TSTP Solution File: ANA005-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ANA005-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n027.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 17:13:48 EDT 2023

% Result   : Unsatisfiable 102.29s 102.33s
% Output   : CNFRefutation 102.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   88 (  15 unt;  16 typ;   0 def)
%            Number of atoms       :  175 (  11 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  227 ( 124   ~; 103   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (  11   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  15 usr;   5 con; 0-2 aty)
%            Number of variables   :  130 (   5 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    n0: $i ).

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

tff(decl_24,type,
    less_than: ( $i * $i ) > $o ).

tff(decl_25,type,
    minimum: ( $i * $i ) > $i ).

tff(decl_26,type,
    half: $i > $i ).

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

tff(decl_28,type,
    minus: $i > $i ).

tff(decl_29,type,
    fp31: $i > $i ).

tff(decl_30,type,
    a: $i ).

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

tff(decl_32,type,
    l1: $i ).

tff(decl_33,type,
    fp32: $i > $i ).

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

tff(decl_35,type,
    l2: $i ).

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

tff(decl_37,type,
    fp33: $i > $i ).

cnf(c_16,negated_conjecture,
    ( ~ less_than(n0,X1)
    | ~ less_than(absolute(add(add(f(fp33(X1)),g(fp33(X1))),minus(add(l1,l2)))),b) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).

cnf(axiom_5,axiom,
    add(add(X1,X2),X3) = add(X1,add(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_5) ).

cnf(c_17,axiom,
    ( less_than(absolute(add(X1,X2)),X3)
    | ~ less_than(add(absolute(X1),absolute(X2)),X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',c_17) ).

cnf(axiom_3,axiom,
    ( less_than(add(X1,X3),X2)
    | ~ less_than(X1,half(X2))
    | ~ less_than(X3,half(X2)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_3) ).

cnf(axiom_6_1,axiom,
    add(X1,X2) = add(X2,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_6_1) ).

cnf(axiom_8,axiom,
    minus(add(X1,X2)) = add(minus(X1),minus(X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_8) ).

cnf(c_13,negated_conjecture,
    ( less_than(absolute(add(g(X2),minus(l2))),X1)
    | ~ less_than(n0,X1)
    | ~ less_than(absolute(add(X2,minus(a))),fp32(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).

cnf(c_11,negated_conjecture,
    ( less_than(absolute(add(f(X2),minus(l1))),X1)
    | ~ less_than(n0,X1)
    | ~ less_than(absolute(add(X2,minus(a))),fp31(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).

cnf(transitivity_of_less_than,axiom,
    ( less_than(X1,X3)
    | ~ less_than(X1,X2)
    | ~ less_than(X2,X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',transitivity_of_less_than) ).

cnf(c_15,negated_conjecture,
    ( less_than(absolute(add(fp33(X1),minus(a))),X1)
    | ~ less_than(n0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).

cnf(left_identity,axiom,
    add(n0,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',left_identity) ).

cnf(axiom_2_2,axiom,
    ( less_than(minimum(X1,X2),X1)
    | ~ less_than(n0,X1)
    | ~ less_than(n0,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_2_2) ).

cnf(axiom_6_2,axiom,
    ( less_than(n0,half(X1))
    | ~ less_than(n0,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_6_2) ).

cnf(c_14,negated_conjecture,
    less_than(n0,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).

cnf(axiom_2_1,axiom,
    ( less_than(n0,minimum(X1,X2))
    | ~ less_than(n0,X1)
    | ~ less_than(n0,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_2_1) ).

cnf(axiom_2_3,axiom,
    ( less_than(minimum(X1,X2),X2)
    | ~ less_than(n0,X1)
    | ~ less_than(n0,X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/ANA001-0.ax',axiom_2_3) ).

cnf(c_10,negated_conjecture,
    ( less_than(n0,fp31(X1))
    | ~ less_than(n0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).

cnf(c_12,negated_conjecture,
    ( less_than(n0,fp32(X1))
    | ~ less_than(n0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).

cnf(c_0_18,negated_conjecture,
    ( ~ less_than(n0,X1)
    | ~ less_than(absolute(add(add(f(fp33(X1)),g(fp33(X1))),minus(add(l1,l2)))),b) ),
    c_16 ).

cnf(c_0_19,axiom,
    add(add(X1,X2),X3) = add(X1,add(X2,X3)),
    axiom_5 ).

cnf(c_0_20,axiom,
    ( less_than(absolute(add(X1,X2)),X3)
    | ~ less_than(add(absolute(X1),absolute(X2)),X3) ),
    c_17 ).

cnf(c_0_21,axiom,
    ( less_than(add(X1,X3),X2)
    | ~ less_than(X1,half(X2))
    | ~ less_than(X3,half(X2)) ),
    axiom_3 ).

cnf(c_0_22,negated_conjecture,
    ( ~ less_than(absolute(add(f(fp33(X1)),add(g(fp33(X1)),minus(add(l1,l2))))),b)
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,axiom,
    add(X1,X2) = add(X2,X1),
    axiom_6_1 ).

cnf(c_0_24,axiom,
    minus(add(X1,X2)) = add(minus(X1),minus(X2)),
    axiom_8 ).

cnf(c_0_25,plain,
    ( less_than(absolute(add(X1,X2)),X3)
    | ~ less_than(absolute(X2),half(X3))
    | ~ less_than(absolute(X1),half(X3)) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    ( ~ less_than(absolute(add(f(fp33(X1)),add(minus(add(l1,l2)),g(fp33(X1))))),b)
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,plain,
    add(X1,add(X2,X3)) = add(X3,add(X1,X2)),
    inference(spm,[status(thm)],[c_0_23,c_0_19]) ).

cnf(c_0_28,plain,
    add(minus(add(X1,X2)),X3) = add(minus(X1),add(minus(X2),X3)),
    inference(spm,[status(thm)],[c_0_19,c_0_24]) ).

cnf(c_0_29,plain,
    ( less_than(absolute(add(X1,add(X2,X3))),X4)
    | ~ less_than(absolute(add(X1,X2)),half(X4))
    | ~ less_than(absolute(X3),half(X4)) ),
    inference(spm,[status(thm)],[c_0_25,c_0_19]) ).

cnf(c_0_30,plain,
    add(X1,add(X2,X3)) = add(X2,add(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_19]) ).

cnf(c_0_31,negated_conjecture,
    ( less_than(absolute(add(g(X2),minus(l2))),X1)
    | ~ less_than(n0,X1)
    | ~ less_than(absolute(add(X2,minus(a))),fp32(X1)) ),
    c_13 ).

cnf(c_0_32,negated_conjecture,
    ( ~ less_than(absolute(add(minus(l1),add(minus(l2),add(f(fp33(X1)),g(fp33(X1)))))),b)
    | ~ less_than(n0,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]),c_0_28]) ).

cnf(c_0_33,plain,
    ( less_than(absolute(add(X1,add(X2,add(X3,X4)))),X5)
    | ~ less_than(absolute(add(X1,X3)),half(X5))
    | ~ less_than(absolute(add(X2,X4)),half(X5)) ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_34,negated_conjecture,
    ( less_than(absolute(add(minus(l2),g(X1))),X2)
    | ~ less_than(absolute(add(X1,minus(a))),fp32(X2))
    | ~ less_than(n0,X2) ),
    inference(rw,[status(thm)],[c_0_31,c_0_23]) ).

cnf(c_0_35,negated_conjecture,
    ( less_than(absolute(add(f(X2),minus(l1))),X1)
    | ~ less_than(n0,X1)
    | ~ less_than(absolute(add(X2,minus(a))),fp31(X1)) ),
    c_11 ).

cnf(c_0_36,axiom,
    ( less_than(X1,X3)
    | ~ less_than(X1,X2)
    | ~ less_than(X2,X3) ),
    transitivity_of_less_than ).

cnf(c_0_37,negated_conjecture,
    ( less_than(absolute(add(fp33(X1),minus(a))),X1)
    | ~ less_than(n0,X1) ),
    c_15 ).

cnf(c_0_38,negated_conjecture,
    ( ~ less_than(absolute(add(minus(l1),f(fp33(X1)))),half(b))
    | ~ less_than(absolute(add(minus(l2),g(fp33(X1)))),half(b))
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,negated_conjecture,
    ( less_than(absolute(add(minus(l2),g(X1))),X2)
    | ~ less_than(absolute(add(minus(a),X1)),fp32(X2))
    | ~ less_than(n0,X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_23]) ).

cnf(c_0_40,negated_conjecture,
    ( less_than(absolute(add(minus(l1),f(X1))),X2)
    | ~ less_than(absolute(add(X1,minus(a))),fp31(X2))
    | ~ less_than(n0,X2) ),
    inference(rw,[status(thm)],[c_0_35,c_0_23]) ).

cnf(c_0_41,plain,
    ( less_than(X1,X2)
    | ~ less_than(X1,add(X3,X4))
    | ~ less_than(X4,half(X2))
    | ~ less_than(X3,half(X2)) ),
    inference(spm,[status(thm)],[c_0_36,c_0_21]) ).

cnf(c_0_42,negated_conjecture,
    ( less_than(absolute(add(minus(a),fp33(X1))),X1)
    | ~ less_than(n0,X1) ),
    inference(rw,[status(thm)],[c_0_37,c_0_23]) ).

cnf(c_0_43,negated_conjecture,
    ( ~ less_than(absolute(add(minus(l1),f(fp33(X1)))),half(b))
    | ~ less_than(absolute(add(minus(a),fp33(X1))),fp32(half(b)))
    | ~ less_than(n0,half(b))
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_38,c_0_39]) ).

cnf(c_0_44,negated_conjecture,
    ( less_than(absolute(add(minus(l1),f(X1))),X2)
    | ~ less_than(absolute(add(minus(a),X1)),fp31(X2))
    | ~ less_than(n0,X2) ),
    inference(spm,[status(thm)],[c_0_40,c_0_23]) ).

cnf(c_0_45,negated_conjecture,
    ( less_than(absolute(add(minus(a),fp33(add(X1,X2)))),X3)
    | ~ less_than(n0,add(X1,X2))
    | ~ less_than(X2,half(X3))
    | ~ less_than(X1,half(X3)) ),
    inference(spm,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_46,axiom,
    add(n0,X1) = X1,
    left_identity ).

cnf(c_0_47,negated_conjecture,
    ( ~ less_than(absolute(add(minus(a),fp33(X1))),fp32(half(b)))
    | ~ less_than(absolute(add(minus(a),fp33(X1))),fp31(half(b)))
    | ~ less_than(n0,half(b))
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_48,negated_conjecture,
    ( less_than(absolute(add(minus(a),fp33(X1))),X2)
    | ~ less_than(X1,half(X2))
    | ~ less_than(n0,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_36]) ).

cnf(c_0_49,negated_conjecture,
    ( ~ less_than(absolute(add(minus(a),fp33(X1))),fp31(half(b)))
    | ~ less_than(X1,half(fp32(half(b))))
    | ~ less_than(n0,half(b))
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_50,axiom,
    ( less_than(minimum(X1,X2),X1)
    | ~ less_than(n0,X1)
    | ~ less_than(n0,X2) ),
    axiom_2_2 ).

cnf(c_0_51,negated_conjecture,
    ( ~ less_than(X1,half(fp32(half(b))))
    | ~ less_than(X1,half(fp31(half(b))))
    | ~ less_than(n0,half(b))
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_49,c_0_48]) ).

cnf(c_0_52,axiom,
    ( less_than(n0,half(X1))
    | ~ less_than(n0,X1) ),
    axiom_6_2 ).

cnf(c_0_53,negated_conjecture,
    less_than(n0,b),
    c_14 ).

cnf(c_0_54,plain,
    ( less_than(minimum(add(X1,X2),X3),X4)
    | ~ less_than(n0,add(X1,X2))
    | ~ less_than(X2,half(X4))
    | ~ less_than(X1,half(X4))
    | ~ less_than(n0,X3) ),
    inference(spm,[status(thm)],[c_0_41,c_0_50]) ).

cnf(c_0_55,negated_conjecture,
    ( ~ less_than(X1,half(fp32(half(b))))
    | ~ less_than(X1,half(fp31(half(b))))
    | ~ less_than(n0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]) ).

cnf(c_0_56,plain,
    ( less_than(minimum(X1,X2),X3)
    | ~ less_than(X1,half(X3))
    | ~ less_than(n0,X1)
    | ~ less_than(n0,X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_46]),c_0_36]) ).

cnf(c_0_57,axiom,
    ( less_than(n0,minimum(X1,X2))
    | ~ less_than(n0,X1)
    | ~ less_than(n0,X2) ),
    axiom_2_1 ).

cnf(c_0_58,negated_conjecture,
    ( ~ less_than(minimum(X1,X2),half(fp31(half(b))))
    | ~ less_than(X1,half(half(fp32(half(b)))))
    | ~ less_than(n0,X1)
    | ~ less_than(n0,X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]) ).

cnf(c_0_59,axiom,
    ( less_than(minimum(X1,X2),X2)
    | ~ less_than(n0,X1)
    | ~ less_than(n0,X2) ),
    axiom_2_3 ).

cnf(c_0_60,negated_conjecture,
    ( ~ less_than(X1,half(half(fp32(half(b)))))
    | ~ less_than(n0,half(fp31(half(b))))
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_61,negated_conjecture,
    ( ~ less_than(X1,half(half(fp32(half(b)))))
    | ~ less_than(n0,fp31(half(b)))
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_60,c_0_52]) ).

cnf(c_0_62,negated_conjecture,
    ( less_than(n0,fp31(X1))
    | ~ less_than(n0,X1) ),
    c_10 ).

cnf(c_0_63,negated_conjecture,
    ( ~ less_than(X1,half(half(fp32(half(b)))))
    | ~ less_than(n0,half(b))
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_61,c_0_62]) ).

cnf(c_0_64,negated_conjecture,
    ( ~ less_than(X1,half(half(fp32(half(b)))))
    | ~ less_than(n0,X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_52]),c_0_53])]) ).

cnf(c_0_65,negated_conjecture,
    ( ~ less_than(n0,half(half(fp32(half(b)))))
    | ~ less_than(n0,X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_50]),c_0_57]) ).

cnf(c_0_66,negated_conjecture,
    ( ~ less_than(n0,half(fp32(half(b))))
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_65,c_0_52]) ).

cnf(c_0_67,negated_conjecture,
    ( ~ less_than(n0,fp32(half(b)))
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_66,c_0_52]) ).

cnf(c_0_68,negated_conjecture,
    ( less_than(n0,fp32(X1))
    | ~ less_than(n0,X1) ),
    c_12 ).

cnf(c_0_69,negated_conjecture,
    ( ~ less_than(n0,half(b))
    | ~ less_than(n0,X1) ),
    inference(spm,[status(thm)],[c_0_67,c_0_68]) ).

cnf(c_0_70,negated_conjecture,
    ~ less_than(n0,X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_52]),c_0_53])]) ).

cnf(c_0_71,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[c_0_53,c_0_70]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : ANA005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n027.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 18:47:49 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.58  start to proof: theBenchmark
% 102.29/102.33  % Version  : CSE_E---1.5
% 102.29/102.33  % Problem  : theBenchmark.p
% 102.29/102.33  % Proof found
% 102.29/102.33  % SZS status Theorem for theBenchmark.p
% 102.29/102.33  % SZS output start Proof
% See solution above
% 102.29/102.34  % Total time : 101.750000 s
% 102.29/102.34  % SZS output end Proof
% 102.29/102.34  % Total time : 101.758000 s
%------------------------------------------------------------------------------