TSTP Solution File: BOO031-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : BOO031-1 : 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 : n023.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 18:11:30 EDT 2023
% Result : Unsatisfiable 5.69s 1.11s
% Output : Proof 5.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO031-1 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 08:52:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.69/1.11 Command-line arguments: --no-flatten-goal
% 5.69/1.11
% 5.69/1.11 % SZS status Unsatisfiable
% 5.69/1.11
% 5.69/1.15 % SZS output start Proof
% 5.69/1.15 Axiom 1 (additive_inverse): add(X, inverse(X)) = n1.
% 5.69/1.15 Axiom 2 (multiplicative_inverse): multiply(X, inverse(X)) = n0.
% 5.69/1.15 Axiom 3 (associativity_of_add): add(add(X, Y), Z) = add(X, add(Y, Z)).
% 5.69/1.15 Axiom 4 (associativity_of_multiply): multiply(multiply(X, Y), Z) = multiply(X, multiply(Y, Z)).
% 5.69/1.15 Axiom 5 (property3_dual): add(multiply(X, inverse(X)), Y) = Y.
% 5.69/1.15 Axiom 6 (property3): multiply(add(X, inverse(X)), Y) = Y.
% 5.69/1.15 Axiom 7 (l1): add(X, multiply(Y, multiply(X, Z))) = X.
% 5.69/1.15 Axiom 8 (l2): multiply(X, add(Y, add(X, Z))) = X.
% 5.69/1.15 Axiom 9 (l3): add(add(multiply(X, Y), multiply(Y, Z)), Y) = Y.
% 5.69/1.15 Axiom 10 (l4): multiply(multiply(add(X, Y), add(Y, Z)), Y) = Y.
% 5.69/1.15 Axiom 11 (distributivity): add(multiply(X, Y), add(multiply(Y, Z), multiply(Z, X))) = multiply(add(X, Y), multiply(add(Y, Z), add(Z, X))).
% 5.69/1.15
% 5.69/1.15 Lemma 12: add(multiply(X, Y), add(multiply(Y, Z), Y)) = Y.
% 5.69/1.15 Proof:
% 5.69/1.15 add(multiply(X, Y), add(multiply(Y, Z), Y))
% 5.69/1.15 = { by axiom 3 (associativity_of_add) R->L }
% 5.69/1.15 add(add(multiply(X, Y), multiply(Y, Z)), Y)
% 5.69/1.15 = { by axiom 9 (l3) }
% 5.69/1.15 Y
% 5.69/1.15
% 5.69/1.15 Lemma 13: multiply(X, multiply(Y, X)) = multiply(X, Y).
% 5.69/1.15 Proof:
% 5.69/1.15 multiply(X, multiply(Y, X))
% 5.69/1.15 = { by axiom 4 (associativity_of_multiply) R->L }
% 5.69/1.15 multiply(multiply(X, Y), X)
% 5.69/1.15 = { by lemma 12 R->L }
% 5.69/1.15 multiply(multiply(X, Y), add(multiply(Z, X), add(multiply(X, Y), X)))
% 5.69/1.15 = { by axiom 8 (l2) }
% 5.69/1.15 multiply(X, Y)
% 5.69/1.15
% 5.69/1.15 Lemma 14: add(n0, X) = X.
% 5.69/1.15 Proof:
% 5.69/1.15 add(n0, X)
% 5.69/1.15 = { by axiom 2 (multiplicative_inverse) R->L }
% 5.69/1.15 add(multiply(Y, inverse(Y)), X)
% 5.69/1.15 = { by axiom 5 (property3_dual) }
% 5.69/1.15 X
% 5.69/1.15
% 5.69/1.15 Lemma 15: add(multiply(X, Y), Y) = Y.
% 5.69/1.15 Proof:
% 5.69/1.15 add(multiply(X, Y), Y)
% 5.69/1.15 = { by lemma 14 R->L }
% 5.69/1.15 add(multiply(X, Y), add(n0, Y))
% 5.69/1.15 = { by axiom 2 (multiplicative_inverse) R->L }
% 5.69/1.15 add(multiply(X, Y), add(multiply(Y, inverse(Y)), Y))
% 5.69/1.15 = { by lemma 12 }
% 5.69/1.15 Y
% 5.69/1.15
% 5.69/1.15 Lemma 16: multiply(add(X, Y), multiply(add(Y, Z), Y)) = Y.
% 5.69/1.15 Proof:
% 5.69/1.15 multiply(add(X, Y), multiply(add(Y, Z), Y))
% 5.69/1.15 = { by axiom 4 (associativity_of_multiply) R->L }
% 5.69/1.15 multiply(multiply(add(X, Y), add(Y, Z)), Y)
% 5.69/1.15 = { by axiom 10 (l4) }
% 5.69/1.15 Y
% 5.69/1.15
% 5.69/1.15 Lemma 17: add(X, multiply(Y, X)) = X.
% 5.69/1.15 Proof:
% 5.69/1.15 add(X, multiply(Y, X))
% 5.69/1.15 = { by axiom 8 (l2) R->L }
% 5.69/1.15 add(X, multiply(Y, multiply(X, add(Z, add(X, W)))))
% 5.69/1.15 = { by axiom 7 (l1) }
% 5.69/1.15 X
% 5.69/1.15
% 5.69/1.15 Lemma 18: multiply(add(X, Y), X) = X.
% 5.69/1.15 Proof:
% 5.69/1.15 multiply(add(X, Y), X)
% 5.69/1.15 = { by lemma 15 R->L }
% 5.69/1.15 add(multiply(add(Z, X), multiply(add(X, Y), X)), multiply(add(X, Y), X))
% 5.69/1.15 = { by lemma 16 }
% 5.69/1.15 add(X, multiply(add(X, Y), X))
% 5.69/1.15 = { by lemma 17 }
% 5.69/1.15 X
% 5.69/1.15
% 5.69/1.15 Lemma 19: multiply(Y, X) = multiply(X, Y).
% 5.69/1.15 Proof:
% 5.69/1.15 multiply(Y, X)
% 5.69/1.15 = { by lemma 13 R->L }
% 5.69/1.15 multiply(Y, multiply(X, Y))
% 5.69/1.15 = { by lemma 12 R->L }
% 5.69/1.15 multiply(add(multiply(X, Y), add(multiply(Y, Z), Y)), multiply(X, Y))
% 5.69/1.15 = { by lemma 18 }
% 5.69/1.15 multiply(X, Y)
% 5.69/1.15
% 5.69/1.15 Lemma 20: multiply(n1, X) = X.
% 5.69/1.15 Proof:
% 5.69/1.15 multiply(n1, X)
% 5.69/1.15 = { by axiom 1 (additive_inverse) R->L }
% 5.69/1.15 multiply(add(Y, inverse(Y)), X)
% 5.69/1.15 = { by axiom 6 (property3) }
% 5.69/1.15 X
% 5.69/1.15
% 5.69/1.15 Lemma 21: multiply(add(X, Y), Y) = Y.
% 5.69/1.15 Proof:
% 5.69/1.15 multiply(add(X, Y), Y)
% 5.69/1.15 = { by lemma 20 R->L }
% 5.69/1.15 multiply(add(X, Y), multiply(n1, Y))
% 5.69/1.15 = { by axiom 1 (additive_inverse) R->L }
% 5.69/1.15 multiply(add(X, Y), multiply(add(Y, inverse(Y)), Y))
% 5.69/1.15 = { by lemma 16 }
% 5.69/1.15 Y
% 5.69/1.15
% 5.69/1.15 Lemma 22: add(X, multiply(X, Y)) = X.
% 5.69/1.15 Proof:
% 5.69/1.15 add(X, multiply(X, Y))
% 5.69/1.15 = { by lemma 20 R->L }
% 5.69/1.15 add(X, multiply(n1, multiply(X, Y)))
% 5.69/1.15 = { by axiom 7 (l1) }
% 5.69/1.15 X
% 5.69/1.15
% 5.69/1.15 Lemma 23: add(Y, X) = add(X, Y).
% 5.69/1.15 Proof:
% 5.69/1.15 add(Y, X)
% 5.69/1.15 = { by lemma 21 R->L }
% 5.69/1.15 multiply(add(X, add(Y, X)), add(Y, X))
% 5.69/1.15 = { by lemma 18 R->L }
% 5.69/1.15 multiply(add(X, add(Y, X)), multiply(add(add(Y, X), Y), add(Y, X)))
% 5.69/1.15 = { by axiom 11 (distributivity) R->L }
% 5.69/1.15 add(multiply(X, add(Y, X)), add(multiply(add(Y, X), Y), multiply(Y, X)))
% 5.69/1.15 = { by axiom 7 (l1) R->L }
% 5.69/1.15 add(multiply(X, add(Y, add(X, multiply(Z, multiply(X, W))))), add(multiply(add(Y, X), Y), multiply(Y, X)))
% 5.69/1.15 = { by axiom 8 (l2) }
% 5.69/1.15 add(X, add(multiply(add(Y, X), Y), multiply(Y, X)))
% 5.69/1.15 = { by lemma 18 }
% 5.69/1.15 add(X, add(Y, multiply(Y, X)))
% 5.69/1.15 = { by lemma 22 }
% 5.69/1.15 add(X, Y)
% 5.69/1.15
% 5.69/1.15 Lemma 24: multiply(X, multiply(Y, Z)) = multiply(Y, multiply(X, Z)).
% 5.69/1.15 Proof:
% 5.69/1.15 multiply(X, multiply(Y, Z))
% 5.69/1.15 = { by lemma 19 }
% 5.69/1.15 multiply(multiply(Y, Z), X)
% 5.69/1.15 = { by axiom 4 (associativity_of_multiply) }
% 5.69/1.15 multiply(Y, multiply(Z, X))
% 5.69/1.15 = { by lemma 19 R->L }
% 5.69/1.15 multiply(Y, multiply(X, Z))
% 5.69/1.15
% 5.69/1.15 Lemma 25: multiply(X, add(X, Y)) = X.
% 5.69/1.15 Proof:
% 5.69/1.15 multiply(X, add(X, Y))
% 5.69/1.15 = { by lemma 14 R->L }
% 5.69/1.15 multiply(X, add(n0, add(X, Y)))
% 5.69/1.15 = { by axiom 8 (l2) }
% 5.69/1.15 X
% 5.69/1.15
% 5.69/1.15 Lemma 26: add(X, add(Y, X)) = add(X, Y).
% 5.69/1.15 Proof:
% 5.69/1.15 add(X, add(Y, X))
% 5.69/1.15 = { by axiom 3 (associativity_of_add) R->L }
% 5.69/1.15 add(add(X, Y), X)
% 5.69/1.15 = { by lemma 16 R->L }
% 5.69/1.15 add(add(X, Y), multiply(add(Z, X), multiply(add(X, Y), X)))
% 5.69/1.15 = { by axiom 7 (l1) }
% 5.69/1.15 add(X, Y)
% 5.69/1.15
% 5.69/1.15 Lemma 27: add(X, add(Y, Z)) = add(Y, add(X, Z)).
% 5.69/1.15 Proof:
% 5.69/1.15 add(X, add(Y, Z))
% 5.69/1.15 = { by lemma 23 }
% 5.69/1.15 add(add(Y, Z), X)
% 5.69/1.15 = { by axiom 3 (associativity_of_add) }
% 5.69/1.15 add(Y, add(Z, X))
% 5.69/1.15 = { by lemma 23 R->L }
% 5.69/1.15 add(Y, add(X, Z))
% 5.69/1.15
% 5.69/1.15 Lemma 28: add(X, add(multiply(X, Y), Z)) = add(X, Z).
% 5.69/1.15 Proof:
% 5.69/1.15 add(X, add(multiply(X, Y), Z))
% 5.69/1.15 = { by axiom 3 (associativity_of_add) R->L }
% 5.69/1.15 add(add(X, multiply(X, Y)), Z)
% 5.69/1.15 = { by lemma 22 }
% 5.69/1.15 add(X, Z)
% 5.69/1.15
% 5.69/1.15 Lemma 29: multiply(add(X, Y), add(Y, Z)) = add(Y, multiply(X, add(Y, Z))).
% 5.69/1.15 Proof:
% 5.69/1.15 multiply(add(X, Y), add(Y, Z))
% 5.69/1.15 = { by lemma 23 }
% 5.69/1.15 multiply(add(X, Y), add(Z, Y))
% 5.69/1.15 = { by lemma 23 }
% 5.69/1.15 multiply(add(Y, X), add(Z, Y))
% 5.69/1.15 = { by lemma 19 }
% 5.69/1.15 multiply(add(Z, Y), add(Y, X))
% 5.69/1.15 = { by lemma 22 R->L }
% 5.69/1.15 multiply(add(Z, add(Y, multiply(Y, add(W, add(Y, V))))), add(Y, X))
% 5.69/1.15 = { by axiom 8 (l2) }
% 5.69/1.15 multiply(add(Z, add(Y, Y)), add(Y, X))
% 5.69/1.15 = { by axiom 3 (associativity_of_add) R->L }
% 5.69/1.15 multiply(add(add(Z, Y), Y), add(Y, X))
% 5.69/1.15 = { by lemma 25 R->L }
% 5.69/1.15 multiply(add(add(Z, Y), Y), multiply(add(Y, X), add(add(Y, X), Z)))
% 5.69/1.15 = { by axiom 3 (associativity_of_add) }
% 5.69/1.15 multiply(add(add(Z, Y), Y), multiply(add(Y, X), add(Y, add(X, Z))))
% 5.69/1.15 = { by lemma 23 R->L }
% 5.69/1.15 multiply(add(add(Z, Y), Y), multiply(add(Y, X), add(add(X, Z), Y)))
% 5.69/1.15 = { by axiom 3 (associativity_of_add) }
% 5.69/1.15 multiply(add(add(Z, Y), Y), multiply(add(Y, X), add(X, add(Z, Y))))
% 5.69/1.15 = { by axiom 11 (distributivity) R->L }
% 5.69/1.15 add(multiply(add(Z, Y), Y), add(multiply(Y, X), multiply(X, add(Z, Y))))
% 5.69/1.15 = { by lemma 21 }
% 5.69/1.15 add(Y, add(multiply(Y, X), multiply(X, add(Z, Y))))
% 5.69/1.15 = { by lemma 28 }
% 5.69/1.15 add(Y, multiply(X, add(Z, Y)))
% 5.69/1.15 = { by lemma 23 R->L }
% 5.69/1.15 add(Y, multiply(X, add(Y, Z)))
% 5.69/1.15
% 5.69/1.15 Lemma 30: multiply(add(X, Y), add(X, Z)) = add(X, multiply(Y, add(X, Z))).
% 5.69/1.15 Proof:
% 5.69/1.15 multiply(add(X, Y), add(X, Z))
% 5.69/1.15 = { by lemma 23 }
% 5.69/1.15 multiply(add(Y, X), add(X, Z))
% 5.69/1.15 = { by lemma 29 }
% 5.69/1.16 add(X, multiply(Y, add(X, Z)))
% 5.69/1.16
% 5.69/1.16 Lemma 31: add(X, multiply(add(X, Y), Z)) = add(X, multiply(Y, add(X, Z))).
% 5.69/1.16 Proof:
% 5.69/1.16 add(X, multiply(add(X, Y), Z))
% 5.69/1.16 = { by lemma 19 }
% 5.69/1.16 add(X, multiply(Z, add(X, Y)))
% 5.69/1.16 = { by lemma 30 R->L }
% 5.69/1.16 multiply(add(X, Z), add(X, Y))
% 5.69/1.16 = { by lemma 17 R->L }
% 5.69/1.16 add(multiply(add(X, Z), add(X, Y)), multiply(X, multiply(add(X, Z), add(X, Y))))
% 5.69/1.16 = { by lemma 19 }
% 5.69/1.16 add(multiply(add(X, Z), add(X, Y)), multiply(X, multiply(add(X, Y), add(X, Z))))
% 5.69/1.16 = { by axiom 4 (associativity_of_multiply) R->L }
% 5.69/1.16 add(multiply(add(X, Z), add(X, Y)), multiply(multiply(X, add(X, Y)), add(X, Z)))
% 5.69/1.16 = { by lemma 25 }
% 5.69/1.16 add(multiply(add(X, Z), add(X, Y)), multiply(X, add(X, Z)))
% 5.69/1.16 = { by lemma 23 R->L }
% 5.69/1.16 add(multiply(X, add(X, Z)), multiply(add(X, Z), add(X, Y)))
% 5.69/1.16 = { by lemma 19 R->L }
% 5.69/1.16 add(multiply(add(X, Z), X), multiply(add(X, Z), add(X, Y)))
% 5.69/1.16 = { by lemma 19 R->L }
% 5.69/1.16 add(multiply(add(X, Z), X), multiply(add(X, Y), add(X, Z)))
% 5.69/1.16 = { by lemma 18 }
% 5.69/1.16 add(X, multiply(add(X, Y), add(X, Z)))
% 5.69/1.16 = { by lemma 30 }
% 5.69/1.16 add(X, add(X, multiply(Y, add(X, Z))))
% 5.69/1.16 = { by lemma 23 }
% 5.69/1.16 add(X, add(multiply(Y, add(X, Z)), X))
% 5.69/1.16 = { by lemma 26 }
% 5.69/1.16 add(X, multiply(Y, add(X, Z)))
% 5.69/1.16
% 5.69/1.16 Lemma 32: add(X, multiply(Y, add(X, Z))) = add(X, multiply(Y, Z)).
% 5.69/1.16 Proof:
% 5.69/1.16 add(X, multiply(Y, add(X, Z)))
% 5.69/1.16 = { by axiom 8 (l2) R->L }
% 5.69/1.16 add(X, multiply(Y, add(X, multiply(Z, add(X, add(Z, Y))))))
% 5.69/1.16 = { by lemma 31 R->L }
% 5.69/1.16 add(X, multiply(Y, add(X, multiply(add(X, Z), add(Z, Y)))))
% 5.69/1.16 = { by lemma 31 R->L }
% 5.69/1.16 add(X, multiply(add(X, Y), multiply(add(X, Z), add(Z, Y))))
% 5.69/1.16 = { by lemma 23 R->L }
% 5.69/1.16 add(X, multiply(add(Y, X), multiply(add(X, Z), add(Z, Y))))
% 5.69/1.16 = { by axiom 11 (distributivity) R->L }
% 5.69/1.16 add(X, add(multiply(Y, X), add(multiply(X, Z), multiply(Z, Y))))
% 5.69/1.16 = { by lemma 27 R->L }
% 5.69/1.16 add(multiply(Y, X), add(X, add(multiply(X, Z), multiply(Z, Y))))
% 5.69/1.16 = { by axiom 3 (associativity_of_add) R->L }
% 5.69/1.16 add(add(multiply(Y, X), X), add(multiply(X, Z), multiply(Z, Y)))
% 5.69/1.16 = { by lemma 15 }
% 5.69/1.16 add(X, add(multiply(X, Z), multiply(Z, Y)))
% 5.69/1.16 = { by lemma 28 }
% 5.69/1.16 add(X, multiply(Z, Y))
% 5.69/1.16 = { by lemma 19 R->L }
% 5.69/1.16 add(X, multiply(Y, Z))
% 5.69/1.16
% 5.69/1.16 Goal 1 (prove_multiply_add_property): multiply(a, add(b, c)) = add(multiply(b, a), multiply(c, a)).
% 5.69/1.16 Proof:
% 5.69/1.16 multiply(a, add(b, c))
% 5.69/1.16 = { by lemma 23 }
% 5.69/1.16 multiply(a, add(c, b))
% 5.69/1.16 = { by lemma 22 R->L }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(multiply(a, add(c, b)), inverse(multiply(a, add(c, b)))))
% 5.69/1.16 = { by axiom 2 (multiplicative_inverse) }
% 5.69/1.16 add(multiply(a, add(c, b)), n0)
% 5.69/1.16 = { by lemma 22 R->L }
% 5.69/1.16 add(multiply(a, add(c, b)), add(n0, multiply(n0, multiply(add(c, X), c))))
% 5.69/1.16 = { by lemma 14 }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(n0, multiply(add(c, X), c)))
% 5.69/1.16 = { by axiom 7 (l1) R->L }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(add(n0, multiply(inverse(add(multiply(a, add(c, b)), c)), multiply(n0, n1))), multiply(add(c, X), c)))
% 5.69/1.16 = { by axiom 1 (additive_inverse) R->L }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(add(n0, multiply(inverse(add(multiply(a, add(c, b)), c)), multiply(n0, add(n0, inverse(n0))))), multiply(add(c, X), c)))
% 5.69/1.16 = { by lemma 14 }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(add(n0, multiply(inverse(add(multiply(a, add(c, b)), c)), multiply(n0, inverse(n0)))), multiply(add(c, X), c)))
% 5.69/1.16 = { by axiom 2 (multiplicative_inverse) }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(add(n0, multiply(inverse(add(multiply(a, add(c, b)), c)), n0)), multiply(add(c, X), c)))
% 5.69/1.16 = { by lemma 14 }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(multiply(inverse(add(multiply(a, add(c, b)), c)), n0), multiply(add(c, X), c)))
% 5.69/1.16 = { by axiom 2 (multiplicative_inverse) R->L }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(multiply(inverse(add(multiply(a, add(c, b)), c)), multiply(add(multiply(a, add(c, b)), c), inverse(add(multiply(a, add(c, b)), c)))), multiply(add(c, X), c)))
% 5.69/1.16 = { by lemma 13 }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(multiply(inverse(add(multiply(a, add(c, b)), c)), add(multiply(a, add(c, b)), c)), multiply(add(c, X), c)))
% 5.69/1.16 = { by axiom 4 (associativity_of_multiply) }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(inverse(add(multiply(a, add(c, b)), c)), multiply(add(multiply(a, add(c, b)), c), multiply(add(c, X), c))))
% 5.69/1.16 = { by lemma 16 }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(inverse(add(multiply(a, add(c, b)), c)), c))
% 5.69/1.16 = { by lemma 19 R->L }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(c, inverse(add(multiply(a, add(c, b)), c))))
% 5.69/1.16 = { by lemma 23 R->L }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(c, inverse(add(c, multiply(a, add(c, b))))))
% 5.69/1.16 = { by lemma 32 R->L }
% 5.69/1.16 add(multiply(a, add(c, b)), multiply(c, add(multiply(a, add(c, b)), inverse(add(c, multiply(a, add(c, b)))))))
% 5.69/1.16 = { by lemma 29 R->L }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(multiply(a, add(c, b)), inverse(add(c, multiply(a, add(c, b))))))
% 5.69/1.16 = { by lemma 23 R->L }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, add(c, b))))
% 5.69/1.16 = { by lemma 16 R->L }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(add(c, multiply(a, add(c, b))), multiply(add(multiply(a, add(c, b)), add(multiply(add(c, b), Y), add(c, b))), multiply(a, add(c, b))))))
% 5.69/1.16 = { by lemma 12 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(add(c, multiply(a, add(c, b))), multiply(add(c, b), multiply(a, add(c, b))))))
% 5.69/1.16 = { by lemma 13 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(add(c, multiply(a, add(c, b))), multiply(add(c, b), a))))
% 5.69/1.16 = { by lemma 24 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(add(c, b), multiply(add(c, multiply(a, add(c, b))), a))))
% 5.69/1.16 = { by lemma 19 R->L }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(add(c, b), multiply(a, add(c, multiply(a, add(c, b)))))))
% 5.69/1.16 = { by lemma 24 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, multiply(add(c, b), add(c, multiply(a, add(c, b)))))))
% 5.69/1.16 = { by lemma 23 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, multiply(add(b, c), add(c, multiply(a, add(c, b)))))))
% 5.69/1.16 = { by lemma 23 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, multiply(add(b, c), add(c, multiply(a, add(b, c)))))))
% 5.69/1.16 = { by lemma 18 R->L }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, multiply(add(b, c), multiply(add(add(c, multiply(a, add(b, c))), Z), add(c, multiply(a, add(b, c))))))))
% 5.69/1.16 = { by lemma 12 R->L }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, multiply(add(multiply(a, add(b, c)), add(multiply(add(b, c), multiply(add(c, W), c)), add(b, c))), multiply(add(add(c, multiply(a, add(b, c))), Z), add(c, multiply(a, add(b, c))))))))
% 5.69/1.16 = { by lemma 16 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, multiply(add(multiply(a, add(b, c)), add(c, add(b, c))), multiply(add(add(c, multiply(a, add(b, c))), Z), add(c, multiply(a, add(b, c))))))))
% 5.69/1.16 = { by lemma 26 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, multiply(add(multiply(a, add(b, c)), add(c, b)), multiply(add(add(c, multiply(a, add(b, c))), Z), add(c, multiply(a, add(b, c))))))))
% 5.69/1.16 = { by lemma 27 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, multiply(add(c, add(multiply(a, add(b, c)), b)), multiply(add(add(c, multiply(a, add(b, c))), Z), add(c, multiply(a, add(b, c))))))))
% 5.69/1.16 = { by lemma 23 R->L }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, multiply(add(c, add(b, multiply(a, add(b, c)))), multiply(add(add(c, multiply(a, add(b, c))), Z), add(c, multiply(a, add(b, c))))))))
% 5.69/1.16 = { by lemma 27 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, multiply(add(b, add(c, multiply(a, add(b, c)))), multiply(add(add(c, multiply(a, add(b, c))), Z), add(c, multiply(a, add(b, c))))))))
% 5.69/1.16 = { by lemma 16 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, add(c, multiply(a, add(b, c))))))
% 5.69/1.16 = { by lemma 23 R->L }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, add(c, multiply(a, add(c, b))))))
% 5.69/1.16 = { by lemma 23 }
% 5.69/1.16 multiply(add(c, multiply(a, add(c, b))), add(multiply(a, add(c, multiply(a, add(c, b)))), inverse(add(c, multiply(a, add(c, b))))))
% 5.69/1.16 = { by lemma 15 R->L }
% 5.69/1.16 multiply(add(multiply(a, add(c, multiply(a, add(c, b)))), add(c, multiply(a, add(c, b)))), add(multiply(a, add(c, multiply(a, add(c, b)))), inverse(add(c, multiply(a, add(c, b))))))
% 5.69/1.16 = { by lemma 23 }
% 5.69/1.16 multiply(add(multiply(a, add(c, multiply(a, add(c, b)))), add(c, multiply(a, add(c, b)))), add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, add(c, multiply(a, add(c, b))))))
% 5.69/1.16 = { by lemma 19 }
% 5.69/1.16 multiply(add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, add(c, multiply(a, add(c, b))))), add(multiply(a, add(c, multiply(a, add(c, b)))), add(c, multiply(a, add(c, b)))))
% 5.69/1.16 = { by lemma 20 R->L }
% 5.69/1.16 multiply(n1, multiply(add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, add(c, multiply(a, add(c, b))))), add(multiply(a, add(c, multiply(a, add(c, b)))), add(c, multiply(a, add(c, b))))))
% 5.69/1.16 = { by axiom 1 (additive_inverse) R->L }
% 5.69/1.16 multiply(add(add(c, multiply(a, add(c, b))), inverse(add(c, multiply(a, add(c, b))))), multiply(add(inverse(add(c, multiply(a, add(c, b)))), multiply(a, add(c, multiply(a, add(c, b))))), add(multiply(a, add(c, multiply(a, add(c, b)))), add(c, multiply(a, add(c, b))))))
% 5.69/1.16 = { by axiom 11 (distributivity) R->L }
% 5.69/1.16 add(multiply(add(c, multiply(a, add(c, b))), inverse(add(c, multiply(a, add(c, b))))), add(multiply(inverse(add(c, multiply(a, add(c, b)))), multiply(a, add(c, multiply(a, add(c, b))))), multiply(multiply(a, add(c, multiply(a, add(c, b)))), add(c, multiply(a, add(c, b))))))
% 5.69/1.16 = { by axiom 2 (multiplicative_inverse) }
% 5.69/1.16 add(n0, add(multiply(inverse(add(c, multiply(a, add(c, b)))), multiply(a, add(c, multiply(a, add(c, b))))), multiply(multiply(a, add(c, multiply(a, add(c, b)))), add(c, multiply(a, add(c, b))))))
% 5.69/1.16 = { by lemma 14 }
% 5.69/1.16 add(multiply(inverse(add(c, multiply(a, add(c, b)))), multiply(a, add(c, multiply(a, add(c, b))))), multiply(multiply(a, add(c, multiply(a, add(c, b)))), add(c, multiply(a, add(c, b)))))
% 5.69/1.17 = { by lemma 23 R->L }
% 5.69/1.17 add(multiply(multiply(a, add(c, multiply(a, add(c, b)))), add(c, multiply(a, add(c, b)))), multiply(inverse(add(c, multiply(a, add(c, b)))), multiply(a, add(c, multiply(a, add(c, b))))))
% 5.69/1.17 = { by lemma 19 R->L }
% 5.69/1.17 add(multiply(multiply(a, add(c, multiply(a, add(c, b)))), add(c, multiply(a, add(c, b)))), multiply(multiply(a, add(c, multiply(a, add(c, b)))), inverse(add(c, multiply(a, add(c, b))))))
% 5.69/1.17 = { by axiom 4 (associativity_of_multiply) }
% 5.69/1.17 add(multiply(a, multiply(add(c, multiply(a, add(c, b))), add(c, multiply(a, add(c, b))))), multiply(multiply(a, add(c, multiply(a, add(c, b)))), inverse(add(c, multiply(a, add(c, b))))))
% 5.69/1.17 = { by axiom 7 (l1) R->L }
% 5.69/1.17 add(multiply(a, multiply(add(c, multiply(a, add(c, b))), add(add(c, multiply(a, add(c, b))), multiply(V, multiply(add(c, multiply(a, add(c, b))), U))))), multiply(multiply(a, add(c, multiply(a, add(c, b)))), inverse(add(c, multiply(a, add(c, b))))))
% 5.69/1.17 = { by lemma 25 }
% 5.69/1.17 add(multiply(a, add(c, multiply(a, add(c, b)))), multiply(multiply(a, add(c, multiply(a, add(c, b)))), inverse(add(c, multiply(a, add(c, b))))))
% 5.69/1.17 = { by lemma 22 }
% 5.69/1.17 multiply(a, add(c, multiply(a, add(c, b))))
% 5.69/1.17 = { by lemma 19 R->L }
% 5.69/1.17 multiply(add(c, multiply(a, add(c, b))), a)
% 5.69/1.17 = { by lemma 32 }
% 5.69/1.17 multiply(add(c, multiply(a, b)), a)
% 5.69/1.17 = { by lemma 19 R->L }
% 5.69/1.17 multiply(a, add(c, multiply(a, b)))
% 5.69/1.17 = { by lemma 19 }
% 5.69/1.17 multiply(a, add(c, multiply(b, a)))
% 5.69/1.17 = { by lemma 19 }
% 5.69/1.17 multiply(add(c, multiply(b, a)), a)
% 5.69/1.17 = { by lemma 12 R->L }
% 5.69/1.17 multiply(add(c, multiply(b, a)), add(multiply(b, a), add(multiply(a, T), a)))
% 5.69/1.17 = { by lemma 29 }
% 5.69/1.17 add(multiply(b, a), multiply(c, add(multiply(b, a), add(multiply(a, T), a))))
% 5.69/1.17 = { by lemma 12 }
% 5.69/1.17 add(multiply(b, a), multiply(c, a))
% 5.69/1.17 % SZS output end Proof
% 5.69/1.17
% 5.69/1.17 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------