%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 09:35:24 AM UTC 2026
% Result : Unsatisfiable 1.24s 0.45s
% Output : Proof 1.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.16 % Computer : n017.cluster.edu
% 0.05/0.16 % Model : x86_64 x86_64
% 0.05/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.16 % Memory : 8046.5625MB
% 0.05/0.16 % OS : Linux 6.8.0-71-generic
% 0.05/0.16 % CPULimit : 300
% 0.05/0.16 % WCLimit : 300
% 0.05/0.16 % DateTime : Mon Sep 28 20:59:21 UTC 2026
% 0.05/0.16 % CPUTime :
% 0.05/0.16 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.24/0.45 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
% 1.24/0.45
% 1.24/0.45 % SZS status Unsatisfiable
% 1.24/0.45
% 1.24/0.46 % SZS output start Proof
% 1.24/0.46 Axiom 1 (additive_identity1): sum(additive_identity, X, X) = true.
% 1.24/0.46 Axiom 2 (sum_to_multiplicative_identity1): sum(x, y, multiplicative_identity) = true.
% 1.24/0.46 Axiom 3 (sum_to_multiplicative_identity2): sum(x, z, multiplicative_identity) = true.
% 1.24/0.46 Axiom 4 (multiplicative_identity1): product(multiplicative_identity, X, X) = true.
% 1.24/0.46 Axiom 5 (product_to_additive_identity1): product(x, y, additive_identity) = true.
% 1.24/0.46 Axiom 6 (product_to_additive_identity2): product(x, z, additive_identity) = true.
% 1.24/0.46 Axiom 7 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 1.24/0.46 Axiom 8 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 1.24/0.47 Axiom 9 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 1.24/0.47 Axiom 10 (commutativity_of_addition): ifeq(sum(X, Y, Z), true, sum(Y, X, Z), true) = true.
% 1.24/0.47 Axiom 11 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 1.24/0.47 Axiom 12 (distributivity7): ifeq(product(X, Y, Z), true, ifeq(sum(Z, W, V), true, ifeq(sum(Y, W, U), true, ifeq(sum(X, W, T), true, product(T, U, V), true), true), true), true) = true.
% 1.24/0.47
% 1.24/0.47 Lemma 13: ifeq2(product(multiplicative_identity, X, Y), true, Y, X) = X.
% 1.24/0.47 Proof:
% 1.24/0.47 ifeq2(product(multiplicative_identity, X, Y), true, Y, X)
% 1.24/0.47 = { by axiom 8 (ifeq_axiom) R->L }
% 1.24/0.47 ifeq2(true, true, ifeq2(product(multiplicative_identity, X, Y), true, Y, X), X)
% 1.24/0.47 = { by axiom 4 (multiplicative_identity1) R->L }
% 1.24/0.47 ifeq2(product(multiplicative_identity, X, X), true, ifeq2(product(multiplicative_identity, X, Y), true, Y, X), X)
% 1.24/0.47 = { by axiom 11 (multiplication_is_well_defined) }
% 1.24/0.47 X
% 1.24/0.47
% 1.24/0.47 Goal 1 (prove_both_inverse_are_equal): y = z.
% 1.24/0.47 Proof:
% 1.24/0.47 y
% 1.24/0.47 = { by axiom 8 (ifeq_axiom) R->L }
% 1.24/0.47 ifeq2(true, true, y, z)
% 1.24/0.47 = { by axiom 12 (distributivity7) R->L }
% 1.24/0.47 ifeq2(ifeq(product(x, z, additive_identity), true, ifeq(sum(additive_identity, y, y), true, ifeq(sum(z, y, add(y, z)), true, ifeq(sum(x, y, multiplicative_identity), true, product(multiplicative_identity, add(y, z), y), true), true), true), true), true, y, z)
% 1.24/0.47 = { by axiom 1 (additive_identity1) }
% 1.24/0.47 ifeq2(ifeq(product(x, z, additive_identity), true, ifeq(true, true, ifeq(sum(z, y, add(y, z)), true, ifeq(sum(x, y, multiplicative_identity), true, product(multiplicative_identity, add(y, z), y), true), true), true), true), true, y, z)
% 1.24/0.47 = { by axiom 7 (ifeq_axiom) }
% 1.24/0.47 ifeq2(ifeq(product(x, z, additive_identity), true, ifeq(sum(z, y, add(y, z)), true, ifeq(sum(x, y, multiplicative_identity), true, product(multiplicative_identity, add(y, z), y), true), true), true), true, y, z)
% 1.24/0.47 = { by axiom 6 (product_to_additive_identity2) }
% 1.24/0.47 ifeq2(ifeq(true, true, ifeq(sum(z, y, add(y, z)), true, ifeq(sum(x, y, multiplicative_identity), true, product(multiplicative_identity, add(y, z), y), true), true), true), true, y, z)
% 1.24/0.47 = { by axiom 7 (ifeq_axiom) }
% 1.24/0.47 ifeq2(ifeq(sum(z, y, add(y, z)), true, ifeq(sum(x, y, multiplicative_identity), true, product(multiplicative_identity, add(y, z), y), true), true), true, y, z)
% 1.24/0.47 = { by axiom 2 (sum_to_multiplicative_identity1) }
% 1.24/0.47 ifeq2(ifeq(sum(z, y, add(y, z)), true, ifeq(true, true, product(multiplicative_identity, add(y, z), y), true), true), true, y, z)
% 1.24/0.47 = { by axiom 7 (ifeq_axiom) }
% 1.24/0.47 ifeq2(ifeq(sum(z, y, add(y, z)), true, product(multiplicative_identity, add(y, z), y), true), true, y, z)
% 1.24/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 1.24/0.47 ifeq2(ifeq(ifeq(true, true, sum(z, y, add(y, z)), true), true, product(multiplicative_identity, add(y, z), y), true), true, y, z)
% 1.24/0.47 = { by axiom 9 (closure_of_addition) R->L }
% 1.24/0.47 ifeq2(ifeq(ifeq(sum(y, z, add(y, z)), true, sum(z, y, add(y, z)), true), true, product(multiplicative_identity, add(y, z), y), true), true, y, z)
% 1.24/0.47 = { by axiom 10 (commutativity_of_addition) }
% 1.24/0.47 ifeq2(ifeq(true, true, product(multiplicative_identity, add(y, z), y), true), true, y, z)
% 1.24/0.47 = { by axiom 7 (ifeq_axiom) }
% 1.24/0.47 ifeq2(product(multiplicative_identity, add(y, z), y), true, y, z)
% 1.24/0.47 = { by lemma 13 R->L }
% 1.24/0.47 ifeq2(product(multiplicative_identity, ifeq2(product(multiplicative_identity, add(y, z), z), true, z, add(y, z)), y), true, y, z)
% 1.24/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 1.24/0.47 ifeq2(product(multiplicative_identity, ifeq2(ifeq(true, true, product(multiplicative_identity, add(y, z), z), true), true, z, add(y, z)), y), true, y, z)
% 1.24/0.47 = { by axiom 9 (closure_of_addition) R->L }
% 1.24/0.47 ifeq2(product(multiplicative_identity, ifeq2(ifeq(sum(y, z, add(y, z)), true, product(multiplicative_identity, add(y, z), z), true), true, z, add(y, z)), y), true, y, z)
% 1.24/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 1.24/0.47 ifeq2(product(multiplicative_identity, ifeq2(ifeq(sum(y, z, add(y, z)), true, ifeq(true, true, product(multiplicative_identity, add(y, z), z), true), true), true, z, add(y, z)), y), true, y, z)
% 1.24/0.47 = { by axiom 3 (sum_to_multiplicative_identity2) R->L }
% 1.24/0.47 ifeq2(product(multiplicative_identity, ifeq2(ifeq(sum(y, z, add(y, z)), true, ifeq(sum(x, z, multiplicative_identity), true, product(multiplicative_identity, add(y, z), z), true), true), true, z, add(y, z)), y), true, y, z)
% 1.24/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 1.24/0.47 ifeq2(product(multiplicative_identity, ifeq2(ifeq(true, true, ifeq(sum(y, z, add(y, z)), true, ifeq(sum(x, z, multiplicative_identity), true, product(multiplicative_identity, add(y, z), z), true), true), true), true, z, add(y, z)), y), true, y, z)
% 1.24/0.47 = { by axiom 5 (product_to_additive_identity1) R->L }
% 1.24/0.47 ifeq2(product(multiplicative_identity, ifeq2(ifeq(product(x, y, additive_identity), true, ifeq(sum(y, z, add(y, z)), true, ifeq(sum(x, z, multiplicative_identity), true, product(multiplicative_identity, add(y, z), z), true), true), true), true, z, add(y, z)), y), true, y, z)
% 1.24/0.47 = { by axiom 7 (ifeq_axiom) R->L }
% 1.24/0.47 ifeq2(product(multiplicative_identity, ifeq2(ifeq(product(x, y, additive_identity), true, ifeq(true, true, ifeq(sum(y, z, add(y, z)), true, ifeq(sum(x, z, multiplicative_identity), true, product(multiplicative_identity, add(y, z), z), true), true), true), true), true, z, add(y, z)), y), true, y, z)
% 1.24/0.47 = { by axiom 1 (additive_identity1) R->L }
% 1.24/0.47 ifeq2(product(multiplicative_identity, ifeq2(ifeq(product(x, y, additive_identity), true, ifeq(sum(additive_identity, z, z), true, ifeq(sum(y, z, add(y, z)), true, ifeq(sum(x, z, multiplicative_identity), true, product(multiplicative_identity, add(y, z), z), true), true), true), true), true, z, add(y, z)), y), true, y, z)
% 1.24/0.47 = { by axiom 12 (distributivity7) }
% 1.24/0.47 ifeq2(product(multiplicative_identity, ifeq2(true, true, z, add(y, z)), y), true, y, z)
% 1.24/0.47 = { by axiom 8 (ifeq_axiom) }
% 1.24/0.47 ifeq2(product(multiplicative_identity, z, y), true, y, z)
% 1.24/0.47 = { by lemma 13 }
% 1.24/0.47 z
% 1.24/0.47 % SZS output end Proof
% 1.24/0.47
% 1.24/0.47 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------