%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : LCL172-3 : TPTP v9.3.1. Released v2.3.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n018.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 : Mon Sep 7 12:45:41 PM UTC 2026 % Result : Unsatisfiable 0.10s 0.43s % Output : Proof 0.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL172-3 : TPTP v9.3.1. Released v2.3.0. % 0.00/0.04 % Command : moca.sh %s % 0.10/0.36 % Computer : n018.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 13:28:34 UTC 2026 % 0.10/0.36 % CPUTime : % 0.10/0.43 % SZS status Unsatisfiable % 0.10/0.43 % SZS output start Proof % 0.10/0.43 The input problem is unsatisfiable because % 0.10/0.43 % 0.10/0.43 [1] the following set of Horn clauses is unsatisfiable: % 0.10/0.43 % 0.10/0.43 axiom(implies(or(A, A), A)) % 0.10/0.43 axiom(implies(A, or(B, A))) % 0.10/0.43 axiom(implies(or(A, B), or(B, A))) % 0.10/0.43 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) % 0.10/0.43 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) % 0.10/0.43 implies(X, Y) = or(not(X), Y) % 0.10/0.43 axiom(X) ==> theorem(X) % 0.10/0.43 theorem(implies(Y, X)) & theorem(Y) ==> theorem(X) % 0.10/0.43 theorem(implies(implies(p, implies(q, r)), implies(q, implies(p, r)))) ==> \bottom % 0.10/0.43 % 0.10/0.43 This holds because % 0.10/0.43 % 0.10/0.43 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.10/0.43 % 0.10/0.43 E: % 0.10/0.43 axiom(implies(A, or(B, A))) = true__ % 0.10/0.43 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) = true__ % 0.10/0.43 axiom(implies(or(A, A), A)) = true__ % 0.10/0.43 axiom(implies(or(A, B), or(B, A))) = true__ % 0.10/0.43 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) = true__ % 0.10/0.43 f1(axiom(X), X) = true__ % 0.10/0.43 f1(true__, X) = theorem(X) % 0.10/0.43 f2(true__, X) = theorem(X) % 0.10/0.43 f3(theorem(Y), Y, X) = true__ % 0.10/0.43 f3(true__, Y, X) = f2(theorem(implies(Y, X)), X) % 0.10/0.43 f4(theorem(implies(implies(p, implies(q, r)), implies(q, implies(p, r))))) = true__ % 0.10/0.43 f4(true__) = false__ % 0.10/0.43 implies(X, Y) = or(not(X), Y) % 0.10/0.43 G: % 0.10/0.43 true__ = false__ % 0.10/0.43 % 0.10/0.43 This holds because % 0.10/0.43 % 0.10/0.43 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.10/0.43 % 0.10/0.43 % 0.10/0.43 axiom(implies(A, or(B, A))) -> true__ % 0.10/0.43 axiom(implies(implies(A, B), implies(or(C, A), or(C, B)))) -> true__ % 0.10/0.43 axiom(implies(or(A, A), A)) -> true__ % 0.10/0.43 axiom(implies(or(A, B), or(B, A))) -> true__ % 0.10/0.43 axiom(implies(or(A, or(B, C)), or(B, or(A, C)))) -> true__ % 0.10/0.43 axiom(or(not(Y0), or(Y1, Y0))) -> true__ % 0.10/0.43 axiom(or(not(or(Y0, Y0)), Y0)) -> true__ % 0.10/0.43 axiom(or(not(or(Y0, Y1)), or(Y1, Y0))) -> true__ % 0.10/0.43 axiom(or(not(or(Y0, or(Y1, Y2))), or(Y1, or(Y0, Y2)))) -> true__ % 0.10/0.43 f1(axiom(X), X) -> true__ % 0.10/0.43 f1(true__, or(not(X0), or(X1, X0))) -> true__ % 0.10/0.43 f1(true__, or(not(or(X0, X0)), X0)) -> true__ % 0.10/0.43 f1(true__, or(not(or(X0, X1)), or(X1, X0))) -> true__ % 0.10/0.43 f1(true__, or(not(or(X0, or(X1, X2))), or(X1, or(X0, X2)))) -> true__ % 0.10/0.43 f1(true__, or(not(or(not(X0), X1)), or(not(or(X2, X0)), or(X2, X1)))) -> true__ % 0.10/0.43 f2(f1(true__, or(not(or(not(X0), or(X1, X0))), Y1)), Y1) -> true__ % 0.10/0.43 f2(f1(true__, or(not(or(not(or(X0, X0)), X0)), Y1)), Y1) -> true__ % 0.10/0.43 f2(f1(true__, or(not(or(not(or(X0, X1)), or(X1, X0))), Y1)), Y1) -> true__ % 0.10/0.43 f2(true__, X) -> theorem(X) % 0.10/0.43 f3(f1(true__, Y0), Y0, Y1) -> true__ % 0.10/0.43 f3(theorem(Y), Y, X) -> true__ % 0.10/0.43 f3(true__, Y, X) -> f2(theorem(implies(Y, X)), X) % 0.10/0.43 f4(theorem(implies(implies(p, implies(q, r)), implies(q, implies(p, r))))) -> true__ % 0.10/0.43 f4(true__) -> false__ % 0.10/0.43 false__ -> true__ % 0.10/0.43 implies(X, Y) -> or(not(X), Y) % 0.10/0.43 theorem(X) -> f1(true__, X) % 0.10/0.43 with the LPO induced by % 0.10/0.43 r > q > p > f4 > f3 > f2 > theorem > f1 > axiom > implies > not > or > false__ > true__ % 0.10/0.43 % 0.10/0.43 % SZS output end Proof % 0.10/0.43 %------------------------------------------------------------------------------