%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 10:08:53 AM UTC 2026
% Result : Unsatisfiable 2.19s 0.71s
% Output : Proof 2.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 09:15:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.19/0.71 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
% 2.19/0.71
% 2.19/0.71 % SZS status Unsatisfiable
% 2.19/0.71
% 2.19/0.72 % SZS output start Proof
% 2.19/0.72 Axiom 1 (right_identity): product(X, identity, X) = true.
% 2.19/0.72 Axiom 2 (right_inverse): product(X, inverse(X), identity) = true.
% 2.19/0.72 Axiom 3 (left_identity): product(identity, X, X) = true.
% 2.19/0.72 Axiom 4 (left_inverse): product(inverse(X), X, identity) = true.
% 2.19/0.72 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.19/0.72 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 2.19/0.72 Axiom 7 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 2.19/0.72 Axiom 8 (total_function2): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 2.19/0.72 Axiom 9 (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.
% 2.19/0.73 Axiom 10 (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.
% 2.19/0.73
% 2.19/0.73 Goal 1 (prove_inverse_of_product_is_product_of_inverses): inverse(multiply(a, b)) = multiply(inverse(b), inverse(a)).
% 2.19/0.73 Proof:
% 2.19/0.73 inverse(multiply(a, b))
% 2.19/0.73 = { by axiom 8 (total_function2) R->L }
% 2.19/0.73 ifeq2(product(inverse(b), inverse(a), inverse(multiply(a, b))), true, ifeq2(product(inverse(b), inverse(a), multiply(inverse(b), inverse(a))), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b))), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 7 (total_function1) }
% 2.19/0.73 ifeq2(product(inverse(b), inverse(a), inverse(multiply(a, b))), true, ifeq2(true, true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b))), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 6 (ifeq_axiom) }
% 2.19/0.73 ifeq2(product(inverse(b), inverse(a), inverse(multiply(a, b))), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 5 (ifeq_axiom) R->L }
% 2.19/0.73 ifeq2(ifeq(true, true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 10 (associativity2) R->L }
% 2.19/0.73 ifeq2(ifeq(ifeq(product(multiply(a, b), inverse(multiply(a, b)), identity), true, ifeq(product(inverse(a), identity, inverse(a)), true, ifeq(product(inverse(a), multiply(a, b), b), true, product(b, inverse(multiply(a, b)), inverse(a)), true), true), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 1 (right_identity) }
% 2.19/0.73 ifeq2(ifeq(ifeq(product(multiply(a, b), inverse(multiply(a, b)), identity), true, ifeq(true, true, ifeq(product(inverse(a), multiply(a, b), b), true, product(b, inverse(multiply(a, b)), inverse(a)), true), true), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 5 (ifeq_axiom) }
% 2.19/0.73 ifeq2(ifeq(ifeq(product(multiply(a, b), inverse(multiply(a, b)), identity), true, ifeq(product(inverse(a), multiply(a, b), b), true, product(b, inverse(multiply(a, b)), inverse(a)), true), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 2 (right_inverse) }
% 2.19/0.73 ifeq2(ifeq(ifeq(true, true, ifeq(product(inverse(a), multiply(a, b), b), true, product(b, inverse(multiply(a, b)), inverse(a)), true), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 5 (ifeq_axiom) }
% 2.19/0.73 ifeq2(ifeq(ifeq(product(inverse(a), multiply(a, b), b), true, product(b, inverse(multiply(a, b)), inverse(a)), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 5 (ifeq_axiom) R->L }
% 2.19/0.73 ifeq2(ifeq(ifeq(ifeq(true, true, product(inverse(a), multiply(a, b), b), true), true, product(b, inverse(multiply(a, b)), inverse(a)), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 7 (total_function1) R->L }
% 2.19/0.73 ifeq2(ifeq(ifeq(ifeq(product(a, b, multiply(a, b)), true, product(inverse(a), multiply(a, b), b), true), true, product(b, inverse(multiply(a, b)), inverse(a)), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 5 (ifeq_axiom) R->L }
% 2.19/0.73 ifeq2(ifeq(ifeq(ifeq(product(a, b, multiply(a, b)), true, ifeq(true, true, product(inverse(a), multiply(a, b), b), true), true), true, product(b, inverse(multiply(a, b)), inverse(a)), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 4 (left_inverse) R->L }
% 2.19/0.73 ifeq2(ifeq(ifeq(ifeq(product(a, b, multiply(a, b)), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, b), b), true), true), true, product(b, inverse(multiply(a, b)), inverse(a)), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 5 (ifeq_axiom) R->L }
% 2.19/0.73 ifeq2(ifeq(ifeq(ifeq(true, true, ifeq(product(a, b, multiply(a, b)), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, b), b), true), true), true), true, product(b, inverse(multiply(a, b)), inverse(a)), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 3 (left_identity) R->L }
% 2.19/0.73 ifeq2(ifeq(ifeq(ifeq(product(identity, b, b), true, ifeq(product(a, b, multiply(a, b)), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, b), b), true), true), true), true, product(b, inverse(multiply(a, b)), inverse(a)), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 9 (associativity1) }
% 2.19/0.73 ifeq2(ifeq(ifeq(true, true, product(b, inverse(multiply(a, b)), inverse(a)), true), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 5 (ifeq_axiom) }
% 2.19/0.73 ifeq2(ifeq(product(b, inverse(multiply(a, b)), inverse(a)), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 5 (ifeq_axiom) R->L }
% 2.19/0.73 ifeq2(ifeq(product(b, inverse(multiply(a, b)), inverse(a)), true, ifeq(true, true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 4 (left_inverse) R->L }
% 2.19/0.73 ifeq2(ifeq(product(b, inverse(multiply(a, b)), inverse(a)), true, ifeq(product(inverse(b), b, identity), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 5 (ifeq_axiom) R->L }
% 2.19/0.73 ifeq2(ifeq(true, true, ifeq(product(b, inverse(multiply(a, b)), inverse(a)), true, ifeq(product(inverse(b), b, identity), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 3 (left_identity) R->L }
% 2.19/0.73 ifeq2(ifeq(product(identity, inverse(multiply(a, b)), inverse(multiply(a, b))), true, ifeq(product(b, inverse(multiply(a, b)), inverse(a)), true, ifeq(product(inverse(b), b, identity), true, product(inverse(b), inverse(a), inverse(multiply(a, b))), true), true), true), true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 9 (associativity1) }
% 2.19/0.73 ifeq2(true, true, multiply(inverse(b), inverse(a)), inverse(multiply(a, b)))
% 2.19/0.73 = { by axiom 6 (ifeq_axiom) }
% 2.19/0.73 multiply(inverse(b), inverse(a))
% 2.19/0.73 % SZS output end Proof
% 2.19/0.73
% 2.19/0.73 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------