%------------------------------------------------------------------------------
% File     : Twee---2.4.2
% Problem  : BOO013-4 : TPTP v8.1.2. Released v1.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof

% 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 : Wed Aug 30 18:11:23 EDT 2023

% Result   : Unsatisfiable 0.16s 0.37s
% Output   : Proof 0.16s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : BOO013-4 : TPTP v8.1.2. Released v1.1.0.
% 0.00/0.12  % Command  : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.32  % Computer : n006.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sun Aug 27 07:45:22 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.16/0.37  Command-line arguments: --ground-connectedness --complete-subsets
% 0.16/0.37  
% 0.16/0.37  % SZS status Unsatisfiable
% 0.16/0.37  
% 0.16/0.38  % SZS output start Proof
% 0.16/0.38  Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 0.16/0.38  Axiom 2 (additive_id1): add(X, additive_identity) = X.
% 0.16/0.38  Axiom 3 (b_a_multiplicative_identity): add(a, b) = multiplicative_identity.
% 0.16/0.38  Axiom 4 (commutativity_of_multiply): multiply(X, Y) = multiply(Y, X).
% 0.16/0.38  Axiom 5 (multiplicative_id1): multiply(X, multiplicative_identity) = X.
% 0.16/0.38  Axiom 6 (b_an_additive_identity): multiply(a, b) = additive_identity.
% 0.16/0.38  Axiom 7 (additive_inverse1): add(X, inverse(X)) = multiplicative_identity.
% 0.16/0.38  Axiom 8 (multiplicative_inverse1): multiply(X, inverse(X)) = additive_identity.
% 0.16/0.38  Axiom 9 (distributivity1): add(X, multiply(Y, Z)) = multiply(add(X, Y), add(X, Z)).
% 0.16/0.38  
% 0.16/0.38  Goal 1 (prove_a_inverse_is_b): b = inverse(a).
% 0.16/0.38  Proof:
% 0.16/0.38    b
% 0.16/0.38  = { by axiom 2 (additive_id1) R->L }
% 0.16/0.38    add(b, additive_identity)
% 0.16/0.38  = { by axiom 8 (multiplicative_inverse1) R->L }
% 0.16/0.38    add(b, multiply(a, inverse(a)))
% 0.16/0.38  = { by axiom 4 (commutativity_of_multiply) }
% 0.16/0.38    add(b, multiply(inverse(a), a))
% 0.16/0.38  = { by axiom 9 (distributivity1) }
% 0.16/0.38    multiply(add(b, inverse(a)), add(b, a))
% 0.16/0.38  = { by axiom 1 (commutativity_of_add) R->L }
% 0.16/0.38    multiply(add(b, inverse(a)), add(a, b))
% 0.16/0.38  = { by axiom 3 (b_a_multiplicative_identity) }
% 0.16/0.38    multiply(add(b, inverse(a)), multiplicative_identity)
% 0.16/0.38  = { by axiom 5 (multiplicative_id1) }
% 0.16/0.38    add(b, inverse(a))
% 0.16/0.38  = { by axiom 1 (commutativity_of_add) R->L }
% 0.16/0.38    add(inverse(a), b)
% 0.16/0.38  = { by axiom 5 (multiplicative_id1) R->L }
% 0.16/0.38    multiply(add(inverse(a), b), multiplicative_identity)
% 0.16/0.38  = { by axiom 4 (commutativity_of_multiply) }
% 0.16/0.38    multiply(multiplicative_identity, add(inverse(a), b))
% 0.16/0.38  = { by axiom 7 (additive_inverse1) R->L }
% 0.16/0.38    multiply(add(a, inverse(a)), add(inverse(a), b))
% 0.16/0.38  = { by axiom 1 (commutativity_of_add) }
% 0.16/0.38    multiply(add(inverse(a), a), add(inverse(a), b))
% 0.16/0.38  = { by axiom 9 (distributivity1) R->L }
% 0.16/0.38    add(inverse(a), multiply(a, b))
% 0.16/0.38  = { by axiom 6 (b_an_additive_identity) }
% 0.16/0.38    add(inverse(a), additive_identity)
% 0.16/0.38  = { by axiom 2 (additive_id1) }
% 0.16/0.38    inverse(a)
% 0.16/0.38  % SZS output end Proof
% 0.16/0.38  
% 0.16/0.38  RESULT: Unsatisfiable (the axioms are contradictory).
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