U_35) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( relation(sK8)
& empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_35,sK8)],[f_19_2]) ).
cnf(f_19_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_20_2,plain,
? [U_36] : empty(U_36),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_36,sK9)],[f_20_2]) ).
cnf(f_20_4,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_21_2,plain,
? [U_37] :
( function(U_37)
& empty(U_37)
& relation(U_37) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( function(sK10)
& empty(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_37,sK10)],[f_21_2]) ).
cnf(f_21_4,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_6,plain,
function(sK10),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_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_22_2,plain,
? [U_38] :
( ordinal(U_38)
& epsilon_connected(U_38)
& epsilon_transitive(U_38)
& empty(U_38)
& one_to_one(U_38)
& function(U_38)
& relation(U_38) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& empty(sK11)
& one_to_one(sK11)
& function(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_38,sK11)],[f_22_2]) ).
cnf(f_22_4,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
function(sK11),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_6,plain,
one_to_one(sK11),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_7,plain,
empty(sK11),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_8,plain,
epsilon_transitive(sK11),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_9,plain,
epsilon_connected(sK11),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_10,plain,
ordinal(sK11),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_23_2,plain,
? [U_39] :
( relation(U_39)
& ~ empty(U_39) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_39,sK12)],[f_23_2]) ).
cnf(f_23_4,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_24_2,plain,
? [U_40] : ~ empty(U_40),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
~ empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_40,sK13)],[f_24_2]) ).
cnf(f_24_4,plain,
~ empty(sK13),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_25_2,plain,
? [U_41] :
( one_to_one(U_41)
& function(U_41)
& relation(U_41) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( one_to_one(sK14)
& function(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_41,sK14)],[f_25_2]) ).
cnf(f_25_4,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
function(sK14),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_6,plain,
one_to_one(sK14),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_26_2,plain,
? [U_42] :
( ordinal(U_42)
& epsilon_connected(U_42)
& epsilon_transitive(U_42)
& ~ empty(U_42) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ordinal(sK15)
& epsilon_connected(sK15)
& epsilon_transitive(sK15)
& ~ empty(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_42,sK15)],[f_26_2]) ).
cnf(f_26_4,plain,
~ empty(sK15),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
epsilon_transitive(sK15),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
epsilon_connected(sK15),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_7,plain,
ordinal(sK15),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_27_2,plain,
? [U_43] :
( relation_empty_yielding(U_43)
& relation(U_43) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( relation_empty_yielding(sK16)
& relation(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_43,sK16)],[f_27_2]) ).
cnf(f_27_4,plain,
relation(sK16),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
relation_empty_yielding(sK16),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_28_2,plain,
? [U_44] :
( function(U_44)
& relation_empty_yielding(U_44)
& relation(U_44) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( function(sK17)
& relation_empty_yielding(sK17)
& relation(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_44,sK17)],[f_28_2]) ).
cnf(f_28_4,plain,
relation(sK17),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_5,plain,
relation_empty_yielding(sK17),
inference(clausify,[status(thm)],[f_28_3]) ).
cnf(f_28_6,plain,
function(sK17),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc5_funct_1]) ).
fof(f_29_2,plain,
? [U_45] :
( function(U_45)
& relation_non_empty(U_45)
& relation(U_45) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( function(sK18)
& relation_non_empty(sK18)
& relation(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_45,sK18)],[f_29_2]) ).
cnf(f_29_4,plain,
relation(sK18),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
relation_non_empty(sK18),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_6,plain,
function(sK18),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_30_2,plain,
! [U_47,U_46] : subset(U_47,U_47),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_47] : subset(U_47,U_47),
inference(miniscope,[status(thm)],[f_30_2]) ).
cnf(f_30_4,plain,
subset(U_47,U_47),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_31_2,plain,
! [U_49,U_48] :
( element(U_49,U_48)
| ~ in(U_49,U_48) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( element(U_49,U_48)
| ~ in(U_49,U_48) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_32_2,plain,
! [U_51,U_50] :
( ordinal(U_51)
| ~ in(U_51,U_50)
| ~ ordinal(U_50) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( ordinal(U_51)
| ~ in(U_51,U_50)
| ~ ordinal(U_50) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A] :
( ! [B] :
( in(B,A)
| A = B
| in(A,B)
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t24_ordinal1]) ).
fof(f_33_2,plain,
! [U_53] :
( ! [U_52] :
( in(U_52,U_53)
| U_53 = U_52
| in(U_53,U_52)
| ~ ordinal(U_52) )
| ~ ordinal(U_53) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( in(U_52,U_53)
| U_53 = U_52
| in(U_53,U_52)
| ~ ordinal(U_52)
| ~ ordinal(U_53) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_34_2,plain,
! [U_55,U_54] :
( in(U_55,U_54)
| empty(U_54)
| ~ element(U_55,U_54) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( in(U_55,U_54)
| empty(U_54)
| ~ element(U_55,U_54) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,negated_conjecture,
~ ! [A] :
~ ! [B] :
( in(B,A)
<=> ordinal(B) ),
inference(negate,[status(cth)],[t37_ordinal1]) ).
fof(f_35_2,negated_conjecture,
? [A] :
! [B] :
( ( in(B,A)
| ~ ordinal(B) )
& ( ordinal(B)
| ~ in(B,A) ) ),
inference(fof_nnf,[status(thm)],[f_35_1]) ).
fof(f_35_3,negated_conjecture,
? [U_57] :
! [U_56] :
( ( in(U_56,U_57)
| ~ ordinal(U_56) )
& ( ordinal(U_56)
| ~ in(U_56,U_57) ) ),
inference(variable_rename,[status(thm)],[f_35_2]) ).
fof(f_35_4,negated_conjecture,
? [U_57] :
( ! [U_59] :
( in(U_59,U_57)
| ~ ordinal(U_59) )
& ! [U_58] :
( ordinal(U_58)
| ~ in(U_58,U_57) ) ),
inference(miniscope,[status(thm)],[f_35_3]) ).
fof(f_35_5,negated_conjecture,
( ! [U_59] :
( in(U_59,sK19)
| ~ ordinal(U_59) )
& ! [U_58] :
( ordinal(U_58)
| ~ in(U_58,sK19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_57,sK19)],[f_35_4]) ).
fof(f_35_6,negated_conjecture,
( ! [U_59] :
( in(U_59,sK19)
| ~ ordinal(U_59) )
& ! [U_58] :
( ordinal(U_58)
| ~ in(U_58,sK19) ) ),
inference(definitional_conversion,[status(esa)],[f_35_5]) ).
cnf(f_35_7,negated_conjecture,
( ordinal(U_58)
| ~ in(U_58,sK19) ),
inference(clausify,[status(thm)],[f_35_6]) ).
cnf(f_35_8,negated_conjecture,
( in(U_59,sK19)
| ~ ordinal(U_59) ),
inference(clausify,[status(thm)],[f_35_6]) ).
fof(f_36_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_36_2,plain,
! [U_61,U_60] :
( ( element(U_61,powerset(U_60))
| ~ subset(U_61,U_60) )
& ( subset(U_61,U_60)
| ~ element(U_61,powerset(U_60)) ) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ! [U_65,U_63] :
( element(U_65,powerset(U_63))
| ~ subset(U_65,U_63) )
& ! [U_64,U_62] :
( subset(U_64,U_62)
| ~ element(U_64,powerset(U_62)) ) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( subset(U_64,U_62)
| ~ element(U_64,powerset(U_62)) ),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
( element(U_65,powerset(U_63))
| ~ subset(U_65,U_63) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_37_2,plain,
! [U_68,U_67,U_66] :
( element(U_68,U_66)
| ~ element(U_67,powerset(U_66))
| ~ in(U_68,U_67) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( element(U_68,U_66)
| ~ element(U_67,powerset(U_66))
| ~ in(U_68,U_67) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_38_2,plain,
! [U_71,U_70,U_69] :
( ~ empty(U_69)
| ~ element(U_70,powerset(U_69))
| ~ in(U_71,U_70) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_71,U_70] :
( ! [U_69] :
( ~ empty(U_69)
| ~ element(U_70,powerset(U_69)) )
| ~ in(U_71,U_70) ),
inference(miniscope,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( ~ empty(U_69)
| ~ element(U_70,powerset(U_69))
| ~ in(U_71,U_70) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_39_2,plain,
! [U_72] :
( U_72 = empty_set
| ~ empty(U_72) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
cnf(f_39_3,plain,
( U_72 = empty_set
| ~ empty(U_72) ),
inference(clausify,[status(thm)],[f_39_2]) ).
fof(f_40_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_40_2,plain,
! [U_74,U_73] :
( ~ empty(U_73)
| ~ in(U_74,U_73) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
cnf(f_40_3,plain,
( ~ empty(U_73)
| ~ in(U_74,U_73) ),
inference(clausify,[status(thm)],[f_40_2]) ).
fof(f_41_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_41_2,plain,
! [U_76,U_75] :
( ~ empty(U_75)
| U_76 = U_75
| ~ empty(U_76) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_76] :
( ! [U_75] :
( ~ empty(U_75)
| U_76 = U_75 )
| ~ empty(U_76) ),
inference(miniscope,[status(thm)],[f_41_2]) ).
cnf(f_41_4,plain,
( ~ empty(U_75)
| U_76 = U_75
| ~ empty(U_76) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_5_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_3]) ).
cnf(f_5_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_5_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,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK5(Eq_x_0) = sK5(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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,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_18,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_19,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_20,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_21,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
% 0.00/0.03 % Problem : NUM404+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 18:21:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 18.66/18.90 % SZS status Theorem for theBenchmark
% 18.66/18.90 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------