%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : NUM849+2 : TPTP v9.3.1. Released v4.1.0.
% 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 12:11:17 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM849+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 21:33:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.46 Command-line arguments: --flatten --complete-subsets
% 0.12/0.46
% 0.12/0.46 % SZS status Theorem
% 0.12/0.46
% 0.12/0.46 % SZS output start Proof
% 0.12/0.46 Axiom 1 (ass(cond(61, 0), 0)): vplus(X, Y) = vplus(Y, X).
% 0.12/0.46 Axiom 2 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))): vmul(X, v1) = X.
% 0.12/0.46 Axiom 3 (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).
% 0.12/0.46 Axiom 4 (qu(ind(296), imp(296))): vmul(vmul(vd448, vd449), vd454) = vmul(vd448, vmul(vd449, vd454)).
% 0.12/0.46 Axiom 5 (ass(cond(281, 0), 0)): vmul(X, vplus(Y, Z)) = vplus(vmul(X, Y), vmul(X, Z)).
% 0.12/0.46
% 0.12/0.46 Lemma 6: vplus(X, vmul(X, Y)) = vmul(X, vsucc(Y)).
% 0.12/0.46 Proof:
% 0.12/0.46 vplus(X, vmul(X, Y))
% 0.12/0.46 = { by axiom 1 (ass(cond(61, 0), 0)) R->L }
% 0.12/0.46 vplus(vmul(X, Y), X)
% 0.12/0.46 = { by axiom 3 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))_1) R->L }
% 0.12/0.46 vmul(X, vsucc(Y))
% 0.12/0.46
% 0.12/0.46 Goal 1 (qu(ind(296), imp(296))_1): vmul(vmul(vd448, vd449), vsucc(vd454)) = vmul(vd448, vmul(vd449, vsucc(vd454))).
% 0.12/0.46 Proof:
% 0.12/0.46 vmul(vmul(vd448, vd449), vsucc(vd454))
% 0.12/0.46 = { by axiom 2 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) R->L }
% 0.12/0.46 vmul(vmul(vd448, vmul(vd449, v1)), vsucc(vd454))
% 0.12/0.46 = { by lemma 6 R->L }
% 0.12/0.46 vplus(vmul(vd448, vmul(vd449, v1)), vmul(vmul(vd448, vmul(vd449, v1)), vd454))
% 0.12/0.46 = { by axiom 2 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) }
% 0.12/0.46 vplus(vmul(vd448, vmul(vd449, v1)), vmul(vmul(vd448, vd449), vd454))
% 0.12/0.46 = { by axiom 4 (qu(ind(296), imp(296))) }
% 0.12/0.46 vplus(vmul(vd448, vmul(vd449, v1)), vmul(vd448, vmul(vd449, vd454)))
% 0.12/0.46 = { by axiom 2 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) }
% 0.12/0.46 vplus(vmul(vd448, vd449), vmul(vd448, vmul(vd449, vd454)))
% 0.12/0.46 = { by axiom 5 (ass(cond(281, 0), 0)) R->L }
% 0.12/0.46 vmul(vd448, vplus(vd449, vmul(vd449, vd454)))
% 0.12/0.46 = { by axiom 2 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) R->L }
% 0.12/0.46 vmul(vd448, vplus(vmul(vd449, v1), vmul(vd449, vd454)))
% 0.12/0.46 = { by axiom 2 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) R->L }
% 0.12/0.46 vmul(vd448, vplus(vmul(vd449, v1), vmul(vmul(vd449, v1), vd454)))
% 0.12/0.46 = { by lemma 6 }
% 0.12/0.46 vmul(vd448, vmul(vmul(vd449, v1), vsucc(vd454)))
% 0.12/0.46 = { by axiom 2 (qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) }
% 0.12/0.46 vmul(vd448, vmul(vd449, vsucc(vd454)))
% 0.12/0.46 % SZS output end Proof
% 0.12/0.46
% 0.12/0.46 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------