TSTP Solution File: LCL897-10 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL897-10 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 12:56:49 EDT 2022
% Result : Unsatisfiable 2.84s 3.05s
% Output : CNFRefutation 2.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 25
% Syntax : Number of clauses : 91 ( 50 unt; 0 nHn; 50 RR)
% Number of literals : 150 ( 149 equ; 62 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 211 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos_01,axiom,
add(add(A,B),C) = add(A,add(B,C)) ).
cnf(sos_02,axiom,
add(A,B) = add(B,A) ).
cnf(sos_07,axiom,
' = =>'(add(A,B),C) = ' = =>'(A,' = =>'(B,C)) ).
cnf(sos_08,axiom,
add(A,' = =>'(A,B)) = add(B,' = =>'(B,A)) ).
cnf(goals_09,negated_conjecture,
add(add(a,' = =>'(a,b)),' = =>'(add(a,' = =>'(a,b)),c)) != add(a,' = =>'(a,add(b,' = =>'(b,c)))) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( add(A,' = =>'(A,B)) != add(B,' = =>'(B,A))
| add(B,' = =>'(B,A)) = add(A,' = =>'(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(add(A,' = =>'(A,B)))),bind(Y,$fot(add(B,' = =>'(B,A))))]]) ).
cnf(refute_0_4,plain,
add(B,' = =>'(B,A)) = add(A,' = =>'(A,B)),
inference(resolve,[$cnf( $equal(add(A,' = =>'(A,B)),add(B,' = =>'(B,A))) )],[sos_08,refute_0_3]) ).
cnf(refute_0_5,plain,
add(add(a,' = =>'(a,b)),' = =>'(add(a,' = =>'(a,b)),c)) = add(c,' = =>'(c,add(a,' = =>'(a,b)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(c)),bind(B,$fot(add(a,' = =>'(a,b))))]]) ).
cnf(refute_0_6,plain,
( add(add(a,' = =>'(a,b)),' = =>'(add(a,' = =>'(a,b)),c)) != add(c,' = =>'(c,add(a,' = =>'(a,b))))
| add(c,' = =>'(c,add(a,' = =>'(a,b)))) != add(a,' = =>'(a,add(b,' = =>'(b,c))))
| add(add(a,' = =>'(a,b)),' = =>'(add(a,' = =>'(a,b)),c)) = add(a,' = =>'(a,add(b,' = =>'(b,c)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(add(a,' = =>'(a,b)),' = =>'(add(a,' = =>'(a,b)),c)),add(a,' = =>'(a,add(b,' = =>'(b,c))))) ),[0],$fot(add(c,' = =>'(c,add(a,' = =>'(a,b)))))]]) ).
cnf(refute_0_7,plain,
( add(c,' = =>'(c,add(a,' = =>'(a,b)))) != add(a,' = =>'(a,add(b,' = =>'(b,c))))
| add(add(a,' = =>'(a,b)),' = =>'(add(a,' = =>'(a,b)),c)) = add(a,' = =>'(a,add(b,' = =>'(b,c)))) ),
inference(resolve,[$cnf( $equal(add(add(a,' = =>'(a,b)),' = =>'(add(a,' = =>'(a,b)),c)),add(c,' = =>'(c,add(a,' = =>'(a,b))))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
add(c,' = =>'(c,add(a,' = =>'(a,b)))) != add(a,' = =>'(a,add(b,' = =>'(b,c)))),
inference(resolve,[$cnf( $equal(add(add(a,' = =>'(a,b)),' = =>'(add(a,' = =>'(a,b)),c)),add(a,' = =>'(a,add(b,' = =>'(b,c))))) )],[refute_0_7,goals_09]) ).
cnf(refute_0_9,plain,
add(A,' = =>'(A,add(X_18,X_19))) = add(add(X_18,X_19),' = =>'(add(X_18,X_19),A)),
inference(subst,[],[sos_08:[bind(B,$fot(add(X_18,X_19)))]]) ).
cnf(refute_0_10,plain,
add(add(X_18,X_19),' = =>'(add(X_18,X_19),A)) = add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))),
inference(subst,[],[sos_01:[bind(A,$fot(X_18)),bind(B,$fot(X_19)),bind(C,$fot(' = =>'(add(X_18,X_19),A)))]]) ).
cnf(refute_0_11,plain,
( add(A,' = =>'(A,add(X_18,X_19))) != add(add(X_18,X_19),' = =>'(add(X_18,X_19),A))
| add(add(X_18,X_19),' = =>'(add(X_18,X_19),A)) != add(X_18,add(X_19,' = =>'(add(X_18,X_19),A)))
| add(A,' = =>'(A,add(X_18,X_19))) = add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(A,' = =>'(A,add(X_18,X_19))),add(X_18,add(X_19,' = =>'(add(X_18,X_19),A)))) ),[0],$fot(add(add(X_18,X_19),' = =>'(add(X_18,X_19),A)))]]) ).
cnf(refute_0_12,plain,
( add(A,' = =>'(A,add(X_18,X_19))) != add(add(X_18,X_19),' = =>'(add(X_18,X_19),A))
| add(A,' = =>'(A,add(X_18,X_19))) = add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))) ),
inference(resolve,[$cnf( $equal(add(add(X_18,X_19),' = =>'(add(X_18,X_19),A)),add(X_18,add(X_19,' = =>'(add(X_18,X_19),A)))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
add(A,' = =>'(A,add(X_18,X_19))) = add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))),
inference(resolve,[$cnf( $equal(add(A,' = =>'(A,add(X_18,X_19))),add(add(X_18,X_19),' = =>'(add(X_18,X_19),A))) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
' = =>'(add(X_18,X_19),A) = ' = =>'(X_18,' = =>'(X_19,A)),
inference(subst,[],[sos_07:[bind(A,$fot(X_18)),bind(B,$fot(X_19)),bind(C,$fot(A))]]) ).
cnf(refute_0_15,plain,
add(X_19,' = =>'(add(X_18,X_19),A)) = add(X_19,' = =>'(add(X_18,X_19),A)),
introduced(tautology,[refl,[$fot(add(X_19,' = =>'(add(X_18,X_19),A)))]]) ).
cnf(refute_0_16,plain,
( ' = =>'(add(X_18,X_19),A) != ' = =>'(X_18,' = =>'(X_19,A))
| add(X_19,' = =>'(add(X_18,X_19),A)) != add(X_19,' = =>'(add(X_18,X_19),A))
| add(X_19,' = =>'(add(X_18,X_19),A)) = add(X_19,' = =>'(X_18,' = =>'(X_19,A))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_19,' = =>'(add(X_18,X_19),A)),add(X_19,' = =>'(add(X_18,X_19),A))) ),[1,1],$fot(' = =>'(X_18,' = =>'(X_19,A)))]]) ).
cnf(refute_0_17,plain,
( ' = =>'(add(X_18,X_19),A) != ' = =>'(X_18,' = =>'(X_19,A))
| add(X_19,' = =>'(add(X_18,X_19),A)) = add(X_19,' = =>'(X_18,' = =>'(X_19,A))) ),
inference(resolve,[$cnf( $equal(add(X_19,' = =>'(add(X_18,X_19),A)),add(X_19,' = =>'(add(X_18,X_19),A))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
add(X_19,' = =>'(add(X_18,X_19),A)) = add(X_19,' = =>'(X_18,' = =>'(X_19,A))),
inference(resolve,[$cnf( $equal(' = =>'(add(X_18,X_19),A),' = =>'(X_18,' = =>'(X_19,A))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))) = add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))),
introduced(tautology,[refl,[$fot(add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))))]]) ).
cnf(refute_0_20,plain,
( add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))) != add(X_18,add(X_19,' = =>'(add(X_18,X_19),A)))
| add(X_19,' = =>'(add(X_18,X_19),A)) != add(X_19,' = =>'(X_18,' = =>'(X_19,A)))
| add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))) = add(X_18,add(X_19,' = =>'(X_18,' = =>'(X_19,A)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))),add(X_18,add(X_19,' = =>'(add(X_18,X_19),A)))) ),[1,1],$fot(add(X_19,' = =>'(X_18,' = =>'(X_19,A))))]]) ).
cnf(refute_0_21,plain,
( add(X_19,' = =>'(add(X_18,X_19),A)) != add(X_19,' = =>'(X_18,' = =>'(X_19,A)))
| add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))) = add(X_18,add(X_19,' = =>'(X_18,' = =>'(X_19,A)))) ),
inference(resolve,[$cnf( $equal(add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))),add(X_18,add(X_19,' = =>'(add(X_18,X_19),A)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))) = add(X_18,add(X_19,' = =>'(X_18,' = =>'(X_19,A)))),
inference(resolve,[$cnf( $equal(add(X_19,' = =>'(add(X_18,X_19),A)),add(X_19,' = =>'(X_18,' = =>'(X_19,A)))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( add(A,' = =>'(A,add(X_18,X_19))) != add(X_18,add(X_19,' = =>'(add(X_18,X_19),A)))
| add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))) != add(X_18,add(X_19,' = =>'(X_18,' = =>'(X_19,A))))
| add(A,' = =>'(A,add(X_18,X_19))) = add(X_18,add(X_19,' = =>'(X_18,' = =>'(X_19,A)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(A,' = =>'(A,add(X_18,X_19))),add(X_18,add(X_19,' = =>'(X_18,' = =>'(X_19,A))))) ),[0],$fot(add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))))]]) ).
cnf(refute_0_24,plain,
( add(A,' = =>'(A,add(X_18,X_19))) != add(X_18,add(X_19,' = =>'(add(X_18,X_19),A)))
| add(A,' = =>'(A,add(X_18,X_19))) = add(X_18,add(X_19,' = =>'(X_18,' = =>'(X_19,A)))) ),
inference(resolve,[$cnf( $equal(add(X_18,add(X_19,' = =>'(add(X_18,X_19),A))),add(X_18,add(X_19,' = =>'(X_18,' = =>'(X_19,A))))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
add(A,' = =>'(A,add(X_18,X_19))) = add(X_18,add(X_19,' = =>'(X_18,' = =>'(X_19,A)))),
inference(resolve,[$cnf( $equal(add(A,' = =>'(A,add(X_18,X_19))),add(X_18,add(X_19,' = =>'(add(X_18,X_19),A)))) )],[refute_0_13,refute_0_24]) ).
cnf(refute_0_26,plain,
add(X_31,' = =>'(X_31,add(X_32,X_33))) = add(X_32,add(X_33,' = =>'(X_32,' = =>'(X_33,X_31)))),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_31)),bind(X_18,$fot(X_32)),bind(X_19,$fot(X_33))]]) ).
cnf(refute_0_27,plain,
' = =>'(add(X_9,X_10),X_11) = ' = =>'(X_9,' = =>'(X_10,X_11)),
inference(subst,[],[sos_07:[bind(A,$fot(X_9)),bind(B,$fot(X_10)),bind(C,$fot(X_11))]]) ).
cnf(refute_0_28,plain,
add(X_10,X_9) = add(X_9,X_10),
inference(subst,[],[sos_02:[bind(A,$fot(X_10)),bind(B,$fot(X_9))]]) ).
cnf(refute_0_29,plain,
( add(X_10,X_9) != add(X_9,X_10)
| add(X_9,X_10) = add(X_10,X_9) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(add(X_10,X_9))),bind(Y,$fot(add(X_9,X_10)))]]) ).
cnf(refute_0_30,plain,
add(X_9,X_10) = add(X_10,X_9),
inference(resolve,[$cnf( $equal(add(X_10,X_9),add(X_9,X_10)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( ' = =>'(add(X_9,X_10),X_11) != ' = =>'(X_9,' = =>'(X_10,X_11))
| add(X_9,X_10) != add(X_10,X_9)
| ' = =>'(add(X_10,X_9),X_11) = ' = =>'(X_9,' = =>'(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(' = =>'(add(X_9,X_10),X_11),' = =>'(X_9,' = =>'(X_10,X_11))) ),[0,0],$fot(add(X_10,X_9))]]) ).
cnf(refute_0_32,plain,
( ' = =>'(add(X_9,X_10),X_11) != ' = =>'(X_9,' = =>'(X_10,X_11))
| ' = =>'(add(X_10,X_9),X_11) = ' = =>'(X_9,' = =>'(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(add(X_9,X_10),add(X_10,X_9)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
' = =>'(add(X_10,X_9),X_11) = ' = =>'(X_9,' = =>'(X_10,X_11)),
inference(resolve,[$cnf( $equal(' = =>'(add(X_9,X_10),X_11),' = =>'(X_9,' = =>'(X_10,X_11))) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
' = =>'(add(X_10,X_9),X_11) = ' = =>'(X_10,' = =>'(X_9,X_11)),
inference(subst,[],[sos_07:[bind(A,$fot(X_10)),bind(B,$fot(X_9)),bind(C,$fot(X_11))]]) ).
cnf(refute_0_35,plain,
( ' = =>'(add(X_10,X_9),X_11) != ' = =>'(X_10,' = =>'(X_9,X_11))
| ' = =>'(add(X_10,X_9),X_11) != ' = =>'(X_9,' = =>'(X_10,X_11))
| ' = =>'(X_10,' = =>'(X_9,X_11)) = ' = =>'(X_9,' = =>'(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(' = =>'(add(X_10,X_9),X_11),' = =>'(X_9,' = =>'(X_10,X_11))) ),[0],$fot(' = =>'(X_10,' = =>'(X_9,X_11)))]]) ).
cnf(refute_0_36,plain,
( ' = =>'(add(X_10,X_9),X_11) != ' = =>'(X_9,' = =>'(X_10,X_11))
| ' = =>'(X_10,' = =>'(X_9,X_11)) = ' = =>'(X_9,' = =>'(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(' = =>'(add(X_10,X_9),X_11),' = =>'(X_10,' = =>'(X_9,X_11))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
' = =>'(X_10,' = =>'(X_9,X_11)) = ' = =>'(X_9,' = =>'(X_10,X_11)),
inference(resolve,[$cnf( $equal(' = =>'(add(X_10,X_9),X_11),' = =>'(X_9,' = =>'(X_10,X_11))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
' = =>'(X_33,' = =>'(X_32,X_31)) = ' = =>'(X_32,' = =>'(X_33,X_31)),
inference(subst,[],[refute_0_37:[bind(X_10,$fot(X_33)),bind(X_11,$fot(X_31)),bind(X_9,$fot(X_32))]]) ).
cnf(refute_0_39,plain,
( ' = =>'(X_33,' = =>'(X_32,X_31)) != ' = =>'(X_32,' = =>'(X_33,X_31))
| ' = =>'(X_32,' = =>'(X_33,X_31)) = ' = =>'(X_33,' = =>'(X_32,X_31)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(' = =>'(X_33,' = =>'(X_32,X_31)))),bind(Y,$fot(' = =>'(X_32,' = =>'(X_33,X_31))))]]) ).
cnf(refute_0_40,plain,
' = =>'(X_32,' = =>'(X_33,X_31)) = ' = =>'(X_33,' = =>'(X_32,X_31)),
inference(resolve,[$cnf( $equal(' = =>'(X_33,' = =>'(X_32,X_31)),' = =>'(X_32,' = =>'(X_33,X_31))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( ' = =>'(X_32,' = =>'(X_33,X_31)) != ' = =>'(X_33,' = =>'(X_32,X_31))
| add(X_31,' = =>'(X_31,add(X_32,X_33))) != add(X_32,add(X_33,' = =>'(X_32,' = =>'(X_33,X_31))))
| add(X_31,' = =>'(X_31,add(X_32,X_33))) = add(X_32,add(X_33,' = =>'(X_33,' = =>'(X_32,X_31)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_31,' = =>'(X_31,add(X_32,X_33))),add(X_32,add(X_33,' = =>'(X_32,' = =>'(X_33,X_31))))) ),[1,1,1],$fot(' = =>'(X_33,' = =>'(X_32,X_31)))]]) ).
cnf(refute_0_42,plain,
( add(X_31,' = =>'(X_31,add(X_32,X_33))) != add(X_32,add(X_33,' = =>'(X_32,' = =>'(X_33,X_31))))
| add(X_31,' = =>'(X_31,add(X_32,X_33))) = add(X_32,add(X_33,' = =>'(X_33,' = =>'(X_32,X_31)))) ),
inference(resolve,[$cnf( $equal(' = =>'(X_32,' = =>'(X_33,X_31)),' = =>'(X_33,' = =>'(X_32,X_31))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
add(X_31,' = =>'(X_31,add(X_32,X_33))) = add(X_32,add(X_33,' = =>'(X_33,' = =>'(X_32,X_31)))),
inference(resolve,[$cnf( $equal(add(X_31,' = =>'(X_31,add(X_32,X_33))),add(X_32,add(X_33,' = =>'(X_32,' = =>'(X_33,X_31))))) )],[refute_0_26,refute_0_42]) ).
cnf(refute_0_44,plain,
add(X_129,' = =>'(X_129,add(X_130,' = =>'(X_130,A)))) = add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129)))),
inference(subst,[],[refute_0_43:[bind(X_31,$fot(X_129)),bind(X_32,$fot(X_130)),bind(X_33,$fot(' = =>'(X_130,A)))]]) ).
cnf(refute_0_45,plain,
add(A,' = =>'(A,X_130)) = add(X_130,' = =>'(X_130,A)),
inference(subst,[],[sos_08:[bind(B,$fot(X_130))]]) ).
cnf(refute_0_46,plain,
( add(A,' = =>'(A,X_130)) != add(X_130,' = =>'(X_130,A))
| add(X_130,' = =>'(X_130,A)) = add(A,' = =>'(A,X_130)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(add(A,' = =>'(A,X_130)))),bind(Y,$fot(add(X_130,' = =>'(X_130,A))))]]) ).
cnf(refute_0_47,plain,
add(X_130,' = =>'(X_130,A)) = add(A,' = =>'(A,X_130)),
inference(resolve,[$cnf( $equal(add(A,' = =>'(A,X_130)),add(X_130,' = =>'(X_130,A))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( add(X_129,' = =>'(X_129,add(X_130,' = =>'(X_130,A)))) != add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129))))
| add(X_130,' = =>'(X_130,A)) != add(A,' = =>'(A,X_130))
| add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))) = add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_129,' = =>'(X_129,add(X_130,' = =>'(X_130,A)))),add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129))))) ),[0,1,1],$fot(add(A,' = =>'(A,X_130)))]]) ).
cnf(refute_0_49,plain,
( add(X_129,' = =>'(X_129,add(X_130,' = =>'(X_130,A)))) != add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129))))
| add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))) = add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129)))) ),
inference(resolve,[$cnf( $equal(add(X_130,' = =>'(X_130,A)),add(A,' = =>'(A,X_130))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))) = add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129)))),
inference(resolve,[$cnf( $equal(add(X_129,' = =>'(X_129,add(X_130,' = =>'(X_130,A)))),add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129))))) )],[refute_0_44,refute_0_49]) ).
cnf(refute_0_51,plain,
add(add(X_18,X_19),' = =>'(X_19,A)) = add(X_18,add(X_19,' = =>'(X_19,A))),
inference(subst,[],[sos_01:[bind(A,$fot(X_18)),bind(B,$fot(X_19)),bind(C,$fot(' = =>'(X_19,A)))]]) ).
cnf(refute_0_52,plain,
add(A,' = =>'(A,X_19)) = add(X_19,' = =>'(X_19,A)),
inference(subst,[],[sos_08:[bind(B,$fot(X_19))]]) ).
cnf(refute_0_53,plain,
( add(A,' = =>'(A,X_19)) != add(X_19,' = =>'(X_19,A))
| add(X_19,' = =>'(X_19,A)) = add(A,' = =>'(A,X_19)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(add(A,' = =>'(A,X_19)))),bind(Y,$fot(add(X_19,' = =>'(X_19,A))))]]) ).
cnf(refute_0_54,plain,
add(X_19,' = =>'(X_19,A)) = add(A,' = =>'(A,X_19)),
inference(resolve,[$cnf( $equal(add(A,' = =>'(A,X_19)),add(X_19,' = =>'(X_19,A))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( add(X_19,' = =>'(X_19,A)) != add(A,' = =>'(A,X_19))
| add(add(X_18,X_19),' = =>'(X_19,A)) != add(X_18,add(X_19,' = =>'(X_19,A)))
| add(add(X_18,X_19),' = =>'(X_19,A)) = add(X_18,add(A,' = =>'(A,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_18,X_19),' = =>'(X_19,A)),add(X_18,add(X_19,' = =>'(X_19,A)))) ),[1,1],$fot(add(A,' = =>'(A,X_19)))]]) ).
cnf(refute_0_56,plain,
( add(add(X_18,X_19),' = =>'(X_19,A)) != add(X_18,add(X_19,' = =>'(X_19,A)))
| add(add(X_18,X_19),' = =>'(X_19,A)) = add(X_18,add(A,' = =>'(A,X_19))) ),
inference(resolve,[$cnf( $equal(add(X_19,' = =>'(X_19,A)),add(A,' = =>'(A,X_19))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
add(add(X_18,X_19),' = =>'(X_19,A)) = add(X_18,add(A,' = =>'(A,X_19))),
inference(resolve,[$cnf( $equal(add(add(X_18,X_19),' = =>'(X_19,A)),add(X_18,add(X_19,' = =>'(X_19,A)))) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
( add(add(X_18,X_19),' = =>'(X_19,A)) != add(X_18,add(A,' = =>'(A,X_19)))
| add(add(X_18,X_19),' = =>'(X_19,A)) != add(X_18,add(X_19,' = =>'(X_19,A)))
| add(X_18,add(X_19,' = =>'(X_19,A))) = add(X_18,add(A,' = =>'(A,X_19))) ),
introduced(tautology,[equality,[$cnf( $equal(add(add(X_18,X_19),' = =>'(X_19,A)),add(X_18,add(A,' = =>'(A,X_19)))) ),[0],$fot(add(X_18,add(X_19,' = =>'(X_19,A))))]]) ).
cnf(refute_0_59,plain,
( add(add(X_18,X_19),' = =>'(X_19,A)) != add(X_18,add(A,' = =>'(A,X_19)))
| add(X_18,add(X_19,' = =>'(X_19,A))) = add(X_18,add(A,' = =>'(A,X_19))) ),
inference(resolve,[$cnf( $equal(add(add(X_18,X_19),' = =>'(X_19,A)),add(X_18,add(X_19,' = =>'(X_19,A)))) )],[refute_0_51,refute_0_58]) ).
cnf(refute_0_60,plain,
add(X_18,add(X_19,' = =>'(X_19,A))) = add(X_18,add(A,' = =>'(A,X_19))),
inference(resolve,[$cnf( $equal(add(add(X_18,X_19),' = =>'(X_19,A)),add(X_18,add(A,' = =>'(A,X_19)))) )],[refute_0_57,refute_0_59]) ).
cnf(refute_0_61,plain,
add(X_18,add(' = =>'(X_18,X_129),' = =>'(' = =>'(X_18,X_129),A))) = add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129)))),
inference(subst,[],[refute_0_60:[bind(X_19,$fot(' = =>'(X_18,X_129)))]]) ).
cnf(refute_0_62,plain,
add(X_129,' = =>'(X_129,add(X_18,A))) = add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129)))),
inference(subst,[],[refute_0_43:[bind(X_31,$fot(X_129)),bind(X_32,$fot(X_18)),bind(X_33,$fot(A))]]) ).
cnf(refute_0_63,plain,
( add(X_129,' = =>'(X_129,add(X_18,A))) != add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129))))
| add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129)))) = add(X_129,' = =>'(X_129,add(X_18,A))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(add(X_129,' = =>'(X_129,add(X_18,A))))),bind(Y,$fot(add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129))))))]]) ).
cnf(refute_0_64,plain,
add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129)))) = add(X_129,' = =>'(X_129,add(X_18,A))),
inference(resolve,[$cnf( $equal(add(X_129,' = =>'(X_129,add(X_18,A))),add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129))))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129)))) != add(X_129,' = =>'(X_129,add(X_18,A)))
| add(X_18,add(' = =>'(X_18,X_129),' = =>'(' = =>'(X_18,X_129),A))) != add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129))))
| add(X_18,add(' = =>'(X_18,X_129),' = =>'(' = =>'(X_18,X_129),A))) = add(X_129,' = =>'(X_129,add(X_18,A))) ),
introduced(tautology,[equality,[$cnf( $equal(add(X_18,add(' = =>'(X_18,X_129),' = =>'(' = =>'(X_18,X_129),A))),add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129))))) ),[1],$fot(add(X_129,' = =>'(X_129,add(X_18,A))))]]) ).
cnf(refute_0_66,plain,
( add(X_18,add(' = =>'(X_18,X_129),' = =>'(' = =>'(X_18,X_129),A))) != add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129))))
| add(X_18,add(' = =>'(X_18,X_129),' = =>'(' = =>'(X_18,X_129),A))) = add(X_129,' = =>'(X_129,add(X_18,A))) ),
inference(resolve,[$cnf( $equal(add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129)))),add(X_129,' = =>'(X_129,add(X_18,A)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
add(X_18,add(' = =>'(X_18,X_129),' = =>'(' = =>'(X_18,X_129),A))) = add(X_129,' = =>'(X_129,add(X_18,A))),
inference(resolve,[$cnf( $equal(add(X_18,add(' = =>'(X_18,X_129),' = =>'(' = =>'(X_18,X_129),A))),add(X_18,add(A,' = =>'(A,' = =>'(X_18,X_129))))) )],[refute_0_61,refute_0_66]) ).
cnf(refute_0_68,plain,
add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129)))) = add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129)))),
inference(subst,[],[refute_0_67:[bind(A,$fot(' = =>'(X_130,X_129))),bind(X_129,$fot(A)),bind(X_18,$fot(X_130))]]) ).
cnf(refute_0_69,plain,
( add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))) != add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129))))
| add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129)))) != add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129))))
| add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))) = add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))),add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129))))) ),[0],$fot(add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129)))))]]) ).
cnf(refute_0_70,plain,
( add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))) != add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129))))
| add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))) = add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129)))) ),
inference(resolve,[$cnf( $equal(add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129)))),add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129))))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))) = add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129)))),
inference(resolve,[$cnf( $equal(add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))),add(X_130,add(' = =>'(X_130,A),' = =>'(' = =>'(X_130,A),' = =>'(X_130,X_129))))) )],[refute_0_50,refute_0_70]) ).
cnf(refute_0_72,plain,
( add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))) != add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129))))
| add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129)))) = add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))))),bind(Y,$fot(add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129))))))]]) ).
cnf(refute_0_73,plain,
add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129)))) = add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))),
inference(resolve,[$cnf( $equal(add(X_129,' = =>'(X_129,add(A,' = =>'(A,X_130)))),add(A,' = =>'(A,add(X_130,' = =>'(X_130,X_129))))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
add(b,' = =>'(b,add(c,' = =>'(c,a)))) = add(a,' = =>'(a,add(b,' = =>'(b,c)))),
inference(subst,[],[refute_0_73:[bind(A,$fot(b)),bind(X_129,$fot(a)),bind(X_130,$fot(c))]]) ).
cnf(refute_0_75,plain,
add(c,' = =>'(c,add(a,' = =>'(a,b)))) = add(b,' = =>'(b,add(c,' = =>'(c,a)))),
inference(subst,[],[refute_0_73:[bind(A,$fot(c)),bind(X_129,$fot(b)),bind(X_130,$fot(a))]]) ).
cnf(refute_0_76,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_77,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_76]) ).
cnf(refute_0_78,plain,
( add(b,' = =>'(b,add(c,' = =>'(c,a)))) != add(a,' = =>'(a,add(b,' = =>'(b,c))))
| add(c,' = =>'(c,add(a,' = =>'(a,b)))) != add(b,' = =>'(b,add(c,' = =>'(c,a))))
| add(c,' = =>'(c,add(a,' = =>'(a,b)))) = add(a,' = =>'(a,add(b,' = =>'(b,c)))) ),
inference(subst,[],[refute_0_77:[bind(X,$fot(add(c,' = =>'(c,add(a,' = =>'(a,b)))))),bind(Y,$fot(add(b,' = =>'(b,add(c,' = =>'(c,a)))))),bind(Z,$fot(add(a,' = =>'(a,add(b,' = =>'(b,c))))))]]) ).
cnf(refute_0_79,plain,
( add(b,' = =>'(b,add(c,' = =>'(c,a)))) != add(a,' = =>'(a,add(b,' = =>'(b,c))))
| add(c,' = =>'(c,add(a,' = =>'(a,b)))) = add(a,' = =>'(a,add(b,' = =>'(b,c)))) ),
inference(resolve,[$cnf( $equal(add(c,' = =>'(c,add(a,' = =>'(a,b)))),add(b,' = =>'(b,add(c,' = =>'(c,a))))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
add(c,' = =>'(c,add(a,' = =>'(a,b)))) = add(a,' = =>'(a,add(b,' = =>'(b,c)))),
inference(resolve,[$cnf( $equal(add(b,' = =>'(b,add(c,' = =>'(c,a)))),add(a,' = =>'(a,add(b,' = =>'(b,c))))) )],[refute_0_74,refute_0_79]) ).
cnf(refute_0_81,plain,
( add(a,' = =>'(a,add(b,' = =>'(b,c)))) != add(a,' = =>'(a,add(b,' = =>'(b,c))))
| add(c,' = =>'(c,add(a,' = =>'(a,b)))) != add(a,' = =>'(a,add(b,' = =>'(b,c))))
| add(c,' = =>'(c,add(a,' = =>'(a,b)))) = add(a,' = =>'(a,add(b,' = =>'(b,c)))) ),
introduced(tautology,[equality,[$cnf( $equal(add(c,' = =>'(c,add(a,' = =>'(a,b)))),add(a,' = =>'(a,add(b,' = =>'(b,c))))) ),[1],$fot(add(a,' = =>'(a,add(b,' = =>'(b,c)))))]]) ).
cnf(refute_0_82,plain,
( add(a,' = =>'(a,add(b,' = =>'(b,c)))) != add(a,' = =>'(a,add(b,' = =>'(b,c))))
| add(c,' = =>'(c,add(a,' = =>'(a,b)))) = add(a,' = =>'(a,add(b,' = =>'(b,c)))) ),
inference(resolve,[$cnf( $equal(add(c,' = =>'(c,add(a,' = =>'(a,b)))),add(a,' = =>'(a,add(b,' = =>'(b,c))))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
add(a,' = =>'(a,add(b,' = =>'(b,c)))) != add(a,' = =>'(a,add(b,' = =>'(b,c)))),
inference(resolve,[$cnf( $equal(add(c,' = =>'(c,add(a,' = =>'(a,b)))),add(a,' = =>'(a,add(b,' = =>'(b,c))))) )],[refute_0_82,refute_0_8]) ).
cnf(refute_0_84,plain,
add(a,' = =>'(a,add(b,' = =>'(b,c)))) = add(a,' = =>'(a,add(b,' = =>'(b,c)))),
introduced(tautology,[refl,[$fot(add(a,' = =>'(a,add(b,' = =>'(b,c)))))]]) ).
cnf(refute_0_85,plain,
$false,
inference(resolve,[$cnf( $equal(add(a,' = =>'(a,add(b,' = =>'(b,c)))),add(a,' = =>'(a,add(b,' = =>'(b,c))))) )],[refute_0_84,refute_0_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL897-10 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % 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 : Mon Jul 4 15:08:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.84/3.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.84/3.05
% 2.84/3.05 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.84/3.06
%------------------------------------------------------------------------------