%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU153+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 : n010.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 192.25s 192.53s
% Output : Proof 194.19s
% 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(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d1_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
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(l25_zfmisc_1,conjecture,
! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
file('theBenchmark.p',l25_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(symmetry_r1_xboole_0,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('theBenchmark.p',symmetry_r1_xboole_0) ).
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_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]) ).
cnf(f_2_3,plain,
set_intersection2(U_3,U_2) = set_intersection2(U_2,U_3),
inference(clausify,[status(thm)],[f_2_2]) ).
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_7,U_6] :
( ( U_6 = singleton(U_7)
| ? [U_5] :
( ( ~ in(U_5,U_6)
& U_5 = U_7 )
| ( U_5 != U_7
& in(U_5,U_6) ) ) )
& ( ! [U_4] :
( ( in(U_4,U_6)
| U_4 != U_7 )
& ( U_4 = U_7
| ~ in(U_4,U_6) ) )
| U_6 != singleton(U_7) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& U_11 = U_15 )
| ? [U_10] :
( U_10 != U_15
& in(U_10,U_13) ) )
& ! [U_14,U_12] :
( ( ! [U_9] :
( in(U_9,U_12)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(U_14) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_15,U_13] :
( U_13 = singleton(U_15)
| ? [U_11] :
( ~ in(U_11,U_13)
& U_11 = U_15 )
| ( 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)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(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 = singleton(U_15)
| ( ~ in(sK2(U_15,U_13),U_13)
& sK2(U_15,U_13) = U_15 )
| ( 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)
| U_9 != U_14 )
& ! [U_8] :
( U_8 = U_14
| ~ in(U_8,U_12) ) )
| U_12 != singleton(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,
( U_8 = U_14
| ~ in(U_8,U_12)
| U_12 != singleton(U_14) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_7,plain,
( in(U_9,U_12)
| U_9 != U_14
| U_12 != singleton(U_14) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_8,plain,
( sK2(U_15,U_13) = U_15
| in(sK1(U_15,U_13),U_13)
| U_13 = singleton(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 = singleton(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_10,plain,
( sK2(U_15,U_13) = U_15
| sK1(U_15,U_13) != U_15
| U_13 = singleton(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(f_3_11,plain,
( ~ in(sK2(U_15,U_13),U_13)
| sK1(U_15,U_13) != U_15
| U_13 = singleton(U_15) ),
inference(clausify,[status(thm)],[f_3_5]) ).
fof(f_4_1,plain,
! [A] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_4_2,plain,
! [U_18] :
( ( U_18 = empty_set
| ? [U_17] : in(U_17,U_18) )
& ( ! [U_16] : ~ in(U_16,U_18)
| U_18 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_20] :
( U_20 = empty_set
| ? [U_17] : in(U_17,U_20) )
& ! [U_19] :
( ! [U_16] : ~ in(U_16,U_19)
| U_19 != empty_set ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_20] :
( U_20 = empty_set
| in(sK3(U_20),U_20) )
& ! [U_19] :
( ! [U_16] : ~ in(U_16,U_19)
| U_19 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3(U_20))],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ in(U_16,U_19)
| U_19 != empty_set ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( U_20 = empty_set
| in(sK3(U_20),U_20) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_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_5_2,plain,
! [U_25,U_24,U_23] :
( ( U_23 = set_intersection2(U_25,U_24)
| ? [U_22] :
( ( ~ in(U_22,U_23)
& in(U_22,U_24)
& in(U_22,U_25) )
| ( ( ~ in(U_22,U_24)
| ~ in(U_22,U_25) )
& in(U_22,U_23) ) ) )
& ( ! [U_21] :
( ( in(U_21,U_23)
| ~ in(U_21,U_24)
| ~ in(U_21,U_25) )
& ( ( in(U_21,U_24)
& in(U_21,U_25) )
| ~ in(U_21,U_23) ) )
| U_23 != set_intersection2(U_25,U_24) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_intersection2(U_35,U_33)
| ? [U_29] :
( ~ in(U_29,U_31)
& in(U_29,U_33)
& in(U_29,U_35) )
| ? [U_28] :
( ( ~ in(U_28,U_33)
| ~ in(U_28,U_35) )
& in(U_28,U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ~ in(U_27,U_32)
| ~ in(U_27,U_34) )
& ! [U_26] :
( ( in(U_26,U_32)
& in(U_26,U_34) )
| ~ in(U_26,U_30) ) )
| U_30 != set_intersection2(U_34,U_32) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_intersection2(U_35,U_33)
| ? [U_29] :
( ~ in(U_29,U_31)
& in(U_29,U_33)
& in(U_29,U_35) )
| ( ( ~ in(sK4(U_35,U_33,U_31),U_33)
| ~ in(sK4(U_35,U_33,U_31),U_35) )
& in(sK4(U_35,U_33,U_31),U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ~ in(U_27,U_32)
| ~ in(U_27,U_34) )
& ! [U_26] :
( ( in(U_26,U_32)
& in(U_26,U_34) )
| ~ in(U_26,U_30) ) )
| U_30 != set_intersection2(U_34,U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_28,sK4(U_35,U_33,U_31))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_35,U_33,U_31] :
( U_31 = set_intersection2(U_35,U_33)
| ( ~ in(sK5(U_35,U_33,U_31),U_31)
& in(sK5(U_35,U_33,U_31),U_33)
& in(sK5(U_35,U_33,U_31),U_35) )
| ( ( ~ in(sK4(U_35,U_33,U_31),U_33)
| ~ in(sK4(U_35,U_33,U_31),U_35) )
& in(sK4(U_35,U_33,U_31),U_31) ) )
& ! [U_34,U_32,U_30] :
( ( ! [U_27] :
( in(U_27,U_30)
| ~ in(U_27,U_32)
| ~ in(U_27,U_34) )
& ! [U_26] :
( ( in(U_26,U_32)
& in(U_26,U_34) )
| ~ in(U_26,U_30) ) )
| U_30 != set_intersection2(U_34,U_32) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_29,sK5(U_35,U_33,U_31))],[f_5_4]) ).
cnf(f_5_6,plain,
( in(U_26,U_34)
| ~ in(U_26,U_30)
| U_30 != set_intersection2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( in(U_26,U_32)
| ~ in(U_26,U_30)
| U_30 != set_intersection2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( in(U_27,U_30)
| ~ in(U_27,U_32)
| ~ in(U_27,U_34)
| U_30 != set_intersection2(U_34,U_32) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( in(sK5(U_35,U_33,U_31),U_35)
| in(sK4(U_35,U_33,U_31),U_31)
| U_31 = set_intersection2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_10,plain,
( in(sK5(U_35,U_33,U_31),U_33)
| in(sK4(U_35,U_33,U_31),U_31)
| U_31 = set_intersection2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_11,plain,
( ~ in(sK5(U_35,U_33,U_31),U_31)
| in(sK4(U_35,U_33,U_31),U_31)
| U_31 = set_intersection2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_12,plain,
( in(sK5(U_35,U_33,U_31),U_35)
| ~ in(sK4(U_35,U_33,U_31),U_33)
| ~ in(sK4(U_35,U_33,U_31),U_35)
| U_31 = set_intersection2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_13,plain,
( in(sK5(U_35,U_33,U_31),U_33)
| ~ in(sK4(U_35,U_33,U_31),U_33)
| ~ in(sK4(U_35,U_33,U_31),U_35)
| U_31 = set_intersection2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_14,plain,
( ~ in(sK5(U_35,U_33,U_31),U_31)
| ~ in(sK4(U_35,U_33,U_31),U_33)
| ~ in(sK4(U_35,U_33,U_31),U_35)
| U_31 = set_intersection2(U_35,U_33) ),
inference(clausify,[status(thm)],[f_5_5]) ).
fof(f_6_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_6_2,plain,
! [U_37,U_36] :
( ( disjoint(U_37,U_36)
| set_intersection2(U_37,U_36) != empty_set )
& ( set_intersection2(U_37,U_36) = empty_set
| ~ disjoint(U_37,U_36) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_41,U_39] :
( disjoint(U_41,U_39)
| set_intersection2(U_41,U_39) != empty_set )
& ! [U_40,U_38] :
( set_intersection2(U_40,U_38) = empty_set
| ~ disjoint(U_40,U_38) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( set_intersection2(U_40,U_38) = empty_set
| ~ disjoint(U_40,U_38) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( disjoint(U_41,U_39)
| set_intersection2(U_41,U_39) != empty_set ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_7_2,plain,
$true,
inference(clausify,[status(thm)],[f_7_1]) ).
fof(f_8_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_9_2,plain,
$true,
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_10_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_11_2,plain,
! [U_43,U_42] : set_intersection2(U_43,U_43) = U_43,
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_43] : set_intersection2(U_43,U_43) = U_43,
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
set_intersection2(U_43,U_43) = U_43,
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,negated_conjecture,
~ ! [A,B] :
~ ( in(A,B)
& disjoint(singleton(A),B) ),
inference(negate,[status(cth)],[l25_zfmisc_1]) ).
fof(f_12_2,negated_conjecture,
? [A,B] :
( in(A,B)
& disjoint(singleton(A),B) ),
inference(fof_nnf,[status(thm)],[f_12_1]) ).
fof(f_12_3,negated_conjecture,
? [U_45,U_44] :
( in(U_45,U_44)
& disjoint(singleton(U_45),U_44) ),
inference(variable_rename,[status(thm)],[f_12_2]) ).
fof(f_12_4,negated_conjecture,
? [U_44] :
( in(sK6,U_44)
& disjoint(singleton(sK6),U_44) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_45,sK6)],[f_12_3]) ).
fof(f_12_5,negated_conjecture,
( in(sK6,sK7)
& disjoint(singleton(sK6),sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_44,sK7)],[f_12_4]) ).
cnf(f_12_6,negated_conjecture,
disjoint(singleton(sK6),sK7),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,negated_conjecture,
in(sK6,sK7),
inference(clausify,[status(thm)],[f_12_5]) ).
fof(f_13_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_13_2,plain,
? [U_46] : empty(U_46),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_46,sK8)],[f_13_2]) ).
cnf(f_13_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_14_2,plain,
? [U_47] : ~ empty(U_47),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_47,sK9)],[f_14_2]) ).
cnf(f_14_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_15_2,plain,
! [U_49,U_48] :
( disjoint(U_48,U_49)
| ~ disjoint(U_49,U_48) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( disjoint(U_48,U_49)
| ~ disjoint(U_49,U_48) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_7_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_7_2]) ).
cnf(f_8_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_8_2]) ).
cnf(f_9_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_9_2]) ).
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) = sK3(Eq_y_0)
| 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,
( 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_13,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 : SEU153+1 : TPTP v9.3.1. Released v3.3.0.
% 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
% 0.09/0.34 % Computer : n010.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 19 23:23:39 UTC 2026
% 0.09/0.35 % CPUTime :
% 192.25/192.53 % SZS status Theorem for theBenchmark
% 192.25/192.53 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------