%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP710+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 10:11:50 AM UTC 2026
% Result : Theorem 0.14s 0.46s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP710+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.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 10:39:40 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.46 Command-line arguments: --flatten --complete-subsets
% 0.14/0.46
% 0.14/0.46 % SZS status Theorem
% 0.14/0.46
% 0.14/0.47 % SZS output start Proof
% 0.14/0.47 Axiom 1 (f01): mult(X, unit) = X.
% 0.14/0.47 Axiom 2 (f04): mult(X, i(X)) = unit.
% 0.14/0.47 Axiom 3 (f02): mult(unit, X) = X.
% 0.14/0.47 Axiom 4 (f05): mult(i(X), X) = unit.
% 0.14/0.47 Axiom 5 (f03): mult(X, mult(Y, mult(Y, Z))) = mult(mult(mult(X, Y), Y), Z).
% 0.14/0.47
% 0.14/0.47 Lemma 6: mult(mult(X, Y), Y) = mult(X, mult(Y, Y)).
% 0.14/0.47 Proof:
% 0.14/0.47 mult(mult(X, Y), Y)
% 0.14/0.47 = { by axiom 1 (f01) R->L }
% 0.14/0.47 mult(mult(mult(X, Y), Y), unit)
% 0.14/0.47 = { by axiom 5 (f03) R->L }
% 0.14/0.47 mult(X, mult(Y, mult(Y, unit)))
% 0.14/0.47 = { by axiom 1 (f01) }
% 0.14/0.47 mult(X, mult(Y, Y))
% 0.14/0.47
% 0.14/0.47 Lemma 7: mult(i(X), mult(X, mult(X, Y))) = mult(X, Y).
% 0.14/0.47 Proof:
% 0.14/0.47 mult(i(X), mult(X, mult(X, Y)))
% 0.14/0.47 = { by axiom 5 (f03) }
% 0.14/0.47 mult(mult(mult(i(X), X), X), Y)
% 0.14/0.47 = { by axiom 4 (f05) }
% 0.14/0.47 mult(mult(unit, X), Y)
% 0.14/0.47 = { by axiom 3 (f02) }
% 0.14/0.47 mult(X, Y)
% 0.14/0.47
% 0.14/0.47 Lemma 8: mult(X, mult(i(X), mult(i(X), Y))) = mult(i(X), Y).
% 0.14/0.47 Proof:
% 0.14/0.47 mult(X, mult(i(X), mult(i(X), Y)))
% 0.14/0.47 = { by axiom 5 (f03) }
% 0.14/0.47 mult(mult(mult(X, i(X)), i(X)), Y)
% 0.14/0.47 = { by axiom 2 (f04) }
% 0.14/0.47 mult(mult(unit, i(X)), Y)
% 0.14/0.47 = { by axiom 3 (f02) }
% 0.14/0.47 mult(i(X), Y)
% 0.14/0.47
% 0.14/0.47 Lemma 9: mult(i(mult(X, X)), mult(X, mult(X, Y))) = Y.
% 0.14/0.47 Proof:
% 0.14/0.47 mult(i(mult(X, X)), mult(X, mult(X, Y)))
% 0.14/0.47 = { by axiom 5 (f03) }
% 0.14/0.47 mult(mult(mult(i(mult(X, X)), X), X), Y)
% 0.14/0.47 = { by lemma 6 }
% 0.14/0.47 mult(mult(i(mult(X, X)), mult(X, X)), Y)
% 0.14/0.47 = { by axiom 4 (f05) }
% 0.14/0.47 mult(unit, Y)
% 0.14/0.47 = { by axiom 3 (f02) }
% 0.14/0.47 Y
% 0.14/0.47
% 0.14/0.47 Goal 1 (goals): tuple(mult(X, x4), mult(x0, Y)) = tuple(x3, x1).
% 0.14/0.47 The goal is true when:
% 0.14/0.47 X = mult(x3, i(x4))
% 0.14/0.47 Y = mult(i(x0), mult(i(x0), mult(x0, x1)))
% 0.14/0.47
% 0.14/0.47 Proof:
% 0.14/0.47 tuple(mult(mult(x3, i(x4)), x4), mult(x0, mult(i(x0), mult(i(x0), mult(x0, x1)))))
% 0.14/0.47 = { by lemma 8 }
% 0.14/0.47 tuple(mult(mult(x3, i(x4)), x4), mult(i(x0), mult(x0, x1)))
% 0.14/0.47 = { by lemma 9 R->L }
% 0.14/0.47 tuple(mult(mult(x3, i(x4)), x4), mult(i(mult(x0, x0)), mult(x0, mult(x0, mult(i(x0), mult(x0, x1))))))
% 0.14/0.47 = { by lemma 7 R->L }
% 0.14/0.47 tuple(mult(mult(x3, i(x4)), x4), mult(i(mult(x0, x0)), mult(x0, mult(x0, mult(i(x0), mult(i(x0), mult(x0, mult(x0, x1))))))))
% 0.14/0.47 = { by lemma 8 }
% 0.14/0.47 tuple(mult(mult(x3, i(x4)), x4), mult(i(mult(x0, x0)), mult(x0, mult(i(x0), mult(x0, mult(x0, x1))))))
% 0.14/0.47 = { by lemma 7 }
% 0.14/0.47 tuple(mult(mult(x3, i(x4)), x4), mult(i(mult(x0, x0)), mult(x0, mult(x0, x1))))
% 0.14/0.47 = { by lemma 9 }
% 0.14/0.47 tuple(mult(mult(x3, i(x4)), x4), x1)
% 0.14/0.47 = { by axiom 1 (f01) R->L }
% 0.14/0.47 tuple(mult(mult(x3, mult(i(x4), unit)), x4), x1)
% 0.14/0.47 = { by axiom 4 (f05) R->L }
% 0.14/0.47 tuple(mult(mult(x3, mult(i(x4), mult(i(x4), x4))), x4), x1)
% 0.14/0.47 = { by axiom 5 (f03) }
% 0.14/0.47 tuple(mult(mult(mult(mult(x3, i(x4)), i(x4)), x4), x4), x1)
% 0.14/0.47 = { by lemma 6 }
% 0.14/0.47 tuple(mult(mult(mult(x3, i(x4)), i(x4)), mult(x4, x4)), x1)
% 0.14/0.47 = { by axiom 5 (f03) R->L }
% 0.14/0.47 tuple(mult(x3, mult(i(x4), mult(i(x4), mult(x4, x4)))), x1)
% 0.14/0.47 = { by lemma 6 R->L }
% 0.14/0.47 tuple(mult(x3, mult(i(x4), mult(mult(i(x4), x4), x4))), x1)
% 0.14/0.47 = { by axiom 4 (f05) }
% 0.14/0.47 tuple(mult(x3, mult(i(x4), mult(unit, x4))), x1)
% 0.14/0.47 = { by axiom 3 (f02) }
% 0.14/0.47 tuple(mult(x3, mult(i(x4), x4)), x1)
% 0.14/0.47 = { by axiom 4 (f05) }
% 0.14/0.47 tuple(mult(x3, unit), x1)
% 0.14/0.47 = { by axiom 1 (f01) }
% 0.14/0.47 tuple(x3, x1)
% 0.14/0.47 % SZS output end Proof
% 0.14/0.47
% 0.14/0.47 RESULT: Theorem (the conjecture is true).
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