%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU122+2 : 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 : n004.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 08:58:05 AM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : Proof 0.10s
% 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_xboole_0,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('theBenchmark.p',d1_xboole_0) ).
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_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(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(t1_xboole_1,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t2_xboole_1,conjecture,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t3_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] :
( in(C,B)
& in(C,A) ) )
& ~ ( ! [C] :
~ ( in(C,B)
& in(C,A) )
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t3_xboole_0) ).
fof(t4_xboole_0,lemma,
! [A,B] :
( ~ ( disjoint(A,B)
& ? [C] : in(C,set_intersection2(A,B)) )
& ~ ( ! [C] : ~ in(C,set_intersection2(A,B))
& ~ disjoint(A,B) ) ),
file('theBenchmark.p',t4_xboole_0) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
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] :
( ( A = empty_set
| ? [B] : in(B,A) )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(fof_nnf,[status(thm)],[d1_xboole_0]) ).
fof(f_3_2,plain,
! [U_6] :
( ( U_6 = empty_set
| ? [U_5] : in(U_5,U_6) )
& ( ! [U_4] : ~ in(U_4,U_6)
| U_6 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_8] :
( U_8 = empty_set
| ? [U_5] : in(U_5,U_8) )
& ! [U_7] :
( ! [U_4] : ~ in(U_4,U_7)
| U_7 != empty_set ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_8] :
( U_8 = empty_set
| in(sK1(U_8),U_8) )
& ! [U_7] :
( ! [U_4] : ~ in(U_4,U_7)
| U_7 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1(U_8))],[f_3_3]) ).
cnf(f_3_5,plain,
( ~ in(U_4,U_7)
| U_7 != empty_set ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( U_8 = empty_set
| in(sK1(U_8),U_8) ),
inference(clausify,[status(thm)],[f_3_4]) ).
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_12,U_11] :
( ( subset(U_12,U_11)
| ? [U_10] :
( ~ in(U_10,U_11)
& in(U_10,U_12) ) )
& ( ! [U_9] :
( in(U_9,U_11)
| ~ in(U_9,U_12) )
| ~ subset(U_12,U_11) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_16,U_14] :
( subset(U_16,U_14)
| ? [U_10] :
( ~ in(U_10,U_14)
& in(U_10,U_16) ) )
& ! [U_15,U_13] :
( ! [U_9] :
( in(U_9,U_13)
| ~ in(U_9,U_15) )
| ~ subset(U_15,U_13) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_16,U_14] :
( subset(U_16,U_14)
| ( ~ in(sK2(U_16,U_14),U_14)
& in(sK2(U_16,U_14),U_16) ) )
& ! [U_15,U_13] :
( ! [U_9] :
( in(U_9,U_13)
| ~ in(U_9,U_15) )
| ~ subset(U_15,U_13) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_10,sK2(U_16,U_14))],[f_4_3]) ).
cnf(f_4_5,plain,
( in(U_9,U_13)
| ~ in(U_9,U_15)
| ~ subset(U_15,U_13) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( in(sK2(U_16,U_14),U_16)
| subset(U_16,U_14) ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_7,plain,
( ~ in(sK2(U_16,U_14),U_14)
| subset(U_16,U_14) ),
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_21,U_20,U_19] :
( ( U_19 = set_intersection2(U_21,U_20)
| ? [U_18] :
( ( ~ in(U_18,U_19)
& in(U_18,U_20)
& in(U_18,U_21) )
| ( ( ~ in(U_18,U_20)
| ~ in(U_18,U_21) )
& in(U_18,U_19) ) ) )
& ( ! [U_17] :
( ( in(U_17,U_19)
| ~ in(U_17,U_20)
| ~ in(U_17,U_21) )
& ( ( in(U_17,U_20)
& in(U_17,U_21) )
| ~ in(U_17,U_19) ) )
| U_19 != set_intersection2(U_21,U_20) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_31,U_29,U_27] :
( U_27 = set_intersection2(U_31,U_29)
| ? [U_25] :
( ~ in(U_25,U_27)
& in(U_25,U_29)
& in(U_25,U_31) )
| ? [U_24] :
( ( ~ in(U_24,U_29)
| ~ in(U_24,U_31) )
& in(U_24,U_27) ) )
& ! [U_30,U_28,U_26] :
( ( ! [U_23] :
( in(U_23,U_26)
| ~ in(U_23,U_28)
| ~ in(U_23,U_30) )
& ! [U_22] :
( ( in(U_22,U_28)
& in(U_22,U_30) )
| ~ in(U_22,U_26) ) )
| U_26 != set_intersection2(U_30,U_28) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_31,U_29,U_27] :
( U_27 = set_intersection2(U_31,U_29)
| ? [U_25] :
( ~ in(U_25,U_27)
& in(U_25,U_29)
& in(U_25,U_31) )
| ( ( ~ in(sK3(U_31,U_29,U_27),U_29)
| ~ in(sK3(U_31,U_29,U_27),U_31) )
& in(sK3(U_31,U_29,U_27),U_27) ) )
& ! [U_30,U_28,U_26] :
( ( ! [U_23] :
( in(U_23,U_26)
| ~ in(U_23,U_28)
| ~ in(U_23,U_30) )
& ! [U_22] :
( ( in(U_22,U_28)
& in(U_22,U_30) )
| ~ in(U_22,U_26) ) )
| U_26 != set_intersection2(U_30,U_28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_24,sK3(U_31,U_29,U_27))],[f_5_3]) ).
fof(f_5_5,plain,
( ! [U_31,U_29,U_27] :
( U_27 = set_intersection2(U_31,U_29)
| ( ~ in(sK4(U_31,U_29,U_27),U_27)
& in(sK4(U_31,U_29,U_27),U_29)
& in(sK4(U_31,U_29,U_27),U_31) )
| ( ( ~ in(sK3(U_31,U_29,U_27),U_29)
| ~ in(sK3(U_31,U_29,U_27),U_31) )
& in(sK3(U_31,U_29,U_27),U_27) ) )
& ! [U_30,U_28,U_26] :
( ( ! [U_23] :
( in(U_23,U_26)
| ~ in(U_23,U_28)
| ~ in(U_23,U_30) )
& ! [U_22] :
( ( in(U_22,U_28)
& in(U_22,U_30) )
| ~ in(U_22,U_26) ) )
| U_26 != set_intersection2(U_30,U_28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_25,sK4(U_31,U_29,U_27))],[f_5_4]) ).
cnf(f_5_6,plain,
( in(U_22,U_30)
| ~ in(U_22,U_26)
| U_26 != set_intersection2(U_30,U_28) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_7,plain,
( in(U_22,U_28)
| ~ in(U_22,U_26)
| U_26 != set_intersection2(U_30,U_28) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_8,plain,
( in(U_23,U_26)
| ~ in(U_23,U_28)
| ~ in(U_23,U_30)
| U_26 != set_intersection2(U_30,U_28) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_9,plain,
( in(sK4(U_31,U_29,U_27),U_31)
| in(sK3(U_31,U_29,U_27),U_27)
| U_27 = set_intersection2(U_31,U_29) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_10,plain,
( in(sK4(U_31,U_29,U_27),U_29)
| in(sK3(U_31,U_29,U_27),U_27)
| U_27 = set_intersection2(U_31,U_29) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_11,plain,
( ~ in(sK4(U_31,U_29,U_27),U_27)
| in(sK3(U_31,U_29,U_27),U_27)
| U_27 = set_intersection2(U_31,U_29) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_12,plain,
( in(sK4(U_31,U_29,U_27),U_31)
| ~ in(sK3(U_31,U_29,U_27),U_29)
| ~ in(sK3(U_31,U_29,U_27),U_31)
| U_27 = set_intersection2(U_31,U_29) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_13,plain,
( in(sK4(U_31,U_29,U_27),U_29)
| ~ in(sK3(U_31,U_29,U_27),U_29)
| ~ in(sK3(U_31,U_29,U_27),U_31)
| U_27 = set_intersection2(U_31,U_29) ),
inference(clausify,[status(thm)],[f_5_5]) ).
cnf(f_5_14,plain,
( ~ in(sK4(U_31,U_29,U_27),U_27)
| ~ in(sK3(U_31,U_29,U_27),U_29)
| ~ in(sK3(U_31,U_29,U_27),U_31)
| U_27 = set_intersection2(U_31,U_29) ),
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_33,U_32] :
( ( disjoint(U_33,U_32)
| set_intersection2(U_33,U_32) != empty_set )
& ( set_intersection2(U_33,U_32) = empty_set
| ~ disjoint(U_33,U_32) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_37,U_35] :
( disjoint(U_37,U_35)
| set_intersection2(U_37,U_35) != empty_set )
& ! [U_36,U_34] :
( set_intersection2(U_36,U_34) = empty_set
| ~ disjoint(U_36,U_34) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( set_intersection2(U_36,U_34) = empty_set
| ~ disjoint(U_36,U_34) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( disjoint(U_37,U_35)
| set_intersection2(U_37,U_35) != empty_set ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
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_k3_xboole_0]) ).
cnf(f_8_2,plain,
$true,
inference(clausify,[status(thm)],[f_8_1]) ).
fof(f_9_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_9_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_9_1]) ).
fof(f_10_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_10_2,plain,
! [U_39,U_38] : set_intersection2(U_39,U_39) = U_39,
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_39] : set_intersection2(U_39,U_39) = U_39,
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
set_intersection2(U_39,U_39) = U_39,
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_40] : empty(U_40),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_40,sK5)],[f_11_2]) ).
cnf(f_11_4,plain,
empty(sK5),
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_41] : ~ empty(U_41),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
~ empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_41,sK6)],[f_12_2]) ).
cnf(f_12_4,plain,
~ empty(sK6),
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_43,U_42] : subset(U_43,U_43),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_43] : subset(U_43,U_43),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
subset(U_43,U_43),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_14_2,plain,
! [U_45,U_44] :
( disjoint(U_44,U_45)
| ~ disjoint(U_45,U_44) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( disjoint(U_44,U_45)
| ~ disjoint(U_45,U_44) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_15_2,plain,
! [U_48,U_47,U_46] :
( subset(U_48,U_46)
| ~ subset(U_47,U_46)
| ~ subset(U_48,U_47) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( subset(U_48,U_46)
| ~ subset(U_47,U_46)
| ~ subset(U_48,U_47) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,negated_conjecture,
~ ! [A] : subset(empty_set,A),
inference(negate,[status(cth)],[t2_xboole_1]) ).
fof(f_16_2,negated_conjecture,
? [A] : ~ subset(empty_set,A),
inference(fof_nnf,[status(thm)],[f_16_1]) ).
fof(f_16_3,negated_conjecture,
? [U_49] : ~ subset(empty_set,U_49),
inference(variable_rename,[status(thm)],[f_16_2]) ).
fof(f_16_4,negated_conjecture,
~ subset(empty_set,sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_49,sK7)],[f_16_3]) ).
fof(f_16_5,negated_conjecture,
~ subset(empty_set,sK7),
inference(definitional_conversion,[status(esa)],[f_16_4]) ).
cnf(f_16_6,negated_conjecture,
~ subset(empty_set,sK7),
inference(clausify,[status(thm)],[f_16_5]) ).
fof(f_17_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] :
( ~ in(C,B)
| ~ in(C,A) ) )
& ( ? [C] :
( in(C,B)
& in(C,A) )
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t3_xboole_0]) ).
fof(f_17_2,plain,
! [U_53,U_52] :
( ( ~ disjoint(U_53,U_52)
| ! [U_51] :
( ~ in(U_51,U_52)
| ~ in(U_51,U_53) ) )
& ( ? [U_50] :
( in(U_50,U_52)
& in(U_50,U_53) )
| disjoint(U_53,U_52) ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_57,U_55] :
( ~ disjoint(U_57,U_55)
| ! [U_51] :
( ~ in(U_51,U_55)
| ~ in(U_51,U_57) ) )
& ! [U_56,U_54] :
( ? [U_50] :
( in(U_50,U_54)
& in(U_50,U_56) )
| disjoint(U_56,U_54) ) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
fof(f_17_4,plain,
( ! [U_57,U_55] :
( ~ disjoint(U_57,U_55)
| ! [U_51] :
( ~ in(U_51,U_55)
| ~ in(U_51,U_57) ) )
& ! [U_56,U_54] :
( ( in(sK8(U_56,U_54),U_54)
& in(sK8(U_56,U_54),U_56) )
| disjoint(U_56,U_54) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_50,sK8(U_56,U_54))],[f_17_3]) ).
cnf(f_17_5,plain,
( in(sK8(U_56,U_54),U_56)
| disjoint(U_56,U_54) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_6,plain,
( in(sK8(U_56,U_54),U_54)
| disjoint(U_56,U_54) ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_7,plain,
( ~ disjoint(U_57,U_55)
| ~ in(U_51,U_55)
| ~ in(U_51,U_57) ),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_1,plain,
! [A,B] :
( ( ~ disjoint(A,B)
| ! [C] : ~ in(C,set_intersection2(A,B)) )
& ( ? [C] : in(C,set_intersection2(A,B))
| disjoint(A,B) ) ),
inference(fof_nnf,[status(thm)],[t4_xboole_0]) ).
fof(f_18_2,plain,
! [U_61,U_60] :
( ( ~ disjoint(U_61,U_60)
| ! [U_59] : ~ in(U_59,set_intersection2(U_61,U_60)) )
& ( ? [U_58] : in(U_58,set_intersection2(U_61,U_60))
| disjoint(U_61,U_60) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_65,U_63] :
( ~ disjoint(U_65,U_63)
| ! [U_59] : ~ in(U_59,set_intersection2(U_65,U_63)) )
& ! [U_64,U_62] :
( ? [U_58] : in(U_58,set_intersection2(U_64,U_62))
| disjoint(U_64,U_62) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_65,U_63] :
( ~ disjoint(U_65,U_63)
| ! [U_59] : ~ in(U_59,set_intersection2(U_65,U_63)) )
& ! [U_64,U_62] :
( in(sK9(U_64,U_62),set_intersection2(U_64,U_62))
| disjoint(U_64,U_62) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_58,sK9(U_64,U_62))],[f_18_3]) ).
cnf(f_18_5,plain,
( in(sK9(U_64,U_62),set_intersection2(U_64,U_62))
| disjoint(U_64,U_62) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
( ~ disjoint(U_65,U_63)
| ~ in(U_59,set_intersection2(U_65,U_63)) ),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_19_2,plain,
! [U_66] :
( U_66 = empty_set
| ~ empty(U_66) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( U_66 = empty_set
| ~ empty(U_66) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_20_2,plain,
! [U_68,U_67] :
( ~ empty(U_67)
| ~ in(U_68,U_67) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( ~ empty(U_67)
| ~ in(U_68,U_67) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_21_2,plain,
! [U_70,U_69] :
( ~ empty(U_69)
| U_70 = U_69
| ~ empty(U_70) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_70] :
( ! [U_69] :
( ~ empty(U_69)
| U_70 = U_69 )
| ~ empty(U_70) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( ~ empty(U_69)
| U_70 = U_69
| ~ empty(U_70) ),
inference(clausify,[status(thm)],[f_21_3]) ).
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(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,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,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_8,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_9,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_10,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(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,
( 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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU122+2 : 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
% 0.10/0.37 % Computer : n004.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 23:20:19 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.43 % SZS status Theorem for theBenchmark
% 0.10/0.43 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------