TSTP Solution File: SET200+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET200+3 : 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 : n018.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 14:33:36 EDT 2023
% Result : Theorem 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 34 ( 4 unt; 9 typ; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 60 ( 21 ~; 26 |; 8 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 2 sgn; 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
union: ( $i * $i ) > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_26,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk3_0: $i ).
tff(decl_28,type,
esk4_0: $i ).
tff(decl_29,type,
esk5_0: $i ).
tff(decl_30,type,
esk6_0: $i ).
fof(prove_th34,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(union(X1,X3),union(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th34) ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(union(X1,X3),union(X2,X4)) ),
inference(assume_negation,[status(cth)],[prove_th34]) ).
fof(c_0_4,plain,
! [X8,X9,X10,X11,X12] :
( ( ~ subset(X8,X9)
| ~ member(X10,X8)
| member(X10,X9) )
& ( member(esk1_2(X11,X12),X11)
| subset(X11,X12) )
& ( ~ member(esk1_2(X11,X12),X12)
| subset(X11,X12) ) ),
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_defn])])])])])]) ).
fof(c_0_5,plain,
! [X5,X6,X7] :
( ( ~ member(X7,union(X5,X6))
| member(X7,X5)
| member(X7,X6) )
& ( ~ member(X7,X5)
| member(X7,union(X5,X6)) )
& ( ~ member(X7,X6)
| member(X7,union(X5,X6)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
fof(c_0_6,negated_conjecture,
( subset(esk3_0,esk4_0)
& subset(esk5_0,esk6_0)
& ~ subset(union(esk3_0,esk5_0),union(esk4_0,esk6_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_7,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( member(X1,esk6_0)
| ~ member(X1,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_18,negated_conjecture,
( member(X1,esk4_0)
| ~ member(X1,esk3_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_19,negated_conjecture,
( subset(X1,union(X2,esk6_0))
| ~ member(esk1_2(X1,union(X2,esk6_0)),esk5_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( subset(union(X1,X2),X3)
| member(esk1_2(union(X1,X2),X3),X1)
| member(esk1_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( subset(X1,union(esk4_0,X2))
| ~ member(esk1_2(X1,union(esk4_0,X2)),esk3_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
( subset(union(X1,esk5_0),union(X2,esk6_0))
| member(esk1_2(union(X1,esk5_0),union(X2,esk6_0)),X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
~ subset(union(esk3_0,esk5_0),union(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n018.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 : Sat Aug 26 14:27:00 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.63 % Version : CSE_E---1.5
% 0.20/0.63 % Problem : theBenchmark.p
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark.p
% 0.20/0.63 % SZS output start Proof
% See solution above
% 0.20/0.63 % Total time : 0.062000 s
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time : 0.065000 s
%------------------------------------------------------------------------------