TSTP Solution File: GRP354-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP354-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n018.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  : 600s
% DateTime : Sat Jul 16 11:37:58 EDT 2022

% Result   : Unsatisfiable 55.58s 55.82s
% Output   : Refutation 55.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   21
% Syntax   : Number of clauses     :  105 (  32 unt;  66 nHn;  82 RR)
%            Number of literals    :  210 ( 209 equ;  49 neg)
%            Maximal clause size   :   14 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :   50 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
    multiply(identity,X) = X,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(left_inverse,axiom,
    multiply(inverse(X),X) = identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).

cnf(associativity,axiom,
    multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).

cnf(prove_this_1,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c9
    | multiply(sk_c3,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).

cnf(prove_this_2,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c9
    | inverse(sk_c3) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).

cnf(prove_this_4,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c9
    | inverse(sk_c4) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).

cnf(prove_this_5,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c9
    | multiply(sk_c4,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).

cnf(prove_this_17,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c3,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).

cnf(prove_this_20,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | inverse(sk_c4) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_20) ).

cnf(prove_this_21,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c4,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).

cnf(prove_this_27,negated_conjecture,
    ( inverse(sk_c9) = sk_c7
    | multiply(sk_c9,sk_c7) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).

cnf(prove_this_38,negated_conjecture,
    ( multiply(sk_c2,sk_c7) = sk_c8
    | multiply(sk_c5,sk_c6) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_38) ).

cnf(prove_this_39,negated_conjecture,
    ( multiply(sk_c2,sk_c7) = sk_c8
    | inverse(sk_c5) = sk_c6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_39) ).

cnf(prove_this_41,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c3,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_41) ).

cnf(prove_this_42,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | inverse(sk_c3) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_42) ).

cnf(prove_this_43,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c9,sk_c7) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_43) ).

cnf(prove_this_44,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | inverse(sk_c4) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_44) ).

cnf(prove_this_45,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c4,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_45) ).

cnf(prove_this_46,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c5,sk_c6) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_46) ).

cnf(prove_this_47,negated_conjecture,
    ( inverse(sk_c2) = sk_c7
    | inverse(sk_c5) = sk_c6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_47) ).

cnf(prove_this_49,negated_conjecture,
    ( multiply(sk_c8,sk_c7) != sk_c9
    | multiply(X,sk_c9) != sk_c8
    | inverse(X) != sk_c9
    | inverse(sk_c9) != sk_c7
    | multiply(Y,sk_c7) != sk_c8
    | inverse(Y) != sk_c7
    | multiply(Z,sk_c9) != sk_c8
    | inverse(Z) != sk_c9
    | multiply(sk_c9,sk_c7) != sk_c8
    | inverse(U) != sk_c9
    | multiply(U,sk_c8) != sk_c9
    | multiply(V,W) != sk_c8
    | inverse(V) != W
    | multiply(W,sk_c7) != sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).

cnf(53,plain,
    ( multiply(sk_c8,sk_c7) != sk_c9
    | inverse(sk_c9) != sk_c7
    | multiply(X,sk_c9) != sk_c8
    | inverse(X) != sk_c9
    | multiply(sk_c9,sk_c7) != sk_c8
    | inverse(Y) != sk_c9
    | multiply(Y,sk_c8) != sk_c9 ),
    inference('CONDENSE',[status(thm)],[prove_this_49]) ).

cnf(64,plain,
    X = multiply(inverse(Y),multiply(Y,X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).

cnf(65,plain,
    multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
    inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).

cnf(119,plain,
    ( multiply(sk_c8,sk_c7) = sk_c9
    | multiply(sk_c8,X) = multiply(sk_c3,multiply(sk_c9,X)) ),
    inference('PARAMODULATE',[status(thm)],[associativity,prove_this_1,theory(equality)]) ).

cnf(151,plain,
    ( multiply(sk_c8,sk_c7) != sk_c9
    | inverse(sk_c9) != sk_c7
    | identity != sk_c8
    | inverse(inverse(sk_c9)) != sk_c9
    | multiply(sk_c9,sk_c7) != sk_c8
    | inverse(X) != sk_c9
    | multiply(X,sk_c8) != sk_c9 ),
    inference('PARAMODULATE',[status(thm)],[53,left_inverse,theory(equality)]) ).

cnf(200,plain,
    X = multiply(inverse(inverse(X)),identity),
    inference('PARAMODULATE',[status(thm)],[64,left_inverse,theory(equality)]) ).

cnf(201,plain,
    multiply(X,Y) = multiply(inverse(inverse(X)),Y),
    inference('PARAMODULATE',[status(thm)],[64,64,theory(equality)]) ).

cnf(202,plain,
    X = multiply(X,identity),
    inference('REWRITE',[status(thm)],[200,201,theory(equality)]) ).

cnf(203,plain,
    multiply(multiply(X,inverse(Y)),Y) = X,
    inference('REWRITE',[status(thm)],[65,202,theory(equality)]) ).

cnf(204,plain,
    ( inverse(sk_c2) = sk_c7
    | sk_c6 = multiply(inverse(sk_c5),sk_c8) ),
    inference('PARAMODULATE',[status(thm)],[64,prove_this_46,theory(equality)]) ).

cnf(207,plain,
    ( inverse(sk_c2) = sk_c7
    | sk_c9 = multiply(inverse(sk_c3),sk_c8) ),
    inference('PARAMODULATE',[status(thm)],[64,prove_this_41,theory(equality)]) ).

cnf(216,plain,
    ( inverse(sk_c2) = sk_c7
    | sk_c7 = multiply(inverse(sk_c9),sk_c8) ),
    inference('PARAMODULATE',[status(thm)],[64,prove_this_43,theory(equality)]) ).

cnf(217,plain,
    ( inverse(sk_c9) = sk_c7
    | sk_c7 = multiply(inverse(sk_c9),sk_c8) ),
    inference('PARAMODULATE',[status(thm)],[64,prove_this_27,theory(equality)]) ).

cnf(225,plain,
    ( inverse(sk_c2) = sk_c7
    | sk_c8 = multiply(inverse(sk_c4),sk_c9) ),
    inference('PARAMODULATE',[status(thm)],[64,prove_this_45,theory(equality)]) ).

cnf(227,plain,
    ( inverse(sk_c1) = sk_c9
    | sk_c8 = multiply(inverse(sk_c4),sk_c9) ),
    inference('PARAMODULATE',[status(thm)],[64,prove_this_21,theory(equality)]) ).

cnf(228,plain,
    multiply(multiply(X,inverse(Y)),multiply(Y,Z)) = multiply(X,Z),
    inference('PARAMODULATE',[status(thm)],[associativity,64,theory(equality)]) ).

cnf(254,plain,
    inverse(identity) = identity,
    inference('PARAMODULATE',[status(thm)],[left_inverse,202,theory(equality)]) ).

cnf(257,plain,
    X = inverse(inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[203,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).

cnf(258,plain,
    ( multiply(sk_c8,sk_c7) != sk_c9
    | inverse(sk_c9) != sk_c7
    | identity != sk_c8
    | multiply(sk_c9,sk_c7) != sk_c8
    | inverse(X) != sk_c9
    | multiply(X,sk_c8) != sk_c9 ),
    inference('REWRITE',[status(thm)],[151,257,theory(equality)]) ).

cnf(262,plain,
    ( inverse(sk_c2) = sk_c7
    | multiply(multiply(X,sk_c9),sk_c4) = X ),
    inference('PARAMODULATE',[status(thm)],[203,prove_this_44,theory(equality)]) ).

cnf(263,plain,
    ( inverse(sk_c1) = sk_c9
    | multiply(multiply(X,sk_c9),sk_c4) = X ),
    inference('PARAMODULATE',[status(thm)],[203,prove_this_20,theory(equality)]) ).

cnf(271,plain,
    multiply(X,inverse(X)) = identity,
    inference('PARAMODULATE',[status(thm)],[left_inverse,257,theory(equality)]) ).

cnf(272,plain,
    multiply(multiply(X,Y),inverse(Y)) = X,
    inference('PARAMODULATE',[status(thm)],[203,257,theory(equality)]) ).

cnf(273,plain,
    X = multiply(Y,multiply(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[64,257,theory(equality)]) ).

cnf(278,plain,
    ( inverse(sk_c2) = sk_c7
    | sk_c3 = inverse(sk_c9) ),
    inference('PARAMODULATE',[status(thm)],[257,prove_this_42,theory(equality)]) ).

cnf(294,plain,
    inverse(X) = multiply(inverse(multiply(Y,X)),Y),
    inference('PARAMODULATE',[status(thm)],[64,272,theory(equality)]) ).

cnf(295,plain,
    multiply(X,inverse(multiply(Y,X))) = inverse(Y),
    inference('PARAMODULATE',[status(thm)],[272,64,theory(equality)]) ).

cnf(323,plain,
    ( multiply(sk_c8,sk_c7) = sk_c9
    | multiply(sk_c8,inverse(sk_c9)) = sk_c3 ),
    inference('PARAMODULATE',[status(thm)],[272,prove_this_1,theory(equality)]) ).

cnf(414,plain,
    ( inverse(sk_c2) = sk_c7
    | sk_c6 = multiply(sk_c6,sk_c8) ),
    inference('PARAMODULATE',[status(thm)],[204,prove_this_47,theory(equality)]) ).

cnf(420,plain,
    ( inverse(sk_c2) = sk_c7
    | identity = sk_c8 ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[64,414,theory(equality)]),left_inverse,theory(equality)]) ).

cnf(425,plain,
    ( identity = sk_c8
    | multiply(sk_c2,sk_c7) = identity ),
    inference('PARAMODULATE',[status(thm)],[271,420,theory(equality)]) ).

cnf(438,plain,
    ( identity = sk_c8
    | inverse(sk_c5) = sk_c6 ),
    inference('PARAMODULATE',[status(thm)],[prove_this_39,425,theory(equality)]) ).

cnf(441,plain,
    ( identity = sk_c8
    | multiply(sk_c5,sk_c6) = sk_c8 ),
    inference('PARAMODULATE',[status(thm)],[prove_this_38,425,theory(equality)]) ).

cnf(443,plain,
    ( identity = sk_c8
    | multiply(sk_c5,sk_c6) = identity ),
    inference('PARAMODULATE',[status(thm)],[271,438,theory(equality)]) ).

cnf(498,plain,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c9,sk_c8) = sk_c9 ),
    inference('PARAMODULATE',[status(thm)],[207,prove_this_42,theory(equality)]) ).

cnf(548,plain,
    ( inverse(sk_c2) = sk_c7
    | sk_c7 = multiply(sk_c3,sk_c8) ),
    inference('PARAMODULATE',[status(thm)],[216,278,theory(equality)]) ).

cnf(594,plain,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c9,sk_c9) = sk_c8 ),
    inference('PARAMODULATE',[status(thm)],[225,prove_this_44,theory(equality)]) ).

cnf(609,plain,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c9,sk_c9) = sk_c8 ),
    inference('PARAMODULATE',[status(thm)],[227,prove_this_20,theory(equality)]) ).

cnf(623,plain,
    multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[203,294,theory(equality)]) ).

cnf(625,plain,
    ( inverse(sk_c9) = sk_c7
    | sk_c7 = inverse(multiply(inverse(sk_c8),sk_c9)) ),
    inference('REWRITE',[status(thm)],[217,623,theory(equality)]) ).

cnf(632,plain,
    inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
    inference('PARAMODULATE',[status(thm)],[273,295,theory(equality)]) ).

cnf(658,plain,
    ( multiply(sk_c8,sk_c7) = sk_c9
    | inverse(multiply(sk_c9,inverse(sk_c8))) = sk_c3 ),
    inference('REWRITE',[status(thm)],[323,632,theory(equality)]) ).

cnf(871,plain,
    ( inverse(sk_c2) = sk_c7
    | X = multiply(X,sk_c8) ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[228,498,theory(equality)]),203,theory(equality)]) ).

cnf(997,plain,
    ( inverse(sk_c2) = sk_c7
    | sk_c3 = sk_c7 ),
    inference('PARAMODULATE',[status(thm)],[548,871,theory(equality)]) ).

cnf(1043,plain,
    ( sk_c3 = sk_c7
    | sk_c2 = inverse(sk_c7) ),
    inference('PARAMODULATE',[status(thm)],[257,997,theory(equality)]) ).

cnf(1235,plain,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c8,sk_c4) = sk_c3 ),
    inference('PARAMODULATE',[status(thm)],[262,prove_this_41,theory(equality)]) ).

cnf(1236,plain,
    ( inverse(sk_c2) = sk_c7
    | multiply(sk_c8,sk_c4) = sk_c9 ),
    inference('PARAMODULATE',[status(thm)],[262,594,theory(equality)]) ).

cnf(1244,plain,
    ( inverse(sk_c2) = sk_c7
    | sk_c3 = sk_c9 ),
    inference('PARAMODULATE',[status(thm)],[1235,1236,theory(equality)]) ).

cnf(1250,plain,
    ( sk_c3 = sk_c9
    | sk_c2 = inverse(sk_c7) ),
    inference('PARAMODULATE',[status(thm)],[257,1244,theory(equality)]) ).

cnf(1289,plain,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c8,sk_c4) = sk_c3 ),
    inference('PARAMODULATE',[status(thm)],[263,prove_this_17,theory(equality)]) ).

cnf(1290,plain,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c8,sk_c4) = sk_c9 ),
    inference('PARAMODULATE',[status(thm)],[263,609,theory(equality)]) ).

cnf(1298,plain,
    ( inverse(sk_c1) = sk_c9
    | sk_c3 = sk_c9 ),
    inference('PARAMODULATE',[status(thm)],[1289,1290,theory(equality)]) ).

cnf(1304,plain,
    ( sk_c3 = sk_c9
    | sk_c1 = inverse(sk_c9) ),
    inference('PARAMODULATE',[status(thm)],[257,1298,theory(equality)]) ).

cnf(1447,plain,
    identity = sk_c8,
    inference('PARAMODULATE',[status(thm)],[441,443,theory(equality)]) ).

cnf(1449,plain,
    ( sk_c7 = sk_c9
    | inverse(sk_c3) = sk_c9 ),
    inference('REWRITE',[status(thm)],[prove_this_2,left_identity,1447,theory(equality)]) ).

cnf(1451,plain,
    ( sk_c7 = sk_c9
    | inverse(sk_c4) = sk_c9 ),
    inference('REWRITE',[status(thm)],[prove_this_4,left_identity,1447,theory(equality)]) ).

cnf(1452,plain,
    ( sk_c7 = sk_c9
    | sk_c4 = sk_c9 ),
    inference('REWRITE',[status(thm)],[prove_this_5,202,left_identity,1447,theory(equality)]) ).

cnf(1514,plain,
    ( sk_c7 = sk_c9
    | X = multiply(sk_c3,multiply(sk_c9,X)) ),
    inference('REWRITE',[status(thm)],[119,left_identity,1447,theory(equality)]) ).

cnf(1592,plain,
    ( sk_c7 != sk_c9
    | inverse(sk_c9) != sk_c7
    | multiply(sk_c9,sk_c7) != identity
    | inverse(X) != sk_c9
    | X != sk_c9 ),
    inference('REWRITE',[status(thm)],[258,202,left_identity,1447,theory(equality)]) ).

cnf(1678,plain,
    inverse(sk_c9) = sk_c7,
    inference('REWRITE',[status(thm)],[625,left_identity,254,1447,theory(equality)]) ).

cnf(1702,plain,
    ( sk_c3 = sk_c9
    | sk_c1 = sk_c7 ),
    inference('REWRITE',[status(thm)],[1304,1678,theory(equality)]) ).

cnf(1716,plain,
    ( sk_c7 != sk_c9
    | multiply(sk_c9,sk_c7) != identity
    | inverse(X) != sk_c9
    | X != sk_c9 ),
    inference('REWRITE',[status(thm)],[1592,1678,theory(equality)]) ).

cnf(1730,plain,
    ( sk_c7 = sk_c9
    | sk_c3 = sk_c7 ),
    inference('REWRITE',[status(thm)],[658,1678,202,254,left_identity,1447,theory(equality)]) ).

cnf(1874,plain,
    ( sk_c7 = sk_c9
    | multiply(sk_c9,sk_c4) = identity ),
    inference('PARAMODULATE',[status(thm)],[left_inverse,1451,theory(equality)]) ).

cnf(1903,plain,
    sk_c9 = inverse(sk_c7),
    inference('PARAMODULATE',[status(thm)],[257,1678,theory(equality)]) ).

cnf(1911,plain,
    ( sk_c3 = sk_c7
    | sk_c9 = sk_c2 ),
    inference('REWRITE',[status(thm)],[1043,1903,theory(equality)]) ).

cnf(1918,plain,
    ( sk_c3 = sk_c9
    | sk_c9 = sk_c2 ),
    inference('REWRITE',[status(thm)],[1250,1903,theory(equality)]) ).

cnf(1933,plain,
    multiply(sk_c9,sk_c7) = identity,
    inference('PARAMODULATE',[status(thm)],[271,1678,theory(equality)]) ).

cnf(1945,plain,
    ( sk_c7 != sk_c9
    | inverse(X) != sk_c9
    | X != sk_c9 ),
    inference('REWRITE',[status(thm)],[1716,1933,theory(equality)]) ).

cnf(2166,plain,
    ( sk_c1 = sk_c7
    | inverse(sk_c3) = sk_c7 ),
    inference('PARAMODULATE',[status(thm)],[1678,1702,theory(equality)]) ).

cnf(2268,plain,
    ( sk_c3 = sk_c7
    | sk_c7 = sk_c2 ),
    inference('PARAMODULATE',[status(thm)],[1730,1911,theory(equality)]) ).

cnf(2281,plain,
    ( sk_c9 = sk_c2
    | inverse(sk_c3) = sk_c7 ),
    inference('PARAMODULATE',[status(thm)],[1678,1918,theory(equality)]) ).

cnf(2314,plain,
    ( sk_c7 = sk_c9
    | sk_c4 = sk_c3 ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1514,1874,theory(equality)]),202,theory(equality)]) ).

cnf(2462,plain,
    sk_c4 = sk_c3,
    inference('HYPERRESOLVE',[status(thm)],[1945,2314,1903,2314]) ).

cnf(2473,plain,
    ( sk_c7 = sk_c9
    | sk_c3 = sk_c9 ),
    inference('REWRITE',[status(thm)],[1452,2462,theory(equality)]) ).

cnf(2530,plain,
    sk_c7 != sk_c9,
    inference('UR-RESOLVE',[status(thm)],[1945,1903]) ).

cnf(2566,plain,
    inverse(sk_c3) = sk_c9,
    inference('REWRITE',[status(thm)],[1449,2530]) ).

cnf(2568,plain,
    sk_c1 = sk_c7,
    inference('REWRITE',[status(thm)],[2166,2530,2566,theory(equality)]) ).

cnf(2598,plain,
    ( sk_c1 = sk_c3
    | sk_c1 = sk_c2 ),
    inference('REWRITE',[status(thm)],[2268,2568,theory(equality)]) ).

cnf(2641,plain,
    sk_c1 != sk_c9,
    inference('REWRITE',[status(thm)],[2530,2568,theory(equality)]) ).

cnf(2667,plain,
    sk_c9 = sk_c2,
    inference('REWRITE',[status(thm)],[2281,2641,2568,2566,theory(equality)]) ).

cnf(2708,plain,
    sk_c1 != sk_c2,
    inference('REWRITE',[status(thm)],[2641,2667,theory(equality)]) ).

cnf(2722,plain,
    sk_c1 = sk_c3,
    inference('REWRITE',[status(thm)],[2598,2708]) ).

cnf(2737,plain,
    $false,
    inference('REWRITE',[status(thm)],[2473,2708,2667,2722,2530,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP354-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 14 07:58:58 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.46  /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.47  * 
% 0.20/0.47  * 
% 0.20/0.48  #<PACKAGE "SNARK-USER">
% 0.20/0.48  * 
% 0.20/0.48  SNARK-TPTP-OPTIONS
% 0.20/0.48  * 
% 0.20/0.48  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.48   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.48   (USE-FACTORING :POS)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.48   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.48   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.48   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.48   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.48   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.48   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.48   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.48   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.48   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.48  * 
% 0.20/0.48  "."
% 0.20/0.48  * 
% 0.20/0.48  ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T07:58:58
% 0.20/0.48  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n018.cluster.edu at 2022-06-14T07:58:58
% 0.20/0.50  
% 0.20/0.50  ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.20/0.50  ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 55.58/55.82  ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 55.58/55.82  
% 55.58/55.82  #||
% 55.58/55.82  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 55.58/55.82  % SZS output start Refutation
% See solution above
% 55.65/55.83  ||#
% 55.65/55.83  
% 55.65/55.83  ; Summary of computation:
% 55.65/55.83  ;    180537 formulas have been input or derived (from 349 formulas).
% 55.65/55.83  ;      2737 ( 2%) were retained.  Of these,
% 55.65/55.83  ;         2691 (98%) were simplified or subsumed later,
% 55.65/55.83  ;           46 ( 2%) are still being kept.
% 55.65/55.83  ; 
% 55.65/55.83  ; Run time in seconds excluding printing time:
% 55.65/55.83  ;     0.009   0%   Read assertion file          (1 call)
% 55.65/55.83  ;     0.003   0%   Assert                       (52 calls)
% 55.65/55.83  ;     0.772   1%   Process new row              (123,393 calls)
% 55.65/55.83  ;    11.976  22%   Resolution                   (696 calls)
% 55.65/55.83  ;     0.110   0%   Paramodulation               (348 calls)
% 55.65/55.83  ;     0.000   0%   Factoring                    (322 calls)
% 55.65/55.83  ;     0.237   0%   Condensing                   (120,326 calls)
% 55.65/55.83  ;    35.018  63%   Forward subsumption          (120,326 calls)
% 55.65/55.83  ;     0.084   0%   Backward subsumption         (2,629 calls)
% 55.65/55.83  ;     1.987   4%   Clause clause subsumption    (389,571 calls)
% 55.65/55.83  ;     4.522   8%   Forward simplification       (122,858 calls)
% 55.65/55.83  ;     0.083   0%   Backward simplification      (2,736 calls)
% 55.65/55.83  ;     0.075   0%   Ordering                     (36,305 calls)
% 55.65/55.83  ;     0.000   0%   Sortal reasoning             (32 calls)
% 55.65/55.83  ;     0.000   0%   Purity testing               (1 call)
% 55.65/55.83  ;     0.459   1%   Other
% 55.65/55.83  ;    55.335        Total
% 55.65/55.83  ;    55.352        Real time
% 55.65/55.83  ; 
% 55.65/55.83  ; Term-hash-array has 1,041 terms in all.
% 55.65/55.83  ; Feature-vector-row-index has 1 entry (1,304 at peak, 2,629 added, 2,628 deleted).
% 55.65/55.83  ; Feature-vector-row-index has 10 nodes (8,097 at peak, 15,219 added, 15,209 deleted).
% 55.65/55.83  ;  Retrieved 2,916,714 possibly forward subsuming rows in 120,326 calls.
% 55.65/55.83  ;  Retrieved 1,761 possibly backward subsumed rows in 2,629 calls.
% 55.65/55.83  ; Path-index has 129 entries (640 at peak, 1,227 added, 1,098 deleted).
% 55.65/55.83  ; Path-index has 203 nodes (381 at peak, 498 added, 295 deleted).
% 55.65/55.83  ; Trie-index has 129 entries (640 at peak, 1,227 added, 1,098 deleted).
% 55.65/55.83  ; Trie-index has 366 nodes (1,514 at peak, 2,698 added, 2,332 deleted).
% 55.65/55.83  ; Retrieved 7,969 generalization terms in 1,228,274 calls.
% 55.65/55.83  ; Retrieved 198 instance terms in 125 calls.
% 55.65/55.83  ; Retrieved 10,400,361 unifiable terms in 282,772 calls.
% 55.65/55.83  ; 
% 55.65/55.83  ; The agenda of rows to process has 258 entries:
% 55.65/55.83  ;     3 with value 9               2 with value 16              62 with value 21
% 55.65/55.83  ;     2 with value 11             11 with value 17               8 with value 22
% 55.65/55.83  ;     6 with value 12              7 with value 18               5 with value 23
% 55.65/55.83  ;    24 with value 13             38 with value 19               5 with value 24
% 55.65/55.83  ;    59 with value 15             12 with value 20              14 with value 25
% 55.65/55.83  ; The agenda of input rows to give has 1 entry:
% 55.65/55.83  ;     1 with value 4
% 55.65/55.83  ; The agenda of rows to give has 31 entries:
% 55.65/55.83  ;     2 with value (4 8)           1 with value (4 18)           1 with value (4 22)
% 55.65/55.83  ;     2 with value (4 10)          2 with value (4 19)           1 with value (4 23)
% 55.65/55.83  ;     6 with value (4 11)          7 with value (4 20)           3 with value (4 24)
% 55.65/55.83  ;     1 with value (4 13)          2 with value (4 21)           1 with value (4 26)
% 55.65/55.83  ;     2 with value (4 16)
% 55.65/55.83  Evaluation took:
% 55.65/55.83    55.352 seconds of real time
% 55.65/55.83    53.827744 seconds of user run time
% 55.65/55.83    1.521948 seconds of system run time
% 55.65/55.83    [Run times include 2.366 seconds GC run time.]
% 55.65/55.83    0 calls to %EVAL
% 55.65/55.83    0 page faults and
% 55.65/55.83    6,147,068,600 bytes consed.
% 55.65/55.83  :PROOF-FOUND
% 55.65/55.83  ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T07:59:54
% 55.65/55.83  :PROOF-FOUND
% 55.65/55.83  * 
%------------------------------------------------------------------------------