TSTP Solution File: LCL134-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL134-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 12:49:50 EDT 2022
% Result : Unsatisfiable 0.18s 0.50s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of clauses : 61 ( 35 unt; 0 nHn; 30 RR)
% Number of literals : 99 ( 98 equ; 40 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 70 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(prove_wajsberg_lemma,negated_conjecture,
implies(x,truth) != truth ).
cnf(refute_0_0,plain,
implies(implies(truth,X_16),implies(implies(X_16,X_17),implies(truth,X_17))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_16)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_1,plain,
implies(truth,X_17) = X_17,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_2,plain,
( implies(implies(truth,X_16),implies(implies(X_16,X_17),implies(truth,X_17))) != truth
| implies(truth,X_17) != X_17
| implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),implies(truth,X_17))),truth) ),[0,1,1],$fot(X_17)]]) ).
cnf(refute_0_3,plain,
( implies(implies(truth,X_16),implies(implies(X_16,X_17),implies(truth,X_17))) != truth
| implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_17),X_17) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),implies(truth,X_17))),truth) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
implies(truth,X_16) = X_16,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_16))]]) ).
cnf(refute_0_6,plain,
implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)))]]) ).
cnf(refute_0_7,plain,
( implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) != implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17))
| implies(truth,X_16) != X_16
| implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = implies(X_16,implies(implies(X_16,X_17),X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17))) ),[1,0],$fot(X_16)]]) ).
cnf(refute_0_8,plain,
( implies(truth,X_16) != X_16
| implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = implies(X_16,implies(implies(X_16,X_17),X_17)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) = implies(X_16,implies(implies(X_16,X_17),X_17)),
inference(resolve,[$cnf( $equal(implies(truth,X_16),X_16) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) != implies(X_16,implies(implies(X_16,X_17),X_17))
| implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) != truth
| implies(X_16,implies(implies(X_16,X_17),X_17)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),truth) ),[0],$fot(implies(X_16,implies(implies(X_16,X_17),X_17)))]]) ).
cnf(refute_0_11,plain,
( implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)) != truth
| implies(X_16,implies(implies(X_16,X_17),X_17)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),implies(X_16,implies(implies(X_16,X_17),X_17))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
implies(X_16,implies(implies(X_16,X_17),X_17)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_16),implies(implies(X_16,X_17),X_17)),truth) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(X_23,implies(implies(X_23,truth),truth)) = truth,
inference(subst,[],[refute_0_12:[bind(X_16,$fot(X_23)),bind(X_17,$fot(truth))]]) ).
cnf(refute_0_14,plain,
implies(implies(truth,X_6),X_6) = implies(implies(X_6,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_15,plain,
implies(truth,X_6) = X_6,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_16,plain,
( implies(implies(truth,X_6),X_6) != implies(implies(X_6,truth),truth)
| implies(truth,X_6) != X_6
| implies(X_6,X_6) = implies(implies(X_6,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_6),X_6),implies(implies(X_6,truth),truth)) ),[0,0],$fot(X_6)]]) ).
cnf(refute_0_17,plain,
( implies(implies(truth,X_6),X_6) != implies(implies(X_6,truth),truth)
| implies(X_6,X_6) = implies(implies(X_6,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_6),X_6) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(X_6,X_6) = implies(implies(X_6,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_6),X_6),implies(implies(X_6,truth),truth)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
implies(X_23,X_23) = implies(implies(X_23,truth),truth),
inference(subst,[],[refute_0_18:[bind(X_6,$fot(X_23))]]) ).
cnf(refute_0_20,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_21,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( implies(X_23,X_23) != implies(implies(X_23,truth),truth)
| implies(implies(X_23,truth),truth) = implies(X_23,X_23) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(implies(X_23,X_23))),bind(Y0,$fot(implies(implies(X_23,truth),truth)))]]) ).
cnf(refute_0_24,plain,
implies(implies(X_23,truth),truth) = implies(X_23,X_23),
inference(resolve,[$cnf( $equal(implies(X_23,X_23),implies(implies(X_23,truth),truth)) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
( implies(X_23,implies(implies(X_23,truth),truth)) != truth
| implies(implies(X_23,truth),truth) != implies(X_23,X_23)
| implies(X_23,implies(X_23,X_23)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_23,implies(implies(X_23,truth),truth)),truth) ),[0,1],$fot(implies(X_23,X_23))]]) ).
cnf(refute_0_26,plain,
( implies(X_23,implies(implies(X_23,truth),truth)) != truth
| implies(X_23,implies(X_23,X_23)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_23,truth),truth),implies(X_23,X_23)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(X_23,implies(X_23,X_23)) = truth,
inference(resolve,[$cnf( $equal(implies(X_23,implies(implies(X_23,truth),truth)),truth) )],[refute_0_13,refute_0_26]) ).
cnf(refute_0_28,plain,
implies(truth,implies(implies(truth,X_24),X_24)) = implies(implies(truth,X_24),X_24),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,X_24),X_24)))]]) ).
cnf(refute_0_29,plain,
implies(truth,implies(implies(truth,X_24),X_24)) = truth,
inference(subst,[],[refute_0_12:[bind(X_16,$fot(truth)),bind(X_17,$fot(X_24))]]) ).
cnf(refute_0_30,plain,
( implies(truth,implies(implies(truth,X_24),X_24)) != implies(implies(truth,X_24),X_24)
| implies(truth,implies(implies(truth,X_24),X_24)) != truth
| truth = implies(implies(truth,X_24),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_24),X_24)),implies(implies(truth,X_24),X_24)) ),[0],$fot(truth)]]) ).
cnf(refute_0_31,plain,
( implies(truth,implies(implies(truth,X_24),X_24)) != implies(implies(truth,X_24),X_24)
| truth = implies(implies(truth,X_24),X_24) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_24),X_24)),truth) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
truth = implies(implies(truth,X_24),X_24),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_24),X_24)),implies(implies(truth,X_24),X_24)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
implies(truth,X_24) = X_24,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_34,plain,
implies(implies(truth,X_24),X_24) = implies(implies(truth,X_24),X_24),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_24),X_24))]]) ).
cnf(refute_0_35,plain,
( implies(implies(truth,X_24),X_24) != implies(implies(truth,X_24),X_24)
| implies(truth,X_24) != X_24
| implies(implies(truth,X_24),X_24) = implies(X_24,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_24),X_24),implies(implies(truth,X_24),X_24)) ),[1,0],$fot(X_24)]]) ).
cnf(refute_0_36,plain,
( implies(truth,X_24) != X_24
| implies(implies(truth,X_24),X_24) = implies(X_24,X_24) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_24),X_24),implies(implies(truth,X_24),X_24)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
implies(implies(truth,X_24),X_24) = implies(X_24,X_24),
inference(resolve,[$cnf( $equal(implies(truth,X_24),X_24) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( implies(implies(truth,X_24),X_24) != implies(X_24,X_24)
| truth != implies(implies(truth,X_24),X_24)
| truth = implies(X_24,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(implies(truth,X_24),X_24)) ),[1],$fot(implies(X_24,X_24))]]) ).
cnf(refute_0_39,plain,
( truth != implies(implies(truth,X_24),X_24)
| truth = implies(X_24,X_24) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_24),X_24),implies(X_24,X_24)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
truth = implies(X_24,X_24),
inference(resolve,[$cnf( $equal(truth,implies(implies(truth,X_24),X_24)) )],[refute_0_32,refute_0_39]) ).
cnf(refute_0_41,plain,
( truth != implies(X_24,X_24)
| implies(X_24,X_24) = truth ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X_24,X_24)))]]) ).
cnf(refute_0_42,plain,
implies(X_24,X_24) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X_24,X_24)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(X_23,X_23) = truth,
inference(subst,[],[refute_0_42:[bind(X_24,$fot(X_23))]]) ).
cnf(refute_0_44,plain,
implies(X_23,implies(X_23,X_23)) = implies(X_23,implies(X_23,X_23)),
introduced(tautology,[refl,[$fot(implies(X_23,implies(X_23,X_23)))]]) ).
cnf(refute_0_45,plain,
( implies(X_23,X_23) != truth
| implies(X_23,implies(X_23,X_23)) != implies(X_23,implies(X_23,X_23))
| implies(X_23,implies(X_23,X_23)) = implies(X_23,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_23,implies(X_23,X_23)),implies(X_23,implies(X_23,X_23))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_46,plain,
( implies(X_23,X_23) != truth
| implies(X_23,implies(X_23,X_23)) = implies(X_23,truth) ),
inference(resolve,[$cnf( $equal(implies(X_23,implies(X_23,X_23)),implies(X_23,implies(X_23,X_23))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
implies(X_23,implies(X_23,X_23)) = implies(X_23,truth),
inference(resolve,[$cnf( $equal(implies(X_23,X_23),truth) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( implies(X_23,implies(X_23,X_23)) != implies(X_23,truth)
| implies(X_23,implies(X_23,X_23)) != truth
| implies(X_23,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_23,implies(X_23,X_23)),truth) ),[0],$fot(implies(X_23,truth))]]) ).
cnf(refute_0_49,plain,
( implies(X_23,implies(X_23,X_23)) != truth
| implies(X_23,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(X_23,implies(X_23,X_23)),implies(X_23,truth)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(X_23,truth) = truth,
inference(resolve,[$cnf( $equal(implies(X_23,implies(X_23,X_23)),truth) )],[refute_0_27,refute_0_49]) ).
cnf(refute_0_51,plain,
implies(x,truth) = truth,
inference(subst,[],[refute_0_50:[bind(X_23,$fot(x))]]) ).
cnf(refute_0_52,plain,
( implies(x,truth) != truth
| truth != truth
| implies(x,truth) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(x,truth),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_53,plain,
( truth != truth
| implies(x,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(x,truth),truth) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
truth != truth,
inference(resolve,[$cnf( $equal(implies(x,truth),truth) )],[refute_0_53,prove_wajsberg_lemma]) ).
cnf(refute_0_55,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_56,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_55,refute_0_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL134-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n006.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 : Sun Jul 3 04:28:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.50
% 0.18/0.50 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.51
%------------------------------------------------------------------------------