%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % Computer : n006.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 : Tue May 5 07:03:25 PM UTC 2026 % Result : Theorem 4.86s 1.08s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX222+1 : TPTP v9.3.0. Released v9.3.0. % 0.12/0.12 % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % 0.15/0.33 % Computer : n006.cluster.edu % 0.15/0.33 % Model : x86_64 x86_64 % 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.33 % Memory : 8042.1875MB % 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.33 % CPULimit : 300 % 0.15/0.33 % WCLimit : 300 % 0.15/0.33 % DateTime : Tue May 5 12:33:00 EDT 2026 % 0.15/0.34 % CPUTime : % 4.86/1.08 % SZS status Theorem % 4.86/1.08 % SZS output begin IncompleteProof % 4.86/1.08 cnf(c0, axiom, % 4.86/1.08 ~tc(nil,X0,arr(a,arr(b,b))) | ~nf(X0)). % 4.86/1.08 cnf(c1, plain, % 4.86/1.08 ~tc(nil,X0,arr(a,arr(b,b))) | ~nf(X0), % 4.86/1.08 inference(start, [], [c0])). % 4.86/1.08 % 4.86/1.08 cnf(c2, axiom, % 4.86/1.08 tc(X1,lam(X2),arr(X3,X4)) | ~tc(cons(X3,X1),X2,X4)). % 4.86/1.08 cnf(a0, assumption, % 4.86/1.08 nil = X1). % 4.86/1.08 cnf(a1, assumption, % 4.86/1.08 X0 = lam(X2)). % 4.86/1.08 cnf(a2, assumption, % 4.86/1.08 arr(a,arr(b,b)) = arr(X3,X4)). % 4.86/1.08 cnf(c3, plain, % 4.86/1.08 ~nf(X0), % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a0, a1, a2])], [c1, c2])). % 4.86/1.08 cnf(c4, plain, % 4.86/1.08 ~tc(cons(X3,X1),X2,X4), % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a0, a1, a2])], [c1, c2])). % 4.86/1.08 % 4.86/1.08 cnf(c5, axiom, % 4.86/1.08 tc(X5,lam(X6),arr(X7,X8)) | ~tc(cons(X7,X5),X6,X8)). % 4.86/1.08 cnf(a3, assumption, % 4.86/1.08 cons(X3,X1) = X5). % 4.86/1.08 cnf(a4, assumption, % 4.86/1.08 X2 = lam(X6)). % 4.86/1.08 cnf(a5, assumption, % 4.86/1.08 X4 = arr(X7,X8)). % 4.86/1.08 cnf(c6, plain, % 4.86/1.08 $false, % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a3, a4, a5])], [c4, c5])). % 4.86/1.08 cnf(c7, plain, % 4.86/1.08 ~tc(cons(X7,X5),X6,X8), % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a3, a4, a5])], [c4, c5])). % 4.86/1.08 % 4.86/1.08 cnf(c8, axiom, % 4.86/1.08 tc(X9,var(X10),X11) | index(X9,X10) != just(X11)). % 4.86/1.08 cnf(a6, assumption, % 4.86/1.08 cons(X7,X5) = X9). % 4.86/1.08 cnf(a7, assumption, % 4.86/1.08 X6 = var(X10)). % 4.86/1.08 cnf(a8, assumption, % 4.86/1.08 X8 = X11). % 4.86/1.08 cnf(c9, plain, % 4.86/1.08 $false, % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a6, a7, a8])], [c7, c8])). % 4.86/1.08 cnf(c10, plain, % 4.86/1.08 index(X9,X10) != just(X11), % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a6, a7, a8])], [c7, c8])). % 4.86/1.08 % 4.86/1.08 cnf(c11, axiom, % 4.86/1.08 just(X12) = index(cons(X12,X13),zero)). % 4.86/1.08 cnf(a9, assumption, % 4.86/1.08 index(X9,X10) = index(cons(X12,X13),zero)). % 4.86/1.08 cnf(c12, plain, % 4.86/1.08 $false, % 4.86/1.08 inference(strict_function_extension, [assumptions([a9])], [c10, c11])). % 4.86/1.08 cnf(c13, plain, % 4.86/1.08 $false, % 4.86/1.08 inference(strict_function_extension, [assumptions([a9])], [c10, c11])). % 4.86/1.08 cnf(c14, plain, % 4.86/1.08 X14 != just(X12) | X14 != just(X11), % 4.86/1.08 inference(strict_function_extension, [assumptions([a9])], [c10, c11])). % 4.86/1.08 % 4.86/1.08 cnf(a10, assumption, % 4.86/1.08 X14 = just(X12)). % 4.86/1.08 cnf(c15, plain, % 4.86/1.08 X14 != just(X11), % 4.86/1.08 inference(reflexivity, [assumptions([a10])], [c14])). % 4.86/1.08 % 4.86/1.08 cnf(a11, assumption, % 4.86/1.08 X14 = just(X11)). % 4.86/1.08 cnf(c16, plain, % 4.86/1.08 $false, % 4.86/1.08 inference(reflexivity, [assumptions([a11])], [c15])). % 4.86/1.08 % 4.86/1.08 cnf(c17, axiom, % 4.86/1.08 nf(lam(X15)) | ~nf(X15)). % 4.86/1.08 cnf(a12, assumption, % 4.86/1.08 X0 = lam(X15)). % 4.86/1.08 cnf(c18, plain, % 4.86/1.08 $false, % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a12])], [c3, c17])). % 4.86/1.08 cnf(c19, plain, % 4.86/1.08 ~nf(X15), % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a12])], [c3, c17])). % 4.86/1.08 % 4.86/1.08 cnf(c20, axiom, % 4.86/1.08 nf(lam(X16)) | ~nf(X16)). % 4.86/1.08 cnf(a13, assumption, % 4.86/1.08 X15 = lam(X16)). % 4.86/1.08 cnf(c21, plain, % 4.86/1.08 $false, % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a13])], [c19, c20])). % 4.86/1.08 cnf(c22, plain, % 4.86/1.08 ~nf(X16), % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a13])], [c19, c20])). % 4.86/1.08 % 4.86/1.08 cnf(c23, axiom, % 4.86/1.08 nf(var(X17))). % 4.86/1.08 cnf(a14, assumption, % 4.86/1.08 X16 = var(X17)). % 4.86/1.08 cnf(c24, plain, % 4.86/1.08 $false, % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a14])], [c22, c23])). % 4.86/1.08 cnf(c25, plain, % 4.86/1.08 $false, % 4.86/1.08 inference(strict_predicate_extension, [assumptions([a14])], [c22, c23])). % 4.86/1.08 % 4.86/1.08 cnf(c26, plain, % 4.86/1.08 $false, % 4.86/1.08 inference(constraint_solving, [ % 4.86/1.08 bind(X0, lam(X2)), % 4.86/1.08 bind(X1, nil), % 4.86/1.08 bind(X2, lam(X6)), % 4.86/1.08 bind(X3, a), % 4.86/1.08 bind(X4, arr(b,b)), % 4.86/1.08 bind(X5, cons(X3,X1)), % 4.86/1.08 bind(X6, var(X10)), % 4.86/1.08 bind(X7, b), % 4.86/1.08 bind(X8, b), % 4.86/1.08 bind(X9, cons(X7,X5)), % 4.86/1.08 bind(X10, zero), % 4.86/1.08 bind(X11, b), % 4.86/1.08 bind(X12, b), % 4.86/1.08 bind(X13, cons(X3,X1)), % 4.86/1.08 bind(X14, just(X12)), % 4.86/1.08 bind(X15, lam(X6)), % 4.86/1.08 bind(X16, var(X10)), % 4.86/1.08 bind(X17, zero) % 4.86/1.08 ], % 4.86/1.08 [a0, a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13, a14])). % 4.86/1.08 % 4.86/1.08 % SZS output end IncompleteProof %------------------------------------------------------------------------------