TSTP Solution File: GRP344-1 by SNARK---20120808r022

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SNARK---20120808r022
% Problem  : GRP344-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run-snark %s %d

% Computer : n017.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 11:37:56 EDT 2022

% Result   : Unsatisfiable 238.64s 238.82s
% Output   : Refutation 238.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :   17
% Syntax   : Number of clauses     :  132 (  50 unt;  76 nHn;  84 RR)
%            Number of literals    :  243 ( 242 equ;  41 neg)
%            Maximal clause size   :    9 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   85 (   0 sgn)

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

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

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

cnf(prove_this_1,negated_conjecture,
    multiply(sk_c6,sk_c7) = sk_c5,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).

cnf(prove_this_2,negated_conjecture,
    ( inverse(sk_c1) = sk_c7
    | multiply(sk_c3,sk_c6) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_2) ).

cnf(prove_this_3,negated_conjecture,
    ( inverse(sk_c1) = sk_c7
    | inverse(sk_c3) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).

cnf(prove_this_6,negated_conjecture,
    ( multiply(sk_c1,sk_c6) = sk_c7
    | multiply(sk_c3,sk_c6) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).

cnf(prove_this_7,negated_conjecture,
    ( multiply(sk_c1,sk_c6) = sk_c7
    | inverse(sk_c3) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_7) ).

cnf(prove_this_10,negated_conjecture,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c3,sk_c6) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).

cnf(prove_this_11,negated_conjecture,
    ( inverse(sk_c2) = sk_c6
    | inverse(sk_c3) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).

cnf(prove_this_12,negated_conjecture,
    ( inverse(sk_c2) = sk_c6
    | inverse(sk_c4) = sk_c5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).

cnf(prove_this_13,negated_conjecture,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c4,sk_c6) = sk_c5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).

cnf(prove_this_14,negated_conjecture,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | multiply(sk_c3,sk_c6) = sk_c7 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).

cnf(prove_this_15,negated_conjecture,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | inverse(sk_c3) = sk_c6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).

cnf(prove_this_16,negated_conjecture,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | inverse(sk_c4) = sk_c5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).

cnf(prove_this_17,negated_conjecture,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | multiply(sk_c4,sk_c6) = sk_c5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).

cnf(prove_this_18,negated_conjecture,
    ( multiply(sk_c6,sk_c7) != sk_c5
    | inverse(X) != sk_c7
    | multiply(X,sk_c6) != sk_c7
    | inverse(Y) != sk_c6
    | multiply(Y,sk_c5) != sk_c6
    | multiply(Z,sk_c6) != sk_c7
    | inverse(Z) != sk_c6
    | inverse(U) != sk_c5
    | multiply(U,sk_c6) != sk_c5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).

cnf(22,plain,
    ( inverse(X) != sk_c7
    | multiply(X,sk_c6) != sk_c7
    | inverse(Y) != sk_c6
    | multiply(Y,sk_c5) != sk_c6
    | multiply(Z,sk_c6) != sk_c7
    | inverse(Z) != sk_c6
    | inverse(U) != sk_c5
    | multiply(U,sk_c6) != sk_c5 ),
    inference('REWRITE',[status(thm)],[prove_this_18,prove_this_1,theory(equality)]) ).

cnf(25,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c6,sk_c3) = identity ),
    inference('PARAMODULATE',[status(thm)],[left_inverse,prove_this_11,theory(equality)]) ).

cnf(27,plain,
    multiply(sk_c5,X) = multiply(sk_c6,multiply(sk_c7,X)),
    inference('PARAMODULATE',[status(thm)],[associativity,prove_this_1,theory(equality)]) ).

cnf(28,plain,
    multiply(multiply(X,sk_c6),sk_c7) = multiply(X,sk_c5),
    inference('PARAMODULATE',[status(thm)],[associativity,prove_this_1,theory(equality)]) ).

cnf(30,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(31,plain,
    multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
    inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).

cnf(34,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c7,X) = multiply(sk_c3,multiply(sk_c6,X)) ),
    inference('PARAMODULATE',[status(thm)],[associativity,prove_this_10,theory(equality)]) ).

cnf(41,plain,
    ( inverse(sk_c3) = sk_c6
    | multiply(multiply(X,sk_c2),sk_c5) = multiply(X,sk_c6) ),
    inference('PARAMODULATE',[status(thm)],[associativity,prove_this_15,theory(equality)]) ).

cnf(52,plain,
    multiply(multiply(X,Y),multiply(Z,U)) = multiply(X,multiply(multiply(Y,Z),U)),
    inference('PARAMODULATE',[status(thm)],[associativity,associativity,theory(equality)]) ).

cnf(57,plain,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | multiply(sk_c7,X) = multiply(sk_c3,multiply(sk_c6,X)) ),
    inference('PARAMODULATE',[status(thm)],[associativity,prove_this_14,theory(equality)]) ).

cnf(58,plain,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | multiply(multiply(X,sk_c3),sk_c6) = multiply(X,sk_c7) ),
    inference('PARAMODULATE',[status(thm)],[associativity,prove_this_14,theory(equality)]) ).

cnf(64,plain,
    ( inverse(X) != sk_c7
    | multiply(X,sk_c6) != sk_c7
    | inverse(Y) != sk_c6
    | multiply(Y,sk_c5) != sk_c6
    | multiply(Z,sk_c6) != sk_c7
    | inverse(Z) != sk_c6
    | inverse(identity) != sk_c5
    | sk_c5 != sk_c6 ),
    inference('PARAMODULATE',[status(thm)],[22,left_identity,theory(equality)]) ).

cnf(121,plain,
    sk_c7 = multiply(inverse(sk_c6),sk_c5),
    inference('PARAMODULATE',[status(thm)],[30,prove_this_1,theory(equality)]) ).

cnf(123,plain,
    X = multiply(inverse(inverse(X)),identity),
    inference('PARAMODULATE',[status(thm)],[30,left_inverse,theory(equality)]) ).

cnf(124,plain,
    multiply(X,Y) = multiply(inverse(inverse(X)),Y),
    inference('PARAMODULATE',[status(thm)],[30,30,theory(equality)]) ).

cnf(125,plain,
    X = multiply(X,identity),
    inference('REWRITE',[status(thm)],[123,124,theory(equality)]) ).

cnf(126,plain,
    multiply(multiply(X,inverse(Y)),Y) = X,
    inference('REWRITE',[status(thm)],[31,125,theory(equality)]) ).

cnf(129,plain,
    ( inverse(sk_c2) = sk_c6
    | sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
    inference('PARAMODULATE',[status(thm)],[30,prove_this_10,theory(equality)]) ).

cnf(130,plain,
    ( inverse(sk_c1) = sk_c7
    | sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
    inference('PARAMODULATE',[status(thm)],[30,prove_this_2,theory(equality)]) ).

cnf(131,plain,
    ( inverse(sk_c2) = sk_c6
    | sk_c6 = multiply(inverse(sk_c4),sk_c5) ),
    inference('PARAMODULATE',[status(thm)],[30,prove_this_13,theory(equality)]) ).

cnf(134,plain,
    ( inverse(sk_c3) = sk_c6
    | sk_c6 = multiply(inverse(sk_c1),sk_c7) ),
    inference('PARAMODULATE',[status(thm)],[30,prove_this_7,theory(equality)]) ).

cnf(135,plain,
    multiply(multiply(X,inverse(Y)),multiply(Y,Z)) = multiply(X,Z),
    inference('PARAMODULATE',[status(thm)],[associativity,30,theory(equality)]) ).

cnf(138,plain,
    ( inverse(sk_c2) = sk_c6
    | X = multiply(sk_c6,multiply(sk_c3,X)) ),
    inference('PARAMODULATE',[status(thm)],[30,prove_this_11,theory(equality)]) ).

cnf(141,plain,
    ( multiply(sk_c1,sk_c6) = sk_c7
    | sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
    inference('PARAMODULATE',[status(thm)],[30,prove_this_6,theory(equality)]) ).

cnf(142,plain,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | sk_c6 = multiply(inverse(sk_c4),sk_c5) ),
    inference('PARAMODULATE',[status(thm)],[30,prove_this_17,theory(equality)]) ).

cnf(145,plain,
    inverse(identity) = identity,
    inference('PARAMODULATE',[status(thm)],[left_inverse,125,theory(equality)]) ).

cnf(149,plain,
    ( inverse(X) != sk_c7
    | multiply(X,sk_c6) != sk_c7
    | inverse(Y) != sk_c6
    | multiply(Y,sk_c5) != sk_c6
    | multiply(Z,sk_c6) != sk_c7
    | inverse(Z) != sk_c6
    | identity != sk_c5
    | sk_c5 != sk_c6 ),
    inference('REWRITE',[status(thm)],[64,145,theory(equality)]) ).

cnf(150,plain,
    multiply(sk_c7,X) = multiply(inverse(sk_c6),multiply(sk_c5,X)),
    inference('PARAMODULATE',[status(thm)],[associativity,121,theory(equality)]) ).

cnf(154,plain,
    sk_c7 = multiply(inverse(multiply(X,sk_c6)),multiply(X,sk_c5)),
    inference('PARAMODULATE',[status(thm)],[30,28,theory(equality)]) ).

cnf(157,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c5,sk_c7) = multiply(sk_c4,sk_c5) ),
    inference('PARAMODULATE',[status(thm)],[28,prove_this_13,theory(equality)]) ).

cnf(165,plain,
    X = inverse(inverse(X)),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[126,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).

cnf(169,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(multiply(X,sk_c5),sk_c4) = X ),
    inference('PARAMODULATE',[status(thm)],[126,prove_this_12,theory(equality)]) ).

cnf(177,plain,
    multiply(X,inverse(X)) = identity,
    inference('PARAMODULATE',[status(thm)],[left_inverse,165,theory(equality)]) ).

cnf(178,plain,
    multiply(multiply(X,Y),inverse(Y)) = X,
    inference('PARAMODULATE',[status(thm)],[126,165,theory(equality)]) ).

cnf(179,plain,
    X = multiply(Y,multiply(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[30,165,theory(equality)]) ).

cnf(180,plain,
    ( inverse(sk_c2) = sk_c6
    | sk_c4 = inverse(sk_c5) ),
    inference('PARAMODULATE',[status(thm)],[165,prove_this_12,theory(equality)]) ).

cnf(188,plain,
    multiply(sk_c5,inverse(sk_c7)) = sk_c6,
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[27,177,theory(equality)]),125,theory(equality)]) ).

cnf(194,plain,
    multiply(multiply(X,sk_c5),inverse(sk_c7)) = multiply(X,sk_c6),
    inference('PARAMODULATE',[status(thm)],[associativity,188,theory(equality)]) ).

cnf(196,plain,
    multiply(sk_c7,inverse(sk_c5)) = inverse(sk_c6),
    inference('PARAMODULATE',[status(thm)],[178,121,theory(equality)]) ).

cnf(197,plain,
    inverse(X) = multiply(inverse(multiply(Y,X)),Y),
    inference('PARAMODULATE',[status(thm)],[30,178,theory(equality)]) ).

cnf(208,plain,
    multiply(X,Y) = multiply(multiply(X,Z),multiply(inverse(Z),Y)),
    inference('PARAMODULATE',[status(thm)],[associativity,178,theory(equality)]) ).

cnf(221,plain,
    ( inverse(sk_c2) = sk_c6
    | X = multiply(sk_c4,multiply(sk_c5,X)) ),
    inference('PARAMODULATE',[status(thm)],[179,prove_this_12,theory(equality)]) ).

cnf(225,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c7,sk_c4) = inverse(sk_c6) ),
    inference('PARAMODULATE',[status(thm)],[196,180,theory(equality)]) ).

cnf(268,plain,
    ( inverse(sk_c4) = sk_c5
    | sk_c7 = multiply(inverse(multiply(sk_c2,sk_c6)),sk_c6) ),
    inference('PARAMODULATE',[status(thm)],[154,prove_this_16,theory(equality)]) ).

cnf(269,plain,
    ( inverse(sk_c3) = sk_c6
    | sk_c7 = multiply(inverse(multiply(sk_c2,sk_c6)),sk_c6) ),
    inference('PARAMODULATE',[status(thm)],[154,prove_this_15,theory(equality)]) ).

cnf(324,plain,
    ( inverse(sk_c1) = sk_c7
    | sk_c5 = sk_c6 ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[130,prove_this_3,theory(equality)]),prove_this_1,theory(equality)]) ).

cnf(328,plain,
    ( sk_c5 = sk_c6
    | sk_c1 = inverse(sk_c7) ),
    inference('PARAMODULATE',[status(thm)],[165,324,theory(equality)]) ).

cnf(334,plain,
    ( sk_c5 = sk_c6
    | X = multiply(sk_c7,multiply(sk_c1,X)) ),
    inference('PARAMODULATE',[status(thm)],[30,324,theory(equality)]) ).

cnf(338,plain,
    ( sk_c5 = sk_c6
    | multiply(sk_c5,sk_c1) = sk_c6 ),
    inference('PARAMODULATE',[status(thm)],[188,328,theory(equality)]) ).

cnf(474,plain,
    multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
    inference('PARAMODULATE',[status(thm)],[178,197,theory(equality)]) ).

cnf(475,plain,
    multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
    inference('PARAMODULATE',[status(thm)],[126,197,theory(equality)]) ).

cnf(482,plain,
    ( inverse(sk_c4) = sk_c5
    | sk_c7 = inverse(multiply(inverse(sk_c6),multiply(sk_c2,sk_c6))) ),
    inference('REWRITE',[status(thm)],[268,475,theory(equality)]) ).

cnf(483,plain,
    ( inverse(sk_c3) = sk_c6
    | sk_c7 = inverse(multiply(inverse(sk_c6),multiply(sk_c2,sk_c6))) ),
    inference('REWRITE',[status(thm)],[269,475,theory(equality)]) ).

cnf(697,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c6,sk_c4) = inverse(sk_c4) ),
    inference('PARAMODULATE',[status(thm)],[169,131,theory(equality)]) ).

cnf(915,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c6,X) = multiply(sk_c5,X) ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[138,34,theory(equality)]),27,theory(equality)]) ).

cnf(922,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c5,sk_c3) = identity ),
    inference('PARAMODULATE',[status(thm)],[25,915,theory(equality)]) ).

cnf(924,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c5,sk_c4) = inverse(sk_c4) ),
    inference('PARAMODULATE',[status(thm)],[697,915,theory(equality)]) ).

cnf(929,plain,
    ( inverse(sk_c2) = sk_c6
    | X = multiply(sk_c7,X) ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[30,915,theory(equality)]),150,theory(equality)]) ).

cnf(960,plain,
    ( inverse(sk_c2) = sk_c6
    | inverse(sk_c3) = sk_c5 ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[178,922,theory(equality)]),left_identity,theory(equality)]) ).

cnf(995,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c5,sk_c4) = sk_c7 ),
    inference('PARAMODULATE',[status(thm)],[169,929,theory(equality)]) ).

cnf(1028,plain,
    ( inverse(sk_c2) = sk_c6
    | sk_c6 = multiply(sk_c5,sk_c7) ),
    inference('PARAMODULATE',[status(thm)],[129,960,theory(equality)]) ).

cnf(1135,plain,
    ( inverse(sk_c2) = sk_c6
    | inverse(sk_c4) = sk_c7 ),
    inference('PARAMODULATE',[status(thm)],[924,995,theory(equality)]) ).

cnf(1520,plain,
    ( inverse(sk_c3) = sk_c6
    | multiply(X,sk_c6) = multiply(X,multiply(sk_c2,sk_c5)) ),
    inference('PARAMODULATE',[status(thm)],[associativity,41,theory(equality)]) ).

cnf(1672,plain,
    ( inverse(sk_c2) = sk_c6
    | sk_c4 = inverse(sk_c6) ),
    inference('PARAMODULATE',[status(thm)],[929,225,theory(equality)]) ).

cnf(1673,plain,
    ( inverse(sk_c2) = sk_c6
    | inverse(sk_c4) = sk_c6 ),
    inference('PARAMODULATE',[status(thm)],[165,1672,theory(equality)]) ).

cnf(2295,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c4,sk_c5) = sk_c6 ),
    inference('PARAMODULATE',[status(thm)],[157,1028,theory(equality)]) ).

cnf(6058,plain,
    ( inverse(sk_c2) = sk_c6
    | multiply(sk_c4,sk_c6) = sk_c7 ),
    inference('PARAMODULATE',[status(thm)],[221,1028,theory(equality)]) ).

cnf(9579,plain,
    inverse(sk_c2) = sk_c6,
    inference('HYPERRESOLVE',[status(thm)],[22,6058,1135,1673,2295,prove_this_10,prove_this_11,prove_this_12,prove_this_13]) ).

cnf(9665,plain,
    sk_c2 = inverse(sk_c6),
    inference('PARAMODULATE',[status(thm)],[165,9579,theory(equality)]) ).

cnf(9666,plain,
    multiply(sk_c7,X) = multiply(sk_c2,multiply(sk_c5,X)),
    inference('REWRITE',[status(thm)],[150,9665,theory(equality)]) ).

cnf(9681,plain,
    multiply(sk_c7,inverse(sk_c5)) = sk_c2,
    inference('REWRITE',[status(thm)],[196,9665,theory(equality)]) ).

cnf(9797,plain,
    ( inverse(sk_c4) = sk_c5
    | sk_c7 = inverse(multiply(multiply(sk_c2,sk_c2),sk_c6)) ),
    inference('REWRITE',[status(thm)],[482,associativity,9665,theory(equality)]) ).

cnf(9798,plain,
    ( inverse(sk_c3) = sk_c6
    | sk_c7 = inverse(multiply(multiply(sk_c2,sk_c2),sk_c6)) ),
    inference('REWRITE',[status(thm)],[483,associativity,9665,theory(equality)]) ).

cnf(10170,plain,
    multiply(sk_c2,sk_c6) = identity,
    inference('PARAMODULATE',[status(thm)],[177,9579,theory(equality)]) ).

cnf(10196,plain,
    multiply(sk_c6,sk_c2) = identity,
    inference('PARAMODULATE',[status(thm)],[left_inverse,9579,theory(equality)]) ).

cnf(10198,plain,
    multiply(multiply(X,sk_c2),sk_c6) = X,
    inference('PARAMODULATE',[status(thm)],[178,9579,theory(equality)]) ).

cnf(10199,plain,
    ( inverse(sk_c4) = sk_c5
    | sk_c6 = sk_c7 ),
    inference('REWRITE',[status(thm)],[9797,9579,10198,theory(equality)]) ).

cnf(10200,plain,
    ( inverse(sk_c3) = sk_c6
    | sk_c6 = sk_c7 ),
    inference('REWRITE',[status(thm)],[9798,9579,10198,theory(equality)]) ).

cnf(10207,plain,
    multiply(sk_c6,inverse(X)) = inverse(multiply(X,sk_c2)),
    inference('PARAMODULATE',[status(thm)],[474,9579,theory(equality)]) ).

cnf(10347,plain,
    multiply(inverse(X),sk_c6) = inverse(multiply(sk_c2,X)),
    inference('PARAMODULATE',[status(thm)],[474,9579,theory(equality)]) ).

cnf(10391,plain,
    multiply(multiply(X,sk_c6),multiply(sk_c2,Y)) = multiply(X,Y),
    inference('PARAMODULATE',[status(thm)],[135,9579,theory(equality)]) ).

cnf(10414,plain,
    sk_c7 = multiply(sk_c2,sk_c5),
    inference('PARAMODULATE',[status(thm)],[126,9681,theory(equality)]) ).

cnf(10417,plain,
    ( sk_c6 = sk_c7
    | multiply(sk_c7,X) = multiply(sk_c3,multiply(sk_c6,X)) ),
    inference('REWRITE',[status(thm)],[57,10414,theory(equality)]) ).

cnf(10418,plain,
    ( sk_c6 = sk_c7
    | multiply(multiply(X,sk_c3),sk_c6) = multiply(X,sk_c7) ),
    inference('REWRITE',[status(thm)],[58,10414,theory(equality)]) ).

cnf(10428,plain,
    ( sk_c6 = sk_c7
    | sk_c6 = multiply(inverse(sk_c4),sk_c5) ),
    inference('REWRITE',[status(thm)],[142,10414,theory(equality)]) ).

cnf(10458,plain,
    ( inverse(sk_c3) = sk_c6
    | multiply(X,sk_c6) = multiply(X,sk_c7) ),
    inference('REWRITE',[status(thm)],[1520,10414,theory(equality)]) ).

cnf(10763,plain,
    multiply(X,multiply(sk_c7,Y)) = multiply(multiply(X,sk_c2),multiply(sk_c5,Y)),
    inference('PARAMODULATE',[status(thm)],[52,10414,theory(equality)]) ).

cnf(10849,plain,
    ( sk_c6 = sk_c7
    | multiply(sk_c6,sk_c3) = identity ),
    inference('PARAMODULATE',[status(thm)],[left_inverse,10200,theory(equality)]) ).

cnf(10853,plain,
    ( sk_c6 = sk_c7
    | X = multiply(sk_c6,multiply(sk_c3,X)) ),
    inference('PARAMODULATE',[status(thm)],[30,10200,theory(equality)]) ).

cnf(11028,plain,
    ( sk_c6 = sk_c7
    | multiply(sk_c5,sk_c5) = sk_c6 ),
    inference('PARAMODULATE',[status(thm)],[10428,10199,theory(equality)]) ).

cnf(11212,plain,
    ( sk_c6 = sk_c7
    | multiply(sk_c7,sk_c5) = identity ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[9666,11028,theory(equality)]),10170,theory(equality)]) ).

cnf(11499,plain,
    ( sk_c6 = sk_c7
    | inverse(sk_c7) = multiply(sk_c7,sk_c6) ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[194,11212,theory(equality)]),left_identity,theory(equality)]) ).

cnf(11677,plain,
    ( sk_c6 = sk_c7
    | multiply(sk_c7,sk_c3) = sk_c3 ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10417,10849,theory(equality)]),125,theory(equality)]) ).

cnf(11686,plain,
    ( sk_c6 = sk_c7
    | X = multiply(sk_c7,X) ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[208,11677,theory(equality)]),179,theory(equality)]) ).

cnf(11727,plain,
    ( inverse(sk_c3) = sk_c6
    | sk_c6 = inverse(multiply(sk_c2,sk_c1)) ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[134,10458,theory(equality)]),10347,theory(equality)]) ).

cnf(12975,plain,
    ( sk_c6 = sk_c7
    | multiply(sk_c6,X) = multiply(sk_c5,X) ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10853,10417,theory(equality)]),left_identity,10196,10763,theory(equality)]) ).

cnf(13332,plain,
    ( sk_c6 = sk_c7
    | inverse(sk_c7) = sk_c6 ),
    inference('PARAMODULATE',[status(thm)],[11686,11499,theory(equality)]) ).

cnf(13554,plain,
    ( inverse(sk_c3) = sk_c6
    | multiply(X,sk_c1) = X ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[126,11727,theory(equality)]),10391,theory(equality)]) ).

cnf(13567,plain,
    ( inverse(sk_c3) = sk_c6
    | sk_c5 = sk_c6 ),
    inference('PARAMODULATE',[status(thm)],[338,13554,theory(equality)]) ).

cnf(13606,plain,
    ( sk_c5 = sk_c6
    | multiply(sk_c1,sk_c6) = sk_c7 ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[141,13567,theory(equality)]),prove_this_1,theory(equality)]) ).

cnf(14114,plain,
    ( sk_c6 = sk_c7
    | multiply(sk_c5,sk_c3) = identity ),
    inference('PARAMODULATE',[status(thm)],[10849,12975,theory(equality)]) ).

cnf(14145,plain,
    ( sk_c6 = sk_c7
    | sk_c6 = multiply(sk_c5,sk_c7) ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[10418,14114,theory(equality)]),left_identity,theory(equality)]) ).

cnf(14545,plain,
    ( sk_c5 = sk_c6
    | sk_c6 = multiply(sk_c7,sk_c7) ),
    inference('PARAMODULATE',[status(thm)],[334,13606,theory(equality)]) ).

cnf(14730,plain,
    ( sk_c6 = sk_c7
    | inverse(sk_c7) = sk_c7 ),
    inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[30,14145,theory(equality)]),10414,10347,theory(equality)]) ).

cnf(14841,plain,
    sk_c6 = sk_c7,
    inference('PARAMODULATE',[status(thm)],[13332,14730,theory(equality)]) ).

cnf(14842,plain,
    multiply(sk_c6,sk_c6) = sk_c5,
    inference('REWRITE',[status(thm)],[prove_this_1,14841,theory(equality)]) ).

cnf(14915,plain,
    ( inverse(X) != sk_c6
    | multiply(X,sk_c5) != sk_c6
    | multiply(Y,sk_c6) != sk_c6
    | inverse(Y) != sk_c6
    | identity != sk_c5
    | sk_c5 != sk_c6 ),
    inference('CONDENSE',[status(thm)],[inference('REWRITE',[status(thm)],[149,14841,theory(equality)])]) ).

cnf(17690,plain,
    inverse(multiply(sk_c5,sk_c2)) = sk_c2,
    inference('REWRITE',[status(thm)],[9681,10207,14841,theory(equality)]) ).

cnf(18472,plain,
    sk_c5 = sk_c6,
    inference('REWRITE',[status(thm)],[14545,14842,14841,theory(equality)]) ).

cnf(18549,plain,
    inverse(sk_c2) = sk_c5,
    inference('REWRITE',[status(thm)],[9579,18472,theory(equality)]) ).

cnf(18588,plain,
    multiply(sk_c5,sk_c2) = identity,
    inference('REWRITE',[status(thm)],[10196,18472,theory(equality)]) ).

cnf(18595,plain,
    sk_c2 = identity,
    inference('REWRITE',[status(thm)],[17690,145,18588,theory(equality)]) ).

cnf(18754,plain,
    identity = sk_c5,
    inference('REWRITE',[status(thm)],[18549,145,18595,theory(equality)]) ).

cnf(18869,plain,
    ( X != identity
    | inverse(X) != identity ),
    inference('CONDENSE',[status(thm)],[inference('REWRITE',[status(thm)],[14915,125,18754,18472,theory(equality)])]) ).

cnf(19119,plain,
    $false,
    inference('HYPERRESOLVE',[status(thm)],[18869,145,theory(equality)]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12  % Problem  : GRP344-1 : TPTP v8.1.0. Released v2.5.0.
% 0.13/0.13  % Command  : run-snark %s %d
% 0.13/0.34  % Computer : n017.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 : Mon Jun 13 03:59:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.45  /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46  * 
% 0.20/0.46  * 
% 0.20/0.46  #<PACKAGE "SNARK-USER">
% 0.20/0.46  * 
% 0.20/0.46  SNARK-TPTP-OPTIONS
% 0.20/0.46  * 
% 0.20/0.46  ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.20/0.46   (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.20/0.46   (USE-FACTORING :POS)
% 0.20/0.46   (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.20/0.46   (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.20/0.46   (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.20/0.46   (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.20/0.46   (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.20/0.46   (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.20/0.46   (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.20/0.46   (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.20/0.46   (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.20/0.46   (DECLARE-TPTP-SYMBOLS2))
% 0.20/0.46  * 
% 0.20/0.46  "."
% 0.20/0.46  * 
% 0.20/0.46  ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T03:59:22
% 0.20/0.46  ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n017.cluster.edu at 2022-06-13T03:59:22
% 0.20/0.48  
% 0.20/0.48  ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.20/0.48  ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 238.64/238.82  ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 238.64/238.82  
% 238.64/238.82  #||
% 238.64/238.82  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 238.64/238.82  % SZS output start Refutation
% See solution above
% 238.64/238.83  ||#
% 238.64/238.83  
% 238.64/238.83  ; Summary of computation:
% 238.64/238.83  ;    619638 formulas have been input or derived (from 805 formulas).
% 238.64/238.83  ;     19119 ( 3%) were retained.  Of these,
% 238.64/238.83  ;        18347 (96%) were simplified or subsumed later,
% 238.64/238.83  ;          772 ( 4%) are still being kept.
% 238.64/238.83  ; 
% 238.64/238.83  ; Run time in seconds excluding printing time:
% 238.64/238.83  ;     0.004   0%   Read assertion file          (1 call)
% 238.64/238.83  ;     0.001   0%   Assert                       (21 calls)
% 238.64/238.83  ;     2.871   1%   Process new row              (300,054 calls)
% 238.64/238.83  ;    90.396  38%   Resolution                   (1,608 calls)
% 238.64/238.83  ;     0.733   0%   Paramodulation               (804 calls)
% 238.64/238.83  ;     0.002   0%   Factoring                    (751 calls)
% 238.64/238.83  ;     0.762   0%   Condensing                   (254,016 calls)
% 238.64/238.83  ;   109.410  46%   Forward subsumption          (254,016 calls)
% 238.64/238.83  ;     2.108   1%   Backward subsumption         (18,525 calls)
% 238.64/238.83  ;    16.341   7%   Clause clause subsumption    (3,436,053 calls)
% 238.64/238.83  ;    11.944   5%   Forward simplification       (266,563 calls)
% 238.64/238.83  ;     1.099   0%   Backward simplification      (19,118 calls)
% 238.64/238.83  ;     1.544   1%   Ordering                     (430,239 calls)
% 238.64/238.83  ;     0.001   0%   Sortal reasoning             (32 calls)
% 238.64/238.83  ;     0.000   0%   Purity testing               (1 call)
% 238.64/238.83  ;     1.136   0%   Other
% 238.64/238.83  ;   238.352        Total
% 238.64/238.83  ;   238.363        Real time
% 238.64/238.83  ; 
% 238.64/238.83  ; Term-hash-array has 10,128 terms in all.
% 238.64/238.83  ; Feature-vector-row-index has 416 entries (8,784 at peak, 18,525 added, 18,109 deleted).
% 238.64/238.83  ; Feature-vector-row-index has 832 nodes (33,352 at peak, 68,107 added, 67,275 deleted).
% 238.64/238.83  ;  Retrieved 19,240,206 possibly forward subsuming rows in 254,016 calls.
% 238.64/238.83  ;  Retrieved 104,686 possibly backward subsumed rows in 18,525 calls.
% 238.64/238.83  ; Path-index has 1,263 entries (6,850 at peak, 13,171 added, 11,908 deleted).
% 238.64/238.83  ; Path-index has 985 nodes (1,763 at peak, 2,450 added, 1,465 deleted).
% 238.64/238.83  ; Trie-index has 1,263 entries (6,850 at peak, 13,171 added, 11,908 deleted).
% 238.64/238.83  ; Trie-index has 5,093 nodes (23,512 at peak, 42,562 added, 37,469 deleted).
% 238.64/238.83  ; Retrieved 216,691 generalization terms in 2,502,481 calls.
% 238.64/238.83  ; Retrieved 4,963 instance terms in 1,410 calls.
% 238.64/238.83  ; Retrieved 76,821,623 unifiable terms in 533,865 calls.
% 238.64/238.83  ; 
% 238.64/238.83  ; The agenda of rows to process has 18 entries:
% 238.64/238.83  ;     2 with value 8               3 with value 13               1 with value 17
% 238.64/238.83  ;     1 with value 9               2 with value 15               1 with value 18
% 238.64/238.83  ;     2 with value 11              1 with value 16               2 with value 24
% 238.64/238.83  ;     3 with value 12
% 238.64/238.83  ; The agenda of rows to give has 748 entries:
% 238.64/238.83  ;     2 with value (4 12)          2 with value (4 20)          33 with value (4 27)
% 238.64/238.83  ;     2 with value (4 13)         43 with value (4 21)          56 with value (4 28)
% 238.64/238.83  ;     1 with value (4 15)         29 with value (4 22)          53 with value (4 29)
% 238.64/238.83  ;     6 with value (4 16)         61 with value (4 23)          99 with value (4 30)
% 238.64/238.83  ;     6 with value (4 17)         50 with value (4 24)         141 with value (4 31)
% 238.64/238.83  ;    12 with value (4 18)         57 with value (4 25)           4 with value (4 32)
% 238.64/238.83  ;    17 with value (4 19)         73 with value (4 26)           1 with value (4 51)
% 238.64/238.83  Evaluation took:
% 238.64/238.83    238.364 seconds of real time
% 238.64/238.83    230.76738 seconds of user run time
% 238.64/238.83    7.594043 seconds of system run time
% 238.64/238.83    [Run times include 19.713 seconds GC run time.]
% 238.64/238.83    0 calls to %EVAL
% 238.64/238.83    0 page faults and
% 238.64/238.83    22,141,179,112 bytes consed.
% 238.64/238.83  :PROOF-FOUND
% 238.64/238.83  ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T04:03:21
% 238.64/238.83  :PROOF-FOUND
% 238.64/238.83  * 
%------------------------------------------------------------------------------