%------------------------------------------------------------------------------ % File : lazyCoP---0.1 % Problem : LCL777-1 : TPTP v9.3.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % Computer : n011.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 12:29:21 PM UTC 2026 % Result : Unsatisfiable 0.58s 0.52s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL777-1 : TPTP v9.3.1. Released v4.1.0. % 0.00/0.04 % Command : vampire -t 0 --mode clausify %d -updr off -nm 2 -erd input_only -icip on | lazycop % 0.09/0.36 % Computer : n011.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sun Sep 6 01:41:59 UTC 2026 % 0.09/0.36 % CPUTime : % 0.58/0.52 % SZS status Unsatisfiable % 0.58/0.52 % SZS output begin IncompleteProof % 0.58/0.52 cnf(c0, axiom, % 0.58/0.52 ~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)))). % 0.58/0.52 cnf(c1, plain, % 0.58/0.52 ~hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))), % 0.58/0.52 inference(start, [], [c0])). % 0.58/0.52 % 0.58/0.52 cnf(c2, axiom, % 0.58/0.52 hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2) = c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)). % 0.58/0.52 cnf(a0, assumption, % 0.58/0.52 c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Oappend(v_ss,c_List_Olist_OCons(c_Lambda_OdB_OVar(v_i),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_List_Ofoldl(c_Lambda_OdB_OApp,X0,c_List_Oappend(X1,c_List_Olist_OCons(X2,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)). % 0.58/0.52 cnf(c3, plain, % 0.58/0.52 $false, % 0.58/0.52 inference(strict_function_extension, [assumptions([a0])], [c1, c2])). % 0.58/0.52 cnf(c4, plain, % 0.58/0.52 $false, % 0.58/0.52 inference(strict_function_extension, [assumptions([a0])], [c1, c2])). % 0.58/0.52 cnf(c5, plain, % 0.58/0.52 X3 != hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2) | ~hBOOL(hAPP(c_InductTermi_OIT,X3)), % 0.58/0.52 inference(strict_function_extension, [assumptions([a0])], [c1, c2])). % 0.58/0.52 % 0.58/0.52 cnf(a1, assumption, % 0.58/0.52 X3 = hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2)). % 0.58/0.52 cnf(c6, plain, % 0.58/0.52 ~hBOOL(hAPP(c_InductTermi_OIT,X3)), % 0.58/0.52 inference(reflexivity, [assumptions([a1])], [c5])). % 0.58/0.52 % 0.58/0.52 cnf(c7, axiom, % 0.58/0.52 hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i))))). % 0.58/0.52 cnf(a2, assumption, % 0.58/0.52 hAPP(c_InductTermi_OIT,X3) = hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB)),c_Lambda_OdB_OVar(v_i)))). % 0.58/0.52 cnf(c8, plain, % 0.58/0.52 $false, % 0.58/0.52 inference(strict_predicate_extension, [assumptions([a2])], [c6, c7])). % 0.58/0.52 cnf(c9, plain, % 0.58/0.52 $false, % 0.58/0.52 inference(strict_predicate_extension, [assumptions([a2])], [c6, c7])). % 0.58/0.52 % 0.58/0.52 cnf(c10, plain, % 0.58/0.52 $false, % 0.58/0.52 inference(constraint_solving, [ % 0.58/0.52 bind(X0, c_Lambda_Osubst(v_r,v_s,c_HOL_Ozero__class_Ozero(tc_nat))), % 0.58/0.52 bind(X1, v_ss), % 0.58/0.52 bind(X2, c_Lambda_OdB_OVar(v_i)), % 0.58/0.52 bind(X3, hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),X2)) % 0.58/0.52 ], % 0.58/0.52 [a0, a1, a2])). % 0.58/0.52 % 0.58/0.52 % SZS output end IncompleteProof %------------------------------------------------------------------------------