TSTP Solution File: SYO691-1.000 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYO691-1.000 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% 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 : 600s
% DateTime : Thu Jul 21 18:40:56 EDT 2022
% Result : Unsatisfiable 0.20s 0.46s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 32 ( 16 unt; 0 nHn; 16 RR)
% Number of literals : 52 ( 0 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 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 : 104 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(rule_1,axiom,
top(f(f(Z,Y),f(X,a)),f(f(X,f(Y,a)),Z)) ).
cnf(prove,negated_conjecture,
~ seq(succ(succ(succ(zero))),X,X) ).
cnf(rewrite_top,axiom,
( ~ top(X,Y)
| step(X,Y) ) ).
cnf(rewrite_left,axiom,
( ~ step(X,Y)
| step(f(X,Z),f(Y,Z)) ) ).
cnf(rewrite_right,axiom,
( ~ step(Y,Z)
| step(f(X,Y),f(X,Z)) ) ).
cnf(rewrite_sequence_zero,axiom,
seq(zero,X,X) ).
cnf(rewrite_sequence_succ,axiom,
( ~ seq(N,X,Y)
| ~ step(Y,Z)
| seq(succ(N),X,Z) ) ).
cnf(refute_0_0,plain,
~ seq(succ(succ(succ(zero))),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(a,a)),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a))),
inference(subst,[],[prove:[bind(X,$fot(f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a))))]]) ).
cnf(refute_0_1,plain,
( ~ top(f(f(X_6,X_5),f(X_4,a)),f(f(X_4,f(X_5,a)),X_6))
| step(f(f(X_6,X_5),f(X_4,a)),f(f(X_4,f(X_5,a)),X_6)) ),
inference(subst,[],[rewrite_top:[bind(X,$fot(f(f(X_6,X_5),f(X_4,a)))),bind(Y,$fot(f(f(X_4,f(X_5,a)),X_6)))]]) ).
cnf(refute_0_2,plain,
top(f(f(X_6,X_5),f(X_4,a)),f(f(X_4,f(X_5,a)),X_6)),
inference(subst,[],[rule_1:[bind(X,$fot(X_4)),bind(Y,$fot(X_5)),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_3,plain,
step(f(f(X_6,X_5),f(X_4,a)),f(f(X_4,f(X_5,a)),X_6)),
inference(resolve,[$cnf( top(f(f(X_6,X_5),f(X_4,a)),f(f(X_4,f(X_5,a)),X_6)) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
( ~ step(f(f(X_6,X_5),f(X_4,a)),f(f(X_4,f(X_5,a)),X_6))
| step(f(f(f(X_6,X_5),f(X_4,a)),X_12),f(f(f(X_4,f(X_5,a)),X_6),X_12)) ),
inference(subst,[],[rewrite_left:[bind(X,$fot(f(f(X_6,X_5),f(X_4,a)))),bind(Y,$fot(f(f(X_4,f(X_5,a)),X_6))),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_5,plain,
step(f(f(f(X_6,X_5),f(X_4,a)),X_12),f(f(f(X_4,f(X_5,a)),X_6),X_12)),
inference(resolve,[$cnf( step(f(f(X_6,X_5),f(X_4,a)),f(f(X_4,f(X_5,a)),X_6)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
seq(zero,X_70,X_70),
inference(subst,[],[rewrite_sequence_zero:[bind(X,$fot(X_70))]]) ).
cnf(refute_0_7,plain,
( ~ seq(zero,X_70,X_70)
| ~ step(X_70,X_71)
| seq(succ(zero),X_70,X_71) ),
inference(subst,[],[rewrite_sequence_succ:[bind(N,$fot(zero)),bind(X,$fot(X_70)),bind(Y,$fot(X_70)),bind(Z,$fot(X_71))]]) ).
cnf(refute_0_8,plain,
( ~ step(X_70,X_71)
| seq(succ(zero),X_70,X_71) ),
inference(resolve,[$cnf( seq(zero,X_70,X_70) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ step(f(f(f(X_6,X_5),f(X_4,a)),X_12),f(f(f(X_4,f(X_5,a)),X_6),X_12))
| seq(succ(zero),f(f(f(X_6,X_5),f(X_4,a)),X_12),f(f(f(X_4,f(X_5,a)),X_6),X_12)) ),
inference(subst,[],[refute_0_8:[bind(X_70,$fot(f(f(f(X_6,X_5),f(X_4,a)),X_12))),bind(X_71,$fot(f(f(f(X_4,f(X_5,a)),X_6),X_12)))]]) ).
cnf(refute_0_10,plain,
seq(succ(zero),f(f(f(X_6,X_5),f(X_4,a)),X_12),f(f(f(X_4,f(X_5,a)),X_6),X_12)),
inference(resolve,[$cnf( step(f(f(f(X_6,X_5),f(X_4,a)),X_12),f(f(f(X_4,f(X_5,a)),X_6),X_12)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
seq(succ(zero),f(f(f(X_341,X_5),f(X_4,a)),f(X_340,a)),f(f(f(X_4,f(X_5,a)),X_341),f(X_340,a))),
inference(subst,[],[refute_0_10:[bind(X_12,$fot(f(X_340,a))),bind(X_6,$fot(X_341))]]) ).
cnf(refute_0_12,plain,
( ~ seq(X_68,X_69,f(f(X_6,X_5),f(X_4,a)))
| ~ step(f(f(X_6,X_5),f(X_4,a)),f(f(X_4,f(X_5,a)),X_6))
| seq(succ(X_68),X_69,f(f(X_4,f(X_5,a)),X_6)) ),
inference(subst,[],[rewrite_sequence_succ:[bind(N,$fot(X_68)),bind(X,$fot(X_69)),bind(Y,$fot(f(f(X_6,X_5),f(X_4,a)))),bind(Z,$fot(f(f(X_4,f(X_5,a)),X_6)))]]) ).
cnf(refute_0_13,plain,
( ~ seq(X_68,X_69,f(f(X_6,X_5),f(X_4,a)))
| seq(succ(X_68),X_69,f(f(X_4,f(X_5,a)),X_6)) ),
inference(resolve,[$cnf( step(f(f(X_6,X_5),f(X_4,a)),f(f(X_4,f(X_5,a)),X_6)) )],[refute_0_3,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ seq(succ(zero),f(f(f(X_341,X_5),f(X_4,a)),f(X_340,a)),f(f(f(X_4,f(X_5,a)),X_341),f(X_340,a)))
| seq(succ(succ(zero)),f(f(f(X_341,X_5),f(X_4,a)),f(X_340,a)),f(f(X_340,f(X_341,a)),f(X_4,f(X_5,a)))) ),
inference(subst,[],[refute_0_13:[bind(X_4,$fot(X_340)),bind(X_5,$fot(X_341)),bind(X_6,$fot(f(X_4,f(X_5,a)))),bind(X_68,$fot(succ(zero))),bind(X_69,$fot(f(f(f(X_341,X_5),f(X_4,a)),f(X_340,a))))]]) ).
cnf(refute_0_15,plain,
seq(succ(succ(zero)),f(f(f(X_341,X_5),f(X_4,a)),f(X_340,a)),f(f(X_340,f(X_341,a)),f(X_4,f(X_5,a)))),
inference(resolve,[$cnf( seq(succ(zero),f(f(f(X_341,X_5),f(X_4,a)),f(X_340,a)),f(f(f(X_4,f(X_5,a)),X_341),f(X_340,a))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
seq(succ(succ(zero)),f(f(f(X_341,X_522),f(f(X_524,X_523),a)),f(X_340,a)),f(f(X_340,f(X_341,a)),f(f(X_524,X_523),f(X_522,a)))),
inference(subst,[],[refute_0_15:[bind(X_4,$fot(f(X_524,X_523))),bind(X_5,$fot(X_522))]]) ).
cnf(refute_0_17,plain,
( ~ step(f(f(X_6,X_5),f(X_4,a)),f(f(X_4,f(X_5,a)),X_6))
| step(f(X_13,f(f(X_6,X_5),f(X_4,a))),f(X_13,f(f(X_4,f(X_5,a)),X_6))) ),
inference(subst,[],[rewrite_right:[bind(X,$fot(X_13)),bind(Y,$fot(f(f(X_6,X_5),f(X_4,a)))),bind(Z,$fot(f(f(X_4,f(X_5,a)),X_6)))]]) ).
cnf(refute_0_18,plain,
step(f(X_13,f(f(X_6,X_5),f(X_4,a))),f(X_13,f(f(X_4,f(X_5,a)),X_6))),
inference(resolve,[$cnf( step(f(f(X_6,X_5),f(X_4,a)),f(f(X_4,f(X_5,a)),X_6)) )],[refute_0_3,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ seq(X_68,X_69,f(X_13,f(f(X_6,X_5),f(X_4,a))))
| ~ step(f(X_13,f(f(X_6,X_5),f(X_4,a))),f(X_13,f(f(X_4,f(X_5,a)),X_6)))
| seq(succ(X_68),X_69,f(X_13,f(f(X_4,f(X_5,a)),X_6))) ),
inference(subst,[],[rewrite_sequence_succ:[bind(N,$fot(X_68)),bind(X,$fot(X_69)),bind(Y,$fot(f(X_13,f(f(X_6,X_5),f(X_4,a))))),bind(Z,$fot(f(X_13,f(f(X_4,f(X_5,a)),X_6))))]]) ).
cnf(refute_0_20,plain,
( ~ seq(X_68,X_69,f(X_13,f(f(X_6,X_5),f(X_4,a))))
| seq(succ(X_68),X_69,f(X_13,f(f(X_4,f(X_5,a)),X_6))) ),
inference(resolve,[$cnf( step(f(X_13,f(f(X_6,X_5),f(X_4,a))),f(X_13,f(f(X_4,f(X_5,a)),X_6))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ seq(succ(succ(zero)),f(f(f(X_341,X_522),f(f(X_524,X_523),a)),f(X_340,a)),f(f(X_340,f(X_341,a)),f(f(X_524,X_523),f(X_522,a))))
| seq(succ(succ(succ(zero))),f(f(f(X_341,X_522),f(f(X_524,X_523),a)),f(X_340,a)),f(f(X_340,f(X_341,a)),f(f(X_522,f(X_523,a)),X_524))) ),
inference(subst,[],[refute_0_20:[bind(X_13,$fot(f(X_340,f(X_341,a)))),bind(X_4,$fot(X_522)),bind(X_5,$fot(X_523)),bind(X_6,$fot(X_524)),bind(X_68,$fot(succ(succ(zero)))),bind(X_69,$fot(f(f(f(X_341,X_522),f(f(X_524,X_523),a)),f(X_340,a))))]]) ).
cnf(refute_0_22,plain,
seq(succ(succ(succ(zero))),f(f(f(X_341,X_522),f(f(X_524,X_523),a)),f(X_340,a)),f(f(X_340,f(X_341,a)),f(f(X_522,f(X_523,a)),X_524))),
inference(resolve,[$cnf( seq(succ(succ(zero)),f(f(f(X_341,X_522),f(f(X_524,X_523),a)),f(X_340,a)),f(f(X_340,f(X_341,a)),f(f(X_524,X_523),f(X_522,a)))) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
seq(succ(succ(succ(zero))),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a)),f(f(f(f(a,a),f(a,a)),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a))),
inference(subst,[],[refute_0_22:[bind(X_340,$fot(f(f(a,a),f(a,a)))),bind(X_341,$fot(f(a,a))),bind(X_522,$fot(f(a,a))),bind(X_523,$fot(a)),bind(X_524,$fot(a))]]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( seq(succ(succ(succ(zero))),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(a,a)),f(f(a,a),a)),f(f(f(a,a),f(a,a)),a))) )],[refute_0_23,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYO691-1.000 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 8 19:00:38 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46
% 0.20/0.46 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.47
%------------------------------------------------------------------------------