TSTP Solution File: GRP655-14 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP655-14 : 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 : n005.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 00:22:47 EDT 2023

% Result   : Unsatisfiable 12.86s 12.95s
% Output   : CNFRefutation 12.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   84 (  79 unt;   5 typ;   0 def)
%            Number of atoms       :   79 (  78 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    7 (   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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  195 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    x1: $i ).

tff(decl_26,type,
    x0: $i ).

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

cnf(f01,axiom,
    mult(X1,ld(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).

cnf(f02,axiom,
    ld(X1,mult(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).

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

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

cnf(goal,negated_conjecture,
    mult(ld(x1,x1),x0) != x0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).

cnf(c_0_6,axiom,
    mult(X1,mult(X2,mult(X3,X2))) = mult(mult(mult(X1,X2),X3),X2),
    f05 ).

cnf(c_0_7,axiom,
    mult(X1,ld(X1,X2)) = X2,
    f01 ).

cnf(c_0_8,axiom,
    ld(X1,mult(X1,X2)) = X2,
    f02 ).

cnf(c_0_9,plain,
    mult(X1,mult(X2,mult(ld(mult(X1,X2),X3),X2))) = mult(X3,X2),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,plain,
    mult(X1,mult(ld(mult(X2,X1),X3),X1)) = ld(X2,mult(X3,X1)),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

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

cnf(c_0_12,plain,
    ld(X1,ld(X2,mult(X3,X1))) = mult(ld(mult(X2,X1),X3),X1),
    inference(spm,[status(thm)],[c_0_8,c_0_10]) ).

cnf(c_0_13,plain,
    rd(mult(X1,mult(X2,mult(X3,X2))),X2) = mult(mult(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_11,c_0_6]) ).

cnf(c_0_14,plain,
    mult(ld(mult(X1,X2),X1),X2) = ld(X2,X2),
    inference(spm,[status(thm)],[c_0_12,c_0_8]) ).

cnf(c_0_15,plain,
    mult(mult(X1,X2),ld(mult(X3,X2),X3)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_7]),c_0_11]) ).

cnf(c_0_16,axiom,
    mult(rd(X1,X2),X2) = X1,
    f03 ).

cnf(c_0_17,plain,
    mult(mult(X1,ld(X2,X3)),ld(X3,X2)) = X1,
    inference(spm,[status(thm)],[c_0_15,c_0_7]) ).

cnf(c_0_18,plain,
    mult(ld(mult(X1,X2),rd(X3,X2)),X2) = ld(X2,ld(X1,X3)),
    inference(spm,[status(thm)],[c_0_12,c_0_16]) ).

cnf(c_0_19,plain,
    mult(X1,ld(X2,X3)) = rd(X1,ld(X3,X2)),
    inference(spm,[status(thm)],[c_0_11,c_0_17]) ).

cnf(c_0_20,plain,
    ld(mult(X1,X2),rd(X3,X2)) = rd(ld(X2,ld(X1,X3)),X2),
    inference(spm,[status(thm)],[c_0_11,c_0_18]) ).

cnf(c_0_21,plain,
    rd(X1,ld(mult(X2,X3),X2)) = mult(X1,X3),
    inference(spm,[status(thm)],[c_0_19,c_0_8]) ).

cnf(c_0_22,plain,
    ld(rd(X1,X2),mult(X3,X2)) = mult(X2,mult(ld(X1,X3),X2)),
    inference(spm,[status(thm)],[c_0_10,c_0_16]) ).

cnf(c_0_23,plain,
    ld(mult(mult(X1,X2),X3),mult(X1,mult(X2,mult(X3,X2)))) = X2,
    inference(spm,[status(thm)],[c_0_8,c_0_6]) ).

cnf(c_0_24,plain,
    mult(ld(ld(mult(X1,X2),X1),ld(X3,X4)),X2) = mult(X2,mult(ld(X3,X4),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]),c_0_8]),c_0_22]),c_0_21]) ).

cnf(c_0_25,plain,
    ld(rd(mult(X1,X2),ld(X3,mult(X4,X2))),rd(X1,ld(mult(X3,X2),X4))) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_10]),c_0_19]),c_0_19]) ).

cnf(c_0_26,plain,
    mult(X1,mult(ld(X2,rd(X3,X1)),X1)) = ld(rd(X2,X1),X3),
    inference(spm,[status(thm)],[c_0_22,c_0_16]) ).

cnf(c_0_27,plain,
    mult(ld(ld(mult(X1,X2),X1),X3),X2) = mult(X2,mult(X3,X2)),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,plain,
    ld(rd(ld(mult(X1,X2),X1),X2),X3) = mult(X2,mult(X2,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_16]) ).

cnf(c_0_29,plain,
    mult(X1,mult(X1,mult(rd(ld(mult(X2,X1),X2),X1),X3))) = X3,
    inference(spm,[status(thm)],[c_0_8,c_0_28]) ).

cnf(c_0_30,plain,
    mult(X1,mult(rd(ld(mult(X2,X1),X2),X1),X3)) = ld(X1,X3),
    inference(spm,[status(thm)],[c_0_8,c_0_29]) ).

cnf(c_0_31,plain,
    mult(rd(ld(mult(X1,X2),X1),X2),X3) = ld(X2,ld(X2,X3)),
    inference(spm,[status(thm)],[c_0_8,c_0_30]) ).

cnf(c_0_32,plain,
    mult(X1,mult(ld(ld(X2,ld(X2,X1)),X3),X1)) = mult(X2,mult(X2,mult(X3,X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_31]),c_0_28]) ).

cnf(c_0_33,plain,
    ld(rd(ld(X1,ld(X1,X2)),X2),X3) = mult(X1,mult(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_32]),c_0_16]) ).

cnf(c_0_34,plain,
    mult(X1,mult(X1,mult(rd(ld(X1,ld(X1,X2)),X2),X3))) = X3,
    inference(spm,[status(thm)],[c_0_8,c_0_33]) ).

cnf(c_0_35,plain,
    rd(ld(X1,X1),X1) = ld(mult(X2,X1),X2),
    inference(spm,[status(thm)],[c_0_11,c_0_14]) ).

cnf(c_0_36,plain,
    ld(X1,rd(X1,ld(X2,X3))) = ld(X3,X2),
    inference(spm,[status(thm)],[c_0_8,c_0_19]) ).

cnf(c_0_37,plain,
    ld(rd(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_8,c_0_16]) ).

cnf(c_0_38,plain,
    ld(ld(mult(X1,X2),X1),ld(X2,X2)) = X2,
    inference(spm,[status(thm)],[c_0_8,c_0_14]) ).

cnf(c_0_39,plain,
    mult(X1,mult(rd(ld(X1,ld(X1,X2)),X2),X3)) = ld(X1,X3),
    inference(spm,[status(thm)],[c_0_8,c_0_34]) ).

cnf(c_0_40,plain,
    ld(mult(X1,X2),X1) = ld(mult(X3,X2),X3),
    inference(spm,[status(thm)],[c_0_35,c_0_35]) ).

cnf(c_0_41,plain,
    mult(ld(X1,X2),rd(ld(X2,X1),ld(X2,X1))) = ld(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_36]),c_0_19]),c_0_37]) ).

cnf(c_0_42,plain,
    mult(X1,mult(ld(X1,X1),X1)) = mult(X1,X1),
    inference(spm,[status(thm)],[c_0_24,c_0_38]) ).

cnf(c_0_43,plain,
    mult(rd(ld(X1,ld(X1,X2)),X2),X3) = ld(X1,ld(X1,X3)),
    inference(spm,[status(thm)],[c_0_8,c_0_39]) ).

cnf(c_0_44,plain,
    ld(mult(X1,X2),X1) = ld(X3,rd(X3,X2)),
    inference(spm,[status(thm)],[c_0_40,c_0_16]) ).

cnf(c_0_45,plain,
    mult(ld(mult(X1,X2),X1),rd(X2,X2)) = ld(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_41,c_0_8]) ).

cnf(c_0_46,plain,
    ld(ld(X1,X2),ld(X1,X2)) = rd(ld(X2,X1),ld(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_19]),c_0_19]),c_0_37]) ).

cnf(c_0_47,plain,
    mult(mult(X1,X2),rd(X3,X2)) = rd(mult(X1,mult(X2,X3)),X2),
    inference(spm,[status(thm)],[c_0_13,c_0_16]) ).

cnf(c_0_48,plain,
    mult(ld(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_42]),c_0_8]) ).

cnf(c_0_49,plain,
    mult(rd(ld(X1,X2),mult(X1,X2)),X3) = ld(X1,ld(X1,X3)),
    inference(spm,[status(thm)],[c_0_43,c_0_8]) ).

cnf(c_0_50,plain,
    ld(X1,rd(X1,rd(X2,X2))) = rd(X2,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_8]),c_0_8]) ).

cnf(c_0_51,plain,
    rd(rd(mult(X1,mult(X2,X3)),X2),rd(X3,X2)) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_11,c_0_47]) ).

cnf(c_0_52,plain,
    ld(X1,X1) = rd(X1,X1),
    inference(spm,[status(thm)],[c_0_11,c_0_48]) ).

cnf(c_0_53,plain,
    mult(X1,rd(X2,X2)) = rd(X1,rd(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_45]),c_0_46]),c_0_8]),c_0_8]) ).

cnf(c_0_54,plain,
    mult(X1,mult(mult(ld(mult(X2,X1),X2),X3),X1)) = mult(X3,X1),
    inference(spm,[status(thm)],[c_0_27,c_0_8]) ).

cnf(c_0_55,plain,
    mult(rd(X1,mult(X2,mult(X2,X1))),X3) = ld(X2,ld(X2,X3)),
    inference(spm,[status(thm)],[c_0_49,c_0_8]) ).

cnf(c_0_56,plain,
    mult(X1,mult(ld(mult(X2,mult(X1,X1)),X2),X1)) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_22]) ).

cnf(c_0_57,plain,
    rd(X1,rd(X1,X1)) = X1,
    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_24,c_0_52]),c_0_21]),c_0_14]),c_0_52]),c_0_16]),c_0_14]),c_0_52]),c_0_53]) ).

cnf(c_0_58,plain,
    mult(ld(mult(rd(mult(X1,X2),X3),X2),X1),X2) = ld(X2,X3),
    inference(spm,[status(thm)],[c_0_12,c_0_37]) ).

cnf(c_0_59,plain,
    mult(mult(ld(mult(X1,X2),X1),X3),X2) = ld(X2,mult(X3,X2)),
    inference(spm,[status(thm)],[c_0_8,c_0_54]) ).

cnf(c_0_60,plain,
    mult(X1,mult(mult(ld(mult(X2,mult(X3,X1)),X4),mult(X3,X1)),X1)) = ld(X3,mult(ld(X2,mult(X4,mult(X3,X1))),X1)),
    inference(spm,[status(thm)],[c_0_10,c_0_12]) ).

cnf(c_0_61,plain,
    mult(ld(mult(X1,mult(X2,X2)),X1),X3) = ld(X2,ld(X2,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_53]),c_0_57]),c_0_11]) ).

cnf(c_0_62,plain,
    rd(X1,ld(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_11,c_0_7]) ).

cnf(c_0_63,plain,
    ld(mult(rd(mult(X1,X2),X3),X2),X1) = rd(ld(X2,X3),X2),
    inference(spm,[status(thm)],[c_0_11,c_0_58]) ).

cnf(c_0_64,plain,
    rd(ld(X1,mult(X2,X1)),X1) = mult(ld(mult(X3,X1),X3),X2),
    inference(spm,[status(thm)],[c_0_11,c_0_59]) ).

cnf(c_0_65,plain,
    ld(X1,mult(mult(X1,X1),X1)) = mult(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_8]),c_0_52]),c_0_16]),c_0_8]) ).

cnf(c_0_66,plain,
    ld(mult(mult(X1,mult(ld(mult(X2,X3),X4),X3)),X3),mult(X1,rd(mult(ld(mult(X2,X3),X4),X3),ld(mult(X4,X3),X2)))) = mult(ld(mult(X2,X3),X4),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_10]),c_0_19]) ).

cnf(c_0_67,plain,
    mult(rd(mult(X1,X2),X3),X2) = rd(X1,rd(ld(X2,X3),X2)),
    inference(spm,[status(thm)],[c_0_62,c_0_63]) ).

cnf(c_0_68,plain,
    mult(ld(mult(X1,X2),X1),mult(X2,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_11]) ).

cnf(c_0_69,plain,
    ld(mult(mult(X1,mult(rd(X2,X2),X3)),X3),mult(X1,rd(mult(rd(X2,X2),X3),rd(ld(X3,rd(X2,X2)),X3)))) = mult(rd(X2,X2),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_50]),c_0_67]),c_0_37]) ).

cnf(c_0_70,plain,
    rd(rd(X1,X2),rd(ld(X2,X3),X2)) = mult(rd(X1,X3),X2),
    inference(spm,[status(thm)],[c_0_67,c_0_16]) ).

cnf(c_0_71,plain,
    rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_68]),c_0_14]),c_0_52]) ).

cnf(c_0_72,plain,
    rd(rd(X1,X1),rd(X2,X2)) = rd(X2,X2),
    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_69,c_0_53]),c_0_53]),c_0_70]),c_0_71]),c_0_53]),c_0_37]) ).

cnf(c_0_73,negated_conjecture,
    mult(ld(x1,x1),x0) != x0,
    goal ).

cnf(c_0_74,plain,
    mult(rd(ld(mult(X1,X2),X1),ld(X3,X4)),X2) = ld(X2,mult(ld(X4,X3),X2)),
    inference(spm,[status(thm)],[c_0_59,c_0_19]) ).

cnf(c_0_75,plain,
    rd(X1,X1) = rd(X2,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_72]),c_0_53]),c_0_71]) ).

cnf(c_0_76,negated_conjecture,
    mult(rd(x1,x1),x0) != x0,
    inference(rw,[status(thm)],[c_0_73,c_0_52]) ).

cnf(c_0_77,plain,
    mult(rd(X1,X1),X2) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_8]),c_0_8]) ).

cnf(c_0_78,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP655-14 : TPTP v8.1.2. Released v8.1.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n005.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   : Mon Aug 28 22:01:53 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 12.86/12.95  % Version  : CSE_E---1.5
% 12.86/12.95  % Problem  : theBenchmark.p
% 12.86/12.95  % Proof found
% 12.86/12.95  % SZS status Theorem for theBenchmark.p
% 12.86/12.95  % SZS output start Proof
% See solution above
% 12.86/12.96  % Total time : 12.368000 s
% 12.86/12.96  % SZS output end Proof
% 12.86/12.96  % Total time : 12.371000 s
%------------------------------------------------------------------------------