%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SYO691-1.000 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 09:12:17 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 32 ( 20 unt; 0 nHn; 28 RR)
% Number of literals : 48 ( 0 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(rule_1,axiom,
top(f(f(Z,Y),f(X,a)),f(f(X,f(Y,a)),Z)),
file('theBenchmark.p',rule_1) ).
cnf(prove,negated_conjecture,
~ seq(succ(succ(succ(zero))),X,X),
file('theBenchmark.p',prove) ).
cnf(rewrite_top,axiom,
( step(X,Y)
| ~ top(X,Y) ),
file('theBenchmark.p',rewrite_top) ).
cnf(rewrite_left,axiom,
( step(f(X,Z),f(Y,Z))
| ~ step(X,Y) ),
file('theBenchmark.p',rewrite_left) ).
cnf(rewrite_right,axiom,
( step(f(X,Y),f(X,Z))
| ~ step(Y,Z) ),
file('theBenchmark.p',rewrite_right) ).
cnf(rewrite_sequence_zero,axiom,
seq(zero,X,X),
file('theBenchmark.p',rewrite_sequence_zero) ).
cnf(rewrite_sequence_succ,axiom,
( seq(succ(N),X,Z)
| ~ step(Y,Z)
| ~ seq(N,X,Y) ),
file('theBenchmark.p',rewrite_sequence_succ) ).
cnf(t1,plain,
~ seq(succ(succ(succ(zero))),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a))),
inference(start,[status(thm),parent(0:0)],[prove]) ).
cnf(t2,plain,
( ~ step(f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)))
| ~ seq(succ(succ(zero)),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a)))
| seq(succ(succ(succ(zero))),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a))) ),
inference(extension,[status(thm),parent(t1:1)],[rewrite_sequence_succ]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ step(f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(a,a),f(f(a,a),a))),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a)))
| ~ seq(succ(zero),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(a,a),f(f(a,a),a))))
| seq(succ(succ(zero)),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a))) ),
inference(extension,[status(thm),parent(t2:2)],[rewrite_sequence_succ]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ step(f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(a,a),f(f(a,a),a))))
| ~ seq(zero,f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)))
| seq(succ(zero),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(a,a),f(f(a,a),a)))) ),
inference(extension,[status(thm),parent(t4:2)],[rewrite_sequence_succ]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
seq(zero,f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a))),
inference(extension,[status(thm),parent(t6:2)],[rewrite_sequence_zero]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ top(f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(a,a),f(f(a,a),a))))
| step(f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(a,a),f(f(a,a),a)))) ),
inference(extension,[status(thm),parent(t6:3)],[rewrite_top]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
top(f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(a,a),f(f(a,a),a)))),
inference(extension,[status(thm),parent(t10:2)],[rule_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ step(f(f(a,a),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a))
| step(f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(a,a),f(f(a,a),a))),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a))) ),
inference(extension,[status(thm),parent(t4:3)],[rewrite_right]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:3]) ).
cnf(t16,plain,
( ~ top(f(f(a,a),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a))
| step(f(f(a,a),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a)) ),
inference(extension,[status(thm),parent(t14:2)],[rewrite_top]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
top(f(f(a,a),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a)),
inference(extension,[status(thm),parent(t16:2)],[rule_1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ step(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(f(a,a),a)),f(a,a)))
| step(f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(f(a,a),a)),f(a,a)),f(f(f(a,a),f(a,a)),a))) ),
inference(extension,[status(thm),parent(t2:3)],[rewrite_left]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:3]) ).
cnf(t22,plain,
( ~ top(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(f(a,a),a)),f(a,a)))
| step(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(f(a,a),a)),f(a,a))) ),
inference(extension,[status(thm),parent(t20:2)],[rewrite_top]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
top(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(f(a,a),a)),f(a,a))),
inference(extension,[status(thm),parent(t22:2)],[rule_1]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO691-1.000 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 07:50:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------