TSTP Solution File: LDA007-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LDA007-2 : TPTP v8.1.0. Bugfixed v2.6.0.
% 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 : Sun Jul 17 16:44:59 EDT 2022
% Result : Unsatisfiable 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of clauses : 54 ( 28 unt; 0 nHn; 48 RR)
% Number of literals : 90 ( 89 equ; 37 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a1,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)) ).
cnf(clause_1,axiom,
tt = f(t,t) ).
cnf(clause_3,axiom,
ts = f(t,s) ).
cnf(clause_4,axiom,
tt_ts = f(tt,ts) ).
cnf(clause_7,axiom,
tk = f(t,k) ).
cnf(clause_9,axiom,
tsk = f(ts,k) ).
cnf(prove_equation,negated_conjecture,
f(t,tsk) != f(tt_ts,tk) ).
cnf(refute_0_0,plain,
f(t,f(X_14,k)) = f(f(t,X_14),f(t,k)),
inference(subst,[],[a1:[bind(X,$fot(t)),bind(Y,$fot(X_14)),bind(Z,$fot(k))]]) ).
cnf(refute_0_1,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_2,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_3,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( tk != f(t,k)
| f(t,k) = tk ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(tk)),bind(Y0,$fot(f(t,k)))]]) ).
cnf(refute_0_5,plain,
f(t,k) = tk,
inference(resolve,[$cnf( $equal(tk,f(t,k)) )],[clause_7,refute_0_4]) ).
cnf(refute_0_6,plain,
( f(t,f(X_14,k)) != f(f(t,X_14),f(t,k))
| f(t,k) != tk
| f(t,f(X_14,k)) = f(f(t,X_14),tk) ),
introduced(tautology,[equality,[$cnf( $equal(f(t,f(X_14,k)),f(f(t,X_14),f(t,k))) ),[1,1],$fot(tk)]]) ).
cnf(refute_0_7,plain,
( f(t,f(X_14,k)) != f(f(t,X_14),f(t,k))
| f(t,f(X_14,k)) = f(f(t,X_14),tk) ),
inference(resolve,[$cnf( $equal(f(t,k),tk) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
f(t,f(X_14,k)) = f(f(t,X_14),tk),
inference(resolve,[$cnf( $equal(f(t,f(X_14,k)),f(f(t,X_14),f(t,k))) )],[refute_0_0,refute_0_7]) ).
cnf(refute_0_9,plain,
f(t,f(ts,k)) = f(f(t,ts),tk),
inference(subst,[],[refute_0_8:[bind(X_14,$fot(ts))]]) ).
cnf(refute_0_10,plain,
f(t,f(X_14,s)) = f(f(t,X_14),f(t,s)),
inference(subst,[],[a1:[bind(X,$fot(t)),bind(Y,$fot(X_14)),bind(Z,$fot(s))]]) ).
cnf(refute_0_11,plain,
( ts != f(t,s)
| f(t,s) = ts ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(ts)),bind(Y0,$fot(f(t,s)))]]) ).
cnf(refute_0_12,plain,
f(t,s) = ts,
inference(resolve,[$cnf( $equal(ts,f(t,s)) )],[clause_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( f(t,f(X_14,s)) != f(f(t,X_14),f(t,s))
| f(t,s) != ts
| f(t,f(X_14,s)) = f(f(t,X_14),ts) ),
introduced(tautology,[equality,[$cnf( $equal(f(t,f(X_14,s)),f(f(t,X_14),f(t,s))) ),[1,1],$fot(ts)]]) ).
cnf(refute_0_14,plain,
( f(t,f(X_14,s)) != f(f(t,X_14),f(t,s))
| f(t,f(X_14,s)) = f(f(t,X_14),ts) ),
inference(resolve,[$cnf( $equal(f(t,s),ts) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
f(t,f(X_14,s)) = f(f(t,X_14),ts),
inference(resolve,[$cnf( $equal(f(t,f(X_14,s)),f(f(t,X_14),f(t,s))) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
f(t,f(t,s)) = f(f(t,t),ts),
inference(subst,[],[refute_0_15:[bind(X_14,$fot(t))]]) ).
cnf(refute_0_17,plain,
( tt != f(t,t)
| f(t,t) = tt ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(tt)),bind(Y0,$fot(f(t,t)))]]) ).
cnf(refute_0_18,plain,
f(t,t) = tt,
inference(resolve,[$cnf( $equal(tt,f(t,t)) )],[clause_1,refute_0_17]) ).
cnf(refute_0_19,plain,
( f(t,f(t,s)) != f(f(t,t),ts)
| f(t,t) != tt
| f(t,f(t,s)) = f(tt,ts) ),
introduced(tautology,[equality,[$cnf( $equal(f(t,f(t,s)),f(f(t,t),ts)) ),[1,0],$fot(tt)]]) ).
cnf(refute_0_20,plain,
( f(t,f(t,s)) != f(f(t,t),ts)
| f(t,f(t,s)) = f(tt,ts) ),
inference(resolve,[$cnf( $equal(f(t,t),tt) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
f(t,f(t,s)) = f(tt,ts),
inference(resolve,[$cnf( $equal(f(t,f(t,s)),f(f(t,t),ts)) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
f(t,f(t,s)) = f(t,f(t,s)),
introduced(tautology,[refl,[$fot(f(t,f(t,s)))]]) ).
cnf(refute_0_23,plain,
( f(t,f(t,s)) != f(t,f(t,s))
| f(t,s) != ts
| f(t,f(t,s)) = f(t,ts) ),
introduced(tautology,[equality,[$cnf( $equal(f(t,f(t,s)),f(t,f(t,s))) ),[1,1],$fot(ts)]]) ).
cnf(refute_0_24,plain,
( f(t,s) != ts
| f(t,f(t,s)) = f(t,ts) ),
inference(resolve,[$cnf( $equal(f(t,f(t,s)),f(t,f(t,s))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
f(t,f(t,s)) = f(t,ts),
inference(resolve,[$cnf( $equal(f(t,s),ts) )],[refute_0_12,refute_0_24]) ).
cnf(refute_0_26,plain,
( f(t,f(t,s)) != f(t,ts)
| f(t,f(t,s)) != f(tt,ts)
| f(t,ts) = f(tt,ts) ),
introduced(tautology,[equality,[$cnf( $equal(f(t,f(t,s)),f(tt,ts)) ),[0],$fot(f(t,ts))]]) ).
cnf(refute_0_27,plain,
( f(t,f(t,s)) != f(tt,ts)
| f(t,ts) = f(tt,ts) ),
inference(resolve,[$cnf( $equal(f(t,f(t,s)),f(t,ts)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( tt_ts != f(tt,ts)
| f(tt,ts) = tt_ts ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(tt_ts)),bind(Y0,$fot(f(tt,ts)))]]) ).
cnf(refute_0_29,plain,
f(tt,ts) = tt_ts,
inference(resolve,[$cnf( $equal(tt_ts,f(tt,ts)) )],[clause_4,refute_0_28]) ).
cnf(refute_0_30,plain,
( f(t,ts) != f(tt,ts)
| f(tt,ts) != tt_ts
| f(t,ts) = tt_ts ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(t,ts),tt_ts) ),[0],$fot(f(tt,ts))]]) ).
cnf(refute_0_31,plain,
( f(t,ts) != f(tt,ts)
| f(t,ts) = tt_ts ),
inference(resolve,[$cnf( $equal(f(tt,ts),tt_ts) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( f(t,f(t,s)) != f(tt,ts)
| f(t,ts) = tt_ts ),
inference(resolve,[$cnf( $equal(f(t,ts),f(tt,ts)) )],[refute_0_27,refute_0_31]) ).
cnf(refute_0_33,plain,
f(t,ts) = tt_ts,
inference(resolve,[$cnf( $equal(f(t,f(t,s)),f(tt,ts)) )],[refute_0_21,refute_0_32]) ).
cnf(refute_0_34,plain,
( f(t,f(ts,k)) != f(f(t,ts),tk)
| f(t,ts) != tt_ts
| f(t,f(ts,k)) = f(tt_ts,tk) ),
introduced(tautology,[equality,[$cnf( $equal(f(t,f(ts,k)),f(f(t,ts),tk)) ),[1,0],$fot(tt_ts)]]) ).
cnf(refute_0_35,plain,
( f(t,f(ts,k)) != f(f(t,ts),tk)
| f(t,f(ts,k)) = f(tt_ts,tk) ),
inference(resolve,[$cnf( $equal(f(t,ts),tt_ts) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
f(t,f(ts,k)) = f(tt_ts,tk),
inference(resolve,[$cnf( $equal(f(t,f(ts,k)),f(f(t,ts),tk)) )],[refute_0_9,refute_0_35]) ).
cnf(refute_0_37,plain,
( tsk != f(ts,k)
| f(ts,k) = tsk ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(tsk)),bind(Y0,$fot(f(ts,k)))]]) ).
cnf(refute_0_38,plain,
f(ts,k) = tsk,
inference(resolve,[$cnf( $equal(tsk,f(ts,k)) )],[clause_9,refute_0_37]) ).
cnf(refute_0_39,plain,
f(t,f(ts,k)) = f(t,f(ts,k)),
introduced(tautology,[refl,[$fot(f(t,f(ts,k)))]]) ).
cnf(refute_0_40,plain,
( f(t,f(ts,k)) != f(t,f(ts,k))
| f(ts,k) != tsk
| f(t,f(ts,k)) = f(t,tsk) ),
introduced(tautology,[equality,[$cnf( $equal(f(t,f(ts,k)),f(t,f(ts,k))) ),[1,1],$fot(tsk)]]) ).
cnf(refute_0_41,plain,
( f(ts,k) != tsk
| f(t,f(ts,k)) = f(t,tsk) ),
inference(resolve,[$cnf( $equal(f(t,f(ts,k)),f(t,f(ts,k))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
f(t,f(ts,k)) = f(t,tsk),
inference(resolve,[$cnf( $equal(f(ts,k),tsk) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( f(t,f(ts,k)) != f(t,tsk)
| f(t,f(ts,k)) != f(tt_ts,tk)
| f(t,tsk) = f(tt_ts,tk) ),
introduced(tautology,[equality,[$cnf( $equal(f(t,f(ts,k)),f(tt_ts,tk)) ),[0],$fot(f(t,tsk))]]) ).
cnf(refute_0_44,plain,
( f(t,f(ts,k)) != f(tt_ts,tk)
| f(t,tsk) = f(tt_ts,tk) ),
inference(resolve,[$cnf( $equal(f(t,f(ts,k)),f(t,tsk)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
f(t,tsk) = f(tt_ts,tk),
inference(resolve,[$cnf( $equal(f(t,f(ts,k)),f(tt_ts,tk)) )],[refute_0_36,refute_0_44]) ).
cnf(refute_0_46,plain,
$false,
inference(resolve,[$cnf( $equal(f(t,tsk),f(tt_ts,tk)) )],[refute_0_45,prove_equation]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LDA007-2 : TPTP v8.1.0. Bugfixed v2.6.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n018.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon May 30 04:27:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.50
% 0.19/0.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.50
%------------------------------------------------------------------------------