%------------------------------------------------------------------------------ % File : Moca---0.1 % Problem : GEO079-1 : TPTP v8.1.0. Released v1.1.0. % Transfm : none % Format : tptp:raw % Command : moca.sh %s % Computer : n020.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 : 600s % DateTime : Sat Jul 16 05:29:12 EDT 2022 % Result : Unsatisfiable 0.95s 1.12s % Output : Proof 0.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO079-1 : TPTP v8.1.0. Released v1.1.0. % 0.03/0.13 % Command : moca.sh %s % 0.13/0.34 % Computer : n020.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sat Jun 18 18:37:33 EDT 2022 % 0.13/0.34 % CPUTime : % 0.95/1.12 % SZS status Unsatisfiable % 0.95/1.12 % SZS output start Proof % 0.95/1.12 The input problem is unsatisfiable because % 0.95/1.12 % 0.95/1.12 [1] the following set of Horn clauses is unsatisfiable: % 0.95/1.12 % 0.95/1.12 right_angle(U, V, W) & right_angle(X, Y, Z) ==> eq(U, V, W, X, Y, Z) % 0.95/1.12 congruent(U, V, W, X, Y, Z) ==> eq(U, V, W, X, Y, Z) % 0.95/1.12 trapezoid(U, V, W, X) ==> parallel(V, W, U, X) % 0.95/1.12 parallel(U, V, X, Y) ==> eq(X, V, U, V, X, Y) % 0.95/1.12 trapezoid(a, b, c, d) % 0.95/1.12 eq(a, c, b, c, a, d) ==> \bottom % 0.95/1.12 % 0.95/1.12 This holds because % 0.95/1.12 % 0.95/1.12 [2] the following E entails the following G (Claessen-Smallbone's transformation (2018)): % 0.95/1.12 % 0.95/1.12 E: % 0.95/1.12 f1(true__, U, V, W, X, Y, Z) = eq(U, V, W, X, Y, Z) % 0.95/1.12 f2(right_angle(X, Y, Z), U, V, W, X, Y, Z) = true__ % 0.95/1.12 f2(true__, U, V, W, X, Y, Z) = f1(right_angle(U, V, W), U, V, W, X, Y, Z) % 0.95/1.12 f3(congruent(U, V, W, X, Y, Z), U, V, W, X, Y, Z) = true__ % 0.95/1.12 f3(true__, U, V, W, X, Y, Z) = eq(U, V, W, X, Y, Z) % 0.95/1.12 f4(trapezoid(U, V, W, X), V, W, U, X) = true__ % 0.95/1.12 f4(true__, V, W, U, X) = parallel(V, W, U, X) % 0.95/1.12 f5(parallel(U, V, X, Y), X, V, U, Y) = true__ % 0.95/1.12 f5(true__, X, V, U, Y) = eq(X, V, U, V, X, Y) % 0.95/1.12 f6(eq(a, c, b, c, a, d)) = true__ % 0.95/1.12 f6(true__) = false__ % 0.95/1.12 trapezoid(a, b, c, d) = true__ % 0.95/1.12 G: % 0.95/1.12 true__ = false__ % 0.95/1.12 % 0.95/1.12 This holds because % 0.95/1.12 % 0.95/1.12 [3] E entails the following ordered TRS and the lhs and rhs of G join by the TRS: % 0.95/1.12 % 0.95/1.12 % 0.95/1.12 eq(U, V, W, X, Y, Z) -> f3(true__, U, V, W, X, Y, Z) % 0.95/1.12 f1(right_angle(U, V, W), U, V, W, X, Y, Z) -> f2(true__, U, V, W, X, Y, Z) % 0.95/1.12 f1(true__, U, V, W, X, Y, Z) -> f3(true__, U, V, W, X, Y, Z) % 0.95/1.12 f2(right_angle(X, Y, Z), U, V, W, X, Y, Z) -> true__ % 0.95/1.12 f3(congruent(U, V, W, X, Y, Z), U, V, W, X, Y, Z) -> true__ % 0.95/1.12 f3(true__, a, c, b, c, a, d) -> true__ % 0.95/1.12 f4(trapezoid(U, V, W, X), V, W, U, X) -> true__ % 0.95/1.12 f4(true__, V, W, U, X) -> parallel(V, W, U, X) % 0.95/1.12 f5(parallel(U, V, X, Y), X, V, U, Y) -> true__ % 0.95/1.12 f5(true__, X, V, U, Y) -> f3(true__, X, V, U, V, X, Y) % 0.95/1.12 f6(eq(a, c, b, c, a, d)) -> true__ % 0.95/1.12 f6(true__) -> false__ % 0.95/1.12 false__ -> true__ % 0.95/1.12 parallel(b, c, a, d) -> true__ % 0.95/1.12 trapezoid(a, b, c, d) -> true__ % 0.95/1.12 with the LPO induced by % 0.95/1.12 congruent > f1 > f5 > eq > f3 > f2 > right_angle > f4 > parallel > d > c > b > a > trapezoid > f6 > false__ > true__ % 0.95/1.12 % 0.95/1.12 % SZS output end Proof % 0.95/1.12 %------------------------------------------------------------------------------