TSTP Solution File: SET655+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET655+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 14:35:04 EDT 2023
% Result : Theorem 1.74s 1.81s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 37
% Syntax : Number of formulae : 105 ( 18 unt; 26 typ; 0 def)
% Number of atoms : 312 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 382 ( 149 ~; 153 |; 28 &)
% ( 7 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 31 ( 20 >; 11 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-2 aty)
% Number of variables : 153 ( 3 sgn; 65 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_26,type,
subset_type: $i > $i ).
tff(decl_27,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_28,type,
member: ( $i * $i ) > $o ).
tff(decl_29,type,
power_set: $i > $i ).
tff(decl_30,type,
member_type: $i > $i ).
tff(decl_31,type,
empty: $i > $o ).
tff(decl_32,type,
relation_like: $i > $o ).
tff(decl_33,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_34,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk3_1: $i > $i ).
tff(decl_37,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk5_1: $i > $i ).
tff(decl_39,type,
esk6_1: $i > $i ).
tff(decl_40,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk9_1: $i > $i ).
tff(decl_43,type,
esk10_0: $i ).
tff(decl_44,type,
esk11_0: $i ).
tff(decl_45,type,
esk12_0: $i ).
tff(decl_46,type,
esk13_0: $i ).
tff(decl_47,type,
esk14_0: $i ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p19,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(prove_relset_1_17,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X3))
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> ilf_type(X5,relation_type(X2,X4)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_17) ).
fof(p12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7) ).
fof(p11,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(p5,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14) ).
fof(c_0_11,plain,
! [X13,X14,X15,X16] :
( ( ~ ilf_type(X15,subset_type(cross_product(X13,X14)))
| ilf_type(X15,relation_type(X13,X14))
| ~ ilf_type(X14,set_type)
| ~ ilf_type(X13,set_type) )
& ( ~ ilf_type(X16,relation_type(X13,X14))
| ilf_type(X16,subset_type(cross_product(X13,X14)))
| ~ ilf_type(X14,set_type)
| ~ ilf_type(X13,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])]) ).
fof(c_0_12,plain,
! [X56] : ilf_type(X56,set_type),
inference(variable_rename,[status(thm)],[p19]) ).
fof(c_0_13,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X3))
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> ilf_type(X5,relation_type(X2,X4)) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_17]) ).
fof(c_0_14,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p12]) ).
fof(c_0_15,plain,
! [X26,X27] :
( ( ~ ilf_type(X27,subset_type(X26))
| ilf_type(X27,member_type(power_set(X26)))
| ~ ilf_type(X27,set_type)
| ~ ilf_type(X26,set_type) )
& ( ~ ilf_type(X27,member_type(power_set(X26)))
| ilf_type(X27,subset_type(X26))
| ~ ilf_type(X27,set_type)
| ~ ilf_type(X26,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])]) ).
cnf(c_0_16,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,negated_conjecture,
( ilf_type(esk10_0,set_type)
& ilf_type(esk11_0,set_type)
& ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,relation_type(esk10_0,esk12_0))
& subset(esk10_0,esk11_0)
& subset(esk12_0,esk13_0)
& ~ ilf_type(esk14_0,relation_type(esk11_0,esk13_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_13])])]) ).
fof(c_0_19,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p11]) ).
fof(c_0_20,plain,
! [X9,X10,X11,X12] :
( ~ ilf_type(X9,set_type)
| ~ ilf_type(X10,set_type)
| ~ ilf_type(X11,set_type)
| ~ ilf_type(X12,set_type)
| ~ subset(X9,X10)
| ~ subset(X11,X12)
| subset(cross_product(X9,X11),cross_product(X10,X12)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])]) ).
fof(c_0_21,plain,
! [X31,X32,X33] :
( ( ~ member(X31,power_set(X32))
| ~ ilf_type(X33,set_type)
| ~ member(X33,X31)
| member(X33,X32)
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) )
& ( ilf_type(esk4_2(X31,X32),set_type)
| member(X31,power_set(X32))
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) )
& ( member(esk4_2(X31,X32),X31)
| member(X31,power_set(X32))
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) )
& ( ~ member(esk4_2(X31,X32),X32)
| member(X31,power_set(X32))
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])])])]) ).
fof(c_0_22,plain,
! [X20,X21,X22] :
( ( ~ subset(X20,X21)
| ~ ilf_type(X22,set_type)
| ~ member(X22,X20)
| member(X22,X21)
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X20,set_type) )
& ( ilf_type(esk2_2(X20,X21),set_type)
| subset(X20,X21)
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X20,set_type) )
& ( member(esk2_2(X20,X21),X20)
| subset(X20,X21)
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X20,set_type) )
& ( ~ member(esk2_2(X20,X21),X21)
| subset(X20,X21)
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X20,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])])]) ).
fof(c_0_23,plain,
! [X36,X37] :
( ( ~ ilf_type(X36,member_type(X37))
| member(X36,X37)
| empty(X37)
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) )
& ( ~ member(X36,X37)
| ilf_type(X36,member_type(X37))
| empty(X37)
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
cnf(c_0_24,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_25,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17])]) ).
cnf(c_0_26,negated_conjecture,
ilf_type(esk14_0,relation_type(esk10_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_27,plain,
! [X35] :
( ( ~ empty(power_set(X35))
| ~ ilf_type(X35,set_type) )
& ( ilf_type(power_set(X35),set_type)
| ~ ilf_type(X35,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_28,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ subset(X1,X2)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
( member(X3,X2)
| ~ member(X1,power_set(X2))
| ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,plain,
( member(esk2_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( member(X1,X2)
| empty(X2)
| ~ ilf_type(X1,member_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_17]),c_0_17])]) ).
cnf(c_0_33,negated_conjecture,
ilf_type(esk14_0,subset_type(cross_product(esk10_0,esk12_0))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_34,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_35,plain,
! [X6,X7,X8] :
( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X8,set_type)
| ~ subset(X6,X7)
| ~ subset(X7,X8)
| subset(X6,X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_36,plain,
( subset(cross_product(X1,X2),cross_product(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_17]),c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_37,negated_conjecture,
subset(esk12_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_38,plain,
( member(X1,X2)
| ~ member(X3,power_set(X2))
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_39,plain,
( member(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_17]),c_0_17])]) ).
cnf(c_0_40,plain,
( empty(X1)
| member(X2,X1)
| ~ ilf_type(X2,member_type(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_17]),c_0_17])]) ).
cnf(c_0_41,negated_conjecture,
ilf_type(esk14_0,member_type(power_set(cross_product(esk10_0,esk12_0)))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_17])]) ).
cnf(c_0_43,plain,
( subset(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_44,negated_conjecture,
( subset(cross_product(X1,esk12_0),cross_product(X2,esk13_0))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,negated_conjecture,
subset(esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_46,plain,
( subset(X1,X2)
| ~ member(esk2_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_47,plain,
( member(esk2_2(X1,X2),X3)
| subset(X1,X2)
| ~ member(X1,power_set(X3)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
member(esk14_0,power_set(cross_product(esk10_0,esk12_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
fof(c_0_49,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p14]) ).
cnf(c_0_50,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_51,plain,
( member(esk4_2(X1,X2),X1)
| member(X1,power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_52,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_53,negated_conjecture,
subset(cross_product(esk10_0,esk12_0),cross_product(esk11_0,esk13_0)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_54,plain,
( subset(X1,X2)
| ~ member(esk2_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_17]),c_0_17])]) ).
cnf(c_0_55,negated_conjecture,
( member(esk2_2(esk14_0,X1),cross_product(esk10_0,esk12_0))
| subset(esk14_0,X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
fof(c_0_56,plain,
! [X40,X41] :
( ( ~ empty(X40)
| ~ ilf_type(X41,set_type)
| ~ member(X41,X40)
| ~ ilf_type(X40,set_type) )
& ( ilf_type(esk6_1(X40),set_type)
| empty(X40)
| ~ ilf_type(X40,set_type) )
& ( member(esk6_1(X40),X40)
| empty(X40)
| ~ ilf_type(X40,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])])]) ).
cnf(c_0_57,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_58,plain,
( member(esk4_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_17]),c_0_17])]) ).
cnf(c_0_59,negated_conjecture,
( subset(X1,cross_product(esk11_0,esk13_0))
| ~ subset(X1,cross_product(esk10_0,esk12_0)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
subset(esk14_0,cross_product(esk10_0,esk12_0)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_62,plain,
( member(X1,power_set(X2))
| ~ member(esk4_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_63,plain,
( member(esk4_2(X1,X2),X3)
| member(X1,power_set(X2))
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,negated_conjecture,
subset(esk14_0,cross_product(esk11_0,esk13_0)),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,plain,
( ilf_type(X1,member_type(X2))
| empty(X2)
| ~ member(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_66,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_17]),c_0_17])]) ).
cnf(c_0_67,plain,
( member(X1,power_set(X2))
| ~ member(esk4_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_17]),c_0_17])]) ).
cnf(c_0_68,negated_conjecture,
( member(esk4_2(esk14_0,X1),cross_product(esk11_0,esk13_0))
| member(esk14_0,power_set(X1)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_69,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_70,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_17]),c_0_17])]),c_0_66]) ).
cnf(c_0_71,negated_conjecture,
member(esk14_0,power_set(cross_product(esk11_0,esk13_0))),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_73,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_17]),c_0_17])]) ).
cnf(c_0_74,negated_conjecture,
ilf_type(esk14_0,member_type(power_set(cross_product(esk11_0,esk13_0)))),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_17]),c_0_17])]) ).
cnf(c_0_76,negated_conjecture,
ilf_type(esk14_0,subset_type(cross_product(esk11_0,esk13_0))),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
~ ilf_type(esk14_0,relation_type(esk11_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET655+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n015.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 : Sat Aug 26 11:24:07 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 1.74/1.81 % Version : CSE_E---1.5
% 1.74/1.81 % Problem : theBenchmark.p
% 1.74/1.81 % Proof found
% 1.74/1.81 % SZS status Theorem for theBenchmark.p
% 1.74/1.81 % SZS output start Proof
% See solution above
% 1.74/1.82 % Total time : 1.245000 s
% 1.74/1.82 % SZS output end Proof
% 1.74/1.82 % Total time : 1.248000 s
%------------------------------------------------------------------------------