TSTP Solution File: SYN986+1.003 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SYN986+1.003 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 : Fri Sep 1 02:00:29 EDT 2023
% Result : Theorem 0.20s 0.55s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 5 unt; 3 typ; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 77 ( 38 ~; 31 |; 6 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 16 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 66 ( 5 sgn; 14 !; 8 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
zero: $i ).
tff(decl_23,type,
succ: $i > $i ).
tff(decl_24,type,
r: ( $i * $i * $i ) > $o ).
fof(hyp2,axiom,
! [X1,X2,X3,X4] :
( r(X1,X2,X3)
=> ( r(X3,X2,X4)
=> r(X1,succ(X2),X4) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN002+0.ax',hyp2) ).
fof(hyp1,axiom,
! [X1] : r(X1,zero,succ(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SYN002+0.ax',hyp1) ).
fof(ck,conjecture,
? [X5,X6,X4,X7] :
( r(zero,zero,X5)
& r(zero,X5,X6)
& r(zero,X6,X4)
& r(zero,X4,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ck) ).
fof(c_0_3,plain,
! [X9,X10,X11,X12] :
( ~ r(X9,X10,X11)
| ~ r(X11,X10,X12)
| r(X9,succ(X10),X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[hyp2])]) ).
fof(c_0_4,plain,
! [X8] : r(X8,zero,succ(X8)),
inference(variable_rename,[status(thm)],[hyp1]) ).
cnf(c_0_5,plain,
( r(X1,succ(X2),X4)
| ~ r(X1,X2,X3)
| ~ r(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_6,plain,
r(X1,zero,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( r(X1,succ(zero),succ(X2))
| ~ r(X1,zero,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
( r(X1,succ(succ(zero)),succ(X2))
| ~ r(X1,succ(zero),X3)
| ~ r(X3,zero,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_9,plain,
( r(X1,succ(succ(zero)),succ(X2))
| ~ r(succ(X3),zero,X2)
| ~ r(X1,zero,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_10,plain,
( r(X1,succ(succ(zero)),succ(succ(succ(X2))))
| ~ r(X1,zero,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_6]) ).
fof(c_0_11,negated_conjecture,
~ ? [X5,X6,X4,X7] :
( r(zero,zero,X5)
& r(zero,X5,X6)
& r(zero,X6,X4)
& r(zero,X4,X7) ),
inference(assume_negation,[status(cth)],[ck]) ).
cnf(c_0_12,plain,
( r(X1,succ(succ(succ(zero))),succ(succ(succ(X2))))
| ~ r(X1,succ(succ(zero)),X3)
| ~ r(X3,zero,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_10]) ).
fof(c_0_13,negated_conjecture,
! [X13,X14,X15,X16] :
( ~ r(zero,zero,X13)
| ~ r(zero,X13,X14)
| ~ r(zero,X14,X15)
| ~ r(zero,X15,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
cnf(c_0_14,plain,
( r(X1,succ(succ(succ(zero))),succ(succ(succ(X2))))
| ~ r(succ(succ(succ(X3))),zero,X2)
| ~ r(X1,zero,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( ~ r(zero,zero,X1)
| ~ r(zero,X1,X2)
| ~ r(zero,X2,X3)
| ~ r(zero,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
( r(X1,succ(succ(succ(zero))),succ(succ(succ(succ(succ(succ(succ(X2))))))))
| ~ r(X1,zero,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_6]) ).
cnf(c_0_17,negated_conjecture,
( ~ r(zero,succ(zero),X1)
| ~ r(zero,X2,X3)
| ~ r(zero,X1,X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_6]) ).
cnf(c_0_18,plain,
( r(X1,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(X2))))))))
| ~ r(X1,succ(succ(succ(zero))),X3)
| ~ r(X3,zero,X2) ),
inference(spm,[status(thm)],[c_0_5,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( ~ r(zero,succ(X1),X2)
| ~ r(zero,zero,X1)
| ~ r(zero,X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_7]) ).
cnf(c_0_20,plain,
( r(X1,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(X2))))))))
| ~ r(succ(succ(succ(succ(succ(succ(succ(X3))))))),zero,X2)
| ~ r(X1,zero,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( ~ r(zero,succ(succ(succ(X1))),X2)
| ~ r(zero,zero,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_10]),c_0_6])]) ).
cnf(c_0_22,plain,
( r(X1,succ(succ(succ(succ(zero)))),succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(succ(X2))))))))))))))))
| ~ r(X1,zero,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_6]) ).
cnf(c_0_23,negated_conjecture,
~ r(zero,zero,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_6])]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_23,c_0_6]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SYN986+1.003 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 17:49:12 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.54 start to proof: theBenchmark
% 0.20/0.55 % Version : CSE_E---1.5
% 0.20/0.55 % Problem : theBenchmark.p
% 0.20/0.55 % Proof found
% 0.20/0.55 % SZS status Theorem for theBenchmark.p
% 0.20/0.55 % SZS output start Proof
% See solution above
% 0.20/0.56 % Total time : 0.006000 s
% 0.20/0.56 % SZS output end Proof
% 0.20/0.56 % Total time : 0.009000 s
%------------------------------------------------------------------------------