TSTP Solution File: GRP781-1 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP781-1 : TPTP v8.1.0. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n029.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 11:40:44 EDT 2022
% Result : Unsatisfiable 80.47s 80.65s
% Output : Refutation 80.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 6
% Syntax : Number of clauses : 143 ( 123 unt; 0 nHn; 22 RR)
% Number of literals : 163 ( 162 equ; 22 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 388 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity,axiom,
m(X,m(Y,Z)) = m(m(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(cancellation,axiom,
( m(X,Y) != m(Z,Y)
| X = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation) ).
cnf(cancellation_001,axiom,
( m(X,Y) != m(X,Z)
| Y = Z ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_001) ).
cnf(commutator,axiom,
m(X,m(Y,c(Y,X))) = m(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
cnf(5,plain,
m(m(X,Y),c(Y,X)) = m(Y,X),
inference('REWRITE',[status(thm)],[commutator,associativity,theory(equality)]) ).
cnf(assumption,axiom,
m(X,m(Y,m(Z,m(Y,X)))) = m(Y,m(X,m(Z,m(X,Y)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
cnf(7,plain,
m(m(X,m(Y,Z)),m(Y,X)) = m(m(Y,m(X,Z)),m(X,Y)),
inference('REWRITE',[status(thm)],[assumption,associativity,theory(equality)]) ).
cnf(distributivity,negated_conjecture,
c(m(x,y),z) != m(c(x,z),c(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity) ).
cnf(9,plain,
( m(m(X,Y),Z) != m(U,m(Y,Z))
| X = U ),
inference('PARAMODULATE',[status(thm)],[cancellation,associativity,theory(equality)]) ).
cnf(10,plain,
( m(X,m(Y,Z)) != m(m(X,Y),U)
| Z = U ),
inference('PARAMODULATE',[status(thm)],[cancellation_001,associativity,theory(equality)]) ).
cnf(11,plain,
m(X,m(m(Y,Z),U)) = m(m(X,Y),m(Z,U)),
inference('PARAMODULATE',[status(thm)],[associativity,associativity,theory(equality)]) ).
cnf(12,plain,
( m(m(X,Y),Z) != m(X,U)
| m(Y,Z) = U ),
inference('PARAMODULATE',[status(thm)],[cancellation_001,associativity,theory(equality)]) ).
cnf(14,plain,
m(X,m(Y,m(Z,U))) = m(m(m(X,Y),Z),U),
inference('PARAMODULATE',[status(thm)],[associativity,associativity,theory(equality)]) ).
cnf(15,plain,
m(X,m(Y,m(Z,U))) = m(m(X,m(Y,Z)),U),
inference('PARAMODULATE',[status(thm)],[associativity,associativity,theory(equality)]) ).
cnf(16,plain,
( m(X,m(Y,Z)) != m(U,Z)
| m(X,Y) = U ),
inference('PARAMODULATE',[status(thm)],[cancellation,associativity,theory(equality)]) ).
cnf(17,plain,
m(m(X,Y),m(Z,U)) = m(m(X,m(Y,Z)),U),
inference('PARAMODULATE',[status(thm)],[associativity,associativity,theory(equality)]) ).
cnf(18,plain,
m(X,m(Y,Z)) = m(m(X,Z),m(Y,c(Y,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,5,theory(equality)]),17,theory(equality)]) ).
cnf(19,plain,
( m(X,Y) != m(m(Y,X),Z)
| c(X,Y) = Z ),
inference('PARAMODULATE',[status(thm)],[cancellation_001,5,theory(equality)]) ).
cnf(21,plain,
m(m(X,Y),m(c(Y,X),Z)) = m(m(Y,X),Z),
inference('PARAMODULATE',[status(thm)],[associativity,5,theory(equality)]) ).
cnf(22,plain,
m(m(X,m(Y,Z)),c(Z,m(X,Y))) = m(Z,m(X,Y)),
inference('PARAMODULATE',[status(thm)],[5,associativity,theory(equality)]) ).
cnf(23,plain,
m(m(m(X,Y),Z),c(m(Y,Z),X)) = m(m(Y,Z),X),
inference('PARAMODULATE',[status(thm)],[5,associativity,theory(equality)]) ).
cnf(44,plain,
( m(X,Y) != m(Z,m(X,c(X,Y)))
| Y = Z ),
inference('PARAMODULATE',[status(thm)],[9,5,theory(equality)]) ).
cnf(59,plain,
( m(X,m(Y,Z)) != m(Y,X)
| Z = c(Y,X) ),
inference('PARAMODULATE',[status(thm)],[10,5,theory(equality)]) ).
cnf(78,plain,
m(m(X,Y),m(m(Z,U),V)) = m(m(X,m(Y,Z)),m(U,V)),
inference('PARAMODULATE',[status(thm)],[11,associativity,theory(equality)]) ).
cnf(123,plain,
m(X,c(X,X)) = X,
inference('HYPERRESOLVE',[status(thm)],[12,5]) ).
cnf(124,plain,
( m(X,Y) != m(Y,Z)
| m(X,c(X,Y)) = Z ),
inference('PARAMODULATE',[status(thm)],[12,5,theory(equality)]) ).
cnf(141,plain,
m(X,Y) = m(m(X,Y),c(Y,Y)),
inference('PARAMODULATE',[status(thm)],[associativity,123,theory(equality)]) ).
cnf(142,plain,
( X != m(X,Y)
| c(X,X) = Y ),
inference('PARAMODULATE',[status(thm)],[cancellation_001,123,theory(equality)]) ).
cnf(145,plain,
m(X,m(c(X,X),Y)) = m(X,Y),
inference('PARAMODULATE',[status(thm)],[associativity,123,theory(equality)]) ).
cnf(152,plain,
m(m(X,Y),m(Y,X)) = m(m(m(Y,X),c(Y,Y)),m(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7,123,theory(equality)]),associativity,theory(equality)]) ).
cnf(172,plain,
c(m(X,Y),m(X,Y)) = c(Y,Y),
inference('HYPERRESOLVE',[status(thm)],[142,141]) ).
cnf(180,plain,
m(c(X,X),Y) = Y,
inference('HYPERRESOLVE',[status(thm)],[cancellation_001,145]) ).
cnf(186,plain,
m(X,Y) = m(m(X,c(Z,Z)),Y),
inference('PARAMODULATE',[status(thm)],[associativity,180,theory(equality)]) ).
cnf(187,plain,
m(m(X,Y),m(Y,X)) = m(m(Y,X),m(X,Y)),
inference('REWRITE',[status(thm)],[152,186,theory(equality)]) ).
cnf(196,plain,
c(X,X) = c(Y,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[172,7,theory(equality)]),172,theory(equality)]) ).
cnf(197,plain,
m(X,c(Y,Y)) = X,
inference('PARAMODULATE',[status(thm)],[123,196,theory(equality)]) ).
cnf(500,plain,
m(m(X,Y),m(Z,m(Y,X))) = m(m(Y,m(X,Z)),m(X,Y)),
inference('PARAMODULATE',[status(thm)],[7,17,theory(equality)]) ).
cnf(613,plain,
m(m(X,Y),m(Z,c(Y,X))) = m(m(Y,X),m(Z,c(Z,c(Y,X)))),
inference('PARAMODULATE',[status(thm)],[18,5,theory(equality)]) ).
cnf(650,plain,
m(m(x,y),z) != m(m(z,m(x,y)),m(c(x,z),c(y,z))),
inference('UR-RESOLVE',[status(thm)],[19,distributivity]) ).
cnf(718,plain,
m(X,m(c(Y,X),Y)) = m(m(Y,X),c(c(Y,X),Y)),
inference('PARAMODULATE',[status(thm)],[18,21,theory(equality)]) ).
cnf(810,plain,
( m(X,Y) != m(Z,m(X,Y))
| Y = m(Z,Y) ),
inference('PARAMODULATE',[status(thm)],[44,18,theory(equality)]) ).
cnf(811,plain,
( m(X,Y) != m(X,c(X,Y))
| c(Z,Z) = Y ),
inference('PARAMODULATE',[status(thm)],[44,180,theory(equality)]) ).
cnf(820,plain,
( m(X,Y) != m(Z,m(m(Y,X),c(m(Y,X),c(X,Y))))
| c(X,Y) = Z ),
inference('PARAMODULATE',[status(thm)],[44,5,theory(equality)]) ).
cnf(843,plain,
c(X,Y) = c(X,m(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[59,18]) ).
cnf(881,plain,
c(X,m(Y,Z)) = c(X,m(m(X,Y),Z)),
inference('PARAMODULATE',[status(thm)],[843,associativity,theory(equality)]) ).
cnf(882,plain,
c(m(X,Y),c(Y,X)) = c(m(X,Y),m(Y,X)),
inference('PARAMODULATE',[status(thm)],[843,5,theory(equality)]) ).
cnf(883,plain,
c(m(X,Y),Z) = c(m(X,Y),m(X,m(Y,Z))),
inference('PARAMODULATE',[status(thm)],[843,associativity,theory(equality)]) ).
cnf(1011,plain,
m(m(X,Y),c(m(X,Y),X)) = m(Y,X),
inference('HYPERRESOLVE',[status(thm)],[124,associativity]) ).
cnf(1012,plain,
m(m(X,Y),c(m(X,Y),c(Y,X))) = m(c(X,Y),m(Y,X)),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[124,21]),882,theory(equality)]) ).
cnf(1013,plain,
( m(X,Y) != m(Z,m(c(Y,X),m(X,Y)))
| c(X,Y) = Z ),
inference('REWRITE',[status(thm)],[820,1012,theory(equality)]) ).
cnf(1053,plain,
c(X,Y) = c(m(Y,X),Y),
inference('HYPERRESOLVE',[status(thm)],[19,1011]) ).
cnf(1054,plain,
c(m(X,Y),Z) = c(m(m(Z,X),Y),Z),
inference('PARAMODULATE',[status(thm)],[1053,associativity,theory(equality)]) ).
cnf(1069,plain,
m(c(X,Y),m(Y,X)) = m(X,Y),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[124,187]),1012,882,theory(equality)]) ).
cnf(1070,plain,
( m(X,Y) != m(Z,m(Y,X))
| c(X,Y) = Z ),
inference('REWRITE',[status(thm)],[1013,1069,theory(equality)]) ).
cnf(1159,plain,
m(X,m(Y,Z)) = m(m(X,c(Y,Z)),m(Z,Y)),
inference('PARAMODULATE',[status(thm)],[associativity,1069,theory(equality)]) ).
cnf(1160,plain,
m(m(c(X,Y),Y),m(X,Z)) = m(m(X,Y),Z),
inference('PARAMODULATE',[status(thm)],[17,1069,theory(equality)]) ).
cnf(1161,plain,
( m(X,Y) != m(Z,X)
| m(c(X,Y),Y) = Z ),
inference('PARAMODULATE',[status(thm)],[16,1069,theory(equality)]) ).
cnf(1678,plain,
c(X,m(Y,c(Y,X))) = c(X,m(Y,X)),
inference('PARAMODULATE',[status(thm)],[881,5,theory(equality)]) ).
cnf(1736,plain,
m(m(X,m(Y,Z)),c(m(Z,Y),m(X,c(Y,Z)))) = m(m(Z,Y),m(X,c(Y,Z))),
inference('PARAMODULATE',[status(thm)],[22,1069,theory(equality)]) ).
cnf(1794,plain,
m(m(X,Y),c(m(X,c(X,Y)),Y)) = m(m(X,c(X,Y)),Y),
inference('PARAMODULATE',[status(thm)],[23,5,theory(equality)]) ).
cnf(1936,plain,
( m(X,Y) != m(m(Z,X),Y)
| Y = m(Z,Y) ),
inference('PARAMODULATE',[status(thm)],[810,associativity,theory(equality)]) ).
cnf(2024,plain,
c(m(X,c(X,Y)),Y) = c(m(X,Y),Y),
inference('PARAMODULATE',[status(thm)],[1054,5,theory(equality)]) ).
cnf(2025,plain,
m(m(X,Y),c(m(X,Y),Y)) = m(m(X,c(X,Y)),Y),
inference('REWRITE',[status(thm)],[1794,2024,theory(equality)]) ).
cnf(2703,plain,
c(m(X,c(X,Y)),m(Y,c(Y,m(X,Y)))) = c(m(X,c(X,Y)),m(X,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1678,1678,theory(equality)]),5,associativity,theory(equality)]) ).
cnf(2864,plain,
m(m(X,Y),c(c(X,Y),X)) = m(m(Y,c(X,Y)),X),
inference('PARAMODULATE',[status(thm)],[associativity,718,theory(equality)]) ).
cnf(2870,plain,
m(m(X,c(Y,X)),m(Y,Z)) = m(m(m(Y,X),c(c(Y,X),Y)),Z),
inference('PARAMODULATE',[status(thm)],[17,718,theory(equality)]) ).
cnf(2871,plain,
m(X,m(c(Y,X),m(Y,Z))) = m(m(m(Y,X),c(c(Y,X),Y)),Z),
inference('PARAMODULATE',[status(thm)],[15,718,theory(equality)]) ).
cnf(2872,plain,
m(X,m(m(Y,Z),c(c(Y,Z),Y))) = m(m(X,Z),m(c(Y,Z),Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[15,718,theory(equality)]),17,theory(equality)]) ).
cnf(2873,plain,
m(X,m(m(Y,Z),c(c(Y,Z),Y))) = m(m(m(X,Z),c(Y,Z)),Y),
inference('PARAMODULATE',[status(thm)],[14,718,theory(equality)]) ).
cnf(2875,plain,
( m(m(X,Y),c(c(X,Y),X)) != m(Z,X)
| m(Y,c(X,Y)) = Z ),
inference('PARAMODULATE',[status(thm)],[16,718,theory(equality)]) ).
cnf(2958,plain,
c(m(c(X,Y),Y),X) = c(m(c(X,Y),Y),m(X,Y)),
inference('PARAMODULATE',[status(thm)],[883,1069,theory(equality)]) ).
cnf(3357,plain,
c(m(X,c(X,m(Y,X))),m(Y,c(Y,X))) = c(m(Y,X),m(Y,c(Y,X))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2024,1678,theory(equality)]),5,associativity,theory(equality)]) ).
cnf(3376,plain,
c(m(c(X,Y),Y),X) = c(m(Y,c(m(X,Y),Y)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1054,2025,theory(equality)]),1054,theory(equality)]) ).
cnf(4413,plain,
m(m(c(X,Y),Y),c(m(c(X,Y),Y),X)) = Y,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[124,1160]),2958,theory(equality)]) ).
cnf(4567,plain,
m(c(X,m(Y,X)),m(Y,X)) = m(X,Y),
inference('HYPERRESOLVE',[status(thm)],[1161,associativity]) ).
cnf(4577,plain,
m(c(m(X,c(X,Y)),m(X,Y)),m(X,Y)) = m(m(X,Y),c(m(X,Y),Y)),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[1161,18]),2025,theory(equality)]) ).
cnf(4640,plain,
c(X,Y) = c(X,m(Y,X)),
inference('HYPERRESOLVE',[status(thm)],[1070,4567]) ).
cnf(4654,plain,
c(m(X,c(X,Y)),m(Y,c(Y,X))) = c(m(X,c(X,Y)),m(X,Y)),
inference('REWRITE',[status(thm)],[2703,4640,theory(equality)]) ).
cnf(4668,plain,
c(X,m(Y,c(Y,X))) = c(X,Y),
inference('REWRITE',[status(thm)],[1678,4640,theory(equality)]) ).
cnf(4671,plain,
c(m(X,c(X,Y)),m(X,Y)) = c(m(Y,X),m(Y,c(Y,X))),
inference('REWRITE',[status(thm)],[3357,4654,4640,theory(equality)]) ).
cnf(4701,plain,
c(m(X,Y),m(Z,c(Y,X))) = c(m(X,Y),m(Z,m(Y,X))),
inference('PARAMODULATE',[status(thm)],[4640,1159,theory(equality)]) ).
cnf(4726,plain,
c(m(X,Y),m(X,c(X,Y))) = c(Y,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4668,843,theory(equality)]),1053,theory(equality)]) ).
cnf(4727,plain,
c(m(X,c(X,Y)),m(X,Y)) = c(X,Y),
inference('REWRITE',[status(thm)],[4671,4726,theory(equality)]) ).
cnf(4728,plain,
m(c(X,Y),m(X,Y)) = m(m(X,Y),c(m(X,Y),Y)),
inference('REWRITE',[status(thm)],[4577,4727,theory(equality)]) ).
cnf(4797,plain,
m(c(X,Y),m(X,Y)) = m(m(X,c(X,Y)),Y),
inference('REWRITE',[status(thm)],[2025,4728,theory(equality)]) ).
cnf(4851,plain,
c(m(X,c(X,Y)),m(Y,c(Y,X))) = c(X,Y),
inference('REWRITE',[status(thm)],[4654,4727,theory(equality)]) ).
cnf(4854,plain,
c(X,Y) = c(m(X,Y),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4668,4668,theory(equality)]),2024,4851,theory(equality)]) ).
cnf(4870,plain,
c(m(c(X,Y),Y),X) = c(m(Y,c(X,Y)),X),
inference('REWRITE',[status(thm)],[3376,4854,theory(equality)]) ).
cnf(4938,plain,
m(c(X,Y),X) = m(X,c(X,Y)),
inference('HYPERRESOLVE',[status(thm)],[16,4797]) ).
cnf(4987,plain,
m(X,c(X,c(X,Y))) = X,
inference('HYPERRESOLVE',[status(thm)],[124,4938]) ).
cnf(4995,plain,
m(c(X,Y),m(X,Z)) = m(m(X,c(X,Y)),Z),
inference('PARAMODULATE',[status(thm)],[associativity,4938,theory(equality)]) ).
cnf(5003,plain,
m(X,m(Y,Z)) = m(m(X,Z),m(c(Y,Z),Y)),
inference('PARAMODULATE',[status(thm)],[18,4938,theory(equality)]) ).
cnf(5013,plain,
m(X,m(m(Y,Z),c(c(Y,Z),Y))) = m(X,m(Y,Z)),
inference('REWRITE',[status(thm)],[2872,5003,theory(equality)]) ).
cnf(5022,plain,
m(X,m(Y,Z)) = m(m(m(X,Z),c(Y,Z)),Y),
inference('REWRITE',[status(thm)],[2873,5013,theory(equality)]) ).
cnf(5033,plain,
m(X,m(c(Y,Z),Y)) = m(m(X,Y),c(Y,Z)),
inference('PARAMODULATE',[status(thm)],[associativity,4938,theory(equality)]) ).
cnf(5042,plain,
m(X,Y) = m(m(X,Y),c(c(X,Y),X)),
inference('REWRITE',[status(thm)],[718,5,5033,theory(equality)]) ).
cnf(5067,plain,
m(X,Y) = m(m(Y,c(X,Y)),X),
inference('REWRITE',[status(thm)],[2864,5042,theory(equality)]) ).
cnf(5070,plain,
( m(X,Y) != m(Z,X)
| m(Y,c(X,Y)) = Z ),
inference('REWRITE',[status(thm)],[2875,5042,theory(equality)]) ).
cnf(5099,plain,
m(m(X,c(Y,X)),m(Y,Z)) = m(m(Y,X),Z),
inference('REWRITE',[status(thm)],[2870,5042,theory(equality)]) ).
cnf(5100,plain,
m(X,m(c(Y,X),m(Y,Z))) = m(m(Y,X),Z),
inference('REWRITE',[status(thm)],[2871,5042,theory(equality)]) ).
cnf(5286,plain,
m(c(X,c(X,Y)),X) = X,
inference('PARAMODULATE',[status(thm)],[4938,4987,theory(equality)]) ).
cnf(5348,plain,
m(m(X,c(Y,X)),c(m(X,c(Y,X)),Y)) = X,
inference('HYPERRESOLVE',[status(thm)],[124,5067]) ).
cnf(5350,plain,
c(m(X,c(Y,X)),Y) = c(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[4854,5067,theory(equality)]),1053,theory(equality)]) ).
cnf(5352,plain,
m(m(X,c(Y,X)),c(X,Y)) = X,
inference('REWRITE',[status(thm)],[5348,5350,theory(equality)]) ).
cnf(5353,plain,
c(m(c(X,Y),Y),X) = c(Y,X),
inference('REWRITE',[status(thm)],[4870,5350,theory(equality)]) ).
cnf(5355,plain,
m(m(c(X,Y),Y),c(Y,X)) = Y,
inference('REWRITE',[status(thm)],[4413,5353,theory(equality)]) ).
cnf(5449,plain,
X = m(c(Y,c(Y,Z)),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1936,5286,theory(equality)]),theory(equality)]) ).
cnf(5618,plain,
c(X,m(c(Y,X),c(X,Y))) = c(X,X),
inference('PARAMODULATE',[status(thm)],[881,5352,theory(equality)]) ).
cnf(5635,plain,
c(m(X,c(Y,X)),c(X,Y)) = c(X,c(X,Y)),
inference('PARAMODULATE',[status(thm)],[4854,5352,theory(equality)]) ).
cnf(5636,plain,
c(X,c(X,Y)) = c(c(Y,X),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[843,5352,theory(equality)]),1053,5635,theory(equality)]) ).
cnf(5790,plain,
m(X,m(c(Y,X),Z)) = m(m(c(Y,X),X),Z),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1160,5636,theory(equality)]),5449,theory(equality)]) ).
cnf(7402,plain,
m(m(X,m(Y,Z)),m(c(Y,X),U)) = m(m(Y,X),m(c(Z,c(Y,X)),m(Z,U))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[21,5100,theory(equality)]),78,theory(equality)]) ).
cnf(7661,plain,
c(X,X) = m(c(Y,Z),c(Z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[811,5618,theory(equality)]),197,5355,5790,theory(equality)]) ).
cnf(7691,plain,
X = m(m(X,c(Y,Z)),c(Z,Y)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,7661,theory(equality)]),197,theory(equality)]) ).
cnf(7694,plain,
m(c(X,Y),m(c(Y,X),Z)) = Z,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,7661,theory(equality)]),180,theory(equality)]) ).
cnf(7851,plain,
c(m(X,c(Y,Z)),c(Z,Y)) = c(X,c(Z,Y)),
inference('PARAMODULATE',[status(thm)],[4854,7691,theory(equality)]) ).
cnf(7855,plain,
c(c(X,Y),m(Z,c(Y,X))) = c(c(X,Y),Z),
inference('PARAMODULATE',[status(thm)],[4640,7691,theory(equality)]) ).
cnf(7861,plain,
m(X,c(c(Y,Z),X)) = m(m(c(Y,Z),X),c(Z,Y)),
inference('HYPERRESOLVE',[status(thm)],[5070,7691]) ).
cnf(7863,plain,
c(X,c(Y,Z)) = c(c(Z,Y),X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[843,7691,theory(equality)]),1053,7851,theory(equality)]) ).
cnf(7889,plain,
m(X,c(c(Y,Z),X)) = m(c(Y,Z),m(X,c(Z,Y))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[5,7691,theory(equality)]),7855,theory(equality)]) ).
cnf(7890,plain,
m(m(X,c(Y,Z)),m(U,c(Z,Y))) = m(m(X,c(U,c(Z,Y))),U),
inference('PARAMODULATE',[status(thm)],[5022,7691,theory(equality)]) ).
cnf(7893,plain,
m(m(X,c(Y,Z)),m(U,c(Z,Y))) = m(X,m(U,c(U,c(Z,Y)))),
inference('PARAMODULATE',[status(thm)],[18,7691,theory(equality)]) ).
cnf(7932,plain,
c(m(c(X,Y),Z),c(Y,X)) = c(Z,c(Y,X)),
inference('PARAMODULATE',[status(thm)],[1053,7694,theory(equality)]) ).
cnf(7962,plain,
m(m(X,c(c(Y,Z),X)),U) = m(m(c(Y,Z),X),m(c(Z,Y),U)),
inference('PARAMODULATE',[status(thm)],[5099,7694,theory(equality)]) ).
cnf(7965,plain,
m(m(c(c(X,Y),Z),Z),U) = m(m(c(X,Y),Z),m(c(Y,X),U)),
inference('PARAMODULATE',[status(thm)],[1160,7694,theory(equality)]) ).
cnf(7983,plain,
m(c(c(X,Y),m(Z,c(c(Y,X),Z))),m(Z,c(c(Y,X),Z))) = Z,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[1161,7694]),7889,theory(equality)]) ).
cnf(7985,plain,
m(X,m(c(X,c(Y,Z)),U)) = m(m(X,c(c(Z,Y),X)),U),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[21,7694,theory(equality)]),7861,7932,theory(equality)]) ).
cnf(7986,plain,
m(X,m(Y,c(c(Z,U),Y))) = m(m(X,c(Z,U)),m(Y,c(U,Z))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1159,7694,theory(equality)]),7890,7932,7861,theory(equality)]) ).
cnf(8092,plain,
c(c(X,Y),m(Z,c(c(Y,X),Z))) = c(c(X,Y),Z),
inference('PARAMODULATE',[status(thm)],[4668,7863,theory(equality)]) ).
cnf(8093,plain,
m(c(c(X,Y),Z),m(Z,c(c(Y,X),Z))) = Z,
inference('REWRITE',[status(thm)],[7983,8092,theory(equality)]) ).
cnf(8295,plain,
m(X,m(c(X,Y),Z)) = m(c(X,Y),m(X,Z)),
inference('PARAMODULATE',[status(thm)],[associativity,4995,theory(equality)]) ).
cnf(8297,plain,
m(c(X,c(Y,Z)),m(X,U)) = m(m(X,c(c(Z,Y),X)),U),
inference('REWRITE',[status(thm)],[7985,8295,theory(equality)]) ).
cnf(18499,plain,
m(m(X,Y),m(Z,c(Y,X))) = m(Y,m(X,Z)),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[5070,500]),1736,4701,theory(equality)]) ).
cnf(18514,plain,
m(X,m(Y,Z)) = m(m(X,Y),m(Z,c(Z,c(X,Y)))),
inference('REWRITE',[status(thm)],[613,18499,theory(equality)]) ).
cnf(19557,plain,
X = m(X,c(X,c(Y,Z))),
inference('HYPERRESOLVE',[status(thm)],[10,18514]) ).
cnf(19603,plain,
m(m(X,c(Y,Z)),m(U,c(Z,Y))) = m(X,U),
inference('REWRITE',[status(thm)],[7893,19557,theory(equality)]) ).
cnf(19635,plain,
m(X,m(Y,c(c(Z,U),Y))) = m(X,Y),
inference('REWRITE',[status(thm)],[7986,19603,theory(equality)]) ).
cnf(19638,plain,
m(c(c(X,Y),Z),Z) = Z,
inference('REWRITE',[status(thm)],[8093,19635,theory(equality)]) ).
cnf(19687,plain,
m(X,Y) = m(m(c(Z,U),X),m(c(U,Z),Y)),
inference('REWRITE',[status(thm)],[7965,19638,theory(equality)]) ).
cnf(19692,plain,
m(m(X,c(c(Y,Z),X)),U) = m(X,U),
inference('REWRITE',[status(thm)],[7962,19687,theory(equality)]) ).
cnf(19696,plain,
m(c(X,c(Y,Z)),m(X,U)) = m(X,U),
inference('REWRITE',[status(thm)],[8297,19692,theory(equality)]) ).
cnf(19709,plain,
m(m(X,m(Y,Z)),m(c(Y,X),U)) = m(m(Y,X),m(Z,U)),
inference('REWRITE',[status(thm)],[7402,19696,theory(equality)]) ).
cnf(19710,plain,
$false,
inference('REWRITE',[status(thm)],[650,associativity,18,19709,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP781-1 : TPTP v8.1.0. Released v5.4.0.
% 0.03/0.13 % Command : run-snark %s %d
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 04:11:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.47 #<PACKAGE "SNARK-USER">
% 0.19/0.47 *
% 0.19/0.47 SNARK-TPTP-OPTIONS
% 0.19/0.47 *
% 0.19/0.47 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.47 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.47 (USE-FACTORING :POS)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.47 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.47 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.47 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.47 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.47 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.47 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.47 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.47 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.47 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.47 *
% 0.19/0.47 "."
% 0.19/0.47 *
% 0.19/0.47 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T04:11:55
% 0.19/0.47 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n029.cluster.edu at 2022-06-14T04:11:55
% 0.19/0.48
% 80.47/80.65 ; Recognized associativity assertion (= (|m| ?X (|m| ?Y ?Z)) (|m| (|m| ?X ?Y) ?Z)).
% 80.47/80.65
% 80.47/80.65 #||
% 80.47/80.65 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 80.47/80.66 % SZS output start Refutation
% See solution above
% 80.47/80.68 ||#
% 80.47/80.68
% 80.47/80.68 ; Summary of computation:
% 80.47/80.68 ; 62434 formulas have been input or derived (from 260 formulas).
% 80.47/80.68 ; 19710 (32%) were retained. Of these,
% 80.47/80.68 ; 3517 (18%) were simplified or subsumed later,
% 80.47/80.68 ; 16193 (82%) are still being kept.
% 80.47/80.68 ;
% 80.47/80.68 ; Run time in seconds excluding printing time:
% 80.47/80.68 ; 0.002 0% Read assertion file (1 call)
% 80.47/80.68 ; 0.000 0% Assert (6 calls)
% 80.47/80.68 ; 2.547 3% Process new row (59,955 calls)
% 80.47/80.68 ; 1.738 2% Resolution (518 calls)
% 80.47/80.68 ; 1.056 1% Paramodulation (259 calls)
% 80.47/80.68 ; 0.254 0% Condensing (17,976 calls)
% 80.47/80.68 ; 7.459 9% Forward subsumption (17,976 calls)
% 80.47/80.68 ; 4.228 5% Backward subsumption (9,193 calls)
% 80.47/80.68 ; 10.600 13% Clause clause subsumption (4,138,638 calls)
% 80.47/80.68 ; 12.367 15% Forward simplification (58,111 calls)
% 80.47/80.68 ; 2.998 4% Backward simplification (19,708 calls)
% 80.47/80.68 ; 36.683 46% Ordering (2,686,144 calls)
% 80.47/80.68 ; 0.000 0% Sortal reasoning (32 calls)
% 80.47/80.68 ; 0.000 0% Purity testing (1 call)
% 80.47/80.68 ; 0.253 0% Other
% 80.47/80.68 ; 80.185 Total
% 80.47/80.68 ; 80.214 Real time
% 80.47/80.69 ;
% 80.47/80.69 ; Term-hash-array has 39,200 terms in all.
% 80.47/80.69 ; Feature-vector-row-index has 8,023 entries (8,107 at peak, 9,193 added, 1,170 deleted).
% 80.47/80.69 ; Feature-vector-row-index has 3,134 nodes (3,203 at peak, 4,842 added, 1,708 deleted).
% 80.47/80.69 ; Retrieved 3,320,262 possibly forward subsuming rows in 17,976 calls.
% 80.47/80.69 ; Retrieved 1,389,911 possibly backward subsumed rows in 9,193 calls.
% 80.47/80.69 ; Path-index has 32,052 entries (32,677 at peak, 40,171 added, 8,119 deleted).
% 80.47/80.69 ; Path-index has 6,041 nodes (6,109 at peak, 7,444 added, 1,403 deleted).
% 80.47/80.69 ; Trie-index has 32,052 entries (32,677 at peak, 40,171 added, 8,119 deleted).
% 80.47/80.69 ; Trie-index has 139,126 nodes (142,930 at peak, 175,945 added, 36,819 deleted).
% 80.47/80.69 ; Retrieved 2,157,524 generalization terms in 587,942 calls.
% 80.47/80.69 ; Retrieved 612,592 instance terms in 17,575 calls.
% 80.47/80.69 ; Retrieved 3,614,378 unifiable terms in 3,742 calls.
% 80.47/80.69 ;
% 80.47/80.69 ; The agenda of backward simplifiable rows to process has 58 entries:
% 80.47/80.69 ; 58 with value 0
% 80.47/80.69 ; The agenda of rows to process has 650 entries:
% 80.47/80.69 ; 2 with value 17 27 with value 33 31 with value 45
% 80.47/80.69 ; 1 with value 21 31 with value 34 12 with value 46
% 80.47/80.69 ; 1 with value 22 53 with value 35 10 with value 47
% 80.47/80.69 ; 2 with value 23 33 with value 36 6 with value 48
% 80.47/80.69 ; 3 with value 24 43 with value 37 5 with value 49
% 80.47/80.69 ; 2 with value 25 67 with value 38 3 with value 50
% 80.47/80.69 ; 5 with value 26 70 with value 39 5 with value 51
% 80.47/80.69 ; 1 with value 27 42 with value 40 4 with value 52
% 80.47/80.69 ; 9 with value 28 25 with value 41 1 with value 53
% 80.47/80.69 ; 21 with value 29 37 with value 42 2 with value 54
% 80.47/80.69 ; 23 with value 30 17 with value 43 4 with value 55
% 80.47/80.69 ; 17 with value 31 12 with value 44 1 with value 58
% 80.47/80.69 ; 22 with value 32
% 80.47/80.69 ; The agenda of rows to give has 15999 entries:
% 80.47/80.69 ; 1 with value (4 16) 910 with value (4 34) 113 with value (4 48)
% 80.47/80.69 ; 1 with value (4 21) 1519 with value (4 35) 86 with value (4 49)
% 80.47/80.69 ; 1 with value (4 22) 1528 with value (4 36) 39 with value (4 50)
% 80.47/80.69 ; 5 with value (4 23) 1081 with value (4 37) 68 with value (4 51)
% 80.47/80.69 ; 4 with value (4 24) 1223 with value (4 38) 110 with value (4 52)
% 80.47/80.69 ; 90 with value (4 25) 1347 with value (4 39) 17 with value (4 53)
% 80.47/80.69 ; 174 with value (4 26) 1154 with value (4 40) 9 with value (4 54)
% 80.47/80.69 ; 218 with value (4 27) 644 with value (4 41) 5 with value (4 55)
% 80.47/80.69 ; 265 with value (4 28) 497 with value (4 42) 1 with value (4 56)
% 80.47/80.69 ; 348 with value (4 29) 514 with value (4 43) 7 with value (4 57)
% 80.47/80.69 ; 604 with value (4 30) 448 with value (4 44) 3 with value (4 58)
% 80.47/80.69 ; 827 with value (4 31) 322 with value (4 45) 5 with value (4 62)
% 80.47/80.69 ; 742 with value (4 32) 170 with value (4 46) 1 with value (4 63)
% 80.47/80.69 ; 739 with value (4 33) 154 with value (4 47) 5 with value (4 66)
% 80.47/80.69 Evaluation took:
% 80.47/80.69 80.215 seconds of real time
% 80.47/80.69 72.41358 seconds of user run time
% 80.47/80.69 7.802998 seconds of system run time
% 80.47/80.69 [Run times include 9.939 seconds GC run time.]
% 80.47/80.69 0 calls to %EVAL
% 80.47/80.69 0 page faults and
% 80.47/80.69 5,734,801,488 bytes consed.
% 80.47/80.69 :PROOF-FOUND
% 80.47/80.69 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T04:13:16
% 80.47/80.69 :PROOF-FOUND
% 80.47/80.69 *
%------------------------------------------------------------------------------