TSTP Solution File: GRP226-1 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP226-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% 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 : 600s
% DateTime : Sat Jul 16 11:37:36 EDT 2022
% Result : Unsatisfiable 132.99s 133.21s
% Output : Refutation 133.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 23
% Syntax : Number of clauses : 118 ( 36 unt; 79 nHn; 79 RR)
% Number of literals : 215 ( 214 equ; 22 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 : 66 ( 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,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_1) ).
cnf(prove_this_2,negated_conjecture,
( inverse(sk_c1) = sk_c7
| multiply(sk_c4,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
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_3) ).
cnf(prove_this_4,negated_conjecture,
( inverse(sk_c1) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_4) ).
cnf(prove_this_5,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_5) ).
cnf(prove_this_6,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_6) ).
cnf(prove_this_8,negated_conjecture,
( multiply(sk_c1,sk_c6) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_8) ).
cnf(prove_this_9,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_9) ).
cnf(prove_this_10,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_10) ).
cnf(prove_this_11,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_11) ).
cnf(prove_this_12,negated_conjecture,
( multiply(sk_c7,sk_c3) = sk_c6
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_12) ).
cnf(prove_this_13,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_13) ).
cnf(prove_this_14,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_14) ).
cnf(prove_this_15,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_15) ).
cnf(prove_this_16,negated_conjecture,
( multiply(sk_c2,sk_c7) = sk_c3
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_16) ).
cnf(prove_this_17,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_17) ).
cnf(prove_this_18,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c4,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_18) ).
cnf(prove_this_19,negated_conjecture,
( inverse(sk_c2) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_19) ).
cnf(prove_this_20,negated_conjecture,
( inverse(sk_c2) = sk_c7
| inverse(sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_20) ).
cnf(prove_this_21,negated_conjecture,
( inverse(X) != sk_c7
| multiply(X,sk_c6) != sk_c7
| multiply(sk_c7,Y) != sk_c6
| multiply(Z,sk_c7) != Y
| inverse(Z) != sk_c7
| inverse(U) != sk_c7
| multiply(U,sk_c6) != sk_c7
| multiply(V,sk_c6) != sk_c7
| inverse(V) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this_21) ).
cnf(25,plain,
( multiply(sk_c7,X) != sk_c6
| multiply(Y,sk_c7) != X
| inverse(Y) != sk_c7
| inverse(Z) != sk_c7
| multiply(Z,sk_c6) != sk_c7
| multiply(U,sk_c6) != sk_c7
| inverse(U) != sk_c6 ),
inference('CONDENSE',[status(thm)],[prove_this_21]) ).
cnf(31,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(32,plain,
multiply(multiply(X,inverse(Y)),Y) = multiply(X,identity),
inference('PARAMODULATE',[status(thm)],[associativity,left_inverse,theory(equality)]) ).
cnf(51,plain,
( inverse(sk_c5) = sk_c6
| multiply(multiply(X,sk_c2),sk_c7) = multiply(X,sk_c3) ),
inference('PARAMODULATE',[status(thm)],[associativity,prove_this_16,theory(equality)]) ).
cnf(52,plain,
( inverse(sk_c4) = sk_c7
| multiply(multiply(X,sk_c2),sk_c7) = multiply(X,sk_c3) ),
inference('PARAMODULATE',[status(thm)],[associativity,prove_this_13,theory(equality)]) ).
cnf(67,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(multiply(X,sk_c2),sk_c7) = multiply(X,sk_c3) ),
inference('PARAMODULATE',[status(thm)],[associativity,prove_this_14,theory(equality)]) ).
cnf(69,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(multiply(X,sk_c2),sk_c7) = multiply(X,sk_c3) ),
inference('PARAMODULATE',[status(thm)],[associativity,prove_this_15,theory(equality)]) ).
cnf(117,plain,
X = multiply(inverse(inverse(X)),identity),
inference('PARAMODULATE',[status(thm)],[31,left_inverse,theory(equality)]) ).
cnf(118,plain,
multiply(X,Y) = multiply(inverse(inverse(X)),Y),
inference('PARAMODULATE',[status(thm)],[31,31,theory(equality)]) ).
cnf(119,plain,
X = multiply(X,identity),
inference('REWRITE',[status(thm)],[117,118,theory(equality)]) ).
cnf(120,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[32,119,theory(equality)]) ).
cnf(121,plain,
( inverse(sk_c5) = sk_c6
| sk_c3 = multiply(inverse(sk_c7),sk_c6) ),
inference('PARAMODULATE',[status(thm)],[31,prove_this_12,theory(equality)]) ).
cnf(122,plain,
( inverse(sk_c4) = sk_c7
| sk_c3 = multiply(inverse(sk_c7),sk_c6) ),
inference('PARAMODULATE',[status(thm)],[31,prove_this_9,theory(equality)]) ).
cnf(123,plain,
( inverse(sk_c2) = sk_c7
| sk_c6 = multiply(inverse(sk_c4),sk_c7) ),
inference('PARAMODULATE',[status(thm)],[31,prove_this_18,theory(equality)]) ).
cnf(124,plain,
( inverse(sk_c1) = sk_c7
| sk_c6 = multiply(inverse(sk_c4),sk_c7) ),
inference('PARAMODULATE',[status(thm)],[31,prove_this_2,theory(equality)]) ).
cnf(125,plain,
( inverse(sk_c2) = sk_c7
| sk_c6 = multiply(inverse(sk_c5),sk_c7) ),
inference('PARAMODULATE',[status(thm)],[31,prove_this_19,theory(equality)]) ).
cnf(126,plain,
( inverse(sk_c1) = sk_c7
| sk_c6 = multiply(inverse(sk_c5),sk_c7) ),
inference('PARAMODULATE',[status(thm)],[31,prove_this_3,theory(equality)]) ).
cnf(131,plain,
multiply(multiply(X,inverse(Y)),multiply(Y,Z)) = multiply(X,Z),
inference('PARAMODULATE',[status(thm)],[associativity,31,theory(equality)]) ).
cnf(143,plain,
inverse(identity) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,119,theory(equality)]) ).
cnf(148,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[120,left_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(159,plain,
multiply(X,inverse(X)) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,148,theory(equality)]) ).
cnf(160,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('PARAMODULATE',[status(thm)],[120,148,theory(equality)]) ).
cnf(161,plain,
X = multiply(Y,multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[31,148,theory(equality)]) ).
cnf(176,plain,
inverse(X) = multiply(inverse(multiply(Y,X)),Y),
inference('PARAMODULATE',[status(thm)],[31,160,theory(equality)]) ).
cnf(188,plain,
multiply(X,Y) = multiply(multiply(X,Z),multiply(inverse(Z),Y)),
inference('PARAMODULATE',[status(thm)],[associativity,160,theory(equality)]) ).
cnf(227,plain,
( inverse(sk_c2) = sk_c7
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference('PARAMODULATE',[status(thm)],[123,prove_this_17,theory(equality)]) ).
cnf(233,plain,
( inverse(sk_c2) = sk_c7
| sk_c7 = multiply(inverse(sk_c7),sk_c6) ),
inference('PARAMODULATE',[status(thm)],[31,227,theory(equality)]) ).
cnf(238,plain,
( inverse(sk_c1) = sk_c7
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference('PARAMODULATE',[status(thm)],[124,prove_this_1,theory(equality)]) ).
cnf(249,plain,
( inverse(sk_c2) = sk_c7
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference('PARAMODULATE',[status(thm)],[125,prove_this_20,theory(equality)]) ).
cnf(280,plain,
( inverse(sk_c1) = sk_c7
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference('PARAMODULATE',[status(thm)],[126,prove_this_4,theory(equality)]) ).
cnf(344,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[160,176,theory(equality)]) ).
cnf(345,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[120,176,theory(equality)]) ).
cnf(346,plain,
( inverse(sk_c5) = sk_c6
| sk_c3 = inverse(multiply(inverse(sk_c6),sk_c7)) ),
inference('REWRITE',[status(thm)],[121,345,theory(equality)]) ).
cnf(347,plain,
( inverse(sk_c4) = sk_c7
| sk_c3 = inverse(multiply(inverse(sk_c6),sk_c7)) ),
inference('REWRITE',[status(thm)],[122,345,theory(equality)]) ).
cnf(350,plain,
( inverse(sk_c2) = sk_c7
| sk_c7 = inverse(multiply(inverse(sk_c6),sk_c7)) ),
inference('REWRITE',[status(thm)],[233,345,theory(equality)]) ).
cnf(401,plain,
( inverse(sk_c1) = sk_c7
| X = multiply(X,sk_c7) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[131,280,theory(equality)]),120,theory(equality)]) ).
cnf(402,plain,
( inverse(sk_c2) = sk_c7
| X = multiply(X,sk_c7) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[131,249,theory(equality)]),120,theory(equality)]) ).
cnf(415,plain,
( inverse(sk_c1) = sk_c7
| inverse(sk_c4) = sk_c6 ),
inference('PARAMODULATE',[status(thm)],[124,401,theory(equality)]) ).
cnf(416,plain,
( inverse(sk_c1) = sk_c7
| inverse(sk_c7) = identity ),
inference('PARAMODULATE',[status(thm)],[left_inverse,401,theory(equality)]) ).
cnf(417,plain,
( inverse(sk_c1) = sk_c7
| multiply(X,inverse(sk_c7)) = X ),
inference('PARAMODULATE',[status(thm)],[160,401,theory(equality)]) ).
cnf(460,plain,
( inverse(sk_c2) = sk_c7
| inverse(sk_c4) = sk_c6 ),
inference('PARAMODULATE',[status(thm)],[123,402,theory(equality)]) ).
cnf(547,plain,
( inverse(sk_c1) = sk_c7
| X = multiply(sk_c7,X) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[161,416,theory(equality)]),left_identity,theory(equality)]) ).
cnf(1375,plain,
( inverse(sk_c2) = sk_c7
| multiply(inverse(sk_c7),X) = X ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[345,402,theory(equality)]),148,theory(equality)]) ).
cnf(5120,plain,
( inverse(sk_c1) = sk_c7
| inverse(sk_c7) = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[547,417,theory(equality)]) ).
cnf(5142,plain,
inverse(sk_c1) = sk_c7,
inference('HYPERRESOLVE',[status(thm)],[25,5120,238,401,prove_this_1,prove_this_2,prove_this_2,415]) ).
cnf(5199,plain,
sk_c1 = inverse(sk_c7),
inference('PARAMODULATE',[status(thm)],[148,5142,theory(equality)]) ).
cnf(5226,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,X) = X ),
inference('REWRITE',[status(thm)],[1375,5199,theory(equality)]) ).
cnf(5292,plain,
multiply(sk_c1,sk_c7) = identity,
inference('PARAMODULATE',[status(thm)],[159,5142,theory(equality)]) ).
cnf(5295,plain,
multiply(sk_c7,sk_c1) = identity,
inference('PARAMODULATE',[status(thm)],[left_inverse,5142,theory(equality)]) ).
cnf(5297,plain,
multiply(multiply(X,sk_c1),sk_c7) = X,
inference('PARAMODULATE',[status(thm)],[160,5142,theory(equality)]) ).
cnf(5404,plain,
multiply(inverse(X),sk_c7) = inverse(multiply(sk_c1,X)),
inference('PARAMODULATE',[status(thm)],[344,5142,theory(equality)]) ).
cnf(5417,plain,
( inverse(sk_c5) = sk_c6
| sk_c3 = multiply(sk_c1,sk_c6) ),
inference('REWRITE',[status(thm)],[346,148,5404,theory(equality)]) ).
cnf(5418,plain,
( inverse(sk_c4) = sk_c7
| sk_c3 = multiply(sk_c1,sk_c6) ),
inference('REWRITE',[status(thm)],[347,148,5404,theory(equality)]) ).
cnf(5421,plain,
( inverse(sk_c2) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference('REWRITE',[status(thm)],[350,148,5404,theory(equality)]) ).
cnf(5581,plain,
( inverse(sk_c5) = sk_c6
| sk_c3 = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[prove_this_8,5417,theory(equality)]) ).
cnf(5591,plain,
( sk_c3 = sk_c7
| sk_c5 = inverse(sk_c6) ),
inference('PARAMODULATE',[status(thm)],[148,5581,theory(equality)]) ).
cnf(5596,plain,
( sk_c3 = sk_c7
| multiply(multiply(X,sk_c6),sk_c5) = X ),
inference('PARAMODULATE',[status(thm)],[120,5581,theory(equality)]) ).
cnf(5616,plain,
( inverse(sk_c4) = sk_c7
| sk_c3 = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[prove_this_5,5418,theory(equality)]) ).
cnf(5627,plain,
( sk_c3 = sk_c7
| multiply(sk_c4,sk_c7) = identity ),
inference('PARAMODULATE',[status(thm)],[159,5616,theory(equality)]) ).
cnf(5765,plain,
( sk_c3 = sk_c7
| multiply(sk_c4,X) = multiply(sk_c1,X) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[188,5627,theory(equality)]),left_identity,5199,theory(equality)]) ).
cnf(6839,plain,
( sk_c3 = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[prove_this_6,5765,theory(equality)]) ).
cnf(6871,plain,
( sk_c3 = sk_c7
| multiply(sk_c7,sk_c5) = sk_c1 ),
inference('PARAMODULATE',[status(thm)],[5596,6839,theory(equality)]) ).
cnf(6873,plain,
( sk_c3 = sk_c7
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[31,6839,theory(equality)]),5142,theory(equality)]) ).
cnf(7113,plain,
inverse(sk_c2) = sk_c7,
inference('HYPERRESOLVE',[status(thm)],[25,5226,227,5142,5142,5421,prove_this_18,460]) ).
cnf(7219,plain,
sk_c2 = sk_c1,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[148,7113,theory(equality)]),5199,theory(equality)]) ).
cnf(7222,plain,
( identity = sk_c3
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference('REWRITE',[status(thm)],[prove_this_15,5292,7219,theory(equality)]) ).
cnf(7223,plain,
( identity = sk_c3
| inverse(sk_c5) = sk_c6 ),
inference('REWRITE',[status(thm)],[prove_this_16,5292,7219,theory(equality)]) ).
cnf(7226,plain,
( inverse(sk_c5) = sk_c6
| X = multiply(X,sk_c3) ),
inference('REWRITE',[status(thm)],[51,5297,7219,theory(equality)]) ).
cnf(7227,plain,
( inverse(sk_c4) = sk_c7
| X = multiply(X,sk_c3) ),
inference('REWRITE',[status(thm)],[52,5297,7219,theory(equality)]) ).
cnf(7229,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| X = multiply(X,sk_c3) ),
inference('REWRITE',[status(thm)],[67,5297,7219,theory(equality)]) ).
cnf(7231,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| X = multiply(X,sk_c3) ),
inference('REWRITE',[status(thm)],[69,5297,7219,theory(equality)]) ).
cnf(7613,plain,
( identity = sk_c3
| multiply(sk_c5,sk_c6) = identity ),
inference('PARAMODULATE',[status(thm)],[159,7223,theory(equality)]) ).
cnf(7712,plain,
( inverse(sk_c5) = sk_c6
| sk_c6 = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[prove_this_12,7226,theory(equality)]) ).
cnf(7724,plain,
( sk_c6 = sk_c7
| X = multiply(sk_c6,multiply(sk_c5,X)) ),
inference('PARAMODULATE',[status(thm)],[31,7712,theory(equality)]) ).
cnf(7741,plain,
( inverse(sk_c4) = sk_c7
| sk_c6 = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[prove_this_9,7227,theory(equality)]) ).
cnf(7753,plain,
( sk_c6 = sk_c7
| X = multiply(sk_c7,multiply(sk_c4,X)) ),
inference('PARAMODULATE',[status(thm)],[31,7741,theory(equality)]) ).
cnf(7866,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| sk_c6 = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[prove_this_10,7229,theory(equality)]) ).
cnf(7953,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| sk_c6 = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[prove_this_11,7231,theory(equality)]) ).
cnf(8012,plain,
( identity = sk_c3
| identity = sk_c7 ),
inference('PARAMODULATE',[status(thm)],[7222,7613,theory(equality)]) ).
cnf(8022,plain,
( identity = sk_c3
| identity = sk_c6 ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[6873,8012,theory(equality)]),left_identity,theory(equality)]) ).
cnf(9294,plain,
( sk_c6 = sk_c7
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference('PARAMODULATE',[status(thm)],[7724,7953,theory(equality)]) ).
cnf(9307,plain,
( sk_c6 = sk_c7
| X = multiply(X,sk_c7) ),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[131,9294,theory(equality)]),120,theory(equality)]) ).
cnf(9415,plain,
( sk_c6 = sk_c7
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference('PARAMODULATE',[status(thm)],[7753,7866,theory(equality)]) ).
cnf(9429,plain,
sk_c6 = sk_c7,
inference('PARAMODULATE',[status(thm)],[9307,9415,theory(equality)]) ).
cnf(9436,plain,
( multiply(sk_c6,X) != sk_c6
| multiply(Y,sk_c6) != X
| inverse(Y) != sk_c6
| multiply(Z,sk_c6) != sk_c6
| inverse(Z) != sk_c6 ),
inference('CONDENSE',[status(thm)],[inference('REWRITE',[status(thm)],[25,9429,theory(equality)])]) ).
cnf(9913,plain,
inverse(sk_c1) = sk_c6,
inference('REWRITE',[status(thm)],[5142,9429,theory(equality)]) ).
cnf(9946,plain,
inverse(sk_c6) = sk_c1,
inference('REWRITE',[status(thm)],[5199,9429,theory(equality)]) ).
cnf(10169,plain,
multiply(sk_c6,sk_c1) = identity,
inference('REWRITE',[status(thm)],[5295,9429,theory(equality)]) ).
cnf(10299,plain,
( sk_c3 = sk_c6
| sk_c5 = sk_c1 ),
inference('REWRITE',[status(thm)],[5591,9946,9429,theory(equality)]) ).
cnf(10560,plain,
( sk_c3 = sk_c6
| sk_c1 = multiply(sk_c6,sk_c5) ),
inference('REWRITE',[status(thm)],[6871,9429,theory(equality)]) ).
cnf(11315,plain,
identity != sk_c6,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[9436,119,left_inverse,148,left_identity]),143,theory(equality)]) ).
cnf(11316,plain,
identity = sk_c3,
inference('REWRITE',[status(thm)],[8022,11315]) ).
cnf(11364,plain,
sk_c5 = sk_c1,
inference('REWRITE',[status(thm)],[10299,11315,11316,theory(equality)]) ).
cnf(11371,plain,
sk_c1 = identity,
inference('REWRITE',[status(thm)],[10560,10169,11364,11315,11316,theory(equality)]) ).
cnf(11373,plain,
$false,
inference('REWRITE',[status(thm)],[9913,11315,143,11371,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GRP226-1 : TPTP v8.1.0. Released v2.5.0.
% 0.09/0.15 % Command : run-snark %s %d
% 0.15/0.37 % Computer : n019.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 600
% 0.15/0.37 % DateTime : Tue Jun 14 10:59:54 EDT 2022
% 0.15/0.37 % CPUTime :
% 0.22/0.50 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.51 *
% 0.22/0.51 *
% 0.22/0.52 #<PACKAGE "SNARK-USER">
% 0.22/0.52 *
% 0.22/0.52 SNARK-TPTP-OPTIONS
% 0.22/0.52 *
% 0.22/0.52 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.22/0.52 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.22/0.52 (USE-FACTORING :POS)
% 0.22/0.52 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.22/0.52 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.22/0.52 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.22/0.52 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.22/0.52 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.22/0.52 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.22/0.52 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.22/0.52 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.22/0.52 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.22/0.52 (DECLARE-TPTP-SYMBOLS2))
% 0.22/0.52 *
% 0.22/0.52 "."
% 0.22/0.52 *
% 0.22/0.52 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T10:59:55
% 0.22/0.52 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n019.cluster.edu at 2022-06-14T10:59:55
% 0.34/0.53
% 0.34/0.53 ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.34/0.53 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 132.99/133.21 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 132.99/133.21
% 132.99/133.21 #||
% 132.99/133.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 132.99/133.21 % SZS output start Refutation
% See solution above
% 133.04/133.23 ||#
% 133.04/133.23
% 133.04/133.23 ; Summary of computation:
% 133.04/133.23 ; 324484 formulas have been input or derived (from 522 formulas).
% 133.04/133.23 ; 11373 ( 4%) were retained. Of these,
% 133.04/133.23 ; 11001 (97%) were simplified or subsumed later,
% 133.04/133.23 ; 372 ( 3%) are still being kept.
% 133.04/133.23 ;
% 133.04/133.23 ; Run time in seconds excluding printing time:
% 133.04/133.23 ; 0.005 0% Read assertion file (1 call)
% 133.04/133.23 ; 0.001 0% Assert (24 calls)
% 133.04/133.23 ; 1.884 1% Process new row (204,859 calls)
% 133.04/133.23 ; 37.774 28% Resolution (1,042 calls)
% 133.04/133.23 ; 0.376 0% Paramodulation (521 calls)
% 133.04/133.23 ; 0.003 0% Factoring (489 calls)
% 133.04/133.23 ; 0.814 1% Condensing (189,439 calls)
% 133.04/133.23 ; 69.750 53% Forward subsumption (189,439 calls)
% 133.04/133.23 ; 0.790 1% Backward subsumption (10,951 calls)
% 133.04/133.23 ; 10.562 8% Clause clause subsumption (2,265,511 calls)
% 133.04/133.23 ; 8.669 7% Forward simplification (197,206 calls)
% 133.04/133.23 ; 0.458 0% Backward simplification (11,372 calls)
% 133.04/133.23 ; 0.852 1% Ordering (254,375 calls)
% 133.04/133.23 ; 0.000 0% Sortal reasoning (32 calls)
% 133.04/133.23 ; 0.000 0% Purity testing (1 call)
% 133.04/133.23 ; 0.749 1% Other
% 133.04/133.23 ; 132.687 Total
% 133.04/133.23 ; 132.718 Real time
% 133.04/133.23 ;
% 133.04/133.23 ; Term-hash-array has 6,017 terms in all.
% 133.04/133.23 ; Feature-vector-row-index has 15 entries (4,575 at peak, 10,951 added, 10,936 deleted).
% 133.04/133.23 ; Feature-vector-row-index has 54 nodes (19,542 at peak, 43,262 added, 43,208 deleted).
% 133.04/133.23 ; Retrieved 9,469,575 possibly forward subsuming rows in 189,439 calls.
% 133.04/133.23 ; Retrieved 50,172 possibly backward subsumed rows in 10,951 calls.
% 133.04/133.23 ; Path-index has 834 entries (4,179 at peak, 7,219 added, 6,385 deleted).
% 133.04/133.23 ; Path-index has 807 nodes (1,366 at peak, 1,605 added, 798 deleted).
% 133.04/133.23 ; Trie-index has 834 entries (4,179 at peak, 7,219 added, 6,385 deleted).
% 133.04/133.23 ; Trie-index has 3,879 nodes (13,804 at peak, 22,883 added, 19,004 deleted).
% 133.04/133.23 ; Retrieved 109,169 generalization terms in 1,874,675 calls.
% 133.04/133.23 ; Retrieved 2,995 instance terms in 1,038 calls.
% 133.04/133.23 ; Retrieved 40,816,103 unifiable terms in 368,525 calls.
% 133.04/133.23 ;
% 133.04/133.23 ; The agenda of backward simplifiable rows to process has 867 entries:
% 133.04/133.23 ; 867 with value 0
% 133.04/133.23 ; The agenda of rows to process has 67 entries:
% 133.04/133.23 ; 1 with value 10 3 with value 35 2 with value 42
% 133.04/133.23 ; 1 with value 12 5 with value 36 3 with value 43
% 133.04/133.23 ; 1 with value 13 2 with value 37 1 with value 44
% 133.04/133.23 ; 1 with value 14 4 with value 38 4 with value 45
% 133.04/133.23 ; 1 with value 15 4 with value 39 6 with value 46
% 133.04/133.23 ; 2 with value 31 4 with value 40 10 with value 47
% 133.04/133.23 ; 3 with value 33 9 with value 41
% 133.04/133.23 ; The agenda of rows to give has 349 entries:
% 133.04/133.23 ; 1 with value (4 7) 5 with value (4 24) 125 with value (4 31)
% 133.04/133.23 ; 1 with value (4 10) 18 with value (4 25) 1 with value (4 39)
% 133.04/133.23 ; 1 with value (4 11) 47 with value (4 26) 1 with value (4 40)
% 133.04/133.23 ; 1 with value (4 12) 2 with value (4 27) 1 with value (4 45)
% 133.04/133.23 ; 1 with value (4 14) 8 with value (4 28) 4 with value (4 46)
% 133.04/133.23 ; 4 with value (4 21) 32 with value (4 29) 4 with value (4 47)
% 133.04/133.23 ; 4 with value (4 23) 87 with value (4 30) 1 with value (4 49)
% 133.04/133.23 Evaluation took:
% 133.04/133.23 132.718 seconds of real time
% 133.04/133.23 127.97043 seconds of user run time
% 133.04/133.24 4.739908 seconds of system run time
% 133.04/133.24 [Run times include 8.277 seconds GC run time.]
% 133.04/133.24 0 calls to %EVAL
% 133.04/133.24 0 page faults and
% 133.04/133.24 14,022,257,136 bytes consed.
% 133.04/133.24 :PROOF-FOUND
% 133.04/133.24 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T11:02:07
% 133.04/133.24 :PROOF-FOUND
% 133.04/133.24 *
%------------------------------------------------------------------------------