%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU154+1 : TPTP v9.3.1. Released v3.3.0.
% 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 : n011.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 08:58:14 AM UTC 2026
% Result : Theorem 36.44s 36.75s
% Output : Proof 36.61s
% 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_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_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(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d3_xboole_0) ).
fof(d7_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
<=> set_intersection2(A,B) = empty_set ),
file('theBenchmark.p',d7_xboole_0) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(dt_k3_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(l28_zfmisc_1,conjecture,
! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
file('theBenchmark.p',l28_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(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t2_xboole_1,axiom,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_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]) ).
fof(f_1_3,plain,
! [U_0,U_1] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] : set_intersection2(U_3,U_2) = set_intersection2(U_2,U_3),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_2,U_3] : set_intersection2(U_3,U_2) = set_intersection2(U_2,U_3),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
set_intersection2(U_3,U_2) = set_intersection2(U_2,U_3),
inference(clausify,[status(thm)],[f_2_3]) ).
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]) ).
fof(f_3_4,plain,
( ! [U_8,U_6] :
( subset(U_6,U_8)
| ~ sP0(U_8,U_6) )
& ! [U_8,U_6] :
( subset(U_8,U_6)
| ~ sP0(U_8,U_6) )
& ! [U_9,U_7] :
( U_9 = U_7
| ~ subset(U_7,U_9)
| ~ subset(U_9,U_7) )
& ! [U_8,U_6] :
( sP0(U_8,U_6)
| U_8 != U_6 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_3]) ).
cnf(f_3_5,plain,
( sP0(U_8,U_6)
| U_8 != U_6 ),
inference(clausify,[status(thm)],[f_3_4]) ).
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_4]) ).
cnf(f_3_7,plain,
( subset(U_8,U_6)
| ~ sP0(U_8,U_6) ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_8,plain,
( subset(U_6,U_8)
| ~ sP0(U_8,U_6) ),
inference(clausify,[status(thm)],[f_3_4]) ).
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]) ).
fof(f_4_6,plain,
( ! [U_21,U_19] :
( ~ in(sK2(U_21,U_19),U_19)
| ~ sP3(U_21,U_19) )
& ! [U_21,U_19] :
( sK2(U_21,U_19) = U_21
| ~ sP3(U_21,U_19) )
& ! [U_21,U_19] :
( sK1(U_21,U_19) != U_21
| ~ sP2(U_21,U_19) )
& ! [U_21,U_19] :
( in(sK1(U_21,U_19),U_19)
| ~ sP2(U_21,U_19) )
& ! [U_18,U_20,U_15,U_14] :
( in(U_15,U_18)
| U_15 != U_20
| ~ sP1(U_18,U_20,U_15,U_14) )
& ! [U_18,U_20,U_15,U_14] :
( U_14 = U_20
| ~ in(U_14,U_18)
| ~ sP1(U_18,U_20,U_15,U_14) )
& ! [U_21,U_19] :
( U_19 = singleton(U_21)
| sP3(U_21,U_19)
| sP2(U_21,U_19) )
& ! [U_18,U_20,U_15,U_14] :
( sP1(U_18,U_20,U_15,U_14)
| U_18 != singleton(U_20) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2,sP3])],[f_4_5]) ).
cnf(f_4_7,plain,
( sP1(U_18,U_20,U_15,U_14)
| U_18 != singleton(U_20) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_8,plain,
( U_19 = singleton(U_21)
| sP3(U_21,U_19)
| sP2(U_21,U_19) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_9,plain,
( U_14 = U_20
| ~ in(U_14,U_18)
| ~ sP1(U_18,U_20,U_15,U_14) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_10,plain,
( in(U_15,U_18)
| U_15 != U_20
| ~ sP1(U_18,U_20,U_15,U_14) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_11,plain,
( in(sK1(U_21,U_19),U_19)
| ~ sP2(U_21,U_19) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_12,plain,
( sK1(U_21,U_19) != U_21
| ~ sP2(U_21,U_19) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_13,plain,
( sK2(U_21,U_19) = U_21
| ~ sP3(U_21,U_19) ),
inference(clausify,[status(thm)],[f_4_6]) ).
cnf(f_4_14,plain,
( ~ in(sK2(U_21,U_19),U_19)
| ~ sP3(U_21,U_19) ),
inference(clausify,[status(thm)],[f_4_6]) ).
fof(f_5_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_5_2,plain,
! [U_25,U_24] :
( ( subset(U_25,U_24)
| ? [U_23] :
( ~ in(U_23,U_24)
& in(U_23,U_25) ) )
& ( ! [U_22] :
( in(U_22,U_24)
| ~ in(U_22,U_25) )
| ~ subset(U_25,U_24) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_29,U_27] :
( subset(U_29,U_27)
| ? [U_23] :
( ~ in(U_23,U_27)
& in(U_23,U_29) ) )
& ! [U_28,U_26] :
( ! [U_22] :
( in(U_22,U_26)
| ~ in(U_22,U_28) )
| ~ subset(U_28,U_26) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_29,U_27] :
( subset(U_29,U_27)
| ( ~ in(sK3(U_29,U_27),U_27)
& in(sK3(U_29,U_27),U_29) ) )
& ! [U_28,U_26] :
( ! [U_22] :
( in(U_22,U_26)
| ~ in(U_22,U_28) )
| ~ subset(U_28,U_26) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_23,sK3(U_29,U_27))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_29,U_27] :
( ~ in(sK3(U_29,U_27),U_27)
| ~ sP4(U_29,U_27) )
& ! [U_29,U_27] :
( in(sK3(U_29,U_27),U_29)
| ~ sP4(U_29,U_27) )
& ! [U_29,U_27] :
( subset(U_29,U_27)
| sP4(U_29,U_27) )
& ! [U_26,U_22,U_28] :
( in(U_22,U_26)
| ~ in(U_22,U_28)
| ~ subset(U_28,U_26) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_5_4]) ).
cnf(f_5_6,plain,
( in(U_22,U_26)
| ~ in(U_22,U_28)
| ~ subset(U_28,U_26) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( subset(U_29,U_27)
| sP4(U_29,U_27) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( in(sK3(U_29,U_27),U_29)
| ~ sP4(U_29,U_27) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( ~ in(sK3(U_29,U_27),U_27)
| ~ sP4(U_29,U_27) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_1,plain,
! [A,B,C] :
( ( C = set_intersection2(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_intersection2(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_xboole_0]) ).
fof(f_6_2,plain,
! [U_34,U_33,U_32] :
( ( U_32 = set_intersection2(U_34,U_33)
| ? [U_31] :
( ( ~ in(U_31,U_32)
& in(U_31,U_33)
& in(U_31,U_34) )
| ( ( ~ in(U_31,U_33)
| ~ in(U_31,U_34) )
& in(U_31,U_32) ) ) )
& ( ! [U_30] :
( ( in(U_30,U_32)
| ~ in(U_30,U_33)
| ~ in(U_30,U_34) )
& ( ( in(U_30,U_33)
& in(U_30,U_34) )
| ~ in(U_30,U_32) ) )
| U_32 != set_intersection2(U_34,U_33) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_44,U_42,U_40] :
( U_40 = set_intersection2(U_44,U_42)
| ? [U_38] :
( ~ in(U_38,U_40)
& in(U_38,U_42)
& in(U_38,U_44) )
| ? [U_37] :
( ( ~ in(U_37,U_42)
| ~ in(U_37,U_44) )
& in(U_37,U_40) ) )
& ! [U_43,U_41,U_39] :
( ( ! [U_36] :
( in(U_36,U_39)
| ~ in(U_36,U_41)
| ~ in(U_36,U_43) )
& ! [U_35] :
( ( in(U_35,U_41)
& in(U_35,U_43) )
| ~ in(U_35,U_39) ) )
| U_39 != set_intersection2(U_43,U_41) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_44,U_42,U_40] :
( U_40 = set_intersection2(U_44,U_42)
| ? [U_38] :
( ~ in(U_38,U_40)
& in(U_38,U_42)
& in(U_38,U_44) )
| ( ( ~ in(sK4(U_44,U_42,U_40),U_42)
| ~ in(sK4(U_44,U_42,U_40),U_44) )
& in(sK4(U_44,U_42,U_40),U_40) ) )
& ! [U_43,U_41,U_39] :
( ( ! [U_36] :
( in(U_36,U_39)
| ~ in(U_36,U_41)
| ~ in(U_36,U_43) )
& ! [U_35] :
( ( in(U_35,U_41)
& in(U_35,U_43) )
| ~ in(U_35,U_39) ) )
| U_39 != set_intersection2(U_43,U_41) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_37,sK4(U_44,U_42,U_40))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_44,U_42,U_40] :
( U_40 = set_intersection2(U_44,U_42)
| ( ~ in(sK5(U_44,U_42,U_40),U_40)
& in(sK5(U_44,U_42,U_40),U_42)
& in(sK5(U_44,U_42,U_40),U_44) )
| ( ( ~ in(sK4(U_44,U_42,U_40),U_42)
| ~ in(sK4(U_44,U_42,U_40),U_44) )
& in(sK4(U_44,U_42,U_40),U_40) ) )
& ! [U_43,U_41,U_39] :
( ( ! [U_36] :
( in(U_36,U_39)
| ~ in(U_36,U_41)
| ~ in(U_36,U_43) )
& ! [U_35] :
( ( in(U_35,U_41)
& in(U_35,U_43) )
| ~ in(U_35,U_39) ) )
| U_39 != set_intersection2(U_43,U_41) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_38,sK5(U_44,U_42,U_40))],[f_6_4]) ).
fof(f_6_6,plain,
( ! [U_42,U_40,U_44] :
( ~ in(sK5(U_44,U_42,U_40),U_40)
| ~ sP8(U_42,U_40,U_44) )
& ! [U_42,U_40,U_44] :
( in(sK5(U_44,U_42,U_40),U_42)
| ~ sP8(U_42,U_40,U_44) )
& ! [U_42,U_40,U_44] :
( in(sK5(U_44,U_42,U_40),U_44)
| ~ sP8(U_42,U_40,U_44) )
& ! [U_42,U_40,U_44] :
( ~ in(sK4(U_44,U_42,U_40),U_42)
| ~ in(sK4(U_44,U_42,U_40),U_44)
| ~ sP7(U_42,U_40,U_44) )
& ! [U_42,U_40,U_44] :
( in(sK4(U_44,U_42,U_40),U_40)
| ~ sP7(U_42,U_40,U_44) )
& ! [U_41,U_35,U_43] :
( in(U_35,U_41)
| ~ sP5(U_41,U_35,U_43) )
& ! [U_41,U_35,U_43] :
( in(U_35,U_43)
| ~ sP5(U_41,U_35,U_43) )
& ! [U_41,U_36,U_35,U_39,U_43] :
( in(U_36,U_39)
| ~ in(U_36,U_41)
| ~ in(U_36,U_43)
| ~ sP6(U_41,U_36,U_35,U_39,U_43) )
& ! [U_41,U_36,U_35,U_39,U_43] :
( sP5(U_41,U_35,U_43)
| ~ in(U_35,U_39)
| ~ sP6(U_41,U_36,U_35,U_39,U_43) )
& ! [U_42,U_40,U_44] :
( U_40 = set_intersection2(U_44,U_42)
| sP8(U_42,U_40,U_44)
| sP7(U_42,U_40,U_44) )
& ! [U_41,U_36,U_35,U_39,U_43] :
( sP6(U_41,U_36,U_35,U_39,U_43)
| U_39 != set_intersection2(U_43,U_41) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5,sP6,sP7,sP8])],[f_6_5]) ).
cnf(f_6_7,plain,
( sP6(U_41,U_36,U_35,U_39,U_43)
| U_39 != set_intersection2(U_43,U_41) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_8,plain,
( U_40 = set_intersection2(U_44,U_42)
| sP8(U_42,U_40,U_44)
| sP7(U_42,U_40,U_44) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_9,plain,
( sP5(U_41,U_35,U_43)
| ~ in(U_35,U_39)
| ~ sP6(U_41,U_36,U_35,U_39,U_43) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_10,plain,
( in(U_36,U_39)
| ~ in(U_36,U_41)
| ~ in(U_36,U_43)
| ~ sP6(U_41,U_36,U_35,U_39,U_43) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_11,plain,
( in(U_35,U_43)
| ~ sP5(U_41,U_35,U_43) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_12,plain,
( in(U_35,U_41)
| ~ sP5(U_41,U_35,U_43) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_13,plain,
( in(sK4(U_44,U_42,U_40),U_40)
| ~ sP7(U_42,U_40,U_44) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_14,plain,
( ~ in(sK4(U_44,U_42,U_40),U_42)
| ~ in(sK4(U_44,U_42,U_40),U_44)
| ~ sP7(U_42,U_40,U_44) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_15,plain,
( in(sK5(U_44,U_42,U_40),U_44)
| ~ sP8(U_42,U_40,U_44) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_16,plain,
( in(sK5(U_44,U_42,U_40),U_42)
| ~ sP8(U_42,U_40,U_44) ),
inference(clausify,[status(thm)],[f_6_6]) ).
cnf(f_6_17,plain,
( ~ in(sK5(U_44,U_42,U_40),U_40)
| ~ sP8(U_42,U_40,U_44) ),
inference(clausify,[status(thm)],[f_6_6]) ).
fof(f_7_1,plain,
! [A,B] :
( ( disjoint(A,B)
| set_intersection2(A,B) != empty_set )
& ( set_intersection2(A,B) = empty_set
| ~ disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[d7_xboole_0]) ).
fof(f_7_2,plain,
! [U_46,U_45] :
( ( disjoint(U_46,U_45)
| set_intersection2(U_46,U_45) != empty_set )
& ( set_intersection2(U_46,U_45) = empty_set
| ~ disjoint(U_46,U_45) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_50,U_48] :
( disjoint(U_50,U_48)
| set_intersection2(U_50,U_48) != empty_set )
& ! [U_49,U_47] :
( set_intersection2(U_49,U_47) = empty_set
| ~ disjoint(U_49,U_47) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_48,U_50] :
( disjoint(U_50,U_48)
| set_intersection2(U_50,U_48) != empty_set )
& ! [U_49,U_47] :
( set_intersection2(U_49,U_47) = empty_set
| ~ disjoint(U_49,U_47) ) ),
inference(definitional_conversion,[status(esa)],[f_7_3]) ).
cnf(f_7_5,plain,
( set_intersection2(U_49,U_47) = empty_set
| ~ disjoint(U_49,U_47) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
( disjoint(U_50,U_48)
| set_intersection2(U_50,U_48) != empty_set ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_8_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_8_1]) ).
cnf(f_8_3,plain,
$true,
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_9_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_9_1]) ).
cnf(f_9_3,plain,
$true,
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
fof(f_10_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_10_1]) ).
cnf(f_10_3,plain,
$true,
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_11_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_11_1]) ).
cnf(f_11_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_12_2,plain,
! [U_52,U_51] : set_intersection2(U_52,U_52) = U_52,
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_52] : set_intersection2(U_52,U_52) = U_52,
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
! [U_52] : set_intersection2(U_52,U_52) = U_52,
inference(definitional_conversion,[status(esa)],[f_12_3]) ).
cnf(f_12_5,plain,
set_intersection2(U_52,U_52) = U_52,
inference(clausify,[status(thm)],[f_12_4]) ).
fof(f_13_1,negated_conjecture,
~ ! [A,B] :
( ~ in(A,B)
=> disjoint(singleton(A),B) ),
inference(negate,[status(cth)],[l28_zfmisc_1]) ).
fof(f_13_2,negated_conjecture,
? [A,B] :
( ~ disjoint(singleton(A),B)
& ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_54,U_53] :
( ~ disjoint(singleton(U_54),U_53)
& ~ in(U_54,U_53) ),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
? [U_53] :
( ~ disjoint(singleton(sK6),U_53)
& ~ in(sK6,U_53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_54,sK6)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
( ~ disjoint(singleton(sK6),sK7)
& ~ in(sK6,sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_53,sK7)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
( ~ disjoint(singleton(sK6),sK7)
& ~ in(sK6,sK7) ),
inference(definitional_conversion,[status(esa)],[f_13_5]) ).
cnf(f_13_7,negated_conjecture,
~ in(sK6,sK7),
inference(clausify,[status(thm)],[f_13_6]) ).
cnf(f_13_8,negated_conjecture,
~ disjoint(singleton(sK6),sK7),
inference(clausify,[status(thm)],[f_13_6]) ).
fof(f_14_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_14_2,plain,
? [U_55] : empty(U_55),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_55,sK8)],[f_14_2]) ).
fof(f_14_4,plain,
empty(sK8),
inference(definitional_conversion,[status(esa)],[f_14_3]) ).
cnf(f_14_5,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_15_2,plain,
? [U_56] : ~ empty(U_56),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_56,sK9)],[f_15_2]) ).
fof(f_15_4,plain,
~ empty(sK9),
inference(definitional_conversion,[status(esa)],[f_15_3]) ).
cnf(f_15_5,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_16_2,plain,
! [U_58,U_57] : subset(U_58,U_58),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_58] : subset(U_58,U_58),
inference(miniscope,[status(thm)],[f_16_2]) ).
fof(f_16_4,plain,
! [U_58] : subset(U_58,U_58),
inference(definitional_conversion,[status(esa)],[f_16_3]) ).
cnf(f_16_5,plain,
subset(U_58,U_58),
inference(clausify,[status(thm)],[f_16_4]) ).
fof(f_17_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_17_2,plain,
! [U_60,U_59] :
( disjoint(U_59,U_60)
| ~ disjoint(U_60,U_59) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_60,U_59] :
( disjoint(U_59,U_60)
| ~ disjoint(U_60,U_59) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( disjoint(U_59,U_60)
| ~ disjoint(U_60,U_59) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_18_2,plain,
! [U_61] : subset(empty_set,U_61),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_61] : subset(empty_set,U_61),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
subset(empty_set,U_61),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_8_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_3]) ).
cnf(f_9_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_3]) ).
cnf(f_10_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_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_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(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,
( 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,Eq_x_2) = sK5(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,
( 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_12,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_13,axiom,
( disjoint(Eq_y_0,Eq_y_1)
| ~ disjoint(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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(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,
( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(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,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(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,
( sP4(Eq_y_0,Eq_y_1)
| ~ sP4(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,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| 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 : SEU154+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 19 23:23:24 UTC 2026
% 0.08/0.34 % CPUTime :
% 36.44/36.75 % SZS status Theorem for theBenchmark
% 36.44/36.75 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------