%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO010-1 : 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 09:35:23 AM UTC 2026
% Result : Unsatisfiable 62.51s 8.21s
% Output : Proof 62.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 21:06:22 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.51/8.21 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
% 62.51/8.21
% 62.51/8.21 % SZS status Unsatisfiable
% 62.51/8.21
% 62.51/8.23 % SZS output start Proof
% 62.51/8.23 Axiom 1 (additive_inverse1): sum(inverse(X), X, multiplicative_identity) = true.
% 62.51/8.23 Axiom 2 (multiplicative_identity2): product(X, multiplicative_identity, X) = true.
% 62.51/8.23 Axiom 3 (multiplicative_identity1): product(multiplicative_identity, X, X) = true.
% 62.51/8.23 Axiom 4 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 62.51/8.23 Axiom 5 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 62.51/8.23 Axiom 6 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 62.51/8.23 Axiom 7 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 62.51/8.23 Axiom 8 (commutativity_of_addition): ifeq(sum(X, Y, Z), true, sum(Y, X, Z), true) = true.
% 62.51/8.23 Axiom 9 (addition_is_well_defined): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, W), true, W, Z), Z) = Z.
% 62.51/8.23 Axiom 10 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 62.51/8.23 Axiom 11 (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.
% 62.51/8.23 Axiom 12 (distributivity2): ifeq(product(X, Y, Z), true, ifeq(product(X, W, V), true, ifeq(sum(V, Z, U), true, ifeq(sum(W, Y, T), true, product(X, T, U), true), true), true), true) = true.
% 62.51/8.23 Axiom 13 (distributivity8): ifeq(product(X, Y, Z), true, ifeq(product(W, V, U), true, ifeq(sum(V, T, Y), true, ifeq(sum(W, T, X), true, sum(U, T, Z), true), true), true), true) = true.
% 62.51/8.23
% 62.51/8.23 Lemma 14: add(X, Y) = add(Y, X).
% 62.51/8.23 Proof:
% 62.51/8.23 add(X, Y)
% 62.51/8.23 = { by axiom 9 (addition_is_well_defined) R->L }
% 62.51/8.23 ifeq2(sum(Y, X, add(X, Y)), true, ifeq2(sum(Y, X, add(Y, X)), true, add(Y, X), add(X, Y)), add(X, Y))
% 62.51/8.23 = { by axiom 6 (closure_of_addition) }
% 62.51/8.23 ifeq2(sum(Y, X, add(X, Y)), true, ifeq2(true, true, add(Y, X), add(X, Y)), add(X, Y))
% 62.51/8.23 = { by axiom 5 (ifeq_axiom) }
% 62.51/8.23 ifeq2(sum(Y, X, add(X, Y)), true, add(Y, X), add(X, Y))
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq2(ifeq(true, true, sum(Y, X, add(X, Y)), true), true, add(Y, X), add(X, Y))
% 62.51/8.23 = { by axiom 6 (closure_of_addition) R->L }
% 62.51/8.23 ifeq2(ifeq(sum(X, Y, add(X, Y)), true, sum(Y, X, add(X, Y)), true), true, add(Y, X), add(X, Y))
% 62.51/8.23 = { by axiom 8 (commutativity_of_addition) }
% 62.51/8.23 ifeq2(true, true, add(Y, X), add(X, Y))
% 62.51/8.23 = { by axiom 5 (ifeq_axiom) }
% 62.51/8.23 add(Y, X)
% 62.51/8.23
% 62.51/8.23 Lemma 15: add(X, multiplicative_identity) = multiplicative_identity.
% 62.51/8.23 Proof:
% 62.51/8.23 add(X, multiplicative_identity)
% 62.51/8.23 = { by axiom 10 (multiplication_is_well_defined) R->L }
% 62.51/8.23 ifeq2(product(multiplicative_identity, add(X, multiplicative_identity), add(X, multiplicative_identity)), true, ifeq2(product(multiplicative_identity, add(X, multiplicative_identity), multiplicative_identity), true, multiplicative_identity, add(X, multiplicative_identity)), add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 3 (multiplicative_identity1) }
% 62.51/8.23 ifeq2(true, true, ifeq2(product(multiplicative_identity, add(X, multiplicative_identity), multiplicative_identity), true, multiplicative_identity, add(X, multiplicative_identity)), add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 5 (ifeq_axiom) }
% 62.51/8.23 ifeq2(product(multiplicative_identity, add(X, multiplicative_identity), multiplicative_identity), true, multiplicative_identity, add(X, multiplicative_identity))
% 62.51/8.23 = { by lemma 14 R->L }
% 62.51/8.23 ifeq2(product(multiplicative_identity, add(multiplicative_identity, X), multiplicative_identity), true, multiplicative_identity, add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq2(ifeq(true, true, product(multiplicative_identity, add(multiplicative_identity, X), multiplicative_identity), true), true, multiplicative_identity, add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 6 (closure_of_addition) R->L }
% 62.51/8.23 ifeq2(ifeq(sum(multiplicative_identity, X, add(multiplicative_identity, X)), true, product(multiplicative_identity, add(multiplicative_identity, X), multiplicative_identity), true), true, multiplicative_identity, add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq2(ifeq(sum(multiplicative_identity, X, add(multiplicative_identity, X)), true, ifeq(true, true, product(multiplicative_identity, add(multiplicative_identity, X), multiplicative_identity), true), true), true, multiplicative_identity, add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 1 (additive_inverse1) R->L }
% 62.51/8.23 ifeq2(ifeq(sum(multiplicative_identity, X, add(multiplicative_identity, X)), true, ifeq(sum(inverse(X), X, multiplicative_identity), true, product(multiplicative_identity, add(multiplicative_identity, X), multiplicative_identity), true), true), true, multiplicative_identity, add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq2(ifeq(true, true, ifeq(sum(multiplicative_identity, X, add(multiplicative_identity, X)), true, ifeq(sum(inverse(X), X, multiplicative_identity), true, product(multiplicative_identity, add(multiplicative_identity, X), multiplicative_identity), true), true), true), true, multiplicative_identity, add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 1 (additive_inverse1) R->L }
% 62.51/8.23 ifeq2(ifeq(sum(inverse(X), X, multiplicative_identity), true, ifeq(sum(multiplicative_identity, X, add(multiplicative_identity, X)), true, ifeq(sum(inverse(X), X, multiplicative_identity), true, product(multiplicative_identity, add(multiplicative_identity, X), multiplicative_identity), true), true), true), true, multiplicative_identity, add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq2(ifeq(true, true, ifeq(sum(inverse(X), X, multiplicative_identity), true, ifeq(sum(multiplicative_identity, X, add(multiplicative_identity, X)), true, ifeq(sum(inverse(X), X, multiplicative_identity), true, product(multiplicative_identity, add(multiplicative_identity, X), multiplicative_identity), true), true), true), true), true, multiplicative_identity, add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 2 (multiplicative_identity2) R->L }
% 62.51/8.23 ifeq2(ifeq(product(inverse(X), multiplicative_identity, inverse(X)), true, ifeq(sum(inverse(X), X, multiplicative_identity), true, ifeq(sum(multiplicative_identity, X, add(multiplicative_identity, X)), true, ifeq(sum(inverse(X), X, multiplicative_identity), true, product(multiplicative_identity, add(multiplicative_identity, X), multiplicative_identity), true), true), true), true), true, multiplicative_identity, add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 11 (distributivity7) }
% 62.51/8.23 ifeq2(true, true, multiplicative_identity, add(X, multiplicative_identity))
% 62.51/8.23 = { by axiom 5 (ifeq_axiom) }
% 62.51/8.23 multiplicative_identity
% 62.51/8.23
% 62.51/8.23 Goal 1 (prove_equations): sum(x, multiply(x, y), x) = true.
% 62.51/8.23 Proof:
% 62.51/8.23 sum(x, multiply(x, y), x)
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq(true, true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 2 (multiplicative_identity2) R->L }
% 62.51/8.23 ifeq(product(x, multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 10 (multiplication_is_well_defined) R->L }
% 62.51/8.23 ifeq(product(ifeq2(product(x, multiplicative_identity, x), true, ifeq2(product(x, multiplicative_identity, add(x, multiply(x, y))), true, add(x, multiply(x, y)), x), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 2 (multiplicative_identity2) }
% 62.51/8.23 ifeq(product(ifeq2(true, true, ifeq2(product(x, multiplicative_identity, add(x, multiply(x, y))), true, add(x, multiply(x, y)), x), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 5 (ifeq_axiom) }
% 62.51/8.23 ifeq(product(ifeq2(product(x, multiplicative_identity, add(x, multiply(x, y))), true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by lemma 14 R->L }
% 62.51/8.23 ifeq(product(ifeq2(product(x, multiplicative_identity, add(multiply(x, y), x)), true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq(product(ifeq2(ifeq(true, true, product(x, multiplicative_identity, add(multiply(x, y), x)), true), true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 6 (closure_of_addition) R->L }
% 62.51/8.23 ifeq(product(ifeq2(ifeq(sum(multiply(x, y), x, add(multiply(x, y), x)), true, product(x, multiplicative_identity, add(multiply(x, y), x)), true), true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq(product(ifeq2(ifeq(true, true, ifeq(sum(multiply(x, y), x, add(multiply(x, y), x)), true, product(x, multiplicative_identity, add(multiply(x, y), x)), true), true), true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 7 (closure_of_multiplication) R->L }
% 62.51/8.23 ifeq(product(ifeq2(ifeq(product(x, y, multiply(x, y)), true, ifeq(sum(multiply(x, y), x, add(multiply(x, y), x)), true, product(x, multiplicative_identity, add(multiply(x, y), x)), true), true), true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by lemma 15 R->L }
% 62.51/8.23 ifeq(product(ifeq2(ifeq(product(x, y, multiply(x, y)), true, ifeq(sum(multiply(x, y), x, add(multiply(x, y), x)), true, product(x, add(y, multiplicative_identity), add(multiply(x, y), x)), true), true), true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq(product(ifeq2(ifeq(product(x, y, multiply(x, y)), true, ifeq(sum(multiply(x, y), x, add(multiply(x, y), x)), true, ifeq(true, true, product(x, add(y, multiplicative_identity), add(multiply(x, y), x)), true), true), true), true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 6 (closure_of_addition) R->L }
% 62.51/8.23 ifeq(product(ifeq2(ifeq(product(x, y, multiply(x, y)), true, ifeq(sum(multiply(x, y), x, add(multiply(x, y), x)), true, ifeq(sum(y, multiplicative_identity, add(y, multiplicative_identity)), true, product(x, add(y, multiplicative_identity), add(multiply(x, y), x)), true), true), true), true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq(product(ifeq2(ifeq(true, true, ifeq(product(x, y, multiply(x, y)), true, ifeq(sum(multiply(x, y), x, add(multiply(x, y), x)), true, ifeq(sum(y, multiplicative_identity, add(y, multiplicative_identity)), true, product(x, add(y, multiplicative_identity), add(multiply(x, y), x)), true), true), true), true), true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 2 (multiplicative_identity2) R->L }
% 62.51/8.23 ifeq(product(ifeq2(ifeq(product(x, multiplicative_identity, x), true, ifeq(product(x, y, multiply(x, y)), true, ifeq(sum(multiply(x, y), x, add(multiply(x, y), x)), true, ifeq(sum(y, multiplicative_identity, add(y, multiplicative_identity)), true, product(x, add(y, multiplicative_identity), add(multiply(x, y), x)), true), true), true), true), true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 12 (distributivity2) }
% 62.51/8.23 ifeq(product(ifeq2(true, true, add(x, multiply(x, y)), x), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 5 (ifeq_axiom) }
% 62.51/8.23 ifeq(product(add(x, multiply(x, y)), multiplicative_identity, x), true, sum(x, multiply(x, y), x), true)
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq(product(add(x, multiply(x, y)), multiplicative_identity, x), true, ifeq(true, true, sum(x, multiply(x, y), x), true), true)
% 62.51/8.23 = { by axiom 6 (closure_of_addition) R->L }
% 62.51/8.23 ifeq(product(add(x, multiply(x, y)), multiplicative_identity, x), true, ifeq(sum(x, multiply(x, y), add(x, multiply(x, y))), true, sum(x, multiply(x, y), x), true), true)
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.23 ifeq(product(add(x, multiply(x, y)), multiplicative_identity, x), true, ifeq(true, true, ifeq(sum(x, multiply(x, y), add(x, multiply(x, y))), true, sum(x, multiply(x, y), x), true), true), true)
% 62.51/8.23 = { by lemma 15 R->L }
% 62.51/8.23 ifeq(product(add(x, multiply(x, y)), add(multiply(x, y), multiplicative_identity), x), true, ifeq(true, true, ifeq(sum(x, multiply(x, y), add(x, multiply(x, y))), true, sum(x, multiply(x, y), x), true), true), true)
% 62.51/8.23 = { by lemma 14 }
% 62.51/8.23 ifeq(product(add(x, multiply(x, y)), add(multiplicative_identity, multiply(x, y)), x), true, ifeq(true, true, ifeq(sum(x, multiply(x, y), add(x, multiply(x, y))), true, sum(x, multiply(x, y), x), true), true), true)
% 62.51/8.23 = { by axiom 6 (closure_of_addition) R->L }
% 62.51/8.23 ifeq(product(add(x, multiply(x, y)), add(multiplicative_identity, multiply(x, y)), x), true, ifeq(sum(multiplicative_identity, multiply(x, y), add(multiplicative_identity, multiply(x, y))), true, ifeq(sum(x, multiply(x, y), add(x, multiply(x, y))), true, sum(x, multiply(x, y), x), true), true), true)
% 62.51/8.23 = { by axiom 4 (ifeq_axiom) R->L }
% 62.51/8.24 ifeq(product(add(x, multiply(x, y)), add(multiplicative_identity, multiply(x, y)), x), true, ifeq(true, true, ifeq(sum(multiplicative_identity, multiply(x, y), add(multiplicative_identity, multiply(x, y))), true, ifeq(sum(x, multiply(x, y), add(x, multiply(x, y))), true, sum(x, multiply(x, y), x), true), true), true), true)
% 62.51/8.24 = { by axiom 2 (multiplicative_identity2) R->L }
% 62.51/8.24 ifeq(product(add(x, multiply(x, y)), add(multiplicative_identity, multiply(x, y)), x), true, ifeq(product(x, multiplicative_identity, x), true, ifeq(sum(multiplicative_identity, multiply(x, y), add(multiplicative_identity, multiply(x, y))), true, ifeq(sum(x, multiply(x, y), add(x, multiply(x, y))), true, sum(x, multiply(x, y), x), true), true), true), true)
% 62.51/8.24 = { by axiom 13 (distributivity8) }
% 62.51/8.24 true
% 62.51/8.24 % SZS output end Proof
% 62.51/8.24
% 62.51/8.24 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------