TSTP Solution File: LCL186-10 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL186-10 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 12:50:21 EDT 2022
% Result : Unsatisfiable 0.42s 0.58s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of clauses : 43 ( 27 unt; 0 nHn; 20 RR)
% Number of literals : 67 ( 66 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 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 : 84 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq(A,A,B,C) = B ).
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(rule_1,axiom,
ifeq(axiom(X),true,theorem(X),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(not(p)),or(not(p),q))) != true ).
cnf(refute_0_0,plain,
ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(axiom(or(not(X_32),or(B,X_32))),true,theorem(or(not(X_32),X_34)),true),true) = true,
inference(subst,[],[rule_3:[bind(X,$fot(X_32)),bind(Y,$fot(or(B,X_32))),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_1,plain,
axiom(or(not(X_32),or(B,X_32))) = true,
inference(subst,[],[axiom_1_3:[bind(A,$fot(X_32))]]) ).
cnf(refute_0_2,plain,
( axiom(or(not(X_32),or(B,X_32))) != true
| ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(axiom(or(not(X_32),or(B,X_32))),true,theorem(or(not(X_32),X_34)),true),true) != true
| ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(axiom(or(not(X_32),or(B,X_32))),true,theorem(or(not(X_32),X_34)),true),true),true) ),[0,2,0],$fot(true)]]) ).
cnf(refute_0_3,plain,
( ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(axiom(or(not(X_32),or(B,X_32))),true,theorem(or(not(X_32),X_34)),true),true) != true
| ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true) = true ),
inference(resolve,[$cnf( $equal(axiom(or(not(X_32),or(B,X_32))),true) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(axiom(or(not(X_32),or(B,X_32))),true,theorem(or(not(X_32),X_34)),true),true),true) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
ifeq(true,true,theorem(or(not(X_32),X_34)),true) = theorem(or(not(X_32),X_34)),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(X_32),X_34)))),bind(C,$fot(true))]]) ).
cnf(refute_0_6,plain,
ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true) = ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true),
introduced(tautology,[refl,[$fot(ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true))]]) ).
cnf(refute_0_7,plain,
( ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true) != ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true)
| ifeq(true,true,theorem(or(not(X_32),X_34)),true) != theorem(or(not(X_32),X_34))
| ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true) = ifeq(theorem(or(not(or(B,X_32)),X_34)),true,theorem(or(not(X_32),X_34)),true) ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true),ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true)) ),[1,2],$fot(theorem(or(not(X_32),X_34)))]]) ).
cnf(refute_0_8,plain,
( ifeq(true,true,theorem(or(not(X_32),X_34)),true) != theorem(or(not(X_32),X_34))
| ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true) = ifeq(theorem(or(not(or(B,X_32)),X_34)),true,theorem(or(not(X_32),X_34)),true) ),
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true),ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true) = ifeq(theorem(or(not(or(B,X_32)),X_34)),true,theorem(or(not(X_32),X_34)),true),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_32),X_34)),true),theorem(or(not(X_32),X_34))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true) != ifeq(theorem(or(not(or(B,X_32)),X_34)),true,theorem(or(not(X_32),X_34)),true)
| ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true) != true
| ifeq(theorem(or(not(or(B,X_32)),X_34)),true,theorem(or(not(X_32),X_34)),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true),true) ),[0],$fot(ifeq(theorem(or(not(or(B,X_32)),X_34)),true,theorem(or(not(X_32),X_34)),true))]]) ).
cnf(refute_0_11,plain,
( ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true) != true
| ifeq(theorem(or(not(or(B,X_32)),X_34)),true,theorem(or(not(X_32),X_34)),true) = true ),
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true),ifeq(theorem(or(not(or(B,X_32)),X_34)),true,theorem(or(not(X_32),X_34)),true)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
ifeq(theorem(or(not(or(B,X_32)),X_34)),true,theorem(or(not(X_32),X_34)),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(B,X_32)),X_34)),true,ifeq(true,true,theorem(or(not(X_32),X_34)),true),true),true) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
ifeq(theorem(or(not(or(X_165,X_166)),or(X_166,X_165))),true,theorem(or(not(X_166),or(X_166,X_165))),true) = true,
inference(subst,[],[refute_0_12:[bind(B,$fot(X_165)),bind(X_32,$fot(X_166)),bind(X_34,$fot(or(X_166,X_165)))]]) ).
cnf(refute_0_14,plain,
ifeq(axiom(or(not(or(X_8,X_9)),or(X_9,X_8))),true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true) = true,
inference(subst,[],[rule_1:[bind(X,$fot(or(not(or(X_8,X_9)),or(X_9,X_8))))]]) ).
cnf(refute_0_15,plain,
axiom(or(not(or(X_8,X_9)),or(X_9,X_8))) = true,
inference(subst,[],[axiom_1_4:[bind(A,$fot(X_8)),bind(B,$fot(X_9))]]) ).
cnf(refute_0_16,plain,
( axiom(or(not(or(X_8,X_9)),or(X_9,X_8))) != true
| ifeq(axiom(or(not(or(X_8,X_9)),or(X_9,X_8))),true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true) != true
| ifeq(true,true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(axiom(or(not(or(X_8,X_9)),or(X_9,X_8))),true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_17,plain,
( ifeq(axiom(or(not(or(X_8,X_9)),or(X_9,X_8))),true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true) != true
| ifeq(true,true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true) = true ),
inference(resolve,[$cnf( $equal(axiom(or(not(or(X_8,X_9)),or(X_9,X_8))),true) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
ifeq(true,true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(axiom(or(not(or(X_8,X_9)),or(X_9,X_8))),true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true),true) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
ifeq(true,true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true) = theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(or(X_8,X_9)),or(X_9,X_8))))),bind(C,$fot(true))]]) ).
cnf(refute_0_20,plain,
( ifeq(true,true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true) != theorem(or(not(or(X_8,X_9)),or(X_9,X_8)))
| ifeq(true,true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true) != true
| theorem(or(not(or(X_8,X_9)),or(X_9,X_8))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true),true) ),[0],$fot(theorem(or(not(or(X_8,X_9)),or(X_9,X_8))))]]) ).
cnf(refute_0_21,plain,
( ifeq(true,true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true) != true
| theorem(or(not(or(X_8,X_9)),or(X_9,X_8))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true),theorem(or(not(or(X_8,X_9)),or(X_9,X_8)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
theorem(or(not(or(X_8,X_9)),or(X_9,X_8))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(or(X_8,X_9)),or(X_9,X_8))),true),true) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
theorem(or(not(or(X_165,X_166)),or(X_166,X_165))) = true,
inference(subst,[],[refute_0_22:[bind(X_8,$fot(X_165)),bind(X_9,$fot(X_166))]]) ).
cnf(refute_0_24,plain,
( ifeq(theorem(or(not(or(X_165,X_166)),or(X_166,X_165))),true,theorem(or(not(X_166),or(X_166,X_165))),true) != true
| theorem(or(not(or(X_165,X_166)),or(X_166,X_165))) != true
| ifeq(true,true,theorem(or(not(X_166),or(X_166,X_165))),true) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(theorem(or(not(or(X_165,X_166)),or(X_166,X_165))),true,theorem(or(not(X_166),or(X_166,X_165))),true),true) ),[0,0],$fot(true)]]) ).
cnf(refute_0_25,plain,
( ifeq(theorem(or(not(or(X_165,X_166)),or(X_166,X_165))),true,theorem(or(not(X_166),or(X_166,X_165))),true) != true
| ifeq(true,true,theorem(or(not(X_166),or(X_166,X_165))),true) = true ),
inference(resolve,[$cnf( $equal(theorem(or(not(or(X_165,X_166)),or(X_166,X_165))),true) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
ifeq(true,true,theorem(or(not(X_166),or(X_166,X_165))),true) = true,
inference(resolve,[$cnf( $equal(ifeq(theorem(or(not(or(X_165,X_166)),or(X_166,X_165))),true,theorem(or(not(X_166),or(X_166,X_165))),true),true) )],[refute_0_13,refute_0_25]) ).
cnf(refute_0_27,plain,
ifeq(true,true,theorem(or(not(X_166),or(X_166,X_165))),true) = theorem(or(not(X_166),or(X_166,X_165))),
inference(subst,[],[ifeq_axiom:[bind(A,$fot(true)),bind(B,$fot(theorem(or(not(X_166),or(X_166,X_165))))),bind(C,$fot(true))]]) ).
cnf(refute_0_28,plain,
( ifeq(true,true,theorem(or(not(X_166),or(X_166,X_165))),true) != theorem(or(not(X_166),or(X_166,X_165)))
| ifeq(true,true,theorem(or(not(X_166),or(X_166,X_165))),true) != true
| theorem(or(not(X_166),or(X_166,X_165))) = true ),
introduced(tautology,[equality,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_166),or(X_166,X_165))),true),true) ),[0],$fot(theorem(or(not(X_166),or(X_166,X_165))))]]) ).
cnf(refute_0_29,plain,
( ifeq(true,true,theorem(or(not(X_166),or(X_166,X_165))),true) != true
| theorem(or(not(X_166),or(X_166,X_165))) = true ),
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_166),or(X_166,X_165))),true),theorem(or(not(X_166),or(X_166,X_165)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
theorem(or(not(X_166),or(X_166,X_165))) = true,
inference(resolve,[$cnf( $equal(ifeq(true,true,theorem(or(not(X_166),or(X_166,X_165))),true),true) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
theorem(or(not(not(p)),or(not(p),q))) = true,
inference(subst,[],[refute_0_30:[bind(X_165,$fot(q)),bind(X_166,$fot(not(p)))]]) ).
cnf(refute_0_32,plain,
( theorem(or(not(not(p)),or(not(p),q))) != true
| true != true
| theorem(or(not(not(p)),or(not(p),q))) = true ),
introduced(tautology,[equality,[$cnf( ~ $equal(theorem(or(not(not(p)),or(not(p),q))),true) ),[0],$fot(true)]]) ).
cnf(refute_0_33,plain,
( true != true
| theorem(or(not(not(p)),or(not(p),q))) = true ),
inference(resolve,[$cnf( $equal(theorem(or(not(not(p)),or(not(p),q))),true) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
true != true,
inference(resolve,[$cnf( $equal(theorem(or(not(not(p)),or(not(p),q))),true) )],[refute_0_33,prove_this]) ).
cnf(refute_0_35,plain,
true = true,
introduced(tautology,[refl,[$fot(true)]]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( $equal(true,true) )],[refute_0_35,refute_0_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL186-10 : TPTP v8.1.0. Released v7.5.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 03:56:56 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.42/0.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.58
% 0.42/0.58 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.42/0.59
%------------------------------------------------------------------------------