%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:09:09 AM UTC 2026
% Result : Unsatisfiable 111.08s 14.40s
% Output : Proof 111.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 09:19:55 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 111.08/14.40 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 111.08/14.40
% 111.08/14.40 % SZS status Unsatisfiable
% 111.08/14.40
% 111.08/14.45 % SZS output start Proof
% 111.08/14.45 Axiom 1 (a_equals_b): equalish(a, b) = true.
% 111.08/14.45 Axiom 2 (left_identity): product(identity, X, X) = true.
% 111.08/14.45 Axiom 3 (left_inverse): product(inverse(X), X, identity) = true.
% 111.08/14.45 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 111.08/14.45 Axiom 5 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 111.08/14.45 Axiom 6 (product_substitution3): ifeq(equalish(X, Y), true, ifeq(product(Z, W, X), true, product(Z, W, Y), true), true) = true.
% 111.08/14.45 Axiom 7 (total_function2): ifeq(product(X, Y, Z), true, ifeq(product(X, Y, W), true, equalish(W, Z), true), true) = true.
% 111.08/14.45 Axiom 8 (associativity1): ifeq(product(X, Y, Z), true, ifeq(product(W, Y, V), true, ifeq(product(U, W, X), true, product(U, V, Z), true), true), true) = true.
% 111.08/14.46 Axiom 9 (associativity2): ifeq(product(X, Y, Z), true, ifeq(product(W, Z, V), true, ifeq(product(W, X, U), true, product(U, Y, V), true), true), true) = true.
% 111.08/14.46
% 111.08/14.46 Goal 1 (prove_inverse_substitution): equalish(inverse(a), inverse(b)) = true.
% 111.08/14.46 Proof:
% 111.08/14.46 equalish(inverse(a), inverse(b))
% 111.08/14.46 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.46 ifeq(true, true, equalish(inverse(a), inverse(b)), true)
% 111.08/14.46 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.46 ifeq(true, true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 8 (associativity1) R->L }
% 111.08/14.46 ifeq(ifeq(product(identity, inverse(b), inverse(b)), true, ifeq(product(inverse(inverse(b)), inverse(b), identity), true, ifeq(product(inverse(b), inverse(inverse(b)), identity), true, product(inverse(b), identity, inverse(b)), true), true), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 2 (left_identity) }
% 111.08/14.46 ifeq(ifeq(true, true, ifeq(product(inverse(inverse(b)), inverse(b), identity), true, ifeq(product(inverse(b), inverse(inverse(b)), identity), true, product(inverse(b), identity, inverse(b)), true), true), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.46 ifeq(ifeq(product(inverse(inverse(b)), inverse(b), identity), true, ifeq(product(inverse(b), inverse(inverse(b)), identity), true, product(inverse(b), identity, inverse(b)), true), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 3 (left_inverse) }
% 111.08/14.46 ifeq(ifeq(true, true, ifeq(product(inverse(b), inverse(inverse(b)), identity), true, product(inverse(b), identity, inverse(b)), true), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.46 ifeq(ifeq(product(inverse(b), inverse(inverse(b)), identity), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.46 ifeq(ifeq(ifeq(true, true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 7 (total_function2) R->L }
% 111.08/14.46 ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(inverse(b))), inverse(inverse(b)), identity), true, ifeq(product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 3 (left_inverse) }
% 111.08/14.46 ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.46 ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.46 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 8 (associativity1) R->L }
% 111.08/14.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(product(identity, inverse(inverse(b)), inverse(inverse(b))), true, ifeq(product(inverse(b), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true, ifeq(product(inverse(inverse(b)), inverse(b), identity), true, product(inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b))), inverse(inverse(b))), true), true), true), true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.46 = { by axiom 2 (left_identity) }
% 111.08/14.46 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(b), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true, ifeq(product(inverse(inverse(b)), inverse(b), identity), true, product(inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b))), inverse(inverse(b))), true), true), true), true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(b), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true, ifeq(product(inverse(inverse(b)), inverse(b), identity), true, product(inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b))), inverse(inverse(b))), true), true), true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 3 (left_inverse) }
% 111.08/14.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(b), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true, ifeq(true, true, product(inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b))), inverse(inverse(b))), true), true), true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(b), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true, product(inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b))), inverse(inverse(b))), true), true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 5 (total_function1) }
% 111.08/14.47 ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b))), inverse(inverse(b))), true), true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.47 ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b))), inverse(inverse(b))), true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.47 ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b))), inverse(inverse(b))), true, ifeq(true, true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 3 (left_inverse) R->L }
% 111.08/14.47 ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b))), inverse(inverse(b))), true, ifeq(product(inverse(inverse(inverse(b))), inverse(inverse(b)), identity), true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.47 ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b))), inverse(inverse(b))), true, ifeq(product(inverse(inverse(inverse(b))), inverse(inverse(b)), identity), true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 2 (left_identity) R->L }
% 111.08/14.47 ifeq(ifeq(ifeq(ifeq(ifeq(product(identity, multiply(inverse(b), inverse(inverse(b))), multiply(inverse(b), inverse(inverse(b)))), true, ifeq(product(inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b))), inverse(inverse(b))), true, ifeq(product(inverse(inverse(inverse(b))), inverse(inverse(b)), identity), true, product(inverse(inverse(inverse(b))), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true), true), true), true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 8 (associativity1) }
% 111.08/14.47 ifeq(ifeq(ifeq(ifeq(true, true, equalish(multiply(inverse(b), inverse(inverse(b))), identity), true), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.47 ifeq(ifeq(ifeq(equalish(multiply(inverse(b), inverse(inverse(b))), identity), true, product(inverse(b), inverse(inverse(b)), identity), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.47 ifeq(ifeq(ifeq(equalish(multiply(inverse(b), inverse(inverse(b))), identity), true, ifeq(true, true, product(inverse(b), inverse(inverse(b)), identity), true), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 5 (total_function1) R->L }
% 111.08/14.47 ifeq(ifeq(ifeq(equalish(multiply(inverse(b), inverse(inverse(b))), identity), true, ifeq(product(inverse(b), inverse(inverse(b)), multiply(inverse(b), inverse(inverse(b)))), true, product(inverse(b), inverse(inverse(b)), identity), true), true), true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 6 (product_substitution3) }
% 111.08/14.47 ifeq(ifeq(true, true, product(inverse(b), identity, inverse(b)), true), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.47 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(true, true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 8 (associativity1) R->L }
% 111.08/14.47 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, ifeq(product(inverse(b), inverse(inverse(a)), multiply(inverse(b), inverse(inverse(a)))), true, product(inverse(b), identity, inverse(a)), true), true), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 3 (left_inverse) }
% 111.08/14.47 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true, ifeq(true, true, ifeq(product(inverse(b), inverse(inverse(a)), multiply(inverse(b), inverse(inverse(a)))), true, product(inverse(b), identity, inverse(a)), true), true), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.47 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true, ifeq(product(inverse(b), inverse(inverse(a)), multiply(inverse(b), inverse(inverse(a)))), true, product(inverse(b), identity, inverse(a)), true), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 5 (total_function1) }
% 111.08/14.47 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true, ifeq(true, true, product(inverse(b), identity, inverse(a)), true), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.47 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.47 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(true, true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.47 = { by axiom 9 (associativity2) R->L }
% 111.08/14.47 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(a)), identity, b), true, ifeq(product(inverse(b), b, identity), true, ifeq(product(inverse(b), inverse(inverse(a)), multiply(inverse(b), inverse(inverse(a)))), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 3 (left_inverse) }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(a)), identity, b), true, ifeq(true, true, ifeq(product(inverse(b), inverse(inverse(a)), multiply(inverse(b), inverse(inverse(a)))), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(a)), identity, b), true, ifeq(product(inverse(b), inverse(inverse(a)), multiply(inverse(b), inverse(inverse(a)))), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 5 (total_function1) }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(a)), identity, b), true, ifeq(true, true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(a)), identity, b), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(inverse(a)), identity, b), true), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 8 (associativity1) R->L }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(product(identity, a, a), true, ifeq(product(inverse(a), a, identity), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), identity, a), true), true), true), true, product(inverse(inverse(a)), identity, b), true), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 2 (left_identity) }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(a), a, identity), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), identity, a), true), true), true), true, product(inverse(inverse(a)), identity, b), true), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(a), a, identity), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), identity, a), true), true), true, product(inverse(inverse(a)), identity, b), true), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 3 (left_inverse) }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), identity, a), true), true), true, product(inverse(inverse(a)), identity, b), true), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), identity, a), true), true, product(inverse(inverse(a)), identity, b), true), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 3 (left_inverse) }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(inverse(a)), identity, a), true), true, product(inverse(inverse(a)), identity, b), true), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(ifeq(product(inverse(inverse(a)), identity, a), true, product(inverse(inverse(a)), identity, b), true), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(inverse(a)), identity, a), true, product(inverse(inverse(a)), identity, b), true), true), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 1 (a_equals_b) R->L }
% 111.08/14.48 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(ifeq(equalish(a, b), true, ifeq(product(inverse(inverse(a)), identity, a), true, product(inverse(inverse(a)), identity, b), true), true), true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.48 = { by axiom 6 (product_substitution3) }
% 111.08/14.49 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(ifeq(true, true, product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.49 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.49 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.49 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.49 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(true, true, ifeq(product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.49 = { by axiom 2 (left_identity) R->L }
% 111.08/14.49 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(product(identity, inverse(a), inverse(a)), true, ifeq(product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.49 = { by axiom 4 (ifeq_axiom) R->L }
% 111.08/14.49 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(true, true, ifeq(product(identity, inverse(a), inverse(a)), true, ifeq(product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.49 = { by axiom 2 (left_identity) R->L }
% 111.08/14.49 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(ifeq(product(identity, inverse(a), inverse(a)), true, ifeq(product(identity, inverse(a), inverse(a)), true, ifeq(product(multiply(inverse(b), inverse(inverse(a))), identity, identity), true, product(multiply(inverse(b), inverse(inverse(a))), inverse(a), inverse(a)), true), true), true), true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.49 = { by axiom 8 (associativity1) }
% 111.08/14.49 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(ifeq(true, true, product(inverse(b), identity, inverse(a)), true), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.49 = { by axiom 4 (ifeq_axiom) }
% 111.08/14.49 ifeq(product(inverse(b), identity, inverse(b)), true, ifeq(product(inverse(b), identity, inverse(a)), true, equalish(inverse(a), inverse(b)), true), true)
% 111.08/14.49 = { by axiom 7 (total_function2) }
% 111.08/14.49 true
% 111.08/14.49 % SZS output end Proof
% 111.08/14.49
% 111.08/14.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------