TSTP Solution File: COL032-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL032-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 : Fri Jul 15 00:36:15 EDT 2022
% Result : Unsatisfiable 1.38s 1.62s
% Output : CNFRefutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 29 ( 18 unt; 0 nHn; 20 RR)
% Number of literals : 45 ( 44 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(m_definition,axiom,
apply(m,X) = apply(X,X) ).
cnf(q_definition,axiom,
apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)) ).
cnf(prove_fixed_point,negated_conjecture,
apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))) ).
cnf(refute_0_0,plain,
apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))) != apply(f(apply(apply(q,X_2),X_3)),apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3)))),
inference(subst,[],[prove_fixed_point:[bind(Y,$fot(apply(apply(q,X_2),X_3)))]]) ).
cnf(refute_0_1,plain,
apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))) = apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3)))),
inference(subst,[],[q_definition:[bind(X,$fot(X_2)),bind(Y,$fot(X_3)),bind(Z,$fot(f(apply(apply(q,X_2),X_3))))]]) ).
cnf(refute_0_2,plain,
( apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))) != apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3))))
| apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))) != apply(f(apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3)))))
| apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))) = apply(f(apply(apply(q,X_2),X_3)),apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))),apply(f(apply(apply(q,X_2),X_3)),apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))))) ),[1,1],$fot(apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3)))))]]) ).
cnf(refute_0_3,plain,
( apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))) != apply(f(apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3)))))
| apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))) = apply(f(apply(apply(q,X_2),X_3)),apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3)))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3))))) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))) != apply(f(apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))),apply(f(apply(apply(q,X_2),X_3)),apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))))) )],[refute_0_3,refute_0_0]) ).
cnf(refute_0_5,plain,
( apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3)))) != apply(f(apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3)))))
| apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))) != apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3))))
| apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))) = apply(f(apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3))))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3))))) ),[1],$fot(apply(f(apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3))))))]]) ).
cnf(refute_0_6,plain,
( apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3)))) != apply(f(apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3)))))
| apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))) = apply(f(apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3))))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3))))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3)))) != apply(f(apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3))))),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,X_2),X_3),f(apply(apply(q,X_2),X_3))),apply(f(apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,f(apply(apply(q,X_2),X_3)))))) )],[refute_0_6,refute_0_4]) ).
cnf(refute_0_8,plain,
apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))) != apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))),
inference(subst,[],[refute_0_7:[bind(X_2,$fot(apply(q,X_48))),bind(X_3,$fot(X_48))]]) ).
cnf(refute_0_9,plain,
apply(m,apply(apply(q,X_2),X_3)) = apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3)),
inference(subst,[],[m_definition:[bind(X,$fot(apply(apply(q,X_2),X_3)))]]) ).
cnf(refute_0_10,plain,
apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3)) = apply(X_3,apply(X_2,apply(apply(q,X_2),X_3))),
inference(subst,[],[q_definition:[bind(X,$fot(X_2)),bind(Y,$fot(X_3)),bind(Z,$fot(apply(apply(q,X_2),X_3)))]]) ).
cnf(refute_0_11,plain,
( apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3)) != apply(X_3,apply(X_2,apply(apply(q,X_2),X_3)))
| apply(m,apply(apply(q,X_2),X_3)) != apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3))
| apply(m,apply(apply(q,X_2),X_3)) = apply(X_3,apply(X_2,apply(apply(q,X_2),X_3))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(m,apply(apply(q,X_2),X_3)),apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3))) ),[1],$fot(apply(X_3,apply(X_2,apply(apply(q,X_2),X_3))))]]) ).
cnf(refute_0_12,plain,
( apply(m,apply(apply(q,X_2),X_3)) != apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3))
| apply(m,apply(apply(q,X_2),X_3)) = apply(X_3,apply(X_2,apply(apply(q,X_2),X_3))) ),
inference(resolve,[$cnf( $equal(apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3)),apply(X_3,apply(X_2,apply(apply(q,X_2),X_3)))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
apply(m,apply(apply(q,X_2),X_3)) = apply(X_3,apply(X_2,apply(apply(q,X_2),X_3))),
inference(resolve,[$cnf( $equal(apply(m,apply(apply(q,X_2),X_3)),apply(apply(apply(q,X_2),X_3),apply(apply(q,X_2),X_3))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))) = apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))),
inference(subst,[],[refute_0_13:[bind(X_2,$fot(X_48)),bind(X_3,$fot(f(apply(apply(q,apply(q,X_48)),X_48))))]]) ).
cnf(refute_0_15,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_17,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))) != apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))))
| apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))) = apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))))),bind(Y0,$fot(apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))))))]]) ).
cnf(refute_0_19,plain,
apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))) = apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))),
inference(resolve,[$cnf( $equal(apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))),apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))))) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))) != apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))
| apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))) != apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))
| apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))) = apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))),apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))))) ),[1],$fot(apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))))]]) ).
cnf(refute_0_21,plain,
( apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))) != apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))
| apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))) = apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))) ),
inference(resolve,[$cnf( $equal(apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))),apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48))))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))) != apply(m,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))),
inference(resolve,[$cnf( $equal(apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))),apply(f(apply(apply(q,apply(q,X_48)),X_48)),apply(X_48,apply(apply(q,X_48),f(apply(apply(q,apply(q,X_48)),X_48)))))) )],[refute_0_21,refute_0_8]) ).
cnf(refute_0_23,plain,
apply(m,apply(apply(q,m),f(apply(apply(q,apply(q,m)),m)))) != apply(m,apply(apply(q,m),f(apply(apply(q,apply(q,m)),m)))),
inference(subst,[],[refute_0_22:[bind(X_48,$fot(m))]]) ).
cnf(refute_0_24,plain,
apply(m,apply(apply(q,m),f(apply(apply(q,apply(q,m)),m)))) = apply(m,apply(apply(q,m),f(apply(apply(q,apply(q,m)),m)))),
introduced(tautology,[refl,[$fot(apply(m,apply(apply(q,m),f(apply(apply(q,apply(q,m)),m)))))]]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( $equal(apply(m,apply(apply(q,m),f(apply(apply(q,apply(q,m)),m)))),apply(m,apply(apply(q,m),f(apply(apply(q,apply(q,m)),m))))) )],[refute_0_24,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL032-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue May 31 12:13:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.38/1.62 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.38/1.62
% 1.38/1.62 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.38/1.62
%------------------------------------------------------------------------------