%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN986+1.002 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.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 1.24s 1.72s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 5 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 44 ( 22 ~; 16 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 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 : 42 ( 4 sgn 13 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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,X4,X6] :
( r(zero,zero,X5)
& r(zero,X5,X4)
& r(zero,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ck) ).
fof(c_0_3,plain,
! [X16,X17,X18,X19] :
( ~ r(X16,X17,X18)
| ~ r(X18,X17,X19)
| r(X16,succ(X17),X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[hyp2])]) ).
fof(c_0_4,plain,
! [X15] : r(X15,zero,succ(X15)),
inference(variable_rename,[status(thm)],[hyp1]) ).
fof(c_0_5,negated_conjecture,
~ ? [X5,X4,X6] :
( r(zero,zero,X5)
& r(zero,X5,X4)
& r(zero,X4,X6) ),
inference(assume_negation,[status(cth)],[ck]) ).
cnf(c_0_6,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_7,plain,
r(X1,zero,succ(X1)),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
! [X20,X21,X22] :
( ~ r(zero,zero,X20)
| ~ r(zero,X20,X21)
| ~ r(zero,X21,X22) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])]) ).
cnf(c_0_9,plain,
( r(X1,succ(zero),succ(X2))
| ~ r(X1,zero,X2) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,negated_conjecture,
( ~ r(zero,zero,X1)
| ~ r(zero,X1,X2)
| ~ r(zero,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
( r(X1,succ(succ(zero)),succ(X2))
| ~ r(X1,succ(zero),X3)
| ~ r(X3,zero,X2) ),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( ~ r(zero,succ(zero),X1)
| ~ r(zero,X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_13,plain,
( r(X1,succ(succ(zero)),succ(X2))
| ~ r(succ(X3),zero,X2)
| ~ r(X1,zero,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( ~ r(zero,succ(X1),X2)
| ~ r(zero,zero,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_15,plain,
( r(X1,succ(succ(zero)),succ(succ(succ(X2))))
| ~ r(X1,zero,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_7]) ).
cnf(c_0_16,negated_conjecture,
~ r(zero,zero,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_7])]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_16,c_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN986+1.002 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 08:51:59 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.24/1.72 % Version : CSE_E---1.7
% 1.24/1.72 % Problem : theBenchmark.p
% 1.24/1.72 % SZS status Theorem for theBenchmark.p
% 1.24/1.72 % SZS output start CNFRefutation
% See solution above
% 1.24/1.72 % Total time : 1.375s
%------------------------------------------------------------------------------