TSTP Solution File: SWV254-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SWV254-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n015.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 Apr 30 20:46:23 EDT 2024
% Result : Unsatisfiable 12.13s 2.00s
% Output : CNFRefutation 12.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV254-1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 30 01:19:02 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.19/0.45 % Drodi V3.6.0
% 12.13/2.00 % Refutation found
% 12.13/2.00 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 12.13/2.00 % SZS output start CNFRefutation for theBenchmark
% 12.13/2.00 fof(f28,axiom,(
% 12.13/2.00 (![T_a]: (c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(T_a)) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f45,axiom,(
% 12.13/2.00 (![V_xs,T_a]: (c_in(c_List_Oset(V_xs,T_a),c_Finite__Set_OFinites,tc_set(T_a)) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f64,axiom,(
% 12.13/2.00 (![V_n]: (c_lessequals(c_0,V_n,tc_nat) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f65,axiom,(
% 12.13/2.00 (![V_n]: (c_less(V_n,c_Suc(V_n),tc_nat) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f66,axiom,(
% 12.13/2.00 (![V_n]: (~ c_less(V_n,V_n,tc_nat) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f98,axiom,(
% 12.13/2.00 (![V_x,T_a]: (c_in(V_x,c_UNIV,T_a) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f133,axiom,(
% 12.13/2.00 class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f138,axiom,(
% 12.13/2.00 class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f151,axiom,(
% 12.13/2.00 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f153,axiom,(
% 12.13/2.00 class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f154,axiom,(
% 12.13/2.00 class_Orderings_Oorder(tc_IntDef_Oint) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f158,axiom,(
% 12.13/2.00 class_Orderings_Olinorder(tc_IntDef_Oint) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f181,axiom,(
% 12.13/2.00 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f183,axiom,(
% 12.13/2.00 class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f186,axiom,(
% 12.13/2.00 class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f203,axiom,(
% 12.13/2.00 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f243,axiom,(
% 12.13/2.00 class_Orderings_Olinorder(tc_nat) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f249,axiom,(
% 12.13/2.00 (![T_1]: (class_Orderings_Oorder(tc_set(T_1)) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f1165,axiom,(
% 12.13/2.00 (![V_n]: (c_Binomial_Obinomial(V_n,V_n) = c_1 ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f1173,axiom,(
% 12.13/2.00 (![V_a_H,T_a]: (c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(V_a_H,T_a) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f1213,axiom,(
% 12.13/2.00 (![V_m]: (c_div(c_0,V_m,tc_nat) = c_0 ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f1214,axiom,(
% 12.13/2.00 (![V_y]: (c_div(V_y,c_Suc(c_0),tc_nat) = V_y ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f1350,axiom,(
% 12.13/2.00 c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f1352,axiom,(
% 12.13/2.00 (![V_w,V_z]: (( ~ c_lessequals(V_w,V_z,tc_IntDef_Oint)| c_less(V_w,c_plus(V_z,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f1357,axiom,(
% 12.13/2.00 (![T_a]: (( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)| c_in(c_0,c_IntDef_OInts,T_a) ) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f1367,axiom,(
% 12.13/2.00 (![V_m]: (c_HOL_Oabs(c_IntDef_Oint(V_m),tc_IntDef_Oint) = c_IntDef_Oint(V_m) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f1371,axiom,(
% 12.13/2.00 c_IntDef_Oint(c_1) = c_1 ),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f1372,axiom,(
% 12.13/2.00 (![V_m]: (c_IntDef_Oint(c_Suc(V_m)) = c_plus(c_1,c_IntDef_Oint(V_m),tc_IntDef_Oint) ))),
% 12.13/2.00 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.00 fof(f1374,axiom,(
% 12.13/2.02 c_IntDef_Oint(c_0) = c_0 ),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1378,axiom,(
% 12.13/2.02 (![V_k]: (~ c_less(c_IntDef_Oint(V_k),c_0,tc_IntDef_Oint) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1379,axiom,(
% 12.13/2.02 (![V_z]: (( ~ c_lessequals(c_0,V_z,tc_IntDef_Oint)| c_IntDef_Oint(c_IntDef_Onat(V_z)) = V_z ) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1388,axiom,(
% 12.13/2.02 (![V_n]: (c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(V_n)),tc_IntDef_Oint),tc_IntDef_Oint) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1391,axiom,(
% 12.13/2.02 c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint) = c_IntDef_Oint(c_0) ),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1393,axiom,(
% 12.13/2.02 (![V_n]: (~ c_IntDef_Oneg(c_IntDef_Oint(V_n),tc_IntDef_Oint) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1394,axiom,(
% 12.13/2.02 (![V_n]: (~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(V_n)),tc_IntDef_Oint),tc_IntDef_Oint) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1426,axiom,(
% 12.13/2.02 (![V_m,V_n]: (( ~ c_lessequals(V_m,V_n,tc_nat)| c_lessequals(c_IntDef_Oint(V_m),c_IntDef_Oint(V_n),tc_IntDef_Oint) ) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1466,axiom,(
% 12.13/2.02 (![V_y]: (c_div(V_y,c_1,tc_IntDef_Oint) = V_y ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1472,axiom,(
% 12.13/2.02 (![V_a,V_b]: (( V_a = c_0| c_div(c_plus(V_a,V_b,tc_IntDef_Oint),V_a,tc_IntDef_Oint) = c_plus(c_div(V_b,V_a,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1482,axiom,(
% 12.13/2.02 (![V_m]: (c_Divides_Oop_Advd(V_m,V_m,tc_IntDef_Oint) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1689,axiom,(
% 12.13/2.02 (![V_xs,V_x,T_a]: (V_xs != c_List_Olist_OCons(V_x,V_xs,T_a) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f1866,axiom,(
% 12.13/2.02 c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) = c_0 ),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2016,axiom,(
% 12.13/2.02 c_1 = c_Suc(c_0) ),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2023,axiom,(
% 12.13/2.02 (![V_m]: (c_Suc(V_m) != c_0 ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2042,axiom,(
% 12.13/2.02 (![V_i]: (( ~ c_lessequals(V_i,c_0,tc_nat)| V_i = c_0 ) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2049,axiom,(
% 12.13/2.02 c_less(c_0,c_1,tc_nat) ),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2091,axiom,(
% 12.13/2.02 (![V_n]: (~ c_less(V_n,c_0,tc_nat) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2102,axiom,(
% 12.13/2.02 (![V_y]: (c_minus(V_y,c_0,tc_nat) = V_y ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2159,axiom,(
% 12.13/2.02 c_Numeral_Obit_OB0 != c_Numeral_Obit_OB1 ),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2269,axiom,(
% 12.13/2.02 (![T_a,V_x]: (( ~ class_Orderings_Oorder(T_a)| ~ c_less(V_x,V_x,T_a) ) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2395,axiom,(
% 12.13/2.02 (![T_a]: (( ~ class_Ring__and__Field_Oaxclass__0__neq__1(T_a)| c_0 != c_1 ) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2567,axiom,(
% 12.13/2.02 c_SetInterval_OlessThan(c_0,tc_nat) = c_emptyset ),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2629,axiom,(
% 12.13/2.02 c_UNIV != c_emptyset ),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2672,axiom,(
% 12.13/2.02 (![V_c,T_a]: (~ c_in(V_c,c_emptyset,T_a) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2788,negated_conjecture,(
% 12.13/2.02 (![V_U]: (c_lessequals(V_U,v_x(V_U),tc_nat) ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2789,negated_conjecture,(
% 12.13/2.02 (![V_U]: (v_x(V_U) = v_nat ))),
% 12.13/2.02 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 12.13/2.02 fof(f2831,plain,(
% 12.13/2.02 ![X0]: (c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f28])).
% 12.13/2.02 fof(f2852,plain,(
% 12.13/2.02 ![X0,X1]: (c_in(c_List_Oset(X0,X1),c_Finite__Set_OFinites,tc_set(X1)))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f45])).
% 12.13/2.02 fof(f2876,plain,(
% 12.13/2.02 ![X0]: (c_lessequals(c_0,X0,tc_nat))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f64])).
% 12.13/2.02 fof(f2877,plain,(
% 12.13/2.02 ![X0]: (c_less(X0,c_Suc(X0),tc_nat))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f65])).
% 12.13/2.02 fof(f2878,plain,(
% 12.13/2.02 ![X0]: (~c_less(X0,X0,tc_nat))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f66])).
% 12.13/2.02 fof(f2915,plain,(
% 12.13/2.02 ![X0,X1]: (c_in(X0,c_UNIV,X1))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f98])).
% 12.13/2.02 fof(f2961,plain,(
% 12.13/2.02 class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f133])).
% 12.13/2.02 fof(f2966,plain,(
% 12.13/2.02 class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f138])).
% 12.13/2.02 fof(f2979,plain,(
% 12.13/2.02 class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f151])).
% 12.13/2.02 fof(f2981,plain,(
% 12.13/2.02 class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f153])).
% 12.13/2.02 fof(f2982,plain,(
% 12.13/2.02 class_Orderings_Oorder(tc_IntDef_Oint)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f154])).
% 12.13/2.02 fof(f2986,plain,(
% 12.13/2.02 class_Orderings_Olinorder(tc_IntDef_Oint)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f158])).
% 12.13/2.02 fof(f3009,plain,(
% 12.13/2.02 class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f181])).
% 12.13/2.02 fof(f3011,plain,(
% 12.13/2.02 class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f183])).
% 12.13/2.02 fof(f3014,plain,(
% 12.13/2.02 class_Numeral_Onumber__ring(tc_IntDef_Oint)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f186])).
% 12.13/2.02 fof(f3032,plain,(
% 12.13/2.02 class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f203])).
% 12.13/2.02 fof(f3072,plain,(
% 12.13/2.02 class_Orderings_Olinorder(tc_nat)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f243])).
% 12.13/2.02 fof(f3079,plain,(
% 12.13/2.02 ![X0]: (class_Orderings_Oorder(tc_set(X0)))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f249])).
% 12.13/2.02 fof(f3996,plain,(
% 12.13/2.02 ![X0]: (c_Binomial_Obinomial(X0,X0)=c_1)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1165])).
% 12.13/2.02 fof(f4007,plain,(
% 12.13/2.02 ![X0,X1]: (~c_Datatype_Ooption_ONone=c_Datatype_Ooption_OSome(X0,X1))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1173])).
% 12.13/2.02 fof(f4053,plain,(
% 12.13/2.02 ![X0]: (c_div(c_0,X0,tc_nat)=c_0)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1213])).
% 12.13/2.02 fof(f4054,plain,(
% 12.13/2.02 ![X0]: (c_div(X0,c_Suc(c_0),tc_nat)=X0)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1214])).
% 12.13/2.02 fof(f4236,plain,(
% 12.13/2.02 c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1350])).
% 12.13/2.02 fof(f4238,plain,(
% 12.13/2.02 ![X0,X1]: (~c_lessequals(X0,X1,tc_IntDef_Oint)|c_less(X0,c_plus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1352])).
% 12.13/2.02 fof(f4243,plain,(
% 12.13/2.02 ![X0]: (~class_Ring__and__Field_Ocomm__ring__1(X0)|c_in(c_0,c_IntDef_OInts,X0))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1357])).
% 12.13/2.02 fof(f4253,plain,(
% 12.13/2.02 ![X0]: (c_HOL_Oabs(c_IntDef_Oint(X0),tc_IntDef_Oint)=c_IntDef_Oint(X0))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1367])).
% 12.13/2.02 fof(f4257,plain,(
% 12.13/2.02 c_IntDef_Oint(c_1)=c_1),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1371])).
% 12.13/2.02 fof(f4258,plain,(
% 12.13/2.02 ![X0]: (c_IntDef_Oint(c_Suc(X0))=c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1372])).
% 12.13/2.02 fof(f4260,plain,(
% 12.13/2.02 c_IntDef_Oint(c_0)=c_0),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1374])).
% 12.13/2.02 fof(f4264,plain,(
% 12.13/2.02 ![X0]: (~c_less(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1378])).
% 12.13/2.02 fof(f4265,plain,(
% 12.13/2.02 ![X0]: (~c_lessequals(c_0,X0,tc_IntDef_Oint)|c_IntDef_Oint(c_IntDef_Onat(X0))=X0)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1379])).
% 12.13/2.02 fof(f4274,plain,(
% 12.13/2.02 ![X0]: (c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X0)),tc_IntDef_Oint),tc_IntDef_Oint))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1388])).
% 12.13/2.02 fof(f4279,plain,(
% 12.13/2.02 c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint)=c_IntDef_Oint(c_0)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1391])).
% 12.13/2.02 fof(f4281,plain,(
% 12.13/2.02 ![X0]: (~c_IntDef_Oneg(c_IntDef_Oint(X0),tc_IntDef_Oint))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1393])).
% 12.13/2.02 fof(f4282,plain,(
% 12.13/2.02 ![X0]: (~c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X0)),tc_IntDef_Oint),tc_IntDef_Oint))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1394])).
% 12.13/2.02 fof(f4330,plain,(
% 12.13/2.02 ![X0,X1]: (~c_lessequals(X0,X1,tc_nat)|c_lessequals(c_IntDef_Oint(X0),c_IntDef_Oint(X1),tc_IntDef_Oint))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1426])).
% 12.13/2.02 fof(f4375,plain,(
% 12.13/2.02 ![X0]: (c_div(X0,c_1,tc_IntDef_Oint)=X0)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1466])).
% 12.13/2.02 fof(f4383,plain,(
% 12.13/2.02 ![V_a]: (V_a=c_0|(![V_b]: c_div(c_plus(V_a,V_b,tc_IntDef_Oint),V_a,tc_IntDef_Oint)=c_plus(c_div(V_b,V_a,tc_IntDef_Oint),c_1,tc_IntDef_Oint)))),
% 12.13/2.02 inference(miniscoping,[status(esa)],[f1472])).
% 12.13/2.02 fof(f4384,plain,(
% 12.13/2.02 ![X0,X1]: (X0=c_0|c_div(c_plus(X0,X1,tc_IntDef_Oint),X0,tc_IntDef_Oint)=c_plus(c_div(X1,X0,tc_IntDef_Oint),c_1,tc_IntDef_Oint))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f4383])).
% 12.13/2.02 fof(f4397,plain,(
% 12.13/2.02 ![X0]: (c_Divides_Oop_Advd(X0,X0,tc_IntDef_Oint))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1482])).
% 12.13/2.02 fof(f4666,plain,(
% 12.13/2.02 ![X0,X1,X2]: (~X0=c_List_Olist_OCons(X1,X0,X2))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1689])).
% 12.13/2.02 fof(f4904,plain,(
% 12.13/2.02 c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)=c_0),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f1866])).
% 12.13/2.02 fof(f5123,plain,(
% 12.13/2.02 c_1=c_Suc(c_0)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2016])).
% 12.13/2.02 fof(f5130,plain,(
% 12.13/2.02 ![X0]: (~c_Suc(X0)=c_0)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2023])).
% 12.13/2.02 fof(f5155,plain,(
% 12.13/2.02 ![X0]: (~c_lessequals(X0,c_0,tc_nat)|X0=c_0)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2042])).
% 12.13/2.02 fof(f5162,plain,(
% 12.13/2.02 c_less(c_0,c_1,tc_nat)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2049])).
% 12.13/2.02 fof(f5227,plain,(
% 12.13/2.02 ![X0]: (~c_less(X0,c_0,tc_nat))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2091])).
% 12.13/2.02 fof(f5242,plain,(
% 12.13/2.02 ![X0]: (c_minus(X0,c_0,tc_nat)=X0)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2102])).
% 12.13/2.02 fof(f5308,plain,(
% 12.13/2.02 ~c_Numeral_Obit_OB0=c_Numeral_Obit_OB1),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2159])).
% 12.13/2.02 fof(f5476,plain,(
% 12.13/2.02 ![T_a]: (~class_Orderings_Oorder(T_a)|(![V_x]: ~c_less(V_x,V_x,T_a)))),
% 12.13/2.02 inference(miniscoping,[status(esa)],[f2269])).
% 12.13/2.02 fof(f5477,plain,(
% 12.13/2.02 ![X0,X1]: (~class_Orderings_Oorder(X0)|~c_less(X1,X1,X0))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f5476])).
% 12.13/2.02 fof(f5663,plain,(
% 12.13/2.02 (![T_a]: ~class_Ring__and__Field_Oaxclass__0__neq__1(T_a))|~c_0=c_1),
% 12.13/2.02 inference(miniscoping,[status(esa)],[f2395])).
% 12.13/2.02 fof(f5664,plain,(
% 12.13/2.02 ![X0]: (~class_Ring__and__Field_Oaxclass__0__neq__1(X0)|~c_0=c_1)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f5663])).
% 12.13/2.02 fof(f5921,plain,(
% 12.13/2.02 c_SetInterval_OlessThan(c_0,tc_nat)=c_emptyset),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2567])).
% 12.13/2.02 fof(f5998,plain,(
% 12.13/2.02 ~c_UNIV=c_emptyset),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2629])).
% 12.13/2.02 fof(f6056,plain,(
% 12.13/2.02 ![X0,X1]: (~c_in(X0,c_emptyset,X1))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2672])).
% 12.13/2.02 fof(f6201,plain,(
% 12.13/2.02 ![X0]: (c_lessequals(X0,v_x(X0),tc_nat))),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2788])).
% 12.13/2.02 fof(f6202,plain,(
% 12.13/2.02 ![X0]: (v_x(X0)=v_nat)),
% 12.13/2.02 inference(cnf_transformation,[status(esa)],[f2789])).
% 12.13/2.02 fof(f6203,plain,(
% 12.13/2.02 spl0_0 <=> ~class_Ring__and__Field_Oaxclass__0__neq__1(X0)),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f6204,plain,(
% 12.13/2.02 ![X0]: (~class_Ring__and__Field_Oaxclass__0__neq__1(X0)|~spl0_0)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f6203])).
% 12.13/2.02 fof(f6206,plain,(
% 12.13/2.02 spl0_1 <=> c_0=c_1),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f6209,plain,(
% 12.13/2.02 spl0_0|~spl0_1),
% 12.13/2.02 inference(split_clause,[status(thm)],[f5664,f6203,f6206])).
% 12.13/2.02 fof(f6212,plain,(
% 12.13/2.02 ![X0]: (c_lessequals(X0,v_nat,tc_nat))),
% 12.13/2.02 inference(forward_demodulation,[status(thm)],[f6202,f6201])).
% 12.13/2.02 fof(f7929,plain,(
% 12.13/2.02 ~c_less(c_1,c_0,tc_IntDef_Oint)),
% 12.13/2.02 inference(paramodulation,[status(thm)],[f4257,f4264])).
% 12.13/2.02 fof(f7946,plain,(
% 12.13/2.02 ![X0]: (c_div(X0,c_1,tc_nat)=X0)),
% 12.13/2.02 inference(forward_demodulation,[status(thm)],[f5123,f4054])).
% 12.13/2.02 fof(f7969,plain,(
% 12.13/2.02 spl0_21 <=> ~c_less(c_0,X0,tc_nat)),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f7970,plain,(
% 12.13/2.02 ![X0]: (~c_less(c_0,X0,tc_nat)|~spl0_21)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f7969])).
% 12.13/2.02 fof(f7983,plain,(
% 12.13/2.02 spl0_24 <=> ~c_less(c_1,X0,tc_nat)),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f7984,plain,(
% 12.13/2.02 ![X0]: (~c_less(c_1,X0,tc_nat)|~spl0_24)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f7983])).
% 12.13/2.02 fof(f7998,plain,(
% 12.13/2.02 spl0_27 <=> ~c_less(c_0,X0,tc_nat)|c_less(X0,X0,tc_nat)),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f7999,plain,(
% 12.13/2.02 ![X0]: (~c_less(c_0,X0,tc_nat)|c_less(X0,X0,tc_nat)|~spl0_27)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f7998])).
% 12.13/2.02 fof(f8209,plain,(
% 12.13/2.02 $false|~spl0_0),
% 12.13/2.02 inference(backward_subsumption_resolution,[status(thm)],[f3032,f6204])).
% 12.13/2.02 fof(f8210,plain,(
% 12.13/2.02 ~spl0_0),
% 12.13/2.02 inference(contradiction_clause,[status(thm)],[f8209])).
% 12.13/2.02 fof(f8245,plain,(
% 12.13/2.02 spl0_56 <=> c_0=c_div(c_1,X0,tc_nat)),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f8246,plain,(
% 12.13/2.02 ![X0]: (c_0=c_div(c_1,X0,tc_nat)|~spl0_56)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f8245])).
% 12.13/2.02 fof(f8255,plain,(
% 12.13/2.02 spl0_58 <=> c_div(c_0,c_0,tc_nat)=c_div(c_1,X0,tc_nat)),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f8256,plain,(
% 12.13/2.02 ![X0]: (c_div(c_0,c_0,tc_nat)=c_div(c_1,X0,tc_nat)|~spl0_58)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f8255])).
% 12.13/2.02 fof(f8425,plain,(
% 12.13/2.02 spl0_65 <=> c_0=c_Suc(c_div(X0,c_0,tc_nat))),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f8426,plain,(
% 12.13/2.02 ![X0]: (c_0=c_Suc(c_div(X0,c_0,tc_nat))|~spl0_65)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f8425])).
% 12.13/2.02 fof(f8972,plain,(
% 12.13/2.02 c_HOL_Oabs(c_0,tc_IntDef_Oint)=c_IntDef_Oint(c_0)),
% 12.13/2.02 inference(paramodulation,[status(thm)],[f4260,f4253])).
% 12.13/2.02 fof(f8973,plain,(
% 12.13/2.02 c_HOL_Oabs(c_0,tc_IntDef_Oint)=c_0),
% 12.13/2.02 inference(forward_demodulation,[status(thm)],[f4260,f8972])).
% 12.13/2.02 fof(f9004,plain,(
% 12.13/2.02 spl0_73 <=> ~c_List_Olist_ONil=X0),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f9005,plain,(
% 12.13/2.02 ![X0]: (~c_List_Olist_ONil=X0|~spl0_73)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f9004])).
% 12.13/2.02 fof(f9063,plain,(
% 12.13/2.02 spl0_78 <=> c_0=c_Suc(c_1)),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f9064,plain,(
% 12.13/2.02 c_0=c_Suc(c_1)|~spl0_78),
% 12.13/2.02 inference(component_clause,[status(thm)],[f9063])).
% 12.13/2.02 fof(f9083,plain,(
% 12.13/2.02 spl0_81 <=> c_0=c_Suc(c_div(c_1,c_0,tc_nat))),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f9084,plain,(
% 12.13/2.02 c_0=c_Suc(c_div(c_1,c_0,tc_nat))|~spl0_81),
% 12.13/2.02 inference(component_clause,[status(thm)],[f9083])).
% 12.13/2.02 fof(f9605,plain,(
% 12.13/2.02 spl0_151 <=> c_0=c_Suc(c_div(c_Binomial_Obinomial(c_0,c_Suc(c_1)),c_0,tc_nat))),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f9606,plain,(
% 12.13/2.02 c_0=c_Suc(c_div(c_Binomial_Obinomial(c_0,c_Suc(c_1)),c_0,tc_nat))|~spl0_151),
% 12.13/2.02 inference(component_clause,[status(thm)],[f9605])).
% 12.13/2.02 fof(f9696,plain,(
% 12.13/2.02 spl0_159 <=> c_less(X0,c_0,tc_nat)),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f9697,plain,(
% 12.13/2.02 ![X0]: (c_less(X0,c_0,tc_nat)|~spl0_159)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f9696])).
% 12.13/2.02 fof(f10719,plain,(
% 12.13/2.02 spl0_193 <=> ~X0=c_emptyset),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f10720,plain,(
% 12.13/2.02 ![X0]: (~X0=c_emptyset|~spl0_193)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f10719])).
% 12.13/2.02 fof(f10724,plain,(
% 12.13/2.02 spl0_194 <=> X0=c_emptyset),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f10725,plain,(
% 12.13/2.02 ![X0]: (X0=c_emptyset|~spl0_194)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f10724])).
% 12.13/2.02 fof(f10738,plain,(
% 12.13/2.02 spl0_195 <=> ~class_Orderings_Olinorder(X0)|~c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0))),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f10739,plain,(
% 12.13/2.02 ![X0]: (~class_Orderings_Olinorder(X0)|~c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0))|~spl0_195)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f10738])).
% 12.13/2.02 fof(f11186,plain,(
% 12.13/2.02 spl0_255 <=> c_0=c_Binomial_Obinomial(c_Suc(c_1),c_Suc(c_1))),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f11187,plain,(
% 12.13/2.02 c_0=c_Binomial_Obinomial(c_Suc(c_1),c_Suc(c_1))|~spl0_255),
% 12.13/2.02 inference(component_clause,[status(thm)],[f11186])).
% 12.13/2.02 fof(f11775,plain,(
% 12.13/2.02 spl0_314 <=> ~X0=c_0),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f11776,plain,(
% 12.13/2.02 ![X0]: (~X0=c_0|~spl0_314)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f11775])).
% 12.13/2.02 fof(f12251,plain,(
% 12.13/2.02 spl0_362 <=> ~class_Orderings_Oorder(tc_set(X0))),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f12252,plain,(
% 12.13/2.02 ![X0]: (~class_Orderings_Oorder(tc_set(X0))|~spl0_362)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f12251])).
% 12.13/2.02 fof(f12683,plain,(
% 12.13/2.02 spl0_406 <=> c_Datatype_Ooption_OSome(X0,X1)=c_Datatype_Ooption_ONone),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f12684,plain,(
% 12.13/2.02 ![X0,X1]: (c_Datatype_Ooption_OSome(X0,X1)=c_Datatype_Ooption_ONone|~spl0_406)),
% 12.13/2.02 inference(component_clause,[status(thm)],[f12683])).
% 12.13/2.02 fof(f12735,plain,(
% 12.13/2.02 c_less(c_0,c_1,tc_IntDef_Oint)),
% 12.13/2.02 inference(forward_demodulation,[status(thm)],[f8973,f4236])).
% 12.13/2.02 fof(f12751,plain,(
% 12.13/2.02 spl0_412 <=> class_Orderings_Olinorder(tc_IntDef_Oint)),
% 12.13/2.02 introduced(split_symbol_definition)).
% 12.13/2.02 fof(f12753,plain,(
% 12.13/2.02 ~class_Orderings_Olinorder(tc_IntDef_Oint)|spl0_412),
% 12.13/2.02 inference(component_clause,[status(thm)],[f12751])).
% 12.13/2.02 fof(f12760,plain,(
% 12.13/2.02 spl0_414 <=> class_Orderings_Oorder(tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f12762,plain,(
% 12.42/2.02 ~class_Orderings_Oorder(tc_IntDef_Oint)|spl0_414),
% 12.42/2.02 inference(component_clause,[status(thm)],[f12760])).
% 12.42/2.02 fof(f12765,plain,(
% 12.42/2.02 $false|spl0_414),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f12762,f2982])).
% 12.42/2.02 fof(f12766,plain,(
% 12.42/2.02 spl0_414),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f12765])).
% 12.42/2.02 fof(f12767,plain,(
% 12.42/2.02 $false|spl0_412),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f12753,f2986])).
% 12.42/2.02 fof(f12768,plain,(
% 12.42/2.02 spl0_412),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f12767])).
% 12.42/2.02 fof(f12769,plain,(
% 12.42/2.02 c_uminus(c_0,tc_IntDef_Oint)=c_IntDef_Oint(c_0)),
% 12.42/2.02 inference(forward_demodulation,[status(thm)],[f4260,f4279])).
% 12.42/2.02 fof(f12770,plain,(
% 12.42/2.02 c_uminus(c_0,tc_IntDef_Oint)=c_0),
% 12.42/2.02 inference(forward_demodulation,[status(thm)],[f4260,f12769])).
% 12.42/2.02 fof(f12772,plain,(
% 12.42/2.02 spl0_415 <=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f12774,plain,(
% 12.42/2.02 ~class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)|spl0_415),
% 12.42/2.02 inference(component_clause,[status(thm)],[f12772])).
% 12.42/2.02 fof(f12782,plain,(
% 12.42/2.02 $false|spl0_415),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f12774,f2966])).
% 12.42/2.02 fof(f12783,plain,(
% 12.42/2.02 spl0_415),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f12782])).
% 12.42/2.02 fof(f12784,plain,(
% 12.42/2.02 spl0_417 <=> ~class_Ring__and__Field_Oordered__idom(X0)|~class_Ring__and__Field_Oordered__idom(X0)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f12785,plain,(
% 12.42/2.02 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|~class_Ring__and__Field_Oordered__idom(X0)|~spl0_417)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f12784])).
% 12.42/2.02 fof(f12801,plain,(
% 12.42/2.02 spl0_419 <=> c_in(c_SetInterval_OlessThan(c_0,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f12803,plain,(
% 12.42/2.02 ~c_in(c_SetInterval_OlessThan(c_0,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))|spl0_419),
% 12.42/2.02 inference(component_clause,[status(thm)],[f12801])).
% 12.42/2.02 fof(f12806,plain,(
% 12.42/2.02 spl0_420 <=> ~c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0))),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f12807,plain,(
% 12.42/2.02 ![X0]: (~c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0))|~spl0_420)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f12806])).
% 12.42/2.02 fof(f12815,plain,(
% 12.42/2.02 ~c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_nat))|spl0_419),
% 12.42/2.02 inference(forward_demodulation,[status(thm)],[f5921,f12803])).
% 12.42/2.02 fof(f12816,plain,(
% 12.42/2.02 $false|spl0_419),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f12815,f2831])).
% 12.42/2.02 fof(f12817,plain,(
% 12.42/2.02 spl0_419),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f12816])).
% 12.42/2.02 fof(f12930,plain,(
% 12.42/2.02 ![X0]: (c_0=c_div(c_1,X0,tc_nat)|~spl0_58)),
% 12.42/2.02 inference(forward_demodulation,[status(thm)],[f4053,f8256])).
% 12.42/2.02 fof(f12934,plain,(
% 12.42/2.02 $false|~spl0_420),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f12807,f2831])).
% 12.42/2.02 fof(f12935,plain,(
% 12.42/2.02 ~spl0_420),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f12934])).
% 12.42/2.02 fof(f12936,plain,(
% 12.42/2.02 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|~spl0_417)),
% 12.42/2.02 inference(duplicate_literals_removal,[status(esa)],[f12785])).
% 12.42/2.02 fof(f12937,plain,(
% 12.42/2.02 $false|~spl0_362),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f12252,f3079])).
% 12.42/2.02 fof(f12938,plain,(
% 12.42/2.02 ~spl0_362),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f12937])).
% 12.42/2.02 fof(f12939,plain,(
% 12.42/2.02 $false|~spl0_406),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f12684,f4007])).
% 12.42/2.02 fof(f12940,plain,(
% 12.42/2.02 ~spl0_406),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f12939])).
% 12.42/2.02 fof(f12975,plain,(
% 12.42/2.02 $false|~spl0_417),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f3011,f12936])).
% 12.42/2.02 fof(f12976,plain,(
% 12.42/2.02 ~spl0_417),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f12975])).
% 12.42/2.02 fof(f13007,plain,(
% 12.42/2.02 $false|~spl0_24),
% 12.42/2.02 inference(resolution,[status(thm)],[f7984,f2877])).
% 12.42/2.02 fof(f13008,plain,(
% 12.42/2.02 ~spl0_24),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13007])).
% 12.42/2.02 fof(f13133,plain,(
% 12.42/2.02 $false|~spl0_314),
% 12.42/2.02 inference(destructive_equality_resolution,[status(esa)],[f11776])).
% 12.42/2.02 fof(f13134,plain,(
% 12.42/2.02 ~spl0_314),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13133])).
% 12.42/2.02 fof(f13152,plain,(
% 12.42/2.02 ![X0]: (~class_Orderings_Olinorder(X0)|~spl0_195)),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f10739,f2831])).
% 12.42/2.02 fof(f13153,plain,(
% 12.42/2.02 $false|~spl0_193),
% 12.42/2.02 inference(destructive_equality_resolution,[status(esa)],[f10720])).
% 12.42/2.02 fof(f13154,plain,(
% 12.42/2.02 ~spl0_193),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13153])).
% 12.42/2.02 fof(f13158,plain,(
% 12.42/2.02 $false|~spl0_159),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f9697,f5227])).
% 12.42/2.02 fof(f13159,plain,(
% 12.42/2.02 ~spl0_159),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13158])).
% 12.42/2.02 fof(f13164,plain,(
% 12.42/2.02 $false|~spl0_151),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f9606,f5130])).
% 12.42/2.02 fof(f13165,plain,(
% 12.42/2.02 ~spl0_151),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13164])).
% 12.42/2.02 fof(f13206,plain,(
% 12.42/2.02 $false|~spl0_81),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f9084,f5130])).
% 12.42/2.02 fof(f13207,plain,(
% 12.42/2.02 ~spl0_81),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13206])).
% 12.42/2.02 fof(f13208,plain,(
% 12.42/2.02 $false|~spl0_78),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f9064,f5130])).
% 12.42/2.02 fof(f13209,plain,(
% 12.42/2.02 ~spl0_78),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13208])).
% 12.42/2.02 fof(f13210,plain,(
% 12.42/2.02 $false|~spl0_73),
% 12.42/2.02 inference(destructive_equality_resolution,[status(esa)],[f9005])).
% 12.42/2.02 fof(f13211,plain,(
% 12.42/2.02 ~spl0_73),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13210])).
% 12.42/2.02 fof(f13212,plain,(
% 12.42/2.02 $false|~spl0_65),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f8426,f5130])).
% 12.42/2.02 fof(f13213,plain,(
% 12.42/2.02 ~spl0_65),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13212])).
% 12.42/2.02 fof(f13217,plain,(
% 12.42/2.02 ![X0]: (~c_less(c_0,X0,tc_nat)|~spl0_27)),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f7999,f2878])).
% 12.42/2.02 fof(f13221,plain,(
% 12.42/2.02 $false|~spl0_194),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f5998,f10725])).
% 12.42/2.02 fof(f13222,plain,(
% 12.42/2.02 ~spl0_194),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13221])).
% 12.42/2.02 fof(f13230,plain,(
% 12.42/2.02 $false|~spl0_195),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f3072,f13152])).
% 12.42/2.02 fof(f13231,plain,(
% 12.42/2.02 ~spl0_195),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13230])).
% 12.42/2.02 fof(f13292,plain,(
% 12.42/2.02 $false|~spl0_27),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f5162,f13217])).
% 12.42/2.02 fof(f13293,plain,(
% 12.42/2.02 ~spl0_27),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13292])).
% 12.42/2.02 fof(f13296,plain,(
% 12.42/2.02 $false|~spl0_21),
% 12.42/2.02 inference(resolution,[status(thm)],[f7970,f2877])).
% 12.42/2.02 fof(f13297,plain,(
% 12.42/2.02 ~spl0_21),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13296])).
% 12.42/2.02 fof(f13746,plain,(
% 12.42/2.02 spl0_462 <=> c_in(c_List_Oset(c_List_Olist_ONil,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f13748,plain,(
% 12.42/2.02 ~c_in(c_List_Oset(c_List_Olist_ONil,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat))|spl0_462),
% 12.42/2.02 inference(component_clause,[status(thm)],[f13746])).
% 12.42/2.02 fof(f13762,plain,(
% 12.42/2.02 $false|spl0_462),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f13748,f2852])).
% 12.42/2.02 fof(f13763,plain,(
% 12.42/2.02 spl0_462),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f13762])).
% 12.42/2.02 fof(f14276,plain,(
% 12.42/2.02 spl0_489 <=> c_in(c_0,c_UNIV,tc_nat)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f14278,plain,(
% 12.42/2.02 ~c_in(c_0,c_UNIV,tc_nat)|spl0_489),
% 12.42/2.02 inference(component_clause,[status(thm)],[f14276])).
% 12.42/2.02 fof(f14298,plain,(
% 12.42/2.02 $false|spl0_489),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f14278,f2915])).
% 12.42/2.02 fof(f14299,plain,(
% 12.42/2.02 spl0_489),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f14298])).
% 12.42/2.02 fof(f14357,plain,(
% 12.42/2.02 ~c_1=c_0),
% 12.42/2.02 inference(paramodulation,[status(thm)],[f5123,f5130])).
% 12.42/2.02 fof(f14447,plain,(
% 12.42/2.02 spl0_497 <=> c_less(c_1,c_0,tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f14448,plain,(
% 12.42/2.02 c_less(c_1,c_0,tc_IntDef_Oint)|~spl0_497),
% 12.42/2.02 inference(component_clause,[status(thm)],[f14447])).
% 12.42/2.02 fof(f14458,plain,(
% 12.42/2.02 $false|~spl0_497),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f14448,f7929])).
% 12.42/2.02 fof(f14459,plain,(
% 12.42/2.02 ~spl0_497),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f14458])).
% 12.42/2.02 fof(f14501,plain,(
% 12.42/2.02 spl0_499 <=> ~c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f14502,plain,(
% 12.42/2.02 ![X0]: (~c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)|~spl0_499)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f14501])).
% 12.42/2.02 fof(f14504,plain,(
% 12.42/2.02 ![X0]: (~c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)|~class_Orderings_Oorder(tc_IntDef_Oint))),
% 12.42/2.02 inference(resolution,[status(thm)],[f4238,f5477])).
% 12.42/2.02 fof(f14505,plain,(
% 12.42/2.02 spl0_499|~spl0_414),
% 12.42/2.02 inference(split_clause,[status(thm)],[f14504,f14501,f12760])).
% 12.42/2.02 fof(f14541,plain,(
% 12.42/2.02 spl0_504 <=> c_lessequals(c_1,c_Numeral_Onumber__of(X0,tc_nat),tc_nat)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f14542,plain,(
% 12.42/2.02 ![X0]: (c_lessequals(c_1,c_Numeral_Onumber__of(X0,tc_nat),tc_nat)|~spl0_504)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f14541])).
% 12.42/2.02 fof(f14650,plain,(
% 12.42/2.02 spl0_509 <=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f14652,plain,(
% 12.42/2.02 ~class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)|spl0_509),
% 12.42/2.02 inference(component_clause,[status(thm)],[f14650])).
% 12.42/2.02 fof(f14669,plain,(
% 12.42/2.02 $false|spl0_509),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f14652,f2981])).
% 12.42/2.02 fof(f14670,plain,(
% 12.42/2.02 spl0_509),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f14669])).
% 12.42/2.02 fof(f14722,plain,(
% 12.42/2.02 spl0_516 <=> c_minus(c_1,c_Numeral_Onumber__of(X0,tc_nat),tc_nat)=c_0),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f14723,plain,(
% 12.42/2.02 ![X0]: (c_minus(c_1,c_Numeral_Onumber__of(X0,tc_nat),tc_nat)=c_0|~spl0_516)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f14722])).
% 12.42/2.02 fof(f14732,plain,(
% 12.42/2.02 spl0_518 <=> ~c_lessequals(c_Numeral_Onumber__of(X0,tc_nat),c_1,tc_nat)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f14733,plain,(
% 12.42/2.02 ![X0]: (~c_lessequals(c_Numeral_Onumber__of(X0,tc_nat),c_1,tc_nat)|~spl0_518)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f14732])).
% 12.42/2.02 fof(f14737,plain,(
% 12.42/2.02 spl0_519 <=> c_less(c_1,c_Numeral_Onumber__of(X0,tc_nat),tc_nat)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f14738,plain,(
% 12.42/2.02 ![X0]: (c_less(c_1,c_Numeral_Onumber__of(X0,tc_nat),tc_nat)|~spl0_519)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f14737])).
% 12.42/2.02 fof(f14777,plain,(
% 12.42/2.02 spl0_525 <=> ~c_lessequals(c_Numeral_Onumber__of(X0,tc_nat),c_0,tc_nat)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f14778,plain,(
% 12.42/2.02 ![X0]: (~c_lessequals(c_Numeral_Onumber__of(X0,tc_nat),c_0,tc_nat)|~spl0_525)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f14777])).
% 12.42/2.02 fof(f14782,plain,(
% 12.42/2.02 spl0_526 <=> c_less(c_0,c_Numeral_Onumber__of(X0,tc_nat),tc_nat)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f14783,plain,(
% 12.42/2.02 ![X0]: (c_less(c_0,c_Numeral_Onumber__of(X0,tc_nat),tc_nat)|~spl0_526)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f14782])).
% 12.42/2.02 fof(f15004,plain,(
% 12.42/2.02 spl0_548 <=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f15006,plain,(
% 12.42/2.02 ~class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)|spl0_548),
% 12.42/2.02 inference(component_clause,[status(thm)],[f15004])).
% 12.42/2.02 fof(f15025,plain,(
% 12.42/2.02 $false|spl0_548),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15006,f2979])).
% 12.42/2.02 fof(f15026,plain,(
% 12.42/2.02 spl0_548),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15025])).
% 12.42/2.02 fof(f15160,plain,(
% 12.42/2.02 spl0_559 <=> class_Numeral_Onumber__ring(tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f15162,plain,(
% 12.42/2.02 ~class_Numeral_Onumber__ring(tc_IntDef_Oint)|spl0_559),
% 12.42/2.02 inference(component_clause,[status(thm)],[f15160])).
% 12.42/2.02 fof(f15170,plain,(
% 12.42/2.02 spl0_561 <=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f15172,plain,(
% 12.42/2.02 ~class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)|spl0_561),
% 12.42/2.02 inference(component_clause,[status(thm)],[f15170])).
% 12.42/2.02 fof(f15189,plain,(
% 12.42/2.02 $false|spl0_559),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15162,f3014])).
% 12.42/2.02 fof(f15190,plain,(
% 12.42/2.02 spl0_559),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15189])).
% 12.42/2.02 fof(f15191,plain,(
% 12.42/2.02 $false|spl0_561),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15172,f3009])).
% 12.42/2.02 fof(f15192,plain,(
% 12.42/2.02 spl0_561),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15191])).
% 12.42/2.02 fof(f15205,plain,(
% 12.42/2.02 spl0_566 <=> c_IntDef_Oint(c_1)=c_0),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f15206,plain,(
% 12.42/2.02 c_IntDef_Oint(c_1)=c_0|~spl0_566),
% 12.42/2.02 inference(component_clause,[status(thm)],[f15205])).
% 12.42/2.02 fof(f15219,plain,(
% 12.42/2.02 spl0_569 <=> c_lessequals(c_0,X1,tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f15220,plain,(
% 12.42/2.02 ![X0]: (c_lessequals(c_0,X0,tc_IntDef_Oint)|~spl0_569)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f15219])).
% 12.42/2.02 fof(f15266,plain,(
% 12.42/2.02 c_1=c_0|~spl0_566),
% 12.42/2.02 inference(forward_demodulation,[status(thm)],[f4257,f15206])).
% 12.42/2.02 fof(f15267,plain,(
% 12.42/2.02 $false|~spl0_566),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15266,f14357])).
% 12.42/2.02 fof(f15268,plain,(
% 12.42/2.02 ~spl0_566),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15267])).
% 12.42/2.02 fof(f15519,plain,(
% 12.42/2.02 ![X0]: (c_IntDef_Oint(c_IntDef_Onat(X0))=X0|~spl0_569)),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f4265,f15220])).
% 12.42/2.02 fof(f15543,plain,(
% 12.42/2.02 ![X0]: (~c_IntDef_Oneg(X0,tc_IntDef_Oint)|~spl0_569)),
% 12.42/2.02 inference(paramodulation,[status(thm)],[f15519,f4281])).
% 12.42/2.02 fof(f15547,plain,(
% 12.42/2.02 $false|~spl0_569),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f4274,f15543])).
% 12.42/2.02 fof(f15548,plain,(
% 12.42/2.02 ~spl0_569),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15547])).
% 12.42/2.02 fof(f15566,plain,(
% 12.42/2.02 c_0=c_1|~spl0_58),
% 12.42/2.02 inference(paramodulation,[status(thm)],[f7946,f12930])).
% 12.42/2.02 fof(f15567,plain,(
% 12.42/2.02 $false|~spl0_58),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15566,f14357])).
% 12.42/2.02 fof(f15568,plain,(
% 12.42/2.02 ~spl0_58),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15567])).
% 12.42/2.02 fof(f15569,plain,(
% 12.42/2.02 c_0=c_1|~spl0_56),
% 12.42/2.02 inference(paramodulation,[status(thm)],[f7946,f8246])).
% 12.42/2.02 fof(f15570,plain,(
% 12.42/2.02 $false|~spl0_56),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15569,f14357])).
% 12.42/2.02 fof(f15571,plain,(
% 12.42/2.02 ~spl0_56),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15570])).
% 12.42/2.02 fof(f15648,plain,(
% 12.42/2.02 spl0_587 <=> ~c_uminus(c_0,tc_IntDef_Oint)=c_IntDef_Oint(X0)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f15649,plain,(
% 12.42/2.02 ![X0]: (~c_uminus(c_0,tc_IntDef_Oint)=c_IntDef_Oint(X0)|~spl0_587)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f15648])).
% 12.42/2.02 fof(f15658,plain,(
% 12.42/2.02 ![X0]: (~c_0=c_IntDef_Oint(X0)|~spl0_587)),
% 12.42/2.02 inference(forward_demodulation,[status(thm)],[f12770,f15649])).
% 12.42/2.02 fof(f15766,plain,(
% 12.42/2.02 c_less(c_0,c_0,tc_nat)|~spl0_526),
% 12.42/2.02 inference(paramodulation,[status(thm)],[f4904,f14783])).
% 12.42/2.02 fof(f15767,plain,(
% 12.42/2.02 $false|~spl0_526),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15766,f5227])).
% 12.42/2.02 fof(f15768,plain,(
% 12.42/2.02 ~spl0_526),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15767])).
% 12.42/2.02 fof(f15769,plain,(
% 12.42/2.02 ~c_lessequals(c_0,c_0,tc_nat)|~spl0_525),
% 12.42/2.02 inference(paramodulation,[status(thm)],[f4904,f14778])).
% 12.42/2.02 fof(f15770,plain,(
% 12.42/2.02 $false|~spl0_525),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15769,f2876])).
% 12.42/2.02 fof(f15771,plain,(
% 12.42/2.02 ~spl0_525),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15770])).
% 12.42/2.02 fof(f15774,plain,(
% 12.42/2.02 c_less(c_1,c_0,tc_nat)|~spl0_519),
% 12.42/2.02 inference(paramodulation,[status(thm)],[f4904,f14738])).
% 12.42/2.02 fof(f15775,plain,(
% 12.42/2.02 $false|~spl0_519),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15774,f5227])).
% 12.42/2.02 fof(f15776,plain,(
% 12.42/2.02 ~spl0_519),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15775])).
% 12.42/2.02 fof(f15777,plain,(
% 12.42/2.02 ~c_lessequals(c_0,c_1,tc_nat)|~spl0_518),
% 12.42/2.02 inference(paramodulation,[status(thm)],[f4904,f14733])).
% 12.42/2.02 fof(f15778,plain,(
% 12.42/2.02 $false|~spl0_518),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15777,f2876])).
% 12.42/2.02 fof(f15779,plain,(
% 12.42/2.02 ~spl0_518),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15778])).
% 12.42/2.02 fof(f15786,plain,(
% 12.42/2.02 $false|~spl0_587),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f4260,f15658])).
% 12.42/2.02 fof(f15787,plain,(
% 12.42/2.02 ~spl0_587),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15786])).
% 12.42/2.02 fof(f15797,plain,(
% 12.42/2.02 c_lessequals(c_1,c_0,tc_nat)|~spl0_504),
% 12.42/2.02 inference(paramodulation,[status(thm)],[f4904,f14542])).
% 12.42/2.02 fof(f15876,plain,(
% 12.42/2.02 spl0_597 <=> c_in(X2,c_emptyset,X3)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f15877,plain,(
% 12.42/2.02 ![X0,X1]: (c_in(X0,c_emptyset,X1)|~spl0_597)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f15876])).
% 12.42/2.02 fof(f15881,plain,(
% 12.42/2.02 $false|~spl0_597),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15877,f6056])).
% 12.42/2.02 fof(f15882,plain,(
% 12.42/2.02 ~spl0_597),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15881])).
% 12.42/2.02 fof(f15905,plain,(
% 12.42/2.02 spl0_599 <=> ~class_Ring__and__Field_Oordered__idom(X0)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f15906,plain,(
% 12.42/2.02 ![X0]: (~class_Ring__and__Field_Oordered__idom(X0)|~spl0_599)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f15905])).
% 12.42/2.02 fof(f15925,plain,(
% 12.42/2.02 spl0_600 <=> X0=c_List_Olist_ONil),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f15926,plain,(
% 12.42/2.02 ![X0]: (X0=c_List_Olist_ONil|~spl0_600)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f15925])).
% 12.42/2.02 fof(f15935,plain,(
% 12.42/2.02 $false|~spl0_600),
% 12.42/2.02 inference(resolution,[status(thm)],[f15926,f4666])).
% 12.42/2.02 fof(f15936,plain,(
% 12.42/2.02 ~spl0_600),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15935])).
% 12.42/2.02 fof(f15964,plain,(
% 12.42/2.02 $false|~spl0_599),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f3011,f15906])).
% 12.42/2.02 fof(f15965,plain,(
% 12.42/2.02 ~spl0_599),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15964])).
% 12.42/2.02 fof(f15971,plain,(
% 12.42/2.02 c_1=c_0|~spl0_504),
% 12.42/2.02 inference(resolution,[status(thm)],[f15797,f5155])).
% 12.42/2.02 fof(f15972,plain,(
% 12.42/2.02 $false|~spl0_504),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f15971,f14357])).
% 12.42/2.02 fof(f15973,plain,(
% 12.42/2.02 ~spl0_504),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f15972])).
% 12.42/2.02 fof(f16138,plain,(
% 12.42/2.02 spl0_614 <=> ~c_lessequals(c_0,c_IntDef_Oof__int(X0,tc_nat),tc_nat)|c_lessequals(c_0,X0,tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f16139,plain,(
% 12.42/2.02 ![X0]: (~c_lessequals(c_0,c_IntDef_Oof__int(X0,tc_nat),tc_nat)|c_lessequals(c_0,X0,tc_IntDef_Oint)|~spl0_614)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f16138])).
% 12.42/2.02 fof(f16171,plain,(
% 12.42/2.02 ![X0]: (c_lessequals(c_0,X0,tc_IntDef_Oint)|~spl0_614)),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f16139,f2876])).
% 12.42/2.02 fof(f16172,plain,(
% 12.42/2.02 $false|~spl0_614),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f4282,f16171])).
% 12.42/2.02 fof(f16173,plain,(
% 12.42/2.02 ~spl0_614),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f16172])).
% 12.42/2.02 fof(f16324,plain,(
% 12.42/2.02 spl0_621 <=> c_less(c_0,c_1,tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f16326,plain,(
% 12.42/2.02 ~c_less(c_0,c_1,tc_IntDef_Oint)|spl0_621),
% 12.42/2.02 inference(component_clause,[status(thm)],[f16324])).
% 12.42/2.02 fof(f16329,plain,(
% 12.42/2.02 $false|spl0_621),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f16326,f12735])).
% 12.42/2.02 fof(f16330,plain,(
% 12.42/2.02 spl0_621),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f16329])).
% 12.42/2.02 fof(f16351,plain,(
% 12.42/2.02 c_minus(c_1,c_0,tc_nat)=c_0|~spl0_516),
% 12.42/2.02 inference(paramodulation,[status(thm)],[f4904,f14723])).
% 12.42/2.02 fof(f16352,plain,(
% 12.42/2.02 c_1=c_0|~spl0_516),
% 12.42/2.02 inference(forward_demodulation,[status(thm)],[f5242,f16351])).
% 12.42/2.02 fof(f16353,plain,(
% 12.42/2.02 $false|~spl0_516),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f16352,f14357])).
% 12.42/2.02 fof(f16354,plain,(
% 12.42/2.02 ~spl0_516),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f16353])).
% 12.42/2.02 fof(f16465,plain,(
% 12.42/2.02 c_0=c_1|~spl0_255),
% 12.42/2.02 inference(forward_demodulation,[status(thm)],[f3996,f11187])).
% 12.42/2.02 fof(f16466,plain,(
% 12.42/2.02 $false|~spl0_255),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f16465,f14357])).
% 12.42/2.02 fof(f16467,plain,(
% 12.42/2.02 ~spl0_255),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f16466])).
% 12.42/2.02 fof(f17176,plain,(
% 12.42/2.02 spl0_735 <=> c_IntDef_OInts=c_emptyset),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f17177,plain,(
% 12.42/2.02 c_IntDef_OInts=c_emptyset|~spl0_735),
% 12.42/2.02 inference(component_clause,[status(thm)],[f17176])).
% 12.42/2.02 fof(f17762,plain,(
% 12.42/2.02 spl0_782 <=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f17764,plain,(
% 12.42/2.02 ~class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)|spl0_782),
% 12.42/2.02 inference(component_clause,[status(thm)],[f17762])).
% 12.42/2.02 fof(f17778,plain,(
% 12.42/2.02 $false|spl0_782),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f17764,f2961])).
% 12.42/2.02 fof(f17779,plain,(
% 12.42/2.02 spl0_782),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f17778])).
% 12.42/2.02 fof(f17871,plain,(
% 12.42/2.02 ![X0]: (~class_Ring__and__Field_Ocomm__ring__1(X0)|c_in(c_0,c_emptyset,X0)|~spl0_735)),
% 12.42/2.02 inference(backward_demodulation,[status(thm)],[f17177,f4243])).
% 12.42/2.02 fof(f17872,plain,(
% 12.42/2.02 ![X0]: (~class_Ring__and__Field_Ocomm__ring__1(X0)|~spl0_735)),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f17871,f6056])).
% 12.42/2.02 fof(f17887,plain,(
% 12.42/2.02 $false|~spl0_735),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f2981,f17872])).
% 12.42/2.02 fof(f17888,plain,(
% 12.42/2.02 ~spl0_735),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f17887])).
% 12.42/2.02 fof(f18188,plain,(
% 12.42/2.02 spl0_802 <=> c_less(X0,c_0,tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f18189,plain,(
% 12.42/2.02 ![X0]: (c_less(X0,c_0,tc_IntDef_Oint)|~spl0_802)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f18188])).
% 12.42/2.02 fof(f18233,plain,(
% 12.42/2.02 $false|~spl0_802),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f7929,f18189])).
% 12.42/2.02 fof(f18234,plain,(
% 12.42/2.02 ~spl0_802),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f18233])).
% 12.42/2.02 fof(f18298,plain,(
% 12.42/2.02 spl0_812 <=> X1=c_Numeral_Obit_OB0|X1=c_Numeral_Obit_OB0),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f18299,plain,(
% 12.42/2.02 ![X0]: (X0=c_Numeral_Obit_OB0|X0=c_Numeral_Obit_OB0|~spl0_812)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f18298])).
% 12.42/2.02 fof(f18311,plain,(
% 12.42/2.02 spl0_815 <=> c_Numeral_Obit_OB1=c_Numeral_Obit_OB0),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f18312,plain,(
% 12.42/2.02 c_Numeral_Obit_OB1=c_Numeral_Obit_OB0|~spl0_815),
% 12.42/2.02 inference(component_clause,[status(thm)],[f18311])).
% 12.42/2.02 fof(f18341,plain,(
% 12.42/2.02 spl0_821 <=> X2=c_Numeral_Obit_OB0),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f18342,plain,(
% 12.42/2.02 ![X0]: (X0=c_Numeral_Obit_OB0|~spl0_821)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f18341])).
% 12.42/2.02 fof(f18346,plain,(
% 12.42/2.02 $false|~spl0_815),
% 12.42/2.02 inference(forward_subsumption_resolution,[status(thm)],[f18312,f5308])).
% 12.42/2.02 fof(f18347,plain,(
% 12.42/2.02 ~spl0_815),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f18346])).
% 12.42/2.02 fof(f18349,plain,(
% 12.42/2.02 ![X0]: (X0=c_Numeral_Obit_OB0|~spl0_812)),
% 12.42/2.02 inference(duplicate_literals_removal,[status(esa)],[f18299])).
% 12.42/2.02 fof(f18358,plain,(
% 12.42/2.02 spl0_824 <=> c_plus(c_1,X0,tc_IntDef_Oint)=c_plus(c_div(X0,c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
% 12.42/2.02 introduced(split_symbol_definition)).
% 12.42/2.02 fof(f18359,plain,(
% 12.42/2.02 ![X0]: (c_plus(c_1,X0,tc_IntDef_Oint)=c_plus(c_div(X0,c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)|~spl0_824)),
% 12.42/2.02 inference(component_clause,[status(thm)],[f18358])).
% 12.42/2.02 fof(f18361,plain,(
% 12.42/2.02 ![X0]: (c_1=c_0|c_plus(c_1,X0,tc_IntDef_Oint)=c_plus(c_div(X0,c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint))),
% 12.42/2.02 inference(paramodulation,[status(thm)],[f4375,f4384])).
% 12.42/2.02 fof(f18362,plain,(
% 12.42/2.02 spl0_1|spl0_824),
% 12.42/2.02 inference(split_clause,[status(thm)],[f18361,f6206,f18358])).
% 12.42/2.02 fof(f18373,plain,(
% 12.42/2.02 ![X0]: (c_plus(c_1,X0,tc_IntDef_Oint)=c_plus(X0,c_1,tc_IntDef_Oint)|~spl0_824)),
% 12.42/2.02 inference(forward_demodulation,[status(thm)],[f4375,f18359])).
% 12.42/2.02 fof(f18525,plain,(
% 12.42/2.02 $false|~spl0_821),
% 12.42/2.02 inference(backward_subsumption_resolution,[status(thm)],[f5308,f18342])).
% 12.42/2.02 fof(f18526,plain,(
% 12.42/2.02 ~spl0_821),
% 12.42/2.02 inference(contradiction_clause,[status(thm)],[f18525])).
% 12.42/2.02 fof(f18531,plain,(
% 12.42/2.02 $false|~spl0_812),
% 12.42/2.02 inference(resolution,[status(thm)],[f18349,f4666])).
% 12.55/2.05 fof(f18532,plain,(
% 12.55/2.05 ~spl0_812),
% 12.55/2.05 inference(contradiction_clause,[status(thm)],[f18531])).
% 12.55/2.05 fof(f18591,plain,(
% 12.55/2.05 ![X0]: (~c_lessequals(c_plus(c_1,X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)|~spl0_499|~spl0_824)),
% 12.55/2.05 inference(paramodulation,[status(thm)],[f18373,f14502])).
% 12.55/2.05 fof(f18626,plain,(
% 12.55/2.05 ![X0]: (~c_lessequals(c_IntDef_Oint(c_Suc(X0)),c_IntDef_Oint(X0),tc_IntDef_Oint)|~spl0_499|~spl0_824)),
% 12.55/2.05 inference(paramodulation,[status(thm)],[f4258,f18591])).
% 12.55/2.05 fof(f18718,plain,(
% 12.55/2.05 spl0_855 <=> X0=c_0|X0=c_0),
% 12.55/2.05 introduced(split_symbol_definition)).
% 12.55/2.05 fof(f18719,plain,(
% 12.55/2.05 ![X0]: (X0=c_0|X0=c_0|~spl0_855)),
% 12.55/2.05 inference(component_clause,[status(thm)],[f18718])).
% 12.55/2.05 fof(f18742,plain,(
% 12.55/2.05 ![X0]: (X0=c_0|~spl0_855)),
% 12.55/2.05 inference(duplicate_literals_removal,[status(esa)],[f18719])).
% 12.55/2.05 fof(f18778,plain,(
% 12.55/2.05 spl0_859 <=> ~c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)),
% 12.55/2.05 introduced(split_symbol_definition)).
% 12.55/2.05 fof(f18779,plain,(
% 12.55/2.05 ![X0]: (~c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)|~spl0_859)),
% 12.55/2.05 inference(component_clause,[status(thm)],[f18778])).
% 12.55/2.05 fof(f18783,plain,(
% 12.55/2.05 $false|~spl0_859),
% 12.55/2.05 inference(forward_subsumption_resolution,[status(thm)],[f18779,f4397])).
% 12.55/2.05 fof(f18784,plain,(
% 12.55/2.05 ~spl0_859),
% 12.55/2.05 inference(contradiction_clause,[status(thm)],[f18783])).
% 12.55/2.05 fof(f18902,plain,(
% 12.55/2.05 $false|~spl0_855),
% 12.55/2.05 inference(resolution,[status(thm)],[f18742,f4666])).
% 12.55/2.05 fof(f18903,plain,(
% 12.55/2.05 ~spl0_855),
% 12.55/2.05 inference(contradiction_clause,[status(thm)],[f18902])).
% 12.55/2.05 fof(f19151,plain,(
% 12.55/2.05 ![X0]: (~c_lessequals(c_Suc(X0),X0,tc_nat)|~spl0_499|~spl0_824)),
% 12.55/2.05 inference(resolution,[status(thm)],[f18626,f4330])).
% 12.55/2.05 fof(f19158,plain,(
% 12.55/2.05 $false|~spl0_499|~spl0_824),
% 12.55/2.05 inference(resolution,[status(thm)],[f19151,f6212])).
% 12.55/2.05 fof(f19159,plain,(
% 12.55/2.05 ~spl0_499|~spl0_824),
% 12.55/2.05 inference(contradiction_clause,[status(thm)],[f19158])).
% 12.55/2.05 fof(f19160,plain,(
% 12.55/2.05 $false),
% 12.55/2.05 inference(sat_refutation,[status(thm)],[f6209,f8210,f12766,f12768,f12783,f12817,f12935,f12938,f12940,f12976,f13008,f13134,f13154,f13159,f13165,f13207,f13209,f13211,f13213,f13222,f13231,f13293,f13297,f13763,f14299,f14459,f14505,f14670,f15026,f15190,f15192,f15268,f15548,f15568,f15571,f15768,f15771,f15776,f15779,f15787,f15882,f15936,f15965,f15973,f16173,f16330,f16354,f16467,f17779,f17888,f18234,f18347,f18362,f18526,f18532,f18784,f18903,f19159])).
% 12.55/2.05 % SZS output end CNFRefutation for theBenchmark.p
% 12.55/2.08 % Elapsed time: 1.731667 seconds
% 12.55/2.08 % CPU time: 12.633390 seconds
% 12.55/2.08 % Total memory used: 368.822 MB
% 12.55/2.08 % Net memory used: 365.151 MB
%------------------------------------------------------------------------------