%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : NUM845+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:11:16 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM845+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 21:30:33 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.45 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-regeneralise
% 0.14/0.45
% 0.14/0.45 % SZS status Theorem
% 0.14/0.45
% 0.14/0.45 % SZS output start Proof
% 0.14/0.45 Axiom 1 (ass(cond(61, 0), 0)): vplus(X, Y) = vplus(Y, X).
% 0.14/0.45 Axiom 2 (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))_1): vplus(X, vsucc(Y)) = vsucc(vplus(X, Y)).
% 0.14/0.45 Axiom 3 (ass(cond(33, 0), 0)): vplus(vplus(X, Y), Z) = vplus(X, vplus(Y, Z)).
% 0.14/0.45 Axiom 4 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))_1): vmul(X, vsucc(Y)) = vplus(vmul(X, Y), X).
% 0.14/0.45 Axiom 5 (qu(ind(267), imp(267))): vmul(vsucc(vd411), vd416) = vplus(vmul(vd411, vd416), vd416).
% 0.14/0.45 Axiom 6 (ifeq_axiom): ifeq(X, X, Y, Z) = Y.
% 0.14/0.45 Axiom 7 (ass(cond(conseq(263), 1), 3)): ifeq(vmul(vsucc(vd411), X), vplus(vmul(vd411, X), X), vplus(vmul(vd411, X), vplus(vsucc(vd411), X)), vplus(vmul(vd411, X), vsucc(vplus(vd411, X)))) = vplus(vmul(vd411, X), vsucc(vplus(vd411, X))).
% 0.14/0.45
% 0.14/0.45 Lemma 8: vplus(X, vmul(X, Y)) = vmul(X, vsucc(Y)).
% 0.14/0.45 Proof:
% 0.14/0.45 vplus(X, vmul(X, Y))
% 0.14/0.45 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 0.14/0.45 vplus(vmul(X, Y), X)
% 0.14/0.45 = { by axiom 4 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))_1) R->L }
% 0.14/0.45 vmul(X, vsucc(Y))
% 0.14/0.45
% 0.14/0.45 Lemma 9: vplus(vd416, vmul(vd411, vd416)) = vmul(vsucc(vd411), vd416).
% 0.14/0.45 Proof:
% 0.14/0.45 vplus(vd416, vmul(vd411, vd416))
% 0.14/0.45 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 0.14/0.45 vplus(vmul(vd411, vd416), vd416)
% 0.14/0.45 = { by axiom 5 (qu(ind(267), imp(267))) R->L }
% 0.14/0.45 vmul(vsucc(vd411), vd416)
% 0.14/0.45
% 0.14/0.45 Goal 1 (qu(ind(267), imp(267))_1): vmul(vsucc(vd411), vsucc(vd416)) = vplus(vmul(vd411, vsucc(vd416)), vsucc(vd416)).
% 0.14/0.45 Proof:
% 0.14/0.45 vmul(vsucc(vd411), vsucc(vd416))
% 0.14/0.45 = { by lemma 8 R->L }
% 0.14/0.45 vplus(vsucc(vd411), vmul(vsucc(vd411), vd416))
% 0.14/0.45 = { by axiom 6 (ifeq_axiom) R->L }
% 0.14/0.45 ifeq(vmul(vsucc(vd411), vd416), vmul(vsucc(vd411), vd416), vplus(vsucc(vd411), vmul(vsucc(vd411), vd416)), vplus(vd411, vplus(vsucc(vd416), vmul(vd411, vd416))))
% 0.14/0.45 = { by lemma 9 R->L }
% 0.14/0.45 ifeq(vmul(vsucc(vd411), vd416), vmul(vsucc(vd411), vd416), vplus(vsucc(vd411), vplus(vd416, vmul(vd411, vd416))), vplus(vd411, vplus(vsucc(vd416), vmul(vd411, vd416))))
% 0.14/0.45 = { by lemma 9 R->L }
% 0.14/0.45 ifeq(vmul(vsucc(vd411), vd416), vplus(vd416, vmul(vd411, vd416)), vplus(vsucc(vd411), vplus(vd416, vmul(vd411, vd416))), vplus(vd411, vplus(vsucc(vd416), vmul(vd411, vd416))))
% 0.14/0.45 = { by axiom 3 (ass(cond(33, 0), 0)) R->L }
% 0.14/0.45 ifeq(vmul(vsucc(vd411), vd416), vplus(vd416, vmul(vd411, vd416)), vplus(vsucc(vd411), vplus(vd416, vmul(vd411, vd416))), vplus(vplus(vd411, vsucc(vd416)), vmul(vd411, vd416)))
% 0.14/0.45 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 0.14/0.45 ifeq(vmul(vsucc(vd411), vd416), vplus(vd416, vmul(vd411, vd416)), vplus(vsucc(vd411), vplus(vd416, vmul(vd411, vd416))), vplus(vmul(vd411, vd416), vplus(vd411, vsucc(vd416))))
% 0.14/0.45 = { by axiom 3 (ass(cond(33, 0), 0)) R->L }
% 0.14/0.45 ifeq(vmul(vsucc(vd411), vd416), vplus(vd416, vmul(vd411, vd416)), vplus(vplus(vsucc(vd411), vd416), vmul(vd411, vd416)), vplus(vmul(vd411, vd416), vplus(vd411, vsucc(vd416))))
% 0.14/0.45 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 0.14/0.45 ifeq(vmul(vsucc(vd411), vd416), vplus(vd416, vmul(vd411, vd416)), vplus(vmul(vd411, vd416), vplus(vsucc(vd411), vd416)), vplus(vmul(vd411, vd416), vplus(vd411, vsucc(vd416))))
% 0.14/0.45 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 0.14/0.45 ifeq(vmul(vsucc(vd411), vd416), vplus(vmul(vd411, vd416), vd416), vplus(vmul(vd411, vd416), vplus(vsucc(vd411), vd416)), vplus(vmul(vd411, vd416), vplus(vd411, vsucc(vd416))))
% 0.14/0.45 = { by axiom 2 (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))_1) }
% 0.14/0.45 ifeq(vmul(vsucc(vd411), vd416), vplus(vmul(vd411, vd416), vd416), vplus(vmul(vd411, vd416), vplus(vsucc(vd411), vd416)), vplus(vmul(vd411, vd416), vsucc(vplus(vd411, vd416))))
% 0.14/0.45 = { by axiom 7 (ass(cond(conseq(263), 1), 3)) }
% 0.14/0.45 vplus(vmul(vd411, vd416), vsucc(vplus(vd411, vd416)))
% 0.14/0.45 = { by axiom 2 (qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))_1) R->L }
% 0.14/0.45 vplus(vmul(vd411, vd416), vplus(vd411, vsucc(vd416)))
% 0.14/0.45 = { by axiom 1 (ass(cond(61, 0), 0)) }
% 0.14/0.45 vplus(vplus(vd411, vsucc(vd416)), vmul(vd411, vd416))
% 0.14/0.45 = { by axiom 3 (ass(cond(33, 0), 0)) }
% 0.14/0.45 vplus(vd411, vplus(vsucc(vd416), vmul(vd411, vd416)))
% 0.14/0.46 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 0.14/0.46 vplus(vd411, vplus(vmul(vd411, vd416), vsucc(vd416)))
% 0.14/0.46 = { by axiom 3 (ass(cond(33, 0), 0)) R->L }
% 0.14/0.46 vplus(vplus(vd411, vmul(vd411, vd416)), vsucc(vd416))
% 0.14/0.46 = { by axiom 1 (ass(cond(61, 0), 0)) }
% 0.14/0.46 vplus(vsucc(vd416), vplus(vd411, vmul(vd411, vd416)))
% 0.14/0.46 = { by lemma 8 }
% 0.14/0.46 vplus(vsucc(vd416), vmul(vd411, vsucc(vd416)))
% 0.14/0.46 = { by axiom 1 (ass(cond(61, 0), 0)) }
% 0.14/0.46 vplus(vmul(vd411, vsucc(vd416)), vsucc(vd416))
% 0.14/0.46 % SZS output end Proof
% 0.14/0.46
% 0.14/0.46 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------