%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU123+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n013.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 08:58:06 AM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Proof 0.12s
% 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_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,lemma,
! [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(t3_xboole_1,conjecture,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('theBenchmark.p',t3_xboole_1) ).
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,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] :
( ( 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_12] :
( ( U_12 = empty_set
| ? [U_11] : in(U_11,U_12) )
& ( ! [U_10] : ~ in(U_10,U_12)
| U_12 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_14] :
( U_14 = empty_set
| ? [U_11] : in(U_11,U_14) )
& ! [U_13] :
( ! [U_10] : ~ in(U_10,U_13)
| U_13 != empty_set ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
fof(f_4_4,plain,
( ! [U_14] :
( U_14 = empty_set
| in(sK1(U_14),U_14) )
& ! [U_13] :
( ! [U_10] : ~ in(U_10,U_13)
| U_13 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_11,sK1(U_14))],[f_4_3]) ).
cnf(f_4_5,plain,
( ~ in(U_10,U_13)
| U_13 != empty_set ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( U_14 = empty_set
| in(sK1(U_14),U_14) ),
inference(clausify,[status(thm)],[f_4_4]) ).
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_18,U_17] :
( ( subset(U_18,U_17)
| ? [U_16] :
( ~ in(U_16,U_17)
& in(U_16,U_18) ) )
& ( ! [U_15] :
( in(U_15,U_17)
| ~ in(U_15,U_18) )
| ~ subset(U_18,U_17) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_22,U_20] :
( subset(U_22,U_20)
| ? [U_16] :
( ~ in(U_16,U_20)
& in(U_16,U_22) ) )
& ! [U_21,U_19] :
( ! [U_15] :
( in(U_15,U_19)
| ~ in(U_15,U_21) )
| ~ subset(U_21,U_19) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_22,U_20] :
( subset(U_22,U_20)
| ( ~ in(sK2(U_22,U_20),U_20)
& in(sK2(U_22,U_20),U_22) ) )
& ! [U_21,U_19] :
( ! [U_15] :
( in(U_15,U_19)
| ~ in(U_15,U_21) )
| ~ subset(U_21,U_19) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2(U_22,U_20))],[f_5_3]) ).
cnf(f_5_5,plain,
( in(U_15,U_19)
| ~ in(U_15,U_21)
| ~ subset(U_21,U_19) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( in(sK2(U_22,U_20),U_22)
| subset(U_22,U_20) ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_7,plain,
( ~ in(sK2(U_22,U_20),U_20)
| subset(U_22,U_20) ),
inference(clausify,[status(thm)],[f_5_4]) ).
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_27,U_26,U_25] :
( ( U_25 = set_intersection2(U_27,U_26)
| ? [U_24] :
( ( ~ in(U_24,U_25)
& in(U_24,U_26)
& in(U_24,U_27) )
| ( ( ~ in(U_24,U_26)
| ~ in(U_24,U_27) )
& in(U_24,U_25) ) ) )
& ( ! [U_23] :
( ( in(U_23,U_25)
| ~ in(U_23,U_26)
| ~ in(U_23,U_27) )
& ( ( in(U_23,U_26)
& in(U_23,U_27) )
| ~ in(U_23,U_25) ) )
| U_25 != set_intersection2(U_27,U_26) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_37,U_35,U_33] :
( U_33 = set_intersection2(U_37,U_35)
| ? [U_31] :
( ~ in(U_31,U_33)
& in(U_31,U_35)
& in(U_31,U_37) )
| ? [U_30] :
( ( ~ in(U_30,U_35)
| ~ in(U_30,U_37) )
& in(U_30,U_33) ) )
& ! [U_36,U_34,U_32] :
( ( ! [U_29] :
( in(U_29,U_32)
| ~ in(U_29,U_34)
| ~ in(U_29,U_36) )
& ! [U_28] :
( ( in(U_28,U_34)
& in(U_28,U_36) )
| ~ in(U_28,U_32) ) )
| U_32 != set_intersection2(U_36,U_34) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_37,U_35,U_33] :
( U_33 = set_intersection2(U_37,U_35)
| ? [U_31] :
( ~ in(U_31,U_33)
& in(U_31,U_35)
& in(U_31,U_37) )
| ( ( ~ in(sK3(U_37,U_35,U_33),U_35)
| ~ in(sK3(U_37,U_35,U_33),U_37) )
& in(sK3(U_37,U_35,U_33),U_33) ) )
& ! [U_36,U_34,U_32] :
( ( ! [U_29] :
( in(U_29,U_32)
| ~ in(U_29,U_34)
| ~ in(U_29,U_36) )
& ! [U_28] :
( ( in(U_28,U_34)
& in(U_28,U_36) )
| ~ in(U_28,U_32) ) )
| U_32 != set_intersection2(U_36,U_34) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_30,sK3(U_37,U_35,U_33))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_37,U_35,U_33] :
( U_33 = set_intersection2(U_37,U_35)
| ( ~ in(sK4(U_37,U_35,U_33),U_33)
& in(sK4(U_37,U_35,U_33),U_35)
& in(sK4(U_37,U_35,U_33),U_37) )
| ( ( ~ in(sK3(U_37,U_35,U_33),U_35)
| ~ in(sK3(U_37,U_35,U_33),U_37) )
& in(sK3(U_37,U_35,U_33),U_33) ) )
& ! [U_36,U_34,U_32] :
( ( ! [U_29] :
( in(U_29,U_32)
| ~ in(U_29,U_34)
| ~ in(U_29,U_36) )
& ! [U_28] :
( ( in(U_28,U_34)
& in(U_28,U_36) )
| ~ in(U_28,U_32) ) )
| U_32 != set_intersection2(U_36,U_34) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_31,sK4(U_37,U_35,U_33))],[f_6_4]) ).
cnf(f_6_6,plain,
( in(U_28,U_36)
| ~ in(U_28,U_32)
| U_32 != set_intersection2(U_36,U_34) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_7,plain,
( in(U_28,U_34)
| ~ in(U_28,U_32)
| U_32 != set_intersection2(U_36,U_34) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_8,plain,
( in(U_29,U_32)
| ~ in(U_29,U_34)
| ~ in(U_29,U_36)
| U_32 != set_intersection2(U_36,U_34) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_9,plain,
( in(sK4(U_37,U_35,U_33),U_37)
| in(sK3(U_37,U_35,U_33),U_33)
| U_33 = set_intersection2(U_37,U_35) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_10,plain,
( in(sK4(U_37,U_35,U_33),U_35)
| in(sK3(U_37,U_35,U_33),U_33)
| U_33 = set_intersection2(U_37,U_35) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_11,plain,
( ~ in(sK4(U_37,U_35,U_33),U_33)
| in(sK3(U_37,U_35,U_33),U_33)
| U_33 = set_intersection2(U_37,U_35) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_12,plain,
( in(sK4(U_37,U_35,U_33),U_37)
| ~ in(sK3(U_37,U_35,U_33),U_35)
| ~ in(sK3(U_37,U_35,U_33),U_37)
| U_33 = set_intersection2(U_37,U_35) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_13,plain,
( in(sK4(U_37,U_35,U_33),U_35)
| ~ in(sK3(U_37,U_35,U_33),U_35)
| ~ in(sK3(U_37,U_35,U_33),U_37)
| U_33 = set_intersection2(U_37,U_35) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_14,plain,
( ~ in(sK4(U_37,U_35,U_33),U_33)
| ~ in(sK3(U_37,U_35,U_33),U_35)
| ~ in(sK3(U_37,U_35,U_33),U_37)
| U_33 = set_intersection2(U_37,U_35) ),
inference(clausify,[status(thm)],[f_6_5]) ).
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_39,U_38] :
( ( disjoint(U_39,U_38)
| set_intersection2(U_39,U_38) != empty_set )
& ( set_intersection2(U_39,U_38) = empty_set
| ~ disjoint(U_39,U_38) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_43,U_41] :
( disjoint(U_43,U_41)
| set_intersection2(U_43,U_41) != empty_set )
& ! [U_42,U_40] :
( set_intersection2(U_42,U_40) = empty_set
| ~ disjoint(U_42,U_40) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( set_intersection2(U_42,U_40) = empty_set
| ~ disjoint(U_42,U_40) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( disjoint(U_43,U_41)
| set_intersection2(U_43,U_41) != empty_set ),
inference(clausify,[status(thm)],[f_7_3]) ).
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_45,U_44] : set_intersection2(U_45,U_45) = U_45,
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_45] : set_intersection2(U_45,U_45) = U_45,
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
set_intersection2(U_45,U_45) = U_45,
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_12_2,plain,
? [U_46] : empty(U_46),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_46,sK5)],[f_12_2]) ).
cnf(f_12_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_13_2,plain,
? [U_47] : ~ empty(U_47),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
~ empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_47,sK6)],[f_13_2]) ).
cnf(f_13_4,plain,
~ empty(sK6),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_14_2,plain,
! [U_49,U_48] : subset(U_49,U_49),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_49] : subset(U_49,U_49),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
subset(U_49,U_49),
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_51,U_50] :
( disjoint(U_50,U_51)
| ~ disjoint(U_51,U_50) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( disjoint(U_50,U_51)
| ~ disjoint(U_51,U_50) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_16_2,plain,
! [U_54,U_53,U_52] :
( subset(U_54,U_52)
| ~ subset(U_53,U_52)
| ~ subset(U_54,U_53) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( subset(U_54,U_52)
| ~ subset(U_53,U_52)
| ~ subset(U_54,U_53) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_17_2,plain,
! [U_55] : subset(empty_set,U_55),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
subset(empty_set,U_55),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_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_18_2,plain,
! [U_59,U_58] :
( ( ~ disjoint(U_59,U_58)
| ! [U_57] :
( ~ in(U_57,U_58)
| ~ in(U_57,U_59) ) )
& ( ? [U_56] :
( in(U_56,U_58)
& in(U_56,U_59) )
| disjoint(U_59,U_58) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_63,U_61] :
( ~ disjoint(U_63,U_61)
| ! [U_57] :
( ~ in(U_57,U_61)
| ~ in(U_57,U_63) ) )
& ! [U_62,U_60] :
( ? [U_56] :
( in(U_56,U_60)
& in(U_56,U_62) )
| disjoint(U_62,U_60) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_63,U_61] :
( ~ disjoint(U_63,U_61)
| ! [U_57] :
( ~ in(U_57,U_61)
| ~ in(U_57,U_63) ) )
& ! [U_62,U_60] :
( ( in(sK7(U_62,U_60),U_60)
& in(sK7(U_62,U_60),U_62) )
| disjoint(U_62,U_60) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_56,sK7(U_62,U_60))],[f_18_3]) ).
cnf(f_18_5,plain,
( in(sK7(U_62,U_60),U_62)
| disjoint(U_62,U_60) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_6,plain,
( in(sK7(U_62,U_60),U_60)
| disjoint(U_62,U_60) ),
inference(clausify,[status(thm)],[f_18_4]) ).
cnf(f_18_7,plain,
( ~ disjoint(U_63,U_61)
| ~ in(U_57,U_61)
| ~ in(U_57,U_63) ),
inference(clausify,[status(thm)],[f_18_4]) ).
fof(f_19_1,negated_conjecture,
~ ! [A] :
( subset(A,empty_set)
=> A = empty_set ),
inference(negate,[status(cth)],[t3_xboole_1]) ).
fof(f_19_2,negated_conjecture,
? [A] :
( A != empty_set
& subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[f_19_1]) ).
fof(f_19_3,negated_conjecture,
? [U_64] :
( U_64 != empty_set
& subset(U_64,empty_set) ),
inference(variable_rename,[status(thm)],[f_19_2]) ).
fof(f_19_4,negated_conjecture,
( sK8 != empty_set
& subset(sK8,empty_set) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_64,sK8)],[f_19_3]) ).
fof(f_19_5,negated_conjecture,
( sK8 != empty_set
& subset(sK8,empty_set) ),
inference(definitional_conversion,[status(esa)],[f_19_4]) ).
cnf(f_19_6,negated_conjecture,
subset(sK8,empty_set),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_7,negated_conjecture,
sK8 != empty_set,
inference(clausify,[status(thm)],[f_19_5]) ).
fof(f_20_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_20_2,plain,
! [U_68,U_67] :
( ( ~ disjoint(U_68,U_67)
| ! [U_66] : ~ in(U_66,set_intersection2(U_68,U_67)) )
& ( ? [U_65] : in(U_65,set_intersection2(U_68,U_67))
| disjoint(U_68,U_67) ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_72,U_70] :
( ~ disjoint(U_72,U_70)
| ! [U_66] : ~ in(U_66,set_intersection2(U_72,U_70)) )
& ! [U_71,U_69] :
( ? [U_65] : in(U_65,set_intersection2(U_71,U_69))
| disjoint(U_71,U_69) ) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
( ! [U_72,U_70] :
( ~ disjoint(U_72,U_70)
| ! [U_66] : ~ in(U_66,set_intersection2(U_72,U_70)) )
& ! [U_71,U_69] :
( in(sK9(U_71,U_69),set_intersection2(U_71,U_69))
| disjoint(U_71,U_69) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_65,sK9(U_71,U_69))],[f_20_3]) ).
cnf(f_20_5,plain,
( in(sK9(U_71,U_69),set_intersection2(U_71,U_69))
| disjoint(U_71,U_69) ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,plain,
( ~ disjoint(U_72,U_70)
| ~ in(U_66,set_intersection2(U_72,U_70)) ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_21_2,plain,
! [U_73] :
( U_73 = empty_set
| ~ empty(U_73) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( U_73 = empty_set
| ~ empty(U_73) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_22_2,plain,
! [U_75,U_74] :
( ~ empty(U_74)
| ~ in(U_75,U_74) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( ~ empty(U_74)
| ~ in(U_75,U_74) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_23_2,plain,
! [U_77,U_76] :
( ~ empty(U_76)
| U_77 = U_76
| ~ empty(U_77) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_77] :
( ! [U_76] :
( ~ empty(U_76)
| U_77 = U_76 )
| ~ empty(U_77) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( ~ empty(U_76)
| U_77 = U_76
| ~ empty(U_77) ),
inference(clausify,[status(thm)],[f_23_3]) ).
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,
( 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,
( 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_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 : SEU123+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 23:19:50 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------