TSTP Solution File: SET941+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET941+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n026.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 14:36:22 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 34 ( 2 unt; 12 typ; 0 def)
% Number of atoms : 75 ( 9 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 81 ( 28 ~; 36 |; 9 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 53 ( 0 sgn; 26 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
subset: ( $i * $i ) > $o ).
tff(decl_24,type,
union: $i > $i ).
tff(decl_25,type,
empty: $i > $o ).
tff(decl_26,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk5_0: $i ).
tff(decl_31,type,
esk6_0: $i ).
tff(decl_32,type,
esk7_0: $i ).
tff(decl_33,type,
esk8_0: $i ).
fof(d4_tarski,axiom,
! [X1,X2] :
( X2 = union(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X3,X4)
& in(X4,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(t94_zfmisc_1,conjecture,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> subset(X3,X2) )
=> subset(union(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_3,plain,
! [X13,X14,X15,X17,X18,X19,X20,X22] :
( ( in(X15,esk2_3(X13,X14,X15))
| ~ in(X15,X14)
| X14 != union(X13) )
& ( in(esk2_3(X13,X14,X15),X13)
| ~ in(X15,X14)
| X14 != union(X13) )
& ( ~ in(X17,X18)
| ~ in(X18,X13)
| in(X17,X14)
| X14 != union(X13) )
& ( ~ in(esk3_2(X19,X20),X20)
| ~ in(esk3_2(X19,X20),X22)
| ~ in(X22,X19)
| X20 = union(X19) )
& ( in(esk3_2(X19,X20),esk4_2(X19,X20))
| in(esk3_2(X19,X20),X20)
| X20 = union(X19) )
& ( in(esk4_2(X19,X20),X19)
| in(esk3_2(X19,X20),X20)
| X20 = union(X19) ) ),
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)],[d4_tarski])])])])])]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> subset(X3,X2) )
=> subset(union(X1),X2) ),
inference(assume_negation,[status(cth)],[t94_zfmisc_1]) ).
cnf(c_0_5,plain,
( in(esk2_3(X1,X2,X3),X1)
| ~ in(X3,X2)
| X2 != union(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_6,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ subset(X7,X8)
| ~ in(X9,X7)
| in(X9,X8) )
& ( in(esk1_2(X10,X11),X10)
| subset(X10,X11) )
& ( ~ in(esk1_2(X10,X11),X11)
| subset(X10,X11) ) ),
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_7,negated_conjecture,
! [X29] :
( ( ~ in(X29,esk7_0)
| subset(X29,esk8_0) )
& ~ subset(union(esk7_0),esk8_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_8,plain,
( in(esk2_3(X1,union(X1),X2),X1)
| ~ in(X2,union(X1)) ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( in(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( subset(X1,esk8_0)
| ~ in(X1,esk7_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( subset(union(X1),X2)
| in(esk2_3(X1,union(X1),esk1_2(union(X1),X2)),X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
( in(X1,esk2_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != union(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_13,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( subset(esk2_3(esk7_0,union(esk7_0),esk1_2(union(esk7_0),X1)),esk8_0)
| subset(union(esk7_0),X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( in(X1,esk2_3(X2,union(X2),X1))
| ~ in(X1,union(X2)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( subset(union(esk7_0),X1)
| in(X2,esk8_0)
| ~ in(X2,esk2_3(esk7_0,union(esk7_0),esk1_2(union(esk7_0),X1))) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( subset(union(X1),X2)
| in(esk1_2(union(X1),X2),esk2_3(X1,union(X1),esk1_2(union(X1),X2))) ),
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| ~ in(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( subset(union(esk7_0),X1)
| in(esk1_2(union(esk7_0),X1),esk8_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
~ subset(union(esk7_0),esk8_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET941+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 09:10:03 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.014000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.016000 s
%------------------------------------------------------------------------------