%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG039-1 : 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 12:34:51 PM UTC 2026
% Result : Unsatisfiable 0.57s 0.49s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG039-1 : 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 : n004.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 23:01:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.49 Command-line arguments: --no-flatten-goal
% 0.57/0.49
% 0.57/0.49 % SZS status Unsatisfiable
% 0.57/0.49
% 0.57/0.49 % SZS output start Proof
% 0.57/0.49 Axiom 1 (clause34): add(X, X) = additive_identity.
% 0.57/0.49 Axiom 2 (clause33): add(X, additive_identity) = X.
% 0.57/0.49 Axiom 3 (clause35): multiply(X, X) = X.
% 0.57/0.49 Axiom 4 (clause37): multiply(b, a) = d.
% 0.57/0.49 Axiom 5 (clause71): product(X, X, X) = true.
% 0.57/0.49 Axiom 6 (a_times_b): product(a, b, c) = true.
% 0.57/0.49 Axiom 7 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.57/0.49 Axiom 8 (closure_of_multiplication): product(X, Y, multiply(X, Y)) = true.
% 0.57/0.49 Axiom 9 (clause44): product(a, multiply(b, X), multiply(Y, X)) = true.
% 0.57/0.49 Axiom 10 (clause70): product(add(a, b), a, add(a, d)) = true.
% 0.57/0.49 Axiom 11 (clause67): product(add(a, b), b, add(c, b)) = true.
% 0.57/0.49 Axiom 12 (multiplication_is_well_defined): ifeq2(product(X, Y, Z), true, ifeq2(product(X, Y, W), true, W, Z), Z) = Z.
% 0.57/0.49
% 0.57/0.49 Lemma 13: a = d.
% 0.57/0.49 Proof:
% 0.57/0.49 a
% 0.57/0.49 = { by axiom 12 (multiplication_is_well_defined) R->L }
% 0.57/0.49 ifeq2(product(a, d, a), true, ifeq2(product(a, d, d), true, d, a), a)
% 0.57/0.49 = { by axiom 4 (clause37) R->L }
% 0.57/0.49 ifeq2(product(a, d, a), true, ifeq2(product(a, multiply(b, a), d), true, d, a), a)
% 0.57/0.49 = { by axiom 4 (clause37) R->L }
% 0.57/0.50 ifeq2(product(a, d, a), true, ifeq2(product(a, multiply(b, a), multiply(b, a)), true, d, a), a)
% 0.57/0.50 = { by axiom 9 (clause44) }
% 0.57/0.50 ifeq2(product(a, d, a), true, ifeq2(true, true, d, a), a)
% 0.57/0.50 = { by axiom 7 (ifeq_axiom) }
% 0.57/0.50 ifeq2(product(a, d, a), true, d, a)
% 0.57/0.50 = { by axiom 4 (clause37) R->L }
% 0.57/0.50 ifeq2(product(a, multiply(b, a), a), true, d, a)
% 0.57/0.50 = { by axiom 3 (clause35) R->L }
% 0.57/0.50 ifeq2(product(a, multiply(b, a), multiply(a, a)), true, d, a)
% 0.57/0.50 = { by axiom 9 (clause44) }
% 0.57/0.50 ifeq2(true, true, d, a)
% 0.57/0.50 = { by axiom 7 (ifeq_axiom) }
% 0.57/0.50 d
% 0.57/0.50
% 0.57/0.50 Lemma 14: ifeq2(product(a, b, X), true, c, X) = X.
% 0.57/0.50 Proof:
% 0.57/0.50 ifeq2(product(a, b, X), true, c, X)
% 0.57/0.50 = { by axiom 7 (ifeq_axiom) R->L }
% 0.57/0.50 ifeq2(product(a, b, X), true, ifeq2(true, true, c, X), X)
% 0.57/0.50 = { by axiom 6 (a_times_b) R->L }
% 0.57/0.50 ifeq2(product(a, b, X), true, ifeq2(product(a, b, c), true, c, X), X)
% 0.57/0.50 = { by axiom 12 (multiplication_is_well_defined) }
% 0.57/0.50 X
% 0.57/0.50
% 0.57/0.50 Lemma 15: b = c.
% 0.57/0.50 Proof:
% 0.57/0.50 b
% 0.57/0.50 = { by lemma 14 R->L }
% 0.57/0.50 ifeq2(product(a, b, b), true, c, b)
% 0.57/0.50 = { by axiom 3 (clause35) R->L }
% 0.57/0.50 ifeq2(product(a, multiply(b, b), b), true, c, b)
% 0.57/0.50 = { by axiom 3 (clause35) R->L }
% 0.57/0.50 ifeq2(product(a, multiply(b, b), multiply(b, b)), true, c, b)
% 0.57/0.50 = { by axiom 9 (clause44) }
% 0.57/0.50 ifeq2(true, true, c, b)
% 0.57/0.50 = { by axiom 7 (ifeq_axiom) }
% 0.57/0.50 c
% 0.57/0.50
% 0.57/0.50 Lemma 16: c = additive_identity.
% 0.57/0.50 Proof:
% 0.57/0.50 c
% 0.57/0.50 = { by axiom 7 (ifeq_axiom) R->L }
% 0.57/0.50 ifeq2(true, true, c, additive_identity)
% 0.57/0.50 = { by axiom 11 (clause67) R->L }
% 0.57/0.50 ifeq2(product(add(a, b), b, add(c, b)), true, c, additive_identity)
% 0.57/0.50 = { by lemma 15 }
% 0.57/0.50 ifeq2(product(add(a, c), b, add(c, b)), true, c, additive_identity)
% 0.57/0.50 = { by lemma 15 }
% 0.57/0.50 ifeq2(product(add(a, c), b, add(c, c)), true, c, additive_identity)
% 0.57/0.50 = { by lemma 15 }
% 0.57/0.50 ifeq2(product(add(a, c), c, add(c, c)), true, c, additive_identity)
% 0.57/0.50 = { by axiom 1 (clause34) }
% 0.57/0.50 ifeq2(product(add(a, c), c, additive_identity), true, c, additive_identity)
% 0.57/0.50 = { by axiom 7 (ifeq_axiom) R->L }
% 0.57/0.50 ifeq2(product(add(a, c), c, additive_identity), true, ifeq2(true, true, c, additive_identity), additive_identity)
% 0.57/0.50 = { by axiom 8 (closure_of_multiplication) R->L }
% 0.57/0.50 ifeq2(product(add(a, c), c, additive_identity), true, ifeq2(product(add(a, c), c, multiply(add(a, c), c)), true, c, additive_identity), additive_identity)
% 0.57/0.50 = { by lemma 15 R->L }
% 0.57/0.50 ifeq2(product(add(a, c), c, additive_identity), true, ifeq2(product(add(a, c), c, multiply(add(a, c), b)), true, c, additive_identity), additive_identity)
% 0.57/0.50 = { by lemma 14 R->L }
% 0.57/0.50 ifeq2(product(add(a, c), c, additive_identity), true, ifeq2(product(add(a, c), c, ifeq2(product(a, b, multiply(add(a, c), b)), true, c, multiply(add(a, c), b))), true, c, additive_identity), additive_identity)
% 0.57/0.50 = { by axiom 3 (clause35) R->L }
% 0.57/0.50 ifeq2(product(add(a, c), c, additive_identity), true, ifeq2(product(add(a, c), c, ifeq2(product(a, multiply(b, b), multiply(add(a, c), b)), true, c, multiply(add(a, c), b))), true, c, additive_identity), additive_identity)
% 0.57/0.50 = { by axiom 9 (clause44) }
% 0.57/0.50 ifeq2(product(add(a, c), c, additive_identity), true, ifeq2(product(add(a, c), c, ifeq2(true, true, c, multiply(add(a, c), b))), true, c, additive_identity), additive_identity)
% 0.57/0.50 = { by axiom 7 (ifeq_axiom) }
% 0.57/0.50 ifeq2(product(add(a, c), c, additive_identity), true, ifeq2(product(add(a, c), c, c), true, c, additive_identity), additive_identity)
% 0.57/0.50 = { by axiom 12 (multiplication_is_well_defined) }
% 0.57/0.50 additive_identity
% 0.57/0.50
% 0.57/0.50 Goal 1 (prove_c_equals_d): c = d.
% 0.57/0.50 Proof:
% 0.57/0.50 c
% 0.57/0.50 = { by lemma 16 }
% 0.57/0.50 additive_identity
% 0.57/0.50 = { by axiom 7 (ifeq_axiom) R->L }
% 0.57/0.50 ifeq2(true, true, additive_identity, d)
% 0.57/0.50 = { by axiom 10 (clause70) R->L }
% 0.57/0.50 ifeq2(product(add(a, b), a, add(a, d)), true, additive_identity, d)
% 0.57/0.50 = { by lemma 13 }
% 0.57/0.50 ifeq2(product(add(d, b), a, add(a, d)), true, additive_identity, d)
% 0.57/0.50 = { by lemma 15 }
% 0.57/0.50 ifeq2(product(add(d, c), a, add(a, d)), true, additive_identity, d)
% 0.57/0.50 = { by lemma 13 }
% 0.57/0.50 ifeq2(product(add(d, c), a, add(d, d)), true, additive_identity, d)
% 0.57/0.50 = { by lemma 13 }
% 0.57/0.50 ifeq2(product(add(d, c), d, add(d, d)), true, additive_identity, d)
% 0.57/0.50 = { by axiom 1 (clause34) }
% 0.57/0.50 ifeq2(product(add(d, c), d, additive_identity), true, additive_identity, d)
% 0.57/0.50 = { by lemma 16 }
% 0.57/0.50 ifeq2(product(add(d, additive_identity), d, additive_identity), true, additive_identity, d)
% 0.57/0.50 = { by axiom 2 (clause33) }
% 0.57/0.50 ifeq2(product(d, d, additive_identity), true, additive_identity, d)
% 0.57/0.50 = { by axiom 7 (ifeq_axiom) R->L }
% 0.57/0.50 ifeq2(true, true, ifeq2(product(d, d, additive_identity), true, additive_identity, d), d)
% 0.57/0.50 = { by axiom 5 (clause71) R->L }
% 0.57/0.50 ifeq2(product(d, d, d), true, ifeq2(product(d, d, additive_identity), true, additive_identity, d), d)
% 0.57/0.50 = { by axiom 12 (multiplication_is_well_defined) }
% 0.57/0.50 d
% 0.57/0.50 % SZS output end Proof
% 0.57/0.50
% 0.57/0.50 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------