%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN986+1.003 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n002.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 : Tue May 5 05:51:12 PM UTC 2026
% Result : Theorem 1.07s 1.85s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 5 unt; 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 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 ?)
% Comments :
%------------------------------------------------------------------------------
fof(hyp2,axiom,
! [X1,X2,X3,X4] :
( r(X1,X2,X3)
=> ( r(X3,X2,X4)
=> r(X1,succ(X2),X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN002+0.ax',hyp2) ).
fof(hyp1,axiom,
! [X1] : r(X1,zero,succ(X1)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ck) ).
fof(c_0_3,plain,
! [X18,X19,X20,X21] :
( ~ r(X18,X19,X20)
| ~ r(X20,X19,X21)
| r(X18,succ(X19),X21) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[hyp2])]) ).
fof(c_0_4,plain,
! [X17] : r(X17,zero,succ(X17)),
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,
! [X22,X23,X24,X25] :
( ~ r(zero,zero,X22)
| ~ r(zero,X22,X23)
| ~ r(zero,X23,X24)
| ~ r(zero,X24,X25) ),
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
% 0.02/0.21 % Problem : SYN986+1.003 : TPTP v9.2.1. Released v4.0.0.
% 0.02/0.21 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.45 % Computer : n002.cluster.edu
% 0.12/0.45 % Model : x86_64 x86_64
% 0.12/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.45 % Memory : 8042.1875MB
% 0.12/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.45 % CPULimit : 300
% 0.12/0.45 % WCLimit : 300
% 0.12/0.45 % DateTime : Tue May 5 08:52:01 EDT 2026
% 0.14/0.46 % CPUTime :
% 0.14/0.47 % start to proof: theBenchmark
% 1.07/1.85 % Version : CSE_E---1.7
% 1.07/1.85 % Problem : theBenchmark.p
% 1.07/1.85 % SZS status Theorem for theBenchmark.p
% 1.07/1.85 % SZS output start CNFRefutation
% See solution above
% 1.07/1.85 % Total time : 1.379s
%------------------------------------------------------------------------------