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% File     : Toma---0.4
% Problem  : GRP549-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : toma --casc %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  : 300s
% DateTime : Thu Aug 31 01:15:19 EDT 2023

% Result   : Unsatisfiable 0.21s 0.43s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem    : GRP549-1 : TPTP v8.1.2. Released v2.6.0.
% 0.13/0.13  % Command    : toma --casc %s
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 29 01:47:36 EDT 2023
% 0.14/0.35  % CPUTime    : 
% 0.21/0.43  % SZS status Unsatisfiable
% 0.21/0.43  % SZS output start Proof
% 0.21/0.43  original problem:
% 0.21/0.43  axioms:
% 0.21/0.43  divide(divide(identity(), A), divide(divide(divide(B, A), C), B)) = C
% 0.21/0.43  multiply(A, B) = divide(A, divide(identity(), B))
% 0.21/0.43  inverse(A) = divide(identity(), A)
% 0.21/0.43  identity() = divide(A, A)
% 0.21/0.43  goal:
% 0.21/0.43  multiply(inverse(a1()), a1()) != multiply(inverse(b1()), b1())
% 0.21/0.43  To show the unsatisfiability of the original goal,
% 0.21/0.43  it suffices to show that multiply(inverse(a1()), a1()) = multiply(inverse(b1()), b1()) (skolemized goal) is valid under the axioms.
% 0.21/0.43  Here is an equational proof:
% 0.21/0.43  1: multiply(X0, X1) = divide(X0, divide(identity(), X1)).
% 0.21/0.43  Proof: Axiom.
% 0.21/0.43  
% 0.21/0.43  2: inverse(X0) = divide(identity(), X0).
% 0.21/0.43  Proof: Axiom.
% 0.21/0.43  
% 0.21/0.43  3: identity() = divide(X0, X0).
% 0.21/0.43  Proof: Axiom.
% 0.21/0.43  
% 0.21/0.43  5: multiply(X0, X1) = divide(X0, inverse(X1)).
% 0.21/0.43  Proof: Rewrite equation 1,
% 0.21/0.43                 lhs with equations []
% 0.21/0.43                 rhs with equations [2].
% 0.21/0.43  
% 0.21/0.43  6: multiply(inverse(a1()), a1()) = multiply(inverse(b1()), b1()).
% 0.21/0.43  Proof: Rewrite lhs with equations [5,3]
% 0.21/0.43                 rhs with equations [5,3].
% 0.21/0.43  
% 0.21/0.43  % SZS output end Proof
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