TSTP Solution File: LDA002-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : LDA002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n022.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 09:04:38 EDT 2023
% Result : Unsatisfiable 273.18s 274.01s
% Output : CNFRefutation 273.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LDA002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : toma --casc %s
% 0.19/0.36 % Computer : n022.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Sun Aug 27 01:13:39 EDT 2023
% 0.19/0.37 % CPUTime :
% 273.18/274.01 % SZS status Unsatisfiable
% 273.18/274.01 % SZS output start Proof
% 273.18/274.01 original problem:
% 273.18/274.01 axioms:
% 273.18/274.01 f(X, f(Y, Z)) = f(f(X, Y), f(X, Z))
% 273.18/274.01 n2() = f(n1(), n1())
% 273.18/274.01 n3() = f(n2(), n1())
% 273.18/274.01 u() = f(n2(), n2())
% 273.18/274.01 u1() = f(u(), n1())
% 273.18/274.01 u2() = f(u(), n2())
% 273.18/274.01 u3() = f(u(), n3())
% 273.18/274.01 uu() = f(u(), u())
% 273.18/274.01 a() = f(f(n3(), n2()), u2())
% 273.18/274.01 b() = f(u1(), u3())
% 273.18/274.01 v() = f(uu(), uu())
% 273.18/274.01 goal:
% 273.18/274.01 f(a(), v()) != f(b(), v())
% 273.18/274.01 To show the unsatisfiability of the original goal,
% 273.18/274.01 it suffices to show that f(a(), v()) = f(b(), v()) (skolemized goal) is valid under the axioms.
% 273.18/274.01 Here is an equational proof:
% 273.18/274.01 0: f(X0, f(X1, X2)) = f(f(X0, X1), f(X0, X2)).
% 273.18/274.01 Proof: Axiom.
% 273.18/274.01
% 273.18/274.01 1: n2() = f(n1(), n1()).
% 273.18/274.01 Proof: Axiom.
% 273.18/274.01
% 273.18/274.01 2: n3() = f(n2(), n1()).
% 273.18/274.01 Proof: Axiom.
% 273.18/274.01
% 273.18/274.01 3: u() = f(n2(), n2()).
% 273.18/274.01 Proof: Axiom.
% 273.18/274.01
% 273.18/274.01 4: u1() = f(u(), n1()).
% 273.18/274.01 Proof: Axiom.
% 273.18/274.01
% 273.18/274.01 5: u2() = f(u(), n2()).
% 273.18/274.01 Proof: Axiom.
% 273.18/274.01
% 273.18/274.01 6: u3() = f(u(), n3()).
% 273.18/274.01 Proof: Axiom.
% 273.18/274.01
% 273.18/274.01 7: uu() = f(u(), u()).
% 273.18/274.01 Proof: Axiom.
% 273.18/274.01
% 273.18/274.01 8: a() = f(f(n3(), n2()), u2()).
% 273.18/274.01 Proof: Axiom.
% 273.18/274.01
% 273.18/274.01 9: b() = f(u1(), u3()).
% 273.18/274.01 Proof: Axiom.
% 273.18/274.01
% 273.18/274.01 10: v() = f(uu(), uu()).
% 273.18/274.01 Proof: Axiom.
% 273.18/274.01
% 273.18/274.01 11: n3() = f(f(n1(), n1()), n1()).
% 273.18/274.01 Proof: Rewrite equation 2,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 12: u() = f(n1(), f(n1(), n1())).
% 273.18/274.01 Proof: Rewrite equation 3,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1,1,0].
% 273.18/274.01
% 273.18/274.01 13: u1() = f(f(n1(), f(n1(), n1())), n1()).
% 273.18/274.01 Proof: Rewrite equation 4,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [12].
% 273.18/274.01
% 273.18/274.01 14: u2() = f(n1(), f(f(n1(), n1()), n1())).
% 273.18/274.01 Proof: Rewrite equation 5,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [12,1,0].
% 273.18/274.01
% 273.18/274.01 15: u3() = f(f(n1(), f(n1(), n1())), f(f(n1(), n1()), n1())).
% 273.18/274.01 Proof: Rewrite equation 6,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [12,11].
% 273.18/274.01
% 273.18/274.01 16: uu() = f(n1(), f(n1(), f(n1(), n1()))).
% 273.18/274.01 Proof: Rewrite equation 7,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [12,12,0,0].
% 273.18/274.01
% 273.18/274.01 17: a() = f(f(f(f(n1(), n1()), n1()), f(n1(), n1())), f(n1(), f(f(n1(), n1()), n1()))).
% 273.18/274.01 Proof: Rewrite equation 8,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [11,1,14].
% 273.18/274.01
% 273.18/274.01 18: b() = f(n1(), f(f(n1(), n1()), f(f(n1(), n1()), n1()))).
% 273.18/274.01 Proof: Rewrite equation 9,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [13,15,0,0].
% 273.18/274.01
% 273.18/274.01 19: v() = f(n1(), f(n1(), f(n1(), f(n1(), n1())))).
% 273.18/274.01 Proof: Rewrite equation 10,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [16,16,0,0,0].
% 273.18/274.01
% 273.18/274.01 20: f(f(X3, X4), f(X1, f(X3, X5))) = f(f(f(X3, X4), X1), f(X3, f(X4, X5))).
% 273.18/274.01 Proof: A critical pair between equations 0 and 0.
% 273.18/274.01
% 273.18/274.01 21: f(f(X3, X4), f(f(X3, X5), X2)) = f(f(X3, f(X4, X5)), f(f(X3, X4), X2)).
% 273.18/274.01 Proof: A critical pair between equations 0 and 0.
% 273.18/274.01
% 273.18/274.01 22: v() = f(n1(), f(n1(), f(n1(), n2()))).
% 273.18/274.01 Proof: Rewrite equation 19,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 23: b() = f(n1(), f(n2(), f(n2(), n1()))).
% 273.18/274.01 Proof: Rewrite equation 18,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1,1].
% 273.18/274.01
% 273.18/274.01 24: a() = f(f(f(n2(), n1()), n2()), f(n1(), f(n2(), n1()))).
% 273.18/274.01 Proof: Rewrite equation 17,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1,1,1].
% 273.18/274.01
% 273.18/274.01 29: u() = f(n1(), n2()).
% 273.18/274.01 Proof: Rewrite equation 12,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 30: n3() = f(n2(), n1()).
% 273.18/274.01 Proof: Rewrite equation 11,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 37: f(f(f(X6, X7), X6), f(f(f(X6, X7), X8), X2)) = f(f(X6, f(X7, X8)), f(f(f(X6, X7), X6), X2)).
% 273.18/274.01 Proof: A critical pair between equations 21 and 0.
% 273.18/274.01
% 273.18/274.01 43: n3() = f(f(n1(), n1()), n1()).
% 273.18/274.01 Proof: Rewrite equation 30,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 44: u() = f(n1(), f(n1(), n1())).
% 273.18/274.01 Proof: Rewrite equation 29,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 49: a() = f(f(f(f(n1(), n1()), n1()), f(n1(), n1())), f(n1(), f(f(n1(), n1()), n1()))).
% 273.18/274.01 Proof: Rewrite equation 24,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1,1,1].
% 273.18/274.01
% 273.18/274.01 50: b() = f(n1(), f(f(n1(), n1()), f(f(n1(), n1()), n1()))).
% 273.18/274.01 Proof: Rewrite equation 23,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1,1].
% 273.18/274.01
% 273.18/274.01 51: v() = f(n1(), f(n1(), f(n1(), f(n1(), n1())))).
% 273.18/274.01 Proof: Rewrite equation 22,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 64: v() = f(n1(), f(n1(), f(n1(), n2()))).
% 273.18/274.01 Proof: Rewrite equation 51,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 65: b() = f(n1(), f(n2(), f(n2(), n1()))).
% 273.18/274.01 Proof: Rewrite equation 50,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1,1].
% 273.18/274.01
% 273.18/274.01 66: a() = f(f(f(n2(), n1()), n2()), f(n1(), f(n2(), n1()))).
% 273.18/274.01 Proof: Rewrite equation 49,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1,1,1].
% 273.18/274.01
% 273.18/274.01 71: u() = f(n1(), n2()).
% 273.18/274.01 Proof: Rewrite equation 44,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 72: n3() = f(n2(), n1()).
% 273.18/274.01 Proof: Rewrite equation 43,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 74: f(n1(), f(n1(), X2)) = f(n2(), f(n1(), X2)).
% 273.18/274.01 Proof: A critical pair between equations 0 and 1.
% 273.18/274.01
% 273.18/274.01 79: f(f(f(n1(), n1()), n1()), f(f(f(n1(), n1()), X8), X2)) = f(f(n1(), f(n1(), X8)), f(f(n2(), n1()), X2)).
% 273.18/274.01 Proof: A critical pair between equations 37 and 1.
% 273.18/274.01
% 273.18/274.01 85: f(n3(), f(f(n2(), X8), X2)) = f(f(n2(), f(n1(), X8)), f(n3(), X2)).
% 273.18/274.01 Proof: Rewrite equation 79,
% 273.18/274.01 lhs with equations [1,72,1]
% 273.18/274.01 rhs with equations [74,72].
% 273.18/274.01
% 273.18/274.01 90: a() = f(f(n3(), n2()), f(n1(), n3())).
% 273.18/274.01 Proof: Rewrite equation 66,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [72,72].
% 273.18/274.01
% 273.18/274.01 91: b() = f(n1(), f(n2(), n3())).
% 273.18/274.01 Proof: Rewrite equation 65,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [72].
% 273.18/274.01
% 273.18/274.01 92: v() = f(n2(), f(n1(), u())).
% 273.18/274.01 Proof: Rewrite equation 64,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [71,74].
% 273.18/274.01
% 273.18/274.01 106: v() = f(n1(), f(n1(), f(n1(), f(n1(), n1())))).
% 273.18/274.01 Proof: Rewrite equation 92,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1,71,1,0].
% 273.18/274.01
% 273.18/274.01 107: b() = f(n1(), f(f(n1(), n1()), f(f(n1(), n1()), n1()))).
% 273.18/274.01 Proof: Rewrite equation 91,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1,72,1].
% 273.18/274.01
% 273.18/274.01 108: a() = f(f(f(f(n1(), n1()), n1()), f(n1(), n1())), f(n1(), f(f(n1(), n1()), n1()))).
% 273.18/274.01 Proof: Rewrite equation 90,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [72,1,1,72,1].
% 273.18/274.01
% 273.18/274.01 113: u() = f(n1(), f(n1(), n1())).
% 273.18/274.01 Proof: Rewrite equation 71,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 114: n3() = f(f(n1(), n1()), n1()).
% 273.18/274.01 Proof: Rewrite equation 72,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 115: f(f(f(n1(), n1()), n1()), f(f(f(n1(), n1()), X8), X2)) = f(f(n1(), f(n1(), X8)), f(f(f(n1(), n1()), n1()), X2)).
% 273.18/274.01 Proof: Rewrite equation 85,
% 273.18/274.01 lhs with equations [114,1]
% 273.18/274.01 rhs with equations [1,0,114].
% 273.18/274.01
% 273.18/274.01 130: n3() = f(n2(), n1()).
% 273.18/274.01 Proof: Rewrite equation 114,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 131: u() = f(n1(), n2()).
% 273.18/274.01 Proof: Rewrite equation 113,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 136: a() = f(f(f(n2(), n1()), n2()), f(n1(), f(n2(), n1()))).
% 273.18/274.01 Proof: Rewrite equation 108,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1,1,1].
% 273.18/274.01
% 273.18/274.01 137: b() = f(n1(), f(n2(), f(n2(), n1()))).
% 273.18/274.01 Proof: Rewrite equation 107,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1,1].
% 273.18/274.01
% 273.18/274.01 138: v() = f(n1(), f(n1(), f(n1(), n2()))).
% 273.18/274.01 Proof: Rewrite equation 106,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 144: f(f(n2(), n1()), f(f(n2(), X8), X2)) = f(f(n1(), f(n1(), X8)), f(f(n2(), n1()), X2)).
% 273.18/274.01 Proof: Rewrite equation 115,
% 273.18/274.01 lhs with equations [1,1]
% 273.18/274.01 rhs with equations [1].
% 273.18/274.01
% 273.18/274.01 145: f(n1(), f(X1, n1())) = f(f(n1(), X1), n2()).
% 273.18/274.01 Proof: A critical pair between equations 0 and 1.
% 273.18/274.01
% 273.18/274.01 146: f(n1(), f(n1(), X2)) = f(n2(), f(n1(), X2)).
% 273.18/274.01 Proof: A critical pair between equations 0 and 1.
% 273.18/274.01
% 273.18/274.01 151: f(f(n2(), n1()), f(f(n2(), n1()), X2)) = f(f(n1(), n2()), f(f(n2(), n1()), X2)).
% 273.18/274.01 Proof: A critical pair between equations 144 and 1.
% 273.18/274.01
% 273.18/274.01 154: f(f(n2(), n1()), f(f(n2(), X8), f(n2(), X11))) = f(f(n1(), f(n1(), X8)), f(n2(), f(n1(), X11))).
% 273.18/274.01 Proof: A critical pair between equations 144 and 0.
% 273.18/274.01
% 273.18/274.01 158: f(n3(), f(n2(), f(X8, X11))) = f(n1(), f(n1(), f(X8, X11))).
% 273.18/274.01 Proof: Rewrite equation 154,
% 273.18/274.01 lhs with equations [130,0]
% 273.18/274.01 rhs with equations [146,0,0].
% 273.18/274.01
% 273.18/274.01 160: f(n3(), f(n3(), X2)) = f(u(), f(n3(), X2)).
% 273.18/274.01 Proof: Rewrite equation 151,
% 273.18/274.01 lhs with equations [130,130]
% 273.18/274.01 rhs with equations [131,130].
% 273.18/274.01
% 273.18/274.01 163: v() = f(n1(), f(n1(), u())).
% 273.18/274.01 Proof: Rewrite equation 138,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [131].
% 273.18/274.01
% 273.18/274.01 164: b() = f(n1(), f(n2(), n3())).
% 273.18/274.01 Proof: Rewrite equation 137,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [130].
% 273.18/274.01
% 273.18/274.01 165: a() = f(f(n3(), n2()), f(n1(), n3())).
% 273.18/274.01 Proof: Rewrite equation 136,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [130,130].
% 273.18/274.01
% 273.18/274.01 176: f(n1(), f(n1(), n2())) = f(n2(), u()).
% 273.18/274.01 Proof: A critical pair between equations 146 and 131.
% 273.18/274.01
% 273.18/274.01 177: f(n1(), f(n1(), n1())) = f(n2(), n2()).
% 273.18/274.01 Proof: A critical pair between equations 146 and 1.
% 273.18/274.01
% 273.18/274.01 178: f(n1(), f(n2(), n1())) = f(u(), n2()).
% 273.18/274.01 Proof: A critical pair between equations 145 and 131.
% 273.18/274.01
% 273.18/274.01 179: f(n1(), f(X1, n2())) = f(f(n1(), X1), u()).
% 273.18/274.01 Proof: A critical pair between equations 0 and 131.
% 273.18/274.01
% 273.18/274.01 180: f(n1(), f(n2(), X2)) = f(u(), f(n1(), X2)).
% 273.18/274.01 Proof: A critical pair between equations 0 and 131.
% 273.18/274.01
% 273.18/274.01 183: f(n1(), f(n1(), f(n1(), n2()))) = f(n3(), f(n2(), u())).
% 273.18/274.01 Proof: A critical pair between equations 158 and 131.
% 273.18/274.01
% 273.18/274.01 185: f(n1(), f(n1(), f(n1(), n1()))) = f(n3(), f(n2(), n2())).
% 273.18/274.01 Proof: A critical pair between equations 158 and 1.
% 273.18/274.01
% 273.18/274.01 190: f(n1(), u()) = f(n3(), u()).
% 273.18/274.01 Proof: Rewrite equation 185,
% 273.18/274.01 lhs with equations [1,131]
% 273.18/274.01 rhs with equations [177,1,131].
% 273.18/274.01
% 273.18/274.01 192: f(n1(), f(n3(), u())) = f(n3(), f(n3(), u())).
% 273.18/274.01 Proof: Rewrite equation 183,
% 273.18/274.01 lhs with equations [131,190]
% 273.18/274.01 rhs with equations [176,131,190].
% 273.18/274.01
% 273.18/274.01 194: f(n1(), n3()) = f(u(), n2()).
% 273.18/274.01 Proof: Rewrite equation 178,
% 273.18/274.01 lhs with equations [130]
% 273.18/274.01 rhs with equations [].
% 273.18/274.01
% 273.18/274.01 195: u() = f(n2(), n2()).
% 273.18/274.01 Proof: Rewrite equation 177,
% 273.18/274.01 lhs with equations [1,131]
% 273.18/274.01 rhs with equations [].
% 273.18/274.01
% 273.18/274.01 196: f(n3(), u()) = f(n2(), u()).
% 273.18/274.01 Proof: Rewrite equation 176,
% 273.18/274.01 lhs with equations [131,190]
% 273.18/274.01 rhs with equations [].
% 273.18/274.01
% 273.18/274.01 199: a() = f(f(n3(), n2()), f(u(), n2())).
% 273.18/274.01 Proof: Rewrite equation 165,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [194].
% 273.18/274.01
% 273.18/274.01 200: b() = f(u(), f(u(), n2())).
% 273.18/274.01 Proof: Rewrite equation 164,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [180,194].
% 273.18/274.01
% 273.18/274.01 201: v() = f(n3(), f(n3(), u())).
% 273.18/274.01 Proof: Rewrite equation 163,
% 273.18/274.01 lhs with equations []
% 273.18/274.01 rhs with equations [190,192].
% 273.18/274.01
% 273.18/274.01 206: f(n1(), f(n2(), n2())) = f(u(), u()).
% 273.18/274.01 Proof: A critical pair between equations 179 and 131.
% 273.18/274.02
% 273.18/274.02 211: f(n2(), f(n2(), X2)) = f(u(), f(n2(), X2)).
% 273.18/274.02 Proof: A critical pair between equations 0 and 195.
% 273.18/274.02
% 273.18/274.02 215: f(n3(), u()) = f(u(), u()).
% 273.18/274.02 Proof: Rewrite equation 206,
% 273.18/274.02 lhs with equations [195,190]
% 273.18/274.02 rhs with equations [].
% 273.18/274.02
% 273.18/274.02 220: f(u(), f(n2(), u())) = f(n2(), f(n3(), u())).
% 273.18/274.02 Proof: A critical pair between equations 211 and 196.
% 273.18/274.02
% 273.18/274.02 227: f(u(), f(X1, u())) = f(f(u(), X1), f(n3(), u())).
% 273.18/274.02 Proof: A critical pair between equations 0 and 215.
% 273.18/274.02
% 273.18/274.02 233: f(n3(), f(n3(), u())) = f(n2(), f(n3(), u())).
% 273.18/274.02 Proof: Rewrite equation 220,
% 273.18/274.02 lhs with equations [196,160]
% 273.18/274.02 rhs with equations [].
% 273.18/274.02
% 273.18/274.02 320: f(u(), f(X1, f(n3(), X3))) = f(f(u(), X1), f(n3(), f(n3(), X3))).
% 273.18/274.02 Proof: A critical pair between equations 0 and 160.
% 273.18/274.02
% 273.18/274.02 652: f(f(X3, n2()), f(X1, f(X3, u()))) = f(f(f(X3, n2()), X1), f(X3, f(n3(), u()))).
% 273.18/274.02 Proof: A critical pair between equations 20 and 196.
% 273.18/274.02
% 273.18/274.02 658: f(a(), v()) = f(b(), v()).
% 273.18/274.02 Proof: Rewrite lhs with equations [199,201,652,227,196,160,0,233]
% 273.18/274.02 rhs with equations [200,201,320,227,196,160,160].
% 273.18/274.02
% 273.18/274.02 % SZS output end Proof
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