TSTP Solution File: SEU142+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU142+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 : n009.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 16:22:43 EDT 2023
% Result : Theorem 47.62s 47.72s
% Output : CNFRefutation 47.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 51
% Syntax : Number of formulae : 196 ( 72 unt; 24 typ; 0 def)
% Number of atoms : 404 ( 163 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 381 ( 149 ~; 158 |; 49 &)
% ( 18 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 20 >; 21 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 4 con; 0-3 aty)
% Number of variables : 380 ( 40 sgn; 159 !; 4 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_25,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_26,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_27,type,
subset: ( $i * $i ) > $o ).
tff(decl_28,type,
singleton: $i > $i ).
tff(decl_29,type,
empty_set: $i ).
tff(decl_30,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_31,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_32,type,
empty: $i > $o ).
tff(decl_33,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_34,type,
esk2_1: $i > $i ).
tff(decl_35,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk8_0: $i ).
tff(decl_41,type,
esk9_0: $i ).
tff(decl_42,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk13_0: $i ).
fof(t4_xboole_0,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(d1_xboole_0,axiom,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(t48_xboole_1,lemma,
! [X1,X2] : set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_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(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(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
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_boole,axiom,
! [X1] : set_difference(X1,empty_set) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
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(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(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
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(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(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(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t83_xboole_1,lemma,
! [X1,X2] :
( disjoint(X1,X2)
<=> set_difference(X1,X2) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_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(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(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t2_tarski,axiom,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
<=> in(X3,X2) )
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
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(t36_xboole_1,lemma,
! [X1,X2] : subset(set_difference(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(d2_tarski,axiom,
! [X1,X2,X3] :
( X3 = unordered_pair(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( X4 = X1
| X4 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
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(t69_enumset1,conjecture,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(c_0_27,lemma,
! [X1,X2] :
( ~ ( ~ disjoint(X1,X2)
& ! [X3] : ~ in(X3,set_intersection2(X1,X2)) )
& ~ ( ? [X3] : in(X3,set_intersection2(X1,X2))
& disjoint(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[t4_xboole_0]) ).
fof(c_0_28,plain,
! [X1] :
( X1 = empty_set
<=> ! [X2] : ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[d1_xboole_0]) ).
fof(c_0_29,plain,
! [X104] : set_intersection2(X104,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(c_0_30,lemma,
! [X130,X131] : set_difference(X130,set_difference(X130,X131)) = set_intersection2(X130,X131),
inference(variable_rename,[status(thm)],[t48_xboole_1]) ).
fof(c_0_31,lemma,
! [X133,X134,X136,X137,X138] :
( ( disjoint(X133,X134)
| in(esk12_2(X133,X134),set_intersection2(X133,X134)) )
& ( ~ in(X138,set_intersection2(X136,X137))
| ~ disjoint(X136,X137) ) ),
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_27])])])])]) ).
fof(c_0_32,lemma,
! [X102,X103] :
( ~ subset(X102,X103)
| set_intersection2(X102,X103) = X102 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t28_xboole_1])]) ).
fof(c_0_33,plain,
! [X24,X25,X26] :
( ( X24 != empty_set
| ~ in(X25,X24) )
& ( in(esk2_1(X26),X26)
| X26 = empty_set ) ),
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_28])])])])]) ).
fof(c_0_34,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]) ).
fof(c_0_35,lemma,
! [X88,X89] :
( ~ subset(X88,X89)
| set_union2(X88,X89) = X89 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
fof(c_0_36,lemma,
! [X148,X149] : subset(X148,set_union2(X148,X149)),
inference(variable_rename,[status(thm)],[t7_xboole_1]) ).
cnf(c_0_37,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,lemma,
set_difference(X1,set_difference(X1,X2)) = set_intersection2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_39,plain,
! [X118] : set_difference(X118,empty_set) = X118,
inference(variable_rename,[status(thm)],[t3_boole]) ).
cnf(c_0_40,lemma,
( ~ in(X1,set_intersection2(X2,X3))
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_41,lemma,
( set_intersection2(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
( X1 != empty_set
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_43,lemma,
! [X119,X120,X122,X123,X124] :
( ( in(esk11_2(X119,X120),X119)
| disjoint(X119,X120) )
& ( in(esk11_2(X119,X120),X120)
| disjoint(X119,X120) )
& ( ~ in(X124,X122)
| ~ in(X124,X123)
| ~ disjoint(X122,X123) ) ),
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_34])])])])])]) ).
fof(c_0_44,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_45,lemma,
! [X126,X127] : set_difference(set_union2(X126,X127),X127) = set_difference(X126,X127),
inference(variable_rename,[status(thm)],[t40_xboole_1]) ).
cnf(c_0_46,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_47,lemma,
subset(X1,set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_48,plain,
set_difference(X1,set_difference(X1,empty_set)) = empty_set,
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_49,plain,
set_difference(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,lemma,
( ~ disjoint(X2,X3)
| ~ in(X1,set_difference(X2,set_difference(X2,X3))) ),
inference(rw,[status(thm)],[c_0_40,c_0_38]) ).
cnf(c_0_51,lemma,
( set_difference(X1,set_difference(X1,X2)) = X1
| ~ subset(X1,X2) ),
inference(rw,[status(thm)],[c_0_41,c_0_38]) ).
cnf(c_0_52,plain,
~ in(X1,empty_set),
inference(er,[status(thm)],[c_0_42]) ).
cnf(c_0_53,lemma,
( in(esk11_2(X1,X2),X2)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_54,plain,
! [X17,X18,X19,X20,X21,X22] :
( ( ~ in(X19,X18)
| X19 = X17
| X18 != singleton(X17) )
& ( X20 != X17
| in(X20,X18)
| X18 != singleton(X17) )
& ( ~ in(esk1_2(X21,X22),X22)
| esk1_2(X21,X22) != X21
| X22 = singleton(X21) )
& ( in(esk1_2(X21,X22),X22)
| esk1_2(X21,X22) = X21
| X22 = singleton(X21) ) ),
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)],[d1_tarski])])])])])]) ).
fof(c_0_55,plain,
! [X61,X62,X63,X64,X65,X66,X67,X68] :
( ( in(X64,X61)
| ~ in(X64,X63)
| X63 != set_difference(X61,X62) )
& ( ~ in(X64,X62)
| ~ in(X64,X63)
| X63 != set_difference(X61,X62) )
& ( ~ in(X65,X61)
| in(X65,X62)
| in(X65,X63)
| X63 != set_difference(X61,X62) )
& ( ~ in(esk7_3(X66,X67,X68),X68)
| ~ in(esk7_3(X66,X67,X68),X66)
| in(esk7_3(X66,X67,X68),X67)
| X68 = set_difference(X66,X67) )
& ( in(esk7_3(X66,X67,X68),X66)
| in(esk7_3(X66,X67,X68),X68)
| X68 = set_difference(X66,X67) )
& ( ~ in(esk7_3(X66,X67,X68),X67)
| in(esk7_3(X66,X67,X68),X68)
| X68 = set_difference(X66,X67) ) ),
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_44])])])])])]) ).
fof(c_0_56,plain,
! [X13,X14] : set_intersection2(X13,X14) = set_intersection2(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
cnf(c_0_57,lemma,
set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_58,lemma,
set_union2(X1,set_union2(X1,X2)) = set_union2(X1,X2),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_59,plain,
set_difference(X1,X1) = empty_set,
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
fof(c_0_60,plain,
! [X11,X12] : set_union2(X11,X12) = set_union2(X12,X11),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_61,lemma,
( ~ disjoint(X1,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_62,lemma,
disjoint(X1,empty_set),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_63,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_64,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_65,plain,
( in(X1,X2)
| ~ in(X1,X3)
| X3 != set_difference(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_66,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,lemma,
set_difference(X1,set_union2(X1,X2)) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59]) ).
cnf(c_0_68,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_69,lemma,
( ~ subset(X1,empty_set)
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_70,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_63])]) ).
fof(c_0_71,lemma,
! [X81,X82] :
( ( set_difference(X81,X82) != empty_set
| subset(X81,X82) )
& ( ~ subset(X81,X82)
| set_difference(X81,X82) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
cnf(c_0_72,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_64]) ).
cnf(c_0_73,plain,
( in(X1,X2)
| ~ in(X1,set_difference(X2,X3)) ),
inference(er,[status(thm)],[c_0_65]) ).
cnf(c_0_74,plain,
( in(esk2_1(X1),X1)
| X1 = empty_set ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_75,plain,
set_difference(X1,set_difference(X1,X2)) = set_difference(X2,set_difference(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_38]),c_0_38]) ).
cnf(c_0_76,lemma,
set_difference(X1,set_union2(X2,X1)) = empty_set,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,lemma,
~ subset(singleton(X1),empty_set),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_78,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_79,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(c_0_80,lemma,
! [X150,X151] :
( ( ~ disjoint(X150,X151)
| set_difference(X150,X151) = X150 )
& ( set_difference(X150,X151) != X150
| disjoint(X150,X151) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t83_xboole_1])]) ).
cnf(c_0_81,lemma,
( in(esk11_2(X1,X2),X1)
| disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_82,lemma,
( esk11_2(X1,singleton(X2)) = X2
| disjoint(X1,singleton(X2)) ),
inference(spm,[status(thm)],[c_0_72,c_0_53]) ).
cnf(c_0_83,plain,
( set_difference(X1,X2) = empty_set
| in(esk2_1(set_difference(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_84,lemma,
set_difference(set_union2(X1,X2),set_difference(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_57]),c_0_76]),c_0_49]) ).
cnf(c_0_85,plain,
( esk2_1(singleton(X1)) = X1
| singleton(X1) = empty_set ),
inference(spm,[status(thm)],[c_0_72,c_0_74]) ).
cnf(c_0_86,lemma,
singleton(X1) != empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_49]) ).
fof(c_0_87,plain,
! [X5,X6] :
( ~ in(X5,X6)
| ~ in(X6,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_79])]) ).
cnf(c_0_88,lemma,
( set_difference(X1,X2) = X1
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_89,lemma,
( disjoint(X1,singleton(X2))
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_90,lemma,
( X1 = empty_set
| in(esk2_1(X1),set_union2(X2,X1)) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_91,plain,
esk2_1(singleton(X1)) = X1,
inference(sr,[status(thm)],[c_0_85,c_0_86]) ).
fof(c_0_92,plain,
! [X46,X47,X48,X49,X50] :
( ( ~ subset(X46,X47)
| ~ in(X48,X46)
| in(X48,X47) )
& ( in(esk5_2(X49,X50),X49)
| subset(X49,X50) )
& ( ~ in(esk5_2(X49,X50),X50)
| subset(X49,X50) ) ),
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])])])])])]) ).
fof(c_0_93,plain,
! [X70,X71] :
( ( ~ disjoint(X70,X71)
| set_intersection2(X70,X71) = empty_set )
& ( set_intersection2(X70,X71) != empty_set
| disjoint(X70,X71) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_xboole_0])]) ).
cnf(c_0_94,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_95,lemma,
( set_difference(X1,singleton(X2)) = X1
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,lemma,
in(X1,set_union2(X2,singleton(X1))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_86]) ).
cnf(c_0_97,plain,
( in(esk5_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_98,plain,
( disjoint(X1,X2)
| set_intersection2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_99,lemma,
( set_difference(X1,singleton(X2)) = X1
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,lemma,
in(X1,set_union2(singleton(X1),X2)),
inference(spm,[status(thm)],[c_0_96,c_0_68]) ).
cnf(c_0_101,plain,
( subset(X1,X2)
| ~ in(esk5_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_102,plain,
( esk5_2(singleton(X1),X2) = X1
| subset(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_97]) ).
cnf(c_0_103,plain,
( disjoint(X1,X2)
| set_difference(X1,set_difference(X1,X2)) != empty_set ),
inference(rw,[status(thm)],[c_0_98,c_0_38]) ).
cnf(c_0_104,lemma,
set_difference(X1,singleton(set_union2(singleton(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_99,c_0_100]) ).
cnf(c_0_105,lemma,
subset(X1,set_union2(X2,X1)),
inference(spm,[status(thm)],[c_0_47,c_0_68]) ).
cnf(c_0_106,plain,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,lemma,
disjoint(X1,singleton(set_union2(singleton(X1),X2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_59])]) ).
cnf(c_0_108,lemma,
set_union2(X1,set_union2(X2,X1)) = set_union2(X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_105]) ).
cnf(c_0_109,lemma,
( disjoint(X1,X2)
| subset(singleton(esk11_2(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_106,c_0_53]) ).
cnf(c_0_110,lemma,
disjoint(X1,singleton(set_union2(X2,singleton(X1)))),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_111,lemma,
( set_union2(X1,singleton(esk11_2(X2,X1))) = X1
| disjoint(X2,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_109]),c_0_68]) ).
fof(c_0_112,plain,
! [X86,X87] :
( ~ disjoint(X86,X87)
| disjoint(X87,X86) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
cnf(c_0_113,lemma,
( disjoint(esk11_2(X1,X2),singleton(X2))
| disjoint(X1,X2) ),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_114,lemma,
( esk11_2(singleton(X1),X2) = X1
| disjoint(singleton(X1),X2) ),
inference(spm,[status(thm)],[c_0_72,c_0_81]) ).
cnf(c_0_115,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_116,lemma,
( disjoint(singleton(X1),X2)
| disjoint(X1,singleton(X2)) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
fof(c_0_117,plain,
! [X105,X106] :
( ( ~ in(esk10_2(X105,X106),X105)
| ~ in(esk10_2(X105,X106),X106)
| X105 = X106 )
& ( in(esk10_2(X105,X106),X105)
| in(esk10_2(X105,X106),X106)
| X105 = X106 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_tarski])])])]) ).
fof(c_0_118,lemma,
! [X116,X117] : set_union2(X116,set_difference(X117,X116)) = set_union2(X116,X117),
inference(variable_rename,[status(thm)],[t39_xboole_1]) ).
cnf(c_0_119,lemma,
( disjoint(X1,singleton(X2))
| disjoint(X2,singleton(X1)) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_120,plain,
( in(esk10_2(X1,X2),X1)
| in(esk10_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_121,lemma,
set_difference(set_union2(X1,X2),X1) = set_difference(X2,X1),
inference(spm,[status(thm)],[c_0_57,c_0_68]) ).
cnf(c_0_122,lemma,
set_union2(X1,set_difference(X2,X1)) = set_union2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_118]) ).
fof(c_0_123,lemma,
! [X112,X113] : subset(set_difference(X112,X113),X112),
inference(variable_rename,[status(thm)],[t36_xboole_1]) ).
cnf(c_0_124,lemma,
( ~ in(X1,X2)
| ~ in(X1,X3)
| ~ disjoint(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_125,lemma,
disjoint(X1,singleton(X1)),
inference(ef,[status(thm)],[c_0_119]) ).
cnf(c_0_126,plain,
( empty_set = X1
| in(esk10_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_120]) ).
fof(c_0_127,plain,
! [X37,X38,X39,X40,X41,X42,X43,X44] :
( ( ~ in(X40,X39)
| in(X40,X37)
| in(X40,X38)
| X39 != set_union2(X37,X38) )
& ( ~ in(X41,X37)
| in(X41,X39)
| X39 != set_union2(X37,X38) )
& ( ~ in(X41,X38)
| in(X41,X39)
| X39 != set_union2(X37,X38) )
& ( ~ in(esk4_3(X42,X43,X44),X42)
| ~ in(esk4_3(X42,X43,X44),X44)
| X44 = set_union2(X42,X43) )
& ( ~ in(esk4_3(X42,X43,X44),X43)
| ~ in(esk4_3(X42,X43,X44),X44)
| X44 = set_union2(X42,X43) )
& ( in(esk4_3(X42,X43,X44),X44)
| in(esk4_3(X42,X43,X44),X42)
| in(esk4_3(X42,X43,X44),X43)
| X44 = set_union2(X42,X43) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_128,lemma,
set_difference(set_difference(X1,X2),X2) = set_difference(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_121]) ).
cnf(c_0_129,lemma,
subset(set_difference(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_130,lemma,
( ~ in(X1,singleton(X2))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_131,plain,
esk10_2(empty_set,singleton(X1)) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_126]),c_0_86]) ).
cnf(c_0_132,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_127]) ).
fof(c_0_133,plain,
! [X28,X29,X30,X31,X32,X33,X34,X35] :
( ( ~ in(X31,X30)
| X31 = X28
| X31 = X29
| X30 != unordered_pair(X28,X29) )
& ( X32 != X28
| in(X32,X30)
| X30 != unordered_pair(X28,X29) )
& ( X32 != X29
| in(X32,X30)
| X30 != unordered_pair(X28,X29) )
& ( esk3_3(X33,X34,X35) != X33
| ~ in(esk3_3(X33,X34,X35),X35)
| X35 = unordered_pair(X33,X34) )
& ( esk3_3(X33,X34,X35) != X34
| ~ in(esk3_3(X33,X34,X35),X35)
| X35 = unordered_pair(X33,X34) )
& ( in(esk3_3(X33,X34,X35),X35)
| esk3_3(X33,X34,X35) = X33
| esk3_3(X33,X34,X35) = X34
| X35 = unordered_pair(X33,X34) ) ),
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)],[d2_tarski])])])])])]) ).
cnf(c_0_134,lemma,
( set_union2(X1,X2) = X2
| set_difference(X1,X2) != empty_set ),
inference(spm,[status(thm)],[c_0_46,c_0_78]) ).
cnf(c_0_135,lemma,
set_difference(X1,set_difference(X1,set_difference(X2,X1))) = empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_128]),c_0_59]) ).
cnf(c_0_136,lemma,
set_union2(X1,set_difference(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_129]),c_0_68]) ).
cnf(c_0_137,lemma,
~ in(X1,X1),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_126]),c_0_131]),c_0_86]) ).
cnf(c_0_138,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_132]) ).
cnf(c_0_139,plain,
( in(X1,X3)
| X1 != X2
| X3 != unordered_pair(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_140,lemma,
set_difference(X1,set_difference(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]) ).
cnf(c_0_141,lemma,
~ in(set_union2(X1,X2),X2),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_142,plain,
( X1 = X3
| X1 = X4
| ~ in(X1,X2)
| X2 != unordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_143,plain,
in(X1,unordered_pair(X2,X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_139])]) ).
cnf(c_0_144,lemma,
disjoint(X1,set_difference(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_140]),c_0_59])]) ).
cnf(c_0_145,lemma,
set_difference(X1,singleton(set_union2(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_141,c_0_95]) ).
cnf(c_0_146,plain,
( X1 = X2
| X1 = X3
| ~ in(X1,unordered_pair(X3,X2)) ),
inference(er,[status(thm)],[c_0_142]) ).
cnf(c_0_147,lemma,
~ subset(unordered_pair(X1,X2),empty_set),
inference(spm,[status(thm)],[c_0_69,c_0_143]) ).
cnf(c_0_148,plain,
( set_intersection2(X1,X2) = empty_set
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_149,lemma,
disjoint(singleton(set_union2(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
fof(c_0_150,plain,
! [X15,X16] :
( ( subset(X15,X16)
| X15 != X16 )
& ( subset(X16,X15)
| X15 != X16 )
& ( ~ subset(X15,X16)
| ~ subset(X16,X15)
| X15 = X16 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d10_xboole_0])])]) ).
cnf(c_0_151,lemma,
( set_difference(X1,singleton(esk5_2(X2,X1))) = X1
| subset(X2,X1) ),
inference(spm,[status(thm)],[c_0_101,c_0_95]) ).
cnf(c_0_152,plain,
( esk5_2(unordered_pair(X1,X2),X3) = X1
| esk5_2(unordered_pair(X1,X2),X3) = X2
| subset(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_146,c_0_97]) ).
cnf(c_0_153,lemma,
unordered_pair(X1,X2) != empty_set,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_78]),c_0_49]) ).
cnf(c_0_154,plain,
( set_difference(X1,set_difference(X1,X2)) = empty_set
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[c_0_148,c_0_38]) ).
cnf(c_0_155,lemma,
disjoint(singleton(X1),set_difference(X1,X2)),
inference(spm,[status(thm)],[c_0_149,c_0_136]) ).
fof(c_0_156,negated_conjecture,
~ ! [X1] : unordered_pair(X1,X1) = singleton(X1),
inference(assume_negation,[status(cth)],[t69_enumset1]) ).
cnf(c_0_157,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_150]) ).
cnf(c_0_158,plain,
( empty_set = X1
| subset(singleton(esk10_2(empty_set,X1)),X1) ),
inference(spm,[status(thm)],[c_0_106,c_0_126]) ).
cnf(c_0_159,lemma,
( disjoint(singleton(esk5_2(X1,X2)),X2)
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_144,c_0_151]) ).
cnf(c_0_160,plain,
( esk5_2(unordered_pair(X1,X1),X2) = X1
| subset(unordered_pair(X1,X1),X2) ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_152])]) ).
cnf(c_0_161,plain,
( esk10_2(empty_set,unordered_pair(X1,X2)) = X1
| esk10_2(empty_set,unordered_pair(X1,X2)) = X2 ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_126]),c_0_153]) ).
cnf(c_0_162,plain,
( X1 = empty_set
| ~ disjoint(X1,set_difference(X1,X2))
| ~ disjoint(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_154]),c_0_49]) ).
cnf(c_0_163,lemma,
set_difference(singleton(X1),set_difference(X1,X2)) = singleton(X1),
inference(spm,[status(thm)],[c_0_88,c_0_155]) ).
fof(c_0_164,negated_conjecture,
unordered_pair(esk13_0,esk13_0) != singleton(esk13_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_156])])]) ).
cnf(c_0_165,plain,
( singleton(esk10_2(empty_set,X1)) = X1
| empty_set = X1
| ~ subset(X1,singleton(esk10_2(empty_set,X1))) ),
inference(spm,[status(thm)],[c_0_157,c_0_158]) ).
cnf(c_0_166,lemma,
( disjoint(singleton(X1),X2)
| subset(unordered_pair(X1,X1),X2) ),
inference(spm,[status(thm)],[c_0_159,c_0_160]) ).
cnf(c_0_167,plain,
esk10_2(empty_set,unordered_pair(X1,X1)) = X1,
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_161])]) ).
cnf(c_0_168,lemma,
~ disjoint(singleton(X1),singleton(X1)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_155])]),c_0_86]) ).
cnf(c_0_169,negated_conjecture,
unordered_pair(esk13_0,esk13_0) != singleton(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_164]) ).
cnf(c_0_170,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_167]),c_0_167]),c_0_153]),c_0_168]) ).
cnf(c_0_171,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_169,c_0_170])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU142+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
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 12:37:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 47.62/47.72 % Version : CSE_E---1.5
% 47.62/47.72 % Problem : theBenchmark.p
% 47.62/47.72 % Proof found
% 47.62/47.72 % SZS status Theorem for theBenchmark.p
% 47.62/47.72 % SZS output start Proof
% See solution above
% 47.62/47.73 % Total time : 47.137000 s
% 47.62/47.73 % SZS output end Proof
% 47.62/47.73 % Total time : 47.143000 s
%------------------------------------------------------------------------------