%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET890+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 : n009.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 8.54s 8.86s
% Output : Proof 8.72s
% 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(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('theBenchmark.p',d10_xboole_0) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(l50_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',l50_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(t31_zfmisc_1,conjecture,
! [A] : union(singleton(A)) = A,
file('theBenchmark.p',t31_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] :
( ( A = B
| ~ subset(B,A)
| ~ subset(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(fof_nnf,[status(thm)],[d10_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ( U_3 = U_2
| ~ subset(U_2,U_3)
| ~ subset(U_3,U_2) )
& ( ( subset(U_2,U_3)
& subset(U_3,U_2) )
| U_3 != U_2 ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_7,U_5] :
( U_7 = U_5
| ~ subset(U_5,U_7)
| ~ subset(U_7,U_5) )
& ! [U_6,U_4] :
( ( subset(U_4,U_6)
& subset(U_6,U_4) )
| U_6 != U_4 ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( subset(U_6,U_4)
| U_6 != U_4 ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( subset(U_4,U_6)
| U_6 != U_4 ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( U_7 = U_5
| ~ subset(U_5,U_7)
| ~ subset(U_7,U_5) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_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_3_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_3_1]) ).
fof(f_3_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_3_2]) ).
fof(f_3_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_3_3]) ).
fof(f_3_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_3_4]) ).
cnf(f_3_6,plain,
( U_12 = U_18
| ~ in(U_12,U_16)
| U_16 != singleton(U_18) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( in(U_13,U_16)
| U_13 != U_18
| U_16 != singleton(U_18) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_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_3_5]) ).
cnf(f_3_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_3_5]) ).
cnf(f_3_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_3_5]) ).
cnf(f_3_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_3_5]) ).
fof(f_4_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_4_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_4_1]) ).
fof(f_4_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_4_2]) ).
fof(f_4_4,plain,
( ! [U_27,U_25] :
( subset(U_27,U_25)
| ( ~ in(sK3(U_27,U_25),U_25)
& in(sK3(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,[sK3]),skolemize(U_21,sK3(U_27,U_25))],[f_4_3]) ).
cnf(f_4_5,plain,
( in(U_20,U_24)
| ~ in(U_20,U_26)
| ~ subset(U_26,U_24) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( in(sK3(U_27,U_25),U_27)
| subset(U_27,U_25) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( ~ in(sK3(U_27,U_25),U_25)
| subset(U_27,U_25) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
! [A,B] :
( ( B = union(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( in(D,A)
& in(C,D) ) )
| ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( ~ in(D,A)
| ~ in(C,D) ) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(f_5_2,plain,
! [U_35,U_34] :
( ( U_34 = union(U_35)
| ? [U_33] :
( ( ~ in(U_33,U_34)
& ? [U_32] :
( in(U_32,U_35)
& in(U_33,U_32) ) )
| ( ! [U_31] :
( ~ in(U_31,U_35)
| ~ in(U_33,U_31) )
& in(U_33,U_34) ) ) )
& ( ! [U_30] :
( ( in(U_30,U_34)
| ! [U_29] :
( ~ in(U_29,U_35)
| ~ in(U_30,U_29) ) )
& ( ? [U_28] :
( in(U_28,U_35)
& in(U_30,U_28) )
| ~ in(U_30,U_34) ) )
| U_34 != union(U_35) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_43,U_41] :
( U_41 = union(U_43)
| ? [U_39] :
( ~ in(U_39,U_41)
& ? [U_32] :
( in(U_32,U_43)
& in(U_39,U_32) ) )
| ? [U_38] :
( ! [U_31] :
( ~ in(U_31,U_43)
| ~ in(U_38,U_31) )
& in(U_38,U_41) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] :
( ~ in(U_29,U_42)
| ~ in(U_37,U_29) ) )
& ! [U_36] :
( ? [U_28] :
( in(U_28,U_42)
& in(U_36,U_28) )
| ~ in(U_36,U_40) ) )
| U_40 != union(U_42) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_43,U_41] :
( U_41 = union(U_43)
| ? [U_39] :
( ~ in(U_39,U_41)
& ? [U_32] :
( in(U_32,U_43)
& in(U_39,U_32) ) )
| ? [U_38] :
( ! [U_31] :
( ~ in(U_31,U_43)
| ~ in(U_38,U_31) )
& in(U_38,U_41) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] :
( ~ in(U_29,U_42)
| ~ in(U_37,U_29) ) )
& ! [U_36] :
( ( in(sK4(U_42,U_40,U_36),U_42)
& in(U_36,sK4(U_42,U_40,U_36)) )
| ~ in(U_36,U_40) ) )
| U_40 != union(U_42) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_28,sK4(U_42,U_40,U_36))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_43,U_41] :
( U_41 = union(U_43)
| ? [U_39] :
( ~ in(U_39,U_41)
& ? [U_32] :
( in(U_32,U_43)
& in(U_39,U_32) ) )
| ( ! [U_31] :
( ~ in(U_31,U_43)
| ~ in(sK5(U_43,U_41),U_31) )
& in(sK5(U_43,U_41),U_41) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] :
( ~ in(U_29,U_42)
| ~ in(U_37,U_29) ) )
& ! [U_36] :
( ( in(sK4(U_42,U_40,U_36),U_42)
& in(U_36,sK4(U_42,U_40,U_36)) )
| ~ in(U_36,U_40) ) )
| U_40 != union(U_42) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_38,sK5(U_43,U_41))],[f_5_4]) ).
fof(f_5_6,plain,
( ! [U_43,U_41] :
( U_41 = union(U_43)
| ( ~ in(sK6(U_43,U_41),U_41)
& ? [U_32] :
( in(U_32,U_43)
& in(sK6(U_43,U_41),U_32) ) )
| ( ! [U_31] :
( ~ in(U_31,U_43)
| ~ in(sK5(U_43,U_41),U_31) )
& in(sK5(U_43,U_41),U_41) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] :
( ~ in(U_29,U_42)
| ~ in(U_37,U_29) ) )
& ! [U_36] :
( ( in(sK4(U_42,U_40,U_36),U_42)
& in(U_36,sK4(U_42,U_40,U_36)) )
| ~ in(U_36,U_40) ) )
| U_40 != union(U_42) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_39,sK6(U_43,U_41))],[f_5_5]) ).
fof(f_5_7,plain,
( ! [U_43,U_41] :
( U_41 = union(U_43)
| ( ~ in(sK6(U_43,U_41),U_41)
& in(sK7(U_43,U_41),U_43)
& in(sK6(U_43,U_41),sK7(U_43,U_41)) )
| ( ! [U_31] :
( ~ in(U_31,U_43)
| ~ in(sK5(U_43,U_41),U_31) )
& in(sK5(U_43,U_41),U_41) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] :
( ~ in(U_29,U_42)
| ~ in(U_37,U_29) ) )
& ! [U_36] :
( ( in(sK4(U_42,U_40,U_36),U_42)
& in(U_36,sK4(U_42,U_40,U_36)) )
| ~ in(U_36,U_40) ) )
| U_40 != union(U_42) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_32,sK7(U_43,U_41))],[f_5_6]) ).
cnf(f_5_8,plain,
( in(U_36,sK4(U_42,U_40,U_36))
| ~ in(U_36,U_40)
| U_40 != union(U_42) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_9,plain,
( in(sK4(U_42,U_40,U_36),U_42)
| ~ in(U_36,U_40)
| U_40 != union(U_42) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_10,plain,
( in(U_37,U_40)
| ~ in(U_29,U_42)
| ~ in(U_37,U_29)
| U_40 != union(U_42) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_11,plain,
( in(sK6(U_43,U_41),sK7(U_43,U_41))
| in(sK5(U_43,U_41),U_41)
| U_41 = union(U_43) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_12,plain,
( in(sK7(U_43,U_41),U_43)
| in(sK5(U_43,U_41),U_41)
| U_41 = union(U_43) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_13,plain,
( ~ in(sK6(U_43,U_41),U_41)
| in(sK5(U_43,U_41),U_41)
| U_41 = union(U_43) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_14,plain,
( in(sK6(U_43,U_41),sK7(U_43,U_41))
| ~ in(U_31,U_43)
| ~ in(sK5(U_43,U_41),U_31)
| U_41 = union(U_43) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_15,plain,
( in(sK7(U_43,U_41),U_43)
| ~ in(U_31,U_43)
| ~ in(sK5(U_43,U_41),U_31)
| U_41 = union(U_43) ),
inference(clausify,[status(thm)],[f_5_7]) ).
cnf(f_5_16,plain,
( ~ in(sK6(U_43,U_41),U_41)
| ~ in(U_31,U_43)
| ~ in(sK5(U_43,U_41),U_31)
| U_41 = union(U_43) ),
inference(clausify,[status(thm)],[f_5_7]) ).
fof(f_6_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[l50_zfmisc_1]) ).
fof(f_6_2,plain,
! [U_45,U_44] :
( subset(U_45,union(U_44))
| ~ in(U_45,U_44) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( subset(U_45,union(U_44))
| ~ in(U_45,U_44) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_7_2,plain,
? [U_46] : empty(U_46),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_46,sK8)],[f_7_2]) ).
cnf(f_7_4,plain,
empty(sK8),
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_47] : ~ empty(U_47),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_47,sK9)],[f_8_2]) ).
cnf(f_8_4,plain,
~ empty(sK9),
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_49,U_48] : subset(U_49,U_49),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_49] : subset(U_49,U_49),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
subset(U_49,U_49),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,negated_conjecture,
~ ! [A] : union(singleton(A)) = A,
inference(negate,[status(cth)],[t31_zfmisc_1]) ).
fof(f_10_2,negated_conjecture,
? [A] : union(singleton(A)) != A,
inference(fof_nnf,[status(thm)],[f_10_1]) ).
fof(f_10_3,negated_conjecture,
? [U_50] : union(singleton(U_50)) != U_50,
inference(variable_rename,[status(thm)],[f_10_2]) ).
fof(f_10_4,negated_conjecture,
union(singleton(sK10)) != sK10,
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_50,sK10)],[f_10_3]) ).
fof(f_10_5,negated_conjecture,
union(singleton(sK10)) != sK10,
inference(definitional_conversion,[status(esa)],[f_10_4]) ).
cnf(f_10_6,negated_conjecture,
union(singleton(sK10)) != sK10,
inference(clausify,[status(thm)],[f_10_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,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,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_8,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(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,
( 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_10,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(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,
( 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_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 : SET890+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
% 0.10/0.36 % Computer : n009.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:06:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 8.54/8.86 % SZS status Theorem for theBenchmark
% 8.54/8.86 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------