%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP012-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 10:08:52 AM UTC 2026
% Result : Unsatisfiable 0.77s 0.64s
% Output : Proof 1.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:18:31 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.77/0.64 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
% 0.77/0.64
% 0.77/0.64 % SZS status Unsatisfiable
% 0.77/0.64
% 1.97/0.67 % SZS output start Proof
% 1.97/0.67 Axiom 1 (right_identity): product(X, identity, X) = true.
% 1.97/0.67 Axiom 2 (right_inverse): product(X, inverse(X), identity) = true.
% 1.97/0.67 Axiom 3 (left_identity): product(identity, X, X) = true.
% 1.97/0.67 Axiom 4 (a_multiply_b_is_c): product(a, b, c) = true.
% 1.97/0.67 Axiom 5 (left_inverse): product(inverse(X), X, identity) = true.
% 1.97/0.67 Axiom 6 (inverse_b_multiply_inverse_a_is_d): product(inverse(b), inverse(a), d) = true.
% 1.97/0.67 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.97/0.67 Axiom 8 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 1.97/0.67 Axiom 9 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 1.97/0.67 Axiom 10 (total_function2): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 1.97/0.67 Axiom 11 (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.
% 1.97/0.67 Axiom 12 (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.
% 1.97/0.67
% 1.97/0.67 Lemma 13: ifeq2(product(X, Y, Z), true, multiply(X, Y), Z) = Z.
% 1.97/0.67 Proof:
% 1.97/0.67 ifeq2(product(X, Y, Z), true, multiply(X, Y), Z)
% 1.97/0.67 = { by axiom 8 (ifeq_axiom) R->L }
% 1.97/0.67 ifeq2(product(X, Y, Z), true, ifeq2(true, true, multiply(X, Y), Z), Z)
% 1.97/0.67 = { by axiom 9 (total_function1) R->L }
% 1.97/0.67 ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, multiply(X, Y)), true, multiply(X, Y), Z), Z)
% 1.97/0.67 = { by axiom 10 (total_function2) }
% 1.97/0.67 Z
% 1.97/0.67
% 1.97/0.67 Goal 1 (prove_c_multiply_d_is_identity): product(c, d, identity) = true.
% 1.97/0.67 Proof:
% 1.97/0.67 product(c, d, identity)
% 1.97/0.67 = { by axiom 7 (ifeq_axiom) R->L }
% 1.97/0.67 ifeq(true, true, product(c, d, identity), true)
% 1.97/0.67 = { by axiom 3 (left_identity) R->L }
% 1.97/0.67 ifeq(product(identity, c, c), true, product(c, d, identity), true)
% 1.97/0.67 = { by axiom 8 (ifeq_axiom) R->L }
% 1.97/0.67 ifeq(product(identity, ifeq2(true, true, c, multiply(a, b)), c), true, product(c, d, identity), true)
% 1.97/0.67 = { by axiom 9 (total_function1) R->L }
% 1.97/0.67 ifeq(product(identity, ifeq2(product(a, b, multiply(a, b)), true, c, multiply(a, b)), c), true, product(c, d, identity), true)
% 1.97/0.67 = { by axiom 8 (ifeq_axiom) R->L }
% 1.97/0.67 ifeq(product(identity, ifeq2(product(a, b, multiply(a, b)), true, ifeq2(true, true, c, multiply(a, b)), multiply(a, b)), c), true, product(c, d, identity), true)
% 1.97/0.67 = { by axiom 4 (a_multiply_b_is_c) R->L }
% 1.97/0.67 ifeq(product(identity, ifeq2(product(a, b, multiply(a, b)), true, ifeq2(product(a, b, c), true, c, multiply(a, b)), multiply(a, b)), c), true, product(c, d, identity), true)
% 1.97/0.67 = { by axiom 10 (total_function2) }
% 1.97/0.67 ifeq(product(identity, multiply(a, b), c), true, product(c, d, identity), true)
% 1.97/0.67 = { by lemma 13 R->L }
% 1.97/0.67 ifeq(product(identity, multiply(a, ifeq2(product(multiply(b, d), inverse(d), b), true, multiply(multiply(b, d), inverse(d)), b)), c), true, product(c, d, identity), true)
% 1.97/0.67 = { by axiom 7 (ifeq_axiom) R->L }
% 1.97/0.67 ifeq(product(identity, multiply(a, ifeq2(ifeq(true, true, product(multiply(b, d), inverse(d), b), true), true, multiply(multiply(b, d), inverse(d)), b)), c), true, product(c, d, identity), true)
% 1.97/0.67 = { by axiom 9 (total_function1) R->L }
% 1.97/0.67 ifeq(product(identity, multiply(a, ifeq2(ifeq(product(b, d, multiply(b, d)), true, product(multiply(b, d), inverse(d), b), true), true, multiply(multiply(b, d), inverse(d)), b)), c), true, product(c, d, identity), true)
% 1.97/0.67 = { by axiom 7 (ifeq_axiom) R->L }
% 1.97/0.67 ifeq(product(identity, multiply(a, ifeq2(ifeq(true, true, ifeq(product(b, d, multiply(b, d)), true, product(multiply(b, d), inverse(d), b), true), true), true, multiply(multiply(b, d), inverse(d)), b)), c), true, product(c, d, identity), true)
% 1.97/0.67 = { by axiom 2 (right_inverse) R->L }
% 1.97/0.67 ifeq(product(identity, multiply(a, ifeq2(ifeq(product(d, inverse(d), identity), true, ifeq(product(b, d, multiply(b, d)), true, product(multiply(b, d), inverse(d), b), true), true), true, multiply(multiply(b, d), inverse(d)), b)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 7 (ifeq_axiom) R->L }
% 1.97/0.68 ifeq(product(identity, multiply(a, ifeq2(ifeq(product(d, inverse(d), identity), true, ifeq(true, true, ifeq(product(b, d, multiply(b, d)), true, product(multiply(b, d), inverse(d), b), true), true), true), true, multiply(multiply(b, d), inverse(d)), b)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 1 (right_identity) R->L }
% 1.97/0.68 ifeq(product(identity, multiply(a, ifeq2(ifeq(product(d, inverse(d), identity), true, ifeq(product(b, identity, b), true, ifeq(product(b, d, multiply(b, d)), true, product(multiply(b, d), inverse(d), b), true), true), true), true, multiply(multiply(b, d), inverse(d)), b)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 12 (associativity2) }
% 1.97/0.68 ifeq(product(identity, multiply(a, ifeq2(true, true, multiply(multiply(b, d), inverse(d)), b)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 8 (ifeq_axiom) }
% 1.97/0.68 ifeq(product(identity, multiply(a, multiply(multiply(b, d), inverse(d))), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 8 (ifeq_axiom) R->L }
% 1.97/0.68 ifeq(product(identity, multiply(a, multiply(ifeq2(true, true, multiply(b, d), inverse(a)), inverse(d))), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 11 (associativity1) R->L }
% 1.97/0.68 ifeq(product(identity, multiply(a, multiply(ifeq2(ifeq(product(identity, inverse(a), inverse(a)), true, ifeq(product(inverse(b), inverse(a), d), true, ifeq(product(b, inverse(b), identity), true, product(b, d, inverse(a)), true), true), true), true, multiply(b, d), inverse(a)), inverse(d))), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 3 (left_identity) }
% 1.97/0.68 ifeq(product(identity, multiply(a, multiply(ifeq2(ifeq(true, true, ifeq(product(inverse(b), inverse(a), d), true, ifeq(product(b, inverse(b), identity), true, product(b, d, inverse(a)), true), true), true), true, multiply(b, d), inverse(a)), inverse(d))), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 7 (ifeq_axiom) }
% 1.97/0.68 ifeq(product(identity, multiply(a, multiply(ifeq2(ifeq(product(inverse(b), inverse(a), d), true, ifeq(product(b, inverse(b), identity), true, product(b, d, inverse(a)), true), true), true, multiply(b, d), inverse(a)), inverse(d))), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 2 (right_inverse) }
% 1.97/0.68 ifeq(product(identity, multiply(a, multiply(ifeq2(ifeq(product(inverse(b), inverse(a), d), true, ifeq(true, true, product(b, d, inverse(a)), true), true), true, multiply(b, d), inverse(a)), inverse(d))), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 7 (ifeq_axiom) }
% 1.97/0.68 ifeq(product(identity, multiply(a, multiply(ifeq2(ifeq(product(inverse(b), inverse(a), d), true, product(b, d, inverse(a)), true), true, multiply(b, d), inverse(a)), inverse(d))), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 6 (inverse_b_multiply_inverse_a_is_d) }
% 1.97/0.68 ifeq(product(identity, multiply(a, multiply(ifeq2(ifeq(true, true, product(b, d, inverse(a)), true), true, multiply(b, d), inverse(a)), inverse(d))), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 7 (ifeq_axiom) }
% 1.97/0.68 ifeq(product(identity, multiply(a, multiply(ifeq2(product(b, d, inverse(a)), true, multiply(b, d), inverse(a)), inverse(d))), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by lemma 13 }
% 1.97/0.68 ifeq(product(identity, multiply(a, multiply(inverse(a), inverse(d))), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 8 (ifeq_axiom) R->L }
% 1.97/0.68 ifeq(product(identity, ifeq2(true, true, multiply(a, multiply(inverse(a), inverse(d))), inverse(d)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 11 (associativity1) R->L }
% 1.97/0.68 ifeq(product(identity, ifeq2(ifeq(product(identity, inverse(d), inverse(d)), true, ifeq(product(inverse(a), inverse(d), multiply(inverse(a), inverse(d))), true, ifeq(product(a, inverse(a), identity), true, product(a, multiply(inverse(a), inverse(d)), inverse(d)), true), true), true), true, multiply(a, multiply(inverse(a), inverse(d))), inverse(d)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 3 (left_identity) }
% 1.97/0.68 ifeq(product(identity, ifeq2(ifeq(true, true, ifeq(product(inverse(a), inverse(d), multiply(inverse(a), inverse(d))), true, ifeq(product(a, inverse(a), identity), true, product(a, multiply(inverse(a), inverse(d)), inverse(d)), true), true), true), true, multiply(a, multiply(inverse(a), inverse(d))), inverse(d)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 7 (ifeq_axiom) }
% 1.97/0.68 ifeq(product(identity, ifeq2(ifeq(product(inverse(a), inverse(d), multiply(inverse(a), inverse(d))), true, ifeq(product(a, inverse(a), identity), true, product(a, multiply(inverse(a), inverse(d)), inverse(d)), true), true), true, multiply(a, multiply(inverse(a), inverse(d))), inverse(d)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 2 (right_inverse) }
% 1.97/0.68 ifeq(product(identity, ifeq2(ifeq(product(inverse(a), inverse(d), multiply(inverse(a), inverse(d))), true, ifeq(true, true, product(a, multiply(inverse(a), inverse(d)), inverse(d)), true), true), true, multiply(a, multiply(inverse(a), inverse(d))), inverse(d)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 7 (ifeq_axiom) }
% 1.97/0.68 ifeq(product(identity, ifeq2(ifeq(product(inverse(a), inverse(d), multiply(inverse(a), inverse(d))), true, product(a, multiply(inverse(a), inverse(d)), inverse(d)), true), true, multiply(a, multiply(inverse(a), inverse(d))), inverse(d)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 9 (total_function1) }
% 1.97/0.68 ifeq(product(identity, ifeq2(ifeq(true, true, product(a, multiply(inverse(a), inverse(d)), inverse(d)), true), true, multiply(a, multiply(inverse(a), inverse(d))), inverse(d)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 7 (ifeq_axiom) }
% 1.97/0.68 ifeq(product(identity, ifeq2(product(a, multiply(inverse(a), inverse(d)), inverse(d)), true, multiply(a, multiply(inverse(a), inverse(d))), inverse(d)), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by lemma 13 }
% 1.97/0.68 ifeq(product(identity, inverse(d), c), true, product(c, d, identity), true)
% 1.97/0.68 = { by axiom 7 (ifeq_axiom) R->L }
% 1.97/0.68 ifeq(true, true, ifeq(product(identity, inverse(d), c), true, product(c, d, identity), true), true)
% 1.97/0.68 = { by axiom 5 (left_inverse) R->L }
% 1.97/0.68 ifeq(product(inverse(d), d, identity), true, ifeq(product(identity, inverse(d), c), true, product(c, d, identity), true), true)
% 1.97/0.68 = { by axiom 7 (ifeq_axiom) R->L }
% 1.97/0.68 ifeq(product(inverse(d), d, identity), true, ifeq(true, true, ifeq(product(identity, inverse(d), c), true, product(c, d, identity), true), true), true)
% 1.97/0.68 = { by axiom 1 (right_identity) R->L }
% 1.97/0.68 ifeq(product(inverse(d), d, identity), true, ifeq(product(identity, identity, identity), true, ifeq(product(identity, inverse(d), c), true, product(c, d, identity), true), true), true)
% 1.97/0.68 = { by axiom 12 (associativity2) }
% 1.97/0.68 true
% 1.97/0.68 % SZS output end Proof
% 1.97/0.68
% 1.97/0.68 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------