TSTP Solution File: GRP685-10 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP685-10 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n012.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 : Thu Aug 31 00:23:03 EDT 2023

% Result   : Unsatisfiable 0.20s 0.66s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   73 (  67 unt;   6 typ;   0 def)
%            Number of atoms       :   67 (  66 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  139 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    x6: $i ).

tff(decl_26,type,
    x7: $i ).

tff(decl_27,type,
    x8: $i ).

cnf(f01,axiom,
    ld(X1,mult(X1,X1)) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).

cnf(f03,axiom,
    mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).

cnf(f02,axiom,
    rd(mult(X1,X1),X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).

cnf(f04,axiom,
    mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).

cnf(f07,axiom,
    ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).

cnf(f05,axiom,
    ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).

cnf(f06,axiom,
    rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).

cnf(goal,negated_conjecture,
    rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).

cnf(c_0_8,axiom,
    ld(X1,mult(X1,X1)) = X1,
    f01 ).

cnf(c_0_9,axiom,
    mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
    f03 ).

cnf(c_0_10,axiom,
    rd(mult(X1,X1),X1) = X1,
    f02 ).

cnf(c_0_11,axiom,
    mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
    f04 ).

cnf(c_0_12,axiom,
    ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
    f07 ).

cnf(c_0_13,plain,
    mult(X1,ld(X1,X1)) = X1,
    inference(rw,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_14,plain,
    mult(rd(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_15,plain,
    mult(rd(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_9]) ).

cnf(c_0_16,plain,
    mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
    inference(spm,[status(thm)],[c_0_9,c_0_13]) ).

cnf(c_0_17,axiom,
    ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
    f05 ).

cnf(c_0_18,plain,
    rd(X1,X1) = ld(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_14]),c_0_15]),c_0_16]) ).

cnf(c_0_19,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_9]),c_0_9]) ).

cnf(c_0_20,plain,
    mult(ld(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[c_0_14,c_0_18]) ).

cnf(c_0_21,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(X1,ld(X1,X3)),ld(X3,X3)),
    inference(spm,[status(thm)],[c_0_19,c_0_13]) ).

cnf(c_0_22,axiom,
    rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
    f06 ).

cnf(c_0_23,plain,
    mult(ld(X1,X1),ld(ld(X1,X1),X1)) = ld(ld(X1,X1),X1),
    inference(spm,[status(thm)],[c_0_9,c_0_20]) ).

cnf(c_0_24,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_13]),c_0_13]) ).

cnf(c_0_25,plain,
    mult(rd(ld(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
    inference(spm,[status(thm)],[c_0_15,c_0_18]) ).

cnf(c_0_26,plain,
    mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(rd(X2,X4),X4)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_11]),c_0_11]) ).

cnf(c_0_27,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),ld(X1,X1))) = ld(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_16]),c_0_13]) ).

cnf(c_0_28,plain,
    ld(ld(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,plain,
    mult(X1,ld(X1,ld(ld(X1,X1),ld(X1,X1)))) = ld(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_20]) ).

cnf(c_0_30,plain,
    mult(rd(mult(X1,X2),ld(X3,X3)),ld(X3,X3)) = mult(X1,mult(rd(X2,X3),X3)),
    inference(spm,[status(thm)],[c_0_26,c_0_18]) ).

cnf(c_0_31,plain,
    ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).

cnf(c_0_32,plain,
    mult(mult(ld(X1,X1),ld(ld(X1,X1),X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
    inference(spm,[status(thm)],[c_0_19,c_0_28]) ).

cnf(c_0_33,plain,
    mult(X1,mult(rd(X2,ld(X3,X3)),ld(X3,X3))) = mult(X1,mult(rd(X2,X3),X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_30]) ).

cnf(c_0_34,plain,
    mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_31]),c_0_32]),c_0_19]) ).

cnf(c_0_35,plain,
    mult(X1,mult(rd(mult(X2,X3),X4),X4)) = mult(X1,mult(X2,mult(rd(X3,X4),X4))),
    inference(spm,[status(thm)],[c_0_33,c_0_30]) ).

cnf(c_0_36,plain,
    mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_28]),c_0_20]),c_0_9]) ).

cnf(c_0_37,plain,
    rd(mult(X1,ld(X1,mult(X2,X3))),X3) = mult(rd(mult(X1,ld(X1,X2)),X3),X3),
    inference(spm,[status(thm)],[c_0_11,c_0_34]) ).

cnf(c_0_38,plain,
    mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),X1)) = X1,
    inference(spm,[status(thm)],[c_0_24,c_0_9]) ).

cnf(c_0_39,plain,
    mult(X1,mult(rd(X2,X3),X3)) = mult(X1,mult(X2,ld(X3,X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_13]),c_0_25]),c_0_36]) ).

cnf(c_0_40,plain,
    rd(mult(X1,ld(X1,X2)),ld(X2,X2)) = mult(X1,mult(rd(ld(X1,X2),X2),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_13]),c_0_30]) ).

cnf(c_0_41,plain,
    mult(X1,ld(X1,ld(X1,X2))) = ld(X1,X2),
    inference(spm,[status(thm)],[c_0_38,c_0_24]) ).

cnf(c_0_42,plain,
    mult(rd(X1,ld(X1,X1)),ld(X1,X1)) = rd(X1,ld(X1,X1)),
    inference(spm,[status(thm)],[c_0_11,c_0_13]) ).

cnf(c_0_43,plain,
    mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(X2,ld(X4,X4))),
    inference(rw,[status(thm)],[c_0_26,c_0_39]) ).

cnf(c_0_44,plain,
    rd(X1,ld(X1,X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_40]),c_0_25]),c_0_41]),c_0_13]),c_0_42]) ).

cnf(c_0_45,plain,
    mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(X2,ld(X3,X3))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_31]) ).

cnf(c_0_46,plain,
    mult(mult(rd(X1,X2),X2),X2) = mult(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_11]),c_0_13]) ).

cnf(c_0_47,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_34]),c_0_13]) ).

cnf(c_0_48,plain,
    mult(ld(X1,X1),X2) = mult(X1,ld(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_15]),c_0_34]),c_0_20]),c_0_18]) ).

cnf(c_0_49,plain,
    ld(ld(X1,X2),mult(X1,ld(X1,X3))) = ld(ld(X1,X2),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_47]),c_0_41]) ).

cnf(c_0_50,plain,
    rd(mult(X1,ld(X1,X2)),ld(X2,X2)) = mult(X1,mult(ld(X1,X2),ld(X2,X2))),
    inference(rw,[status(thm)],[c_0_40,c_0_39]) ).

cnf(c_0_51,plain,
    ld(ld(X1,X1),X2) = mult(X1,ld(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_48]),c_0_49]),c_0_47]) ).

cnf(c_0_52,plain,
    mult(ld(X1,X2),mult(X1,ld(X1,X3))) = mult(ld(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_36,c_0_47]) ).

cnf(c_0_53,plain,
    mult(X1,mult(ld(X1,X2),ld(X2,X2))) = mult(X1,ld(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[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_50,c_0_51]),c_0_52]),c_0_48]),c_0_50]),c_0_34]),c_0_13]),c_0_52]),c_0_48]) ).

cnf(c_0_54,plain,
    mult(X1,ld(X1,mult(ld(X1,X2),X3))) = mult(ld(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_34,c_0_41]) ).

cnf(c_0_55,plain,
    mult(ld(X1,X2),ld(X2,X2)) = ld(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_53]),c_0_9]),c_0_41]),c_0_54]) ).

cnf(c_0_56,negated_conjecture,
    rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
    goal ).

cnf(c_0_57,plain,
    rd(mult(X1,ld(X1,mult(X2,X3))),X3) = mult(X1,mult(ld(X1,X2),ld(X3,X3))),
    inference(rw,[status(thm)],[c_0_37,c_0_45]) ).

cnf(c_0_58,plain,
    ld(ld(X1,X2),ld(X1,X2)) = mult(X1,ld(X1,ld(X2,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_55]),c_0_47]) ).

cnf(c_0_59,negated_conjecture,
    mult(rd(x6,ld(x7,x8)),ld(x7,x8)) != mult(rd(x6,x8),x8),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_11]),c_0_11]) ).

cnf(c_0_60,plain,
    mult(rd(X1,X2),X2) = mult(X1,ld(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_9]),c_0_36]),c_0_11]),c_0_48]),c_0_36]) ).

cnf(c_0_61,plain,
    mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(X1,ld(X1,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_58]),c_0_34]),c_0_48]),c_0_47]) ).

cnf(c_0_62,negated_conjecture,
    mult(x6,ld(ld(x7,x8),ld(x7,x8))) != mult(x6,ld(x8,x8)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_60]),c_0_60]) ).

cnf(c_0_63,plain,
    ld(X1,mult(X2,ld(X2,X3))) = ld(X1,X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_61]),c_0_9]),c_0_41]),c_0_41]) ).

cnf(c_0_64,negated_conjecture,
    mult(x6,mult(x7,ld(x7,ld(x8,x8)))) != mult(x6,ld(x8,x8)),
    inference(rw,[status(thm)],[c_0_62,c_0_58]) ).

cnf(c_0_65,plain,
    mult(X1,mult(X2,ld(X2,X3))) = mult(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_63]),c_0_36]) ).

cnf(c_0_66,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP685-10 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n012.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   : Tue Aug 29 01:12:24 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.66  % Version  : CSE_E---1.5
% 0.20/0.66  % Problem  : theBenchmark.p
% 0.20/0.66  % Proof found
% 0.20/0.66  % SZS status Theorem for theBenchmark.p
% 0.20/0.66  % SZS output start Proof
% See solution above
% 0.20/0.67  % Total time : 0.069000 s
% 0.20/0.67  % SZS output end Proof
% 0.20/0.67  % Total time : 0.071000 s
%------------------------------------------------------------------------------