%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : RNG003-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 12:34:43 PM UTC 2026
% Result : Unsatisfiable 0.25s 0.56s
% Output : Proof 0.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39 % Computer : n002.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 23:00:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.56 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
% 0.25/0.56
% 0.25/0.56 % SZS status Unsatisfiable
% 0.25/0.56
% 0.25/0.56 % SZS output start Proof
% 0.25/0.56 Axiom 1 (additive_identity2): sum(X, additive_identity, X) = true.
% 0.25/0.56 Axiom 2 (right_inverse): sum(X, additive_inverse(X), additive_identity) = true.
% 0.25/0.56 Axiom 3 (a_plus_c_is_d): sum(a, c, d) = true.
% 0.25/0.56 Axiom 4 (b_plus_c_is_d): sum(b, c, d) = true.
% 0.25/0.56 Axiom 5 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.25/0.56 Axiom 6 (ifeq_axiom): ifeq2(X, X, Y, Z) = Y.
% 0.25/0.56 Axiom 7 (closure_of_addition): sum(X, Y, add(X, Y)) = true.
% 0.25/0.56 Axiom 8 (addition_is_well_defined): ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, W), true, W, Z), Z) = Z.
% 0.25/0.56 Axiom 9 (associativity_of_addition2): ifeq(sum(X, Y, Z), true, ifeq(sum(W, Z, V), true, ifeq(sum(W, X, U), true, sum(U, Y, V), true), true), true) = true.
% 0.25/0.56
% 0.25/0.56 Lemma 10: ifeq2(sum(X, Y, Z), true, add(X, Y), Z) = Z.
% 0.25/0.56 Proof:
% 0.25/0.56 ifeq2(sum(X, Y, Z), true, add(X, Y), Z)
% 0.25/0.56 = { by axiom 6 (ifeq_axiom) R->L }
% 0.25/0.56 ifeq2(sum(X, Y, Z), true, ifeq2(true, true, add(X, Y), Z), Z)
% 0.25/0.56 = { by axiom 7 (closure_of_addition) R->L }
% 0.25/0.56 ifeq2(sum(X, Y, Z), true, ifeq2(sum(X, Y, add(X, Y)), true, add(X, Y), Z), Z)
% 0.25/0.56 = { by axiom 8 (addition_is_well_defined) }
% 0.25/0.56 Z
% 0.25/0.56
% 0.25/0.56 Goal 1 (prove_a_equals_b): a = b.
% 0.25/0.56 Proof:
% 0.25/0.56 a
% 0.25/0.56 = { by lemma 10 R->L }
% 0.25/0.56 ifeq2(sum(d, additive_inverse(c), a), true, add(d, additive_inverse(c)), a)
% 0.25/0.56 = { by axiom 5 (ifeq_axiom) R->L }
% 0.25/0.56 ifeq2(ifeq(true, true, sum(d, additive_inverse(c), a), true), true, add(d, additive_inverse(c)), a)
% 0.25/0.56 = { by axiom 2 (right_inverse) R->L }
% 0.25/0.56 ifeq2(ifeq(sum(c, additive_inverse(c), additive_identity), true, sum(d, additive_inverse(c), a), true), true, add(d, additive_inverse(c)), a)
% 0.25/0.56 = { by axiom 5 (ifeq_axiom) R->L }
% 0.25/0.56 ifeq2(ifeq(sum(c, additive_inverse(c), additive_identity), true, ifeq(true, true, sum(d, additive_inverse(c), a), true), true), true, add(d, additive_inverse(c)), a)
% 0.25/0.56 = { by axiom 3 (a_plus_c_is_d) R->L }
% 0.25/0.56 ifeq2(ifeq(sum(c, additive_inverse(c), additive_identity), true, ifeq(sum(a, c, d), true, sum(d, additive_inverse(c), a), true), true), true, add(d, additive_inverse(c)), a)
% 0.25/0.56 = { by axiom 5 (ifeq_axiom) R->L }
% 0.25/0.56 ifeq2(ifeq(sum(c, additive_inverse(c), additive_identity), true, ifeq(true, true, ifeq(sum(a, c, d), true, sum(d, additive_inverse(c), a), true), true), true), true, add(d, additive_inverse(c)), a)
% 0.25/0.56 = { by axiom 1 (additive_identity2) R->L }
% 0.25/0.56 ifeq2(ifeq(sum(c, additive_inverse(c), additive_identity), true, ifeq(sum(a, additive_identity, a), true, ifeq(sum(a, c, d), true, sum(d, additive_inverse(c), a), true), true), true), true, add(d, additive_inverse(c)), a)
% 0.25/0.56 = { by axiom 9 (associativity_of_addition2) }
% 0.25/0.56 ifeq2(true, true, add(d, additive_inverse(c)), a)
% 0.25/0.56 = { by axiom 6 (ifeq_axiom) }
% 0.25/0.56 add(d, additive_inverse(c))
% 0.25/0.56 = { by axiom 6 (ifeq_axiom) R->L }
% 0.25/0.56 ifeq2(true, true, add(d, additive_inverse(c)), b)
% 0.25/0.56 = { by axiom 9 (associativity_of_addition2) R->L }
% 0.25/0.56 ifeq2(ifeq(sum(c, additive_inverse(c), additive_identity), true, ifeq(sum(b, additive_identity, b), true, ifeq(sum(b, c, d), true, sum(d, additive_inverse(c), b), true), true), true), true, add(d, additive_inverse(c)), b)
% 0.25/0.56 = { by axiom 1 (additive_identity2) }
% 0.25/0.56 ifeq2(ifeq(sum(c, additive_inverse(c), additive_identity), true, ifeq(true, true, ifeq(sum(b, c, d), true, sum(d, additive_inverse(c), b), true), true), true), true, add(d, additive_inverse(c)), b)
% 0.25/0.56 = { by axiom 5 (ifeq_axiom) }
% 0.25/0.56 ifeq2(ifeq(sum(c, additive_inverse(c), additive_identity), true, ifeq(sum(b, c, d), true, sum(d, additive_inverse(c), b), true), true), true, add(d, additive_inverse(c)), b)
% 0.25/0.56 = { by axiom 4 (b_plus_c_is_d) }
% 0.25/0.56 ifeq2(ifeq(sum(c, additive_inverse(c), additive_identity), true, ifeq(true, true, sum(d, additive_inverse(c), b), true), true), true, add(d, additive_inverse(c)), b)
% 0.25/0.56 = { by axiom 5 (ifeq_axiom) }
% 0.25/0.56 ifeq2(ifeq(sum(c, additive_inverse(c), additive_identity), true, sum(d, additive_inverse(c), b), true), true, add(d, additive_inverse(c)), b)
% 0.25/0.56 = { by axiom 2 (right_inverse) }
% 0.25/0.56 ifeq2(ifeq(true, true, sum(d, additive_inverse(c), b), true), true, add(d, additive_inverse(c)), b)
% 0.25/0.56 = { by axiom 5 (ifeq_axiom) }
% 0.25/0.56 ifeq2(sum(d, additive_inverse(c), b), true, add(d, additive_inverse(c)), b)
% 0.25/0.56 = { by lemma 10 }
% 0.25/0.56 b
% 0.25/0.56 % SZS output end Proof
% 0.25/0.56
% 0.25/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
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