0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : toma --casc %s 0.13/0.34 % Computer : n011.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 : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Mon Jul 3 04:24:54 EDT 2023 0.13/0.34 % CPUTime : 34.14/34.43 % SZS status Unsatisfiable 34.14/34.43 % SZS output start Proof 34.14/34.43 original problem: 34.14/34.43 axioms: 34.14/34.43 D = divide(inverse(divide(divide(divide(A, B), C), divide(D, C))), divide(B, A)) 34.14/34.43 divide(A, inverse(B)) = multiply(A, B) 34.14/34.43 goal: 34.14/34.43 a2() != multiply(multiply(inverse(b2()), b2()), a2()) 34.14/34.43 To show the unsatisfiability of the original goal, 34.14/34.43 it suffices to show that a2() = multiply(multiply(inverse(b2()), b2()), a2()) (skolemized goal) is valid under the axioms. 34.14/34.43 Here is an equational proof: 34.14/34.43 0: X0 = divide(inverse(divide(divide(divide(X1, X2), X3), divide(X0, X3))), divide(X2, X1)). 34.14/34.43 Proof: Axiom. 34.14/34.43 34.14/34.43 1: divide(X1, inverse(X2)) = multiply(X1, X2). 34.14/34.43 Proof: Axiom. 34.14/34.43 34.14/34.43 2: X0 = divide(inverse(divide(divide(divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6)))), X3), divide(X0, X3))), X7). 34.14/34.43 Proof: A critical pair between equations 0 and 0. 34.14/34.43 34.14/34.43 3: inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6))) = divide(inverse(divide(divide(divide(X1, X2), divide(X5, X4)), X7)), divide(X2, X1)). 34.14/34.43 Proof: A critical pair between equations 0 and 0. 34.14/34.43 34.14/34.43 4: X0 = divide(inverse(divide(divide(X7, X3), divide(X0, X3))), divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6))))). 34.14/34.43 Proof: A critical pair between equations 0 and 0. 34.14/34.43 34.14/34.43 5: inverse(divide(divide(divide(X4, X5), X6), divide(divide(X11, divide(X5, X4)), X6))) = X11. 34.14/34.43 Proof: A critical pair between equations 3 and 0. 34.14/34.43 34.14/34.43 9: X11 = divide(divide(inverse(divide(divide(divide(X12, X13), divide(inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6))), divide(X5, X4))), X11)), divide(X13, X12)), X7). 34.14/34.43 Proof: A critical pair between equations 2 and 3. 34.14/34.43 34.14/34.43 18: X11 = divide(divide(inverse(divide(divide(divide(X12, X13), X7), X11)), divide(X13, X12)), X7). 34.14/34.43 Proof: Rewrite equation 9, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [0]. 34.14/34.43 34.14/34.43 19: X0 = divide(inverse(divide(divide(multiply(divide(X5, X4), divide(divide(divide(X4, X5), X6), divide(X7, X6))), X3), divide(X0, X3))), X7). 34.14/34.43 Proof: Rewrite equation 2, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 20: X0 = divide(inverse(divide(divide(X7, X3), divide(X0, X3))), multiply(divide(X5, X4), divide(divide(divide(X4, X5), X6), divide(X7, X6)))). 34.14/34.43 Proof: Rewrite equation 4, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 38: X0 = divide(inverse(divide(divide(X7, X3), divide(X0, X3))), divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6))))). 34.14/34.43 Proof: Rewrite equation 20, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 39: X0 = divide(inverse(divide(divide(divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6)))), X3), divide(X0, X3))), X7). 34.14/34.43 Proof: Rewrite equation 19, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 46: X0 = divide(inverse(divide(X17, divide(X0, X16))), divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))). 34.14/34.43 Proof: A critical pair between equations 0 and 18. 34.14/34.43 34.14/34.43 48: X11 = inverse(divide(X17, divide(divide(X11, divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))), X16))). 34.14/34.43 Proof: A critical pair between equations 5 and 18. 34.14/34.43 34.14/34.43 50: divide(X15, divide(X13, X12)) = divide(X15, divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(divide(X12, X13), X6))))). 34.14/34.43 Proof: A critical pair between equations 38 and 5. 34.14/34.43 34.14/34.43 55: X0 = divide(inverse(divide(divide(X17, X3), divide(X0, X3))), divide(X16, divide(inverse(divide(divide(divide(X14, X15), X16), X17)), divide(X15, X14)))). 34.14/34.43 Proof: A critical pair between equations 0 and 18. 34.14/34.43 34.14/34.43 57: X11 = inverse(divide(divide(X17, X6), divide(divide(X11, divide(X16, divide(inverse(divide(divide(divide(X14, X15), X16), X17)), divide(X15, X14)))), X6))). 34.14/34.43 Proof: A critical pair between equations 5 and 18. 34.14/34.43 34.14/34.43 60: divide(X15, divide(X13, X12)) = divide(X15, multiply(divide(X5, X4), divide(divide(divide(X4, X5), X6), divide(divide(X12, X13), X6)))). 34.14/34.43 Proof: Rewrite equation 50, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 62: X11 = inverse(divide(X17, divide(divide(X11, multiply(divide(X15, X14), divide(divide(divide(X14, X15), X16), X17))), X16))). 34.14/34.43 Proof: Rewrite equation 48, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 63: X0 = divide(inverse(divide(X17, divide(X0, X16))), multiply(divide(X15, X14), divide(divide(divide(X14, X15), X16), X17))). 34.14/34.43 Proof: Rewrite equation 46, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 64: X0 = divide(inverse(divide(divide(multiply(divide(X5, X4), divide(divide(divide(X4, X5), X6), divide(X7, X6))), X3), divide(X0, X3))), X7). 34.14/34.43 Proof: Rewrite equation 39, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 71: inverse(divide(divide(X18, X19), divide(X20, X19))) = inverse(divide(divide(X18, X6), divide(X20, X6))). 34.14/34.43 Proof: A critical pair between equations 57 and 55. 34.14/34.43 34.14/34.43 84: X0 = divide(inverse(divide(divide(divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6)))), X3), divide(X0, X3))), X7). 34.14/34.43 Proof: Rewrite equation 64, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 85: X0 = divide(inverse(divide(X17, divide(X0, X16))), divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))). 34.14/34.43 Proof: Rewrite equation 63, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 86: X11 = inverse(divide(X17, divide(divide(X11, divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))), X16))). 34.14/34.43 Proof: Rewrite equation 62, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 88: divide(X15, divide(X13, X12)) = divide(X15, divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(divide(X12, X13), X6))))). 34.14/34.43 Proof: Rewrite equation 60, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 97: inverse(divide(divide(inverse(divide(divide(divide(X21, X22), divide(X20, divide(X22, X21))), X24)), X19), divide(X20, X19))) = inverse(X24). 34.14/34.43 Proof: A critical pair between equations 71 and 18. 34.14/34.43 34.14/34.43 102: X17 = inverse(divide(divide(divide(X4, X5), inverse(divide(divide(divide(divide(X5, X4), X17), X19), divide(divide(X20, X21), X19)))), divide(X21, X20))). 34.14/34.43 Proof: A critical pair between equations 5 and 88. 34.14/34.43 34.14/34.43 110: X17 = inverse(divide(multiply(divide(X4, X5), divide(divide(divide(divide(X5, X4), X17), X19), divide(divide(X20, X21), X19))), divide(X21, X20))). 34.14/34.43 Proof: Rewrite equation 102, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 115: X11 = inverse(divide(X17, divide(divide(X11, multiply(divide(X15, X14), divide(divide(divide(X14, X15), X16), X17))), X16))). 34.14/34.43 Proof: Rewrite equation 86, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 116: X0 = divide(inverse(divide(X17, divide(X0, X16))), multiply(divide(X15, X14), divide(divide(divide(X14, X15), X16), X17))). 34.14/34.43 Proof: Rewrite equation 85, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 117: X0 = divide(inverse(divide(divide(multiply(divide(X5, X4), divide(divide(divide(X4, X5), X6), divide(X7, X6))), X3), divide(X0, X3))), X7). 34.14/34.43 Proof: Rewrite equation 84, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 137: X0 = divide(inverse(divide(divide(divide(divide(X5, X4), inverse(divide(divide(divide(X4, X5), X6), divide(X7, X6)))), X3), divide(X0, X3))), X7). 34.14/34.43 Proof: Rewrite equation 117, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 138: X0 = divide(inverse(divide(X17, divide(X0, X16))), divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))). 34.14/34.43 Proof: Rewrite equation 116, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 139: X11 = inverse(divide(X17, divide(divide(X11, divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X16), X17)))), X16))). 34.14/34.43 Proof: Rewrite equation 115, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 144: X17 = inverse(divide(divide(divide(X4, X5), inverse(divide(divide(divide(divide(X5, X4), X17), X19), divide(divide(X20, X21), X19)))), divide(X21, X20))). 34.14/34.43 Proof: Rewrite equation 110, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [1]. 34.14/34.43 34.14/34.43 154: inverse(divide(divide(X28, divide(X26, X25)), divide(X20, divide(X26, X25)))) = inverse(divide(divide(X28, X19), divide(X20, X19))). 34.14/34.43 Proof: A critical pair between equations 97 and 5. 34.14/34.43 34.14/34.43 155: divide(X27, X26) = divide(divide(X24, divide(X23, X22)), inverse(divide(divide(divide(divide(X23, X22), X24), X25), divide(divide(X26, X27), X25)))). 34.14/34.43 Proof: A critical pair between equations 18 and 144. 34.14/34.43 34.14/34.43 160: inverse(divide(divide(divide(inverse(divide(divide(divide(X21, X22), X23), X24)), divide(X22, X21)), X19), divide(X20, X19))) = inverse(divide(X24, divide(X20, X23))). 34.14/34.43 Proof: A critical pair between equations 71 and 18. 34.14/34.43 34.14/34.43 165: inverse(divide(divide(X29, X6), divide(X31, X6))) = inverse(divide(divide(X29, divide(X32, X33)), divide(X31, divide(X32, X33)))). 34.14/34.43 Proof: A critical pair between equations 71 and 154. 34.14/34.43 34.14/34.43 174: X19 = divide(inverse(X21), divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), X18), inverse(divide(divide(divide(X18, X19), X20), divide(X21, X20))))))). 34.14/34.43 Proof: A critical pair between equations 138 and 0. 34.14/34.43 34.14/34.43 180: divide(X14, X15) = divide(inverse(divide(X32, X33)), divide(divide(X15, X14), inverse(divide(X33, X32)))). 34.14/34.43 Proof: A critical pair between equations 174 and 155. 34.14/34.43 34.14/34.43 190: inverse(divide(divide(X34, divide(X32, X33)), divide(X36, divide(X32, X33)))) = inverse(divide(divide(X34, divide(X37, X38)), divide(X36, divide(X37, X38)))). 34.14/34.43 Proof: A critical pair between equations 165 and 154. 34.14/34.43 34.14/34.43 195: inverse(divide(divide(X39, divide(X37, X38)), divide(X42, divide(X37, X38)))) = inverse(divide(divide(X39, X43), divide(X42, X43))). 34.14/34.43 Proof: A critical pair between equations 190 and 154. 34.14/34.43 34.14/34.43 199: divide(divide(X35, X34), inverse(divide(divide(divide(X34, X35), inverse(divide(X33, X32))), X37))) = divide(inverse(divide(X32, X33)), X37). 34.14/34.43 Proof: A critical pair between equations 180 and 18. 34.14/34.43 34.14/34.43 202: X36 = inverse(divide(divide(divide(X15, X14), inverse(divide(divide(divide(X14, X15), inverse(divide(X35, X34))), inverse(divide(X34, X35))))), X36)). 34.14/34.43 Proof: A critical pair between equations 139 and 180. 34.14/34.43 34.14/34.43 207: X36 = inverse(divide(divide(inverse(divide(X34, X35)), inverse(divide(X34, X35))), X36)). 34.14/34.43 Proof: Rewrite equation 202, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [199]. 34.14/34.43 34.14/34.43 209: inverse(divide(divide(X44, X43), divide(X47, X43))) = inverse(divide(divide(X44, X48), divide(X47, X48))). 34.14/34.43 Proof: A critical pair between equations 195 and 165. 34.14/34.43 34.14/34.43 217: X36 = inverse(divide(divide(X39, inverse(divide(divide(inverse(divide(X37, X38)), inverse(divide(X37, X38))), X39))), X36)). 34.14/34.43 Proof: A critical pair between equations 207 and 207. 34.14/34.43 34.14/34.43 221: X36 = inverse(divide(divide(X39, X39), X36)). 34.14/34.43 Proof: Rewrite equation 217, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [207]. 34.14/34.43 34.14/34.43 227: inverse(divide(divide(X49, X43), divide(X47, X43))) = divide(X47, X49). 34.14/34.43 Proof: A critical pair between equations 209 and 221. 34.14/34.43 34.14/34.43 233: divide(X14, X15) = divide(X41, divide(divide(X15, X14), inverse(divide(X41, divide(X40, X40))))). 34.14/34.43 Proof: A critical pair between equations 180 and 221. 34.14/34.43 34.14/34.43 242: X0 = divide(divide(X0, divide(divide(X5, X4), divide(X7, divide(X4, X5)))), X7). 34.14/34.43 Proof: Rewrite equation 137, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [227,227]. 34.14/34.43 34.14/34.43 245: X11 = divide(divide(X11, divide(X16, divide(inverse(divide(divide(divide(X14, X15), X16), X17)), divide(X15, X14)))), X17). 34.14/34.43 Proof: Rewrite equation 57, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [227]. 34.14/34.43 34.14/34.43 246: X17 = inverse(divide(divide(divide(X4, X5), divide(divide(X20, X21), divide(divide(X5, X4), X17))), divide(X21, X20))). 34.14/34.43 Proof: Rewrite equation 144, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [227]. 34.14/34.43 34.14/34.43 260: divide(X20, divide(inverse(divide(divide(divide(X21, X22), X23), X24)), divide(X22, X21))) = inverse(divide(X24, divide(X20, X23))). 34.14/34.43 Proof: Rewrite equation 160, 34.14/34.43 lhs with equations [227] 34.14/34.43 rhs with equations []. 34.14/34.43 34.14/34.43 261: divide(X5, X4) = inverse(divide(X4, X5)). 34.14/34.43 Proof: A critical pair between equations 246 and 242. 34.14/34.43 34.14/34.43 267: X11 = divide(divide(X11, inverse(divide(X29, divide(X28, X28)))), X29). 34.14/34.43 Proof: A critical pair between equations 245 and 260. 34.14/34.43 34.14/34.43 274: X11 = divide(divide(X11, divide(divide(X28, X28), X29)), X29). 34.14/34.43 Proof: Rewrite equation 267, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [261]. 34.14/34.43 34.14/34.43 280: X36 = divide(X36, divide(X39, X39)). 34.14/34.43 Proof: Rewrite equation 221, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [261]. 34.14/34.43 34.14/34.43 295: divide(X14, X15) = divide(X41, divide(divide(X15, X14), inverse(X41))). 34.14/34.43 Proof: Rewrite equation 233, 34.14/34.43 lhs with equations [] 34.14/34.43 rhs with equations [280]. 34.14/34.43 34.14/34.43 308: X42 = divide(divide(X44, X44), inverse(X42)). 34.14/34.43 Proof: A critical pair between equations 274 and 295. 34.14/34.43 34.14/34.43 322: a2() = multiply(multiply(inverse(b2()), b2()), a2()). 34.14/34.43 Proof: Rewrite lhs with equations [] 34.14/34.43 rhs with equations [1,1,308]. 34.14/34.43 34.14/34.43 % SZS output end Proof 34.14/34.43 EOF