%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL982+1 : TPTP v9.3.1. Released v9.1.0. % Transfm : none % Format : tptp:raw % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % Computer : n028.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 12:29:43 PM UTC 2026 % Result : Theorem 2.46s 0.74s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL982+1 : TPTP v9.3.1. Released v9.1.0. % 0.00/0.04 % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % 0.09/0.38 % Computer : n028.cluster.edu % 0.09/0.38 % Model : x86_64 x86_64 % 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.38 % Memory : 8046.5625MB % 0.09/0.38 % OS : Linux 6.8.0-71-generic % 0.09/0.38 % CPULimit : 300 % 0.09/0.38 % WCLimit : 300 % 0.09/0.38 % DateTime : Sat Sep 5 16:15:44 UTC 2026 % 0.09/0.38 % CPUTime : % 2.46/0.74 % SZS status Theorem % 2.46/0.74 % SZS output begin IncompleteProof % 2.46/0.74 cnf(c0, axiom, % 2.46/0.74 ~is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))). % 2.46/0.74 cnf(c1, plain, % 2.46/0.74 ~is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))), % 2.46/0.74 inference(start, [], [c0])). % 2.46/0.74 % 2.46/0.74 cnf(c2, axiom, % 2.46/0.74 is_a_theorem(X0) | ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0))). % 2.46/0.74 cnf(a0, assumption, % 2.46/0.74 implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))) = X0). % 2.46/0.74 cnf(c3, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 2.46/0.74 cnf(c4, plain, % 2.46/0.74 ~is_a_theorem(X1) | ~is_a_theorem(implies(X1,X0)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a0])], [c1, c2])). % 2.46/0.74 % 2.46/0.74 cnf(c5, axiom, % 2.46/0.74 is_a_theorem(X2) | ~is_a_theorem(X3) | ~is_a_theorem(implies(X3,X2))). % 2.46/0.74 cnf(a1, assumption, % 2.46/0.74 X1 = X2). % 2.46/0.74 cnf(c6, plain, % 2.46/0.74 ~is_a_theorem(implies(X1,X0)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 2.46/0.74 cnf(c7, plain, % 2.46/0.74 ~is_a_theorem(X3) | ~is_a_theorem(implies(X3,X2)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a1])], [c4, c5])). % 2.46/0.74 % 2.46/0.74 cnf(c8, axiom, % 2.46/0.74 is_a_theorem(X4) | ~is_a_theorem(X5) | ~is_a_theorem(implies(X5,X4))). % 2.46/0.74 cnf(a2, assumption, % 2.46/0.74 X3 = X4). % 2.46/0.74 cnf(c9, plain, % 2.46/0.74 ~is_a_theorem(implies(X3,X2)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 2.46/0.74 cnf(c10, plain, % 2.46/0.74 ~is_a_theorem(X5) | ~is_a_theorem(implies(X5,X4)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a2])], [c7, c8])). % 2.46/0.74 % 2.46/0.74 cnf(c11, axiom, % 2.46/0.74 is_a_theorem(implies(implies(X6,X7),implies(implies(implies(X8,implies(X9,X10)),implies(X7,implies(not(X9),not(X6)))),implies(X6,X9))))). % 2.46/0.74 cnf(a3, assumption, % 2.46/0.74 X5 = implies(implies(X6,X7),implies(implies(implies(X8,implies(X9,X10)),implies(X7,implies(not(X9),not(X6)))),implies(X6,X9)))). % 2.46/0.74 cnf(c12, plain, % 2.46/0.74 ~is_a_theorem(implies(X5,X4)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 2.46/0.74 cnf(c13, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a3])], [c10, c11])). % 2.46/0.74 % 2.46/0.74 cnf(c14, axiom, % 2.46/0.74 is_a_theorem(implies(implies(X11,X12),implies(implies(implies(X13,implies(X14,X15)),implies(X12,implies(not(X14),not(X11)))),implies(X11,X14))))). % 2.46/0.74 cnf(a4, assumption, % 2.46/0.74 implies(X5,X4) = implies(implies(X11,X12),implies(implies(implies(X13,implies(X14,X15)),implies(X12,implies(not(X14),not(X11)))),implies(X11,X14)))). % 2.46/0.74 cnf(c15, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a4])], [c12, c14])). % 2.46/0.74 cnf(c16, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a4])], [c12, c14])). % 2.46/0.74 % 2.46/0.74 cnf(c17, axiom, % 2.46/0.74 is_a_theorem(implies(implies(X16,X17),implies(implies(implies(X18,implies(X19,X20)),implies(X17,implies(not(X19),not(X16)))),implies(X16,X19))))). % 2.46/0.74 cnf(a5, assumption, % 2.46/0.74 implies(X3,X2) = implies(implies(X16,X17),implies(implies(implies(X18,implies(X19,X20)),implies(X17,implies(not(X19),not(X16)))),implies(X16,X19)))). % 2.46/0.74 cnf(c18, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a5])], [c9, c17])). % 2.46/0.74 cnf(c19, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a5])], [c9, c17])). % 2.46/0.74 % 2.46/0.74 cnf(c20, axiom, % 2.46/0.74 is_a_theorem(X21) | ~is_a_theorem(X22) | ~is_a_theorem(implies(X22,X21))). % 2.46/0.74 cnf(a6, assumption, % 2.46/0.74 implies(X1,X0) = X21). % 2.46/0.74 cnf(c21, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a6])], [c6, c20])). % 2.46/0.74 cnf(c22, plain, % 2.46/0.74 ~is_a_theorem(X22) | ~is_a_theorem(implies(X22,X21)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a6])], [c6, c20])). % 2.46/0.74 % 2.46/0.74 cnf(c23, axiom, % 2.46/0.74 is_a_theorem(X23) | ~is_a_theorem(X24) | ~is_a_theorem(implies(X24,X23))). % 2.46/0.74 cnf(a7, assumption, % 2.46/0.74 X22 = X23). % 2.46/0.74 cnf(c24, plain, % 2.46/0.74 ~is_a_theorem(implies(X22,X21)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a7])], [c22, c23])). % 2.46/0.74 cnf(c25, plain, % 2.46/0.74 ~is_a_theorem(X24) | ~is_a_theorem(implies(X24,X23)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a7])], [c22, c23])). % 2.46/0.74 % 2.46/0.74 cnf(c26, axiom, % 2.46/0.74 is_a_theorem(X25) | ~is_a_theorem(X26) | ~is_a_theorem(implies(X26,X25))). % 2.46/0.74 cnf(a8, assumption, % 2.46/0.74 X24 = X25). % 2.46/0.74 cnf(c27, plain, % 2.46/0.74 ~is_a_theorem(implies(X24,X23)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a8])], [c25, c26])). % 2.46/0.74 cnf(c28, plain, % 2.46/0.74 ~is_a_theorem(X26) | ~is_a_theorem(implies(X26,X25)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a8])], [c25, c26])). % 2.46/0.74 % 2.46/0.74 cnf(c29, axiom, % 2.46/0.74 is_a_theorem(implies(implies(X27,X28),implies(implies(implies(X29,implies(X30,X31)),implies(X28,implies(not(X30),not(X27)))),implies(X27,X30))))). % 2.46/0.74 cnf(a9, assumption, % 2.46/0.74 X26 = implies(implies(X27,X28),implies(implies(implies(X29,implies(X30,X31)),implies(X28,implies(not(X30),not(X27)))),implies(X27,X30)))). % 2.46/0.74 cnf(c30, plain, % 2.46/0.74 ~is_a_theorem(implies(X26,X25)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 2.46/0.74 cnf(c31, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a9])], [c28, c29])). % 2.46/0.74 % 2.46/0.74 cnf(c32, axiom, % 2.46/0.74 is_a_theorem(implies(implies(X32,X33),implies(implies(implies(X34,implies(X35,X36)),implies(X33,implies(not(X35),not(X32)))),implies(X32,X35))))). % 2.46/0.74 cnf(a10, assumption, % 2.46/0.74 implies(X26,X25) = implies(implies(X32,X33),implies(implies(implies(X34,implies(X35,X36)),implies(X33,implies(not(X35),not(X32)))),implies(X32,X35)))). % 2.46/0.74 cnf(c33, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a10])], [c30, c32])). % 2.46/0.74 cnf(c34, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a10])], [c30, c32])). % 2.46/0.74 % 2.46/0.74 cnf(c35, axiom, % 2.46/0.74 is_a_theorem(X37) | ~is_a_theorem(X38) | ~is_a_theorem(implies(X38,X37))). % 2.46/0.74 cnf(a11, assumption, % 2.46/0.74 implies(X24,X23) = X37). % 2.46/0.74 cnf(c36, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a11])], [c27, c35])). % 2.46/0.74 cnf(c37, plain, % 2.46/0.74 ~is_a_theorem(X38) | ~is_a_theorem(implies(X38,X37)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a11])], [c27, c35])). % 2.46/0.74 % 2.46/0.74 cnf(c38, axiom, % 2.46/0.74 is_a_theorem(implies(implies(X39,X40),implies(implies(implies(X41,implies(X42,X43)),implies(X40,implies(not(X42),not(X39)))),implies(X39,X42))))). % 2.46/0.74 cnf(a12, assumption, % 2.46/0.74 X38 = implies(implies(X39,X40),implies(implies(implies(X41,implies(X42,X43)),implies(X40,implies(not(X42),not(X39)))),implies(X39,X42)))). % 2.46/0.74 cnf(c39, plain, % 2.46/0.74 ~is_a_theorem(implies(X38,X37)), % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a12])], [c37, c38])). % 2.46/0.74 cnf(c40, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a12])], [c37, c38])). % 2.46/0.74 % 2.46/0.74 cnf(c41, axiom, % 2.46/0.74 is_a_theorem(implies(implies(X44,X45),implies(implies(implies(X46,implies(X47,X48)),implies(X45,implies(not(X47),not(X44)))),implies(X44,X47))))). % 2.46/0.74 cnf(a13, assumption, % 2.46/0.74 implies(X38,X37) = implies(implies(X44,X45),implies(implies(implies(X46,implies(X47,X48)),implies(X45,implies(not(X47),not(X44)))),implies(X44,X47)))). % 2.46/0.74 cnf(c42, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a13])], [c39, c41])). % 2.46/0.74 cnf(c43, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a13])], [c39, c41])). % 2.46/0.74 % 2.46/0.74 cnf(c44, axiom, % 2.46/0.74 is_a_theorem(implies(implies(X49,X50),implies(implies(implies(X51,implies(X52,X53)),implies(X50,implies(not(X52),not(X49)))),implies(X49,X52))))). % 2.46/0.74 cnf(a14, assumption, % 2.46/0.74 implies(X22,X21) = implies(implies(X49,X50),implies(implies(implies(X51,implies(X52,X53)),implies(X50,implies(not(X52),not(X49)))),implies(X49,X52)))). % 2.46/0.74 cnf(c45, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a14])], [c24, c44])). % 2.46/0.74 cnf(c46, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(strict_predicate_extension, [assumptions([a14])], [c24, c44])). % 2.46/0.74 % 2.46/0.74 cnf(c47, plain, % 2.46/0.74 $false, % 2.46/0.74 inference(constraint_solving, [ % 2.46/0.74 bind(X0, implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))), % 2.46/0.74 bind(X1, implies(implies(implies(X18,implies(X19,X20)),implies(X17,implies(not(X19),not(X16)))),implies(X16,X19))), % 2.46/0.74 bind(X2, implies(implies(implies(X18,implies(X19,X20)),implies(X17,implies(not(X19),not(X16)))),implies(X16,X19))), % 2.46/0.74 bind(X3, implies(implies(implies(X13,implies(X14,X15)),implies(X12,implies(not(X14),not(X11)))),implies(X11,X14))), % 2.46/0.74 bind(X4, implies(implies(implies(X13,implies(X14,X15)),implies(X12,implies(not(X14),not(X11)))),implies(X11,X14))), % 2.46/0.74 bind(X5, implies(implies(X6,X7),implies(implies(implies(X8,implies(X9,X10)),implies(X7,implies(not(X9),not(X6)))),implies(X6,X9)))), % 2.46/0.74 bind(X6, sK1), % 2.46/0.74 bind(X7, sK2), % 2.46/0.74 bind(X8, X8), % 2.46/0.74 bind(X9, implies(not(X42),not(X39))), % 2.46/0.74 bind(X10, X10), % 2.46/0.74 bind(X11, implies(X6,X7)), % 2.46/0.74 bind(X12, implies(implies(implies(X8,implies(X9,X10)),implies(X7,implies(not(X9),not(X6)))),implies(X6,X9))), % 2.46/0.74 bind(X13, implies(X29,implies(X30,X31))), % 2.46/0.74 bind(X14, implies(X39,X42)), % 2.46/0.74 bind(X15, implies(not(X30),not(X27))), % 2.46/0.74 bind(X16, implies(implies(X13,implies(X14,X15)),implies(X12,implies(not(X14),not(X11))))), % 2.46/0.74 bind(X17, implies(X11,X14)), % 2.46/0.74 bind(X18, X18), % 2.46/0.74 bind(X19, implies(not(X52),not(X49))), % 2.46/0.74 bind(X20, X20), % 2.46/0.74 bind(X21, implies(X1,X0)), % 2.46/0.74 bind(X22, implies(X44,X47)), % 2.46/0.74 bind(X23, implies(X44,X47)), % 2.46/0.74 bind(X24, implies(implies(implies(X34,implies(X35,X36)),implies(X33,implies(not(X35),not(X32)))),implies(X32,X35))), % 2.46/0.74 bind(X25, implies(implies(implies(X34,implies(X35,X36)),implies(X33,implies(not(X35),not(X32)))),implies(X32,X35))), % 2.46/0.74 bind(X26, implies(implies(X27,X28),implies(implies(implies(X29,implies(X30,X31)),implies(X28,implies(not(X30),not(X27)))),implies(X27,X30)))), % 2.46/0.74 bind(X27, implies(implies(X41,implies(X42,X43)),implies(X40,implies(not(X42),not(X39))))), % 2.46/0.74 bind(X28, implies(X39,X42)), % 2.46/0.74 bind(X29, X29), % 2.46/0.74 bind(X30, implies(not(X14),not(X11))), % 2.46/0.74 bind(X31, X31), % 2.46/0.74 bind(X32, implies(X27,X28)), % 2.46/0.74 bind(X33, implies(implies(implies(X29,implies(X30,X31)),implies(X28,implies(not(X30),not(X27)))),implies(X27,X30))), % 2.46/0.74 bind(X34, X34), % 2.46/0.74 bind(X35, implies(not(X47),not(X44))), % 2.46/0.74 bind(X36, X36), % 2.46/0.74 bind(X37, implies(X24,X23)), % 2.46/0.74 bind(X38, implies(implies(X39,X40),implies(implies(implies(X41,implies(X42,X43)),implies(X40,implies(not(X42),not(X39)))),implies(X39,X42)))), % 2.46/0.74 bind(X39, sK0), % 2.46/0.74 bind(X40, sK1), % 2.46/0.74 bind(X41, implies(X8,implies(X9,X10))), % 2.46/0.74 bind(X42, sK2), % 2.46/0.74 bind(X43, implies(not(X9),not(X6))), % 2.46/0.74 bind(X44, implies(X39,X40)), % 2.46/0.74 bind(X45, implies(implies(implies(X41,implies(X42,X43)),implies(X40,implies(not(X42),not(X39)))),implies(X39,X42))), % 2.46/0.74 bind(X46, implies(X34,implies(X35,X36))), % 2.46/0.74 bind(X47, implies(implies(implies(X29,implies(X30,X31)),implies(X28,implies(not(X30),not(X27)))),implies(X27,X30))), % 2.46/0.74 bind(X48, implies(not(X35),not(X32))), % 2.46/0.74 bind(X49, implies(X39,X40)), % 2.46/0.74 bind(X50, implies(implies(implies(X29,implies(X30,X31)),implies(X28,implies(not(X30),not(X27)))),implies(X27,X30))), % 2.46/0.74 bind(X51, implies(X18,implies(X19,X20))), % 2.46/0.74 bind(X52, implies(X11,X14)), % 2.46/0.74 bind(X53, implies(not(X19),not(X16))) % 2.46/0.74 ], % 2.46/0.74 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14])). % 2.46/0.74 % 2.46/0.74 % SZS output end IncompleteProof %------------------------------------------------------------------------------