TSTP Solution File: RNG004-10 by Twee---2.5.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.5.0
% Problem : RNG004-10 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% Computer : n027.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 : Mon Jun 24 14:06:05 EDT 2024
% Result : Unsatisfiable 73.80s 9.68s
% Output : Proof 74.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : RNG004-10 : TPTP v8.2.0. Released v7.5.0.
% 0.03/0.12 % Command : parallel-twee /export/starexec/sandbox2/benchmark/theBenchmark.p --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Jun 18 13:18:54 EDT 2024
% 0.12/0.33 % CPUTime :
% 73.80/9.68 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 73.80/9.68
% 73.80/9.68 % SZS status Unsatisfiable
% 73.80/9.68
% 74.57/9.78 % SZS output start Proof
% 74.57/9.78 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 74.57/9.78 Axiom 2 (additive_identity1): sum(additive_identity, X, X) = true.
% 74.57/9.78 Axiom 3 (a_times_b): product(a, b, c) = true.
% 74.57/9.78 Axiom 4 (ifeq_axiom_001): ifeq(X, X, Y, Z) = Y.
% 74.57/9.78 Axiom 5 (right_inverse): sum(X, additive_inverse(X), additive_identity) = true.
% 74.57/9.78 Axiom 6 (left_inverse): sum(additive_inverse(X), X, additive_identity) = true.
% 74.57/9.78 Axiom 7 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 74.57/9.78 Axiom 8 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 74.57/9.78 Axiom 9 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 74.57/9.78 Axiom 10 (a_inverse_times_b_inverse): product(additive_inverse(a), additive_inverse(b), d) = true.
% 74.57/9.78 Axiom 11 (commutativity_of_addition): ifeq(sum(X, Y, Z), true, sum(Y, X, Z), true) = true.
% 74.57/9.78 Axiom 12 (addition_is_well_defined): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, W), true, W, Z), Z) = Z.
% 74.57/9.78 Axiom 13 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 74.57/9.78 Axiom 14 (associativity_of_addition1): ifeq(sum(X, Y, Z), true, ifeq(sum(W, Y, V), true, ifeq(sum(U, W, X), true, sum(U, V, Z), true), true), true) = true.
% 74.57/9.78 Axiom 15 (associativity_of_addition2): ifeq(sum(X, Y, Z), true, ifeq(sum(W, Z, V), true, ifeq(sum(W, X, U), true, sum(U, Y, V), true), true), true) = true.
% 74.57/9.78 Axiom 16 (distributivity2): ifeq(product(X, Y, Z), true, ifeq(product(X, W, V), true, ifeq(sum(V, Z, U), true, ifeq(sum(W, Y, T), true, product(X, T, U), true), true), true), true) = true.
% 74.57/9.78 Axiom 17 (distributivity4): ifeq(product(X, Y, Z), true, ifeq(product(W, Y, V), true, ifeq(sum(V, Z, U), true, ifeq(sum(W, X, T), true, product(T, Y, U), true), true), true), true) = true.
% 74.57/9.78
% 74.57/9.78 Lemma 18: ifeq2(sum(X, Y, Z), true, add(X, Y), Z) = Z.
% 74.57/9.78 Proof:
% 74.57/9.78 ifeq2(sum(X, Y, Z), true, add(X, Y), Z)
% 74.57/9.78 = { by axiom 7 (ifeq_axiom) R->L }
% 74.57/9.78 ifeq2(sum(X, Y, Z), true, ifeq2(true, true, add(X, Y), Z), Z)
% 74.57/9.78 = { by axiom 8 (closure_of_addition) R->L }
% 74.57/9.78 ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, add(X, Y)), true, add(X, Y), Z), Z)
% 74.57/9.78 = { by axiom 12 (addition_is_well_defined) }
% 74.57/9.78 Z
% 74.57/9.78
% 74.57/9.78 Lemma 19: add(X, Y) = add(Y, X).
% 74.57/9.78 Proof:
% 74.57/9.78 add(X, Y)
% 74.57/9.78 = { by lemma 18 R->L }
% 74.57/9.78 ifeq2(sum(Y, X, add(X, Y)), true, add(Y, X), add(X, Y))
% 74.57/9.78 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.57/9.78 ifeq2(ifeq(true, true, sum(Y, X, add(X, Y)), true), true, add(Y, X), add(X, Y))
% 74.57/9.78 = { by axiom 8 (closure_of_addition) R->L }
% 74.57/9.78 ifeq2(ifeq(sum(X, Y, add(X, Y)), true, sum(Y, X, add(X, Y)), true), true, add(Y, X), add(X, Y))
% 74.57/9.78 = { by axiom 11 (commutativity_of_addition) }
% 74.57/9.78 ifeq2(true, true, add(Y, X), add(X, Y))
% 74.57/9.78 = { by axiom 7 (ifeq_axiom) }
% 74.57/9.78 add(Y, X)
% 74.57/9.78
% 74.57/9.78 Lemma 20: sum(X, add(Y, Z), add(Z, add(X, Y))) = true.
% 74.57/9.78 Proof:
% 74.57/9.78 sum(X, add(Y, Z), add(Z, add(X, Y)))
% 74.57/9.78 = { by lemma 19 R->L }
% 74.57/9.78 sum(X, add(Y, Z), add(add(X, Y), Z))
% 74.57/9.78 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.57/9.78 ifeq(true, true, sum(X, add(Y, Z), add(add(X, Y), Z)), true)
% 74.57/9.78 = { by axiom 8 (closure_of_addition) R->L }
% 74.57/9.78 ifeq(sum(X, Y, add(X, Y)), true, sum(X, add(Y, Z), add(add(X, Y), Z)), true)
% 74.57/9.78 = { by lemma 19 R->L }
% 74.57/9.78 ifeq(sum(X, Y, add(X, Y)), true, sum(X, add(Y, Z), add(Z, add(X, Y))), true)
% 74.57/9.78 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.57/9.78 ifeq(true, true, ifeq(sum(X, Y, add(X, Y)), true, sum(X, add(Y, Z), add(Z, add(X, Y))), true), true)
% 74.57/9.78 = { by axiom 8 (closure_of_addition) R->L }
% 74.57/9.78 ifeq(sum(Y, Z, add(Y, Z)), true, ifeq(sum(X, Y, add(X, Y)), true, sum(X, add(Y, Z), add(Z, add(X, Y))), true), true)
% 74.57/9.78 = { by lemma 19 R->L }
% 74.57/9.78 ifeq(sum(Y, Z, add(Y, Z)), true, ifeq(sum(X, Y, add(X, Y)), true, sum(X, add(Y, Z), add(add(X, Y), Z)), true), true)
% 74.57/9.78 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.57/9.78 ifeq(true, true, ifeq(sum(Y, Z, add(Y, Z)), true, ifeq(sum(X, Y, add(X, Y)), true, sum(X, add(Y, Z), add(add(X, Y), Z)), true), true), true)
% 74.57/9.78 = { by axiom 8 (closure_of_addition) R->L }
% 74.57/9.78 ifeq(sum(add(X, Y), Z, add(add(X, Y), Z)), true, ifeq(sum(Y, Z, add(Y, Z)), true, ifeq(sum(X, Y, add(X, Y)), true, sum(X, add(Y, Z), add(add(X, Y), Z)), true), true), true)
% 74.57/9.78 = { by axiom 14 (associativity_of_addition1) }
% 74.57/9.78 true
% 74.57/9.78
% 74.57/9.78 Lemma 21: add(X, add(Y, Z)) = add(Y, add(X, Z)).
% 74.57/9.78 Proof:
% 74.57/9.78 add(X, add(Y, Z))
% 74.57/9.78 = { by lemma 18 R->L }
% 74.57/9.78 ifeq2(sum(Y, add(Z, X), add(X, add(Y, Z))), true, add(Y, add(Z, X)), add(X, add(Y, Z)))
% 74.57/9.78 = { by lemma 20 }
% 74.57/9.78 ifeq2(true, true, add(Y, add(Z, X)), add(X, add(Y, Z)))
% 74.57/9.78 = { by axiom 7 (ifeq_axiom) }
% 74.57/9.78 add(Y, add(Z, X))
% 74.57/9.78 = { by lemma 19 }
% 74.57/9.78 add(Y, add(X, Z))
% 74.57/9.78
% 74.57/9.78 Lemma 22: add(add(X, Y), Z) = add(X, add(Z, Y)).
% 74.57/9.78 Proof:
% 74.57/9.78 add(add(X, Y), Z)
% 74.57/9.78 = { by lemma 19 R->L }
% 74.57/9.78 add(Z, add(X, Y))
% 74.57/9.78 = { by lemma 21 }
% 74.57/9.78 add(X, add(Z, Y))
% 74.57/9.78
% 74.57/9.78 Lemma 23: ifeq(sum(X, Y, Z), true, ifeq(sum(W, X, additive_identity), true, sum(W, Z, Y), true), true) = true.
% 74.57/9.78 Proof:
% 74.57/9.78 ifeq(sum(X, Y, Z), true, ifeq(sum(W, X, additive_identity), true, sum(W, Z, Y), true), true)
% 74.57/9.78 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.57/9.78 ifeq(true, true, ifeq(sum(X, Y, Z), true, ifeq(sum(W, X, additive_identity), true, sum(W, Z, Y), true), true), true)
% 74.57/9.78 = { by axiom 2 (additive_identity1) R->L }
% 74.57/9.78 ifeq(sum(additive_identity, Y, Y), true, ifeq(sum(X, Y, Z), true, ifeq(sum(W, X, additive_identity), true, sum(W, Z, Y), true), true), true)
% 74.57/9.78 = { by axiom 14 (associativity_of_addition1) }
% 74.57/9.78 true
% 74.57/9.78
% 74.57/9.78 Lemma 24: sum(X, add(Y, additive_inverse(X)), Y) = true.
% 74.57/9.78 Proof:
% 74.57/9.78 sum(X, add(Y, additive_inverse(X)), Y)
% 74.57/9.78 = { by lemma 19 R->L }
% 74.57/9.78 sum(X, add(additive_inverse(X), Y), Y)
% 74.57/9.78 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.57/9.78 ifeq(true, true, sum(X, add(additive_inverse(X), Y), Y), true)
% 74.57/9.78 = { by axiom 8 (closure_of_addition) R->L }
% 74.57/9.78 ifeq(sum(additive_inverse(X), Y, add(additive_inverse(X), Y)), true, sum(X, add(additive_inverse(X), Y), Y), true)
% 74.57/9.78 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.57/9.78 ifeq(sum(additive_inverse(X), Y, add(additive_inverse(X), Y)), true, ifeq(true, true, sum(X, add(additive_inverse(X), Y), Y), true), true)
% 74.57/9.78 = { by axiom 5 (right_inverse) R->L }
% 74.57/9.78 ifeq(sum(additive_inverse(X), Y, add(additive_inverse(X), Y)), true, ifeq(sum(X, additive_inverse(X), additive_identity), true, sum(X, add(additive_inverse(X), Y), Y), true), true)
% 74.57/9.78 = { by lemma 23 }
% 74.57/9.78 true
% 74.57/9.78
% 74.57/9.78 Lemma 25: ifeq2(sum(X, additive_identity, Y), true, Y, X) = X.
% 74.57/9.78 Proof:
% 74.57/9.78 ifeq2(sum(X, additive_identity, Y), true, Y, X)
% 74.57/9.78 = { by axiom 7 (ifeq_axiom) R->L }
% 74.57/9.78 ifeq2(true, true, ifeq2(sum(X, additive_identity, Y), true, Y, X), X)
% 74.57/9.78 = { by axiom 1 (additive_identity2) R->L }
% 74.57/9.78 ifeq2(sum(X, additive_identity, X), true, ifeq2(sum(X, additive_identity, Y), true, Y, X), X)
% 74.57/9.78 = { by axiom 12 (addition_is_well_defined) }
% 74.57/9.78 X
% 74.57/9.78
% 74.57/9.78 Lemma 26: ifeq2(product(X, Y, Z), true, multiply(X, Y), Z) = Z.
% 74.57/9.78 Proof:
% 74.57/9.78 ifeq2(product(X, Y, Z), true, multiply(X, Y), Z)
% 74.57/9.78 = { by axiom 7 (ifeq_axiom) R->L }
% 74.57/9.78 ifeq2(product(X, Y, Z), true, ifeq2(true, true, multiply(X, Y), Z), Z)
% 74.57/9.78 = { by axiom 9 (closure_of_multiplication) R->L }
% 74.57/9.78 ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, multiply(X, Y)), true, multiply(X, Y), Z), Z)
% 74.57/9.78 = { by axiom 13 (multiplication_is_well_defined) }
% 74.57/9.78 Z
% 74.57/9.78
% 74.57/9.78 Lemma 27: add(X, add(Y, add(Z, additive_inverse(add(X, Y))))) = Z.
% 74.57/9.78 Proof:
% 74.57/9.78 add(X, add(Y, add(Z, additive_inverse(add(X, Y)))))
% 74.57/9.78 = { by lemma 19 R->L }
% 74.57/9.78 add(X, add(Y, add(Z, additive_inverse(add(Y, X)))))
% 74.57/9.78 = { by lemma 19 R->L }
% 74.57/9.78 add(X, add(Y, add(additive_inverse(add(Y, X)), Z)))
% 74.57/9.78 = { by lemma 21 R->L }
% 74.57/9.78 add(Y, add(X, add(additive_inverse(add(Y, X)), Z)))
% 74.57/9.78 = { by lemma 21 R->L }
% 74.57/9.78 add(Y, add(additive_inverse(add(Y, X)), add(X, Z)))
% 74.57/9.78 = { by lemma 22 R->L }
% 74.57/9.78 add(Y, add(add(additive_inverse(add(Y, X)), Z), X))
% 74.57/9.78 = { by lemma 22 R->L }
% 74.57/9.78 add(add(Y, X), add(additive_inverse(add(Y, X)), Z))
% 74.57/9.78 = { by lemma 19 R->L }
% 74.57/9.78 add(add(Y, X), add(Z, additive_inverse(add(Y, X))))
% 74.57/9.78 = { by axiom 7 (ifeq_axiom) R->L }
% 74.57/9.78 ifeq2(true, true, add(add(Y, X), add(Z, additive_inverse(add(Y, X)))), Z)
% 74.57/9.78 = { by lemma 24 R->L }
% 74.57/9.78 ifeq2(sum(add(Y, X), add(Z, additive_inverse(add(Y, X))), Z), true, add(add(Y, X), add(Z, additive_inverse(add(Y, X)))), Z)
% 74.57/9.78 = { by lemma 18 }
% 74.57/9.78 Z
% 74.57/9.78
% 74.57/9.78 Lemma 28: add(X, add(Y, add(Z, additive_inverse(add(X, add(Y, Z)))))) = additive_identity.
% 74.57/9.78 Proof:
% 74.57/9.78 add(X, add(Y, add(Z, additive_inverse(add(X, add(Y, Z))))))
% 74.57/9.78 = { by lemma 21 R->L }
% 74.57/9.78 add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z))))))
% 74.57/9.78 = { by axiom 7 (ifeq_axiom) R->L }
% 74.57/9.78 ifeq2(true, true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.78 = { by axiom 15 (associativity_of_addition2) R->L }
% 74.57/9.78 ifeq2(ifeq(sum(add(X, Z), Y, add(add(X, Z), Y)), true, ifeq(sum(additive_inverse(add(add(X, Z), Y)), add(add(X, Z), Y), additive_identity), true, ifeq(sum(additive_inverse(add(add(X, Z), Y)), add(X, Z), add(Z, add(additive_inverse(add(Y, add(X, Z))), X))), true, sum(add(Z, add(additive_inverse(add(Y, add(X, Z))), X)), Y, additive_identity), true), true), true), true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.78 = { by axiom 6 (left_inverse) }
% 74.57/9.78 ifeq2(ifeq(sum(add(X, Z), Y, add(add(X, Z), Y)), true, ifeq(true, true, ifeq(sum(additive_inverse(add(add(X, Z), Y)), add(X, Z), add(Z, add(additive_inverse(add(Y, add(X, Z))), X))), true, sum(add(Z, add(additive_inverse(add(Y, add(X, Z))), X)), Y, additive_identity), true), true), true), true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.78 = { by axiom 4 (ifeq_axiom_001) }
% 74.57/9.78 ifeq2(ifeq(sum(add(X, Z), Y, add(add(X, Z), Y)), true, ifeq(sum(additive_inverse(add(add(X, Z), Y)), add(X, Z), add(Z, add(additive_inverse(add(Y, add(X, Z))), X))), true, sum(add(Z, add(additive_inverse(add(Y, add(X, Z))), X)), Y, additive_identity), true), true), true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.78 = { by axiom 8 (closure_of_addition) }
% 74.57/9.78 ifeq2(ifeq(true, true, ifeq(sum(additive_inverse(add(add(X, Z), Y)), add(X, Z), add(Z, add(additive_inverse(add(Y, add(X, Z))), X))), true, sum(add(Z, add(additive_inverse(add(Y, add(X, Z))), X)), Y, additive_identity), true), true), true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.78 = { by axiom 4 (ifeq_axiom_001) }
% 74.57/9.78 ifeq2(ifeq(sum(additive_inverse(add(add(X, Z), Y)), add(X, Z), add(Z, add(additive_inverse(add(Y, add(X, Z))), X))), true, sum(add(Z, add(additive_inverse(add(Y, add(X, Z))), X)), Y, additive_identity), true), true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.78 = { by lemma 19 }
% 74.57/9.79 ifeq2(ifeq(sum(additive_inverse(add(Y, add(X, Z))), add(X, Z), add(Z, add(additive_inverse(add(Y, add(X, Z))), X))), true, sum(add(Z, add(additive_inverse(add(Y, add(X, Z))), X)), Y, additive_identity), true), true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.79 = { by lemma 20 }
% 74.57/9.79 ifeq2(ifeq(true, true, sum(add(Z, add(additive_inverse(add(Y, add(X, Z))), X)), Y, additive_identity), true), true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.79 = { by axiom 4 (ifeq_axiom_001) }
% 74.57/9.79 ifeq2(sum(add(Z, add(additive_inverse(add(Y, add(X, Z))), X)), Y, additive_identity), true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.79 = { by lemma 19 }
% 74.57/9.79 ifeq2(sum(add(Z, add(X, additive_inverse(add(Y, add(X, Z))))), Y, additive_identity), true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.79 = { by lemma 21 }
% 74.57/9.79 ifeq2(sum(add(X, add(Z, additive_inverse(add(Y, add(X, Z))))), Y, additive_identity), true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.79 = { by lemma 21 }
% 74.57/9.79 ifeq2(sum(add(X, add(Z, additive_inverse(add(X, add(Y, Z))))), Y, additive_identity), true, add(Y, add(X, add(Z, additive_inverse(add(X, add(Y, Z)))))), additive_identity)
% 74.57/9.79 = { by lemma 19 R->L }
% 74.57/9.79 ifeq2(sum(add(X, add(Z, additive_inverse(add(X, add(Y, Z))))), Y, additive_identity), true, add(add(X, add(Z, additive_inverse(add(X, add(Y, Z))))), Y), additive_identity)
% 74.57/9.79 = { by lemma 18 }
% 74.94/9.79 additive_identity
% 74.94/9.79
% 74.94/9.79 Goal 1 (prove_c_equals_d): c = d.
% 74.94/9.79 Proof:
% 74.94/9.79 c
% 74.94/9.79 = { by lemma 25 R->L }
% 74.94/9.79 ifeq2(sum(c, additive_identity, d), true, d, c)
% 74.94/9.79 = { by lemma 28 R->L }
% 74.94/9.79 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))))))), d), true, d, c)
% 74.94/9.79 = { by lemma 26 R->L }
% 74.94/9.79 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, ifeq2(product(additive_inverse(a), Y, add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true, multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity)))))))), d), true, d, c)
% 74.94/9.79 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.94/9.79 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, ifeq2(ifeq(true, true, product(additive_inverse(a), Y, add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true), true, multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity)))))))), d), true, d, c)
% 74.94/9.79 = { by axiom 9 (closure_of_multiplication) R->L }
% 74.94/9.79 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, ifeq2(ifeq(product(additive_inverse(a), Y, multiply(additive_inverse(a), Y)), true, product(additive_inverse(a), Y, add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true), true, multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity)))))))), d), true, d, c)
% 74.94/9.79 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.94/9.79 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, ifeq2(ifeq(true, true, ifeq(product(additive_inverse(a), Y, multiply(additive_inverse(a), Y)), true, product(additive_inverse(a), Y, add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true), true), true, multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity)))))))), d), true, d, c)
% 74.94/9.79 = { by axiom 9 (closure_of_multiplication) R->L }
% 74.94/9.79 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, ifeq2(ifeq(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, ifeq(product(additive_inverse(a), Y, multiply(additive_inverse(a), Y)), true, product(additive_inverse(a), Y, add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true), true), true, multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity)))))))), d), true, d, c)
% 74.94/9.79 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.94/9.79 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, ifeq2(ifeq(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, ifeq(product(additive_inverse(a), Y, multiply(additive_inverse(a), Y)), true, ifeq(true, true, product(additive_inverse(a), Y, add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true), true), true), true, multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity)))))))), d), true, d, c)
% 74.94/9.79 = { by axiom 8 (closure_of_addition) R->L }
% 74.94/9.79 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, ifeq2(ifeq(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, ifeq(product(additive_inverse(a), Y, multiply(additive_inverse(a), Y)), true, ifeq(sum(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true, product(additive_inverse(a), Y, add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true), true), true), true, multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity)))))))), d), true, d, c)
% 74.94/9.79 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.94/9.79 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, ifeq2(ifeq(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, ifeq(product(additive_inverse(a), Y, multiply(additive_inverse(a), Y)), true, ifeq(sum(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true, ifeq(true, true, product(additive_inverse(a), Y, add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true), true), true), true), true, multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity)))))))), d), true, d, c)
% 74.94/9.79 = { by axiom 1 (additive_identity2) R->L }
% 74.94/9.79 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, ifeq2(ifeq(product(additive_inverse(a), additive_identity, multiply(additive_inverse(a), additive_identity)), true, ifeq(product(additive_inverse(a), Y, multiply(additive_inverse(a), Y)), true, ifeq(sum(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true, ifeq(sum(Y, additive_identity, Y), true, product(additive_inverse(a), Y, add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity))), true), true), true), true), true, multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity)))))))), d), true, d, c)
% 74.94/9.79 = { by axiom 16 (distributivity2) }
% 74.94/9.79 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, ifeq2(true, true, multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), Y), multiply(additive_inverse(a), additive_identity)))))))), d), true, d, c)
% 74.94/9.80 = { by axiom 7 (ifeq_axiom) }
% 74.94/9.80 ifeq2(sum(c, add(X, add(multiply(additive_inverse(a), Y), add(multiply(additive_inverse(a), additive_identity), additive_inverse(add(X, multiply(additive_inverse(a), Y)))))), d), true, d, c)
% 74.94/9.80 = { by lemma 27 }
% 74.94/9.80 ifeq2(sum(c, multiply(additive_inverse(a), additive_identity), d), true, d, c)
% 74.94/9.80 = { by axiom 7 (ifeq_axiom) R->L }
% 74.94/9.80 ifeq2(sum(c, ifeq2(true, true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 16 (distributivity2) R->L }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(product(additive_inverse(a), additive_inverse(b), d), true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, ifeq(sum(b, additive_inverse(b), additive_identity), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 5 (right_inverse) }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(product(additive_inverse(a), additive_inverse(b), d), true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, ifeq(true, true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 4 (ifeq_axiom_001) }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(product(additive_inverse(a), additive_inverse(b), d), true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 10 (a_inverse_times_b_inverse) }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(true, true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 4 (ifeq_axiom_001) }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 9 (closure_of_multiplication) }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(true, true, ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 4 (ifeq_axiom_001) }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(multiply(additive_inverse(a), b), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by lemma 25 R->L }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(sum(multiply(additive_inverse(a), b), additive_identity, add(multiply(additive_inverse(a), b), additive_identity)), true, add(multiply(additive_inverse(a), b), additive_identity), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 8 (closure_of_addition) }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(true, true, add(multiply(additive_inverse(a), b), additive_identity), multiply(additive_inverse(a), b)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 7 (ifeq_axiom) }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_identity), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 7 (ifeq_axiom) R->L }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), ifeq2(true, true, additive_identity, additive_inverse(additive_identity))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 6 (left_inverse) R->L }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), ifeq2(sum(additive_inverse(additive_identity), additive_identity, additive_identity), true, additive_identity, additive_inverse(additive_identity))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by lemma 25 }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(additive_identity)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by lemma 28 R->L }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, add(multiply(W, b), multiply(additive_identity, b))))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by lemma 26 R->L }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, ifeq2(product(W, b, add(multiply(W, b), multiply(additive_identity, b))), true, multiply(W, b), add(multiply(W, b), multiply(additive_identity, b)))))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, ifeq2(ifeq(true, true, product(W, b, add(multiply(W, b), multiply(additive_identity, b))), true), true, multiply(W, b), add(multiply(W, b), multiply(additive_identity, b)))))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 9 (closure_of_multiplication) R->L }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, ifeq2(ifeq(product(W, b, multiply(W, b)), true, product(W, b, add(multiply(W, b), multiply(additive_identity, b))), true), true, multiply(W, b), add(multiply(W, b), multiply(additive_identity, b)))))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, ifeq2(ifeq(true, true, ifeq(product(W, b, multiply(W, b)), true, product(W, b, add(multiply(W, b), multiply(additive_identity, b))), true), true), true, multiply(W, b), add(multiply(W, b), multiply(additive_identity, b)))))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 9 (closure_of_multiplication) R->L }
% 74.94/9.80 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, ifeq(product(W, b, multiply(W, b)), true, product(W, b, add(multiply(W, b), multiply(additive_identity, b))), true), true), true, multiply(W, b), add(multiply(W, b), multiply(additive_identity, b)))))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.80 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, ifeq(product(W, b, multiply(W, b)), true, ifeq(true, true, product(W, b, add(multiply(W, b), multiply(additive_identity, b))), true), true), true), true, multiply(W, b), add(multiply(W, b), multiply(additive_identity, b)))))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 8 (closure_of_addition) R->L }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, ifeq(product(W, b, multiply(W, b)), true, ifeq(sum(multiply(W, b), multiply(additive_identity, b), add(multiply(W, b), multiply(additive_identity, b))), true, product(W, b, add(multiply(W, b), multiply(additive_identity, b))), true), true), true), true, multiply(W, b), add(multiply(W, b), multiply(additive_identity, b)))))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, ifeq(product(W, b, multiply(W, b)), true, ifeq(sum(multiply(W, b), multiply(additive_identity, b), add(multiply(W, b), multiply(additive_identity, b))), true, ifeq(true, true, product(W, b, add(multiply(W, b), multiply(additive_identity, b))), true), true), true), true), true, multiply(W, b), add(multiply(W, b), multiply(additive_identity, b)))))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 1 (additive_identity2) R->L }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, ifeq2(ifeq(product(additive_identity, b, multiply(additive_identity, b)), true, ifeq(product(W, b, multiply(W, b)), true, ifeq(sum(multiply(W, b), multiply(additive_identity, b), add(multiply(W, b), multiply(additive_identity, b))), true, ifeq(sum(W, additive_identity, W), true, product(W, b, add(multiply(W, b), multiply(additive_identity, b))), true), true), true), true), true, multiply(W, b), add(multiply(W, b), multiply(additive_identity, b)))))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 17 (distributivity4) }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, ifeq2(true, true, multiply(W, b), add(multiply(W, b), multiply(additive_identity, b)))))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 7 (ifeq_axiom) }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(Z, add(multiply(W, b), add(multiply(additive_identity, b), additive_inverse(add(Z, multiply(W, b)))))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by lemma 27 }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(multiply(additive_identity, b))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 7 (ifeq_axiom) R->L }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(ifeq2(true, true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 17 (distributivity4) R->L }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(ifeq2(ifeq(product(a, b, c), true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), c, add(multiply(additive_inverse(a), b), c)), true, ifeq(sum(additive_inverse(a), a, additive_identity), true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 3 (a_times_b) }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(ifeq2(ifeq(true, true, ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), c, add(multiply(additive_inverse(a), b), c)), true, ifeq(sum(additive_inverse(a), a, additive_identity), true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 4 (ifeq_axiom_001) }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), c, add(multiply(additive_inverse(a), b), c)), true, ifeq(sum(additive_inverse(a), a, additive_identity), true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 6 (left_inverse) }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), c, add(multiply(additive_inverse(a), b), c)), true, ifeq(true, true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 4 (ifeq_axiom_001) }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(sum(multiply(additive_inverse(a), b), c, add(multiply(additive_inverse(a), b), c)), true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 8 (closure_of_addition) }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, ifeq(true, true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 4 (ifeq_axiom_001) }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(ifeq2(ifeq(product(additive_inverse(a), b, multiply(additive_inverse(a), b)), true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 9 (closure_of_multiplication) }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(ifeq2(ifeq(true, true, product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by axiom 4 (ifeq_axiom_001) }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(ifeq2(product(additive_identity, b, add(multiply(additive_inverse(a), b), c)), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by lemma 19 }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(ifeq2(product(additive_identity, b, add(c, multiply(additive_inverse(a), b))), true, multiply(additive_identity, b), add(c, multiply(additive_inverse(a), b))))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.81 = { by lemma 26 }
% 74.94/9.81 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b)))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.82 = { by lemma 19 R->L }
% 74.94/9.82 ifeq2(sum(c, ifeq2(ifeq(sum(add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.82 = { by axiom 7 (ifeq_axiom) R->L }
% 74.94/9.82 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(true, true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.82 = { by axiom 15 (associativity_of_addition2) R->L }
% 74.94/9.82 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(ifeq(sum(add(c, multiply(additive_inverse(a), b)), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_identity), true, ifeq(sum(additive_inverse(c), additive_identity, additive_inverse(c)), true, ifeq(sum(additive_inverse(c), add(c, multiply(additive_inverse(a), b)), multiply(additive_inverse(a), b)), true, sum(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_inverse(c)), true), true), true), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.82 = { by axiom 1 (additive_identity2) }
% 74.94/9.82 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(ifeq(sum(add(c, multiply(additive_inverse(a), b)), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_identity), true, ifeq(true, true, ifeq(sum(additive_inverse(c), add(c, multiply(additive_inverse(a), b)), multiply(additive_inverse(a), b)), true, sum(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_inverse(c)), true), true), true), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.82 = { by axiom 4 (ifeq_axiom_001) }
% 74.94/9.82 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(ifeq(sum(add(c, multiply(additive_inverse(a), b)), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_identity), true, ifeq(sum(additive_inverse(c), add(c, multiply(additive_inverse(a), b)), multiply(additive_inverse(a), b)), true, sum(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_inverse(c)), true), true), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.82 = { by axiom 5 (right_inverse) }
% 74.94/9.82 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(ifeq(true, true, ifeq(sum(additive_inverse(c), add(c, multiply(additive_inverse(a), b)), multiply(additive_inverse(a), b)), true, sum(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_inverse(c)), true), true), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.82 = { by axiom 4 (ifeq_axiom_001) }
% 74.94/9.82 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(ifeq(sum(additive_inverse(c), add(c, multiply(additive_inverse(a), b)), multiply(additive_inverse(a), b)), true, sum(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_inverse(c)), true), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.82 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.94/9.82 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(ifeq(ifeq(true, true, sum(additive_inverse(c), add(c, multiply(additive_inverse(a), b)), multiply(additive_inverse(a), b)), true), true, sum(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_inverse(c)), true), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.82 = { by axiom 8 (closure_of_addition) R->L }
% 74.94/9.82 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(ifeq(ifeq(sum(c, multiply(additive_inverse(a), b), add(c, multiply(additive_inverse(a), b))), true, sum(additive_inverse(c), add(c, multiply(additive_inverse(a), b)), multiply(additive_inverse(a), b)), true), true, sum(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_inverse(c)), true), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.82 = { by axiom 4 (ifeq_axiom_001) R->L }
% 74.94/9.83 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(ifeq(ifeq(sum(c, multiply(additive_inverse(a), b), add(c, multiply(additive_inverse(a), b))), true, ifeq(true, true, sum(additive_inverse(c), add(c, multiply(additive_inverse(a), b)), multiply(additive_inverse(a), b)), true), true), true, sum(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_inverse(c)), true), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.83 = { by axiom 6 (left_inverse) R->L }
% 74.94/9.83 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(ifeq(ifeq(sum(c, multiply(additive_inverse(a), b), add(c, multiply(additive_inverse(a), b))), true, ifeq(sum(additive_inverse(c), c, additive_identity), true, sum(additive_inverse(c), add(c, multiply(additive_inverse(a), b)), multiply(additive_inverse(a), b)), true), true), true, sum(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_inverse(c)), true), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.83 = { by lemma 23 }
% 74.94/9.83 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(ifeq(true, true, sum(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_inverse(c)), true), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.83 = { by axiom 4 (ifeq_axiom_001) }
% 74.94/9.83 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(sum(multiply(additive_inverse(a), b), additive_inverse(add(c, multiply(additive_inverse(a), b))), additive_inverse(c)), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.83 = { by lemma 19 }
% 74.94/9.83 ifeq2(sum(c, ifeq2(ifeq(sum(ifeq2(sum(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c)), additive_inverse(c)), true, add(multiply(additive_inverse(a), b), additive_inverse(add(multiply(additive_inverse(a), b), c))), additive_inverse(c)), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.83 = { by lemma 18 }
% 74.94/9.83 ifeq2(sum(c, ifeq2(ifeq(sum(additive_inverse(c), d, add(additive_inverse(c), d)), true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.83 = { by axiom 8 (closure_of_addition) }
% 74.94/9.83 ifeq2(sum(c, ifeq2(ifeq(true, true, product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.83 = { by axiom 4 (ifeq_axiom_001) }
% 74.94/9.83 ifeq2(sum(c, ifeq2(product(additive_inverse(a), additive_identity, add(additive_inverse(c), d)), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.83 = { by lemma 19 }
% 74.94/9.83 ifeq2(sum(c, ifeq2(product(additive_inverse(a), additive_identity, add(d, additive_inverse(c))), true, multiply(additive_inverse(a), additive_identity), add(d, additive_inverse(c))), d), true, d, c)
% 74.94/9.83 = { by lemma 26 }
% 74.94/9.83 ifeq2(sum(c, add(d, additive_inverse(c)), d), true, d, c)
% 74.94/9.83 = { by lemma 24 }
% 74.94/9.83 ifeq2(true, true, d, c)
% 74.94/9.83 = { by axiom 7 (ifeq_axiom) }
% 74.94/9.83 d
% 74.94/9.83 % SZS output end Proof
% 74.94/9.83
% 74.94/9.83 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------