TSTP Solution File: GRP002-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP002-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 : Thu Aug 31 01:16:29 EDT 2023
% Result : Unsatisfiable 0.22s 0.47s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP002-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.08/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.37 % Computer : n006.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Mon Aug 28 20:08:36 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.22/0.47 Command-line arguments: --no-flatten-goal
% 0.22/0.47
% 0.22/0.47 % SZS status Unsatisfiable
% 0.22/0.47
% 0.22/0.49 % SZS output start Proof
% 0.22/0.49 Axiom 1 (right_identity): multiply(X, identity) = X.
% 0.22/0.49 Axiom 2 (a_times_b_is_c): multiply(a, b) = c.
% 0.22/0.49 Axiom 3 (h_times_b_is_j): multiply(h, b) = j.
% 0.22/0.49 Axiom 4 (left_identity): multiply(identity, X) = X.
% 0.22/0.49 Axiom 5 (right_inverse): multiply(X, inverse(X)) = identity.
% 0.22/0.49 Axiom 6 (c_times_inverse_a_is_d): multiply(c, inverse(a)) = d.
% 0.22/0.49 Axiom 7 (d_times_inverse_b_is_h): multiply(d, inverse(b)) = h.
% 0.22/0.49 Axiom 8 (j_times_inverse_h_is_k): multiply(j, inverse(h)) = k.
% 0.22/0.49 Axiom 9 (left_inverse): multiply(inverse(X), X) = identity.
% 0.22/0.49 Axiom 10 (x_cubed_is_identity): multiply(X, multiply(X, X)) = identity.
% 0.22/0.49 Axiom 11 (associativity): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 0.22/0.49
% 0.22/0.49 Lemma 12: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.22/0.49 Proof:
% 0.22/0.49 multiply(X, multiply(inverse(X), Y))
% 0.22/0.49 = { by axiom 11 (associativity) R->L }
% 0.22/0.49 multiply(multiply(X, inverse(X)), Y)
% 0.22/0.49 = { by axiom 5 (right_inverse) }
% 0.22/0.49 multiply(identity, Y)
% 0.22/0.49 = { by axiom 4 (left_identity) }
% 0.22/0.49 Y
% 0.22/0.49
% 0.22/0.49 Lemma 13: inverse(inverse(X)) = X.
% 0.22/0.49 Proof:
% 0.22/0.49 inverse(inverse(X))
% 0.22/0.49 = { by lemma 12 R->L }
% 0.22/0.49 multiply(X, multiply(inverse(X), inverse(inverse(X))))
% 0.22/0.49 = { by axiom 5 (right_inverse) }
% 0.22/0.49 multiply(X, identity)
% 0.22/0.49 = { by axiom 1 (right_identity) }
% 0.22/0.49 X
% 0.22/0.49
% 0.22/0.49 Lemma 14: j = d.
% 0.22/0.49 Proof:
% 0.22/0.49 j
% 0.22/0.49 = { by axiom 3 (h_times_b_is_j) R->L }
% 0.22/0.49 multiply(h, b)
% 0.22/0.49 = { by lemma 13 R->L }
% 0.22/0.49 multiply(h, inverse(inverse(b)))
% 0.22/0.49 = { by axiom 7 (d_times_inverse_b_is_h) R->L }
% 0.22/0.49 multiply(multiply(d, inverse(b)), inverse(inverse(b)))
% 0.22/0.49 = { by axiom 11 (associativity) }
% 0.22/0.49 multiply(d, multiply(inverse(b), inverse(inverse(b))))
% 0.22/0.49 = { by axiom 5 (right_inverse) }
% 0.22/0.49 multiply(d, identity)
% 0.22/0.49 = { by axiom 1 (right_identity) }
% 0.22/0.49 d
% 0.22/0.49
% 0.22/0.49 Lemma 15: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.22/0.49 Proof:
% 0.22/0.49 multiply(inverse(X), multiply(X, Y))
% 0.22/0.49 = { by axiom 11 (associativity) R->L }
% 0.22/0.49 multiply(multiply(inverse(X), X), Y)
% 0.22/0.49 = { by axiom 9 (left_inverse) }
% 0.22/0.49 multiply(identity, Y)
% 0.22/0.49 = { by axiom 4 (left_identity) }
% 0.22/0.49 Y
% 0.22/0.49
% 0.22/0.49 Lemma 16: multiply(X, multiply(X, multiply(X, Y))) = Y.
% 0.22/0.49 Proof:
% 0.22/0.49 multiply(X, multiply(X, multiply(X, Y)))
% 0.22/0.49 = { by axiom 11 (associativity) R->L }
% 0.22/0.49 multiply(X, multiply(multiply(X, X), Y))
% 0.22/0.49 = { by axiom 11 (associativity) R->L }
% 0.22/0.49 multiply(multiply(X, multiply(X, X)), Y)
% 0.22/0.49 = { by axiom 10 (x_cubed_is_identity) }
% 0.22/0.49 multiply(identity, Y)
% 0.22/0.49 = { by axiom 4 (left_identity) }
% 0.22/0.49 Y
% 0.22/0.49
% 0.22/0.49 Lemma 17: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
% 0.22/0.49 Proof:
% 0.22/0.49 multiply(X, inverse(multiply(Y, X)))
% 0.22/0.49 = { by lemma 15 R->L }
% 0.22/0.49 multiply(inverse(Y), multiply(Y, multiply(X, inverse(multiply(Y, X)))))
% 0.22/0.49 = { by axiom 11 (associativity) R->L }
% 0.22/0.49 multiply(inverse(Y), multiply(multiply(Y, X), inverse(multiply(Y, X))))
% 0.22/0.49 = { by axiom 5 (right_inverse) }
% 0.22/0.49 multiply(inverse(Y), identity)
% 0.22/0.49 = { by axiom 1 (right_identity) }
% 0.22/0.49 inverse(Y)
% 0.22/0.49
% 0.22/0.49 Lemma 18: inverse(multiply(c, d)) = multiply(a, c).
% 0.22/0.49 Proof:
% 0.22/0.49 inverse(multiply(c, d))
% 0.22/0.49 = { by lemma 15 R->L }
% 0.22/0.49 inverse(multiply(inverse(c), multiply(c, multiply(c, d))))
% 0.22/0.49 = { by axiom 6 (c_times_inverse_a_is_d) R->L }
% 0.22/0.49 inverse(multiply(inverse(c), multiply(c, multiply(c, multiply(c, inverse(a))))))
% 0.22/0.49 = { by lemma 16 }
% 0.22/0.49 inverse(multiply(inverse(c), inverse(a)))
% 0.22/0.49 = { by lemma 12 R->L }
% 0.22/0.49 multiply(a, multiply(inverse(a), inverse(multiply(inverse(c), inverse(a)))))
% 0.22/0.49 = { by lemma 17 }
% 0.22/0.49 multiply(a, inverse(inverse(c)))
% 0.22/0.49 = { by lemma 13 }
% 0.22/0.49 multiply(a, c)
% 0.22/0.49
% 0.22/0.49 Goal 1 (prove_k_times_inverse_b_is_e): multiply(k, inverse(b)) = identity.
% 0.22/0.49 Proof:
% 0.22/0.49 multiply(k, inverse(b))
% 0.22/0.49 = { by lemma 17 R->L }
% 0.22/0.49 multiply(k, multiply(d, inverse(multiply(b, d))))
% 0.22/0.49 = { by lemma 15 R->L }
% 0.22/0.49 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(a, multiply(b, d))))))
% 0.22/0.49 = { by axiom 11 (associativity) R->L }
% 0.22/0.49 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(multiply(a, b), d)))))
% 0.22/0.49 = { by axiom 2 (a_times_b_is_c) }
% 0.22/0.49 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(c, d)))))
% 0.22/0.49 = { by axiom 1 (right_identity) R->L }
% 0.22/0.49 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(multiply(c, d), identity)))))
% 0.22/0.49 = { by axiom 10 (x_cubed_is_identity) R->L }
% 0.22/0.49 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(multiply(c, d), multiply(inverse(multiply(c, d)), multiply(inverse(multiply(c, d)), inverse(multiply(c, d)))))))))
% 0.22/0.49 = { by lemma 12 }
% 0.22/0.49 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(inverse(multiply(c, d)), inverse(multiply(c, d)))))))
% 0.22/0.49 = { by lemma 18 }
% 0.22/0.49 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(multiply(a, c), inverse(multiply(c, d)))))))
% 0.22/0.49 = { by axiom 11 (associativity) }
% 0.22/0.49 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(a, multiply(c, inverse(multiply(c, d))))))))
% 0.22/0.49 = { by lemma 18 }
% 0.22/0.49 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(a, multiply(c, multiply(a, c)))))))
% 0.22/0.49 = { by lemma 12 R->L }
% 0.22/0.49 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(a, multiply(c, multiply(inverse(a), multiply(inverse(inverse(a)), multiply(a, c)))))))))
% 0.22/0.50 = { by axiom 11 (associativity) R->L }
% 0.22/0.50 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(a, multiply(multiply(c, inverse(a)), multiply(inverse(inverse(a)), multiply(a, c))))))))
% 0.22/0.50 = { by axiom 6 (c_times_inverse_a_is_d) }
% 0.22/0.50 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(a, multiply(d, multiply(inverse(inverse(a)), multiply(a, c))))))))
% 0.22/0.50 = { by lemma 13 }
% 0.22/0.50 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(a, multiply(d, multiply(a, multiply(a, c))))))))
% 0.22/0.50 = { by axiom 2 (a_times_b_is_c) R->L }
% 0.22/0.50 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(a, multiply(d, multiply(a, multiply(a, multiply(a, b)))))))))
% 0.22/0.50 = { by lemma 16 }
% 0.22/0.50 multiply(k, multiply(d, inverse(multiply(inverse(a), multiply(a, multiply(d, b))))))
% 0.22/0.50 = { by lemma 15 }
% 0.22/0.50 multiply(k, multiply(d, inverse(multiply(d, b))))
% 0.22/0.50 = { by lemma 14 R->L }
% 0.22/0.50 multiply(k, multiply(j, inverse(multiply(d, b))))
% 0.22/0.50 = { by axiom 3 (h_times_b_is_j) R->L }
% 0.22/0.50 multiply(k, multiply(multiply(h, b), inverse(multiply(d, b))))
% 0.22/0.50 = { by axiom 11 (associativity) }
% 0.22/0.50 multiply(k, multiply(h, multiply(b, inverse(multiply(d, b)))))
% 0.22/0.50 = { by lemma 17 }
% 0.22/0.50 multiply(k, multiply(h, inverse(d)))
% 0.22/0.50 = { by axiom 1 (right_identity) R->L }
% 0.22/0.50 multiply(k, multiply(h, multiply(inverse(d), identity)))
% 0.22/0.50 = { by axiom 5 (right_inverse) R->L }
% 0.22/0.50 multiply(k, multiply(h, multiply(inverse(d), multiply(k, inverse(k)))))
% 0.22/0.50 = { by axiom 8 (j_times_inverse_h_is_k) R->L }
% 0.22/0.50 multiply(k, multiply(h, multiply(inverse(d), multiply(multiply(j, inverse(h)), inverse(k)))))
% 0.22/0.50 = { by axiom 11 (associativity) }
% 0.22/0.50 multiply(k, multiply(h, multiply(inverse(d), multiply(j, multiply(inverse(h), inverse(k))))))
% 0.22/0.50 = { by lemma 14 }
% 0.22/0.50 multiply(k, multiply(h, multiply(inverse(d), multiply(d, multiply(inverse(h), inverse(k))))))
% 0.22/0.50 = { by lemma 15 }
% 0.22/0.50 multiply(k, multiply(h, multiply(inverse(h), inverse(k))))
% 0.22/0.50 = { by lemma 12 }
% 0.22/0.50 multiply(k, inverse(k))
% 0.22/0.50 = { by axiom 5 (right_inverse) }
% 0.22/0.50 identity
% 0.22/0.50 % SZS output end Proof
% 0.22/0.50
% 0.22/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
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