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% File     : Toma---0.4
% Problem  : REL049-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %s

% Computer : n032.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  : 300s
% DateTime : Thu Aug 31 13:43:40 EDT 2023

% Result   : Unsatisfiable 0.15s 0.41s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : REL049-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % Command    : toma --casc %s
% 0.11/0.31  % Computer : n032.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Fri Aug 25 19:38:43 EDT 2023
% 0.11/0.31  % CPUTime    : 
% 0.15/0.41  % SZS status Unsatisfiable
% 0.15/0.41  % SZS output start Proof
% 0.15/0.41  original problem:
% 0.15/0.41  axioms:
% 0.15/0.41  join(A, B) = join(B, A)
% 0.15/0.41  join(A, join(B, C)) = join(join(A, B), C)
% 0.15/0.41  A = join(complement(join(complement(A), complement(B))), complement(join(complement(A), B)))
% 0.15/0.41  meet(A, B) = complement(join(complement(A), complement(B)))
% 0.15/0.41  composition(A, composition(B, C)) = composition(composition(A, B), C)
% 0.15/0.41  composition(A, one()) = A
% 0.15/0.41  composition(join(A, B), C) = join(composition(A, C), composition(B, C))
% 0.15/0.41  converse(converse(A)) = A
% 0.15/0.41  converse(join(A, B)) = join(converse(A), converse(B))
% 0.15/0.41  converse(composition(A, B)) = composition(converse(B), converse(A))
% 0.15/0.41  join(composition(converse(A), complement(composition(A, B))), complement(B)) = complement(B)
% 0.15/0.41  top() = join(A, complement(A))
% 0.15/0.41  zero() = meet(A, complement(A))
% 0.15/0.41  join(sk1(), sk2()) = sk2()
% 0.15/0.41  join(sk3(), sk2()) = sk2()
% 0.15/0.41  goal:
% 0.15/0.41  join(join(sk1(), sk3()), sk2()) != sk2()
% 0.15/0.41  To show the unsatisfiability of the original goal,
% 0.15/0.41  it suffices to show that join(join(sk1(), sk3()), sk2()) = sk2() (skolemized goal) is valid under the axioms.
% 0.15/0.41  Here is an equational proof:
% 0.15/0.41  1: join(X0, join(X1, X2)) = join(join(X0, X1), X2).
% 0.15/0.41  Proof: Axiom.
% 0.15/0.41  
% 0.15/0.41  13: join(sk1(), sk2()) = sk2().
% 0.15/0.41  Proof: Axiom.
% 0.15/0.41  
% 0.15/0.41  14: join(sk3(), sk2()) = sk2().
% 0.15/0.41  Proof: Axiom.
% 0.15/0.41  
% 0.15/0.41  18: join(join(sk1(), sk3()), sk2()) = sk2().
% 0.15/0.41  Proof: Rewrite lhs with equations [1,14,13]
% 0.15/0.41                 rhs with equations [].
% 0.15/0.41  
% 0.15/0.41  % SZS output end Proof
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