TSTP Solution File: SEU138+2 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU138+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 16:22:41 EDT 2023
% Result : Theorem 81.77s 82.00s
% Output : CNFRefutation 81.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 39
% Syntax : Number of formulae : 144 ( 66 unt; 20 typ; 0 def)
% Number of atoms : 270 ( 81 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 239 ( 93 ~; 100 |; 33 &)
% ( 10 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 15 >; 16 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-3 aty)
% Number of variables : 320 ( 44 sgn; 106 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_24,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
empty_set: $i ).
tff(decl_27,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_28,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_29,type,
empty: $i > $o ).
tff(decl_30,type,
esk1_1: $i > $i ).
tff(decl_31,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_33,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
esk6_0: $i ).
tff(decl_36,type,
esk7_0: $i ).
tff(decl_37,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk10_0: $i ).
tff(decl_40,type,
esk11_0: $i ).
tff(decl_41,type,
esk12_2: ( $i * $i ) > $i ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t1_xboole_1,lemma,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t17_xboole_1,lemma,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(t28_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_intersection2(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(t7_xboole_1,lemma,
! [X1,X2] : subset(X1,set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(t3_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t40_xboole_1,lemma,
! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(t39_xboole_1,lemma,
! [X1,X2] : set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(d10_xboole_0,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(d7_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_intersection2(X1,X2) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(t48_xboole_1,conjecture,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(c_0_19,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_20,lemma,
! [X73,X74,X75] :
( ~ subset(X73,X74)
| ~ subset(X74,X75)
| subset(X73,X75) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(c_0_21,lemma,
! [X67,X68] : subset(set_intersection2(X67,X68),X67),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(c_0_22,plain,
! [X9,X10] : set_intersection2(X9,X10) = set_intersection2(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(c_0_23,plain,
! [X32,X33,X34,X35,X36,X37,X38,X39] :
( ( in(X35,X32)
| ~ in(X35,X34)
| X34 != set_intersection2(X32,X33) )
& ( in(X35,X33)
| ~ in(X35,X34)
| X34 != set_intersection2(X32,X33) )
& ( ~ in(X36,X32)
| ~ in(X36,X33)
| in(X36,X34)
| X34 != set_intersection2(X32,X33) )
& ( ~ in(esk4_3(X37,X38,X39),X39)
| ~ in(esk4_3(X37,X38,X39),X37)
| ~ in(esk4_3(X37,X38,X39),X38)
| X39 = set_intersection2(X37,X38) )
& ( in(esk4_3(X37,X38,X39),X37)
| in(esk4_3(X37,X38,X39),X39)
| X39 = set_intersection2(X37,X38) )
& ( in(esk4_3(X37,X38,X39),X38)
| in(esk4_3(X37,X38,X39),X39)
| X39 = set_intersection2(X37,X38) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_xboole_0])])])])])]) ).
fof(c_0_24,plain,
! [X41,X42,X43,X44,X45,X46,X47,X48] :
( ( in(X44,X41)
| ~ in(X44,X43)
| X43 != set_difference(X41,X42) )
& ( ~ in(X44,X42)
| ~ in(X44,X43)
| X43 != set_difference(X41,X42) )
& ( ~ in(X45,X41)
| in(X45,X42)
| in(X45,X43)
| X43 != set_difference(X41,X42) )
& ( ~ in(esk5_3(X46,X47,X48),X48)
| ~ in(esk5_3(X46,X47,X48),X46)
| in(esk5_3(X46,X47,X48),X47)
| X48 = set_difference(X46,X47) )
& ( in(esk5_3(X46,X47,X48),X46)
| in(esk5_3(X46,X47,X48),X48)
| X48 = set_difference(X46,X47) )
& ( ~ in(esk5_3(X46,X47,X48),X47)
| in(esk5_3(X46,X47,X48),X48)
| X48 = set_difference(X46,X47) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])])])])]) ).
cnf(c_0_25,lemma,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,lemma,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,lemma,
! [X89,X90] : subset(set_difference(X89,X90),X89),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
fof(c_0_28,lemma,
! [X79,X80] :
( ~ subset(X79,X80)
| set_intersection2(X79,X80) = X79 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
cnf(c_0_29,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_31,plain,
! [X26,X27,X28,X29,X30] :
( ( ~ subset(X26,X27)
| ~ in(X28,X26)
| in(X28,X27) )
& ( in(esk3_2(X29,X30),X29)
| subset(X29,X30) )
& ( ~ in(esk3_2(X29,X30),X30)
| subset(X29,X30) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d3_tarski])])])])])]) ).
cnf(c_0_32,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_intersection2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,lemma,
( subset(X1,X2)
| ~ subset(X1,set_intersection2(X2,X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,lemma,
subset(set_intersection2(X1,X2),X2),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
fof(c_0_38,lemma,
! [X119,X120] : subset(X119,set_union2(X119,X120)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
fof(c_0_39,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] :
~ ( in(X3,X1)
& in(X3,X2) ) )
& ~ ( ? [X3] :
( in(X3,X1)
& in(X3,X2) )
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t3_xboole_0]) ).
cnf(c_0_40,plain,
( ~ in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_41,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X2,X3)) ),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_42,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_43,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_45,plain,
( in(X1,X2)
| ~ in(X1,set_intersection2(X3,X2)) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_46,lemma,
subset(set_difference(set_intersection2(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_47,lemma,
set_intersection2(X1,set_intersection2(X2,X1)) = set_intersection2(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_29]) ).
cnf(c_0_48,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
fof(c_0_49,lemma,
! [X96,X97,X99,X100,X101] :
( ( in(esk9_2(X96,X97),X96)
| disjoint(X96,X97) )
& ( in(esk9_2(X96,X97),X97)
| disjoint(X96,X97) )
& ( ~ in(X101,X99)
| ~ in(X101,X100)
| ~ disjoint(X99,X100) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])])])])]) ).
fof(c_0_50,plain,
! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_51,plain,
( ~ in(X1,set_difference(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_52,plain,
( subset(set_intersection2(X1,X2),X3)
| in(esk3_2(set_intersection2(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_53,plain,
( subset(X1,set_difference(X2,X3))
| in(esk3_2(X1,set_difference(X2,X3)),X3)
| ~ in(esk3_2(X1,set_difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,plain,
( subset(set_intersection2(X1,X2),X3)
| in(esk3_2(set_intersection2(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_42]) ).
cnf(c_0_55,lemma,
subset(set_difference(set_intersection2(X1,X2),X3),X2),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_56,lemma,
set_intersection2(X1,set_union2(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_48]) ).
fof(c_0_57,lemma,
! [X103,X104] : set_difference(set_union2(X103,X104),X104) = set_difference(X103,X104),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
fof(c_0_58,lemma,
! [X93,X94] : set_union2(X93,set_difference(X94,X93)) = set_union2(X93,X94),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
cnf(c_0_59,lemma,
( in(esk9_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_60,lemma,
( in(esk9_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_61,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_50]) ).
fof(c_0_62,lemma,
! [X58,X59] :
( ( set_difference(X58,X59) != empty_set
| subset(X58,X59) )
& ( ~ subset(X58,X59)
| set_difference(X58,X59) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
cnf(c_0_63,plain,
( subset(set_intersection2(set_difference(X1,X2),X3),X4)
| ~ in(esk3_2(set_intersection2(set_difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_64,plain,
( subset(set_intersection2(X1,X2),set_difference(X2,X3))
| in(esk3_2(set_intersection2(X1,X2),set_difference(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_65,lemma,
subset(set_difference(X1,X2),set_union2(X1,X3)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_66,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_67,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_68,lemma,
( disjoint(set_difference(X1,X2),X3)
| ~ in(esk9_2(set_difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_59]) ).
cnf(c_0_69,lemma,
( disjoint(X1,set_intersection2(X2,X3))
| in(esk9_2(X1,set_intersection2(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_45,c_0_60]) ).
cnf(c_0_70,lemma,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_48,c_0_61]) ).
cnf(c_0_71,lemma,
( set_difference(X1,X2) = empty_set
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_72,plain,
! [X72] : set_union2(X72,empty_set) = X72,
inference(variable_rename,[status(thm)],[t1_boole]) ).
cnf(c_0_73,plain,
subset(set_intersection2(set_difference(X1,X2),X3),set_difference(X3,X2)),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_74,lemma,
set_intersection2(set_difference(X1,X2),set_union2(X1,X3)) = set_difference(X1,X2),
inference(spm,[status(thm)],[c_0_36,c_0_65]) ).
cnf(c_0_75,lemma,
set_difference(set_union2(X1,X2),set_difference(X2,X1)) = set_difference(X1,set_difference(X2,X1)),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_76,lemma,
set_union2(X1,set_union2(X2,X1)) = set_union2(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_66]),c_0_67]) ).
cnf(c_0_77,lemma,
disjoint(set_difference(X1,X2),set_intersection2(X3,X2)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_78,lemma,
set_intersection2(X1,set_union2(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_70]) ).
cnf(c_0_79,lemma,
set_difference(set_difference(X1,X2),X1) = empty_set,
inference(spm,[status(thm)],[c_0_71,c_0_35]) ).
cnf(c_0_80,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_81,lemma,
subset(set_difference(X1,X2),set_difference(set_union2(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,lemma,
set_difference(set_union2(X1,X2),set_difference(X1,X2)) = set_difference(X2,set_difference(X1,X2)),
inference(spm,[status(thm)],[c_0_75,c_0_61]) ).
cnf(c_0_83,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_84,plain,
! [X11,X12] :
( ( subset(X11,X12)
| X11 != X12 )
& ( subset(X12,X11)
| X11 != X12 )
& ( ~ subset(X11,X12)
| ~ subset(X12,X11)
| X11 = X12 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_85,lemma,
subset(set_union2(X1,X2),set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_70,c_0_76]) ).
fof(c_0_86,plain,
! [X50,X51] :
( ( ~ disjoint(X50,X51)
| set_intersection2(X50,X51) = empty_set )
& ( set_intersection2(X50,X51) != empty_set
| disjoint(X50,X51) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
cnf(c_0_87,lemma,
disjoint(set_difference(X1,set_union2(X2,X3)),X3),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_88,lemma,
set_union2(X1,set_difference(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_79]),c_0_80]) ).
cnf(c_0_89,lemma,
( subset(X1,X2)
| ~ subset(X1,set_difference(X2,X3)) ),
inference(spm,[status(thm)],[c_0_25,c_0_35]) ).
cnf(c_0_90,lemma,
subset(set_difference(X1,set_difference(X1,X2)),set_difference(X2,set_difference(X1,X2))),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_91,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_83]) ).
cnf(c_0_92,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_93,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_94,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_95,lemma,
set_intersection2(set_union2(X1,X2),set_union2(X2,X1)) = set_union2(X1,X2),
inference(spm,[status(thm)],[c_0_36,c_0_85]) ).
cnf(c_0_96,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_97,lemma,
disjoint(set_difference(X1,X2),set_difference(X2,X3)),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_98,lemma,
subset(set_difference(X1,set_difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_99,plain,
( subset(X1,set_intersection2(X2,X3))
| ~ in(esk3_2(X1,set_intersection2(X2,X3)),X3)
| ~ in(esk3_2(X1,set_intersection2(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_91]) ).
cnf(c_0_100,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_92]) ).
cnf(c_0_101,plain,
( subset(set_intersection2(X1,set_difference(X2,X3)),X4)
| ~ in(esk3_2(set_intersection2(X1,set_difference(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_54]) ).
cnf(c_0_102,plain,
( subset(set_intersection2(X1,X2),set_difference(X1,X3))
| in(esk3_2(set_intersection2(X1,X2),set_difference(X1,X3)),X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_52]) ).
cnf(c_0_103,lemma,
( X1 = X2
| set_difference(X2,X1) != empty_set
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_104,lemma,
subset(set_difference(set_union2(X1,X2),X3),set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_55,c_0_95]) ).
cnf(c_0_105,lemma,
set_intersection2(set_difference(X1,X2),set_difference(X2,X3)) = empty_set,
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_106,lemma,
set_intersection2(X1,set_difference(X2,set_difference(X2,X1))) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_98]),c_0_29]) ).
fof(c_0_107,plain,
! [X56] : set_union2(X56,X56) = X56,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
cnf(c_0_108,plain,
( subset(set_intersection2(X1,X2),set_intersection2(X3,X1))
| ~ in(esk3_2(set_intersection2(X1,X2),set_intersection2(X3,X1)),X3) ),
inference(spm,[status(thm)],[c_0_99,c_0_52]) ).
cnf(c_0_109,plain,
( subset(set_intersection2(X1,set_difference(X2,X3)),X4)
| in(esk3_2(set_intersection2(X1,set_difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_54]) ).
cnf(c_0_110,plain,
subset(set_intersection2(X1,set_difference(X2,X3)),set_difference(X1,X3)),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_111,lemma,
( set_difference(set_union2(X1,X2),X3) = set_union2(X2,X1)
| set_difference(set_union2(X2,X1),set_difference(set_union2(X1,X2),X3)) != empty_set ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_112,lemma,
set_difference(X1,set_difference(X1,set_difference(X2,X1))) = empty_set,
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_113,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_107]) ).
fof(c_0_114,negated_conjecture,
~ ! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(assume_negation,[status(cth)],[t48_xboole_1]) ).
cnf(c_0_115,plain,
subset(set_intersection2(X1,set_difference(X2,X3)),set_intersection2(X2,X1)),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_116,lemma,
set_difference(set_intersection2(X1,set_difference(X2,X3)),set_difference(X1,X3)) = empty_set,
inference(spm,[status(thm)],[c_0_71,c_0_110]) ).
cnf(c_0_117,lemma,
set_difference(X1,set_difference(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_113]),c_0_113]),c_0_113]) ).
fof(c_0_118,negated_conjecture,
set_difference(esk10_0,set_difference(esk10_0,esk11_0)) != set_intersection2(esk10_0,esk11_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_114])])]) ).
cnf(c_0_119,lemma,
subset(set_difference(X1,set_difference(X1,X2)),set_intersection2(X1,X2)),
inference(spm,[status(thm)],[c_0_115,c_0_106]) ).
cnf(c_0_120,lemma,
set_difference(set_intersection2(X1,X2),set_difference(X1,set_difference(X3,X2))) = empty_set,
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_121,negated_conjecture,
set_difference(esk10_0,set_difference(esk10_0,esk11_0)) != set_intersection2(esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_122,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_119]),c_0_120])]) ).
cnf(c_0_123,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_121,c_0_122])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU138+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 19:57:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 81.77/82.00 % Version : CSE_E---1.5
% 81.77/82.00 % Problem : theBenchmark.p
% 81.77/82.00 % Proof found
% 81.77/82.00 % SZS status Theorem for theBenchmark.p
% 81.77/82.00 % SZS output start Proof
% See solution above
% 81.77/82.01 % Total time : 81.313000 s
% 81.77/82.01 % SZS output end Proof
% 81.77/82.01 % Total time : 81.320000 s
%------------------------------------------------------------------------------