%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP700+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 10:11:46 AM UTC 2026
% Result : Theorem 0.13s 0.48s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP700+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.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 10:37:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.48 Command-line arguments: --no-flatten-goal
% 0.13/0.48
% 0.13/0.48 % SZS status Theorem
% 0.13/0.48
% 0.13/0.48 % SZS output start Proof
% 0.13/0.48 Axiom 1 (f05): mult(X, unit) = X.
% 0.13/0.48 Axiom 2 (f06): mult(unit, X) = X.
% 0.13/0.48 Axiom 3 (f04): rd(mult(X, Y), Y) = X.
% 0.13/0.48 Axiom 4 (f03): mult(rd(X, Y), Y) = X.
% 0.13/0.48 Axiom 5 (f07): mult(mult(mult(X, Y), X), mult(X, Z)) = mult(X, mult(mult(mult(Y, X), X), Z)).
% 0.13/0.48
% 0.13/0.48 Goal 1 (goals): tuple(mult(X, x0), mult(x0, X)) = tuple(unit, unit).
% 0.13/0.48 The goal is true when:
% 0.13/0.48 X = rd(unit, x0)
% 0.13/0.48
% 0.13/0.48 Proof:
% 0.13/0.48 tuple(mult(rd(unit, x0), x0), mult(x0, rd(unit, x0)))
% 0.13/0.48 = { by axiom 3 (f04) R->L }
% 0.13/0.48 tuple(mult(rd(unit, x0), x0), rd(mult(mult(x0, rd(unit, x0)), x0), x0))
% 0.13/0.48 = { by axiom 3 (f04) R->L }
% 0.13/0.48 tuple(mult(rd(unit, x0), x0), rd(rd(mult(mult(mult(x0, rd(unit, x0)), x0), x0), x0), x0))
% 0.13/0.48 = { by axiom 1 (f05) R->L }
% 0.13/0.48 tuple(mult(rd(unit, x0), x0), rd(rd(mult(mult(mult(x0, rd(unit, x0)), x0), mult(x0, unit)), x0), x0))
% 0.13/0.48 = { by axiom 5 (f07) }
% 0.13/0.48 tuple(mult(rd(unit, x0), x0), rd(rd(mult(x0, mult(mult(mult(rd(unit, x0), x0), x0), unit)), x0), x0))
% 0.13/0.48 = { by axiom 1 (f05) }
% 0.13/0.48 tuple(mult(rd(unit, x0), x0), rd(rd(mult(x0, mult(mult(rd(unit, x0), x0), x0)), x0), x0))
% 0.13/0.48 = { by axiom 4 (f03) }
% 0.13/0.48 tuple(mult(rd(unit, x0), x0), rd(rd(mult(x0, mult(unit, x0)), x0), x0))
% 0.13/0.48 = { by axiom 2 (f06) }
% 0.13/0.48 tuple(mult(rd(unit, x0), x0), rd(rd(mult(x0, x0), x0), x0))
% 0.13/0.48 = { by axiom 3 (f04) }
% 0.13/0.48 tuple(mult(rd(unit, x0), x0), rd(x0, x0))
% 0.13/0.48 = { by axiom 2 (f06) R->L }
% 0.13/0.48 tuple(mult(rd(unit, x0), x0), rd(mult(unit, x0), x0))
% 0.13/0.48 = { by axiom 3 (f04) }
% 0.13/0.48 tuple(mult(rd(unit, x0), x0), unit)
% 0.13/0.48 = { by axiom 4 (f03) }
% 0.13/0.48 tuple(unit, unit)
% 0.13/0.48 % SZS output end Proof
% 0.13/0.48
% 0.13/0.48 RESULT: Theorem (the conjecture is true).
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