TSTP Solution File: GRP684-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP684-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:16:02 EDT 2023
% Result : Unsatisfiable 2.97s 3.21s
% Output : CNFRefutation 2.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP684-1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : toma --casc %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 21:39:55 EDT 2023
% 0.14/0.35 % CPUTime :
% 2.97/3.21 % SZS status Unsatisfiable
% 2.97/3.21 % SZS output start Proof
% 2.97/3.21 original problem:
% 2.97/3.21 axioms:
% 2.97/3.21 ld(A, mult(A, A)) = A
% 2.97/3.21 rd(mult(A, A), A) = A
% 2.97/3.21 mult(A, ld(A, B)) = ld(A, mult(A, B))
% 2.97/3.21 mult(rd(A, B), B) = rd(mult(A, B), B)
% 2.97/3.21 ld(ld(A, B), mult(ld(A, B), mult(C, D))) = mult(ld(A, mult(A, C)), D)
% 2.97/3.21 rd(mult(mult(A, B), rd(C, D)), rd(C, D)) = mult(A, rd(mult(B, D), D))
% 2.97/3.21 ld(A, mult(A, ld(B, B))) = rd(mult(rd(A, A), B), B)
% 2.97/3.21 goal:
% 2.97/3.21 rd(mult(a(), mult(b(), c())), mult(b(), c())) != rd(mult(a(), c()), c())
% 2.97/3.21 To show the unsatisfiability of the original goal,
% 2.97/3.21 it suffices to show that rd(mult(a(), mult(b(), c())), mult(b(), c())) = rd(mult(a(), c()), c()) (skolemized goal) is valid under the axioms.
% 2.97/3.21 Here is an equational proof:
% 2.97/3.21 0: ld(X0, mult(X0, X0)) = X0.
% 2.97/3.21 Proof: Axiom.
% 2.97/3.21
% 2.97/3.21 1: rd(mult(X0, X0), X0) = X0.
% 2.97/3.21 Proof: Axiom.
% 2.97/3.21
% 2.97/3.21 2: mult(X0, ld(X0, X1)) = ld(X0, mult(X0, X1)).
% 2.97/3.21 Proof: Axiom.
% 2.97/3.21
% 2.97/3.21 3: mult(rd(X0, X1), X1) = rd(mult(X0, X1), X1).
% 2.97/3.21 Proof: Axiom.
% 2.97/3.21
% 2.97/3.21 4: ld(ld(X0, X1), mult(ld(X0, X1), mult(X2, X3))) = mult(ld(X0, mult(X0, X2)), X3).
% 2.97/3.21 Proof: Axiom.
% 2.97/3.21
% 2.97/3.21 5: rd(mult(mult(X0, X1), rd(X2, X3)), rd(X2, X3)) = mult(X0, rd(mult(X1, X3), X3)).
% 2.97/3.22 Proof: Axiom.
% 2.97/3.22
% 2.97/3.22 6: ld(X0, mult(X0, ld(X1, X1))) = rd(mult(rd(X0, X0), X1), X1).
% 2.97/3.22 Proof: Axiom.
% 2.97/3.22
% 2.97/3.22 7: mult(X0, ld(X0, X0)) = X0.
% 2.97/3.22 Proof: Rewrite equation 0,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 8: mult(rd(X0, X0), X0) = X0.
% 2.97/3.22 Proof: Rewrite equation 1,
% 2.97/3.22 lhs with equations [3]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 9: mult(ld(X0, X1), ld(ld(X0, X1), mult(X2, X3))) = mult(mult(X0, ld(X0, X2)), X3).
% 2.97/3.22 Proof: Rewrite equation 4,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 10: mult(rd(mult(X0, X1), rd(X2, X3)), rd(X2, X3)) = mult(X0, mult(rd(X1, X3), X3)).
% 2.97/3.22 Proof: Rewrite equation 5,
% 2.97/3.22 lhs with equations [3]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 11: mult(X0, ld(X0, ld(X1, X1))) = mult(rd(rd(X0, X0), X1), X1).
% 2.97/3.22 Proof: Rewrite equation 6,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 12: mult(X2, ld(X2, ld(X2, X2))) = ld(X2, X2).
% 2.97/3.22 Proof: A critical pair between equations 2 and 7.
% 2.97/3.22
% 2.97/3.22 13: mult(rd(rd(X2, X2), X2), X2) = rd(X2, X2).
% 2.97/3.22 Proof: A critical pair between equations 3 and 8.
% 2.97/3.22
% 2.97/3.22 19: mult(mult(X0, ld(X0, rd(X4, X4))), X4) = mult(ld(X0, X1), ld(ld(X0, X1), X4)).
% 2.97/3.22 Proof: A critical pair between equations 9 and 8.
% 2.97/3.22
% 2.97/3.22 20: mult(X4, mult(rd(ld(X4, X4), X3), X3)) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 2.97/3.22 Proof: A critical pair between equations 10 and 7.
% 2.97/3.22
% 2.97/3.22 21: mult(rd(X4, X4), mult(rd(X4, X3), X3)) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 2.97/3.22 Proof: A critical pair between equations 10 and 8.
% 2.97/3.22
% 2.97/3.22 22: mult(mult(X4, ld(X4, X2)), X3) = mult(ld(X4, mult(X4, X5)), ld(mult(X4, ld(X4, X5)), mult(X2, X3))).
% 2.97/3.22 Proof: A critical pair between equations 9 and 2.
% 2.97/3.22
% 2.97/3.22 28: ld(X2, X2) = rd(X2, X2).
% 2.97/3.22 Proof: Rewrite equation 13,
% 2.97/3.22 lhs with equations [11,12]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 30: ld(X0, mult(X0, ld(X1, X1))) = rd(mult(ld(X0, X0), X1), X1).
% 2.97/3.22 Proof: Rewrite equation 11,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [28,3].
% 2.97/3.22
% 2.97/3.22 31: rd(mult(mult(X0, X1), rd(X2, X3)), rd(X2, X3)) = mult(X0, rd(mult(X1, X3), X3)).
% 2.97/3.22 Proof: Rewrite equation 10,
% 2.97/3.22 lhs with equations [3]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 32: mult(ld(X0, X0), X0) = X0.
% 2.97/3.22 Proof: Rewrite equation 8,
% 2.97/3.22 lhs with equations [28]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 33: ld(X0, mult(X0, X0)) = X0.
% 2.97/3.22 Proof: Rewrite equation 7,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 34: mult(ld(X4, mult(X4, X2)), X3) = ld(ld(X4, mult(X4, X5)), mult(ld(X4, mult(X4, X5)), mult(X2, X3))).
% 2.97/3.22 Proof: Rewrite equation 22,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [2,2].
% 2.97/3.22
% 2.97/3.22 35: mult(ld(X4, X4), rd(mult(X4, X3), X3)) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 2.97/3.22 Proof: Rewrite equation 21,
% 2.97/3.22 lhs with equations [28,3]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 36: ld(X4, mult(X4, mult(X4, ld(X3, X3)))) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 2.97/3.22 Proof: Rewrite equation 20,
% 2.97/3.22 lhs with equations [3,30,2]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 37: mult(ld(X0, mult(X0, ld(X4, X4))), X4) = ld(ld(X0, X1), mult(ld(X0, X1), X4)).
% 2.97/3.22 Proof: Rewrite equation 19,
% 2.97/3.22 lhs with equations [28,2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 48: mult(ld(X6, mult(X6, X2)), X3) = ld(X6, mult(ld(X6, mult(X6, X6)), mult(X2, X3))).
% 2.97/3.22 Proof: A critical pair between equations 34 and 33.
% 2.97/3.22
% 2.97/3.22 49: ld(ld(X6, mult(X6, X5)), mult(ld(X6, mult(X6, X5)), mult(X6, X3))) = mult(X6, X3).
% 2.97/3.22 Proof: A critical pair between equations 34 and 33.
% 2.97/3.22
% 2.97/3.22 50: mult(ld(X5, X5), rd(mult(X5, X7), X7)) = ld(X5, mult(X5, mult(X5, ld(X7, X7)))).
% 2.97/3.22 Proof: A critical pair between equations 35 and 36.
% 2.97/3.22
% 2.97/3.22 51: rd(mult(X6, rd(X2, X6)), rd(X2, X6)) = ld(X6, mult(X6, ld(X6, mult(X6, X6)))).
% 2.97/3.22 Proof: A critical pair between equations 36 and 2.
% 2.97/3.22
% 2.97/3.22 52: mult(rd(X6, rd(X2, X6)), rd(X2, X6)) = X6.
% 2.97/3.22 Proof: Rewrite equation 51,
% 2.97/3.22 lhs with equations [3]
% 2.97/3.22 rhs with equations [33,33].
% 2.97/3.22
% 2.97/3.22 53: mult(ld(X5, X5), mult(rd(X5, X7), X7)) = mult(X5, mult(X5, ld(X5, ld(X7, X7)))).
% 2.97/3.22 Proof: Rewrite equation 50,
% 2.97/3.22 lhs with equations [3]
% 2.97/3.22 rhs with equations [2,2].
% 2.97/3.22
% 2.97/3.22 54: mult(mult(X6, ld(X6, X5)), ld(mult(X6, ld(X6, X5)), mult(X6, X3))) = mult(X6, X3).
% 2.97/3.22 Proof: Rewrite equation 49,
% 2.97/3.22 lhs with equations [2,2,2]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 55: mult(mult(X6, ld(X6, X2)), X3) = mult(X6, ld(X6, mult(X2, X3))).
% 2.97/3.22 Proof: Rewrite equation 48,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [33,2].
% 2.97/3.22
% 2.97/3.22 59: mult(X0, ld(X0, X0)) = X0.
% 2.97/3.22 Proof: Rewrite equation 33,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 60: mult(mult(X0, X1), mult(mult(X0, X1), ld(mult(X0, X1), ld(X3, X3)))) = mult(X0, mult(rd(X1, X3), X3)).
% 2.97/3.22 Proof: Rewrite equation 31,
% 2.97/3.22 lhs with equations [36,2,2]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 61: mult(X0, ld(X0, ld(X1, X1))) = mult(rd(ld(X0, X0), X1), X1).
% 2.97/3.22 Proof: Rewrite equation 30,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 63: mult(X4, mult(X4, ld(X4, ld(X3, X3)))) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 2.97/3.22 Proof: Rewrite equation 35,
% 2.97/3.22 lhs with equations [3,53]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 66: mult(mult(X0, ld(X0, ld(X4, X4))), X4) = mult(ld(X0, X1), ld(ld(X0, X1), X4)).
% 2.97/3.22 Proof: Rewrite equation 37,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 69: X9 = mult(X9, mult(X9, ld(X9, ld(X9, X9)))).
% 2.97/3.22 Proof: A critical pair between equations 52 and 63.
% 2.97/3.22
% 2.97/3.22 70: mult(X2, ld(X2, ld(X2, X2))) = ld(X2, X2).
% 2.97/3.22 Proof: A critical pair between equations 2 and 59.
% 2.97/3.22
% 2.97/3.22 74: X8 = mult(rd(X8, mult(rd(X7, X8), X8)), rd(mult(X7, X8), X8)).
% 2.97/3.22 Proof: A critical pair between equations 52 and 3.
% 2.97/3.22
% 2.97/3.22 76: mult(X7, X3) = mult(X7, ld(mult(X7, ld(X7, X7)), mult(X7, X3))).
% 2.97/3.22 Proof: A critical pair between equations 54 and 59.
% 2.97/3.22
% 2.97/3.22 77: mult(mult(X6, ld(X6, X7)), ld(X7, X7)) = mult(X6, ld(X6, X7)).
% 2.97/3.22 Proof: A critical pair between equations 55 and 59.
% 2.97/3.22
% 2.97/3.22 80: mult(ld(X6, mult(X6, X7)), rd(X7, X7)) = ld(X6, mult(X6, X7)).
% 2.97/3.22 Proof: Rewrite equation 77,
% 2.97/3.22 lhs with equations [2,28]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 81: mult(X7, X3) = mult(X7, ld(mult(X7, rd(X7, X7)), mult(X7, X3))).
% 2.97/3.22 Proof: Rewrite equation 76,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [28].
% 2.97/3.22
% 2.97/3.22 83: X8 = ld(X8, mult(X8, mult(X8, rd(X8, X8)))).
% 2.97/3.22 Proof: Rewrite equation 74,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [3,63,28,2,2].
% 2.97/3.22
% 2.97/3.22 86: ld(X2, mult(X2, rd(X2, X2))) = rd(X2, X2).
% 2.97/3.22 Proof: Rewrite equation 70,
% 2.97/3.22 lhs with equations [28,2]
% 2.97/3.22 rhs with equations [28].
% 2.97/3.22
% 2.97/3.22 87: X9 = mult(X9, rd(X9, X9)).
% 2.97/3.22 Proof: Rewrite equation 69,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [28,2,86].
% 2.97/3.22
% 2.97/3.22 89: ld(X4, mult(X4, mult(X4, rd(X3, X3)))) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 2.97/3.22 Proof: Rewrite equation 63,
% 2.97/3.22 lhs with equations [28,2,2]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 91: ld(X0, mult(X0, rd(X1, X1))) = rd(mult(rd(X0, X0), X1), X1).
% 2.97/3.22 Proof: Rewrite equation 61,
% 2.97/3.22 lhs with equations [28,2]
% 2.97/3.22 rhs with equations [28,3].
% 2.97/3.22
% 2.97/3.22 92: rd(mult(X0, X0), X0) = X0.
% 2.97/3.22 Proof: Rewrite equation 32,
% 2.97/3.22 lhs with equations [28,3]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 95: mult(ld(X6, mult(X6, X2)), X3) = ld(X6, mult(X6, mult(X2, X3))).
% 2.97/3.22 Proof: Rewrite equation 55,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 98: rd(mult(X6, rd(X2, X6)), rd(X2, X6)) = X6.
% 2.97/3.22 Proof: Rewrite equation 52,
% 2.97/3.22 lhs with equations [3]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 99: ld(X0, mult(X0, X4)) = ld(ld(X0, X1), mult(ld(X0, X1), X4)).
% 2.97/3.22 Proof: Rewrite equation 66,
% 2.97/3.22 lhs with equations [28,2,95,3,92]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 100: ld(mult(X0, X1), mult(mult(X0, X1), mult(mult(X0, X1), rd(X3, X3)))) = mult(X0, rd(mult(X1, X3), X3)).
% 2.97/3.22 Proof: Rewrite equation 60,
% 2.97/3.22 lhs with equations [28,2,2]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 101: X10 = ld(X10, mult(X10, X10)).
% 2.97/3.22 Proof: A critical pair between equations 83 and 87.
% 2.97/3.22
% 2.97/3.22 102: X10 = rd(X10, rd(X10, X10)).
% 2.97/3.22 Proof: A critical pair between equations 98 and 87.
% 2.97/3.22
% 2.97/3.22 103: mult(X10, X3) = mult(X10, ld(X10, mult(X10, X3))).
% 2.97/3.22 Proof: A critical pair between equations 81 and 87.
% 2.97/3.22
% 2.97/3.22 106: ld(X3, mult(X3, X3)) = mult(X3, rd(X3, X3)).
% 2.97/3.22 Proof: A critical pair between equations 2 and 28.
% 2.97/3.22
% 2.97/3.22 114: X3 = mult(X3, ld(X3, X3)).
% 2.97/3.22 Proof: Rewrite equation 106,
% 2.97/3.22 lhs with equations [101]
% 2.97/3.22 rhs with equations [28].
% 2.97/3.22
% 2.97/3.22 115: mult(X10, X3) = mult(X10, mult(X10, ld(X10, X3))).
% 2.97/3.22 Proof: Rewrite equation 103,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 116: X10 = rd(X10, ld(X10, X10)).
% 2.97/3.22 Proof: Rewrite equation 102,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [28].
% 2.97/3.22
% 2.97/3.22 117: mult(X0, ld(X0, X4)) = mult(ld(X0, X1), ld(ld(X0, X1), X4)).
% 2.97/3.22 Proof: Rewrite equation 99,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 121: mult(mult(X6, ld(X6, X2)), X3) = mult(X6, ld(X6, mult(X2, X3))).
% 2.97/3.22 Proof: Rewrite equation 95,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 123: mult(ld(X0, X0), X0) = X0.
% 2.97/3.22 Proof: Rewrite equation 92,
% 2.97/3.22 lhs with equations [3,28]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 124: mult(X0, ld(X0, ld(X1, X1))) = mult(rd(ld(X0, X0), X1), X1).
% 2.97/3.22 Proof: Rewrite equation 91,
% 2.97/3.22 lhs with equations [28,2]
% 2.97/3.22 rhs with equations [28,3].
% 2.97/3.22
% 2.97/3.22 126: mult(mult(X6, ld(X6, X7)), ld(X7, X7)) = mult(X6, ld(X6, X7)).
% 2.97/3.22 Proof: Rewrite equation 80,
% 2.97/3.22 lhs with equations [2,28]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 128: mult(X4, ld(X3, X3)) = mult(rd(X4, rd(X2, X3)), rd(X2, X3)).
% 2.97/3.22 Proof: Rewrite equation 89,
% 2.97/3.22 lhs with equations [28,2,2,115]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 129: mult(mult(X0, X1), ld(X3, X3)) = mult(X0, mult(rd(X1, X3), X3)).
% 2.97/3.22 Proof: Rewrite equation 100,
% 2.97/3.22 lhs with equations [28,2,2,115]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 130: ld(X5, X6) = mult(X5, ld(X5, ld(X5, X6))).
% 2.97/3.22 Proof: A critical pair between equations 114 and 117.
% 2.97/3.22
% 2.97/3.22 136: mult(X11, mult(X12, X13)) = mult(X11, mult(mult(X11, ld(X11, X12)), X13)).
% 2.97/3.22 Proof: A critical pair between equations 115 and 121.
% 2.97/3.22
% 2.97/3.22 146: mult(X11, mult(X12, X13)) = mult(X11, mult(ld(X11, mult(X11, X12)), X13)).
% 2.97/3.22 Proof: Rewrite equation 136,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 151: ld(X5, X6) = ld(X5, ld(X5, mult(X5, X6))).
% 2.97/3.22 Proof: Rewrite equation 130,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [2,2].
% 2.97/3.22
% 2.97/3.22 152: mult(X4, rd(X3, X3)) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 2.97/3.22 Proof: Rewrite equation 128,
% 2.97/3.22 lhs with equations [28]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 154: mult(ld(X6, mult(X6, X7)), rd(X7, X7)) = ld(X6, mult(X6, X7)).
% 2.97/3.22 Proof: Rewrite equation 126,
% 2.97/3.22 lhs with equations [2,28]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 156: ld(X0, mult(X0, rd(X1, X1))) = rd(mult(rd(X0, X0), X1), X1).
% 2.97/3.22 Proof: Rewrite equation 124,
% 2.97/3.22 lhs with equations [28,2]
% 2.97/3.22 rhs with equations [28,3].
% 2.97/3.22
% 2.97/3.22 157: rd(mult(X0, X0), X0) = X0.
% 2.97/3.22 Proof: Rewrite equation 123,
% 2.97/3.22 lhs with equations [28,3]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 158: mult(ld(X6, mult(X6, X2)), X3) = ld(X6, mult(X6, mult(X2, X3))).
% 2.97/3.22 Proof: Rewrite equation 121,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 162: ld(X0, mult(X0, X4)) = ld(ld(X0, X1), mult(ld(X0, X1), X4)).
% 2.97/3.22 Proof: Rewrite equation 117,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 163: X10 = rd(X10, rd(X10, X10)).
% 2.97/3.22 Proof: Rewrite equation 116,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [28].
% 2.97/3.22
% 2.97/3.22 165: mult(mult(X0, X1), rd(X3, X3)) = mult(X0, rd(mult(X1, X3), X3)).
% 2.97/3.22 Proof: Rewrite equation 129,
% 2.97/3.22 lhs with equations [28]
% 2.97/3.22 rhs with equations [3].
% 2.97/3.22
% 2.97/3.22 166: mult(rd(X2, X3), rd(X3, X3)) = rd(X2, X3).
% 2.97/3.22 Proof: A critical pair between equations 152 and 157.
% 2.97/3.22
% 2.97/3.22 171: mult(X4, rd(X5, X5)) = rd(mult(X4, X5), rd(mult(X5, X5), X5)).
% 2.97/3.22 Proof: A critical pair between equations 152 and 157.
% 2.97/3.22
% 2.97/3.22 174: ld(ld(X7, X8), X9) = ld(ld(X7, X8), ld(X7, mult(X7, X9))).
% 2.97/3.22 Proof: A critical pair between equations 151 and 162.
% 2.97/3.22
% 2.97/3.22 180: ld(ld(X7, X8), X9) = ld(ld(X7, X8), mult(X7, ld(X7, X9))).
% 2.97/3.22 Proof: Rewrite equation 174,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 183: mult(X4, ld(X5, X5)) = mult(rd(X4, X5), X5).
% 2.97/3.22 Proof: Rewrite equation 171,
% 2.97/3.22 lhs with equations [28]
% 2.97/3.22 rhs with equations [157,3].
% 2.97/3.22
% 2.97/3.22 185: mult(rd(X2, X3), ld(X3, X3)) = rd(X2, X3).
% 2.97/3.22 Proof: Rewrite equation 166,
% 2.97/3.22 lhs with equations [28]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 187: X10 = rd(X10, ld(X10, X10)).
% 2.97/3.22 Proof: Rewrite equation 163,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [28].
% 2.97/3.22
% 2.97/3.22 188: mult(X0, ld(X0, X4)) = mult(ld(X0, X1), ld(ld(X0, X1), X4)).
% 2.97/3.22 Proof: Rewrite equation 162,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 192: mult(mult(X6, ld(X6, X2)), X3) = mult(X6, ld(X6, mult(X2, X3))).
% 2.97/3.22 Proof: Rewrite equation 158,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 193: mult(ld(X0, X0), X0) = X0.
% 2.97/3.22 Proof: Rewrite equation 157,
% 2.97/3.22 lhs with equations [3,28]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 194: mult(X0, ld(X1, X1)) = rd(mult(X0, X1), X1).
% 2.97/3.22 Proof: Rewrite equation 3,
% 2.97/3.22 lhs with equations [183]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 195: mult(X0, ld(X0, ld(X1, X1))) = mult(ld(X0, X0), ld(X1, X1)).
% 2.97/3.22 Proof: Rewrite equation 156,
% 2.97/3.22 lhs with equations [28,2]
% 2.97/3.22 rhs with equations [28,194].
% 2.97/3.22
% 2.97/3.22 197: mult(mult(X6, ld(X6, X7)), ld(X7, X7)) = mult(X6, ld(X6, X7)).
% 2.97/3.22 Proof: Rewrite equation 154,
% 2.97/3.22 lhs with equations [2,28]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 202: mult(X11, mult(X12, X13)) = mult(X11, mult(mult(X11, ld(X11, X12)), X13)).
% 2.97/3.22 Proof: Rewrite equation 146,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 206: mult(X4, ld(X3, X3)) = mult(X4, ld(rd(X2, X3), rd(X2, X3))).
% 2.97/3.22 Proof: Rewrite equation 152,
% 2.97/3.22 lhs with equations [28]
% 2.97/3.22 rhs with equations [194].
% 2.97/3.22
% 2.97/3.22 207: mult(mult(X0, X1), ld(X3, X3)) = mult(X0, mult(X1, ld(X3, X3))).
% 2.97/3.22 Proof: Rewrite equation 165,
% 2.97/3.22 lhs with equations [28]
% 2.97/3.22 rhs with equations [194].
% 2.97/3.22
% 2.97/3.22 214: mult(mult(X6, ld(X6, ld(X7, X7))), X7) = mult(X6, ld(X6, X7)).
% 2.97/3.22 Proof: A critical pair between equations 192 and 193.
% 2.97/3.22
% 2.97/3.22 219: mult(X14, mult(X15, ld(X15, X15))) = mult(X14, mult(X14, ld(X14, X15))).
% 2.97/3.22 Proof: A critical pair between equations 202 and 197.
% 2.97/3.22
% 2.97/3.22 224: mult(ld(X6, mult(X6, rd(X7, X7))), X7) = ld(X6, mult(X6, X7)).
% 2.97/3.22 Proof: Rewrite equation 214,
% 2.97/3.22 lhs with equations [28,2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 231: mult(mult(X0, X1), rd(X3, X3)) = mult(X0, mult(X1, rd(X3, X3))).
% 2.97/3.22 Proof: Rewrite equation 207,
% 2.97/3.22 lhs with equations [28]
% 2.97/3.22 rhs with equations [28].
% 2.97/3.22
% 2.97/3.22 232: mult(X4, rd(X3, X3)) = mult(X4, rd(rd(X2, X3), rd(X2, X3))).
% 2.97/3.22 Proof: Rewrite equation 206,
% 2.97/3.22 lhs with equations [28]
% 2.97/3.22 rhs with equations [28].
% 2.97/3.22
% 2.97/3.22 239: mult(X0, rd(X1, X1)) = rd(mult(X0, X1), X1).
% 2.97/3.22 Proof: Rewrite equation 194,
% 2.97/3.22 lhs with equations [28]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 240: rd(mult(X0, X0), X0) = X0.
% 2.97/3.22 Proof: Rewrite equation 193,
% 2.97/3.22 lhs with equations [28,183,28,239]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 244: ld(X0, mult(X0, X4)) = ld(ld(X0, X1), mult(ld(X0, X1), X4)).
% 2.97/3.22 Proof: Rewrite equation 188,
% 2.97/3.22 lhs with equations [2]
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 245: X10 = rd(X10, rd(X10, X10)).
% 2.97/3.22 Proof: Rewrite equation 187,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [28].
% 2.97/3.22
% 2.97/3.22 247: rd(rd(mult(X2, X3), X3), X3) = rd(X2, X3).
% 2.97/3.22 Proof: Rewrite equation 185,
% 2.97/3.22 lhs with equations [28,239,183,28,239]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 249: rd(mult(X4, X5), X5) = mult(rd(X4, X5), X5).
% 2.97/3.22 Proof: Rewrite equation 183,
% 2.97/3.22 lhs with equations [28,239]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 252: ld(ld(X7, X8), X9) = ld(ld(X7, X8), ld(X7, mult(X7, X9))).
% 2.97/3.22 Proof: Rewrite equation 180,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [2].
% 2.97/3.22
% 2.97/3.22 254: ld(X0, rd(mult(X0, X1), X1)) = rd(mult(rd(X0, X0), X1), X1).
% 2.97/3.22 Proof: Rewrite equation 195,
% 2.97/3.22 lhs with equations [28,2,239]
% 2.97/3.22 rhs with equations [28,28,239].
% 2.97/3.22
% 2.97/3.22 255: mult(X14, X15) = ld(X14, mult(X14, mult(X14, X15))).
% 2.97/3.22 Proof: Rewrite equation 219,
% 2.97/3.22 lhs with equations [28,239,240]
% 2.97/3.22 rhs with equations [2,2].
% 2.97/3.22
% 2.97/3.22 263: ld(X8, mult(X8, X9)) = mult(ld(X8, rd(mult(X8, X9), X9)), X9).
% 2.97/3.22 Proof: A critical pair between equations 224 and 239.
% 2.97/3.22
% 2.97/3.22 274: rd(mult(X4, X3), X3) = rd(mult(X4, rd(X2, X3)), rd(X2, X3)).
% 2.97/3.22 Proof: Rewrite equation 232,
% 2.97/3.22 lhs with equations [239]
% 2.97/3.22 rhs with equations [239].
% 2.97/3.22
% 2.97/3.22 275: rd(mult(mult(X0, X1), X3), X3) = mult(X0, rd(mult(X1, X3), X3)).
% 2.97/3.22 Proof: Rewrite equation 231,
% 2.97/3.22 lhs with equations [239]
% 2.97/3.22 rhs with equations [239].
% 2.97/3.22
% 2.97/3.22 280: ld(ld(X10, X10), X9) = ld(rd(X10, X10), ld(X10, mult(X10, X9))).
% 2.97/3.22 Proof: A critical pair between equations 252 and 28.
% 2.97/3.22
% 2.97/3.22 282: rd(X5, rd(X6, X7)) = rd(rd(mult(X5, X7), X7), rd(X6, X7)).
% 2.97/3.22 Proof: A critical pair between equations 247 and 274.
% 2.97/3.22
% 2.97/3.22 285: ld(X5, mult(X5, X4)) = ld(rd(X5, X5), mult(ld(X5, X5), X4)).
% 2.97/3.22 Proof: A critical pair between equations 244 and 28.
% 2.97/3.22
% 2.97/3.22 288: ld(X5, mult(X5, X4)) = ld(rd(X5, X5), mult(rd(X5, X5), X4)).
% 2.97/3.22 Proof: Rewrite equation 285,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [28].
% 2.97/3.22
% 2.97/3.22 289: ld(rd(X10, X10), X9) = ld(rd(X10, X10), ld(X10, mult(X10, X9))).
% 2.97/3.22 Proof: Rewrite equation 280,
% 2.97/3.22 lhs with equations [28]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 296: rd(mult(X5, X6), X6) = rd(rd(mult(X5, X6), X6), rd(X6, X6)).
% 2.97/3.22 Proof: A critical pair between equations 274 and 239.
% 2.97/3.22
% 2.97/3.22 308: rd(mult(X5, X6), X6) = rd(X5, rd(X6, X6)).
% 2.97/3.22 Proof: Rewrite equation 296,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [282].
% 2.97/3.22
% 2.97/3.22 312: ld(X8, mult(X8, X9)) = mult(ld(X8, rd(X8, rd(X9, X9))), X9).
% 2.97/3.22 Proof: Rewrite equation 263,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [308].
% 2.97/3.22
% 2.97/3.22 314: ld(X0, rd(X0, rd(X1, X1))) = rd(rd(X0, X0), rd(X1, X1)).
% 2.97/3.22 Proof: Rewrite equation 254,
% 2.97/3.22 lhs with equations [308]
% 2.97/3.22 rhs with equations [308].
% 2.97/3.22
% 2.97/3.22 315: rd(X4, rd(X5, X5)) = mult(rd(X4, X5), X5).
% 2.97/3.22 Proof: Rewrite equation 249,
% 2.97/3.22 lhs with equations [308]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 320: rd(X4, rd(X3, X3)) = rd(X4, rd(rd(X2, X3), rd(X2, X3))).
% 2.97/3.22 Proof: Rewrite equation 274,
% 2.97/3.22 lhs with equations [308]
% 2.97/3.22 rhs with equations [308].
% 2.97/3.22
% 2.97/3.22 321: rd(mult(X0, X1), rd(X3, X3)) = mult(X0, rd(X1, rd(X3, X3))).
% 2.97/3.22 Proof: Rewrite equation 275,
% 2.97/3.22 lhs with equations [308]
% 2.97/3.22 rhs with equations [308].
% 2.97/3.22
% 2.97/3.22 324: rd(X5, rd(X6, X7)) = rd(rd(X5, rd(X7, X7)), rd(X6, X7)).
% 2.97/3.22 Proof: Rewrite equation 282,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [308].
% 2.97/3.22
% 2.97/3.22 326: rd(mult(X0, X11), rd(X11, X11)) = mult(X0, X11).
% 2.97/3.22 Proof: A critical pair between equations 321 and 245.
% 2.97/3.22
% 2.97/3.22 330: ld(X10, mult(X10, X11)) = mult(rd(rd(X10, X10), rd(X11, X11)), X11).
% 2.97/3.22 Proof: A critical pair between equations 312 and 314.
% 2.97/3.22
% 2.97/3.22 334: rd(mult(X7, X8), rd(X8, X8)) = mult(rd(X7, rd(X8, X8)), X8).
% 2.97/3.22 Proof: A critical pair between equations 315 and 308.
% 2.97/3.22
% 2.97/3.22 337: mult(X7, X8) = mult(rd(X7, rd(X8, X8)), X8).
% 2.97/3.22 Proof: Rewrite equation 334,
% 2.97/3.22 lhs with equations [326]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 340: ld(X10, mult(X10, X11)) = mult(rd(X10, X10), X11).
% 2.97/3.22 Proof: Rewrite equation 330,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [337].
% 2.97/3.22
% 2.97/3.22 342: ld(X5, mult(X5, X4)) = ld(rd(X5, X5), X4).
% 2.97/3.22 Proof: Rewrite equation 288,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [340,289].
% 2.97/3.22
% 2.97/3.22 354: mult(X14, X15) = ld(rd(X14, X14), mult(X14, X15)).
% 2.97/3.22 Proof: Rewrite equation 255,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [342].
% 2.97/3.22
% 2.97/3.22 370: rd(rd(X12, X12), rd(X13, X13)) = rd(ld(X12, mult(X12, X13)), X13).
% 2.97/3.22 Proof: A critical pair between equations 308 and 340.
% 2.97/3.22
% 2.97/3.22 371: rd(rd(X12, X12), rd(X13, X13)) = rd(ld(rd(X12, X12), X13), X13).
% 2.97/3.22 Proof: Rewrite equation 370,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [342].
% 2.97/3.22
% 2.97/3.22 378: rd(rd(X16, X16), rd(mult(X16, X17), mult(X16, X17))) = rd(mult(X16, X17), mult(X16, X17)).
% 2.97/3.22 Proof: A critical pair between equations 371 and 354.
% 2.97/3.22
% 2.97/3.22 434: rd(X8, rd(X6, rd(X9, X10))) = rd(rd(X8, rd(X10, X10)), rd(X6, rd(X9, X10))).
% 2.97/3.22 Proof: A critical pair between equations 324 and 320.
% 2.97/3.22
% 2.97/3.22 468: rd(X4, rd(X8, X8)) = rd(X4, rd(rd(mult(X7, X8), X8), rd(X7, rd(X8, X8)))).
% 2.97/3.22 Proof: A critical pair between equations 320 and 308.
% 2.97/3.22
% 2.97/3.22 469: rd(X4, rd(X8, X8)) = rd(X4, rd(X7, rd(X7, rd(X8, X8)))).
% 2.97/3.22 Proof: Rewrite equation 468,
% 2.97/3.22 lhs with equations []
% 2.97/3.22 rhs with equations [308,434].
% 2.97/3.22
% 2.97/3.22 474: rd(X4, rd(X13, X13)) = rd(X4, rd(mult(X12, X13), mult(X12, X13))).
% 2.97/3.22 Proof: A critical pair between equations 469 and 326.
% 2.97/3.22
% 2.97/3.22 486: rd(rd(X16, X16), rd(X17, X17)) = rd(mult(X16, X17), mult(X16, X17)).
% 2.97/3.22 Proof: Rewrite equation 378,
% 2.97/3.22 lhs with equations [474]
% 2.97/3.22 rhs with equations [].
% 2.97/3.22
% 2.97/3.22 491: rd(X4, rd(X19, X19)) = rd(X4, rd(rd(X18, X18), rd(X19, X19))).
% 2.97/3.22 Proof: A critical pair between equations 474 and 486.
% 2.97/3.22
% 2.97/3.22 502: rd(mult(a(), mult(b(), c())), mult(b(), c())) = rd(mult(a(), c()), c()).
% 2.97/3.22 Proof: Rewrite lhs with equations [308,486,491]
% 2.97/3.22 rhs with equations [308].
% 2.97/3.22
% 2.97/3.22 % SZS output end Proof
%------------------------------------------------------------------------------