TSTP Solution File: ANA034-10 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ANA034-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n003.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 17:14:02 EDT 2023

% Result   : Unsatisfiable 0.19s 0.63s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   66 (  45 unt;  21 typ;   0 def)
%            Number of atoms       :   45 (  44 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   28 (  15   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;   6 con; 0-4 aty)
%            Number of variables   :   59 (   8 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    ifeq2: ( $i * $i * $i * $i ) > $i ).

tff(decl_23,type,
    ifeq: ( $i * $i * $i * $i ) > $i ).

tff(decl_24,type,
    class_Ring__and__Field_Oordered__idom: $i > $i ).

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

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

tff(decl_27,type,
    c_times: ( $i * $i * $i ) > $i ).

tff(decl_28,type,
    c_0: $i ).

tff(decl_29,type,
    c_lessequals: ( $i * $i * $i ) > $i ).

tff(decl_30,type,
    class_Ring__and__Field_Opordered__semiring: $i > $i ).

tff(decl_31,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $i > $i ).

tff(decl_32,type,
    c_less: ( $i * $i * $i ) > $i ).

tff(decl_33,type,
    class_Orderings_Oorder: $i > $i ).

tff(decl_34,type,
    class_OrderedGroup_Olordered__ab__group__abs: $i > $i ).

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

tff(decl_36,type,
    t_b: $i ).

tff(decl_37,type,
    v_x: $i ).

tff(decl_38,type,
    v_a: $i > $i ).

tff(decl_39,type,
    v_f: $i > $i ).

tff(decl_40,type,
    v_b: $i > $i ).

tff(decl_41,type,
    v_ca: $i ).

tff(decl_42,type,
    v_g: $i > $i ).

cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
    ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Olordered__ab__group__abs(X1),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).

cnf(tfree_tcs,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_b) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).

cnf(ifeq_axiom_001,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).

cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
    ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,class_Orderings_Oorder(X1),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).

cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
    ifeq(c_less(X1,X2,X3),true,ifeq(class_Orderings_Oorder(X3),true,c_lessequals(X1,X2,X3),true),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_less(c_0,v_c,t_b) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
    ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Ring__and__Field_Opordered__cancel__semiring(X1),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).

cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
    ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).

cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
    ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Ring__and__Field_Opordered__semiring(X1),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).

cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
    ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(c_0,X3,X1),true,c_lessequals(c_0,c_times(X2,X3,X1),X1),true),true),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).

cnf(cls_Ring__and__Field_Omult__mono_0,axiom,
    ifeq(c_lessequals(c_0,X1,X2),true,ifeq(c_lessequals(c_0,X3,X2),true,ifeq(c_lessequals(X4,X1,X2),true,ifeq(c_lessequals(X3,X5,X2),true,ifeq(class_Ring__and__Field_Opordered__semiring(X2),true,c_lessequals(c_times(X4,X3,X2),c_times(X1,X5,X2),X2),true),true),true),true),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).

cnf(cls_conjecture_3,negated_conjecture,
    c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
    ifeq2(class_Ring__and__Field_Oordered__idom(X1),true,c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1),c_HOL_Oabs(c_times(X2,X3,X1),X1)) = c_HOL_Oabs(c_times(X2,X3,X1),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).

cnf(ifeq_axiom,axiom,
    ifeq2(X1,X1,X2,X3) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).

cnf(cls_conjecture_2,negated_conjecture,
    c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

cnf(cls_conjecture_4,negated_conjecture,
    c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

cnf(cls_conjecture_5,negated_conjecture,
    c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

cnf(c_0_17,axiom,
    ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Olordered__ab__group__abs(X1),true) = true,
    clsrel_Ring__and__Field_Oordered__idom_50 ).

cnf(c_0_18,negated_conjecture,
    class_Ring__and__Field_Oordered__idom(t_b) = true,
    tfree_tcs ).

cnf(c_0_19,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    ifeq_axiom_001 ).

cnf(c_0_20,axiom,
    ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,class_Orderings_Oorder(X1),true) = true,
    clsrel_OrderedGroup_Olordered__ab__group__abs_17 ).

cnf(c_0_21,negated_conjecture,
    class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).

cnf(c_0_22,axiom,
    ifeq(c_less(X1,X2,X3),true,ifeq(class_Orderings_Oorder(X3),true,c_lessequals(X1,X2,X3),true),true) = true,
    cls_Orderings_Oorder__less__imp__le_0 ).

cnf(c_0_23,negated_conjecture,
    c_less(c_0,v_c,t_b) = true,
    cls_conjecture_0 ).

cnf(c_0_24,negated_conjecture,
    class_Orderings_Oorder(t_b) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).

cnf(c_0_25,axiom,
    ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Ring__and__Field_Opordered__cancel__semiring(X1),true) = true,
    clsrel_Ring__and__Field_Oordered__idom_40 ).

cnf(c_0_26,axiom,
    ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1),true) = true,
    cls_OrderedGroup_Oabs__ge__zero_0 ).

cnf(c_0_27,axiom,
    ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Ring__and__Field_Opordered__semiring(X1),true) = true,
    clsrel_Ring__and__Field_Oordered__idom_42 ).

cnf(c_0_28,axiom,
    ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(c_0,X3,X1),true,c_lessequals(c_0,c_times(X2,X3,X1),X1),true),true),true) = true,
    cls_Ring__and__Field_Omult__nonneg__nonneg_0 ).

cnf(c_0_29,negated_conjecture,
    c_lessequals(c_0,v_c,t_b) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19]),c_0_24]),c_0_19]) ).

cnf(c_0_30,negated_conjecture,
    class_Ring__and__Field_Opordered__cancel__semiring(t_b) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_19]) ).

cnf(c_0_31,axiom,
    ifeq(c_lessequals(c_0,X1,X2),true,ifeq(c_lessequals(c_0,X3,X2),true,ifeq(c_lessequals(X4,X1,X2),true,ifeq(c_lessequals(X3,X5,X2),true,ifeq(class_Ring__and__Field_Opordered__semiring(X2),true,c_lessequals(c_times(X4,X3,X2),c_times(X1,X5,X2),X2),true),true),true),true),true) = true,
    cls_Ring__and__Field_Omult__mono_0 ).

cnf(c_0_32,negated_conjecture,
    c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
    cls_conjecture_3 ).

cnf(c_0_33,negated_conjecture,
    c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_19]) ).

cnf(c_0_34,negated_conjecture,
    class_Ring__and__Field_Opordered__semiring(t_b) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_18]),c_0_19]) ).

cnf(c_0_35,negated_conjecture,
    ifeq(c_lessequals(c_0,X1,t_b),true,c_lessequals(c_0,c_times(v_c,X1,t_b),t_b),true) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_19]),c_0_19]) ).

cnf(c_0_36,axiom,
    ifeq2(class_Ring__and__Field_Oordered__idom(X1),true,c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1),c_HOL_Oabs(c_times(X2,X3,X1),X1)) = c_HOL_Oabs(c_times(X2,X3,X1),X1),
    cls_Ring__and__Field_Oabs__mult_0 ).

cnf(c_0_37,axiom,
    ifeq2(X1,X1,X2,X3) = X2,
    ifeq_axiom ).

cnf(c_0_38,negated_conjecture,
    ifeq(c_lessequals(c_0,X1,t_b),true,ifeq(c_lessequals(X2,X1,t_b),true,c_lessequals(c_times(X2,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]),c_0_19]),c_0_19]),c_0_19]) ).

cnf(c_0_39,negated_conjecture,
    c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true,
    cls_conjecture_2 ).

cnf(c_0_40,negated_conjecture,
    c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(X1,t_b),t_b),t_b) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_19]) ).

cnf(c_0_41,negated_conjecture,
    c_times(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(X2,t_b),t_b) = c_HOL_Oabs(c_times(X1,X2,t_b),t_b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_18]),c_0_37]) ).

cnf(c_0_42,negated_conjecture,
    c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
    cls_conjecture_4 ).

cnf(c_0_43,negated_conjecture,
    c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true,
    cls_conjecture_5 ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41]),c_0_42]),c_0_19]),c_0_19]),c_0_43]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ANA034-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33  % Computer : n003.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Fri Aug 25 18:20:53 EDT 2023
% 0.14/0.33  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.63  % Version  : CSE_E---1.5
% 0.19/0.63  % Problem  : theBenchmark.p
% 0.19/0.63  % Proof found
% 0.19/0.63  % SZS status Theorem for theBenchmark.p
% 0.19/0.63  % SZS output start Proof
% See solution above
% 0.19/0.64  % Total time : 0.064000 s
% 0.19/0.64  % SZS output end Proof
% 0.19/0.64  % Total time : 0.067000 s
%------------------------------------------------------------------------------