TSTP Solution File: LCL132-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL132-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 12:49:49 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of clauses : 40 ( 23 unt; 0 nHn; 21 RR)
% Number of literals : 65 ( 64 equ; 27 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 : 48 ( 0 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(prove_wajsberg_lemma,negated_conjecture,
implies(x,x) != truth ).
cnf(refute_0_0,plain,
implies(truth,implies(implies(truth,X_12),X_12)) = implies(implies(truth,X_12),X_12),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,X_12),X_12)))]]) ).
cnf(refute_0_1,plain,
implies(implies(truth,X_6),implies(implies(X_6,X_7),implies(truth,X_7))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_6)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_2,plain,
implies(truth,X_7) = X_7,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_7))]]) ).
cnf(refute_0_3,plain,
( implies(implies(truth,X_6),implies(implies(X_6,X_7),implies(truth,X_7))) != truth
| implies(truth,X_7) != X_7
| implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_6),implies(implies(X_6,X_7),implies(truth,X_7))),truth) ),[0,1,1],$fot(X_7)]]) ).
cnf(refute_0_4,plain,
( implies(implies(truth,X_6),implies(implies(X_6,X_7),implies(truth,X_7))) != truth
| implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_7),X_7) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_6),implies(implies(X_6,X_7),implies(truth,X_7))),truth) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
implies(truth,X_6) = X_6,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_7,plain,
implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)) = implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)))]]) ).
cnf(refute_0_8,plain,
( implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)) != implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7))
| implies(truth,X_6) != X_6
| implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)) = implies(X_6,implies(implies(X_6,X_7),X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)),implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7))) ),[1,0],$fot(X_6)]]) ).
cnf(refute_0_9,plain,
( implies(truth,X_6) != X_6
| implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)) = implies(X_6,implies(implies(X_6,X_7),X_7)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)),implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)) = implies(X_6,implies(implies(X_6,X_7),X_7)),
inference(resolve,[$cnf( $equal(implies(truth,X_6),X_6) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)) != implies(X_6,implies(implies(X_6,X_7),X_7))
| implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)) != truth
| implies(X_6,implies(implies(X_6,X_7),X_7)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)),truth) ),[0],$fot(implies(X_6,implies(implies(X_6,X_7),X_7)))]]) ).
cnf(refute_0_12,plain,
( implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)) != truth
| implies(X_6,implies(implies(X_6,X_7),X_7)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)),implies(X_6,implies(implies(X_6,X_7),X_7))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(X_6,implies(implies(X_6,X_7),X_7)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_6),implies(implies(X_6,X_7),X_7)),truth) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
implies(truth,implies(implies(truth,X_12),X_12)) = truth,
inference(subst,[],[refute_0_13:[bind(X_6,$fot(truth)),bind(X_7,$fot(X_12))]]) ).
cnf(refute_0_15,plain,
( implies(truth,implies(implies(truth,X_12),X_12)) != implies(implies(truth,X_12),X_12)
| implies(truth,implies(implies(truth,X_12),X_12)) != truth
| truth = implies(implies(truth,X_12),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_12),X_12)),implies(implies(truth,X_12),X_12)) ),[0],$fot(truth)]]) ).
cnf(refute_0_16,plain,
( implies(truth,implies(implies(truth,X_12),X_12)) != implies(implies(truth,X_12),X_12)
| truth = implies(implies(truth,X_12),X_12) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_12),X_12)),truth) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
truth = implies(implies(truth,X_12),X_12),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_12),X_12)),implies(implies(truth,X_12),X_12)) )],[refute_0_0,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(truth,X_12) = X_12,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_19,plain,
implies(implies(truth,X_12),X_12) = implies(implies(truth,X_12),X_12),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_12),X_12))]]) ).
cnf(refute_0_20,plain,
( implies(implies(truth,X_12),X_12) != implies(implies(truth,X_12),X_12)
| implies(truth,X_12) != X_12
| implies(implies(truth,X_12),X_12) = implies(X_12,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_12),X_12),implies(implies(truth,X_12),X_12)) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_21,plain,
( implies(truth,X_12) != X_12
| implies(implies(truth,X_12),X_12) = implies(X_12,X_12) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_12),X_12),implies(implies(truth,X_12),X_12)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(implies(truth,X_12),X_12) = implies(X_12,X_12),
inference(resolve,[$cnf( $equal(implies(truth,X_12),X_12) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( implies(implies(truth,X_12),X_12) != implies(X_12,X_12)
| truth != implies(implies(truth,X_12),X_12)
| truth = implies(X_12,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(implies(truth,X_12),X_12)) ),[1],$fot(implies(X_12,X_12))]]) ).
cnf(refute_0_24,plain,
( truth != implies(implies(truth,X_12),X_12)
| truth = implies(X_12,X_12) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_12),X_12),implies(X_12,X_12)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
truth = implies(X_12,X_12),
inference(resolve,[$cnf( $equal(truth,implies(implies(truth,X_12),X_12)) )],[refute_0_17,refute_0_24]) ).
cnf(refute_0_26,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_27,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_28,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( truth != implies(X_12,X_12)
| implies(X_12,X_12) = truth ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X_12,X_12)))]]) ).
cnf(refute_0_30,plain,
implies(X_12,X_12) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X_12,X_12)) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
implies(x,x) = truth,
inference(subst,[],[refute_0_30:[bind(X_12,$fot(x))]]) ).
cnf(refute_0_32,plain,
( implies(x,x) != truth
| truth != truth
| implies(x,x) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(x,x),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_33,plain,
( truth != truth
| implies(x,x) = truth ),
inference(resolve,[$cnf( $equal(implies(x,x),truth) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
truth != truth,
inference(resolve,[$cnf( $equal(implies(x,x),truth) )],[refute_0_33,prove_wajsberg_lemma]) ).
cnf(refute_0_35,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_35,refute_0_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL132-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n009.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jul 4 06:21:37 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------