%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM386+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 : n008.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 22.35s 22.65s
% Output : Proof 22.78s
% 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_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(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_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_ordinal1,axiom,
! [A] : ~ empty(succ(A)),
file('theBenchmark.p',fc1_ordinal1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('theBenchmark.p',fc2_relat_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
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(t13_ordinal1,conjecture,
! [A,B] :
( in(A,succ(B))
<=> ( A = B
| in(A,B) ) ),
file('theBenchmark.p',t13_ordinal1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
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(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] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_3_2,plain,
! [U_3] :
( relation(U_3)
| ~ empty(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( relation(U_3)
| ~ empty(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_4] :
( ( one_to_one(U_4)
& function(U_4)
& relation(U_4) )
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( function(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_5,plain,
( one_to_one(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_5_2,plain,
! [U_6,U_5] : set_union2(U_6,U_5) = set_union2(U_5,U_6),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
set_union2(U_6,U_5) = set_union2(U_5,U_6),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_6_2,plain,
! [U_7] : succ(U_7) = set_union2(U_7,singleton(U_7)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
succ(U_7) = set_union2(U_7,singleton(U_7)),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_7_2,plain,
! [U_11,U_10] :
( ( U_10 = singleton(U_11)
| ? [U_9] :
( ( ~ in(U_9,U_10)
& U_9 = U_11 )
| ( U_9 != U_11
& in(U_9,U_10) ) ) )
& ( ! [U_8] :
( ( in(U_8,U_10)
| U_8 != U_11 )
& ( U_8 = U_11
| ~ in(U_8,U_10) ) )
| U_10 != singleton(U_11) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_19,U_17] :
( U_17 = singleton(U_19)
| ? [U_15] :
( ~ in(U_15,U_17)
& U_15 = U_19 )
| ? [U_14] :
( U_14 != U_19
& in(U_14,U_17) ) )
& ! [U_18,U_16] :
( ( ! [U_13] :
( in(U_13,U_16)
| U_13 != U_18 )
& ! [U_12] :
( U_12 = U_18
| ~ in(U_12,U_16) ) )
| U_16 != singleton(U_18) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_19,U_17] :
( U_17 = singleton(U_19)
| ? [U_15] :
( ~ in(U_15,U_17)
& U_15 = U_19 )
| ( sK1(U_19,U_17) != U_19
& in(sK1(U_19,U_17),U_17) ) )
& ! [U_18,U_16] :
( ( ! [U_13] :
( in(U_13,U_16)
| U_13 != U_18 )
& ! [U_12] :
( U_12 = U_18
| ~ in(U_12,U_16) ) )
| U_16 != singleton(U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_14,sK1(U_19,U_17))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_19,U_17] :
( U_17 = singleton(U_19)
| ( ~ in(sK2(U_19,U_17),U_17)
& sK2(U_19,U_17) = U_19 )
| ( sK1(U_19,U_17) != U_19
& in(sK1(U_19,U_17),U_17) ) )
& ! [U_18,U_16] :
( ( ! [U_13] :
( in(U_13,U_16)
| U_13 != U_18 )
& ! [U_12] :
( U_12 = U_18
| ~ in(U_12,U_16) ) )
| U_16 != singleton(U_18) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2(U_19,U_17))],[f_7_4]) ).
cnf(f_7_6,plain,
( U_12 = U_18
| ~ in(U_12,U_16)
| U_16 != singleton(U_18) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_7,plain,
( in(U_13,U_16)
| U_13 != U_18
| U_16 != singleton(U_18) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_8,plain,
( sK2(U_19,U_17) = U_19
| in(sK1(U_19,U_17),U_17)
| U_17 = singleton(U_19) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_9,plain,
( ~ in(sK2(U_19,U_17),U_17)
| in(sK1(U_19,U_17),U_17)
| U_17 = singleton(U_19) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_10,plain,
( sK2(U_19,U_17) = U_19
| sK1(U_19,U_17) != U_19
| U_17 = singleton(U_19) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_11,plain,
( ~ in(sK2(U_19,U_17),U_17)
| sK1(U_19,U_17) != U_19
| U_17 = singleton(U_19) ),
inference(clausify,[status(thm)],[f_7_5]) ).
fof(f_8_1,plain,
! [A,B,C] :
( ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( in(D,B)
| in(D,A) ) )
| ( ~ in(D,B)
& ~ in(D,A)
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( ~ in(D,B)
& ~ in(D,A) ) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(f_8_2,plain,
! [U_24,U_23,U_22] :
( ( U_22 = set_union2(U_24,U_23)
| ? [U_21] :
( ( ~ in(U_21,U_22)
& ( in(U_21,U_23)
| in(U_21,U_24) ) )
| ( ~ in(U_21,U_23)
& ~ in(U_21,U_24)
& in(U_21,U_22) ) ) )
& ( ! [U_20] :
( ( in(U_20,U_22)
| ( ~ in(U_20,U_23)
& ~ in(U_20,U_24) ) )
& ( in(U_20,U_23)
| in(U_20,U_24)
| ~ in(U_20,U_22) ) )
| U_22 != set_union2(U_24,U_23) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_34,U_32,U_30] :
( U_30 = set_union2(U_34,U_32)
| ? [U_28] :
( ~ in(U_28,U_30)
& ( in(U_28,U_32)
| in(U_28,U_34) ) )
| ? [U_27] :
( ~ in(U_27,U_32)
& ~ in(U_27,U_34)
& in(U_27,U_30) ) )
& ! [U_33,U_31,U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ( ~ in(U_26,U_31)
& ~ in(U_26,U_33) ) )
& ! [U_25] :
( in(U_25,U_31)
| in(U_25,U_33)
| ~ in(U_25,U_29) ) )
| U_29 != set_union2(U_33,U_31) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_34,U_32,U_30] :
( U_30 = set_union2(U_34,U_32)
| ? [U_28] :
( ~ in(U_28,U_30)
& ( in(U_28,U_32)
| in(U_28,U_34) ) )
| ( ~ in(sK3(U_34,U_32,U_30),U_32)
& ~ in(sK3(U_34,U_32,U_30),U_34)
& in(sK3(U_34,U_32,U_30),U_30) ) )
& ! [U_33,U_31,U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ( ~ in(U_26,U_31)
& ~ in(U_26,U_33) ) )
& ! [U_25] :
( in(U_25,U_31)
| in(U_25,U_33)
| ~ in(U_25,U_29) ) )
| U_29 != set_union2(U_33,U_31) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_27,sK3(U_34,U_32,U_30))],[f_8_3]) ).
fof(f_8_5,plain,
( ! [U_34,U_32,U_30] :
( U_30 = set_union2(U_34,U_32)
| ( ~ in(sK4(U_34,U_32,U_30),U_30)
& ( in(sK4(U_34,U_32,U_30),U_32)
| in(sK4(U_34,U_32,U_30),U_34) ) )
| ( ~ in(sK3(U_34,U_32,U_30),U_32)
& ~ in(sK3(U_34,U_32,U_30),U_34)
& in(sK3(U_34,U_32,U_30),U_30) ) )
& ! [U_33,U_31,U_29] :
( ( ! [U_26] :
( in(U_26,U_29)
| ( ~ in(U_26,U_31)
& ~ in(U_26,U_33) ) )
& ! [U_25] :
( in(U_25,U_31)
| in(U_25,U_33)
| ~ in(U_25,U_29) ) )
| U_29 != set_union2(U_33,U_31) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_28,sK4(U_34,U_32,U_30))],[f_8_4]) ).
cnf(f_8_6,plain,
( in(U_25,U_31)
| in(U_25,U_33)
| ~ in(U_25,U_29)
| U_29 != set_union2(U_33,U_31) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_7,plain,
( ~ in(U_26,U_33)
| in(U_26,U_29)
| U_29 != set_union2(U_33,U_31) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_8,plain,
( ~ in(U_26,U_31)
| in(U_26,U_29)
| U_29 != set_union2(U_33,U_31) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_9,plain,
( in(sK4(U_34,U_32,U_30),U_32)
| in(sK4(U_34,U_32,U_30),U_34)
| in(sK3(U_34,U_32,U_30),U_30)
| U_30 = set_union2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_10,plain,
( ~ in(sK4(U_34,U_32,U_30),U_30)
| in(sK3(U_34,U_32,U_30),U_30)
| U_30 = set_union2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_11,plain,
( ~ in(sK3(U_34,U_32,U_30),U_34)
| in(sK4(U_34,U_32,U_30),U_32)
| in(sK4(U_34,U_32,U_30),U_34)
| U_30 = set_union2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_12,plain,
( ~ in(sK3(U_34,U_32,U_30),U_32)
| in(sK4(U_34,U_32,U_30),U_32)
| in(sK4(U_34,U_32,U_30),U_34)
| U_30 = set_union2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_13,plain,
( ~ in(sK3(U_34,U_32,U_30),U_34)
| ~ in(sK4(U_34,U_32,U_30),U_30)
| U_30 = set_union2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_14,plain,
( ~ in(sK3(U_34,U_32,U_30),U_32)
| ~ in(sK4(U_34,U_32,U_30),U_30)
| U_30 = set_union2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_8_5]) ).
fof(f_9_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_9_2,plain,
! [U_36] :
? [U_35] : element(U_35,U_36),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_36] : element(sK5(U_36),U_36),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_35,sK5(U_36))],[f_9_2]) ).
cnf(f_9_4,plain,
element(sK5(U_36),U_36),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_10_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
cnf(f_10_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_11_2,plain,
! [U_37] : ~ empty(succ(U_37)),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
~ empty(succ(U_37)),
inference(clausify,[status(thm)],[f_11_2]) ).
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,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_13_2,plain,
! [U_39,U_38] :
( relation(set_union2(U_39,U_38))
| ~ relation(U_38)
| ~ relation(U_39) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( relation(set_union2(U_39,U_38))
| ~ relation(U_38)
| ~ relation(U_39) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_14_2,plain,
! [U_41,U_40] :
( ~ empty(set_union2(U_41,U_40))
| empty(U_41) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_41] :
( ! [U_40] : ~ empty(set_union2(U_41,U_40))
| empty(U_41) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( ~ empty(set_union2(U_41,U_40))
| empty(U_41) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_15_2,plain,
! [U_43,U_42] :
( ~ empty(set_union2(U_42,U_43))
| empty(U_43) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_43] :
( ! [U_42] : ~ empty(set_union2(U_42,U_43))
| empty(U_43) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( ~ empty(set_union2(U_42,U_43))
| empty(U_43) ),
inference(clausify,[status(thm)],[f_15_3]) ).
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,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_17_2,plain,
! [U_45,U_44] : set_union2(U_45,U_45) = U_45,
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_45] : set_union2(U_45,U_45) = U_45,
inference(miniscope,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
set_union2(U_45,U_45) = U_45,
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_18_2,plain,
? [U_46] :
( function(U_46)
& relation(U_46) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_46,sK6)],[f_18_2]) ).
cnf(f_18_4,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
function(sK6),
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_47] :
( relation(U_47)
& empty(U_47) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( relation(sK7)
& empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_47,sK7)],[f_19_2]) ).
cnf(f_19_4,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
relation(sK7),
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_48] : empty(U_48),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_48,sK8)],[f_20_2]) ).
cnf(f_20_4,plain,
empty(sK8),
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_49] :
( function(U_49)
& empty(U_49)
& relation(U_49) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( function(sK9)
& empty(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_49,sK9)],[f_21_2]) ).
cnf(f_21_4,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_6,plain,
function(sK9),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_22_2,plain,
? [U_50] :
( relation(U_50)
& ~ empty(U_50) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( relation(sK10)
& ~ empty(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_50,sK10)],[f_22_2]) ).
cnf(f_22_4,plain,
~ empty(sK10),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_23_2,plain,
? [U_51] : ~ empty(U_51),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
~ empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_51,sK11)],[f_23_2]) ).
cnf(f_23_4,plain,
~ empty(sK11),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_24_2,plain,
? [U_52] :
( one_to_one(U_52)
& function(U_52)
& relation(U_52) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( one_to_one(sK12)
& function(sK12)
& relation(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_52,sK12)],[f_24_2]) ).
cnf(f_24_4,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
function(sK12),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_6,plain,
one_to_one(sK12),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_25_2,plain,
? [U_53] :
( relation_empty_yielding(U_53)
& relation(U_53) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( relation_empty_yielding(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_53,sK13)],[f_25_2]) ).
cnf(f_25_4,plain,
relation(sK13),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
relation_empty_yielding(sK13),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_26_2,plain,
? [U_54] :
( function(U_54)
& relation_empty_yielding(U_54)
& relation(U_54) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( function(sK14)
& relation_empty_yielding(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_54,sK14)],[f_26_2]) ).
cnf(f_26_4,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
relation_empty_yielding(sK14),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
function(sK14),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc5_funct_1]) ).
fof(f_27_2,plain,
? [U_55] :
( function(U_55)
& relation_non_empty(U_55)
& relation(U_55) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( function(sK15)
& relation_non_empty(sK15)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_55,sK15)],[f_27_2]) ).
cnf(f_27_4,plain,
relation(sK15),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
relation_non_empty(sK15),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
function(sK15),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,negated_conjecture,
~ ! [A,B] :
( in(A,succ(B))
<=> ( A = B
| in(A,B) ) ),
inference(negate,[status(cth)],[t13_ordinal1]) ).
fof(f_28_2,negated_conjecture,
? [A,B] :
( ( ~ in(A,succ(B))
& ( A = B
| in(A,B) ) )
| ( A != B
& ~ in(A,B)
& in(A,succ(B)) ) ),
inference(fof_nnf,[status(thm)],[f_28_1]) ).
fof(f_28_3,negated_conjecture,
? [U_57,U_56] :
( ( ~ in(U_57,succ(U_56))
& ( U_57 = U_56
| in(U_57,U_56) ) )
| ( U_57 != U_56
& ~ in(U_57,U_56)
& in(U_57,succ(U_56)) ) ),
inference(variable_rename,[status(thm)],[f_28_2]) ).
fof(f_28_4,negated_conjecture,
( ? [U_61,U_59] :
( ~ in(U_61,succ(U_59))
& ( U_61 = U_59
| in(U_61,U_59) ) )
| ? [U_60,U_58] :
( U_60 != U_58
& ~ in(U_60,U_58)
& in(U_60,succ(U_58)) ) ),
inference(miniscope,[status(thm)],[f_28_3]) ).
fof(f_28_5,negated_conjecture,
( ? [U_61,U_59] :
( ~ in(U_61,succ(U_59))
& ( U_61 = U_59
| in(U_61,U_59) ) )
| ? [U_58] :
( sK16 != U_58
& ~ in(sK16,U_58)
& in(sK16,succ(U_58)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_60,sK16)],[f_28_4]) ).
fof(f_28_6,negated_conjecture,
( ? [U_61,U_59] :
( ~ in(U_61,succ(U_59))
& ( U_61 = U_59
| in(U_61,U_59) ) )
| ( sK16 != sK17
& ~ in(sK16,sK17)
& in(sK16,succ(sK17)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_58,sK17)],[f_28_5]) ).
fof(f_28_7,negated_conjecture,
( ? [U_59] :
( ~ in(sK18,succ(U_59))
& ( sK18 = U_59
| in(sK18,U_59) ) )
| ( sK16 != sK17
& ~ in(sK16,sK17)
& in(sK16,succ(sK17)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_61,sK18)],[f_28_6]) ).
fof(f_28_8,negated_conjecture,
( ( ~ in(sK18,succ(sK19))
& ( sK18 = sK19
| in(sK18,sK19) ) )
| ( sK16 != sK17
& ~ in(sK16,sK17)
& in(sK16,succ(sK17)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_59,sK19)],[f_28_7]) ).
fof(f_28_9,negated_conjecture,
( ( ~ in(sK18,succ(sK19))
| ~ sP1 )
& ( sK18 = sK19
| in(sK18,sK19)
| ~ sP1 )
& ( sK16 != sK17
| ~ sP0 )
& ( ~ in(sK16,sK17)
| ~ sP0 )
& ( in(sK16,succ(sK17))
| ~ sP0 )
& ( sP1
| sP0 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0,sP1])],[f_28_8]) ).
cnf(f_28_10,negated_conjecture,
( sP1
| sP0 ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_11,negated_conjecture,
( in(sK16,succ(sK17))
| ~ sP0 ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_12,negated_conjecture,
( ~ in(sK16,sK17)
| ~ sP0 ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_13,negated_conjecture,
( sK16 != sK17
| ~ sP0 ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_14,negated_conjecture,
( sK18 = sK19
| in(sK18,sK19)
| ~ sP1 ),
inference(clausify,[status(thm)],[f_28_9]) ).
cnf(f_28_15,negated_conjecture,
( ~ in(sK18,succ(sK19))
| ~ sP1 ),
inference(clausify,[status(thm)],[f_28_9]) ).
fof(f_29_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_29_2,plain,
! [U_62] : set_union2(U_62,empty_set) = U_62,
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
set_union2(U_62,empty_set) = U_62,
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_30_2,plain,
! [U_64,U_63] :
( element(U_64,U_63)
| ~ in(U_64,U_63) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( element(U_64,U_63)
| ~ in(U_64,U_63) ),
inference(clausify,[status(thm)],[f_30_2]) ).
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_66,U_65] :
( in(U_66,U_65)
| empty(U_65)
| ~ element(U_66,U_65) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( in(U_66,U_65)
| empty(U_65)
| ~ element(U_66,U_65) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_32_2,plain,
! [U_67] :
( U_67 = empty_set
| ~ empty(U_67) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( U_67 = empty_set
| ~ empty(U_67) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_33_2,plain,
! [U_69,U_68] :
( ~ empty(U_68)
| ~ in(U_69,U_68) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( ~ empty(U_68)
| ~ in(U_69,U_68) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_34_2,plain,
! [U_71,U_70] :
( ~ empty(U_70)
| U_71 = U_70
| ~ empty(U_71) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_71] :
( ! [U_70] :
( ~ empty(U_70)
| U_71 = U_70 )
| ~ empty(U_71) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( ~ empty(U_70)
| U_71 = U_70
| ~ empty(U_71) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_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,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(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,
( sK3(Eq_x_0,Eq_x_1,Eq_x_2) = sK3(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2) = sK4(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,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_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 : NUM386+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
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 18:22:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 22.35/22.65 % SZS status Theorem for theBenchmark
% 22.35/22.65 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------