TSTP Solution File: BOO028-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO028-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : n014.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 18:11:29 EDT 2023
% Result : Unsatisfiable 2.59s 0.80s
% Output : Proof 2.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO028-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Aug 27 08:15:31 EDT 2023
% 0.13/0.34 % CPUTime :
% 2.59/0.80 Command-line arguments: --no-flatten-goal
% 2.59/0.80
% 2.59/0.80 % SZS status Unsatisfiable
% 2.59/0.80
% 2.59/0.81 % SZS output start Proof
% 2.59/0.81 Axiom 1 (commutativity_of_add): add(X, Y) = add(Y, X).
% 2.59/0.81 Axiom 2 (commutativity_of_multiply): multiply(X, Y) = multiply(Y, X).
% 2.59/0.81 Axiom 3 (associativity_of_add): add(add(X, Y), Z) = add(X, add(Y, Z)).
% 2.59/0.81 Axiom 4 (associativity_of_multiply): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 2.59/0.81 Axiom 5 (l1): add(X, multiply(Y, multiply(X, Z))) = X.
% 2.59/0.81 Axiom 6 (l2): multiply(X, add(Y, add(X, Z))) = X.
% 2.59/0.81 Axiom 7 (b2): add(multiply(X, Y), multiply(X, inverse(Y))) = X.
% 2.59/0.81 Axiom 8 (b1): multiply(add(X, Y), add(X, inverse(Y))) = X.
% 2.59/0.81 Axiom 9 (l3): add(add(multiply(X, Y), multiply(Y, Z)), Y) = Y.
% 2.59/0.81 Axiom 10 (l4): multiply(multiply(add(X, Y), add(Y, Z)), Y) = Y.
% 2.59/0.81
% 2.59/0.81 Lemma 11: multiply(X, add(X, Y)) = X.
% 2.59/0.81 Proof:
% 2.59/0.81 multiply(X, add(X, Y))
% 2.59/0.81 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.81 multiply(X, add(Y, X))
% 2.59/0.81 = { by axiom 5 (l1) R->L }
% 2.59/0.81 multiply(X, add(Y, add(X, multiply(Z, multiply(X, W)))))
% 2.59/0.81 = { by axiom 6 (l2) }
% 2.59/0.81 X
% 2.59/0.81
% 2.59/0.81 Lemma 12: add(X, multiply(X, Y)) = X.
% 2.59/0.81 Proof:
% 2.59/0.81 add(X, multiply(X, Y))
% 2.59/0.81 = { by axiom 2 (commutativity_of_multiply) R->L }
% 2.59/0.81 add(X, multiply(Y, X))
% 2.59/0.81 = { by axiom 6 (l2) R->L }
% 2.59/0.81 add(X, multiply(Y, multiply(X, add(Z, add(X, W)))))
% 2.59/0.81 = { by axiom 5 (l1) }
% 2.59/0.81 X
% 2.59/0.81
% 2.59/0.81 Lemma 13: add(X, add(Y, multiply(X, Z))) = add(X, Y).
% 2.59/0.81 Proof:
% 2.59/0.81 add(X, add(Y, multiply(X, Z)))
% 2.59/0.81 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.81 add(X, add(multiply(X, Z), Y))
% 2.59/0.81 = { by axiom 3 (associativity_of_add) R->L }
% 2.59/0.81 add(add(X, multiply(X, Z)), Y)
% 2.59/0.81 = { by lemma 12 }
% 2.59/0.81 add(X, Y)
% 2.59/0.81
% 2.59/0.81 Lemma 14: add(inverse(X), multiply(X, Y)) = add(Y, inverse(X)).
% 2.59/0.81 Proof:
% 2.59/0.81 add(inverse(X), multiply(X, Y))
% 2.59/0.81 = { by axiom 2 (commutativity_of_multiply) R->L }
% 2.59/0.81 add(inverse(X), multiply(Y, X))
% 2.59/0.81 = { by lemma 13 R->L }
% 2.59/0.81 add(inverse(X), add(multiply(Y, X), multiply(inverse(X), Y)))
% 2.59/0.81 = { by axiom 2 (commutativity_of_multiply) R->L }
% 2.59/0.81 add(inverse(X), add(multiply(Y, X), multiply(Y, inverse(X))))
% 2.59/0.81 = { by axiom 7 (b2) }
% 2.59/0.81 add(inverse(X), Y)
% 2.59/0.81 = { by axiom 1 (commutativity_of_add) }
% 2.59/0.81 add(Y, inverse(X))
% 2.59/0.81
% 2.59/0.81 Lemma 15: multiply(add(X, Y), add(inverse(X), Y)) = Y.
% 2.59/0.81 Proof:
% 2.59/0.81 multiply(add(X, Y), add(inverse(X), Y))
% 2.59/0.81 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.81 multiply(add(X, Y), add(Y, inverse(X)))
% 2.59/0.81 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.81 multiply(add(Y, X), add(Y, inverse(X)))
% 2.59/0.81 = { by axiom 8 (b1) }
% 2.59/0.81 Y
% 2.59/0.81
% 2.59/0.81 Lemma 16: multiply(X, add(Y, inverse(X))) = multiply(X, Y).
% 2.59/0.81 Proof:
% 2.59/0.81 multiply(X, add(Y, inverse(X)))
% 2.59/0.81 = { by lemma 14 R->L }
% 2.59/0.81 multiply(X, add(inverse(X), multiply(X, Y)))
% 2.59/0.81 = { by lemma 12 R->L }
% 2.59/0.81 multiply(add(X, multiply(X, Y)), add(inverse(X), multiply(X, Y)))
% 2.59/0.81 = { by lemma 15 }
% 2.59/0.81 multiply(X, Y)
% 2.59/0.81
% 2.59/0.81 Lemma 17: multiply(X, add(inverse(X), Y)) = multiply(X, Y).
% 2.59/0.81 Proof:
% 2.59/0.81 multiply(X, add(inverse(X), Y))
% 2.59/0.81 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.81 multiply(X, add(Y, inverse(X)))
% 2.59/0.81 = { by lemma 16 }
% 2.59/0.81 multiply(X, Y)
% 2.59/0.81
% 2.59/0.81 Lemma 18: multiply(inverse(X), add(X, Y)) = multiply(Y, inverse(X)).
% 2.59/0.81 Proof:
% 2.59/0.81 multiply(inverse(X), add(X, Y))
% 2.59/0.81 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.81 multiply(inverse(X), add(Y, X))
% 2.59/0.81 = { by lemma 11 R->L }
% 2.59/0.81 multiply(multiply(inverse(X), add(inverse(X), Y)), add(Y, X))
% 2.59/0.81 = { by axiom 4 (associativity_of_multiply) }
% 2.59/0.81 multiply(inverse(X), multiply(add(inverse(X), Y), add(Y, X)))
% 2.59/0.81 = { by axiom 2 (commutativity_of_multiply) }
% 2.59/0.81 multiply(inverse(X), multiply(add(Y, X), add(inverse(X), Y)))
% 2.59/0.81 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.81 multiply(inverse(X), multiply(add(Y, X), add(Y, inverse(X))))
% 2.59/0.81 = { by axiom 8 (b1) }
% 2.59/0.81 multiply(inverse(X), Y)
% 2.59/0.81 = { by axiom 2 (commutativity_of_multiply) }
% 2.59/0.81 multiply(Y, inverse(X))
% 2.59/0.81
% 2.59/0.81 Lemma 19: add(X, multiply(Y, inverse(X))) = add(X, Y).
% 2.59/0.81 Proof:
% 2.59/0.81 add(X, multiply(Y, inverse(X)))
% 2.59/0.81 = { by lemma 18 R->L }
% 2.59/0.81 add(X, multiply(inverse(X), add(X, Y)))
% 2.59/0.81 = { by lemma 11 R->L }
% 2.59/0.81 add(multiply(X, add(X, Y)), multiply(inverse(X), add(X, Y)))
% 2.59/0.81 = { by axiom 2 (commutativity_of_multiply) R->L }
% 2.59/0.81 add(multiply(X, add(X, Y)), multiply(add(X, Y), inverse(X)))
% 2.59/0.81 = { by axiom 2 (commutativity_of_multiply) R->L }
% 2.59/0.81 add(multiply(add(X, Y), X), multiply(add(X, Y), inverse(X)))
% 2.59/0.81 = { by axiom 7 (b2) }
% 2.59/0.81 add(X, Y)
% 2.59/0.81
% 2.59/0.81 Lemma 20: multiply(X, add(Y, multiply(X, Z))) = multiply(X, add(Y, Z)).
% 2.59/0.81 Proof:
% 2.59/0.81 multiply(X, add(Y, multiply(X, Z)))
% 2.59/0.81 = { by axiom 2 (commutativity_of_multiply) R->L }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, X)))
% 2.59/0.81 = { by lemma 11 R->L }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, multiply(X, add(X, inverse(X))))))
% 2.59/0.81 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, multiply(X, add(inverse(X), X)))))
% 2.59/0.81 = { by lemma 19 R->L }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, multiply(X, add(inverse(X), multiply(X, inverse(inverse(X))))))))
% 2.59/0.81 = { by lemma 14 }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, multiply(X, add(inverse(inverse(X)), inverse(X))))))
% 2.59/0.81 = { by axiom 1 (commutativity_of_add) }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, multiply(X, add(inverse(X), inverse(inverse(X)))))))
% 2.59/0.81 = { by lemma 12 R->L }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, multiply(add(X, multiply(X, inverse(X))), add(inverse(X), inverse(inverse(X)))))))
% 2.59/0.81 = { by axiom 2 (commutativity_of_multiply) R->L }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, multiply(add(X, multiply(inverse(X), X)), add(inverse(X), inverse(inverse(X)))))))
% 2.59/0.81 = { by lemma 16 R->L }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, multiply(add(X, multiply(inverse(X), add(X, inverse(inverse(X))))), add(inverse(X), inverse(inverse(X)))))))
% 2.59/0.81 = { by lemma 18 }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, multiply(add(X, multiply(inverse(inverse(X)), inverse(X))), add(inverse(X), inverse(inverse(X)))))))
% 2.59/0.81 = { by lemma 19 }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, multiply(add(X, inverse(inverse(X))), add(inverse(X), inverse(inverse(X)))))))
% 2.59/0.81 = { by lemma 15 }
% 2.59/0.81 multiply(X, add(Y, multiply(Z, inverse(inverse(X)))))
% 2.59/0.81 = { by lemma 17 R->L }
% 2.59/0.81 multiply(X, add(inverse(X), add(Y, multiply(Z, inverse(inverse(X))))))
% 2.59/0.81 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.81 multiply(X, add(inverse(X), add(multiply(Z, inverse(inverse(X))), Y)))
% 2.59/0.81 = { by axiom 3 (associativity_of_add) R->L }
% 2.59/0.81 multiply(X, add(add(inverse(X), multiply(Z, inverse(inverse(X)))), Y))
% 2.59/0.81 = { by lemma 19 }
% 2.59/0.81 multiply(X, add(add(inverse(X), Z), Y))
% 2.59/0.81 = { by axiom 3 (associativity_of_add) }
% 2.59/0.81 multiply(X, add(inverse(X), add(Z, Y)))
% 2.59/0.82 = { by lemma 17 }
% 2.59/0.82 multiply(X, add(Z, Y))
% 2.59/0.82 = { by axiom 1 (commutativity_of_add) }
% 2.59/0.82 multiply(X, add(Y, Z))
% 2.59/0.82
% 2.59/0.82 Goal 1 (prove_multiply_add_property): multiply(a, add(b, c)) = add(multiply(b, a), multiply(c, a)).
% 2.59/0.82 Proof:
% 2.59/0.82 multiply(a, add(b, c))
% 2.59/0.82 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.82 multiply(a, add(c, b))
% 2.59/0.82 = { by lemma 20 R->L }
% 2.59/0.82 multiply(a, add(c, multiply(a, b)))
% 2.59/0.82 = { by axiom 2 (commutativity_of_multiply) }
% 2.59/0.82 multiply(a, add(c, multiply(b, a)))
% 2.59/0.82 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.82 multiply(a, add(multiply(b, a), c))
% 2.59/0.82 = { by lemma 20 R->L }
% 2.59/0.82 multiply(a, add(multiply(b, a), multiply(a, c)))
% 2.59/0.82 = { by lemma 12 R->L }
% 2.59/0.82 multiply(a, add(multiply(b, a), multiply(add(a, multiply(a, X)), c)))
% 2.59/0.82 = { by axiom 9 (l3) R->L }
% 2.59/0.82 multiply(add(add(multiply(b, a), multiply(a, X)), a), add(multiply(b, a), multiply(add(a, multiply(a, X)), c)))
% 2.59/0.82 = { by axiom 3 (associativity_of_add) }
% 2.59/0.82 multiply(add(multiply(b, a), add(multiply(a, X), a)), add(multiply(b, a), multiply(add(a, multiply(a, X)), c)))
% 2.59/0.82 = { by axiom 1 (commutativity_of_add) }
% 2.59/0.82 multiply(add(multiply(b, a), add(a, multiply(a, X))), add(multiply(b, a), multiply(add(a, multiply(a, X)), c)))
% 2.59/0.82 = { by axiom 1 (commutativity_of_add) R->L }
% 2.59/0.82 multiply(add(add(a, multiply(a, X)), multiply(b, a)), add(multiply(b, a), multiply(add(a, multiply(a, X)), c)))
% 2.59/0.82 = { by lemma 11 R->L }
% 2.59/0.82 multiply(add(add(a, multiply(a, X)), multiply(b, a)), multiply(add(multiply(b, a), multiply(add(a, multiply(a, X)), c)), add(add(multiply(b, a), multiply(add(a, multiply(a, X)), c)), Y)))
% 2.59/0.82 = { by lemma 13 R->L }
% 2.59/0.82 multiply(add(add(a, multiply(a, X)), add(multiply(b, a), multiply(add(a, multiply(a, X)), c))), multiply(add(multiply(b, a), multiply(add(a, multiply(a, X)), c)), add(add(multiply(b, a), multiply(add(a, multiply(a, X)), c)), Y)))
% 2.59/0.82 = { by axiom 2 (commutativity_of_multiply) R->L }
% 2.59/0.82 multiply(add(add(a, multiply(a, X)), add(multiply(b, a), multiply(add(a, multiply(a, X)), c))), multiply(add(add(multiply(b, a), multiply(add(a, multiply(a, X)), c)), Y), add(multiply(b, a), multiply(add(a, multiply(a, X)), c))))
% 2.59/0.82 = { by axiom 4 (associativity_of_multiply) R->L }
% 2.59/0.82 multiply(multiply(add(add(a, multiply(a, X)), add(multiply(b, a), multiply(add(a, multiply(a, X)), c))), add(add(multiply(b, a), multiply(add(a, multiply(a, X)), c)), Y)), add(multiply(b, a), multiply(add(a, multiply(a, X)), c)))
% 2.59/0.82 = { by axiom 10 (l4) }
% 2.59/0.82 add(multiply(b, a), multiply(add(a, multiply(a, X)), c))
% 2.59/0.82 = { by lemma 12 }
% 2.59/0.82 add(multiply(b, a), multiply(a, c))
% 2.59/0.82 = { by axiom 2 (commutativity_of_multiply) }
% 2.59/0.82 add(multiply(b, a), multiply(c, a))
% 2.59/0.82 % SZS output end Proof
% 2.59/0.82
% 2.59/0.82 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------