%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SET986+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 : n005.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 08:57:54 AM UTC 2026
% Result : Theorem 252.14s 252.40s
% Output : Proof 253.71s
% 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_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
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(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(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
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(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
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(t140_zfmisc_1,conjecture,
! [A,B] :
( in(A,B)
=> set_union2(set_difference(B,singleton(A)),singleton(A)) = B ),
file('theBenchmark.p',t140_zfmisc_1) ).
fof(t64_zfmisc_1,axiom,
! [A,B,C] :
( in(A,set_difference(B,singleton(C)))
<=> ( A != C
& in(A,B) ) ),
file('theBenchmark.p',t64_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] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] : set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
set_union2(U_3,U_2) = set_union2(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_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_3_2,plain,
! [U_5,U_4] :
( ( U_5 = U_4
| ~ subset(U_4,U_5)
| ~ subset(U_5,U_4) )
& ( ( subset(U_4,U_5)
& subset(U_5,U_4) )
| U_5 != U_4 ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_9,U_7] :
( U_9 = U_7
| ~ subset(U_7,U_9)
| ~ subset(U_9,U_7) )
& ! [U_8,U_6] :
( ( subset(U_6,U_8)
& subset(U_8,U_6) )
| U_8 != U_6 ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( subset(U_8,U_6)
| U_8 != U_6 ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( subset(U_6,U_8)
| U_8 != U_6 ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( U_9 = U_7
| ~ subset(U_7,U_9)
| ~ subset(U_9,U_7) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_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_4_2,plain,
! [U_13,U_12] :
( ( U_12 = singleton(U_13)
| ? [U_11] :
( ( ~ in(U_11,U_12)
& U_11 = U_13 )
| ( U_11 != U_13
& in(U_11,U_12) ) ) )
& ( ! [U_10] :
( ( in(U_10,U_12)
| U_10 != U_13 )
& ( U_10 = U_13
| ~ in(U_10,U_12) ) )
| U_12 != singleton(U_13) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_21,U_19] :
( U_19 = singleton(U_21)
| ? [U_17] :
( ~ in(U_17,U_19)
& U_17 = U_21 )
| ? [U_16] :
( U_16 != U_21
& in(U_16,U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| U_15 != U_20 )
& ! [U_14] :
( U_14 = U_20
| ~ in(U_14,U_18) ) )
| U_18 != singleton(U_20) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_21,U_19] :
( U_19 = singleton(U_21)
| ? [U_17] :
( ~ in(U_17,U_19)
& U_17 = U_21 )
| ( sK1(U_21,U_19) != U_21
& in(sK1(U_21,U_19),U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| U_15 != U_20 )
& ! [U_14] :
( U_14 = U_20
| ~ in(U_14,U_18) ) )
| U_18 != singleton(U_20) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_16,sK1(U_21,U_19))],[f_4_3]) ).
fof(f_4_5,plain,
( ! [U_21,U_19] :
( U_19 = singleton(U_21)
| ( ~ in(sK2(U_21,U_19),U_19)
& sK2(U_21,U_19) = U_21 )
| ( sK1(U_21,U_19) != U_21
& in(sK1(U_21,U_19),U_19) ) )
& ! [U_20,U_18] :
( ( ! [U_15] :
( in(U_15,U_18)
| U_15 != U_20 )
& ! [U_14] :
( U_14 = U_20
| ~ in(U_14,U_18) ) )
| U_18 != singleton(U_20) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_17,sK2(U_21,U_19))],[f_4_4]) ).
cnf(f_4_6,plain,
( U_14 = U_20
| ~ in(U_14,U_18)
| U_18 != singleton(U_20) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_7,plain,
( in(U_15,U_18)
| U_15 != U_20
| U_18 != singleton(U_20) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_8,plain,
( sK2(U_21,U_19) = U_21
| in(sK1(U_21,U_19),U_19)
| U_19 = singleton(U_21) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_9,plain,
( ~ in(sK2(U_21,U_19),U_19)
| in(sK1(U_21,U_19),U_19)
| U_19 = singleton(U_21) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_10,plain,
( sK2(U_21,U_19) = U_21
| sK1(U_21,U_19) != U_21
| U_19 = singleton(U_21) ),
inference(clausify,[status(thm)],[f_4_5]) ).
cnf(f_4_11,plain,
( ~ in(sK2(U_21,U_19),U_19)
| sK1(U_21,U_19) != U_21
| U_19 = singleton(U_21) ),
inference(clausify,[status(thm)],[f_4_5]) ).
fof(f_5_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_5_2,plain,
! [U_26,U_25,U_24] :
( ( U_24 = set_union2(U_26,U_25)
| ? [U_23] :
( ( ~ in(U_23,U_24)
& ( in(U_23,U_25)
| in(U_23,U_26) ) )
| ( ~ in(U_23,U_25)
& ~ in(U_23,U_26)
& in(U_23,U_24) ) ) )
& ( ! [U_22] :
( ( in(U_22,U_24)
| ( ~ in(U_22,U_25)
& ~ in(U_22,U_26) ) )
& ( in(U_22,U_25)
| in(U_22,U_26)
| ~ in(U_22,U_24) ) )
| U_24 != set_union2(U_26,U_25) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_36,U_34,U_32] :
( U_32 = set_union2(U_36,U_34)
| ? [U_30] :
( ~ in(U_30,U_32)
& ( in(U_30,U_34)
| in(U_30,U_36) ) )
| ? [U_29] :
( ~ in(U_29,U_34)
& ~ in(U_29,U_36)
& in(U_29,U_32) ) )
& ! [U_35,U_33,U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ( ~ in(U_28,U_33)
& ~ in(U_28,U_35) ) )
& ! [U_27] :
( in(U_27,U_33)
| in(U_27,U_35)
| ~ in(U_27,U_31) ) )
| U_31 != set_union2(U_35,U_33) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_36,U_34,U_32] :
( U_32 = set_union2(U_36,U_34)
| ? [U_30] :
( ~ in(U_30,U_32)
& ( in(U_30,U_34)
| in(U_30,U_36) ) )
| ( ~ in(sK3(U_36,U_34,U_32),U_34)
& ~ in(sK3(U_36,U_34,U_32),U_36)
& in(sK3(U_36,U_34,U_32),U_32) ) )
& ! [U_35,U_33,U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ( ~ in(U_28,U_33)
& ~ in(U_28,U_35) ) )
& ! [U_27] :
( in(U_27,U_33)
| in(U_27,U_35)
| ~ in(U_27,U_31) ) )
| U_31 != set_union2(U_35,U_33) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_29,sK3(U_36,U_34,U_32))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_36,U_34,U_32] :
( U_32 = set_union2(U_36,U_34)
| ( ~ in(sK4(U_36,U_34,U_32),U_32)
& ( in(sK4(U_36,U_34,U_32),U_34)
| in(sK4(U_36,U_34,U_32),U_36) ) )
| ( ~ in(sK3(U_36,U_34,U_32),U_34)
& ~ in(sK3(U_36,U_34,U_32),U_36)
& in(sK3(U_36,U_34,U_32),U_32) ) )
& ! [U_35,U_33,U_31] :
( ( ! [U_28] :
( in(U_28,U_31)
| ( ~ in(U_28,U_33)
& ~ in(U_28,U_35) ) )
& ! [U_27] :
( in(U_27,U_33)
| in(U_27,U_35)
| ~ in(U_27,U_31) ) )
| U_31 != set_union2(U_35,U_33) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_30,sK4(U_36,U_34,U_32))],[f_5_4]) ).
cnf(f_5_6,plain,
( in(U_27,U_33)
| in(U_27,U_35)
| ~ in(U_27,U_31)
| U_31 != set_union2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( ~ in(U_28,U_35)
| in(U_28,U_31)
| U_31 != set_union2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( ~ in(U_28,U_33)
| in(U_28,U_31)
| U_31 != set_union2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( in(sK4(U_36,U_34,U_32),U_34)
| in(sK4(U_36,U_34,U_32),U_36)
| in(sK3(U_36,U_34,U_32),U_32)
| U_32 = set_union2(U_36,U_34) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_10,plain,
( ~ in(sK4(U_36,U_34,U_32),U_32)
| in(sK3(U_36,U_34,U_32),U_32)
| U_32 = set_union2(U_36,U_34) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_11,plain,
( ~ in(sK3(U_36,U_34,U_32),U_36)
| in(sK4(U_36,U_34,U_32),U_34)
| in(sK4(U_36,U_34,U_32),U_36)
| U_32 = set_union2(U_36,U_34) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_12,plain,
( ~ in(sK3(U_36,U_34,U_32),U_34)
| in(sK4(U_36,U_34,U_32),U_34)
| in(sK4(U_36,U_34,U_32),U_36)
| U_32 = set_union2(U_36,U_34) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_13,plain,
( ~ in(sK3(U_36,U_34,U_32),U_36)
| ~ in(sK4(U_36,U_34,U_32),U_32)
| U_32 = set_union2(U_36,U_34) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_14,plain,
( ~ in(sK3(U_36,U_34,U_32),U_34)
| ~ in(sK4(U_36,U_34,U_32),U_32)
| U_32 = set_union2(U_36,U_34) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_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_6_2,plain,
! [U_40,U_39] :
( ( subset(U_40,U_39)
| ? [U_38] :
( ~ in(U_38,U_39)
& in(U_38,U_40) ) )
& ( ! [U_37] :
( in(U_37,U_39)
| ~ in(U_37,U_40) )
| ~ subset(U_40,U_39) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_44,U_42] :
( subset(U_44,U_42)
| ? [U_38] :
( ~ in(U_38,U_42)
& in(U_38,U_44) ) )
& ! [U_43,U_41] :
( ! [U_37] :
( in(U_37,U_41)
| ~ in(U_37,U_43) )
| ~ subset(U_43,U_41) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_44,U_42] :
( subset(U_44,U_42)
| ( ~ in(sK5(U_44,U_42),U_42)
& in(sK5(U_44,U_42),U_44) ) )
& ! [U_43,U_41] :
( ! [U_37] :
( in(U_37,U_41)
| ~ in(U_37,U_43) )
| ~ subset(U_43,U_41) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_38,sK5(U_44,U_42))],[f_6_3]) ).
cnf(f_6_5,plain,
( in(U_37,U_41)
| ~ in(U_37,U_43)
| ~ subset(U_43,U_41) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_6,plain,
( in(sK5(U_44,U_42),U_44)
| subset(U_44,U_42) ),
inference(clausify,[status(thm)],[f_6_4]) ).
cnf(f_6_7,plain,
( ~ in(sK5(U_44,U_42),U_42)
| subset(U_44,U_42) ),
inference(clausify,[status(thm)],[f_6_4]) ).
fof(f_7_1,plain,
! [A,B,C] :
( ( C = set_difference(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_difference(A,B) ) ),
inference(fof_nnf,[status(thm)],[d4_xboole_0]) ).
fof(f_7_2,plain,
! [U_49,U_48,U_47] :
( ( U_47 = set_difference(U_49,U_48)
| ? [U_46] :
( ( ~ in(U_46,U_47)
& ~ in(U_46,U_48)
& in(U_46,U_49) )
| ( ( in(U_46,U_48)
| ~ in(U_46,U_49) )
& in(U_46,U_47) ) ) )
& ( ! [U_45] :
( ( in(U_45,U_47)
| in(U_45,U_48)
| ~ in(U_45,U_49) )
& ( ( ~ in(U_45,U_48)
& in(U_45,U_49) )
| ~ in(U_45,U_47) ) )
| U_47 != set_difference(U_49,U_48) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_59,U_57,U_55] :
( U_55 = set_difference(U_59,U_57)
| ? [U_53] :
( ~ in(U_53,U_55)
& ~ in(U_53,U_57)
& in(U_53,U_59) )
| ? [U_52] :
( ( in(U_52,U_57)
| ~ in(U_52,U_59) )
& in(U_52,U_55) ) )
& ! [U_58,U_56,U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| in(U_51,U_56)
| ~ in(U_51,U_58) )
& ! [U_50] :
( ( ~ in(U_50,U_56)
& in(U_50,U_58) )
| ~ in(U_50,U_54) ) )
| U_54 != set_difference(U_58,U_56) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_59,U_57,U_55] :
( U_55 = set_difference(U_59,U_57)
| ? [U_53] :
( ~ in(U_53,U_55)
& ~ in(U_53,U_57)
& in(U_53,U_59) )
| ( ( in(sK6(U_59,U_57,U_55),U_57)
| ~ in(sK6(U_59,U_57,U_55),U_59) )
& in(sK6(U_59,U_57,U_55),U_55) ) )
& ! [U_58,U_56,U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| in(U_51,U_56)
| ~ in(U_51,U_58) )
& ! [U_50] :
( ( ~ in(U_50,U_56)
& in(U_50,U_58) )
| ~ in(U_50,U_54) ) )
| U_54 != set_difference(U_58,U_56) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_52,sK6(U_59,U_57,U_55))],[f_7_3]) ).
fof(f_7_5,plain,
( ! [U_59,U_57,U_55] :
( U_55 = set_difference(U_59,U_57)
| ( ~ in(sK7(U_59,U_57,U_55),U_55)
& ~ in(sK7(U_59,U_57,U_55),U_57)
& in(sK7(U_59,U_57,U_55),U_59) )
| ( ( in(sK6(U_59,U_57,U_55),U_57)
| ~ in(sK6(U_59,U_57,U_55),U_59) )
& in(sK6(U_59,U_57,U_55),U_55) ) )
& ! [U_58,U_56,U_54] :
( ( ! [U_51] :
( in(U_51,U_54)
| in(U_51,U_56)
| ~ in(U_51,U_58) )
& ! [U_50] :
( ( ~ in(U_50,U_56)
& in(U_50,U_58) )
| ~ in(U_50,U_54) ) )
| U_54 != set_difference(U_58,U_56) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_53,sK7(U_59,U_57,U_55))],[f_7_4]) ).
cnf(f_7_6,plain,
( in(U_50,U_58)
| ~ in(U_50,U_54)
| U_54 != set_difference(U_58,U_56) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_7,plain,
( ~ in(U_50,U_56)
| ~ in(U_50,U_54)
| U_54 != set_difference(U_58,U_56) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_8,plain,
( in(U_51,U_54)
| in(U_51,U_56)
| ~ in(U_51,U_58)
| U_54 != set_difference(U_58,U_56) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_9,plain,
( in(sK7(U_59,U_57,U_55),U_59)
| in(sK6(U_59,U_57,U_55),U_55)
| U_55 = set_difference(U_59,U_57) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_10,plain,
( ~ in(sK7(U_59,U_57,U_55),U_57)
| in(sK6(U_59,U_57,U_55),U_55)
| U_55 = set_difference(U_59,U_57) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_11,plain,
( ~ in(sK7(U_59,U_57,U_55),U_55)
| in(sK6(U_59,U_57,U_55),U_55)
| U_55 = set_difference(U_59,U_57) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_12,plain,
( in(sK7(U_59,U_57,U_55),U_59)
| in(sK6(U_59,U_57,U_55),U_57)
| ~ in(sK6(U_59,U_57,U_55),U_59)
| U_55 = set_difference(U_59,U_57) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_13,plain,
( ~ in(sK7(U_59,U_57,U_55),U_57)
| in(sK6(U_59,U_57,U_55),U_57)
| ~ in(sK6(U_59,U_57,U_55),U_59)
| U_55 = set_difference(U_59,U_57) ),
inference(clausify,[status(thm)],[f_7_5]) ).
cnf(f_7_14,plain,
( ~ in(sK7(U_59,U_57,U_55),U_55)
| in(sK6(U_59,U_57,U_55),U_57)
| ~ in(sK6(U_59,U_57,U_55),U_59)
| U_55 = set_difference(U_59,U_57) ),
inference(clausify,[status(thm)],[f_7_5]) ).
fof(f_8_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_8_2,plain,
! [U_61,U_60] :
( ~ empty(set_union2(U_61,U_60))
| empty(U_61) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_61] :
( ! [U_60] : ~ empty(set_union2(U_61,U_60))
| empty(U_61) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( ~ empty(set_union2(U_61,U_60))
| empty(U_61) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_9_2,plain,
! [U_63,U_62] :
( ~ empty(set_union2(U_62,U_63))
| empty(U_63) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_63] :
( ! [U_62] : ~ empty(set_union2(U_62,U_63))
| empty(U_63) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( ~ empty(set_union2(U_62,U_63))
| empty(U_63) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_10_2,plain,
! [U_65,U_64] : set_union2(U_65,U_65) = U_65,
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_65] : set_union2(U_65,U_65) = U_65,
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
set_union2(U_65,U_65) = U_65,
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_11_2,plain,
? [U_66] : empty(U_66),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_66,sK8)],[f_11_2]) ).
cnf(f_11_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_12_2,plain,
? [U_67] : ~ empty(U_67),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_67,sK9)],[f_12_2]) ).
cnf(f_12_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_13_2,plain,
! [U_69,U_68] : subset(U_69,U_69),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_69] : subset(U_69,U_69),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
subset(U_69,U_69),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,negated_conjecture,
~ ! [A,B] :
( in(A,B)
=> set_union2(set_difference(B,singleton(A)),singleton(A)) = B ),
inference(negate,[status(cth)],[t140_zfmisc_1]) ).
fof(f_14_2,negated_conjecture,
? [A,B] :
( set_union2(set_difference(B,singleton(A)),singleton(A)) != B
& in(A,B) ),
inference(fof_nnf,[status(thm)],[f_14_1]) ).
fof(f_14_3,negated_conjecture,
? [U_71,U_70] :
( set_union2(set_difference(U_70,singleton(U_71)),singleton(U_71)) != U_70
& in(U_71,U_70) ),
inference(variable_rename,[status(thm)],[f_14_2]) ).
fof(f_14_4,negated_conjecture,
? [U_70] :
( set_union2(set_difference(U_70,singleton(sK10)),singleton(sK10)) != U_70
& in(sK10,U_70) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_71,sK10)],[f_14_3]) ).
fof(f_14_5,negated_conjecture,
( set_union2(set_difference(sK11,singleton(sK10)),singleton(sK10)) != sK11
& in(sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_70,sK11)],[f_14_4]) ).
cnf(f_14_6,negated_conjecture,
in(sK10,sK11),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_7,negated_conjecture,
set_union2(set_difference(sK11,singleton(sK10)),singleton(sK10)) != sK11,
inference(clausify,[status(thm)],[f_14_5]) ).
fof(f_15_1,plain,
! [A,B,C] :
( ( in(A,set_difference(B,singleton(C)))
| A = C
| ~ in(A,B) )
& ( ( A != C
& in(A,B) )
| ~ in(A,set_difference(B,singleton(C))) ) ),
inference(fof_nnf,[status(thm)],[t64_zfmisc_1]) ).
fof(f_15_2,plain,
! [U_74,U_73,U_72] :
( ( in(U_74,set_difference(U_73,singleton(U_72)))
| U_74 = U_72
| ~ in(U_74,U_73) )
& ( ( U_74 != U_72
& in(U_74,U_73) )
| ~ in(U_74,set_difference(U_73,singleton(U_72))) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_80,U_78,U_76] :
( in(U_80,set_difference(U_78,singleton(U_76)))
| U_80 = U_76
| ~ in(U_80,U_78) )
& ! [U_79,U_77,U_75] :
( ( U_79 != U_75
& in(U_79,U_77) )
| ~ in(U_79,set_difference(U_77,singleton(U_75))) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( in(U_79,U_77)
| ~ in(U_79,set_difference(U_77,singleton(U_75))) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( U_79 != U_75
| ~ in(U_79,set_difference(U_77,singleton(U_75))) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_6,plain,
( in(U_80,set_difference(U_78,singleton(U_76)))
| U_80 = U_76
| ~ in(U_80,U_78) ),
inference(clausify,[status(thm)],[f_15_3]) ).
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,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(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,
( 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,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_12,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(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_13,axiom,
( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = sK7(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_14,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_15,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_16,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 : SET986+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 23:10:18 UTC 2026
% 0.09/0.36 % CPUTime :
% 252.14/252.40 % SZS status Theorem for theBenchmark
% 252.14/252.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------