TSTP Solution File: GRP420-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP420-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n011.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 01:18:21 EDT 2023
% Result : Unsatisfiable 0.21s 0.59s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP420-1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n011.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 00:28:26 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.59 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.59
% 0.21/0.59 % SZS status Unsatisfiable
% 0.21/0.59
% 0.21/0.63 % SZS output start Proof
% 0.21/0.63 Axiom 1 (single_axiom): inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))) = Y.
% 0.21/0.63
% 0.21/0.63 Lemma 2: multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z)) = inverse(multiply(inverse(multiply(W, inverse(multiply(Y, inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V))).
% 0.21/0.63 Proof:
% 0.21/0.63 multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))
% 0.21/0.63 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.63 inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(Y), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))), inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))
% 0.21/0.63 = { by axiom 1 (single_axiom) }
% 0.21/0.64 inverse(multiply(inverse(multiply(W, inverse(multiply(Y, inverse(multiply(V, inverse(multiply(inverse(V), V)))))))), multiply(W, V)))
% 0.21/0.64
% 0.21/0.64 Lemma 3: inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y)) = W.
% 0.21/0.64 Proof:
% 0.21/0.64 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), Y))
% 0.21/0.64 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.64 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(Y), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))))
% 0.21/0.64 = { by lemma 2 R->L }
% 0.21/0.64 inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), inverse(multiply(inverse(W), inverse(multiply(multiply(X, Z), inverse(multiply(inverse(multiply(X, Z)), multiply(X, Z))))))))), multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(Y)), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))))
% 0.21/0.64 = { by axiom 1 (single_axiom) }
% 0.21/0.64 W
% 0.21/0.64
% 0.21/0.64 Lemma 4: multiply(inverse(multiply(W, Y)), multiply(W, Z)) = multiply(inverse(multiply(X, Y)), multiply(X, Z)).
% 0.21/0.64 Proof:
% 0.21/0.64 multiply(inverse(multiply(W, Y)), multiply(W, Z))
% 0.21/0.64 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.64 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Z))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.21/0.64 = { by lemma 3 R->L }
% 0.21/0.64 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(T, S), inverse(multiply(inverse(multiply(T, S)), multiply(T, S))))))))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(W, Z))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.21/0.64 = { by axiom 1 (single_axiom) }
% 0.21/0.64 inverse(multiply(inverse(multiply(V, inverse(multiply(multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(T, S), inverse(multiply(inverse(multiply(T, S)), multiply(T, S)))))))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.21/0.64 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.64 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(T, S), inverse(multiply(inverse(multiply(T, S)), multiply(T, S))))))))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.21/0.64 = { by lemma 3 }
% 0.21/0.64 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), multiply(X, Z))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.21/0.64 = { by axiom 1 (single_axiom) }
% 0.21/0.64 multiply(inverse(multiply(X, Y)), multiply(X, Z))
% 0.21/0.64
% 0.21/0.64 Lemma 5: multiply(X, inverse(multiply(inverse(multiply(Y, inverse(multiply(X, inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(Y, Z)))) = multiply(inverse(multiply(W, multiply(V, U))), multiply(W, multiply(V, U))).
% 0.21/0.64 Proof:
% 0.21/0.64 multiply(X, inverse(multiply(inverse(multiply(Y, inverse(multiply(X, inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(Y, Z))))
% 0.21/0.64 = { by lemma 2 R->L }
% 0.21/0.64 multiply(X, multiply(inverse(multiply(V, inverse(multiply(inverse(X), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.21/0.64 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.64 multiply(inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(X), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U))), multiply(inverse(multiply(V, inverse(multiply(inverse(X), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.21/0.64 = { by lemma 4 R->L }
% 0.21/0.64 multiply(inverse(multiply(W, multiply(V, U))), multiply(W, multiply(V, U)))
% 0.21/0.64
% 0.21/0.64 Lemma 6: multiply(inverse(Y), Y) = multiply(inverse(X), X).
% 0.21/0.64 Proof:
% 0.21/0.64 multiply(inverse(Y), Y)
% 0.21/0.64 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.64 multiply(inverse(Y), inverse(multiply(inverse(multiply(S, inverse(multiply(inverse(Y), inverse(multiply(X2, inverse(multiply(inverse(X2), X2)))))))), multiply(S, X2))))
% 0.21/0.64 = { by lemma 5 }
% 0.21/0.64 multiply(inverse(multiply(V, multiply(U, T))), multiply(V, multiply(U, T)))
% 0.21/0.64 = { by lemma 5 R->L }
% 0.21/0.64 multiply(inverse(X), inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(X), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W))))
% 0.21/0.64 = { by axiom 1 (single_axiom) }
% 0.21/0.64 multiply(inverse(X), X)
% 0.21/0.64
% 0.21/0.64 Lemma 7: inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(Y, inverse(multiply(inverse(Z), Z)))))) = Y.
% 0.21/0.64 Proof:
% 0.21/0.64 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(Y, inverse(multiply(inverse(Z), Z))))))
% 0.21/0.64 = { by lemma 6 }
% 0.21/0.64 inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(Y, inverse(multiply(inverse(Y), Y))))))
% 0.21/0.64 = { by lemma 6 }
% 0.21/0.64 inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Y)))), inverse(multiply(Y, inverse(multiply(inverse(Y), Y))))))
% 0.21/0.64 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.64 inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Y)))), inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(inverse(multiply(Y, inverse(multiply(inverse(Y), Y))))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))))
% 0.21/0.64 = { by lemma 2 R->L }
% 0.21/0.64 inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, Y)), multiply(W, Y)))), multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), multiply(T, S))))
% 0.21/0.64 = { by lemma 3 R->L }
% 0.21/0.64 inverse(multiply(inverse(inverse(multiply(inverse(multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(T, S), inverse(multiply(inverse(multiply(T, S)), multiply(T, S))))))))), inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))))), multiply(W, Y)))), multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), multiply(T, S))))
% 0.21/0.64 = { by axiom 1 (single_axiom) }
% 0.21/0.64 inverse(multiply(inverse(multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), inverse(multiply(inverse(Y), inverse(multiply(multiply(T, S), inverse(multiply(inverse(multiply(T, S)), multiply(T, S))))))))), multiply(inverse(multiply(T, inverse(multiply(inverse(inverse(inverse(multiply(Y, inverse(multiply(inverse(Y), Y)))))), inverse(multiply(S, inverse(multiply(inverse(S), S)))))))), multiply(T, S))))
% 0.21/0.64 = { by axiom 1 (single_axiom) }
% 0.21/0.64 Y
% 0.21/0.64
% 0.21/0.64 Lemma 8: inverse(multiply(inverse(X), X)) = multiply(inverse(Y), Y).
% 0.21/0.64 Proof:
% 0.21/0.64 inverse(multiply(inverse(X), X))
% 0.21/0.64 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.64 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 0.21/0.64 = { by lemma 7 R->L }
% 0.21/0.64 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X))))), inverse(multiply(inverse(inverse(multiply(inverse(X), X))), inverse(multiply(inverse(X), X)))))), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 0.21/0.64 = { by lemma 6 R->L }
% 0.21/0.64 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(inverse(Y), Y)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 0.21/0.64 = { by axiom 1 (single_axiom) }
% 0.21/0.64 multiply(inverse(Y), Y)
% 0.21/0.64
% 0.21/0.64 Lemma 9: inverse(multiply(multiply(inverse(X), X), inverse(multiply(Y, multiply(inverse(Z), Z))))) = Y.
% 0.21/0.64 Proof:
% 0.21/0.64 inverse(multiply(multiply(inverse(X), X), inverse(multiply(Y, multiply(inverse(Z), Z)))))
% 0.21/0.64 = { by lemma 8 R->L }
% 0.21/0.64 inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(Y, multiply(inverse(Z), Z)))))
% 0.21/0.64 = { by lemma 8 R->L }
% 0.21/0.64 inverse(multiply(inverse(multiply(inverse(W), W)), inverse(multiply(Y, inverse(multiply(inverse(V), V))))))
% 0.21/0.64 = { by lemma 8 R->L }
% 0.21/0.64 inverse(multiply(inverse(inverse(multiply(inverse(U), U))), inverse(multiply(Y, inverse(multiply(inverse(V), V))))))
% 0.21/0.64 = { by lemma 7 }
% 0.21/0.64 Y
% 0.21/0.64
% 0.21/0.64 Lemma 10: multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(X, Z)) = multiply(Z, multiply(inverse(W), W)).
% 0.21/0.64 Proof:
% 0.21/0.64 multiply(inverse(multiply(X, multiply(inverse(Y), Y))), multiply(X, Z))
% 0.21/0.64 = { by lemma 8 R->L }
% 0.21/0.64 multiply(inverse(multiply(X, inverse(multiply(inverse(inverse(multiply(Z, inverse(multiply(inverse(Z), Z))))), inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))))))), multiply(X, Z))
% 0.21/0.64 = { by lemma 2 }
% 0.21/0.64 inverse(multiply(inverse(multiply(V, inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(Z), Z)))), inverse(multiply(U, inverse(multiply(inverse(U), U)))))))), multiply(V, U)))
% 0.21/0.65 = { by axiom 1 (single_axiom) }
% 0.21/0.65 multiply(Z, inverse(multiply(inverse(Z), Z)))
% 0.21/0.65 = { by lemma 6 R->L }
% 0.21/0.65 multiply(Z, inverse(multiply(inverse(T), T)))
% 0.21/0.65 = { by lemma 8 }
% 0.21/0.65 multiply(Z, multiply(inverse(W), W))
% 0.21/0.65
% 0.21/0.65 Lemma 11: inverse(multiply(inverse(X), multiply(inverse(Y), Y))) = X.
% 0.21/0.65 Proof:
% 0.21/0.65 inverse(multiply(inverse(X), multiply(inverse(Y), Y)))
% 0.21/0.65 = { by lemma 9 R->L }
% 0.21/0.65 inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(Y), Y))), multiply(inverse(X), X)))))
% 0.21/0.65 = { by lemma 10 }
% 0.21/0.65 inverse(multiply(multiply(inverse(Z), Z), inverse(multiply(X, multiply(inverse(W), W)))))
% 0.21/0.65 = { by lemma 9 }
% 0.21/0.65 X
% 0.21/0.65
% 0.21/0.65 Lemma 12: multiply(multiply(inverse(X), X), Y) = Y.
% 0.21/0.65 Proof:
% 0.21/0.65 multiply(multiply(inverse(X), X), Y)
% 0.21/0.65 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.65 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(multiply(inverse(X), X), Y)), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 0.21/0.65 = { by lemma 11 R->L }
% 0.21/0.65 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(multiply(multiply(inverse(X), X), inverse(multiply(inverse(Y), multiply(inverse(V), V))))), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 0.21/0.65 = { by lemma 9 }
% 0.21/0.65 inverse(multiply(inverse(multiply(Z, inverse(multiply(inverse(Y), inverse(multiply(W, inverse(multiply(inverse(W), W)))))))), multiply(Z, W)))
% 0.21/0.65 = { by axiom 1 (single_axiom) }
% 0.21/0.65 Y
% 0.21/0.65
% 0.21/0.65 Lemma 13: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.21/0.65 Proof:
% 0.21/0.65 multiply(X, multiply(inverse(X), Y))
% 0.21/0.65 = { by lemma 11 R->L }
% 0.21/0.65 multiply(inverse(multiply(inverse(X), multiply(inverse(Z), Z))), multiply(inverse(X), Y))
% 0.21/0.65 = { by lemma 4 R->L }
% 0.21/0.65 multiply(inverse(multiply(inverse(multiply(inverse(W), W)), multiply(inverse(Z), Z))), multiply(inverse(multiply(inverse(W), W)), Y))
% 0.21/0.65 = { by lemma 11 }
% 0.21/0.65 multiply(multiply(inverse(W), W), multiply(inverse(multiply(inverse(W), W)), Y))
% 0.21/0.65 = { by lemma 12 }
% 0.21/0.65 multiply(inverse(multiply(inverse(W), W)), Y)
% 0.21/0.65 = { by lemma 8 }
% 0.21/0.65 multiply(multiply(inverse(V), V), Y)
% 0.21/0.65 = { by lemma 12 }
% 0.21/0.65 Y
% 0.21/0.65
% 0.21/0.65 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.21/0.65 Proof:
% 0.21/0.65 multiply(multiply(a3, b3), c3)
% 0.21/0.65 = { by lemma 13 R->L }
% 0.21/0.65 multiply(multiply(a3, b3), multiply(c3, multiply(inverse(c3), c3)))
% 0.21/0.65 = { by lemma 10 R->L }
% 0.21/0.65 multiply(multiply(a3, b3), multiply(inverse(multiply(b3, multiply(inverse(b3), b3))), multiply(b3, c3)))
% 0.21/0.65 = { by lemma 13 }
% 0.21/0.65 multiply(multiply(a3, b3), multiply(inverse(b3), multiply(b3, c3)))
% 0.21/0.65 = { by lemma 12 R->L }
% 0.21/0.65 multiply(multiply(a3, b3), multiply(inverse(b3), multiply(multiply(inverse(X), X), multiply(b3, c3))))
% 0.21/0.65 = { by lemma 12 R->L }
% 0.21/0.65 multiply(multiply(a3, b3), multiply(inverse(multiply(multiply(inverse(X), X), b3)), multiply(multiply(inverse(X), X), multiply(b3, c3))))
% 0.21/0.65 = { by lemma 4 R->L }
% 0.21/0.65 multiply(multiply(a3, b3), multiply(inverse(multiply(a3, b3)), multiply(a3, multiply(b3, c3))))
% 0.21/0.65 = { by lemma 13 }
% 0.21/0.65 multiply(a3, multiply(b3, c3))
% 0.21/0.65 % SZS output end Proof
% 0.21/0.65
% 0.21/0.65 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------