%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP660+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 10:11:37 AM UTC 2026
% Result : Theorem 0.16s 0.62s
% Output : Proof 1.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP660+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n001.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 10:38:45 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.62 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.16/0.62
% 0.16/0.62 % SZS status Theorem
% 0.16/0.62
% 0.16/0.65 % SZS output start Proof
% 0.16/0.65 Axiom 1 (f01): mult(X, ld(X, Y)) = Y.
% 0.16/0.65 Axiom 2 (f03): mult(rd(X, Y), Y) = X.
% 0.16/0.65 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 0.16/0.65 Axiom 4 (f04): rd(mult(X, Y), Y) = X.
% 0.16/0.65 Axiom 5 (f05): mult(mult(mult(X, Y), Z), X) = mult(X, mult(Y, mult(Z, X))).
% 0.16/0.65
% 0.16/0.65 Lemma 6: rd(mult(X, mult(Y, mult(Z, X))), X) = mult(mult(X, Y), Z).
% 0.16/0.65 Proof:
% 0.16/0.65 rd(mult(X, mult(Y, mult(Z, X))), X)
% 0.16/0.65 = { by axiom 5 (f05) R->L }
% 0.16/0.65 rd(mult(mult(mult(X, Y), Z), X), X)
% 0.16/0.65 = { by axiom 4 (f04) }
% 0.16/0.65 mult(mult(X, Y), Z)
% 0.16/0.65
% 0.16/0.66 Lemma 7: rd(rd(mult(X, Y), X), Z) = mult(X, rd(Y, mult(Z, X))).
% 0.16/0.66 Proof:
% 0.16/0.66 rd(rd(mult(X, Y), X), Z)
% 0.16/0.66 = { by axiom 2 (f03) R->L }
% 0.16/0.66 rd(rd(mult(X, mult(rd(Y, mult(Z, X)), mult(Z, X))), X), Z)
% 1.75/0.66 = { by lemma 6 }
% 1.75/0.66 rd(mult(mult(X, rd(Y, mult(Z, X))), Z), Z)
% 1.75/0.66 = { by axiom 4 (f04) }
% 1.75/0.66 mult(X, rd(Y, mult(Z, X)))
% 1.75/0.66
% 1.75/0.66 Lemma 8: ld(rd(X, Y), X) = Y.
% 1.75/0.66 Proof:
% 1.75/0.66 ld(rd(X, Y), X)
% 1.75/0.66 = { by axiom 2 (f03) R->L }
% 1.75/0.66 ld(rd(X, Y), mult(rd(X, Y), Y))
% 1.75/0.66 = { by axiom 3 (f02) }
% 1.75/0.66 Y
% 1.75/0.66
% 1.75/0.66 Lemma 9: mult(X, rd(X, mult(Y, X))) = rd(X, Y).
% 1.75/0.66 Proof:
% 1.75/0.66 mult(X, rd(X, mult(Y, X)))
% 1.75/0.66 = { by lemma 7 R->L }
% 1.75/0.66 rd(rd(mult(X, X), X), Y)
% 1.75/0.66 = { by axiom 4 (f04) }
% 1.75/0.66 rd(X, Y)
% 1.75/0.66
% 1.75/0.66 Lemma 10: rd(X, rd(Y, X)) = mult(X, rd(X, Y)).
% 1.75/0.66 Proof:
% 1.75/0.66 rd(X, rd(Y, X))
% 1.75/0.66 = { by lemma 9 R->L }
% 1.75/0.66 mult(X, rd(X, mult(rd(Y, X), X)))
% 1.75/0.66 = { by axiom 2 (f03) }
% 1.75/0.66 mult(X, rd(X, Y))
% 1.75/0.66
% 1.75/0.66 Lemma 11: rd(X, ld(Y, X)) = Y.
% 1.75/0.66 Proof:
% 1.75/0.66 rd(X, ld(Y, X))
% 1.75/0.66 = { by axiom 1 (f01) R->L }
% 1.75/0.66 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 1.75/0.66 = { by axiom 4 (f04) }
% 1.75/0.66 Y
% 1.75/0.66
% 1.75/0.66 Lemma 12: rd(ld(X, Y), Y) = ld(mult(Y, X), Y).
% 1.75/0.66 Proof:
% 1.75/0.66 rd(ld(X, Y), Y)
% 1.75/0.66 = { by lemma 8 R->L }
% 1.75/0.66 ld(rd(Y, rd(ld(X, Y), Y)), Y)
% 1.75/0.66 = { by lemma 10 }
% 1.75/0.66 ld(mult(Y, rd(Y, ld(X, Y))), Y)
% 1.75/0.66 = { by lemma 11 }
% 1.75/0.66 ld(mult(Y, X), Y)
% 1.75/0.66
% 1.75/0.66 Lemma 13: rd(X, mult(Y, X)) = ld(X, rd(X, Y)).
% 1.75/0.66 Proof:
% 1.75/0.66 rd(X, mult(Y, X))
% 1.75/0.66 = { by axiom 3 (f02) R->L }
% 1.75/0.66 ld(X, mult(X, rd(X, mult(Y, X))))
% 1.75/0.66 = { by lemma 9 }
% 1.75/0.66 ld(X, rd(X, Y))
% 1.75/0.66
% 1.75/0.66 Lemma 14: rd(mult(X, mult(Y, Z)), X) = mult(mult(X, Y), rd(Z, X)).
% 1.75/0.66 Proof:
% 1.75/0.66 rd(mult(X, mult(Y, Z)), X)
% 1.75/0.66 = { by axiom 2 (f03) R->L }
% 1.75/0.66 rd(mult(X, mult(Y, mult(rd(Z, X), X))), X)
% 1.75/0.66 = { by lemma 6 }
% 1.75/0.66 mult(mult(X, Y), rd(Z, X))
% 1.75/0.66
% 1.75/0.66 Lemma 15: mult(mult(X, rd(X, Y)), rd(Y, X)) = X.
% 1.75/0.66 Proof:
% 1.75/0.66 mult(mult(X, rd(X, Y)), rd(Y, X))
% 1.75/0.66 = { by axiom 3 (f02) R->L }
% 1.75/0.66 mult(mult(X, rd(X, Y)), ld(Y, mult(Y, rd(Y, X))))
% 1.75/0.66 = { by lemma 10 R->L }
% 1.75/0.66 mult(mult(X, rd(X, Y)), ld(Y, rd(Y, rd(X, Y))))
% 1.75/0.66 = { by axiom 2 (f03) R->L }
% 1.75/0.66 mult(mult(mult(rd(X, Y), Y), rd(X, Y)), ld(Y, rd(Y, rd(X, Y))))
% 1.75/0.66 = { by lemma 13 R->L }
% 1.75/0.66 mult(mult(mult(rd(X, Y), Y), rd(X, Y)), rd(Y, mult(rd(X, Y), Y)))
% 1.75/0.66 = { by lemma 14 R->L }
% 1.75/0.66 rd(mult(mult(rd(X, Y), Y), mult(rd(X, Y), Y)), mult(rd(X, Y), Y))
% 1.75/0.66 = { by axiom 4 (f04) }
% 1.75/0.66 mult(rd(X, Y), Y)
% 1.75/0.66 = { by axiom 2 (f03) }
% 1.75/0.66 X
% 1.75/0.66
% 1.75/0.66 Lemma 16: ld(rd(X, X), rd(X, X)) = rd(X, X).
% 1.75/0.66 Proof:
% 1.75/0.66 ld(rd(X, X), rd(X, X))
% 1.75/0.66 = { by axiom 4 (f04) R->L }
% 1.75/0.66 ld(rd(X, X), rd(rd(mult(X, rd(X, X)), rd(X, X)), X))
% 1.75/0.66 = { by axiom 1 (f01) R->L }
% 1.75/0.66 ld(rd(X, X), rd(rd(mult(rd(X, X), ld(rd(X, X), mult(X, rd(X, X)))), rd(X, X)), X))
% 1.75/0.66 = { by lemma 7 }
% 1.75/0.66 ld(rd(X, X), mult(rd(X, X), rd(ld(rd(X, X), mult(X, rd(X, X))), mult(X, rd(X, X)))))
% 1.75/0.66 = { by axiom 3 (f02) }
% 1.75/0.66 rd(ld(rd(X, X), mult(X, rd(X, X))), mult(X, rd(X, X)))
% 1.75/0.66 = { by lemma 12 }
% 1.75/0.66 ld(mult(mult(X, rd(X, X)), rd(X, X)), mult(X, rd(X, X)))
% 1.75/0.66 = { by lemma 15 }
% 1.75/0.66 ld(X, mult(X, rd(X, X)))
% 1.75/0.66 = { by axiom 3 (f02) }
% 1.75/0.66 rd(X, X)
% 1.75/0.66
% 1.75/0.66 Lemma 17: mult(rd(X, X), mult(X, rd(X, X))) = X.
% 1.75/0.66 Proof:
% 1.75/0.66 mult(rd(X, X), mult(X, rd(X, X)))
% 1.75/0.66 = { by axiom 1 (f01) R->L }
% 1.75/0.66 mult(rd(X, X), mult(X, mult(rd(X, X), ld(rd(X, X), rd(X, X)))))
% 1.75/0.66 = { by lemma 16 }
% 1.75/0.66 mult(rd(X, X), mult(X, mult(rd(X, X), rd(X, X))))
% 1.75/0.66 = { by axiom 5 (f05) R->L }
% 1.75/0.66 mult(mult(mult(rd(X, X), X), rd(X, X)), rd(X, X))
% 1.75/0.66 = { by axiom 2 (f03) }
% 1.75/0.66 mult(mult(X, rd(X, X)), rd(X, X))
% 1.75/0.66 = { by lemma 15 }
% 1.75/0.66 X
% 1.75/0.66
% 1.75/0.66 Lemma 18: ld(rd(X, X), X) = mult(X, rd(X, X)).
% 1.75/0.66 Proof:
% 1.75/0.66 ld(rd(X, X), X)
% 1.75/0.66 = { by lemma 17 R->L }
% 1.75/0.66 ld(rd(X, X), mult(rd(X, X), mult(X, rd(X, X))))
% 1.75/0.66 = { by axiom 3 (f02) }
% 1.75/0.66 mult(X, rd(X, X))
% 1.75/0.66
% 1.75/0.66 Lemma 19: mult(X, rd(X, X)) = X.
% 1.75/0.66 Proof:
% 1.75/0.66 mult(X, rd(X, X))
% 1.75/0.66 = { by lemma 18 R->L }
% 1.75/0.66 ld(rd(X, X), X)
% 1.75/0.66 = { by lemma 8 }
% 1.75/0.66 X
% 1.75/0.66
% 1.75/0.66 Lemma 20: rd(X, X) = ld(X, X).
% 1.75/0.66 Proof:
% 1.75/0.66 rd(X, X)
% 1.75/0.66 = { by axiom 3 (f02) R->L }
% 1.75/0.66 ld(X, mult(X, rd(X, X)))
% 1.75/0.66 = { by lemma 19 }
% 1.75/0.66 ld(X, X)
% 1.75/0.66
% 1.75/0.66 Lemma 21: mult(ld(X, X), X) = X.
% 1.75/0.66 Proof:
% 1.75/0.66 mult(ld(X, X), X)
% 1.75/0.66 = { by lemma 19 R->L }
% 1.75/0.66 mult(ld(mult(X, rd(X, X)), X), X)
% 1.75/0.66 = { by lemma 12 R->L }
% 1.75/0.66 mult(rd(ld(rd(X, X), X), X), X)
% 1.75/0.66 = { by axiom 2 (f03) }
% 1.75/0.66 ld(rd(X, X), X)
% 1.75/0.66 = { by lemma 18 }
% 1.75/0.66 mult(X, rd(X, X))
% 1.75/0.66 = { by lemma 19 }
% 1.75/0.66 X
% 1.75/0.66
% 1.75/0.66 Lemma 22: mult(mult(X, Y), rd(ld(Y, Z), X)) = rd(mult(X, Z), X).
% 1.75/0.66 Proof:
% 1.75/0.66 mult(mult(X, Y), rd(ld(Y, Z), X))
% 1.75/0.66 = { by lemma 14 R->L }
% 1.75/0.66 rd(mult(X, mult(Y, ld(Y, Z))), X)
% 1.75/0.66 = { by axiom 1 (f01) }
% 1.75/0.66 rd(mult(X, Z), X)
% 1.75/0.66
% 1.75/0.66 Lemma 23: ld(mult(X, Y), rd(mult(X, Z), X)) = rd(ld(Y, Z), X).
% 1.75/0.66 Proof:
% 1.75/0.66 ld(mult(X, Y), rd(mult(X, Z), X))
% 1.75/0.66 = { by lemma 22 R->L }
% 1.75/0.66 ld(mult(X, Y), mult(mult(X, Y), rd(ld(Y, Z), X)))
% 1.75/0.66 = { by axiom 3 (f02) }
% 1.75/0.66 rd(ld(Y, Z), X)
% 1.75/0.66
% 1.75/0.66 Lemma 24: rd(mult(rd(X, Y), Z), rd(X, Y)) = mult(X, rd(ld(Y, Z), rd(X, Y))).
% 1.75/0.66 Proof:
% 1.75/0.66 rd(mult(rd(X, Y), Z), rd(X, Y))
% 1.75/0.66 = { by lemma 22 R->L }
% 1.75/0.66 mult(mult(rd(X, Y), Y), rd(ld(Y, Z), rd(X, Y)))
% 1.75/0.66 = { by axiom 2 (f03) }
% 1.75/0.66 mult(X, rd(ld(Y, Z), rd(X, Y)))
% 1.75/0.66
% 1.75/0.66 Lemma 25: rd(ld(X, Y), ld(Y, Y)) = ld(mult(ld(Y, Y), X), Y).
% 1.75/0.66 Proof:
% 1.75/0.66 rd(ld(X, Y), ld(Y, Y))
% 1.75/0.66 = { by lemma 20 R->L }
% 1.75/0.66 rd(ld(X, Y), rd(Y, Y))
% 1.75/0.66 = { by lemma 19 R->L }
% 1.75/0.66 rd(ld(X, mult(Y, rd(Y, Y))), rd(Y, Y))
% 1.75/0.66 = { by lemma 23 R->L }
% 1.75/0.66 ld(mult(rd(Y, Y), X), rd(mult(rd(Y, Y), mult(Y, rd(Y, Y))), rd(Y, Y)))
% 1.75/0.66 = { by lemma 17 }
% 1.75/0.66 ld(mult(rd(Y, Y), X), rd(Y, rd(Y, Y)))
% 1.75/0.66 = { by lemma 20 }
% 1.75/0.66 ld(mult(ld(Y, Y), X), rd(Y, rd(Y, Y)))
% 1.75/0.66 = { by lemma 20 }
% 1.75/0.66 ld(mult(ld(Y, Y), X), rd(Y, ld(Y, Y)))
% 1.75/0.66 = { by lemma 11 }
% 1.75/0.66 ld(mult(ld(Y, Y), X), Y)
% 1.75/0.66
% 1.75/0.66 Lemma 26: rd(X, ld(Y, Y)) = mult(ld(Y, Y), X).
% 1.75/0.66 Proof:
% 1.75/0.66 rd(X, ld(Y, Y))
% 1.75/0.66 = { by lemma 20 R->L }
% 1.75/0.66 rd(X, rd(Y, Y))
% 1.75/0.66 = { by axiom 1 (f01) R->L }
% 1.75/0.66 mult(Y, ld(Y, rd(X, rd(Y, Y))))
% 1.75/0.66 = { by axiom 2 (f03) R->L }
% 1.75/0.66 mult(Y, ld(mult(rd(Y, Y), Y), rd(X, rd(Y, Y))))
% 1.75/0.66 = { by axiom 1 (f01) R->L }
% 1.75/0.66 mult(Y, ld(mult(rd(Y, Y), Y), rd(mult(rd(Y, Y), ld(rd(Y, Y), X)), rd(Y, Y))))
% 1.75/0.66 = { by lemma 23 }
% 1.75/0.66 mult(Y, rd(ld(Y, ld(rd(Y, Y), X)), rd(Y, Y)))
% 1.75/0.66 = { by lemma 24 R->L }
% 1.75/0.66 rd(mult(rd(Y, Y), ld(rd(Y, Y), X)), rd(Y, Y))
% 1.75/0.66 = { by lemma 16 R->L }
% 1.75/0.66 rd(mult(rd(Y, Y), ld(ld(rd(Y, Y), rd(Y, Y)), X)), rd(Y, Y))
% 1.75/0.66 = { by axiom 2 (f03) R->L }
% 1.75/0.66 rd(mult(rd(Y, Y), mult(rd(ld(ld(rd(Y, Y), rd(Y, Y)), X), rd(Y, Y)), rd(Y, Y))), rd(Y, Y))
% 1.75/0.66 = { by lemma 14 }
% 1.75/0.66 mult(mult(rd(Y, Y), rd(ld(ld(rd(Y, Y), rd(Y, Y)), X), rd(Y, Y))), rd(rd(Y, Y), rd(Y, Y)))
% 1.75/0.66 = { by axiom 1 (f01) R->L }
% 1.75/0.66 mult(mult(mult(rd(Y, Y), ld(rd(Y, Y), rd(Y, Y))), rd(ld(ld(rd(Y, Y), rd(Y, Y)), X), rd(Y, Y))), rd(rd(Y, Y), rd(Y, Y)))
% 1.75/0.66 = { by lemma 22 }
% 1.75/0.66 mult(rd(mult(rd(Y, Y), X), rd(Y, Y)), rd(rd(Y, Y), rd(Y, Y)))
% 1.75/0.66 = { by lemma 24 }
% 1.75/0.66 mult(mult(Y, rd(ld(Y, X), rd(Y, Y))), rd(rd(Y, Y), rd(Y, Y)))
% 1.75/0.66 = { by lemma 20 }
% 1.75/0.66 mult(mult(Y, rd(ld(Y, X), ld(Y, Y))), rd(rd(Y, Y), rd(Y, Y)))
% 1.75/0.67 = { by lemma 20 }
% 1.75/0.67 mult(mult(Y, rd(ld(Y, X), ld(Y, Y))), rd(ld(Y, Y), rd(Y, Y)))
% 1.75/0.67 = { by lemma 20 }
% 1.75/0.67 mult(mult(Y, rd(ld(Y, X), ld(Y, Y))), rd(ld(Y, Y), ld(Y, Y)))
% 1.75/0.67 = { by lemma 25 }
% 1.75/0.67 mult(mult(Y, rd(ld(Y, X), ld(Y, Y))), ld(mult(ld(Y, Y), Y), Y))
% 1.75/0.67 = { by lemma 21 }
% 1.75/0.67 mult(mult(Y, rd(ld(Y, X), ld(Y, Y))), ld(Y, Y))
% 1.75/0.67 = { by axiom 1 (f01) R->L }
% 1.75/0.67 mult(mult(mult(ld(Y, Y), ld(ld(Y, Y), Y)), rd(ld(Y, X), ld(Y, Y))), ld(Y, Y))
% 1.75/0.67 = { by axiom 5 (f05) }
% 1.75/0.67 mult(ld(Y, Y), mult(ld(ld(Y, Y), Y), mult(rd(ld(Y, X), ld(Y, Y)), ld(Y, Y))))
% 1.75/0.67 = { by axiom 2 (f03) }
% 1.75/0.67 mult(ld(Y, Y), mult(ld(ld(Y, Y), Y), ld(Y, X)))
% 1.75/0.67 = { by lemma 11 R->L }
% 1.75/0.67 mult(ld(Y, Y), mult(ld(ld(Y, rd(Y, ld(Y, Y))), Y), ld(Y, X)))
% 1.75/0.67 = { by lemma 13 R->L }
% 1.75/0.67 mult(ld(Y, Y), mult(ld(rd(Y, mult(ld(Y, Y), Y)), Y), ld(Y, X)))
% 1.75/0.67 = { by lemma 8 }
% 1.75/0.67 mult(ld(Y, Y), mult(mult(ld(Y, Y), Y), ld(Y, X)))
% 1.75/0.67 = { by lemma 21 }
% 1.75/0.67 mult(ld(Y, Y), mult(Y, ld(Y, X)))
% 1.75/0.67 = { by axiom 1 (f01) }
% 1.75/0.67 mult(ld(Y, Y), X)
% 1.75/0.67
% 1.75/0.67 Lemma 27: mult(mult(ld(X, X), Y), ld(X, X)) = Y.
% 1.75/0.67 Proof:
% 1.75/0.67 mult(mult(ld(X, X), Y), ld(X, X))
% 1.75/0.67 = { by lemma 26 R->L }
% 1.75/0.67 mult(rd(Y, ld(X, X)), ld(X, X))
% 1.75/0.67 = { by axiom 2 (f03) }
% 1.75/0.67 Y
% 1.75/0.67
% 1.75/0.67 Lemma 28: mult(ld(X, X), Y) = Y.
% 1.75/0.67 Proof:
% 1.75/0.67 mult(ld(X, X), Y)
% 1.75/0.67 = { by lemma 26 R->L }
% 1.75/0.67 rd(Y, ld(X, X))
% 1.75/0.67 = { by axiom 4 (f04) R->L }
% 1.75/0.67 rd(rd(mult(Y, ld(X, X)), ld(X, X)), ld(X, X))
% 1.75/0.67 = { by lemma 26 }
% 1.75/0.67 rd(mult(ld(X, X), mult(Y, ld(X, X))), ld(X, X))
% 1.75/0.67 = { by lemma 14 }
% 1.75/0.67 mult(mult(ld(X, X), Y), rd(ld(X, X), ld(X, X)))
% 1.75/0.67 = { by lemma 25 }
% 1.75/0.67 mult(mult(ld(X, X), Y), ld(mult(ld(X, X), X), X))
% 1.75/0.67 = { by lemma 21 }
% 1.75/0.67 mult(mult(ld(X, X), Y), ld(X, X))
% 1.75/0.67 = { by lemma 27 }
% 1.75/0.67 Y
% 1.75/0.67
% 1.75/0.67 Goal 1 (goals): tuple(mult(X, x1(X)), mult(x1_2(X), X)) = tuple(x1(X), x1_2(X)).
% 1.75/0.67 The goal is true when:
% 1.75/0.67 X = ld(X, X)
% 1.75/0.67
% 1.75/0.67 Proof:
% 1.75/0.67 tuple(mult(ld(X, X), x1(ld(X, X))), mult(x1_2(ld(X, X)), ld(X, X)))
% 1.75/0.67 = { by lemma 28 R->L }
% 1.75/0.67 tuple(mult(ld(X, X), x1(ld(X, X))), mult(mult(ld(X, X), x1_2(ld(X, X))), ld(X, X)))
% 1.75/0.67 = { by lemma 27 }
% 1.75/0.67 tuple(mult(ld(X, X), x1(ld(X, X))), x1_2(ld(X, X)))
% 1.75/0.67 = { by lemma 28 }
% 1.75/0.67 tuple(x1(ld(X, X)), x1_2(ld(X, X)))
% 1.75/0.67 % SZS output end Proof
% 1.75/0.67
% 1.75/0.67 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------