%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO012-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 0.62s 0.36s
% Output : Proof 0.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO012-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n004.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 21:03:51 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.36 Command-line arguments: --no-flatten-goal
% 0.62/0.36
% 0.62/0.36 % SZS status Unsatisfiable
% 0.62/0.36
% 0.62/0.37 % SZS output start Proof
% 0.62/0.37 Axiom 1 (additive_inverse2): sum(X, inverse(X), multiplicative_identity) = true.
% 0.62/0.37 Axiom 2 (additive_identity1): sum(additive_identity, X, X) = true.
% 0.62/0.37 Axiom 3 (additive_inverse1): sum(inverse(X), X, multiplicative_identity) = true.
% 0.62/0.37 Axiom 4 (multiplicative_identity2): product(X, multiplicative_identity, X) = true.
% 0.62/0.37 Axiom 5 (multiplicative_inverse2): product(X, inverse(X), additive_identity) = true.
% 0.62/0.37 Axiom 6 (multiplicative_identity1): product(multiplicative_identity, X, X) = true.
% 0.62/0.37 Axiom 7 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.62/0.37 Axiom 8 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.62/0.37 Axiom 9 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 0.62/0.37 Axiom 10 (commutativity_of_addition): ifeq(sum(X, Y, Z), true, sum(Y, X, Z), true) = true.
% 0.62/0.37 Axiom 11 (addition_is_well_defined): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, W), true, W, Z), Z) = Z.
% 0.62/0.37 Axiom 12 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.62/0.37 Axiom 13 (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.
% 0.62/0.37
% 0.62/0.37 Goal 1 (prove_inverse_is_an_involution): inverse(inverse(x)) = x.
% 0.62/0.37 Proof:
% 0.62/0.37 inverse(inverse(x))
% 0.62/0.37 = { by axiom 7 (ifeq_axiom) R->L }
% 0.62/0.37 ifeq2(true, true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 13 (distributivity7) R->L }
% 0.62/0.37 ifeq2(ifeq(product(x, inverse(x), additive_identity), true, ifeq(sum(additive_identity, inverse(inverse(x)), inverse(inverse(x))), true, ifeq(sum(inverse(x), inverse(inverse(x)), multiplicative_identity), true, ifeq(sum(x, inverse(inverse(x)), add(x, inverse(inverse(x)))), true, product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))), true), true), true), true), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 2 (additive_identity1) }
% 0.62/0.37 ifeq2(ifeq(product(x, inverse(x), additive_identity), true, ifeq(true, true, ifeq(sum(inverse(x), inverse(inverse(x)), multiplicative_identity), true, ifeq(sum(x, inverse(inverse(x)), add(x, inverse(inverse(x)))), true, product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))), true), true), true), true), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 8 (ifeq_axiom) }
% 0.62/0.37 ifeq2(ifeq(product(x, inverse(x), additive_identity), true, ifeq(sum(inverse(x), inverse(inverse(x)), multiplicative_identity), true, ifeq(sum(x, inverse(inverse(x)), add(x, inverse(inverse(x)))), true, product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))), true), true), true), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 5 (multiplicative_inverse2) }
% 0.62/0.37 ifeq2(ifeq(true, true, ifeq(sum(inverse(x), inverse(inverse(x)), multiplicative_identity), true, ifeq(sum(x, inverse(inverse(x)), add(x, inverse(inverse(x)))), true, product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))), true), true), true), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 8 (ifeq_axiom) }
% 0.62/0.37 ifeq2(ifeq(sum(inverse(x), inverse(inverse(x)), multiplicative_identity), true, ifeq(sum(x, inverse(inverse(x)), add(x, inverse(inverse(x)))), true, product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))), true), true), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 1 (additive_inverse2) }
% 0.62/0.37 ifeq2(ifeq(true, true, ifeq(sum(x, inverse(inverse(x)), add(x, inverse(inverse(x)))), true, product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))), true), true), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 8 (ifeq_axiom) }
% 0.62/0.37 ifeq2(ifeq(sum(x, inverse(inverse(x)), add(x, inverse(inverse(x)))), true, product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))), true), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 9 (closure_of_addition) }
% 0.62/0.37 ifeq2(ifeq(true, true, product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))), true), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 8 (ifeq_axiom) }
% 0.62/0.37 ifeq2(product(add(x, inverse(inverse(x))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 12 (multiplication_is_well_defined) R->L }
% 0.62/0.37 ifeq2(product(ifeq2(product(multiplicative_identity, add(x, inverse(inverse(x))), add(x, inverse(inverse(x)))), true, ifeq2(product(multiplicative_identity, add(x, inverse(inverse(x))), x), true, x, add(x, inverse(inverse(x)))), add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 6 (multiplicative_identity1) }
% 0.62/0.37 ifeq2(product(ifeq2(true, true, ifeq2(product(multiplicative_identity, add(x, inverse(inverse(x))), x), true, x, add(x, inverse(inverse(x)))), add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 7 (ifeq_axiom) }
% 0.62/0.37 ifeq2(product(ifeq2(product(multiplicative_identity, add(x, inverse(inverse(x))), x), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 7 (ifeq_axiom) R->L }
% 0.62/0.37 ifeq2(product(ifeq2(product(multiplicative_identity, ifeq2(true, true, add(x, inverse(inverse(x))), add(inverse(inverse(x)), x)), x), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 10 (commutativity_of_addition) R->L }
% 0.62/0.37 ifeq2(product(ifeq2(product(multiplicative_identity, ifeq2(ifeq(sum(inverse(inverse(x)), x, add(inverse(inverse(x)), x)), true, sum(x, inverse(inverse(x)), add(inverse(inverse(x)), x)), true), true, add(x, inverse(inverse(x))), add(inverse(inverse(x)), x)), x), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 9 (closure_of_addition) }
% 0.62/0.37 ifeq2(product(ifeq2(product(multiplicative_identity, ifeq2(ifeq(true, true, sum(x, inverse(inverse(x)), add(inverse(inverse(x)), x)), true), true, add(x, inverse(inverse(x))), add(inverse(inverse(x)), x)), x), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 8 (ifeq_axiom) }
% 0.62/0.37 ifeq2(product(ifeq2(product(multiplicative_identity, ifeq2(sum(x, inverse(inverse(x)), add(inverse(inverse(x)), x)), true, add(x, inverse(inverse(x))), add(inverse(inverse(x)), x)), x), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 7 (ifeq_axiom) R->L }
% 0.62/0.37 ifeq2(product(ifeq2(product(multiplicative_identity, ifeq2(sum(x, inverse(inverse(x)), add(inverse(inverse(x)), x)), true, ifeq2(true, true, add(x, inverse(inverse(x))), add(inverse(inverse(x)), x)), add(inverse(inverse(x)), x)), x), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 9 (closure_of_addition) R->L }
% 0.62/0.37 ifeq2(product(ifeq2(product(multiplicative_identity, ifeq2(sum(x, inverse(inverse(x)), add(inverse(inverse(x)), x)), true, ifeq2(sum(x, inverse(inverse(x)), add(x, inverse(inverse(x)))), true, add(x, inverse(inverse(x))), add(inverse(inverse(x)), x)), add(inverse(inverse(x)), x)), x), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 11 (addition_is_well_defined) }
% 0.62/0.37 ifeq2(product(ifeq2(product(multiplicative_identity, add(inverse(inverse(x)), x), x), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.37 = { by axiom 8 (ifeq_axiom) R->L }
% 0.62/0.37 ifeq2(product(ifeq2(ifeq(true, true, product(multiplicative_identity, add(inverse(inverse(x)), x), x), true), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.38 = { by axiom 9 (closure_of_addition) R->L }
% 0.62/0.38 ifeq2(product(ifeq2(ifeq(sum(inverse(inverse(x)), x, add(inverse(inverse(x)), x)), true, product(multiplicative_identity, add(inverse(inverse(x)), x), x), true), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.38 = { by axiom 8 (ifeq_axiom) R->L }
% 0.62/0.38 ifeq2(product(ifeq2(ifeq(sum(inverse(inverse(x)), x, add(inverse(inverse(x)), x)), true, ifeq(true, true, product(multiplicative_identity, add(inverse(inverse(x)), x), x), true), true), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.38 = { by axiom 3 (additive_inverse1) R->L }
% 0.62/0.38 ifeq2(product(ifeq2(ifeq(sum(inverse(inverse(x)), x, add(inverse(inverse(x)), x)), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, product(multiplicative_identity, add(inverse(inverse(x)), x), x), true), true), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.38 = { by axiom 8 (ifeq_axiom) R->L }
% 0.62/0.38 ifeq2(product(ifeq2(ifeq(true, true, ifeq(sum(inverse(inverse(x)), x, add(inverse(inverse(x)), x)), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, product(multiplicative_identity, add(inverse(inverse(x)), x), x), true), true), true), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.38 = { by axiom 5 (multiplicative_inverse2) R->L }
% 0.62/0.38 ifeq2(product(ifeq2(ifeq(product(inverse(x), inverse(inverse(x)), additive_identity), true, ifeq(sum(inverse(inverse(x)), x, add(inverse(inverse(x)), x)), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, product(multiplicative_identity, add(inverse(inverse(x)), x), x), true), true), true), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.38 = { by axiom 8 (ifeq_axiom) R->L }
% 0.62/0.38 ifeq2(product(ifeq2(ifeq(product(inverse(x), inverse(inverse(x)), additive_identity), true, ifeq(true, true, ifeq(sum(inverse(inverse(x)), x, add(inverse(inverse(x)), x)), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, product(multiplicative_identity, add(inverse(inverse(x)), x), x), true), true), true), true), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.38 = { by axiom 2 (additive_identity1) R->L }
% 0.62/0.38 ifeq2(product(ifeq2(ifeq(product(inverse(x), inverse(inverse(x)), additive_identity), true, ifeq(sum(additive_identity, x, x), true, ifeq(sum(inverse(inverse(x)), x, add(inverse(inverse(x)), x)), true, ifeq(sum(inverse(x), x, multiplicative_identity), true, product(multiplicative_identity, add(inverse(inverse(x)), x), x), true), true), true), true), true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.38 = { by axiom 13 (distributivity7) }
% 0.62/0.38 ifeq2(product(ifeq2(true, true, x, add(x, inverse(inverse(x)))), multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.38 = { by axiom 7 (ifeq_axiom) }
% 0.62/0.38 ifeq2(product(x, multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x)
% 0.62/0.38 = { by axiom 7 (ifeq_axiom) R->L }
% 0.62/0.38 ifeq2(true, true, ifeq2(product(x, multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x), x)
% 0.62/0.38 = { by axiom 4 (multiplicative_identity2) R->L }
% 0.62/0.38 ifeq2(product(x, multiplicative_identity, x), true, ifeq2(product(x, multiplicative_identity, inverse(inverse(x))), true, inverse(inverse(x)), x), x)
% 0.62/0.38 = { by axiom 12 (multiplication_is_well_defined) }
% 0.62/0.38 x
% 0.62/0.38 % SZS output end Proof
% 0.62/0.38
% 0.62/0.38 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------