%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 : n017.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 08:57:45 AM UTC 2026
% Result : Theorem 0.38s 0.67s
% Output : Proof 0.44s
% 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(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('theBenchmark.p',d1_zfmisc_1) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(l4_zfmisc_1,axiom,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('theBenchmark.p',l4_zfmisc_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('theBenchmark.p',t2_tarski) ).
fof(t30_zfmisc_1,conjecture,
! [A] : powerset(singleton(A)) = unordered_pair(empty_set,singleton(A)),
file('theBenchmark.p',t30_zfmisc_1) ).
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] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_2_2,plain,
! [U_3,U_2] : unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
unordered_pair(U_3,U_2) = unordered_pair(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A,B] :
( ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
& subset(C,A) )
| ( ~ subset(C,A)
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ~ subset(C,A) )
& ( subset(C,A)
| ~ in(C,B) ) )
| B != powerset(A) ) ),
inference(fof_nnf,[status(thm)],[d1_zfmisc_1]) ).
fof(f_3_2,plain,
! [U_7,U_6] :
( ( U_6 = powerset(U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& subset(U_5,U_7) )
| ( ~ subset(U_5,U_7)
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| ~ subset(U_4,U_7) )
& ( subset(U_4,U_7)
| ~ in(U_4,U_6) ) )
| U_6 != powerset(U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_15,U_13] :
( U_13 = powerset(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& subset(U_11,U_15) )
| ? [U_10] :
( ~ subset(U_10,U_15)
& in(U_10,U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| ~ subset(U_9,U_14) )
& ! [U_8] :
( subset(U_8,U_14)
| ~ in(U_8,U_12) ) )
| U_12 != powerset(U_14) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_15,U_13] :
( U_13 = powerset(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& subset(U_11,U_15) )
| ( ~ subset(sK1(U_15,U_13),U_15)
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| ~ subset(U_9,U_14) )
& ! [U_8] :
( subset(U_8,U_14)
| ~ in(U_8,U_12) ) )
| U_12 != powerset(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_10,sK1(U_15,U_13))],[f_3_3]) ).
fof(f_3_5,plain,
( ! [U_15,U_13] :
( U_13 = powerset(U_15)
| ( ~ in(sK2(U_15,U_13),U_13)
& subset(sK2(U_15,U_13),U_15) )
| ( ~ subset(sK1(U_15,U_13),U_15)
& in(sK1(U_15,U_13),U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| ~ subset(U_9,U_14) )
& ! [U_8] :
( subset(U_8,U_14)
| ~ in(U_8,U_12) ) )
| U_12 != powerset(U_14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_11,sK2(U_15,U_13))],[f_3_4]) ).
cnf(f_3_6,plain,
( subset(U_8,U_14)
| ~ in(U_8,U_12)
| U_12 != powerset(U_14) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( in(U_9,U_12)
| ~ subset(U_9,U_14)
| U_12 != powerset(U_14) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( subset(sK2(U_15,U_13),U_15)
| in(sK1(U_15,U_13),U_13)
| U_13 = powerset(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_9,plain,
( ~ in(sK2(U_15,U_13),U_13)
| in(sK1(U_15,U_13),U_13)
| U_13 = powerset(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_10,plain,
( subset(sK2(U_15,U_13),U_15)
| ~ subset(sK1(U_15,U_13),U_15)
| U_13 = powerset(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_11,plain,
( ~ in(sK2(U_15,U_13),U_13)
| ~ subset(sK1(U_15,U_13),U_15)
| U_13 = powerset(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,plain,
! [A,B,C] :
( ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
& ( D = B
| D = A ) )
| ( D != B
& D != A
& in(D,C) ) ) )
& ( ! [D] :
( ( in(D,C)
| ( D != B
& D != A ) )
& ( D = B
| D = A
| ~ in(D,C) ) )
| C != unordered_pair(A,B) ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(f_4_2,plain,
! [U_20,U_19,U_18] :
( ( U_18 = unordered_pair(U_20,U_19)
| ? [U_17] :
( ( ~ in(U_17,U_18)
& ( U_17 = U_19
| U_17 = U_20 ) )
| ( U_17 != U_19
& U_17 != U_20
& in(U_17,U_18) ) ) )
& ( ! [U_16] :
( ( in(U_16,U_18)
| ( U_16 != U_19
& U_16 != U_20 ) )
& ( U_16 = U_19
| U_16 = U_20
| ~ in(U_16,U_18) ) )
| U_18 != unordered_pair(U_20,U_19) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_30,U_28,U_26] :
( U_26 = unordered_pair(U_30,U_28)
| ? [U_24] :
( ~ in(U_24,U_26)
& ( U_24 = U_28
| U_24 = U_30 ) )
| ? [U_23] :
( U_23 != U_28
& U_23 != U_30
& in(U_23,U_26) ) )
& ! [U_29,U_27,U_25] :
( ( ! [U_22] :
( in(U_22,U_25)
| ( U_22 != U_27
& U_22 != U_29 ) )
& ! [U_21] :
( U_21 = U_27
| U_21 = U_29
| ~ in(U_21,U_25) ) )
| U_25 != unordered_pair(U_29,U_27) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_30,U_28,U_26] :
( U_26 = unordered_pair(U_30,U_28)
| ? [U_24] :
( ~ in(U_24,U_26)
& ( U_24 = U_28
| U_24 = U_30 ) )
| ( sK3(U_30,U_28,U_26) != U_28
& sK3(U_30,U_28,U_26) != U_30
& in(sK3(U_30,U_28,U_26),U_26) ) )
& ! [U_29,U_27,U_25] :
( ( ! [U_22] :
( in(U_22,U_25)
| ( U_22 != U_27
& U_22 != U_29 ) )
& ! [U_21] :
( U_21 = U_27
| U_21 = U_29
| ~ in(U_21,U_25) ) )
| U_25 != unordered_pair(U_29,U_27) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_23,sK3(U_30,U_28,U_26))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_30,U_28,U_26] :
( U_26 = unordered_pair(U_30,U_28)
| ( ~ in(sK4(U_30,U_28,U_26),U_26)
& ( sK4(U_30,U_28,U_26) = U_28
| sK4(U_30,U_28,U_26) = U_30 ) )
| ( sK3(U_30,U_28,U_26) != U_28
& sK3(U_30,U_28,U_26) != U_30
& in(sK3(U_30,U_28,U_26),U_26) ) )
& ! [U_29,U_27,U_25] :
( ( ! [U_22] :
( in(U_22,U_25)
| ( U_22 != U_27
& U_22 != U_29 ) )
& ! [U_21] :
( U_21 = U_27
| U_21 = U_29
| ~ in(U_21,U_25) ) )
| U_25 != unordered_pair(U_29,U_27) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_24,sK4(U_30,U_28,U_26))],[f_4_4]) ).
cnf(f_4_6,plain,
( U_21 = U_27
| U_21 = U_29
| ~ in(U_21,U_25)
| U_25 != unordered_pair(U_29,U_27) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_7,plain,
( U_22 != U_29
| in(U_22,U_25)
| U_25 != unordered_pair(U_29,U_27) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_8,plain,
( U_22 != U_27
| in(U_22,U_25)
| U_25 != unordered_pair(U_29,U_27) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_9,plain,
( sK4(U_30,U_28,U_26) = U_28
| sK4(U_30,U_28,U_26) = U_30
| in(sK3(U_30,U_28,U_26),U_26)
| U_26 = unordered_pair(U_30,U_28) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_10,plain,
( ~ in(sK4(U_30,U_28,U_26),U_26)
| in(sK3(U_30,U_28,U_26),U_26)
| U_26 = unordered_pair(U_30,U_28) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_11,plain,
( sK3(U_30,U_28,U_26) != U_30
| sK4(U_30,U_28,U_26) = U_28
| sK4(U_30,U_28,U_26) = U_30
| U_26 = unordered_pair(U_30,U_28) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_12,plain,
( sK3(U_30,U_28,U_26) != U_28
| sK4(U_30,U_28,U_26) = U_28
| sK4(U_30,U_28,U_26) = U_30
| U_26 = unordered_pair(U_30,U_28) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_13,plain,
( sK3(U_30,U_28,U_26) != U_30
| ~ in(sK4(U_30,U_28,U_26),U_26)
| U_26 = unordered_pair(U_30,U_28) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_14,plain,
( sK3(U_30,U_28,U_26) != U_28
| ~ in(sK4(U_30,U_28,U_26),U_26)
| U_26 = unordered_pair(U_30,U_28) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_5_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_5_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_5_1]) ).
fof(f_6_1,plain,
! [A,B] :
( ( subset(A,singleton(B))
| ( A != singleton(B)
& A != empty_set ) )
& ( A = singleton(B)
| A = empty_set
| ~ subset(A,singleton(B)) ) ),
inference(fof_nnf,[status(thm)],[l4_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_32,U_31] :
( ( subset(U_32,singleton(U_31))
| ( U_32 != singleton(U_31)
& U_32 != empty_set ) )
& ( U_32 = singleton(U_31)
| U_32 = empty_set
| ~ subset(U_32,singleton(U_31)) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_36,U_34] :
( subset(U_36,singleton(U_34))
| ( U_36 != singleton(U_34)
& U_36 != empty_set ) )
& ! [U_35,U_33] :
( U_35 = singleton(U_33)
| U_35 = empty_set
| ~ subset(U_35,singleton(U_33)) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( U_35 = singleton(U_33)
| U_35 = empty_set
| ~ subset(U_35,singleton(U_33)) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( U_36 != empty_set
| subset(U_36,singleton(U_34)) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( U_36 != singleton(U_34)
| subset(U_36,singleton(U_34)) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_7_2,plain,
? [U_37] : empty(U_37),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_37,sK5)],[f_7_2]) ).
cnf(f_7_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_8_2,plain,
? [U_38] : ~ empty(U_38),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
~ empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_38,sK6)],[f_8_2]) ).
cnf(f_8_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_9_2,plain,
! [U_40,U_39] : subset(U_40,U_40),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_40] : subset(U_40,U_40),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
subset(U_40,U_40),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B] :
( A = B
| ? [C] :
( ( ~ in(C,A)
& in(C,B) )
| ( ~ in(C,B)
& in(C,A) ) ) ),
inference(fof_nnf,[status(thm)],[t2_tarski]) ).
fof(f_10_2,plain,
! [U_43,U_42] :
( U_43 = U_42
| ? [U_41] :
( ( ~ in(U_41,U_43)
& in(U_41,U_42) )
| ( ~ in(U_41,U_42)
& in(U_41,U_43) ) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_43,U_42] :
( U_43 = U_42
| ? [U_45] :
( ~ in(U_45,U_43)
& in(U_45,U_42) )
| ? [U_44] :
( ~ in(U_44,U_42)
& in(U_44,U_43) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
fof(f_10_4,plain,
! [U_43,U_42] :
( U_43 = U_42
| ? [U_45] :
( ~ in(U_45,U_43)
& in(U_45,U_42) )
| ( ~ in(sK7(U_43,U_42),U_42)
& in(sK7(U_43,U_42),U_43) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_44,sK7(U_43,U_42))],[f_10_3]) ).
fof(f_10_5,plain,
! [U_43,U_42] :
( U_43 = U_42
| ( ~ in(sK8(U_43,U_42),U_43)
& in(sK8(U_43,U_42),U_42) )
| ( ~ in(sK7(U_43,U_42),U_42)
& in(sK7(U_43,U_42),U_43) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_45,sK8(U_43,U_42))],[f_10_4]) ).
cnf(f_10_6,plain,
( in(sK8(U_43,U_42),U_42)
| in(sK7(U_43,U_42),U_43)
| U_43 = U_42 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( ~ in(sK8(U_43,U_42),U_43)
| in(sK7(U_43,U_42),U_43)
| U_43 = U_42 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( in(sK8(U_43,U_42),U_42)
| ~ in(sK7(U_43,U_42),U_42)
| U_43 = U_42 ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( ~ in(sK8(U_43,U_42),U_43)
| ~ in(sK7(U_43,U_42),U_42)
| U_43 = U_42 ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_1,negated_conjecture,
~ ! [A] : powerset(singleton(A)) = unordered_pair(empty_set,singleton(A)),
inference(negate,[status(cth)],[t30_zfmisc_1]) ).
fof(f_11_2,negated_conjecture,
? [A] : powerset(singleton(A)) != unordered_pair(empty_set,singleton(A)),
inference(fof_nnf,[status(thm)],[f_11_1]) ).
fof(f_11_3,negated_conjecture,
? [U_46] : powerset(singleton(U_46)) != unordered_pair(empty_set,singleton(U_46)),
inference(variable_rename,[status(thm)],[f_11_2]) ).
fof(f_11_4,negated_conjecture,
powerset(singleton(sK9)) != unordered_pair(empty_set,singleton(sK9)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_46,sK9)],[f_11_3]) ).
fof(f_11_5,negated_conjecture,
powerset(singleton(sK9)) != unordered_pair(empty_set,singleton(sK9)),
inference(definitional_conversion,[status(esa)],[f_11_4]) ).
cnf(f_11_6,negated_conjecture,
powerset(singleton(sK9)) != unordered_pair(empty_set,singleton(sK9)),
inference(clausify,[status(thm)],[f_11_5]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(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,
( powerset(Eq_x_0) = powerset(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,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( 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_14,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_15,axiom,
( empty(Eq_y_0)
| ~ 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 : SET889+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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
% 0.10/0.37 % Computer : n017.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 23:01:57 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.38/0.67 % SZS status Theorem for theBenchmark
% 0.38/0.67 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------