%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU129+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 : 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 08:58:07 AM UTC 2026
% Result : Theorem 6.59s 21.73s
% Output : Proof 6.69s
% 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(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(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(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_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_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(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(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(t12_xboole_1,lemma,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t17_xboole_1,lemma,
! [A,B] : subset(set_intersection2(A,B),A),
file('theBenchmark.p',t17_xboole_1) ).
fof(t19_xboole_1,lemma,
! [A,B,C] :
( ( subset(A,C)
& subset(A,B) )
=> subset(A,set_intersection2(B,C)) ),
file('theBenchmark.p',t19_xboole_1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t1_xboole_1,lemma,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t26_xboole_1,conjecture,
! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
file('theBenchmark.p',t26_xboole_1) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
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,lemma,
! [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(t7_xboole_1,lemma,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(t8_xboole_1,lemma,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_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]) ).
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] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_3_2,plain,
! [U_5,U_4] : set_intersection2(U_5,U_4) = set_intersection2(U_4,U_5),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
set_intersection2(U_5,U_4) = set_intersection2(U_4,U_5),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_7,U_6] :
( ( U_7 = U_6
| ~ subset(U_6,U_7)
| ~ subset(U_7,U_6) )
& ( ( subset(U_6,U_7)
& subset(U_7,U_6) )
| U_7 != U_6 ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_11,U_9] :
( U_11 = U_9
| ~ subset(U_9,U_11)
| ~ subset(U_11,U_9) )
& ! [U_10,U_8] :
( ( subset(U_8,U_10)
& subset(U_10,U_8) )
| U_10 != U_8 ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( subset(U_10,U_8)
| U_10 != U_8 ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( subset(U_8,U_10)
| U_10 != U_8 ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( U_11 = U_9
| ~ subset(U_9,U_11)
| ~ subset(U_11,U_9) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_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_5_2,plain,
! [U_14] :
( ( U_14 = empty_set
| ? [U_13] : in(U_13,U_14) )
& ( ! [U_12] : ~ in(U_12,U_14)
| U_14 != empty_set ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_16] :
( U_16 = empty_set
| ? [U_13] : in(U_13,U_16) )
& ! [U_15] :
( ! [U_12] : ~ in(U_12,U_15)
| U_15 != empty_set ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
fof(f_5_4,plain,
( ! [U_16] :
( U_16 = empty_set
| in(sK1(U_16),U_16) )
& ! [U_15] :
( ! [U_12] : ~ in(U_12,U_15)
| U_15 != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_13,sK1(U_16))],[f_5_3]) ).
cnf(f_5_5,plain,
( ~ in(U_12,U_15)
| U_15 != empty_set ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( U_16 = empty_set
| in(sK1(U_16),U_16) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_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_6_2,plain,
! [U_21,U_20,U_19] :
( ( U_19 = set_union2(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_union2(U_21,U_20) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_31,U_29,U_27] :
( U_27 = set_union2(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_union2(U_30,U_28) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
fof(f_6_4,plain,
( ! [U_31,U_29,U_27] :
( U_27 = set_union2(U_31,U_29)
| ? [U_25] :
( ~ in(U_25,U_27)
& ( in(U_25,U_29)
| in(U_25,U_31) ) )
| ( ~ in(sK2(U_31,U_29,U_27),U_29)
& ~ in(sK2(U_31,U_29,U_27),U_31)
& in(sK2(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_union2(U_30,U_28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_24,sK2(U_31,U_29,U_27))],[f_6_3]) ).
fof(f_6_5,plain,
( ! [U_31,U_29,U_27] :
( U_27 = set_union2(U_31,U_29)
| ( ~ in(sK3(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) ) )
| ( ~ in(sK2(U_31,U_29,U_27),U_29)
& ~ in(sK2(U_31,U_29,U_27),U_31)
& in(sK2(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_union2(U_30,U_28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_25,sK3(U_31,U_29,U_27))],[f_6_4]) ).
cnf(f_6_6,plain,
( in(U_22,U_28)
| in(U_22,U_30)
| ~ in(U_22,U_26)
| U_26 != set_union2(U_30,U_28) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_7,plain,
( ~ in(U_23,U_30)
| in(U_23,U_26)
| U_26 != set_union2(U_30,U_28) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_8,plain,
( ~ in(U_23,U_28)
| in(U_23,U_26)
| U_26 != set_union2(U_30,U_28) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_9,plain,
( in(sK3(U_31,U_29,U_27),U_29)
| in(sK3(U_31,U_29,U_27),U_31)
| in(sK2(U_31,U_29,U_27),U_27)
| U_27 = set_union2(U_31,U_29) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_10,plain,
( ~ in(sK3(U_31,U_29,U_27),U_27)
| in(sK2(U_31,U_29,U_27),U_27)
| U_27 = set_union2(U_31,U_29) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_11,plain,
( ~ in(sK2(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_union2(U_31,U_29) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_12,plain,
( ~ in(sK2(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_union2(U_31,U_29) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_13,plain,
( ~ in(sK2(U_31,U_29,U_27),U_31)
| ~ in(sK3(U_31,U_29,U_27),U_27)
| U_27 = set_union2(U_31,U_29) ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_14,plain,
( ~ in(sK2(U_31,U_29,U_27),U_29)
| ~ in(sK3(U_31,U_29,U_27),U_27)
| U_27 = set_union2(U_31,U_29) ),
inference(clausify,[status(thm)],[f_6_5]) ).
fof(f_7_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_7_2,plain,
! [U_35,U_34] :
( ( subset(U_35,U_34)
| ? [U_33] :
( ~ in(U_33,U_34)
& in(U_33,U_35) ) )
& ( ! [U_32] :
( in(U_32,U_34)
| ~ in(U_32,U_35) )
| ~ subset(U_35,U_34) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_39,U_37] :
( subset(U_39,U_37)
| ? [U_33] :
( ~ in(U_33,U_37)
& in(U_33,U_39) ) )
& ! [U_38,U_36] :
( ! [U_32] :
( in(U_32,U_36)
| ~ in(U_32,U_38) )
| ~ subset(U_38,U_36) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
fof(f_7_4,plain,
( ! [U_39,U_37] :
( subset(U_39,U_37)
| ( ~ in(sK4(U_39,U_37),U_37)
& in(sK4(U_39,U_37),U_39) ) )
& ! [U_38,U_36] :
( ! [U_32] :
( in(U_32,U_36)
| ~ in(U_32,U_38) )
| ~ subset(U_38,U_36) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_33,sK4(U_39,U_37))],[f_7_3]) ).
cnf(f_7_5,plain,
( in(U_32,U_36)
| ~ in(U_32,U_38)
| ~ subset(U_38,U_36) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
( in(sK4(U_39,U_37),U_39)
| subset(U_39,U_37) ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_7,plain,
( ~ in(sK4(U_39,U_37),U_37)
| subset(U_39,U_37) ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_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_8_2,plain,
! [U_44,U_43,U_42] :
( ( U_42 = set_intersection2(U_44,U_43)
| ? [U_41] :
( ( ~ in(U_41,U_42)
& in(U_41,U_43)
& in(U_41,U_44) )
| ( ( ~ in(U_41,U_43)
| ~ in(U_41,U_44) )
& in(U_41,U_42) ) ) )
& ( ! [U_40] :
( ( in(U_40,U_42)
| ~ in(U_40,U_43)
| ~ in(U_40,U_44) )
& ( ( in(U_40,U_43)
& in(U_40,U_44) )
| ~ in(U_40,U_42) ) )
| U_42 != set_intersection2(U_44,U_43) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_54,U_52,U_50] :
( U_50 = set_intersection2(U_54,U_52)
| ? [U_48] :
( ~ in(U_48,U_50)
& in(U_48,U_52)
& in(U_48,U_54) )
| ? [U_47] :
( ( ~ in(U_47,U_52)
| ~ in(U_47,U_54) )
& in(U_47,U_50) ) )
& ! [U_53,U_51,U_49] :
( ( ! [U_46] :
( in(U_46,U_49)
| ~ in(U_46,U_51)
| ~ in(U_46,U_53) )
& ! [U_45] :
( ( in(U_45,U_51)
& in(U_45,U_53) )
| ~ in(U_45,U_49) ) )
| U_49 != set_intersection2(U_53,U_51) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
fof(f_8_4,plain,
( ! [U_54,U_52,U_50] :
( U_50 = set_intersection2(U_54,U_52)
| ? [U_48] :
( ~ in(U_48,U_50)
& in(U_48,U_52)
& in(U_48,U_54) )
| ( ( ~ in(sK5(U_54,U_52,U_50),U_52)
| ~ in(sK5(U_54,U_52,U_50),U_54) )
& in(sK5(U_54,U_52,U_50),U_50) ) )
& ! [U_53,U_51,U_49] :
( ( ! [U_46] :
( in(U_46,U_49)
| ~ in(U_46,U_51)
| ~ in(U_46,U_53) )
& ! [U_45] :
( ( in(U_45,U_51)
& in(U_45,U_53) )
| ~ in(U_45,U_49) ) )
| U_49 != set_intersection2(U_53,U_51) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_47,sK5(U_54,U_52,U_50))],[f_8_3]) ).
fof(f_8_5,plain,
( ! [U_54,U_52,U_50] :
( U_50 = set_intersection2(U_54,U_52)
| ( ~ in(sK6(U_54,U_52,U_50),U_50)
& in(sK6(U_54,U_52,U_50),U_52)
& in(sK6(U_54,U_52,U_50),U_54) )
| ( ( ~ in(sK5(U_54,U_52,U_50),U_52)
| ~ in(sK5(U_54,U_52,U_50),U_54) )
& in(sK5(U_54,U_52,U_50),U_50) ) )
& ! [U_53,U_51,U_49] :
( ( ! [U_46] :
( in(U_46,U_49)
| ~ in(U_46,U_51)
| ~ in(U_46,U_53) )
& ! [U_45] :
( ( in(U_45,U_51)
& in(U_45,U_53) )
| ~ in(U_45,U_49) ) )
| U_49 != set_intersection2(U_53,U_51) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_48,sK6(U_54,U_52,U_50))],[f_8_4]) ).
cnf(f_8_6,plain,
( in(U_45,U_53)
| ~ in(U_45,U_49)
| U_49 != set_intersection2(U_53,U_51) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_7,plain,
( in(U_45,U_51)
| ~ in(U_45,U_49)
| U_49 != set_intersection2(U_53,U_51) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_8,plain,
( in(U_46,U_49)
| ~ in(U_46,U_51)
| ~ in(U_46,U_53)
| U_49 != set_intersection2(U_53,U_51) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_9,plain,
( in(sK6(U_54,U_52,U_50),U_54)
| in(sK5(U_54,U_52,U_50),U_50)
| U_50 = set_intersection2(U_54,U_52) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_10,plain,
( in(sK6(U_54,U_52,U_50),U_52)
| in(sK5(U_54,U_52,U_50),U_50)
| U_50 = set_intersection2(U_54,U_52) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_11,plain,
( ~ in(sK6(U_54,U_52,U_50),U_50)
| in(sK5(U_54,U_52,U_50),U_50)
| U_50 = set_intersection2(U_54,U_52) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_12,plain,
( in(sK6(U_54,U_52,U_50),U_54)
| ~ in(sK5(U_54,U_52,U_50),U_52)
| ~ in(sK5(U_54,U_52,U_50),U_54)
| U_50 = set_intersection2(U_54,U_52) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_13,plain,
( in(sK6(U_54,U_52,U_50),U_52)
| ~ in(sK5(U_54,U_52,U_50),U_52)
| ~ in(sK5(U_54,U_52,U_50),U_54)
| U_50 = set_intersection2(U_54,U_52) ),
inference(clausify,[status(thm)],[f_8_5]) ).
cnf(f_8_14,plain,
( ~ in(sK6(U_54,U_52,U_50),U_50)
| ~ in(sK5(U_54,U_52,U_50),U_52)
| ~ in(sK5(U_54,U_52,U_50),U_54)
| U_50 = set_intersection2(U_54,U_52) ),
inference(clausify,[status(thm)],[f_8_5]) ).
fof(f_9_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_9_2,plain,
! [U_56,U_55] :
( ( disjoint(U_56,U_55)
| set_intersection2(U_56,U_55) != empty_set )
& ( set_intersection2(U_56,U_55) = empty_set
| ~ disjoint(U_56,U_55) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_60,U_58] :
( disjoint(U_60,U_58)
| set_intersection2(U_60,U_58) != empty_set )
& ! [U_59,U_57] :
( set_intersection2(U_59,U_57) = empty_set
| ~ disjoint(U_59,U_57) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( set_intersection2(U_59,U_57) = empty_set
| ~ disjoint(U_59,U_57) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( disjoint(U_60,U_58)
| set_intersection2(U_60,U_58) != empty_set ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_10_2,plain,
$true,
inference(clausify,[status(thm)],[f_10_1]) ).
fof(f_11_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_11_2,plain,
$true,
inference(clausify,[status(thm)],[f_11_1]) ).
fof(f_12_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
cnf(f_12_2,plain,
$true,
inference(clausify,[status(thm)],[f_12_1]) ).
fof(f_13_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_13_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_13_1]) ).
fof(f_14_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_14_2,plain,
! [U_62,U_61] :
( ~ empty(set_union2(U_62,U_61))
| empty(U_62) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_62] :
( ! [U_61] : ~ empty(set_union2(U_62,U_61))
| empty(U_62) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( ~ empty(set_union2(U_62,U_61))
| empty(U_62) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_15_2,plain,
! [U_64,U_63] :
( ~ empty(set_union2(U_63,U_64))
| empty(U_64) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_64] :
( ! [U_63] : ~ empty(set_union2(U_63,U_64))
| empty(U_64) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( ~ empty(set_union2(U_63,U_64))
| empty(U_64) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_16_2,plain,
! [U_66,U_65] : set_union2(U_66,U_66) = U_66,
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_66] : set_union2(U_66,U_66) = U_66,
inference(miniscope,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
set_union2(U_66,U_66) = U_66,
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_17_2,plain,
! [U_68,U_67] : set_intersection2(U_68,U_68) = U_68,
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_68] : set_intersection2(U_68,U_68) = U_68,
inference(miniscope,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
set_intersection2(U_68,U_68) = U_68,
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_18_2,plain,
? [U_69] : empty(U_69),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
empty(sK7),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_69,sK7)],[f_18_2]) ).
cnf(f_18_4,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_19_2,plain,
? [U_70] : ~ empty(U_70),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
~ empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_70,sK8)],[f_19_2]) ).
cnf(f_19_4,plain,
~ empty(sK8),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_20_2,plain,
! [U_72,U_71] : subset(U_72,U_72),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_72] : subset(U_72,U_72),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
subset(U_72,U_72),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0]) ).
fof(f_21_2,plain,
! [U_74,U_73] :
( disjoint(U_73,U_74)
| ~ disjoint(U_74,U_73) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
( disjoint(U_73,U_74)
| ~ disjoint(U_74,U_73) ),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A,B] :
( set_union2(A,B) = B
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1]) ).
fof(f_22_2,plain,
! [U_76,U_75] :
( set_union2(U_76,U_75) = U_75
| ~ subset(U_76,U_75) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( set_union2(U_76,U_75) = U_75
| ~ subset(U_76,U_75) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,B] : subset(set_intersection2(A,B),A),
inference(fof_nnf,[status(thm)],[t17_xboole_1]) ).
fof(f_23_2,plain,
! [U_78,U_77] : subset(set_intersection2(U_78,U_77),U_78),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
subset(set_intersection2(U_78,U_77),U_78),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B,C] :
( subset(A,set_intersection2(B,C))
| ~ subset(A,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t19_xboole_1]) ).
fof(f_24_2,plain,
! [U_81,U_80,U_79] :
( subset(U_81,set_intersection2(U_80,U_79))
| ~ subset(U_81,U_79)
| ~ subset(U_81,U_80) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( subset(U_81,set_intersection2(U_80,U_79))
| ~ subset(U_81,U_79)
| ~ subset(U_81,U_80) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_25_2,plain,
! [U_82] : set_union2(U_82,empty_set) = U_82,
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
set_union2(U_82,empty_set) = U_82,
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_26_2,plain,
! [U_85,U_84,U_83] :
( subset(U_85,U_83)
| ~ subset(U_84,U_83)
| ~ subset(U_85,U_84) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( subset(U_85,U_83)
| ~ subset(U_84,U_83)
| ~ subset(U_85,U_84) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> subset(set_intersection2(A,C),set_intersection2(B,C)) ),
inference(negate,[status(cth)],[t26_xboole_1]) ).
fof(f_27_2,negated_conjecture,
? [A,B,C] :
( ~ subset(set_intersection2(A,C),set_intersection2(B,C))
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[f_27_1]) ).
fof(f_27_3,negated_conjecture,
? [U_88,U_87,U_86] :
( ~ subset(set_intersection2(U_88,U_86),set_intersection2(U_87,U_86))
& subset(U_88,U_87) ),
inference(variable_rename,[status(thm)],[f_27_2]) ).
fof(f_27_4,negated_conjecture,
? [U_88,U_87] :
( ? [U_86] : ~ subset(set_intersection2(U_88,U_86),set_intersection2(U_87,U_86))
& subset(U_88,U_87) ),
inference(miniscope,[status(thm)],[f_27_3]) ).
fof(f_27_5,negated_conjecture,
? [U_87] :
( ? [U_86] : ~ subset(set_intersection2(sK9,U_86),set_intersection2(U_87,U_86))
& subset(sK9,U_87) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_88,sK9)],[f_27_4]) ).
fof(f_27_6,negated_conjecture,
( ? [U_86] : ~ subset(set_intersection2(sK9,U_86),set_intersection2(sK10,U_86))
& subset(sK9,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_87,sK10)],[f_27_5]) ).
fof(f_27_7,negated_conjecture,
( ~ subset(set_intersection2(sK9,sK11),set_intersection2(sK10,sK11))
& subset(sK9,sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_86,sK11)],[f_27_6]) ).
fof(f_27_8,negated_conjecture,
( ~ subset(set_intersection2(sK9,sK11),set_intersection2(sK10,sK11))
& subset(sK9,sK10) ),
inference(definitional_conversion,[status(esa)],[f_27_7]) ).
cnf(f_27_9,negated_conjecture,
subset(sK9,sK10),
inference(clausify,[status(thm)],[f_27_8]) ).
cnf(f_27_10,negated_conjecture,
~ subset(set_intersection2(sK9,sK11),set_intersection2(sK10,sK11)),
inference(clausify,[status(thm)],[f_27_8]) ).
fof(f_28_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_28_2,plain,
! [U_89] : set_intersection2(U_89,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
set_intersection2(U_89,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_29_2,plain,
! [U_90] : subset(empty_set,U_90),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
subset(empty_set,U_90),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_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_30_2,plain,
! [U_94,U_93] :
( ( ~ disjoint(U_94,U_93)
| ! [U_92] :
( ~ in(U_92,U_93)
| ~ in(U_92,U_94) ) )
& ( ? [U_91] :
( in(U_91,U_93)
& in(U_91,U_94) )
| disjoint(U_94,U_93) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_98,U_96] :
( ~ disjoint(U_98,U_96)
| ! [U_92] :
( ~ in(U_92,U_96)
| ~ in(U_92,U_98) ) )
& ! [U_97,U_95] :
( ? [U_91] :
( in(U_91,U_95)
& in(U_91,U_97) )
| disjoint(U_97,U_95) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
( ! [U_98,U_96] :
( ~ disjoint(U_98,U_96)
| ! [U_92] :
( ~ in(U_92,U_96)
| ~ in(U_92,U_98) ) )
& ! [U_97,U_95] :
( ( in(sK12(U_97,U_95),U_95)
& in(sK12(U_97,U_95),U_97) )
| disjoint(U_97,U_95) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_91,sK12(U_97,U_95))],[f_30_3]) ).
cnf(f_30_5,plain,
( in(sK12(U_97,U_95),U_97)
| disjoint(U_97,U_95) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
( in(sK12(U_97,U_95),U_95)
| disjoint(U_97,U_95) ),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_7,plain,
( ~ disjoint(U_98,U_96)
| ~ in(U_92,U_96)
| ~ in(U_92,U_98) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(fof_nnf,[status(thm)],[t3_xboole_1]) ).
fof(f_31_2,plain,
! [U_99] :
( U_99 = empty_set
| ~ subset(U_99,empty_set) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( U_99 = empty_set
| ~ subset(U_99,empty_set) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_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_32_2,plain,
! [U_103,U_102] :
( ( ~ disjoint(U_103,U_102)
| ! [U_101] : ~ in(U_101,set_intersection2(U_103,U_102)) )
& ( ? [U_100] : in(U_100,set_intersection2(U_103,U_102))
| disjoint(U_103,U_102) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_107,U_105] :
( ~ disjoint(U_107,U_105)
| ! [U_101] : ~ in(U_101,set_intersection2(U_107,U_105)) )
& ! [U_106,U_104] :
( ? [U_100] : in(U_100,set_intersection2(U_106,U_104))
| disjoint(U_106,U_104) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_107,U_105] :
( ~ disjoint(U_107,U_105)
| ! [U_101] : ~ in(U_101,set_intersection2(U_107,U_105)) )
& ! [U_106,U_104] :
( in(sK13(U_106,U_104),set_intersection2(U_106,U_104))
| disjoint(U_106,U_104) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_100,sK13(U_106,U_104))],[f_32_3]) ).
cnf(f_32_5,plain,
( in(sK13(U_106,U_104),set_intersection2(U_106,U_104))
| disjoint(U_106,U_104) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
( ~ disjoint(U_107,U_105)
| ~ in(U_101,set_intersection2(U_107,U_105)) ),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_33_2,plain,
! [U_108] :
( U_108 = empty_set
| ~ empty(U_108) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( U_108 = empty_set
| ~ empty(U_108) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_34_2,plain,
! [U_110,U_109] :
( ~ empty(U_109)
| ~ in(U_110,U_109) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( ~ empty(U_109)
| ~ in(U_110,U_109) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,B] : subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1]) ).
fof(f_35_2,plain,
! [U_112,U_111] : subset(U_112,set_union2(U_112,U_111)),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
subset(U_112,set_union2(U_112,U_111)),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_36_2,plain,
! [U_114,U_113] :
( ~ empty(U_113)
| U_114 = U_113
| ~ empty(U_114) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_114] :
( ! [U_113] :
( ~ empty(U_113)
| U_114 = U_113 )
| ~ empty(U_114) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( ~ empty(U_113)
| U_114 = U_113
| ~ empty(U_114) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t8_xboole_1]) ).
fof(f_37_2,plain,
! [U_117,U_116,U_115] :
( subset(set_union2(U_117,U_115),U_116)
| ~ subset(U_115,U_116)
| ~ subset(U_117,U_116) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( subset(set_union2(U_117,U_115),U_116)
| ~ subset(U_115,U_116)
| ~ subset(U_117,U_116) ),
inference(clausify,[status(thm)],[f_37_2]) ).
cnf(f_10_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_10_2]) ).
cnf(f_11_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_2]) ).
cnf(f_12_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_12_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_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,
( 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_6,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK2(Eq_x_0,Eq_x_1,Eq_x_2) = sK2(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,
( 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_9,axiom,
( sK4(Eq_x_0,Eq_x_1) = sK4(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,
( 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,
( 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_12,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| 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,
( 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_17,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
% 0.00/0.02 % Problem : SEU129+2 : 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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/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
% 0.08/15.42 % CPULimit : 300
% 0.08/15.42 % WCLimit : 300
% 0.08/15.42 % DateTime : Sat Sep 19 23:20:37 UTC 2026
% 0.08/15.43 % CPUTime :
% 6.59/21.73 % SZS status Theorem for theBenchmark
% 6.59/21.73 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------