TSTP Solution File: GRP696-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP696-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n019.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 00:23:11 EDT 2023

% Result   : Unsatisfiable 11.21s 11.42s
% Output   : CNFRefutation 11.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   73 (  65 unt;   8 typ;   0 def)
%            Number of atoms       :   65 (  64 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    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  116 (   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,
    unit: $i ).

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

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

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

tff(decl_29,type,
    c: $i ).

cnf(c02,axiom,
    ld(X1,mult(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).

cnf(c11,axiom,
    mult(X1,i(X1)) = unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11) ).

cnf(c04,axiom,
    rd(mult(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).

cnf(c10,axiom,
    mult(i(X1),X1) = unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).

cnf(c03,axiom,
    mult(rd(X1,X2),X2) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).

cnf(c07,axiom,
    mult(X1,i(mult(X2,X1))) = i(X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).

cnf(c01,axiom,
    mult(X1,ld(X1,X2)) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).

cnf(c08,axiom,
    mult(X1,mult(X2,X3)) = mult(rd(mult(X1,X2),X1),mult(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).

cnf(c05,axiom,
    mult(X1,unit) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).

cnf(c09,axiom,
    mult(mult(X1,X2),X3) = mult(mult(X1,X3),ld(X3,mult(X2,X3))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).

cnf(c06,axiom,
    mult(unit,X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).

cnf(goals,negated_conjecture,
    mult(mult(mult(a,b),a),mult(a,c)) != mult(a,mult(mult(mult(b,a),a),c)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

cnf(c_0_12,axiom,
    ld(X1,mult(X1,X2)) = X2,
    c02 ).

cnf(c_0_13,axiom,
    mult(X1,i(X1)) = unit,
    c11 ).

cnf(c_0_14,axiom,
    rd(mult(X1,X2),X2) = X1,
    c04 ).

cnf(c_0_15,axiom,
    mult(i(X1),X1) = unit,
    c10 ).

cnf(c_0_16,plain,
    ld(X1,unit) = i(X1),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,plain,
    i(X1) = rd(unit,X1),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,axiom,
    mult(rd(X1,X2),X2) = X1,
    c03 ).

cnf(c_0_19,axiom,
    mult(X1,i(mult(X2,X1))) = i(X2),
    c07 ).

cnf(c_0_20,plain,
    ld(X1,unit) = rd(unit,X1),
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,plain,
    ld(rd(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_12,c_0_18]) ).

cnf(c_0_22,plain,
    mult(X1,rd(unit,mult(X2,X1))) = rd(unit,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17]),c_0_17]) ).

cnf(c_0_23,axiom,
    mult(X1,ld(X1,X2)) = X2,
    c01 ).

cnf(c_0_24,axiom,
    mult(X1,mult(X2,X3)) = mult(rd(mult(X1,X2),X1),mult(X1,X3)),
    c08 ).

cnf(c_0_25,plain,
    mult(X1,rd(unit,X1)) = unit,
    inference(rw,[status(thm)],[c_0_13,c_0_17]) ).

cnf(c_0_26,axiom,
    mult(X1,unit) = X1,
    c05 ).

cnf(c_0_27,plain,
    rd(unit,rd(unit,X1)) = X1,
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_28,plain,
    ld(X1,rd(unit,X2)) = rd(unit,mult(X2,X1)),
    inference(spm,[status(thm)],[c_0_12,c_0_22]) ).

cnf(c_0_29,plain,
    rd(X1,ld(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_14,c_0_23]) ).

cnf(c_0_30,plain,
    rd(unit,rd(X1,X2)) = mult(X2,rd(unit,X1)),
    inference(spm,[status(thm)],[c_0_22,c_0_18]) ).

cnf(c_0_31,plain,
    mult(X1,mult(X2,rd(unit,X1))) = rd(mult(X1,X2),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).

cnf(c_0_32,plain,
    mult(rd(unit,mult(X1,X2)),X1) = rd(unit,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_22]),c_0_27]) ).

cnf(c_0_33,plain,
    rd(unit,mult(rd(unit,X1),X2)) = ld(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_20]) ).

cnf(c_0_34,plain,
    rd(unit,mult(X1,rd(unit,X2))) = rd(X2,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_30]),c_0_20]) ).

cnf(c_0_35,axiom,
    mult(mult(X1,X2),X3) = mult(mult(X1,X3),ld(X3,mult(X2,X3))),
    c09 ).

cnf(c_0_36,plain,
    ld(X1,mult(X2,rd(unit,X3))) = rd(unit,mult(rd(X3,X2),X1)),
    inference(spm,[status(thm)],[c_0_28,c_0_30]) ).

cnf(c_0_37,axiom,
    mult(unit,X1) = X1,
    c06 ).

cnf(c_0_38,plain,
    ld(X1,rd(mult(X1,X2),X1)) = mult(X2,rd(unit,X1)),
    inference(spm,[status(thm)],[c_0_12,c_0_31]) ).

cnf(c_0_39,plain,
    mult(rd(unit,X1),rd(X1,X2)) = rd(unit,X2),
    inference(spm,[status(thm)],[c_0_32,c_0_18]) ).

cnf(c_0_40,plain,
    rd(rd(unit,X1),X2) = rd(unit,mult(X2,X1)),
    inference(spm,[status(thm)],[c_0_14,c_0_32]) ).

cnf(c_0_41,plain,
    ld(rd(unit,X1),X2) = rd(X1,rd(unit,X2)),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_42,plain,
    rd(unit,ld(X1,X2)) = mult(rd(unit,X2),X1),
    inference(spm,[status(thm)],[c_0_32,c_0_23]) ).

cnf(c_0_43,plain,
    rd(X1,unit) = X1,
    inference(spm,[status(thm)],[c_0_26,c_0_18]) ).

cnf(c_0_44,plain,
    rd(mult(X1,ld(X2,X1)),X1) = mult(X1,rd(unit,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).

cnf(c_0_45,plain,
    rd(X1,rd(X1,X2)) = mult(mult(X1,X2),rd(unit,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_25]),c_0_36]),c_0_34]),c_0_37]) ).

cnf(c_0_46,plain,
    rd(X1,mult(rd(unit,X1),X2)) = mult(rd(X1,X2),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_38,c_0_39]),c_0_40]),c_0_33]),c_0_41]),c_0_42]),c_0_30]),c_0_43]),c_0_26]) ).

cnf(c_0_47,plain,
    rd(X1,rd(X2,rd(unit,X1))) = rd(unit,X2),
    inference(spm,[status(thm)],[c_0_34,c_0_18]) ).

cnf(c_0_48,plain,
    mult(mult(X1,rd(unit,X2)),X1) = mult(X1,ld(X2,X1)),
    inference(spm,[status(thm)],[c_0_18,c_0_44]) ).

cnf(c_0_49,plain,
    mult(mult(rd(unit,X1),X2),X1) = ld(X1,mult(X2,X1)),
    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_40,c_0_45]),c_0_30]),c_0_43]),c_0_26]),c_0_40]),c_0_33]) ).

cnf(c_0_50,plain,
    mult(rd(X1,mult(X2,X1)),X1) = ld(X2,X1),
    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_46,c_0_31]),c_0_47]),c_0_33]),c_0_30]),c_0_43]),c_0_26]) ).

cnf(c_0_51,plain,
    mult(X1,ld(mult(X2,X1),X1)) = mult(rd(unit,X2),X1),
    inference(spm,[status(thm)],[c_0_48,c_0_22]) ).

cnf(c_0_52,plain,
    ld(X1,mult(rd(X1,X2),X1)) = mult(rd(unit,X2),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_22]),c_0_34]) ).

cnf(c_0_53,plain,
    rd(ld(X1,X2),X2) = rd(X2,mult(X1,X2)),
    inference(spm,[status(thm)],[c_0_14,c_0_50]) ).

cnf(c_0_54,plain,
    ld(X1,mult(rd(unit,X2),X1)) = ld(mult(X2,X1),X1),
    inference(spm,[status(thm)],[c_0_12,c_0_51]) ).

cnf(c_0_55,plain,
    mult(X1,mult(rd(unit,X2),X1)) = mult(rd(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_23,c_0_52]) ).

cnf(c_0_56,plain,
    rd(X1,mult(rd(X1,X2),X1)) = rd(X2,X1),
    inference(spm,[status(thm)],[c_0_53,c_0_21]) ).

cnf(c_0_57,plain,
    ld(mult(mult(X1,X2),X1),X1) = rd(unit,mult(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_32]),c_0_28]) ).

cnf(c_0_58,plain,
    mult(rd(X1,rd(unit,X2)),X1) = mult(X1,mult(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_43]),c_0_26]) ).

cnf(c_0_59,plain,
    rd(X1,rd(unit,mult(X2,X1))) = mult(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_29,c_0_57]) ).

cnf(c_0_60,plain,
    mult(mult(mult(X1,X2),X1),X1) = mult(X1,mult(mult(X2,X1),X1)),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_61,plain,
    rd(mult(X1,mult(mult(X2,X1),X1)),X1) = mult(mult(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_14,c_0_60]) ).

cnf(c_0_62,negated_conjecture,
    mult(mult(mult(a,b),a),mult(a,c)) != mult(a,mult(mult(mult(b,a),a),c)),
    goals ).

cnf(c_0_63,plain,
    mult(mult(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(mult(mult(X2,X1),X1),X3)),
    inference(spm,[status(thm)],[c_0_24,c_0_61]) ).

cnf(c_0_64,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP696-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.34  % Computer : n019.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Mon Aug 28 21:48:27 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 11.21/11.42  % Version  : CSE_E---1.5
% 11.21/11.42  % Problem  : theBenchmark.p
% 11.21/11.42  % Proof found
% 11.21/11.42  % SZS status Theorem for theBenchmark.p
% 11.21/11.42  % SZS output start Proof
% See solution above
% 11.21/11.42  % Total time : 10.862000 s
% 11.21/11.42  % SZS output end Proof
% 11.21/11.42  % Total time : 10.865000 s
%------------------------------------------------------------------------------