%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP030-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 10:09:06 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.38s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP030-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sun Sep 27 09:14:49 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.38 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
% 0.07/0.38
% 0.07/0.38 % SZS status Unsatisfiable
% 0.07/0.38
% 0.07/0.38 % SZS output start Proof
% 0.07/0.38 Axiom 1 (left_identity): product(identity, X, X) = true.
% 0.07/0.38 Axiom 2 (left_inverse): product(inverse(X), X, identity) = true.
% 0.07/0.38 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.07/0.38 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.07/0.38 Axiom 5 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 0.07/0.38 Axiom 6 (total_function2): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.07/0.38 Axiom 7 (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.
% 0.07/0.38
% 0.07/0.38 Goal 1 (prove_identity_is_a_right_identity): product(a, identity, a) = true.
% 0.07/0.38 Proof:
% 0.07/0.38 product(a, identity, a)
% 0.07/0.38 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.38 ifeq(true, true, product(a, identity, a), true)
% 0.07/0.38 = { by axiom 5 (total_function1) R->L }
% 0.07/0.38 ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 6 (total_function2) R->L }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true, ifeq2(product(inverse(inverse(a)), inverse(a), identity), true, identity, multiply(a, inverse(a))), multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 2 (left_inverse) }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true, ifeq2(true, true, identity, multiply(a, inverse(a))), multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 4 (ifeq_axiom) }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(true, true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 7 (associativity1) R->L }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(ifeq(product(identity, inverse(a), inverse(a)), true, ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 1 (left_identity) }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(ifeq(true, true, ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 3 (ifeq_axiom) }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(product(inverse(a), a, identity), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 2 (left_inverse) }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, ifeq(true, true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 3 (ifeq_axiom) }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(ifeq(product(a, inverse(a), multiply(a, inverse(a))), true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 5 (total_function1) }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(ifeq(true, true, product(inverse(a), multiply(a, inverse(a)), inverse(a)), true), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 3 (ifeq_axiom) }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(true, true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 2 (left_inverse) R->L }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(true, true, ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 1 (left_identity) R->L }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(ifeq(product(identity, multiply(a, inverse(a)), multiply(a, inverse(a))), true, ifeq(product(inverse(a), multiply(a, inverse(a)), inverse(a)), true, ifeq(product(inverse(inverse(a)), inverse(a), identity), true, product(inverse(inverse(a)), inverse(a), multiply(a, inverse(a))), true), true), true), true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 7 (associativity1) }
% 0.07/0.39 ifeq(product(a, inverse(a), ifeq2(true, true, identity, multiply(a, inverse(a)))), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 4 (ifeq_axiom) }
% 0.07/0.39 ifeq(product(a, inverse(a), identity), true, product(a, identity, a), true)
% 0.07/0.39 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.39 ifeq(true, true, ifeq(product(a, inverse(a), identity), true, product(a, identity, a), true), true)
% 0.07/0.39 = { by axiom 2 (left_inverse) R->L }
% 0.07/0.39 ifeq(product(inverse(a), a, identity), true, ifeq(product(a, inverse(a), identity), true, product(a, identity, a), true), true)
% 0.07/0.39 = { by axiom 3 (ifeq_axiom) R->L }
% 0.07/0.39 ifeq(true, true, ifeq(product(inverse(a), a, identity), true, ifeq(product(a, inverse(a), identity), true, product(a, identity, a), true), true), true)
% 0.07/0.39 = { by axiom 1 (left_identity) R->L }
% 0.07/0.39 ifeq(product(identity, a, a), true, ifeq(product(inverse(a), a, identity), true, ifeq(product(a, inverse(a), identity), true, product(a, identity, a), true), true), true)
% 0.07/0.39 = { by axiom 7 (associativity1) }
% 0.07/0.39 true
% 0.07/0.39 % SZS output end Proof
% 0.07/0.39
% 0.07/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------