%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:41:59 PM UTC 2026
% Result : Unsatisfiable 4.56s 4.83s
% Output : CNFRefutation 4.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 40
% Syntax : Number of clauses : 148 ( 62 unt; 14 nHn; 103 RR)
% Number of literals : 268 ( 218 equ; 108 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 184 ( 15 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(big_V_definition,axiom,
big_V(X,Y) = implies(implies(X,Y),Y) ).
cnf(partial_order_definition1,axiom,
( ~ ordered(X,Y)
| implies(X,Y) = truth ) ).
cnf(partial_order_definition2,axiom,
( implies(X,Y) != truth
| ordered(X,Y) ) ).
cnf(antecedent,negated_conjecture,
( ordered(x,implies(y,z))
| ordered(y,implies(x,z)) ) ).
cnf(prove_wajsberg_theorem,negated_conjecture,
( ~ ordered(x,implies(y,z))
| ~ ordered(y,implies(x,z)) ) ).
cnf(refute_0_0,plain,
( implies(y,implies(x,z)) != truth
| ordered(y,implies(x,z)) ),
inference(subst,[],[partial_order_definition2:[bind(X,$fot(y)),bind(Y,$fot(implies(x,z)))]]) ).
cnf(refute_0_1,plain,
implies(implies(X,big_V(X,X_29)),implies(implies(big_V(X,X_29),Z),implies(X,Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(big_V(X,X_29)))]]) ).
cnf(refute_0_2,plain,
implies(implies(truth,X_24),implies(implies(X_24,X_25),implies(truth,X_25))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_24)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_3,plain,
implies(truth,X_25) = X_25,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_4,plain,
( implies(implies(truth,X_24),implies(implies(X_24,X_25),implies(truth,X_25))) != truth
| implies(truth,X_25) != X_25
| implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_24),implies(implies(X_24,X_25),implies(truth,X_25))),truth) ),[0,1,1],$fot(X_25)]]) ).
cnf(refute_0_5,plain,
( implies(implies(truth,X_24),implies(implies(X_24,X_25),implies(truth,X_25))) != truth
| implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_25),X_25) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_24),implies(implies(X_24,X_25),implies(truth,X_25))),truth) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( big_V(X,Y) != implies(implies(X,Y),Y)
| implies(implies(X,Y),Y) = big_V(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(X,Y))),bind(Y0,$fot(implies(implies(X,Y),Y)))]]) ).
cnf(refute_0_11,plain,
implies(implies(X,Y),Y) = big_V(X,Y),
inference(resolve,[$cnf( $equal(big_V(X,Y),implies(implies(X,Y),Y)) )],[big_V_definition,refute_0_10]) ).
cnf(refute_0_12,plain,
implies(implies(X_24,X_25),X_25) = big_V(X_24,X_25),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_24)),bind(Y,$fot(X_25))]]) ).
cnf(refute_0_13,plain,
implies(X_24,implies(implies(X_24,X_25),X_25)) = implies(X_24,implies(implies(X_24,X_25),X_25)),
introduced(tautology,[refl,[$fot(implies(X_24,implies(implies(X_24,X_25),X_25)))]]) ).
cnf(refute_0_14,plain,
( implies(X_24,implies(implies(X_24,X_25),X_25)) != implies(X_24,implies(implies(X_24,X_25),X_25))
| implies(implies(X_24,X_25),X_25) != big_V(X_24,X_25)
| implies(X_24,implies(implies(X_24,X_25),X_25)) = implies(X_24,big_V(X_24,X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_24,implies(implies(X_24,X_25),X_25)),implies(X_24,implies(implies(X_24,X_25),X_25))) ),[1,1],$fot(big_V(X_24,X_25))]]) ).
cnf(refute_0_15,plain,
( implies(implies(X_24,X_25),X_25) != big_V(X_24,X_25)
| implies(X_24,implies(implies(X_24,X_25),X_25)) = implies(X_24,big_V(X_24,X_25)) ),
inference(resolve,[$cnf( $equal(implies(X_24,implies(implies(X_24,X_25),X_25)),implies(X_24,implies(implies(X_24,X_25),X_25))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
implies(X_24,implies(implies(X_24,X_25),X_25)) = implies(X_24,big_V(X_24,X_25)),
inference(resolve,[$cnf( $equal(implies(implies(X_24,X_25),X_25),big_V(X_24,X_25)) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
implies(truth,X_24) = X_24,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_18,plain,
implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) = implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)))]]) ).
cnf(refute_0_19,plain,
( implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) != implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25))
| implies(truth,X_24) != X_24
| implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) = implies(X_24,implies(implies(X_24,X_25),X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)),implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25))) ),[1,0],$fot(X_24)]]) ).
cnf(refute_0_20,plain,
( implies(truth,X_24) != X_24
| implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) = implies(X_24,implies(implies(X_24,X_25),X_25)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)),implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) = implies(X_24,implies(implies(X_24,X_25),X_25)),
inference(resolve,[$cnf( $equal(implies(truth,X_24),X_24) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_9,refute_0_22]) ).
cnf(refute_0_24,plain,
( implies(X_24,implies(implies(X_24,X_25),X_25)) != implies(X_24,big_V(X_24,X_25))
| implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) != implies(X_24,implies(implies(X_24,X_25),X_25))
| implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) = implies(X_24,big_V(X_24,X_25)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)))),bind(Y0,$fot(implies(X_24,implies(implies(X_24,X_25),X_25)))),bind(Z0,$fot(implies(X_24,big_V(X_24,X_25))))]]) ).
cnf(refute_0_25,plain,
( implies(X_24,implies(implies(X_24,X_25),X_25)) != implies(X_24,big_V(X_24,X_25))
| implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) = implies(X_24,big_V(X_24,X_25)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)),implies(X_24,implies(implies(X_24,X_25),X_25))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) = implies(X_24,big_V(X_24,X_25)),
inference(resolve,[$cnf( $equal(implies(X_24,implies(implies(X_24,X_25),X_25)),implies(X_24,big_V(X_24,X_25))) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
( implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) != implies(X_24,big_V(X_24,X_25))
| implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) != truth
| implies(X_24,big_V(X_24,X_25)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)),truth) ),[0],$fot(implies(X_24,big_V(X_24,X_25)))]]) ).
cnf(refute_0_28,plain,
( implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)) != truth
| implies(X_24,big_V(X_24,X_25)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)),implies(X_24,big_V(X_24,X_25))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
implies(X_24,big_V(X_24,X_25)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_24),implies(implies(X_24,X_25),X_25)),truth) )],[refute_0_6,refute_0_28]) ).
cnf(refute_0_30,plain,
implies(X,big_V(X,X_29)) = truth,
inference(subst,[],[refute_0_29:[bind(X_24,$fot(X)),bind(X_25,$fot(X_29))]]) ).
cnf(refute_0_31,plain,
( implies(X,big_V(X,X_29)) != truth
| implies(implies(X,big_V(X,X_29)),implies(implies(big_V(X,X_29),Z),implies(X,Z))) != truth
| implies(truth,implies(implies(big_V(X,X_29),Z),implies(X,Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,big_V(X,X_29)),implies(implies(big_V(X,X_29),Z),implies(X,Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_32,plain,
( implies(implies(X,big_V(X,X_29)),implies(implies(big_V(X,X_29),Z),implies(X,Z))) != truth
| implies(truth,implies(implies(big_V(X,X_29),Z),implies(X,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(X,big_V(X,X_29)),truth) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
implies(truth,implies(implies(big_V(X,X_29),Z),implies(X,Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,big_V(X,X_29)),implies(implies(big_V(X,X_29),Z),implies(X,Z))),truth) )],[refute_0_1,refute_0_32]) ).
cnf(refute_0_34,plain,
implies(truth,implies(implies(big_V(X,X_29),Z),implies(X,Z))) = implies(implies(big_V(X,X_29),Z),implies(X,Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(big_V(X,X_29),Z),implies(X,Z))))]]) ).
cnf(refute_0_35,plain,
( implies(truth,implies(implies(big_V(X,X_29),Z),implies(X,Z))) != implies(implies(big_V(X,X_29),Z),implies(X,Z))
| implies(truth,implies(implies(big_V(X,X_29),Z),implies(X,Z))) != truth
| implies(implies(big_V(X,X_29),Z),implies(X,Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(big_V(X,X_29),Z),implies(X,Z))),truth) ),[0],$fot(implies(implies(big_V(X,X_29),Z),implies(X,Z)))]]) ).
cnf(refute_0_36,plain,
( implies(truth,implies(implies(big_V(X,X_29),Z),implies(X,Z))) != truth
| implies(implies(big_V(X,X_29),Z),implies(X,Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(big_V(X,X_29),Z),implies(X,Z))),implies(implies(big_V(X,X_29),Z),implies(X,Z))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
implies(implies(big_V(X,X_29),Z),implies(X,Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(big_V(X,X_29),Z),implies(X,Z))),truth) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(implies(big_V(y,z),implies(x,z)),implies(y,implies(x,z))) = truth,
inference(subst,[],[refute_0_37:[bind(X,$fot(y)),bind(Z,$fot(implies(x,z))),bind(X_29,$fot(z))]]) ).
cnf(refute_0_39,plain,
implies(implies(X_23,implies(X,X_25)),implies(implies(implies(X,X_25),X_25),implies(X_23,X_25))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_23)),bind(Y,$fot(implies(X,X_25))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_40,plain,
big_V(X,X_25) = implies(implies(X,X_25),X_25),
inference(subst,[],[big_V_definition:[bind(Y,$fot(X_25))]]) ).
cnf(refute_0_41,plain,
( big_V(X,X_25) != implies(implies(X,X_25),X_25)
| implies(implies(X,X_25),X_25) = big_V(X,X_25) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(X,X_25))),bind(Y0,$fot(implies(implies(X,X_25),X_25)))]]) ).
cnf(refute_0_42,plain,
implies(implies(X,X_25),X_25) = big_V(X,X_25),
inference(resolve,[$cnf( $equal(big_V(X,X_25),implies(implies(X,X_25),X_25)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( implies(implies(X,X_25),X_25) != big_V(X,X_25)
| implies(implies(X_23,implies(X,X_25)),implies(implies(implies(X,X_25),X_25),implies(X_23,X_25))) != truth
| implies(implies(X_23,implies(X,X_25)),implies(big_V(X,X_25),implies(X_23,X_25))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_23,implies(X,X_25)),implies(implies(implies(X,X_25),X_25),implies(X_23,X_25))),truth) ),[0,1,0],$fot(big_V(X,X_25))]]) ).
cnf(refute_0_44,plain,
( implies(implies(X_23,implies(X,X_25)),implies(implies(implies(X,X_25),X_25),implies(X_23,X_25))) != truth
| implies(implies(X_23,implies(X,X_25)),implies(big_V(X,X_25),implies(X_23,X_25))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_25),X_25),big_V(X,X_25)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
implies(implies(X_23,implies(X,X_25)),implies(big_V(X,X_25),implies(X_23,X_25))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_23,implies(X,X_25)),implies(implies(implies(X,X_25),X_25),implies(X_23,X_25))),truth) )],[refute_0_39,refute_0_44]) ).
cnf(refute_0_46,plain,
implies(implies(x,implies(y,z)),implies(big_V(y,z),implies(x,z))) = truth,
inference(subst,[],[refute_0_45:[bind(X,$fot(y)),bind(X_23,$fot(x)),bind(X_25,$fot(z))]]) ).
cnf(refute_0_47,plain,
( ~ ordered(truth,implies(x,implies(y,z)))
| implies(truth,implies(x,implies(y,z))) = truth ),
inference(subst,[],[partial_order_definition1:[bind(X,$fot(truth)),bind(Y,$fot(implies(x,implies(y,z))))]]) ).
cnf(refute_0_48,plain,
( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) != truth
| ordered(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[partial_order_definition2:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_49,plain,
( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) != truth
| truth != truth
| implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_50,plain,
( truth != truth
| implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),truth) )],[wajsberg_2,refute_0_49]) ).
cnf(refute_0_51,plain,
( truth != truth
| ordered(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),truth) )],[refute_0_50,refute_0_48]) ).
cnf(refute_0_52,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_53,plain,
ordered(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_52,refute_0_51]) ).
cnf(refute_0_54,plain,
ordered(implies(X_76,X_77),implies(implies(X_77,big_V(X_77,X_25)),implies(X_76,big_V(X_77,X_25)))),
inference(subst,[],[refute_0_53:[bind(X,$fot(X_76)),bind(Y,$fot(X_77)),bind(Z,$fot(big_V(X_77,X_25)))]]) ).
cnf(refute_0_55,plain,
implies(X_77,big_V(X_77,X_25)) = truth,
inference(subst,[],[refute_0_29:[bind(X_24,$fot(X_77))]]) ).
cnf(refute_0_56,plain,
( implies(X_77,big_V(X_77,X_25)) != truth
| ~ ordered(implies(X_76,X_77),implies(implies(X_77,big_V(X_77,X_25)),implies(X_76,big_V(X_77,X_25))))
| ordered(implies(X_76,X_77),implies(truth,implies(X_76,big_V(X_77,X_25)))) ),
introduced(tautology,[equality,[$cnf( ordered(implies(X_76,X_77),implies(implies(X_77,big_V(X_77,X_25)),implies(X_76,big_V(X_77,X_25)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_57,plain,
( ~ ordered(implies(X_76,X_77),implies(implies(X_77,big_V(X_77,X_25)),implies(X_76,big_V(X_77,X_25))))
| ordered(implies(X_76,X_77),implies(truth,implies(X_76,big_V(X_77,X_25)))) ),
inference(resolve,[$cnf( $equal(implies(X_77,big_V(X_77,X_25)),truth) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
ordered(implies(X_76,X_77),implies(truth,implies(X_76,big_V(X_77,X_25)))),
inference(resolve,[$cnf( ordered(implies(X_76,X_77),implies(implies(X_77,big_V(X_77,X_25)),implies(X_76,big_V(X_77,X_25)))) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
implies(truth,implies(X_76,big_V(X_77,X_25))) = implies(X_76,big_V(X_77,X_25)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_76,big_V(X_77,X_25))))]]) ).
cnf(refute_0_60,plain,
( implies(truth,implies(X_76,big_V(X_77,X_25))) != implies(X_76,big_V(X_77,X_25))
| ~ ordered(implies(X_76,X_77),implies(truth,implies(X_76,big_V(X_77,X_25))))
| ordered(implies(X_76,X_77),implies(X_76,big_V(X_77,X_25))) ),
introduced(tautology,[equality,[$cnf( ordered(implies(X_76,X_77),implies(truth,implies(X_76,big_V(X_77,X_25)))) ),[1],$fot(implies(X_76,big_V(X_77,X_25)))]]) ).
cnf(refute_0_61,plain,
( ~ ordered(implies(X_76,X_77),implies(truth,implies(X_76,big_V(X_77,X_25))))
| ordered(implies(X_76,X_77),implies(X_76,big_V(X_77,X_25))) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_76,big_V(X_77,X_25))),implies(X_76,big_V(X_77,X_25))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
ordered(implies(X_76,X_77),implies(X_76,big_V(X_77,X_25))),
inference(resolve,[$cnf( ordered(implies(X_76,X_77),implies(truth,implies(X_76,big_V(X_77,X_25)))) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
ordered(implies(X_340,big_V(X_340,X_25)),implies(X_340,big_V(big_V(X_340,X_25),X_339))),
inference(subst,[],[refute_0_62:[bind(X_25,$fot(X_339)),bind(X_76,$fot(X_340)),bind(X_77,$fot(big_V(X_340,X_25)))]]) ).
cnf(refute_0_64,plain,
implies(X_340,big_V(X_340,X_25)) = truth,
inference(subst,[],[refute_0_29:[bind(X_24,$fot(X_340))]]) ).
cnf(refute_0_65,plain,
( implies(X_340,big_V(X_340,X_25)) != truth
| ~ ordered(implies(X_340,big_V(X_340,X_25)),implies(X_340,big_V(big_V(X_340,X_25),X_339)))
| ordered(truth,implies(X_340,big_V(big_V(X_340,X_25),X_339))) ),
introduced(tautology,[equality,[$cnf( ordered(implies(X_340,big_V(X_340,X_25)),implies(X_340,big_V(big_V(X_340,X_25),X_339))) ),[0],$fot(truth)]]) ).
cnf(refute_0_66,plain,
( ~ ordered(implies(X_340,big_V(X_340,X_25)),implies(X_340,big_V(big_V(X_340,X_25),X_339)))
| ordered(truth,implies(X_340,big_V(big_V(X_340,X_25),X_339))) ),
inference(resolve,[$cnf( $equal(implies(X_340,big_V(X_340,X_25)),truth) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
ordered(truth,implies(X_340,big_V(big_V(X_340,X_25),X_339))),
inference(resolve,[$cnf( ordered(implies(X_340,big_V(X_340,X_25)),implies(X_340,big_V(big_V(X_340,X_25),X_339))) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
ordered(truth,implies(x,big_V(big_V(x,z),implies(y,z)))),
inference(subst,[],[refute_0_67:[bind(X_25,$fot(z)),bind(X_339,$fot(implies(y,z))),bind(X_340,$fot(x))]]) ).
cnf(refute_0_69,plain,
big_V(big_V(x,z),implies(y,z)) = implies(implies(big_V(x,z),implies(y,z)),implies(y,z)),
inference(subst,[],[big_V_definition:[bind(X,$fot(big_V(x,z))),bind(Y,$fot(implies(y,z)))]]) ).
cnf(refute_0_70,plain,
implies(implies(y,implies(x,z)),implies(implies(implies(x,z),Z),implies(y,Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(y)),bind(Y,$fot(implies(x,z)))]]) ).
cnf(refute_0_71,plain,
( ~ ordered(x,implies(y,z))
| implies(x,implies(y,z)) = truth ),
inference(subst,[],[partial_order_definition1:[bind(X,$fot(x)),bind(Y,$fot(implies(y,z)))]]) ).
cnf(refute_0_72,plain,
( ~ ordered(y,implies(x,z))
| implies(y,implies(x,z)) = truth ),
inference(subst,[],[partial_order_definition1:[bind(X,$fot(y)),bind(Y,$fot(implies(x,z)))]]) ).
cnf(refute_0_73,plain,
( implies(y,implies(x,z)) = truth
| ordered(x,implies(y,z)) ),
inference(resolve,[$cnf( ordered(y,implies(x,z)) )],[antecedent,refute_0_72]) ).
cnf(refute_0_74,plain,
( implies(x,implies(y,z)) = truth
| implies(y,implies(x,z)) = truth ),
inference(resolve,[$cnf( ordered(x,implies(y,z)) )],[refute_0_73,refute_0_71]) ).
cnf(refute_0_75,plain,
( implies(implies(y,implies(x,z)),implies(implies(implies(x,z),Z),implies(y,Z))) != truth
| implies(y,implies(x,z)) != truth
| implies(truth,implies(implies(implies(x,z),Z),implies(y,Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(y,implies(x,z)),implies(implies(implies(x,z),Z),implies(y,Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_76,plain,
( implies(implies(y,implies(x,z)),implies(implies(implies(x,z),Z),implies(y,Z))) != truth
| implies(truth,implies(implies(implies(x,z),Z),implies(y,Z))) = truth
| implies(x,implies(y,z)) = truth ),
inference(resolve,[$cnf( $equal(implies(y,implies(x,z)),truth) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( implies(truth,implies(implies(implies(x,z),Z),implies(y,Z))) = truth
| implies(x,implies(y,z)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(y,implies(x,z)),implies(implies(implies(x,z),Z),implies(y,Z))),truth) )],[refute_0_70,refute_0_76]) ).
cnf(refute_0_78,plain,
implies(truth,implies(implies(implies(x,z),Z),implies(y,Z))) = implies(implies(implies(x,z),Z),implies(y,Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(x,z),Z),implies(y,Z))))]]) ).
cnf(refute_0_79,plain,
( implies(truth,implies(implies(implies(x,z),Z),implies(y,Z))) != implies(implies(implies(x,z),Z),implies(y,Z))
| implies(truth,implies(implies(implies(x,z),Z),implies(y,Z))) != truth
| implies(implies(implies(x,z),Z),implies(y,Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(x,z),Z),implies(y,Z))),truth) ),[0],$fot(implies(implies(implies(x,z),Z),implies(y,Z)))]]) ).
cnf(refute_0_80,plain,
( implies(truth,implies(implies(implies(x,z),Z),implies(y,Z))) != truth
| implies(implies(implies(x,z),Z),implies(y,Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(x,z),Z),implies(y,Z))),implies(implies(implies(x,z),Z),implies(y,Z))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
( implies(implies(implies(x,z),Z),implies(y,Z)) = truth
| implies(x,implies(y,z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(x,z),Z),implies(y,Z))),truth) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
( implies(implies(implies(x,z),z),implies(y,z)) = truth
| implies(x,implies(y,z)) = truth ),
inference(subst,[],[refute_0_81:[bind(Z,$fot(z))]]) ).
cnf(refute_0_83,plain,
big_V(x,z) = implies(implies(x,z),z),
inference(subst,[],[big_V_definition:[bind(X,$fot(x)),bind(Y,$fot(z))]]) ).
cnf(refute_0_84,plain,
( big_V(x,z) != implies(implies(x,z),z)
| implies(implies(x,z),z) = big_V(x,z) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(x,z))),bind(Y0,$fot(implies(implies(x,z),z)))]]) ).
cnf(refute_0_85,plain,
implies(implies(x,z),z) = big_V(x,z),
inference(resolve,[$cnf( $equal(big_V(x,z),implies(implies(x,z),z)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( implies(implies(implies(x,z),z),implies(y,z)) != truth
| implies(implies(x,z),z) != big_V(x,z)
| implies(big_V(x,z),implies(y,z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(x,z),z),implies(y,z)),truth) ),[0,0],$fot(big_V(x,z))]]) ).
cnf(refute_0_87,plain,
( implies(implies(implies(x,z),z),implies(y,z)) != truth
| implies(big_V(x,z),implies(y,z)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(x,z),z),big_V(x,z)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( implies(big_V(x,z),implies(y,z)) = truth
| implies(x,implies(y,z)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(x,z),z),implies(y,z)),truth) )],[refute_0_82,refute_0_87]) ).
cnf(refute_0_89,plain,
( big_V(big_V(x,z),implies(y,z)) != implies(implies(big_V(x,z),implies(y,z)),implies(y,z))
| implies(big_V(x,z),implies(y,z)) != truth
| big_V(big_V(x,z),implies(y,z)) = implies(truth,implies(y,z)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(x,z),implies(y,z)),implies(implies(big_V(x,z),implies(y,z)),implies(y,z))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_90,plain,
( big_V(big_V(x,z),implies(y,z)) != implies(implies(big_V(x,z),implies(y,z)),implies(y,z))
| big_V(big_V(x,z),implies(y,z)) = implies(truth,implies(y,z))
| implies(x,implies(y,z)) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(x,z),implies(y,z)),truth) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( big_V(big_V(x,z),implies(y,z)) = implies(truth,implies(y,z))
| implies(x,implies(y,z)) = truth ),
inference(resolve,[$cnf( $equal(big_V(big_V(x,z),implies(y,z)),implies(implies(big_V(x,z),implies(y,z)),implies(y,z))) )],[refute_0_69,refute_0_90]) ).
cnf(refute_0_92,plain,
implies(truth,implies(y,z)) = implies(y,z),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(y,z)))]]) ).
cnf(refute_0_93,plain,
( big_V(big_V(x,z),implies(y,z)) != implies(truth,implies(y,z))
| implies(truth,implies(y,z)) != implies(y,z)
| big_V(big_V(x,z),implies(y,z)) = implies(y,z) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(big_V(x,z),implies(y,z)),implies(y,z)) ),[0],$fot(implies(truth,implies(y,z)))]]) ).
cnf(refute_0_94,plain,
( big_V(big_V(x,z),implies(y,z)) != implies(truth,implies(y,z))
| big_V(big_V(x,z),implies(y,z)) = implies(y,z) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(y,z)),implies(y,z)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( big_V(big_V(x,z),implies(y,z)) = implies(y,z)
| implies(x,implies(y,z)) = truth ),
inference(resolve,[$cnf( $equal(big_V(big_V(x,z),implies(y,z)),implies(truth,implies(y,z))) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( big_V(big_V(x,z),implies(y,z)) != implies(y,z)
| ~ ordered(truth,implies(x,big_V(big_V(x,z),implies(y,z))))
| ordered(truth,implies(x,implies(y,z))) ),
introduced(tautology,[equality,[$cnf( ordered(truth,implies(x,big_V(big_V(x,z),implies(y,z)))) ),[1,1],$fot(implies(y,z))]]) ).
cnf(refute_0_97,plain,
( ~ ordered(truth,implies(x,big_V(big_V(x,z),implies(y,z))))
| implies(x,implies(y,z)) = truth
| ordered(truth,implies(x,implies(y,z))) ),
inference(resolve,[$cnf( $equal(big_V(big_V(x,z),implies(y,z)),implies(y,z)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( implies(x,implies(y,z)) = truth
| ordered(truth,implies(x,implies(y,z))) ),
inference(resolve,[$cnf( ordered(truth,implies(x,big_V(big_V(x,z),implies(y,z)))) )],[refute_0_68,refute_0_97]) ).
cnf(refute_0_99,plain,
( implies(truth,implies(x,implies(y,z))) = truth
| implies(x,implies(y,z)) = truth ),
inference(resolve,[$cnf( ordered(truth,implies(x,implies(y,z))) )],[refute_0_98,refute_0_47]) ).
cnf(refute_0_100,plain,
implies(truth,implies(x,implies(y,z))) = implies(x,implies(y,z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(x,implies(y,z))))]]) ).
cnf(refute_0_101,plain,
( implies(truth,implies(x,implies(y,z))) != implies(x,implies(y,z))
| implies(truth,implies(x,implies(y,z))) != truth
| implies(x,implies(y,z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(x,implies(y,z))),truth) ),[0],$fot(implies(x,implies(y,z)))]]) ).
cnf(refute_0_102,plain,
( implies(truth,implies(x,implies(y,z))) != truth
| implies(x,implies(y,z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(x,implies(y,z))),implies(x,implies(y,z))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
implies(x,implies(y,z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(x,implies(y,z))),truth) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
( implies(implies(x,implies(y,z)),implies(big_V(y,z),implies(x,z))) != truth
| implies(x,implies(y,z)) != truth
| implies(truth,implies(big_V(y,z),implies(x,z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(x,implies(y,z)),implies(big_V(y,z),implies(x,z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_105,plain,
( implies(implies(x,implies(y,z)),implies(big_V(y,z),implies(x,z))) != truth
| implies(truth,implies(big_V(y,z),implies(x,z))) = truth ),
inference(resolve,[$cnf( $equal(implies(x,implies(y,z)),truth) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
implies(truth,implies(big_V(y,z),implies(x,z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(x,implies(y,z)),implies(big_V(y,z),implies(x,z))),truth) )],[refute_0_46,refute_0_105]) ).
cnf(refute_0_107,plain,
implies(truth,implies(big_V(y,z),implies(x,z))) = implies(big_V(y,z),implies(x,z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(big_V(y,z),implies(x,z))))]]) ).
cnf(refute_0_108,plain,
( implies(truth,implies(big_V(y,z),implies(x,z))) != implies(big_V(y,z),implies(x,z))
| implies(truth,implies(big_V(y,z),implies(x,z))) != truth
| implies(big_V(y,z),implies(x,z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(big_V(y,z),implies(x,z))),truth) ),[0],$fot(implies(big_V(y,z),implies(x,z)))]]) ).
cnf(refute_0_109,plain,
( implies(truth,implies(big_V(y,z),implies(x,z))) != truth
| implies(big_V(y,z),implies(x,z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(big_V(y,z),implies(x,z))),implies(big_V(y,z),implies(x,z))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
implies(big_V(y,z),implies(x,z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(big_V(y,z),implies(x,z))),truth) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
( implies(big_V(y,z),implies(x,z)) != truth
| implies(implies(big_V(y,z),implies(x,z)),implies(y,implies(x,z))) != truth
| implies(truth,implies(y,implies(x,z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(big_V(y,z),implies(x,z)),implies(y,implies(x,z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_112,plain,
( implies(implies(big_V(y,z),implies(x,z)),implies(y,implies(x,z))) != truth
| implies(truth,implies(y,implies(x,z))) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(y,z),implies(x,z)),truth) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
implies(truth,implies(y,implies(x,z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(big_V(y,z),implies(x,z)),implies(y,implies(x,z))),truth) )],[refute_0_38,refute_0_112]) ).
cnf(refute_0_114,plain,
implies(truth,implies(y,implies(x,z))) = implies(y,implies(x,z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(y,implies(x,z))))]]) ).
cnf(refute_0_115,plain,
( implies(truth,implies(y,implies(x,z))) != implies(y,implies(x,z))
| implies(truth,implies(y,implies(x,z))) != truth
| implies(y,implies(x,z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(y,implies(x,z))),truth) ),[0],$fot(implies(y,implies(x,z)))]]) ).
cnf(refute_0_116,plain,
( implies(truth,implies(y,implies(x,z))) != truth
| implies(y,implies(x,z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(y,implies(x,z))),implies(y,implies(x,z))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
implies(y,implies(x,z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(y,implies(x,z))),truth) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( implies(y,implies(x,z)) != truth
| truth != truth
| implies(y,implies(x,z)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(y,implies(x,z)),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_119,plain,
( truth != truth
| implies(y,implies(x,z)) = truth ),
inference(resolve,[$cnf( $equal(implies(y,implies(x,z)),truth) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
( truth != truth
| ordered(y,implies(x,z)) ),
inference(resolve,[$cnf( $equal(implies(y,implies(x,z)),truth) )],[refute_0_119,refute_0_0]) ).
cnf(refute_0_121,plain,
ordered(y,implies(x,z)),
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_52,refute_0_120]) ).
cnf(refute_0_122,plain,
~ ordered(x,implies(y,z)),
inference(resolve,[$cnf( ordered(y,implies(x,z)) )],[refute_0_121,prove_wajsberg_theorem]) ).
cnf(refute_0_123,plain,
( implies(X_47,big_V(X_47,X_25)) != truth
| ordered(X_47,big_V(X_47,X_25)) ),
inference(subst,[],[partial_order_definition2:[bind(X,$fot(X_47)),bind(Y,$fot(big_V(X_47,X_25)))]]) ).
cnf(refute_0_124,plain,
implies(X_47,big_V(X_47,X_25)) = truth,
inference(subst,[],[refute_0_29:[bind(X_24,$fot(X_47))]]) ).
cnf(refute_0_125,plain,
( implies(X_47,big_V(X_47,X_25)) != truth
| truth != truth
| implies(X_47,big_V(X_47,X_25)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_47,big_V(X_47,X_25)),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_126,plain,
( truth != truth
| implies(X_47,big_V(X_47,X_25)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_47,big_V(X_47,X_25)),truth) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( truth != truth
| ordered(X_47,big_V(X_47,X_25)) ),
inference(resolve,[$cnf( $equal(implies(X_47,big_V(X_47,X_25)),truth) )],[refute_0_126,refute_0_123]) ).
cnf(refute_0_128,plain,
ordered(X_47,big_V(X_47,X_25)),
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_52,refute_0_127]) ).
cnf(refute_0_129,plain,
ordered(x,big_V(x,implies(y,z))),
inference(subst,[],[refute_0_128:[bind(X_25,$fot(implies(y,z))),bind(X_47,$fot(x))]]) ).
cnf(refute_0_130,plain,
big_V(x,implies(y,z)) = implies(implies(x,implies(y,z)),implies(y,z)),
inference(subst,[],[big_V_definition:[bind(X,$fot(x)),bind(Y,$fot(implies(y,z)))]]) ).
cnf(refute_0_131,plain,
( big_V(x,implies(y,z)) != implies(implies(x,implies(y,z)),implies(y,z))
| implies(x,implies(y,z)) != truth
| big_V(x,implies(y,z)) = implies(truth,implies(y,z)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(x,implies(y,z)),implies(implies(x,implies(y,z)),implies(y,z))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_132,plain,
( big_V(x,implies(y,z)) != implies(implies(x,implies(y,z)),implies(y,z))
| big_V(x,implies(y,z)) = implies(truth,implies(y,z)) ),
inference(resolve,[$cnf( $equal(implies(x,implies(y,z)),truth) )],[refute_0_103,refute_0_131]) ).
cnf(refute_0_133,plain,
big_V(x,implies(y,z)) = implies(truth,implies(y,z)),
inference(resolve,[$cnf( $equal(big_V(x,implies(y,z)),implies(implies(x,implies(y,z)),implies(y,z))) )],[refute_0_130,refute_0_132]) ).
cnf(refute_0_134,plain,
( big_V(x,implies(y,z)) != implies(truth,implies(y,z))
| implies(truth,implies(y,z)) != implies(y,z)
| big_V(x,implies(y,z)) = implies(y,z) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(x,implies(y,z)),implies(y,z)) ),[0],$fot(implies(truth,implies(y,z)))]]) ).
cnf(refute_0_135,plain,
( big_V(x,implies(y,z)) != implies(truth,implies(y,z))
| big_V(x,implies(y,z)) = implies(y,z) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(y,z)),implies(y,z)) )],[refute_0_92,refute_0_134]) ).
cnf(refute_0_136,plain,
big_V(x,implies(y,z)) = implies(y,z),
inference(resolve,[$cnf( $equal(big_V(x,implies(y,z)),implies(truth,implies(y,z))) )],[refute_0_133,refute_0_135]) ).
cnf(refute_0_137,plain,
( big_V(x,implies(y,z)) != implies(y,z)
| ~ ordered(x,big_V(x,implies(y,z)))
| ordered(x,implies(y,z)) ),
introduced(tautology,[equality,[$cnf( ordered(x,big_V(x,implies(y,z))) ),[1],$fot(implies(y,z))]]) ).
cnf(refute_0_138,plain,
( ~ ordered(x,big_V(x,implies(y,z)))
| ordered(x,implies(y,z)) ),
inference(resolve,[$cnf( $equal(big_V(x,implies(y,z)),implies(y,z)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
ordered(x,implies(y,z)),
inference(resolve,[$cnf( ordered(x,big_V(x,implies(y,z))) )],[refute_0_129,refute_0_138]) ).
cnf(refute_0_140,plain,
$false,
inference(resolve,[$cnf( ordered(x,implies(y,z)) )],[refute_0_139,refute_0_122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL144-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 03:31:48 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.56/4.83 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.56/4.83
% 4.56/4.83 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.56/4.85
%------------------------------------------------------------------------------