TSTP Solution File: ANA019-2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ANA019-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n011.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 : Wed Aug 30 17:13:54 EDT 2023

% Result   : Unsatisfiable 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   62 (  15 unt;  19 typ;   0 def)
%            Number of atoms       :   77 (  11 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   73 (  39   ~;  34   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  14   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-3 aty)
%            Number of variables   :   37 (   2 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    c_0: $i ).

tff(decl_23,type,
    v_f: $i > $i ).

tff(decl_24,type,
    v_x: $i ).

tff(decl_25,type,
    t_a: $i ).

tff(decl_26,type,
    c_less: ( $i * $i * $i ) > $o ).

tff(decl_27,type,
    c_Suc: $i > $i ).

tff(decl_28,type,
    c_HOL_Oabs: ( $i * $i ) > $i ).

tff(decl_29,type,
    v_h: $i > $i ).

tff(decl_30,type,
    c_times: ( $i * $i * $i ) > $i ).

tff(decl_31,type,
    c_lessequals: ( $i * $i * $i ) > $o ).

tff(decl_32,type,
    v_xa: $i > $i ).

tff(decl_33,type,
    class_Ring__and__Field_Oordered__idom: $i > $o ).

tff(decl_34,type,
    tc_nat: $i ).

tff(decl_35,type,
    c_1: $i ).

tff(decl_36,type,
    c_minus: ( $i * $i * $i ) > $i ).

tff(decl_37,type,
    class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).

tff(decl_38,type,
    class_Orderings_Oorder: $i > $o ).

tff(decl_39,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).

tff(decl_40,type,
    class_LOrder_Ojoin__semilorder: $i > $o ).

cnf(cls_conjecture_2,negated_conjecture,
    c_lessequals(c_HOL_Oabs(v_f(c_Suc(X1)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(X1)),t_a),t_a),t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_NatBin_OSuc__pred_H_0,axiom,
    ( X1 = c_Suc(c_minus(X1,c_1,tc_nat))
    | ~ c_less(c_0,X1,tc_nat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).

cnf(cls_conjecture_3,negated_conjecture,
    ( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X1)),t_a),c_times(X1,c_HOL_Oabs(v_h(v_xa(X1)),t_a),t_a),t_a)
    | ~ c_less(c_0,X1,t_a) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_conjecture_1,negated_conjecture,
    c_less(c_0,v_x,t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

cnf(cls_OrderedGroup_Oabs__eq__0_1,axiom,
    ( c_HOL_Oabs(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

cnf(cls_Nat_Onot__gr0_0,axiom,
    ( c_less(c_0,X1,tc_nat)
    | X1 = c_0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).

cnf(tfree_tcs,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).

cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_less(X2,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).

cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_35,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).

cnf(cls_conjecture_0,negated_conjecture,
    v_f(c_0) = c_0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
    ( c_lessequals(c_0,c_times(X3,X2,X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_0,X2,X1)
    | ~ c_lessequals(c_0,X3,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).

cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
    ( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).

cnf(c_0_15,negated_conjecture,
    c_lessequals(c_HOL_Oabs(v_f(c_Suc(X1)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(X1)),t_a),t_a),t_a),
    cls_conjecture_2 ).

cnf(c_0_16,axiom,
    ( X1 = c_Suc(c_minus(X1,c_1,tc_nat))
    | ~ c_less(c_0,X1,tc_nat) ),
    cls_NatBin_OSuc__pred_H_0 ).

cnf(c_0_17,negated_conjecture,
    ( ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X1)),t_a),c_times(X1,c_HOL_Oabs(v_h(v_xa(X1)),t_a),t_a),t_a)
    | ~ c_less(c_0,X1,t_a) ),
    cls_conjecture_3 ).

cnf(c_0_18,negated_conjecture,
    ( c_lessequals(c_HOL_Oabs(v_f(X1),t_a),c_times(v_x,c_HOL_Oabs(v_h(X1),t_a),t_a),t_a)
    | ~ c_less(c_0,X1,tc_nat) ),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_19,negated_conjecture,
    c_less(c_0,v_x,t_a),
    cls_conjecture_1 ).

cnf(c_0_20,axiom,
    ( c_HOL_Oabs(c_0,X1) = c_0
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    cls_OrderedGroup_Oabs__eq__0_1 ).

cnf(c_0_21,axiom,
    ( class_OrderedGroup_Olordered__ab__group__abs(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    clsrel_Ring__and__Field_Oordered__idom_50 ).

cnf(c_0_22,negated_conjecture,
    ~ c_less(c_0,v_xa(v_x),tc_nat),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).

cnf(c_0_23,axiom,
    ( c_less(c_0,X1,tc_nat)
    | X1 = c_0 ),
    cls_Nat_Onot__gr0_0 ).

cnf(c_0_24,plain,
    ( c_HOL_Oabs(c_0,X1) = c_0
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_a),
    tfree_tcs ).

cnf(c_0_26,axiom,
    ( c_lessequals(X2,X3,X1)
    | ~ class_Orderings_Oorder(X1)
    | ~ c_less(X2,X3,X1) ),
    cls_Orderings_Oorder__less__imp__le_0 ).

cnf(c_0_27,axiom,
    ( class_Orderings_Oorder(X1)
    | ~ class_LOrder_Ojoin__semilorder(X1) ),
    clsrel_LOrder_Ojoin__semilorder_1 ).

cnf(c_0_28,axiom,
    ( class_LOrder_Ojoin__semilorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    clsrel_Ring__and__Field_Oordered__idom_35 ).

cnf(c_0_29,negated_conjecture,
    v_xa(v_x) = c_0,
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_30,negated_conjecture,
    v_f(c_0) = c_0,
    cls_conjecture_0 ).

cnf(c_0_31,negated_conjecture,
    c_HOL_Oabs(c_0,t_a) = c_0,
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_32,negated_conjecture,
    ( c_lessequals(c_0,v_x,t_a)
    | ~ class_Orderings_Oorder(t_a) ),
    inference(spm,[status(thm)],[c_0_26,c_0_19]) ).

cnf(c_0_33,plain,
    ( class_Orderings_Oorder(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_34,negated_conjecture,
    ~ c_lessequals(c_0,c_times(v_x,c_HOL_Oabs(v_h(c_0),t_a),t_a),t_a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_29]),c_0_30]),c_0_31]),c_0_19])]) ).

cnf(c_0_35,axiom,
    ( c_lessequals(c_0,c_times(X3,X2,X1),X1)
    | ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ c_lessequals(c_0,X2,X1)
    | ~ c_lessequals(c_0,X3,X1) ),
    cls_Ring__and__Field_Omult__nonneg__nonneg_0 ).

cnf(c_0_36,negated_conjecture,
    c_lessequals(c_0,v_x,t_a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_25])]) ).

cnf(c_0_37,negated_conjecture,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
    | ~ c_lessequals(c_0,c_HOL_Oabs(v_h(c_0),t_a),t_a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).

cnf(c_0_38,axiom,
    ( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
    cls_OrderedGroup_Oabs__ge__zero_0 ).

cnf(c_0_39,negated_conjecture,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_a)
    | ~ class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_40,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(X1)
    | ~ class_Ring__and__Field_Oordered__idom(X1) ),
    clsrel_Ring__and__Field_Oordered__idom_40 ).

cnf(c_0_41,negated_conjecture,
    ~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_25])]) ).

cnf(c_0_42,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_21]),c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : ANA019-2 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n011.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri Aug 25 18:09:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.006000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.008000 s
%------------------------------------------------------------------------------