TSTP Solution File: SET886+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 14:36:08 EDT 2023
% Result : Theorem 0.20s 0.57s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 32 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 31 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 4 |; 1 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 3 sgn; 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
singleton: $i > $i ).
tff(decl_26,type,
esk1_0: $i ).
tff(decl_27,type,
esk2_0: $i ).
tff(decl_28,type,
esk3_0: $i ).
tff(decl_29,type,
esk4_0: $i ).
tff(decl_30,type,
esk5_0: $i ).
fof(t27_zfmisc_1,conjecture,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> unordered_pair(X1,X2) = singleton(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_zfmisc_1) ).
fof(t26_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> X1 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_zfmisc_1) ).
fof(t69_enumset1,axiom,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3] :
( subset(unordered_pair(X1,X2),singleton(X3))
=> unordered_pair(X1,X2) = singleton(X3) ),
inference(assume_negation,[status(cth)],[t27_zfmisc_1]) ).
fof(c_0_5,plain,
! [X9,X10,X11] :
( ~ subset(unordered_pair(X9,X10),singleton(X11))
| X9 = X11 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t26_zfmisc_1])]) ).
fof(c_0_6,plain,
! [X15] : unordered_pair(X15,X15) = singleton(X15),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_7,negated_conjecture,
( subset(unordered_pair(esk3_0,esk4_0),singleton(esk5_0))
& unordered_pair(esk3_0,esk4_0) != singleton(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( X1 = X3
| ~ subset(unordered_pair(X1,X2),singleton(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
subset(unordered_pair(esk3_0,esk4_0),singleton(esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X4,X5] : unordered_pair(X4,X5) = unordered_pair(X5,X4),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,plain,
( X1 = X3
| ~ subset(unordered_pair(X1,X2),unordered_pair(X3,X3)) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
subset(unordered_pair(esk3_0,esk4_0),unordered_pair(esk5_0,esk5_0)),
inference(rw,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
unordered_pair(esk3_0,esk4_0) != singleton(esk5_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
esk3_0 = esk5_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
unordered_pair(esk5_0,esk5_0) != unordered_pair(esk3_0,esk4_0),
inference(rw,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_18,plain,
( X1 = X2
| ~ subset(unordered_pair(X3,X1),unordered_pair(X2,X2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
subset(unordered_pair(esk5_0,esk4_0),unordered_pair(esk5_0,esk5_0)),
inference(spm,[status(thm)],[c_0_13,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
unordered_pair(esk5_0,esk4_0) != unordered_pair(esk5_0,esk5_0),
inference(rw,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
esk4_0 = esk5_0,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET886+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n021.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 16:13:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.55 start to proof: theBenchmark
% 0.20/0.57 % Version : CSE_E---1.5
% 0.20/0.57 % Problem : theBenchmark.p
% 0.20/0.57 % Proof found
% 0.20/0.57 % SZS status Theorem for theBenchmark.p
% 0.20/0.57 % SZS output start Proof
% See solution above
% 0.20/0.57 % Total time : 0.005000 s
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57 % Total time : 0.007000 s
%------------------------------------------------------------------------------