%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYN986+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 09:11:20 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 23 ~; 16 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 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 : 38 ( 1 sgn 27 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(hyp1,axiom,
! [Y] : r(Y,zero,succ(Y)),
file('SYN002+0.ax',hyp1) ).
fof(hyp2,axiom,
! [Y,X,Z,Z1] :
( r(Y,X,Z)
=> ( r(Z,X,Z1)
=> r(Y,succ(X),Z1) ) ),
file('SYN002+0.ax',hyp2) ).
fof(ck,conjecture,
? [Z1,Z0] :
( r(zero,Z1,Z0)
& r(zero,zero,Z1) ),
file('theBenchmark.p',ck) ).
fof(f_1_1,plain,
! [Y] : r(Y,zero,succ(Y)),
inference(fof_nnf,[status(thm)],[hyp1]) ).
fof(f_1_2,plain,
! [U_0] : r(U_0,zero,succ(U_0)),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
r(U_0,zero,succ(U_0)),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [Y,X,Z,Z1] :
( r(Y,succ(X),Z1)
| ~ r(Z,X,Z1)
| ~ r(Y,X,Z) ),
inference(fof_nnf,[status(thm)],[hyp2]) ).
fof(f_2_2,plain,
! [U_4,U_3,U_2,U_1] :
( r(U_4,succ(U_3),U_1)
| ~ r(U_2,U_3,U_1)
| ~ r(U_4,U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_4,U_3,U_2] :
( ! [U_1] :
( r(U_4,succ(U_3),U_1)
| ~ r(U_2,U_3,U_1) )
| ~ r(U_4,U_3,U_2) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( r(U_4,succ(U_3),U_1)
| ~ r(U_2,U_3,U_1)
| ~ r(U_4,U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,negated_conjecture,
~ ? [Z1,Z0] :
( r(zero,Z1,Z0)
& r(zero,zero,Z1) ),
inference(negate,[status(cth)],[ck]) ).
fof(f_3_2,negated_conjecture,
! [Z1,Z0] :
( ~ r(zero,Z1,Z0)
| ~ r(zero,zero,Z1) ),
inference(fof_nnf,[status(thm)],[f_3_1]) ).
fof(f_3_3,negated_conjecture,
! [U_6,U_5] :
( ~ r(zero,U_6,U_5)
| ~ r(zero,zero,U_6) ),
inference(variable_rename,[status(thm)],[f_3_2]) ).
fof(f_3_4,negated_conjecture,
! [U_6] :
( ! [U_5] : ~ r(zero,U_6,U_5)
| ~ r(zero,zero,U_6) ),
inference(miniscope,[status(thm)],[f_3_3]) ).
fof(f_3_5,negated_conjecture,
! [U_6,U_5] :
( ~ r(zero,U_6,U_5)
| ~ r(zero,zero,U_6) ),
inference(definitional_conversion,[status(esa)],[f_3_4]) ).
cnf(f_3_6,negated_conjecture,
( ~ r(zero,U_6,U_5)
| ~ r(zero,zero,U_6) ),
inference(clausify,[status(thm)],[f_3_5]) ).
cnf(t1,plain,
( ~ r(zero,succ(zero),succ(succ(zero)))
| ~ r(zero,zero,succ(zero)) ),
inference(start,[status(thm),parent(0:0)],[f_3_6]) ).
cnf(t2,plain,
r(zero,zero,succ(zero)),
inference(extension,[status(thm),parent(t1:1)],[f_1_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ r(succ(zero),zero,succ(succ(zero)))
| ~ r(zero,zero,succ(zero))
| r(zero,succ(zero),succ(succ(zero))) ),
inference(extension,[status(thm),parent(t1:2)],[f_2_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
r(zero,zero,succ(zero)),
inference(extension,[status(thm),parent(t4:2)],[f_1_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
r(succ(zero),zero,succ(succ(zero))),
inference(extension,[status(thm),parent(t4:3)],[f_1_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN986+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 07:32:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------