TSTP Solution File: SET351+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET351+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 14:34:01 EDT 2023
% Result : Theorem 1.23s 1.45s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 22
% Syntax : Number of formulae : 62 ( 10 unt; 16 typ; 0 def)
% Number of atoms : 108 ( 8 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 116 ( 54 ~; 46 |; 10 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 14 >; 10 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn; 29 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
equal_set: ( $i * $i ) > $o ).
tff(decl_25,type,
power_set: $i > $i ).
tff(decl_26,type,
intersection: ( $i * $i ) > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
difference: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
sum: $i > $i ).
tff(decl_33,type,
product: $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_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk4_0: $i ).
fof(thI39,conjecture,
! [X1] : equal_set(sum(singleton(X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI39) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(sum,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] : equal_set(sum(singleton(X1)),X1),
inference(assume_negation,[status(cth)],[thI39]) ).
fof(c_0_7,negated_conjecture,
~ equal_set(sum(singleton(esk4_0)),esk4_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_8,plain,
! [X12,X13] :
( ( subset(X12,X13)
| ~ equal_set(X12,X13) )
& ( subset(X13,X12)
| ~ equal_set(X12,X13) )
& ( ~ subset(X12,X13)
| ~ subset(X13,X12)
| equal_set(X12,X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_9,negated_conjecture,
~ equal_set(sum(singleton(esk4_0)),esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X6,X7,X8,X9,X10] :
( ( ~ subset(X6,X7)
| ~ member(X8,X6)
| member(X8,X7) )
& ( member(esk1_2(X9,X10),X9)
| subset(X9,X10) )
& ( ~ member(esk1_2(X9,X10),X10)
| subset(X9,X10) ) ),
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)],[subset])])])])])]) ).
fof(c_0_12,plain,
! [X14,X15] :
( ( ~ member(X14,power_set(X15))
| subset(X14,X15) )
& ( ~ subset(X14,X15)
| member(X14,power_set(X15)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
fof(c_0_13,plain,
! [X26,X27] :
( ( ~ member(X26,singleton(X27))
| X26 = X27 )
& ( X26 != X27
| member(X26,singleton(X27)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
fof(c_0_14,plain,
! [X31,X32,X34,X35,X36] :
( ( member(esk2_2(X31,X32),X32)
| ~ member(X31,sum(X32)) )
& ( member(X31,esk2_2(X31,X32))
| ~ member(X31,sum(X32)) )
& ( ~ member(X36,X35)
| ~ member(X34,X36)
| member(X34,sum(X35)) ) ),
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)],[sum])])])])])]) ).
cnf(c_0_15,negated_conjecture,
( ~ subset(esk4_0,sum(singleton(esk4_0)))
| ~ subset(sum(singleton(esk4_0)),esk4_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( member(esk2_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( member(esk1_2(sum(singleton(esk4_0)),esk4_0),sum(singleton(esk4_0)))
| ~ subset(esk4_0,sum(singleton(esk4_0))) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_23,plain,
( member(X3,sum(X2))
| ~ member(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_24,plain,
( member(esk1_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_25,plain,
( esk2_2(X1,singleton(X2)) = X2
| ~ member(X1,sum(singleton(X2))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( member(esk1_2(sum(singleton(esk4_0)),esk4_0),sum(singleton(esk4_0)))
| ~ member(esk4_0,power_set(sum(singleton(esk4_0)))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( member(X1,power_set(X2))
| ~ member(esk1_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_28,plain,
( member(esk1_2(X1,X2),sum(X3))
| member(X1,power_set(X2))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_30,negated_conjecture,
( ~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0)
| ~ subset(esk4_0,sum(singleton(esk4_0))) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
( ~ member(sum(singleton(esk4_0)),power_set(esk4_0))
| ~ subset(esk4_0,sum(singleton(esk4_0))) ),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_32,negated_conjecture,
( esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)) = esk4_0
| ~ member(esk4_0,power_set(sum(singleton(esk4_0)))) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
( member(X1,power_set(sum(X2)))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_29]) ).
cnf(c_0_35,negated_conjecture,
( ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0)))
| ~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_22]) ).
cnf(c_0_36,negated_conjecture,
( ~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0)
| ~ member(esk4_0,power_set(sum(singleton(esk4_0)))) ),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_37,negated_conjecture,
( member(esk1_2(esk4_0,sum(singleton(esk4_0))),esk4_0)
| ~ member(sum(singleton(esk4_0)),power_set(esk4_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_38,plain,
( member(X1,esk2_2(X1,X2))
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_39,negated_conjecture,
esk2_2(esk1_2(sum(singleton(esk4_0)),esk4_0),singleton(esk4_0)) = esk4_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_40,negated_conjecture,
~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),esk4_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_28]),c_0_34])]),c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( ~ member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(singleton(esk4_0)))
| ~ member(sum(singleton(esk4_0)),power_set(esk4_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_42,negated_conjecture,
( member(esk1_2(esk4_0,sum(singleton(esk4_0))),sum(X1))
| ~ member(sum(singleton(esk4_0)),power_set(esk4_0))
| ~ member(esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_37]) ).
cnf(c_0_43,negated_conjecture,
~ member(esk1_2(sum(singleton(esk4_0)),esk4_0),sum(singleton(esk4_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_44,negated_conjecture,
~ member(sum(singleton(esk4_0)),power_set(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_34])]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_24]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET351+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 15:15:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.54 start to proof: theBenchmark
% 1.23/1.45 % Version : CSE_E---1.5
% 1.23/1.45 % Problem : theBenchmark.p
% 1.23/1.45 % Proof found
% 1.23/1.45 % SZS status Theorem for theBenchmark.p
% 1.23/1.45 % SZS output start Proof
% See solution above
% 1.23/1.45 % Total time : 0.897000 s
% 1.23/1.45 % SZS output end Proof
% 1.23/1.45 % Total time : 0.900000 s
%------------------------------------------------------------------------------