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