%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL143-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 1.37s 1.64s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 28 ( 15 unt; 0 nHn; 17 RR)
% Number of literals : 45 ( 35 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 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(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,y) ).
cnf(prove_wajsberg_theorem,negated_conjecture,
~ ordered(implies(z,x),implies(z,y)) ).
cnf(refute_0_0,plain,
( implies(implies(X,x),implies(X,y)) != truth
| ordered(implies(X,x),implies(X,y)) ),
inference(subst,[],[partial_order_definition2:[bind(X,$fot(implies(X,x))),bind(Y,$fot(implies(X,y)))]]) ).
cnf(refute_0_1,plain,
implies(implies(X,x),implies(implies(x,y),implies(X,y))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(x)),bind(Z,$fot(y))]]) ).
cnf(refute_0_2,plain,
( ~ ordered(x,y)
| implies(x,y) = truth ),
inference(subst,[],[partial_order_definition1:[bind(X,$fot(x)),bind(Y,$fot(y))]]) ).
cnf(refute_0_3,plain,
implies(x,y) = truth,
inference(resolve,[$cnf( ordered(x,y) )],[antecedent,refute_0_2]) ).
cnf(refute_0_4,plain,
( implies(implies(X,x),implies(implies(x,y),implies(X,y))) != truth
| implies(x,y) != truth
| implies(implies(X,x),implies(truth,implies(X,y))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,x),implies(implies(x,y),implies(X,y))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_5,plain,
( implies(implies(X,x),implies(implies(x,y),implies(X,y))) != truth
| implies(implies(X,x),implies(truth,implies(X,y))) = truth ),
inference(resolve,[$cnf( $equal(implies(x,y),truth) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
implies(implies(X,x),implies(truth,implies(X,y))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,x),implies(implies(x,y),implies(X,y))),truth) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
implies(truth,implies(X,y)) = implies(X,y),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X,y)))]]) ).
cnf(refute_0_8,plain,
implies(implies(X,x),implies(truth,implies(X,y))) = implies(implies(X,x),implies(truth,implies(X,y))),
introduced(tautology,[refl,[$fot(implies(implies(X,x),implies(truth,implies(X,y))))]]) ).
cnf(refute_0_9,plain,
( implies(implies(X,x),implies(truth,implies(X,y))) != implies(implies(X,x),implies(truth,implies(X,y)))
| implies(truth,implies(X,y)) != implies(X,y)
| implies(implies(X,x),implies(truth,implies(X,y))) = implies(implies(X,x),implies(X,y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,x),implies(truth,implies(X,y))),implies(implies(X,x),implies(truth,implies(X,y)))) ),[1,1],$fot(implies(X,y))]]) ).
cnf(refute_0_10,plain,
( implies(truth,implies(X,y)) != implies(X,y)
| implies(implies(X,x),implies(truth,implies(X,y))) = implies(implies(X,x),implies(X,y)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,x),implies(truth,implies(X,y))),implies(implies(X,x),implies(truth,implies(X,y)))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
implies(implies(X,x),implies(truth,implies(X,y))) = implies(implies(X,x),implies(X,y)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X,y)),implies(X,y)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( implies(implies(X,x),implies(truth,implies(X,y))) != implies(implies(X,x),implies(X,y))
| implies(implies(X,x),implies(truth,implies(X,y))) != truth
| implies(implies(X,x),implies(X,y)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,x),implies(truth,implies(X,y))),truth) ),[0],$fot(implies(implies(X,x),implies(X,y)))]]) ).
cnf(refute_0_13,plain,
( implies(implies(X,x),implies(truth,implies(X,y))) != truth
| implies(implies(X,x),implies(X,y)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,x),implies(truth,implies(X,y))),implies(implies(X,x),implies(X,y))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
implies(implies(X,x),implies(X,y)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,x),implies(truth,implies(X,y))),truth) )],[refute_0_6,refute_0_13]) ).
cnf(refute_0_15,plain,
( implies(implies(X,x),implies(X,y)) != truth
| truth != truth
| implies(implies(X,x),implies(X,y)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X,x),implies(X,y)),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_16,plain,
( truth != truth
| implies(implies(X,x),implies(X,y)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,x),implies(X,y)),truth) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( truth != truth
| ordered(implies(X,x),implies(X,y)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,x),implies(X,y)),truth) )],[refute_0_16,refute_0_0]) ).
cnf(refute_0_18,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_19,plain,
ordered(implies(X,x),implies(X,y)),
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
ordered(implies(z,x),implies(z,y)),
inference(subst,[],[refute_0_19:[bind(X,$fot(z))]]) ).
cnf(refute_0_21,plain,
$false,
inference(resolve,[$cnf( ordered(implies(z,x),implies(z,y)) )],[refute_0_20,prove_wajsberg_theorem]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL143-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Fri Sep 4 23:44:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.37/1.64 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.37/1.64
% 1.37/1.64 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.37/1.64
%------------------------------------------------------------------------------