TSTP Solution File: LCL218-10 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL218-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 12:50:46 EDT 2022
% Result : Unsatisfiable 2.63s 2.84s
% Output : CNFRefutation 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 39
% Syntax : Number of clauses : 123 ( 71 unt; 0 nHn; 56 RR)
% Number of literals : 201 ( 200 equ; 80 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-4 aty)
% Number of variables : 276 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(A,A,B,C) = B ).
cnf(axiom_1_2,axiom,
axiom(or(not(or(A,A)),A)) = true ).
cnf(axiom_1_3,axiom,
axiom(or(not(A),or(B,A))) = true ).
cnf(axiom_1_4,axiom,
axiom(or(not(or(A,B)),or(B,A))) = true ).
cnf(axiom_1_5,axiom,
axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) = true ).
cnf(rule_1,axiom,
ifeq(axiom(X),true,theorem(X),true) = true ).
cnf(rule_2,axiom,
ifeq(theorem(Y),true,ifeq(axiom(or(not(Y),X)),true,theorem(X),true),true) = true ).
cnf(rule_3,axiom,
ifeq(theorem(or(not(Y),Z)),true,ifeq(axiom(or(not(X),Y)),true,theorem(or(not(X),Z)),true),true) = true ).
cnf(prove_this,negated_conjecture,
theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) != true ).
cnf(refute_0_0,plain,
ifeq(theorem(or(A,or(B,C))),true,ifeq(axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),true,theorem(or(B,or(A,C))),true),true) = true,
inference(subst,[],[rule_2:[bind(X,$fot(or(B,or(A,C)))),bind(Y,$fot(or(A,or(B,C))))]]) ).
cnf(refute_0_1,plain,
( axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))) != true
| ifeq(theorem(or(A,or(B,C))),true,ifeq(axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),true,theorem(or(B,or(A,C))),true),true) != true
| ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(A,or(B,C))),true,ifeq(axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),true,theorem(or(B,or(A,C))),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_2,plain,
( ifeq(theorem(or(A,or(B,C))),true,ifeq(axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),true,theorem(or(B,or(A,C))),true),true) != true
| ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) = true ),
inference(resolve,[$cnf( $equal(axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),true) )],[axiom_1_5,refute_0_1]) ).
cnf(refute_0_3,plain,
ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(A,or(B,C))),true,ifeq(axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),true,theorem(or(B,or(A,C))),true),true),true) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
ifeq(true,true,theorem(or(B,or(A,C))),true) = theorem(or(B,or(A,C))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(B,or(A,C))))),bind(C,$fot(true))]]) ).
cnf(refute_0_5,plain,
ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) = ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true))]]) ).
cnf(refute_0_6,plain,
( ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) != ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true)
| ifeq(true,true,theorem(or(B,or(A,C))),true) != theorem(or(B,or(A,C)))
| ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) = ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true),ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true)) ),[1,2],$fot(theorem(or(B,or(A,C))))]]) ).
cnf(refute_0_7,plain,
( ifeq(true,true,theorem(or(B,or(A,C))),true) != theorem(or(B,or(A,C)))
| ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) = ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true),ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) = ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(B,or(A,C))),true),theorem(or(B,or(A,C)))) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
( ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) != ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true)
| ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) != true
| ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true),true) ),[0],$fot(ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true))]]) ).
cnf(refute_0_10,plain,
( ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true) != true
| ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true),ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
ifeq(theorem(or(A,or(B,C))),true,theorem(or(B,or(A,C))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(A,or(B,C))),true,ifeq(true,true,theorem(or(B,or(A,C))),true),true),true) )],[refute_0_3,refute_0_10]) ).
cnf(refute_0_12,plain,
ifeq(theorem(or(not(X_1444),or(not(or(not(or(X_1444,X_1442)),C)),C))),true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true) = true,
inference(subst,[],[refute_0_11:[bind(A,$fot(not(X_1444))),bind(B,$fot(not(or(not(or(X_1444,X_1442)),C))))]]) ).
cnf(refute_0_13,plain,
ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(axiom(or(not(X_39),or(B,X_39))),true,theorem(or(not(X_39),X_41)),true),true) = true,
inference(subst,[],[rule_3:[bind(X,$fot(X_39)),bind(Y,$fot(or(B,X_39))),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_14,plain,
axiom(or(not(X_39),or(B,X_39))) = true,
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_39))]]) ).
cnf(refute_0_15,plain,
( axiom(or(not(X_39),or(B,X_39))) != true
| ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(axiom(or(not(X_39),or(B,X_39))),true,theorem(or(not(X_39),X_41)),true),true) != true
| ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(axiom(or(not(X_39),or(B,X_39))),true,theorem(or(not(X_39),X_41)),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_16,plain,
( ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(axiom(or(not(X_39),or(B,X_39))),true,theorem(or(not(X_39),X_41)),true),true) != true
| ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true) = true ),
inference(resolve,[$cnf( $equal(axiom(or(not(X_39),or(B,X_39))),true) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(axiom(or(not(X_39),or(B,X_39))),true,theorem(or(not(X_39),X_41)),true),true),true) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
ifeq(true,true,theorem(or(not(X_39),X_41)),true) = theorem(or(not(X_39),X_41)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(X_39),X_41)))),bind(C,$fot(true))]]) ).
cnf(refute_0_19,plain,
ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true) = ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true))]]) ).
cnf(refute_0_20,plain,
( ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true) != ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true)
| ifeq(true,true,theorem(or(not(X_39),X_41)),true) != theorem(or(not(X_39),X_41))
| ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true) = ifeq(theorem(or(not(or(B,X_39)),X_41)),true,theorem(or(not(X_39),X_41)),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true),ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true)) ),[1,2],$fot(theorem(or(not(X_39),X_41)))]]) ).
cnf(refute_0_21,plain,
( ifeq(true,true,theorem(or(not(X_39),X_41)),true) != theorem(or(not(X_39),X_41))
| ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true) = ifeq(theorem(or(not(or(B,X_39)),X_41)),true,theorem(or(not(X_39),X_41)),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true),ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true) = ifeq(theorem(or(not(or(B,X_39)),X_41)),true,theorem(or(not(X_39),X_41)),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_39),X_41)),true),theorem(or(not(X_39),X_41))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true) != ifeq(theorem(or(not(or(B,X_39)),X_41)),true,theorem(or(not(X_39),X_41)),true)
| ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true) != true
| ifeq(theorem(or(not(or(B,X_39)),X_41)),true,theorem(or(not(X_39),X_41)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true),true) ),[0],$fot(ifeq(theorem(or(not(or(B,X_39)),X_41)),true,theorem(or(not(X_39),X_41)),true))]]) ).
cnf(refute_0_24,plain,
( ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true) != true
| ifeq(theorem(or(not(or(B,X_39)),X_41)),true,theorem(or(not(X_39),X_41)),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true),ifeq(theorem(or(not(or(B,X_39)),X_41)),true,theorem(or(not(X_39),X_41)),true)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
ifeq(theorem(or(not(or(B,X_39)),X_41)),true,theorem(or(not(X_39),X_41)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_39)),X_41)),true,ifeq(true,true,theorem(or(not(X_39),X_41)),true),true),true) )],[refute_0_17,refute_0_24]) ).
cnf(refute_0_26,plain,
ifeq(theorem(or(not(or(B,X_39)),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true) = true,
inference(subst,[],[refute_0_25:[bind(X_41,$fot(or(not(or(not(or(X_39,B)),X_1076)),X_1076)))]]) ).
cnf(refute_0_27,plain,
ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(axiom(or(not(or(A,B)),or(B,A))),true,theorem(or(not(or(A,B)),X_41)),true),true) = true,
inference(subst,[],[rule_3:[bind(X,$fot(or(A,B))),bind(Y,$fot(or(B,A))),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_28,plain,
( axiom(or(not(or(A,B)),or(B,A))) != true
| ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(axiom(or(not(or(A,B)),or(B,A))),true,theorem(or(not(or(A,B)),X_41)),true),true) != true
| ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(axiom(or(not(or(A,B)),or(B,A))),true,theorem(or(not(or(A,B)),X_41)),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_29,plain,
( ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(axiom(or(not(or(A,B)),or(B,A))),true,theorem(or(not(or(A,B)),X_41)),true),true) != true
| ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true) = true ),
inference(resolve,[$cnf( $equal(axiom(or(not(or(A,B)),or(B,A))),true) )],[axiom_1_4,refute_0_28]) ).
cnf(refute_0_30,plain,
ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(axiom(or(not(or(A,B)),or(B,A))),true,theorem(or(not(or(A,B)),X_41)),true),true),true) )],[refute_0_27,refute_0_29]) ).
cnf(refute_0_31,plain,
ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true) = theorem(or(not(or(A,B)),X_41)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(or(A,B)),X_41)))),bind(C,$fot(true))]]) ).
cnf(refute_0_32,plain,
ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true) = ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true))]]) ).
cnf(refute_0_33,plain,
( ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true) != ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true)
| ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true) != theorem(or(not(or(A,B)),X_41))
| ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true) = ifeq(theorem(or(not(or(B,A)),X_41)),true,theorem(or(not(or(A,B)),X_41)),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true),ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true)) ),[1,2],$fot(theorem(or(not(or(A,B)),X_41)))]]) ).
cnf(refute_0_34,plain,
( ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true) != theorem(or(not(or(A,B)),X_41))
| ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true) = ifeq(theorem(or(not(or(B,A)),X_41)),true,theorem(or(not(or(A,B)),X_41)),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true),ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true) = ifeq(theorem(or(not(or(B,A)),X_41)),true,theorem(or(not(or(A,B)),X_41)),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),theorem(or(not(or(A,B)),X_41))) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true) != ifeq(theorem(or(not(or(B,A)),X_41)),true,theorem(or(not(or(A,B)),X_41)),true)
| ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true) != true
| ifeq(theorem(or(not(or(B,A)),X_41)),true,theorem(or(not(or(A,B)),X_41)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true),true) ),[0],$fot(ifeq(theorem(or(not(or(B,A)),X_41)),true,theorem(or(not(or(A,B)),X_41)),true))]]) ).
cnf(refute_0_37,plain,
( ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true) != true
| ifeq(theorem(or(not(or(B,A)),X_41)),true,theorem(or(not(or(A,B)),X_41)),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true),ifeq(theorem(or(not(or(B,A)),X_41)),true,theorem(or(not(or(A,B)),X_41)),true)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
ifeq(theorem(or(not(or(B,A)),X_41)),true,theorem(or(not(or(A,B)),X_41)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,A)),X_41)),true,ifeq(true,true,theorem(or(not(or(A,B)),X_41)),true),true),true) )],[refute_0_30,refute_0_37]) ).
cnf(refute_0_39,plain,
ifeq(theorem(or(not(or(X_359,X_358)),or(not(or(not(or(X_359,X_358)),C)),C))),true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true) = true,
inference(subst,[],[refute_0_38:[bind(A,$fot(X_358)),bind(B,$fot(X_359)),bind(X_41,$fot(or(not(or(not(or(X_359,X_358)),C)),C)))]]) ).
cnf(refute_0_40,plain,
ifeq(theorem(or(not(X_83),X_83)),true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true) = true,
inference(subst,[],[rule_2:[bind(Y,$fot(or(not(X_83),X_83)))]]) ).
cnf(refute_0_41,plain,
ifeq(theorem(or(not(or(X_41,X_41)),X_41)),true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true) = true,
inference(subst,[],[rule_3:[bind(X,$fot(X_39)),bind(Y,$fot(or(X_41,X_41))),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_42,plain,
ifeq(axiom(or(not(or(A,A)),A)),true,theorem(or(not(or(A,A)),A)),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(A,A)),A)))]]) ).
cnf(refute_0_43,plain,
( axiom(or(not(or(A,A)),A)) != true
| ifeq(axiom(or(not(or(A,A)),A)),true,theorem(or(not(or(A,A)),A)),true) != true
| ifeq(true,true,theorem(or(not(or(A,A)),A)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(or(not(or(A,A)),A)),true,theorem(or(not(or(A,A)),A)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_44,plain,
( ifeq(axiom(or(not(or(A,A)),A)),true,theorem(or(not(or(A,A)),A)),true) != true
| ifeq(true,true,theorem(or(not(or(A,A)),A)),true) = true ),
inference(resolve,[$cnf( $equal(axiom(or(not(or(A,A)),A)),true) )],[axiom_1_2,refute_0_43]) ).
cnf(refute_0_45,plain,
ifeq(true,true,theorem(or(not(or(A,A)),A)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(or(not(or(A,A)),A)),true,theorem(or(not(or(A,A)),A)),true),true) )],[refute_0_42,refute_0_44]) ).
cnf(refute_0_46,plain,
ifeq(true,true,theorem(or(not(or(A,A)),A)),true) = theorem(or(not(or(A,A)),A)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(or(A,A)),A)))),bind(C,$fot(true))]]) ).
cnf(refute_0_47,plain,
( ifeq(true,true,theorem(or(not(or(A,A)),A)),true) != theorem(or(not(or(A,A)),A))
| ifeq(true,true,theorem(or(not(or(A,A)),A)),true) != true
| theorem(or(not(or(A,A)),A)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(A,A)),A)),true),true) ),[0],$fot(theorem(or(not(or(A,A)),A)))]]) ).
cnf(refute_0_48,plain,
( ifeq(true,true,theorem(or(not(or(A,A)),A)),true) != true
| theorem(or(not(or(A,A)),A)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(A,A)),A)),true),theorem(or(not(or(A,A)),A))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
theorem(or(not(or(A,A)),A)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(A,A)),A)),true),true) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
theorem(or(not(or(X_41,X_41)),X_41)) = true,
inference(subst,[],[refute_0_49:[bind(A,$fot(X_41))]]) ).
cnf(refute_0_51,plain,
( ifeq(theorem(or(not(or(X_41,X_41)),X_41)),true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true) != true
| theorem(or(not(or(X_41,X_41)),X_41)) != true
| ifeq(true,true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(X_41,X_41)),X_41)),true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_52,plain,
( ifeq(theorem(or(not(or(X_41,X_41)),X_41)),true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true) != true
| ifeq(true,true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(or(not(or(X_41,X_41)),X_41)),true) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
ifeq(true,true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(X_41,X_41)),X_41)),true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true),true) )],[refute_0_41,refute_0_52]) ).
cnf(refute_0_54,plain,
ifeq(true,true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true) = ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_55,plain,
( ifeq(true,true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true) != ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true)
| ifeq(true,true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true) != true
| ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true),true) ),[0],$fot(ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true))]]) ).
cnf(refute_0_56,plain,
( ifeq(true,true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true) != true
| ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true),ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(axiom(or(not(X_39),or(X_41,X_41))),true,theorem(or(not(X_39),X_41)),true),true),true) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
ifeq(axiom(or(not(X_82),or(X_82,X_82))),true,theorem(or(not(X_82),X_82)),true) = true,
inference(subst,[],[refute_0_57:[bind(X_39,$fot(X_82)),bind(X_41,$fot(X_82))]]) ).
cnf(refute_0_59,plain,
axiom(or(not(X_82),or(X_82,X_82))) = true,
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_82)),bind(B,$fot(X_82))]]) ).
cnf(refute_0_60,plain,
( axiom(or(not(X_82),or(X_82,X_82))) != true
| ifeq(axiom(or(not(X_82),or(X_82,X_82))),true,theorem(or(not(X_82),X_82)),true) != true
| ifeq(true,true,theorem(or(not(X_82),X_82)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(or(not(X_82),or(X_82,X_82))),true,theorem(or(not(X_82),X_82)),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_61,plain,
( ifeq(axiom(or(not(X_82),or(X_82,X_82))),true,theorem(or(not(X_82),X_82)),true) != true
| ifeq(true,true,theorem(or(not(X_82),X_82)),true) = true ),
inference(resolve,[$cnf( $equal(axiom(or(not(X_82),or(X_82,X_82))),true) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
ifeq(true,true,theorem(or(not(X_82),X_82)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(or(not(X_82),or(X_82,X_82))),true,theorem(or(not(X_82),X_82)),true),true) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
ifeq(true,true,theorem(or(not(X_82),X_82)),true) = theorem(or(not(X_82),X_82)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(X_82),X_82)))),bind(C,$fot(true))]]) ).
cnf(refute_0_64,plain,
( ifeq(true,true,theorem(or(not(X_82),X_82)),true) != theorem(or(not(X_82),X_82))
| ifeq(true,true,theorem(or(not(X_82),X_82)),true) != true
| theorem(or(not(X_82),X_82)) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_82),X_82)),true),true) ),[0],$fot(theorem(or(not(X_82),X_82)))]]) ).
cnf(refute_0_65,plain,
( ifeq(true,true,theorem(or(not(X_82),X_82)),true) != true
| theorem(or(not(X_82),X_82)) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_82),X_82)),true),theorem(or(not(X_82),X_82))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
theorem(or(not(X_82),X_82)) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_82),X_82)),true),true) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
theorem(or(not(X_83),X_83)) = true,
inference(subst,[],[refute_0_66:[bind(X_82,$fot(X_83))]]) ).
cnf(refute_0_68,plain,
( ifeq(theorem(or(not(X_83),X_83)),true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true) != true
| theorem(or(not(X_83),X_83)) != true
| ifeq(true,true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(X_83),X_83)),true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_69,plain,
( ifeq(theorem(or(not(X_83),X_83)),true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true) != true
| ifeq(true,true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true) = true ),
inference(resolve,[$cnf( $equal(theorem(or(not(X_83),X_83)),true) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
ifeq(true,true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(X_83),X_83)),true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true),true) )],[refute_0_40,refute_0_69]) ).
cnf(refute_0_71,plain,
ifeq(true,true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true) = ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true))),bind(C,$fot(true))]]) ).
cnf(refute_0_72,plain,
( ifeq(true,true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true) != ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true)
| ifeq(true,true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true) != true
| ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true),true) ),[0],$fot(ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true))]]) ).
cnf(refute_0_73,plain,
( ifeq(true,true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true) != true
| ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true),ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,ifeq(axiom(or(not(or(not(X_83),X_83)),X)),true,theorem(X),true),true),true) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
ifeq(axiom(or(not(or(not(or(B,C)),or(B,C))),or(B,or(not(or(B,C)),C)))),true,theorem(or(B,or(not(or(B,C)),C))),true) = true,
inference(subst,[],[refute_0_74:[bind(X,$fot(or(B,or(not(or(B,C)),C)))),bind(X_83,$fot(or(B,C)))]]) ).
cnf(refute_0_76,plain,
axiom(or(not(or(not(or(B,C)),or(B,C))),or(B,or(not(or(B,C)),C)))) = true,
inference(subst,[],[axiom_1_5:[bind(A,$fot(not(or(B,C))))]]) ).
cnf(refute_0_77,plain,
( axiom(or(not(or(not(or(B,C)),or(B,C))),or(B,or(not(or(B,C)),C)))) != true
| ifeq(axiom(or(not(or(not(or(B,C)),or(B,C))),or(B,or(not(or(B,C)),C)))),true,theorem(or(B,or(not(or(B,C)),C))),true) != true
| ifeq(true,true,theorem(or(B,or(not(or(B,C)),C))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(or(not(or(not(or(B,C)),or(B,C))),or(B,or(not(or(B,C)),C)))),true,theorem(or(B,or(not(or(B,C)),C))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_78,plain,
( ifeq(axiom(or(not(or(not(or(B,C)),or(B,C))),or(B,or(not(or(B,C)),C)))),true,theorem(or(B,or(not(or(B,C)),C))),true) != true
| ifeq(true,true,theorem(or(B,or(not(or(B,C)),C))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(or(not(or(not(or(B,C)),or(B,C))),or(B,or(not(or(B,C)),C)))),true) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
ifeq(true,true,theorem(or(B,or(not(or(B,C)),C))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(or(not(or(not(or(B,C)),or(B,C))),or(B,or(not(or(B,C)),C)))),true,theorem(or(B,or(not(or(B,C)),C))),true),true) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
ifeq(true,true,theorem(or(B,or(not(or(B,C)),C))),true) = theorem(or(B,or(not(or(B,C)),C))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(B,or(not(or(B,C)),C))))),bind(C,$fot(true))]]) ).
cnf(refute_0_81,plain,
( ifeq(true,true,theorem(or(B,or(not(or(B,C)),C))),true) != theorem(or(B,or(not(or(B,C)),C)))
| ifeq(true,true,theorem(or(B,or(not(or(B,C)),C))),true) != true
| theorem(or(B,or(not(or(B,C)),C))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(B,or(not(or(B,C)),C))),true),true) ),[0],$fot(theorem(or(B,or(not(or(B,C)),C))))]]) ).
cnf(refute_0_82,plain,
( ifeq(true,true,theorem(or(B,or(not(or(B,C)),C))),true) != true
| theorem(or(B,or(not(or(B,C)),C))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(B,or(not(or(B,C)),C))),true),theorem(or(B,or(not(or(B,C)),C)))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
theorem(or(B,or(not(or(B,C)),C))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(B,or(not(or(B,C)),C))),true),true) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
theorem(or(not(or(X_359,X_358)),or(not(or(not(or(X_359,X_358)),C)),C))) = true,
inference(subst,[],[refute_0_83:[bind(B,$fot(not(or(X_359,X_358))))]]) ).
cnf(refute_0_85,plain,
( ifeq(theorem(or(not(or(X_359,X_358)),or(not(or(not(or(X_359,X_358)),C)),C))),true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true) != true
| theorem(or(not(or(X_359,X_358)),or(not(or(not(or(X_359,X_358)),C)),C))) != true
| ifeq(true,true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(X_359,X_358)),or(not(or(not(or(X_359,X_358)),C)),C))),true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_86,plain,
( ifeq(theorem(or(not(or(X_359,X_358)),or(not(or(not(or(X_359,X_358)),C)),C))),true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true) != true
| ifeq(true,true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(or(not(or(X_359,X_358)),or(not(or(not(or(X_359,X_358)),C)),C))),true) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
ifeq(true,true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(X_359,X_358)),or(not(or(not(or(X_359,X_358)),C)),C))),true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true),true) )],[refute_0_39,refute_0_86]) ).
cnf(refute_0_88,plain,
ifeq(true,true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true) = theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))))),bind(C,$fot(true))]]) ).
cnf(refute_0_89,plain,
( ifeq(true,true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true) != theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C)))
| ifeq(true,true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true) != true
| theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true),true) ),[0],$fot(theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))))]]) ).
cnf(refute_0_90,plain,
( ifeq(true,true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true) != true
| theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true),theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(X_358,X_359)),or(not(or(not(or(X_359,X_358)),C)),C))),true),true) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
theorem(or(not(or(B,X_39)),or(not(or(not(or(X_39,B)),X_1076)),X_1076))) = true,
inference(subst,[],[refute_0_91:[bind(C,$fot(X_1076)),bind(X_358,$fot(B)),bind(X_359,$fot(X_39))]]) ).
cnf(refute_0_93,plain,
( ifeq(theorem(or(not(or(B,X_39)),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true) != true
| theorem(or(not(or(B,X_39)),or(not(or(not(or(X_39,B)),X_1076)),X_1076))) != true
| ifeq(true,true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_39)),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_94,plain,
( ifeq(theorem(or(not(or(B,X_39)),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true) != true
| ifeq(true,true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(or(not(or(B,X_39)),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
ifeq(true,true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_39)),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true),true) )],[refute_0_26,refute_0_94]) ).
cnf(refute_0_96,plain,
ifeq(true,true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true) = theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))))),bind(C,$fot(true))]]) ).
cnf(refute_0_97,plain,
( ifeq(true,true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true) != theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076)))
| ifeq(true,true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true) != true
| theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true),true) ),[0],$fot(theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))))]]) ).
cnf(refute_0_98,plain,
( ifeq(true,true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true) != true
| theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true),theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076)))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_39),or(not(or(not(or(X_39,B)),X_1076)),X_1076))),true),true) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
theorem(or(not(X_1444),or(not(or(not(or(X_1444,X_1442)),C)),C))) = true,
inference(subst,[],[refute_0_99:[bind(B,$fot(X_1442)),bind(X_1076,$fot(C)),bind(X_39,$fot(X_1444))]]) ).
cnf(refute_0_101,plain,
( ifeq(theorem(or(not(X_1444),or(not(or(not(or(X_1444,X_1442)),C)),C))),true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true) != true
| theorem(or(not(X_1444),or(not(or(not(or(X_1444,X_1442)),C)),C))) != true
| ifeq(true,true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(X_1444),or(not(or(not(or(X_1444,X_1442)),C)),C))),true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_102,plain,
( ifeq(theorem(or(not(X_1444),or(not(or(not(or(X_1444,X_1442)),C)),C))),true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true) != true
| ifeq(true,true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(or(not(X_1444),or(not(or(not(or(X_1444,X_1442)),C)),C))),true) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
ifeq(true,true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(X_1444),or(not(or(not(or(X_1444,X_1442)),C)),C))),true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true),true) )],[refute_0_12,refute_0_102]) ).
cnf(refute_0_104,plain,
ifeq(true,true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true) = theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))))),bind(C,$fot(true))]]) ).
cnf(refute_0_105,plain,
( ifeq(true,true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true) != theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C)))
| ifeq(true,true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true) != true
| theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true),true) ),[0],$fot(theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))))]]) ).
cnf(refute_0_106,plain,
( ifeq(true,true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true) != true
| theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true),theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C)))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(not(or(X_1444,X_1442)),C)),or(not(X_1444),C))),true),true) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) = true,
inference(subst,[],[refute_0_107:[bind(C,$fot(q)),bind(X_1442,$fot(q)),bind(X_1444,$fot(p))]]) ).
cnf(refute_0_109,plain,
( theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) != true
| true != true
| theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) = true ),
introduced(tautology,[equality,[$cnf( ~ $equal(theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))),true) ),[0],$fot(true)]]) ).
cnf(refute_0_110,plain,
( true != true
| theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))) = true ),
inference(resolve,[$cnf( $equal(theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))),true) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
true != true,
inference(resolve,[$cnf( $equal(theorem(or(not(or(not(or(p,q)),q)),or(not(p),q))),true) )],[refute_0_110,prove_this]) ).
cnf(refute_0_112,plain,
true = true,
introduced(tautology,[refl,[$fot(true)]]) ).
cnf(refute_0_113,plain,
$false,
inference(resolve,[$cnf( $equal(true,true) )],[refute_0_112,refute_0_111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL218-10 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n025.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 Jul 4 18:14:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.63/2.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.63/2.84
% 2.63/2.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.63/2.86
%------------------------------------------------------------------------------