TSTP Solution File: COM007+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM007+2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 01:32:28 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of formulae : 79 ( 19 unt; 0 def)
% Number of atoms : 180 ( 50 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 173 ( 72 ~; 88 |; 8 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(assumption,axiom,
( reflexive_rewrite(a,b)
& reflexive_rewrite(a,c) ) ).
fof(goal_ax,axiom,
! [A] :
( ( reflexive_rewrite(b,A)
& reflexive_rewrite(c,A) )
=> goal ) ).
fof(equal_in_reflexive_rewrite,axiom,
! [A,B] :
( A = B
=> reflexive_rewrite(A,B) ) ).
fof(rewrite_in_reflexive_rewrite,axiom,
! [A,B] :
( rewrite(A,B)
=> reflexive_rewrite(A,B) ) ).
fof(equal_or_rewrite,axiom,
! [A,B] :
( reflexive_rewrite(A,B)
=> ( A = B
| rewrite(A,B) ) ) ).
fof(rewrite_diamond,axiom,
! [A,B,C] :
( ( rewrite(A,B)
& rewrite(A,C) )
=> ? [D] :
( rewrite(B,D)
& rewrite(C,D) ) ) ).
fof(goal_to_be_proved,conjecture,
goal ).
fof(subgoal_0,plain,
goal,
inference(strip,[],[goal_to_be_proved]) ).
fof(negate_0_0,plain,
~ goal,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( A != B
| reflexive_rewrite(A,B) ),
inference(canonicalize,[],[equal_in_reflexive_rewrite]) ).
fof(normalize_0_1,plain,
! [A,B] :
( A != B
| reflexive_rewrite(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
( ~ reflexive_rewrite(b,A)
| ~ reflexive_rewrite(c,A)
| goal ),
inference(canonicalize,[],[goal_ax]) ).
fof(normalize_0_3,plain,
! [A] :
( ~ reflexive_rewrite(b,A)
| ~ reflexive_rewrite(c,A)
| goal ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
~ goal,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ rewrite(A,B)
| reflexive_rewrite(A,B) ),
inference(canonicalize,[],[rewrite_in_reflexive_rewrite]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ rewrite(A,B)
| reflexive_rewrite(A,B) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( reflexive_rewrite(a,b)
& reflexive_rewrite(a,c) ),
inference(canonicalize,[],[assumption]) ).
fof(normalize_0_8,plain,
reflexive_rewrite(a,b),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ reflexive_rewrite(A,B)
| A = B
| rewrite(A,B) ),
inference(canonicalize,[],[equal_or_rewrite]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ reflexive_rewrite(A,B)
| A = B
| rewrite(A,B) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
reflexive_rewrite(a,c),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_12,plain,
! [A,B,C] :
( ~ rewrite(A,B)
| ~ rewrite(A,C)
| ? [D] :
( rewrite(B,D)
& rewrite(C,D) ) ),
inference(canonicalize,[],[rewrite_diamond]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ~ rewrite(A,B)
| ~ rewrite(A,C)
| ? [D] :
( rewrite(B,D)
& rewrite(C,D) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] :
( ( ~ rewrite(A,B)
| ~ rewrite(A,C)
| rewrite(B,skolemFOFtoCNF_D(B,C)) )
& ( ~ rewrite(A,B)
| ~ rewrite(A,C)
| rewrite(C,skolemFOFtoCNF_D(B,C)) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,C] :
( ~ rewrite(A,B)
| ~ rewrite(A,C)
| rewrite(B,skolemFOFtoCNF_D(B,C)) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B,C] :
( ~ rewrite(A,B)
| ~ rewrite(A,C)
| rewrite(C,skolemFOFtoCNF_D(B,C)) ),
inference(conjunct,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
( A != B
| reflexive_rewrite(A,B) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( B != B
| reflexive_rewrite(B,B) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(B))]]) ).
cnf(refute_0_2,plain,
B = B,
introduced(tautology,[refl,[$fot(B)]]) ).
cnf(refute_0_3,plain,
reflexive_rewrite(B,B),
inference(resolve,[$cnf( $equal(B,B) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
reflexive_rewrite(c,c),
inference(subst,[],[refute_0_3:[bind(B,$fot(c))]]) ).
cnf(refute_0_5,plain,
( ~ reflexive_rewrite(b,A)
| ~ reflexive_rewrite(c,A)
| goal ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_6,plain,
~ goal,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_7,plain,
( ~ reflexive_rewrite(b,A)
| ~ reflexive_rewrite(c,A) ),
inference(resolve,[$cnf( goal )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ reflexive_rewrite(b,c)
| ~ reflexive_rewrite(c,c) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(c))]]) ).
cnf(refute_0_9,plain,
~ reflexive_rewrite(b,c),
inference(resolve,[$cnf( reflexive_rewrite(c,c) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
reflexive_rewrite(b,b),
inference(subst,[],[refute_0_3:[bind(B,$fot(b))]]) ).
cnf(refute_0_11,plain,
( ~ reflexive_rewrite(b,skolemFOFtoCNF_D(c,b))
| ~ reflexive_rewrite(c,skolemFOFtoCNF_D(c,b)) ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_D(c,b)))]]) ).
cnf(refute_0_12,plain,
( ~ rewrite(A,B)
| reflexive_rewrite(A,B) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_13,plain,
( ~ rewrite(c,skolemFOFtoCNF_D(c,b))
| reflexive_rewrite(c,skolemFOFtoCNF_D(c,b)) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(c)),bind(B,$fot(skolemFOFtoCNF_D(c,b)))]]) ).
cnf(refute_0_14,plain,
reflexive_rewrite(a,b),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_15,plain,
( ~ reflexive_rewrite(A,B)
| A = B
| rewrite(A,B) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_16,plain,
( ~ reflexive_rewrite(a,b)
| a = b
| rewrite(a,b) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(a)),bind(B,$fot(b))]]) ).
cnf(refute_0_17,plain,
( a = b
| rewrite(a,b) ),
inference(resolve,[$cnf( reflexive_rewrite(a,b) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
reflexive_rewrite(a,c),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_19,plain,
( ~ reflexive_rewrite(a,c)
| a = c
| rewrite(a,c) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(a)),bind(B,$fot(c))]]) ).
cnf(refute_0_20,plain,
( a = c
| rewrite(a,c) ),
inference(resolve,[$cnf( reflexive_rewrite(a,c) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ rewrite(A,B)
| ~ rewrite(A,C)
| rewrite(B,skolemFOFtoCNF_D(B,C)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_22,plain,
( ~ rewrite(a,X_10)
| ~ rewrite(a,c)
| rewrite(c,skolemFOFtoCNF_D(c,X_10)) ),
inference(subst,[],[refute_0_21:[bind(A,$fot(a)),bind(B,$fot(c)),bind(C,$fot(X_10))]]) ).
cnf(refute_0_23,plain,
( ~ rewrite(a,X_10)
| a = c
| rewrite(c,skolemFOFtoCNF_D(c,X_10)) ),
inference(resolve,[$cnf( rewrite(a,c) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ rewrite(a,b)
| a = c
| rewrite(c,skolemFOFtoCNF_D(c,b)) ),
inference(subst,[],[refute_0_23:[bind(X_10,$fot(b))]]) ).
cnf(refute_0_25,plain,
( a = b
| a = c
| rewrite(c,skolemFOFtoCNF_D(c,b)) ),
inference(resolve,[$cnf( rewrite(a,b) )],[refute_0_17,refute_0_24]) ).
cnf(refute_0_26,plain,
( a = b
| a = c
| reflexive_rewrite(c,skolemFOFtoCNF_D(c,b)) ),
inference(resolve,[$cnf( rewrite(c,skolemFOFtoCNF_D(c,b)) )],[refute_0_25,refute_0_13]) ).
cnf(refute_0_27,plain,
( ~ reflexive_rewrite(b,skolemFOFtoCNF_D(c,b))
| a = b
| a = c ),
inference(resolve,[$cnf( reflexive_rewrite(c,skolemFOFtoCNF_D(c,b)) )],[refute_0_26,refute_0_11]) ).
cnf(refute_0_28,plain,
( ~ rewrite(b,skolemFOFtoCNF_D(c,b))
| reflexive_rewrite(b,skolemFOFtoCNF_D(c,b)) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(b)),bind(B,$fot(skolemFOFtoCNF_D(c,b)))]]) ).
cnf(refute_0_29,plain,
( ~ rewrite(A,B)
| ~ rewrite(A,C)
| rewrite(C,skolemFOFtoCNF_D(B,C)) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_30,plain,
( ~ rewrite(a,X_16)
| ~ rewrite(a,b)
| rewrite(b,skolemFOFtoCNF_D(X_16,b)) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(a)),bind(B,$fot(X_16)),bind(C,$fot(b))]]) ).
cnf(refute_0_31,plain,
( ~ rewrite(a,X_16)
| a = b
| rewrite(b,skolemFOFtoCNF_D(X_16,b)) ),
inference(resolve,[$cnf( rewrite(a,b) )],[refute_0_17,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ rewrite(a,c)
| a = b
| rewrite(b,skolemFOFtoCNF_D(c,b)) ),
inference(subst,[],[refute_0_31:[bind(X_16,$fot(c))]]) ).
cnf(refute_0_33,plain,
( a = b
| a = c
| rewrite(b,skolemFOFtoCNF_D(c,b)) ),
inference(resolve,[$cnf( rewrite(a,c) )],[refute_0_20,refute_0_32]) ).
cnf(refute_0_34,plain,
( a = b
| a = c
| reflexive_rewrite(b,skolemFOFtoCNF_D(c,b)) ),
inference(resolve,[$cnf( rewrite(b,skolemFOFtoCNF_D(c,b)) )],[refute_0_33,refute_0_28]) ).
cnf(refute_0_35,plain,
( a = b
| a = c ),
inference(resolve,[$cnf( reflexive_rewrite(b,skolemFOFtoCNF_D(c,b)) )],[refute_0_34,refute_0_27]) ).
cnf(refute_0_36,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_37,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_38,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( a != c
| c = a ),
inference(subst,[],[refute_0_38:[bind(X,$fot(a)),bind(Y,$fot(c))]]) ).
cnf(refute_0_40,plain,
( a = b
| c = a ),
inference(resolve,[$cnf( $equal(a,c) )],[refute_0_35,refute_0_39]) ).
cnf(refute_0_41,plain,
( c != a
| ~ reflexive_rewrite(a,A)
| reflexive_rewrite(c,A) ),
introduced(tautology,[equality,[$cnf( ~ reflexive_rewrite(c,A) ),[0],$fot(a)]]) ).
cnf(refute_0_42,plain,
( ~ reflexive_rewrite(a,A)
| a = b
| reflexive_rewrite(c,A) ),
inference(resolve,[$cnf( $equal(c,a) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ reflexive_rewrite(a,A)
| ~ reflexive_rewrite(b,A)
| a = b ),
inference(resolve,[$cnf( reflexive_rewrite(c,A) )],[refute_0_42,refute_0_7]) ).
cnf(refute_0_44,plain,
( ~ reflexive_rewrite(a,b)
| ~ reflexive_rewrite(b,b)
| a = b ),
inference(subst,[],[refute_0_43:[bind(A,$fot(b))]]) ).
cnf(refute_0_45,plain,
( ~ reflexive_rewrite(a,b)
| a = b ),
inference(resolve,[$cnf( reflexive_rewrite(b,b) )],[refute_0_10,refute_0_44]) ).
cnf(refute_0_46,plain,
a = b,
inference(resolve,[$cnf( reflexive_rewrite(a,b) )],[refute_0_14,refute_0_45]) ).
cnf(refute_0_47,plain,
( a != b
| b = a ),
inference(subst,[],[refute_0_38:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_48,plain,
b = a,
inference(resolve,[$cnf( $equal(a,b) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( b != a
| ~ reflexive_rewrite(a,c)
| reflexive_rewrite(b,c) ),
introduced(tautology,[equality,[$cnf( ~ reflexive_rewrite(b,c) ),[0],$fot(a)]]) ).
cnf(refute_0_50,plain,
( ~ reflexive_rewrite(a,c)
| reflexive_rewrite(b,c) ),
inference(resolve,[$cnf( $equal(b,a) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
~ reflexive_rewrite(a,c),
inference(resolve,[$cnf( reflexive_rewrite(b,c) )],[refute_0_50,refute_0_9]) ).
cnf(refute_0_52,plain,
$false,
inference(resolve,[$cnf( reflexive_rewrite(a,c) )],[refute_0_18,refute_0_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM007+2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n017.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 : Thu Jun 16 17:35:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------