%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP029-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 0.13s 0.48s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP029-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 09:18:06 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.48 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 0.13/0.48
% 0.13/0.48 % SZS status Unsatisfiable
% 0.13/0.48
% 0.13/0.49 % SZS output start Proof
% 0.13/0.49 Axiom 1 (left_identity): product(identity, X, X) = true.
% 0.13/0.49 Axiom 2 (left_inverse): product(inverse(X), X, identity) = true.
% 0.13/0.49 Axiom 3 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.13/0.49 Axiom 4 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.13/0.49 Axiom 5 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 0.13/0.49 Axiom 6 (total_function2): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.13/0.49 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.
% 0.13/0.49
% 0.13/0.49 Lemma 8: ifeq2(product(X, Y, Z), true, multiply(X, Y), Z) = Z.
% 0.13/0.49 Proof:
% 0.13/0.49 ifeq2(product(X, Y, Z), true, multiply(X, Y), Z)
% 0.13/0.49 = { by axiom 4 (ifeq_axiom) R->L }
% 0.13/0.49 ifeq2(product(X, Y, Z), true, ifeq2(true, true, multiply(X, Y), Z), Z)
% 0.13/0.49 = { by axiom 5 (total_function1) R->L }
% 0.13/0.49 ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, multiply(X, Y)), true, multiply(X, Y), Z), Z)
% 0.13/0.49 = { by axiom 6 (total_function2) }
% 0.13/0.49 Z
% 0.13/0.49
% 0.13/0.49 Lemma 9: multiply(inverse(inverse(X)), identity) = X.
% 0.13/0.49 Proof:
% 0.13/0.49 multiply(inverse(inverse(X)), identity)
% 0.13/0.49 = { by axiom 4 (ifeq_axiom) R->L }
% 0.13/0.49 ifeq2(true, true, multiply(inverse(inverse(X)), identity), X)
% 0.13/0.49 = { by axiom 7 (associativity1) R->L }
% 0.13/0.49 ifeq2(ifeq(product(identity, X, X), true, ifeq(product(inverse(X), X, identity), true, ifeq(product(inverse(inverse(X)), inverse(X), identity), true, product(inverse(inverse(X)), identity, X), true), true), true), true, multiply(inverse(inverse(X)), identity), X)
% 0.13/0.49 = { by axiom 1 (left_identity) }
% 0.13/0.49 ifeq2(ifeq(true, true, ifeq(product(inverse(X), X, identity), true, ifeq(product(inverse(inverse(X)), inverse(X), identity), true, product(inverse(inverse(X)), identity, X), true), true), true), true, multiply(inverse(inverse(X)), identity), X)
% 0.13/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.13/0.49 ifeq2(ifeq(product(inverse(X), X, identity), true, ifeq(product(inverse(inverse(X)), inverse(X), identity), true, product(inverse(inverse(X)), identity, X), true), true), true, multiply(inverse(inverse(X)), identity), X)
% 0.13/0.49 = { by axiom 2 (left_inverse) }
% 0.13/0.49 ifeq2(ifeq(product(inverse(X), X, identity), true, ifeq(true, true, product(inverse(inverse(X)), identity, X), true), true), true, multiply(inverse(inverse(X)), identity), X)
% 0.13/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.13/0.49 ifeq2(ifeq(product(inverse(X), X, identity), true, product(inverse(inverse(X)), identity, X), true), true, multiply(inverse(inverse(X)), identity), X)
% 0.13/0.49 = { by axiom 2 (left_inverse) }
% 0.13/0.49 ifeq2(ifeq(true, true, product(inverse(inverse(X)), identity, X), true), true, multiply(inverse(inverse(X)), identity), X)
% 0.13/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.13/0.49 ifeq2(product(inverse(inverse(X)), identity, X), true, multiply(inverse(inverse(X)), identity), X)
% 0.13/0.49 = { by lemma 8 }
% 0.13/0.49 X
% 0.13/0.49
% 0.13/0.49 Lemma 10: multiply(inverse(X), multiply(X, Y)) = Y.
% 0.13/0.49 Proof:
% 0.13/0.49 multiply(inverse(X), multiply(X, Y))
% 0.13/0.49 = { by axiom 4 (ifeq_axiom) R->L }
% 0.13/0.49 ifeq2(true, true, multiply(inverse(X), multiply(X, Y)), Y)
% 0.13/0.49 = { by axiom 7 (associativity1) R->L }
% 0.13/0.49 ifeq2(ifeq(product(identity, Y, Y), true, ifeq(product(X, Y, multiply(X, Y)), true, ifeq(product(inverse(X), X, identity), true, product(inverse(X), multiply(X, Y), Y), true), true), true), true, multiply(inverse(X), multiply(X, Y)), Y)
% 0.13/0.49 = { by axiom 1 (left_identity) }
% 0.13/0.49 ifeq2(ifeq(true, true, ifeq(product(X, Y, multiply(X, Y)), true, ifeq(product(inverse(X), X, identity), true, product(inverse(X), multiply(X, Y), Y), true), true), true), true, multiply(inverse(X), multiply(X, Y)), Y)
% 0.13/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.13/0.49 ifeq2(ifeq(product(X, Y, multiply(X, Y)), true, ifeq(product(inverse(X), X, identity), true, product(inverse(X), multiply(X, Y), Y), true), true), true, multiply(inverse(X), multiply(X, Y)), Y)
% 0.13/0.49 = { by axiom 2 (left_inverse) }
% 0.13/0.49 ifeq2(ifeq(product(X, Y, multiply(X, Y)), true, ifeq(true, true, product(inverse(X), multiply(X, Y), Y), true), true), true, multiply(inverse(X), multiply(X, Y)), Y)
% 0.13/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.13/0.49 ifeq2(ifeq(product(X, Y, multiply(X, Y)), true, product(inverse(X), multiply(X, Y), Y), true), true, multiply(inverse(X), multiply(X, Y)), Y)
% 0.13/0.49 = { by axiom 5 (total_function1) }
% 0.13/0.49 ifeq2(ifeq(true, true, product(inverse(X), multiply(X, Y), Y), true), true, multiply(inverse(X), multiply(X, Y)), Y)
% 0.13/0.49 = { by axiom 3 (ifeq_axiom) }
% 0.13/0.49 ifeq2(product(inverse(X), multiply(X, Y), Y), true, multiply(inverse(X), multiply(X, Y)), Y)
% 0.13/0.49 = { by lemma 8 }
% 0.13/0.49 Y
% 0.13/0.49
% 0.13/0.49 Goal 1 (prove_there_is_a_right_identity): product(not_right_identity(X), X, not_right_identity(X)) = true.
% 0.13/0.49 The goal is true when:
% 0.13/0.49 X = identity
% 0.13/0.49
% 0.13/0.49 Proof:
% 0.13/0.49 product(not_right_identity(identity), identity, not_right_identity(identity))
% 0.13/0.49 = { by lemma 10 R->L }
% 0.13/0.49 product(multiply(inverse(inverse(inverse(inverse(not_right_identity(identity))))), multiply(inverse(inverse(inverse(not_right_identity(identity)))), not_right_identity(identity))), identity, not_right_identity(identity))
% 0.13/0.49 = { by lemma 9 R->L }
% 0.13/0.49 product(multiply(inverse(inverse(inverse(inverse(not_right_identity(identity))))), multiply(inverse(inverse(inverse(not_right_identity(identity)))), multiply(inverse(inverse(not_right_identity(identity))), identity))), identity, not_right_identity(identity))
% 0.13/0.49 = { by lemma 10 }
% 0.13/0.49 product(multiply(inverse(inverse(inverse(inverse(not_right_identity(identity))))), identity), identity, not_right_identity(identity))
% 0.13/0.49 = { by lemma 9 }
% 0.13/0.49 product(inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity))
% 0.13/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.13/0.49 ifeq(true, true, product(inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity)), true)
% 0.13/0.49 = { by axiom 2 (left_inverse) R->L }
% 0.13/0.49 ifeq(product(inverse(not_right_identity(identity)), not_right_identity(identity), identity), true, product(inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity)), true)
% 0.13/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.13/0.49 ifeq(product(inverse(not_right_identity(identity)), not_right_identity(identity), identity), true, ifeq(true, true, product(inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity)), true), true)
% 0.13/0.49 = { by axiom 2 (left_inverse) R->L }
% 0.13/0.49 ifeq(product(inverse(not_right_identity(identity)), not_right_identity(identity), identity), true, ifeq(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), identity), true, product(inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity)), true), true)
% 0.13/0.49 = { by axiom 3 (ifeq_axiom) R->L }
% 0.13/0.49 ifeq(true, true, ifeq(product(inverse(not_right_identity(identity)), not_right_identity(identity), identity), true, ifeq(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), identity), true, product(inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity)), true), true), true)
% 0.13/0.49 = { by axiom 1 (left_identity) R->L }
% 0.13/0.49 ifeq(product(identity, not_right_identity(identity), not_right_identity(identity)), true, ifeq(product(inverse(not_right_identity(identity)), not_right_identity(identity), identity), true, ifeq(product(inverse(inverse(not_right_identity(identity))), inverse(not_right_identity(identity)), identity), true, product(inverse(inverse(not_right_identity(identity))), identity, not_right_identity(identity)), true), true), true)
% 0.13/0.49 = { by axiom 7 (associativity1) }
% 0.13/0.49 true
% 0.13/0.49 % SZS output end Proof
% 0.13/0.49
% 0.13/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------