TSTP Solution File: SYN077-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN077-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 08:59:21 EDT 2022
% Result : Unsatisfiable 0.46s 0.69s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of clauses : 48 ( 9 unt; 18 nHn; 40 RR)
% Number of literals : 111 ( 7 equ; 53 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_1,axiom,
( ~ big_f(X,f(Y))
| X = Y ) ).
cnf(clause_2,axiom,
( X != Y
| big_f(X,f(Y)) ) ).
cnf(clause_3,negated_conjecture,
( ~ big_f(X,a)
| ~ big_f(X,Y)
| big_f(g(X,Y),Y) ) ).
cnf(clause_4,negated_conjecture,
( ~ big_f(X,a)
| ~ big_f(X,Y)
| ~ big_f(Z,g(X,Y))
| ~ big_f(Z,Y) ) ).
cnf(clause_5,negated_conjecture,
( big_f(X,h(X))
| big_f(X,a) ) ).
cnf(clause_6,negated_conjecture,
( ~ big_f(X,h(Y))
| big_f(i(Y,X),X)
| big_f(Y,a) ) ).
cnf(clause_7,negated_conjecture,
( big_f(X,a)
| big_f(i(X,Y),h(X))
| ~ big_f(Y,h(X)) ) ).
cnf(refute_0_0,plain,
( Y != Y
| big_f(Y,f(Y)) ),
inference(subst,[],[clause_2:[bind(X,$fot(Y))]]) ).
cnf(refute_0_1,plain,
Y = Y,
introduced(tautology,[refl,[$fot(Y)]]) ).
cnf(refute_0_2,plain,
big_f(Y,f(Y)),
inference(resolve,[$cnf( $equal(Y,Y) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
big_f(a,f(a)),
inference(subst,[],[refute_0_2:[bind(Y,$fot(a))]]) ).
cnf(refute_0_4,plain,
( ~ big_f(Z,f(a))
| ~ big_f(Z,g(a,f(a)))
| ~ big_f(a,a)
| ~ big_f(a,f(a)) ),
inference(subst,[],[clause_4:[bind(X,$fot(a)),bind(Y,$fot(f(a)))]]) ).
cnf(refute_0_5,plain,
( ~ big_f(g(a,f(a)),f(a))
| g(a,f(a)) = a ),
inference(subst,[],[clause_1:[bind(X,$fot(g(a,f(a)))),bind(Y,$fot(a))]]) ).
cnf(refute_0_6,plain,
big_f(X_5,f(X_5)),
inference(subst,[],[refute_0_2:[bind(Y,$fot(X_5))]]) ).
cnf(refute_0_7,plain,
( ~ big_f(X_5,a)
| ~ big_f(X_5,f(X_5))
| big_f(g(X_5,f(X_5)),f(X_5)) ),
inference(subst,[],[clause_3:[bind(X,$fot(X_5)),bind(Y,$fot(f(X_5)))]]) ).
cnf(refute_0_8,plain,
( ~ big_f(X_5,a)
| big_f(g(X_5,f(X_5)),f(X_5)) ),
inference(resolve,[$cnf( big_f(X_5,f(X_5)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ big_f(a,a)
| big_f(g(a,f(a)),f(a)) ),
inference(subst,[],[refute_0_8:[bind(X_5,$fot(a))]]) ).
cnf(refute_0_10,plain,
( big_f(X_9,a)
| big_f(X_9,h(X_9)) ),
inference(subst,[],[clause_5:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_11,plain,
( ~ big_f(X_9,h(X_9))
| big_f(X_9,a)
| big_f(i(X_9,X_9),X_9) ),
inference(subst,[],[clause_6:[bind(X,$fot(X_9)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_12,plain,
( big_f(X_9,a)
| big_f(i(X_9,X_9),X_9) ),
inference(resolve,[$cnf( big_f(X_9,h(X_9)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( big_f(a,a)
| big_f(i(a,a),a) ),
inference(subst,[],[refute_0_12:[bind(X_9,$fot(a))]]) ).
cnf(refute_0_14,plain,
( big_f(X_12,a)
| big_f(X_12,h(X_12)) ),
inference(subst,[],[clause_5:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_15,plain,
( ~ big_f(X_12,h(X_12))
| big_f(X_12,a)
| big_f(i(X_12,X_12),h(X_12)) ),
inference(subst,[],[clause_7:[bind(X,$fot(X_12)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_16,plain,
( big_f(X_12,a)
| big_f(i(X_12,X_12),h(X_12)) ),
inference(resolve,[$cnf( big_f(X_12,h(X_12)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( big_f(a,a)
| big_f(i(a,a),h(a)) ),
inference(subst,[],[refute_0_16:[bind(X_12,$fot(a))]]) ).
cnf(refute_0_18,plain,
( ~ big_f(g(i(a,a),h(a)),h(a))
| big_f(a,a)
| big_f(i(a,g(i(a,a),h(a))),h(a)) ),
inference(subst,[],[clause_7:[bind(X,$fot(a)),bind(Y,$fot(g(i(a,a),h(a))))]]) ).
cnf(refute_0_19,plain,
( ~ big_f(i(a,a),Y)
| ~ big_f(i(a,a),a)
| big_f(g(i(a,a),Y),Y) ),
inference(subst,[],[clause_3:[bind(X,$fot(i(a,a)))]]) ).
cnf(refute_0_20,plain,
( ~ big_f(i(a,a),Y)
| big_f(a,a)
| big_f(g(i(a,a),Y),Y) ),
inference(resolve,[$cnf( big_f(i(a,a),a) )],[refute_0_13,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ big_f(i(a,a),h(a))
| big_f(a,a)
| big_f(g(i(a,a),h(a)),h(a)) ),
inference(subst,[],[refute_0_20:[bind(Y,$fot(h(a)))]]) ).
cnf(refute_0_22,plain,
( big_f(a,a)
| big_f(g(i(a,a),h(a)),h(a)) ),
inference(resolve,[$cnf( big_f(i(a,a),h(a)) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
( big_f(a,a)
| big_f(i(a,g(i(a,a),h(a))),h(a)) ),
inference(resolve,[$cnf( big_f(g(i(a,a),h(a)),h(a)) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( ~ big_f(g(i(a,a),h(a)),h(a))
| big_f(a,a)
| big_f(i(a,g(i(a,a),h(a))),g(i(a,a),h(a))) ),
inference(subst,[],[clause_6:[bind(X,$fot(g(i(a,a),h(a)))),bind(Y,$fot(a))]]) ).
cnf(refute_0_25,plain,
( big_f(a,a)
| big_f(i(a,g(i(a,a),h(a))),g(i(a,a),h(a))) ),
inference(resolve,[$cnf( big_f(g(i(a,a),h(a)),h(a)) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ big_f(i(a,a),a)
| ~ big_f(i(a,a),h(a))
| ~ big_f(i(a,g(i(a,a),h(a))),g(i(a,a),h(a)))
| ~ big_f(i(a,g(i(a,a),h(a))),h(a)) ),
inference(subst,[],[clause_4:[bind(X,$fot(i(a,a))),bind(Y,$fot(h(a))),bind(Z,$fot(i(a,g(i(a,a),h(a)))))]]) ).
cnf(refute_0_27,plain,
( ~ big_f(i(a,a),a)
| ~ big_f(i(a,a),h(a))
| ~ big_f(i(a,g(i(a,a),h(a))),h(a))
| big_f(a,a) ),
inference(resolve,[$cnf( big_f(i(a,g(i(a,a),h(a))),g(i(a,a),h(a))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ big_f(i(a,a),a)
| ~ big_f(i(a,a),h(a))
| big_f(a,a) ),
inference(resolve,[$cnf( big_f(i(a,g(i(a,a),h(a))),h(a)) )],[refute_0_23,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ big_f(i(a,a),a)
| big_f(a,a) ),
inference(resolve,[$cnf( big_f(i(a,a),h(a)) )],[refute_0_17,refute_0_28]) ).
cnf(refute_0_30,plain,
big_f(a,a),
inference(resolve,[$cnf( big_f(i(a,a),a) )],[refute_0_13,refute_0_29]) ).
cnf(refute_0_31,plain,
big_f(g(a,f(a)),f(a)),
inference(resolve,[$cnf( big_f(a,a) )],[refute_0_30,refute_0_9]) ).
cnf(refute_0_32,plain,
g(a,f(a)) = a,
inference(resolve,[$cnf( big_f(g(a,f(a)),f(a)) )],[refute_0_31,refute_0_5]) ).
cnf(refute_0_33,plain,
( g(a,f(a)) != a
| ~ big_f(Z,a)
| big_f(Z,g(a,f(a))) ),
introduced(tautology,[equality,[$cnf( ~ big_f(Z,g(a,f(a))) ),[1],$fot(a)]]) ).
cnf(refute_0_34,plain,
( ~ big_f(Z,a)
| big_f(Z,g(a,f(a))) ),
inference(resolve,[$cnf( $equal(g(a,f(a)),a) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ big_f(Z,a)
| ~ big_f(Z,f(a))
| ~ big_f(a,a)
| ~ big_f(a,f(a)) ),
inference(resolve,[$cnf( big_f(Z,g(a,f(a))) )],[refute_0_34,refute_0_4]) ).
cnf(refute_0_36,plain,
( ~ big_f(Z,a)
| ~ big_f(Z,f(a))
| ~ big_f(a,f(a)) ),
inference(resolve,[$cnf( big_f(a,a) )],[refute_0_30,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ big_f(Z,a)
| ~ big_f(Z,f(a)) ),
inference(resolve,[$cnf( big_f(a,f(a)) )],[refute_0_3,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ big_f(a,a)
| ~ big_f(a,f(a)) ),
inference(subst,[],[refute_0_37:[bind(Z,$fot(a))]]) ).
cnf(refute_0_39,plain,
~ big_f(a,a),
inference(resolve,[$cnf( big_f(a,f(a)) )],[refute_0_3,refute_0_38]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( big_f(a,a) )],[refute_0_30,refute_0_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYN077-1 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.10 % Command : metis --show proof --show saturation %s
% 0.10/0.30 % Computer : n018.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Mon Jul 11 22:47:14 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.14/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.46/0.69 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.46/0.69
% 0.46/0.69 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.46/0.69
%------------------------------------------------------------------------------