%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP047-2 : 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 2.10s 0.74s
% Output : Proof 2.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP047-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 09:19:26 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.10/0.74 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
% 2.10/0.74
% 2.10/0.74 % SZS status Unsatisfiable
% 2.10/0.74
% 2.10/0.76 % SZS output start Proof
% 2.10/0.76 Axiom 1 (a_equals_b): equalish(a, b) = true.
% 2.10/0.76 Axiom 2 (left_identity): product(identity, X, X) = true.
% 2.10/0.76 Axiom 3 (left_inverse): product(inverse(X), X, identity) = true.
% 2.10/0.76 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 2.10/0.76 Axiom 5 (total_function1): product(X, Y, multiply(X, Y)) = true.
% 2.10/0.76 Axiom 6 (product_substitution3): ifeq(equalish(X, Y), true, ifeq(product(Z, W, X), true, product(Z, W, Y), true), true) = true.
% 2.10/0.76 Axiom 7 (total_function2): ifeq(product(X, Y, Z), true, ifeq(product(X, Y, W), true, equalish(W, Z), true), true) = true.
% 2.10/0.76 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.
% 2.10/0.76
% 2.10/0.76 Goal 1 (prove_multiply_substitution2): equalish(multiply(c, a), multiply(c, b)) = true.
% 2.10/0.76 Proof:
% 2.10/0.76 equalish(multiply(c, a), multiply(c, b))
% 2.10/0.76 = { by axiom 4 (ifeq_axiom) R->L }
% 2.10/0.76 ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true)
% 2.10/0.76 = { by axiom 4 (ifeq_axiom) R->L }
% 2.10/0.76 ifeq(true, true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 8 (associativity1) R->L }
% 2.10/0.76 ifeq(ifeq(product(identity, multiply(c, b), multiply(c, b)), true, ifeq(product(inverse(c), multiply(c, b), b), true, ifeq(product(inverse(inverse(c)), inverse(c), identity), true, product(inverse(inverse(c)), b, multiply(c, b)), true), true), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 2 (left_identity) }
% 2.10/0.76 ifeq(ifeq(true, true, ifeq(product(inverse(c), multiply(c, b), b), true, ifeq(product(inverse(inverse(c)), inverse(c), identity), true, product(inverse(inverse(c)), b, multiply(c, b)), true), true), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 4 (ifeq_axiom) }
% 2.10/0.76 ifeq(ifeq(product(inverse(c), multiply(c, b), b), true, ifeq(product(inverse(inverse(c)), inverse(c), identity), true, product(inverse(inverse(c)), b, multiply(c, b)), true), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 3 (left_inverse) }
% 2.10/0.76 ifeq(ifeq(product(inverse(c), multiply(c, b), b), true, ifeq(true, true, product(inverse(inverse(c)), b, multiply(c, b)), true), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 4 (ifeq_axiom) }
% 2.10/0.76 ifeq(ifeq(product(inverse(c), multiply(c, b), b), true, product(inverse(inverse(c)), b, multiply(c, b)), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 4 (ifeq_axiom) R->L }
% 2.10/0.76 ifeq(ifeq(ifeq(true, true, product(inverse(c), multiply(c, b), b), true), true, product(inverse(inverse(c)), b, multiply(c, b)), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 3 (left_inverse) R->L }
% 2.10/0.76 ifeq(ifeq(ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, b), b), true), true, product(inverse(inverse(c)), b, multiply(c, b)), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 4 (ifeq_axiom) R->L }
% 2.10/0.76 ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, b), b), true), true), true, product(inverse(inverse(c)), b, multiply(c, b)), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 5 (total_function1) R->L }
% 2.10/0.76 ifeq(ifeq(ifeq(product(c, b, multiply(c, b)), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, b), b), true), true), true, product(inverse(inverse(c)), b, multiply(c, b)), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 4 (ifeq_axiom) R->L }
% 2.10/0.76 ifeq(ifeq(ifeq(true, true, ifeq(product(c, b, multiply(c, b)), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, b), b), true), true), true), true, product(inverse(inverse(c)), b, multiply(c, b)), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 2 (left_identity) R->L }
% 2.10/0.76 ifeq(ifeq(ifeq(product(identity, b, b), true, ifeq(product(c, b, multiply(c, b)), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, b), b), true), true), true), true, product(inverse(inverse(c)), b, multiply(c, b)), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 8 (associativity1) }
% 2.10/0.76 ifeq(ifeq(true, true, product(inverse(inverse(c)), b, multiply(c, b)), true), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 4 (ifeq_axiom) }
% 2.10/0.76 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(true, true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 8 (associativity1) R->L }
% 2.10/0.76 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(product(identity, multiply(c, a), multiply(c, a)), true, ifeq(product(inverse(c), multiply(c, a), b), true, ifeq(product(inverse(inverse(c)), inverse(c), identity), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 2 (left_identity) }
% 2.10/0.76 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(true, true, ifeq(product(inverse(c), multiply(c, a), b), true, ifeq(product(inverse(inverse(c)), inverse(c), identity), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 4 (ifeq_axiom) }
% 2.10/0.76 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(product(inverse(c), multiply(c, a), b), true, ifeq(product(inverse(inverse(c)), inverse(c), identity), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 3 (left_inverse) }
% 2.10/0.76 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(product(inverse(c), multiply(c, a), b), true, ifeq(true, true, product(inverse(inverse(c)), b, multiply(c, a)), true), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.76 = { by axiom 4 (ifeq_axiom) }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(product(inverse(c), multiply(c, a), b), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 4 (ifeq_axiom) R->L }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(ifeq(true, true, product(inverse(c), multiply(c, a), b), true), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 8 (associativity1) R->L }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(ifeq(ifeq(product(identity, a, a), true, ifeq(product(c, a, multiply(c, a)), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, a), a), true), true), true), true, product(inverse(c), multiply(c, a), b), true), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 2 (left_identity) }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(c, a, multiply(c, a)), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, a), a), true), true), true), true, product(inverse(c), multiply(c, a), b), true), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 4 (ifeq_axiom) }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(ifeq(ifeq(product(c, a, multiply(c, a)), true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, a), a), true), true), true, product(inverse(c), multiply(c, a), b), true), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 5 (total_function1) }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, a), a), true), true), true, product(inverse(c), multiply(c, a), b), true), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 4 (ifeq_axiom) }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(ifeq(ifeq(product(inverse(c), c, identity), true, product(inverse(c), multiply(c, a), a), true), true, product(inverse(c), multiply(c, a), b), true), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 3 (left_inverse) }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(ifeq(ifeq(true, true, product(inverse(c), multiply(c, a), a), true), true, product(inverse(c), multiply(c, a), b), true), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 4 (ifeq_axiom) }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(ifeq(product(inverse(c), multiply(c, a), a), true, product(inverse(c), multiply(c, a), b), true), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 4 (ifeq_axiom) R->L }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(ifeq(true, true, ifeq(product(inverse(c), multiply(c, a), a), true, product(inverse(c), multiply(c, a), b), true), true), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 1 (a_equals_b) R->L }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(ifeq(equalish(a, b), true, ifeq(product(inverse(c), multiply(c, a), a), true, product(inverse(c), multiply(c, a), b), true), true), true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 6 (product_substitution3) }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(ifeq(true, true, product(inverse(inverse(c)), b, multiply(c, a)), true), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 4 (ifeq_axiom) }
% 2.10/0.77 ifeq(product(inverse(inverse(c)), b, multiply(c, b)), true, ifeq(product(inverse(inverse(c)), b, multiply(c, a)), true, equalish(multiply(c, a), multiply(c, b)), true), true)
% 2.10/0.77 = { by axiom 7 (total_function2) }
% 2.10/0.77 true
% 2.10/0.77 % SZS output end Proof
% 2.10/0.77
% 2.10/0.77 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------