TSTP Solution File: GRP129-2.004 by SNARK---20120808r022
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- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP129-2.004 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n028.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 11:36:56 EDT 2022
% Result : Unsatisfiable 5.54s 5.74s
% Output : Refutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 25
% Syntax : Number of clauses : 115 ( 36 unt; 74 nHn; 115 RR)
% Number of literals : 406 ( 0 equ; 35 neg)
% Maximal clause size : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(e_1_then_e_2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_then_e_2) ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_then_e_3) ).
cnf(e_3_greater_e_2,axiom,
greater(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_2) ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_2) ).
cnf(e_4_greater_e_3,axiom,
greater(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_3) ).
cnf(no_redundancy,axiom,
( ~ product(X,e_1,Y)
| ~ next(X,Z)
| ~ greater(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_redundancy) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
cnf(e_1_is_not_e_2,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
cnf(e_1_is_not_e_4,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_4) ).
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(e_4_is_not_e_2,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_2) ).
cnf(product_total_function1,axiom,
( ~ group_element(X)
| ~ group_element(Y)
| product(X,Y,e_1)
| product(X,Y,e_2)
| product(X,Y,e_3)
| product(X,Y,e_4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(product_total_function2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,U)
| equalish(Z,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
cnf(product_right_cancellation,axiom,
( ~ product(X,Y,Z)
| ~ product(X,U,Z)
| equalish(Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(product_left_cancellation,axiom,
( ~ product(X,Y,Z)
| ~ product(U,Y,Z)
| equalish(X,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(qg3,negated_conjecture,
( ~ product(X,Y,Z)
| ~ product(Y,Z,U)
| product(Z,X,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
cnf(32,plain,
~ product(e_2,e_1,e_4),
inference('UR-RESOLVE',[status(thm)],[no_redundancy,e_2_then_e_3,e_4_greater_e_3]) ).
cnf(33,plain,
~ product(e_1,e_1,e_3),
inference('UR-RESOLVE',[status(thm)],[no_redundancy,e_1_then_e_2,e_3_greater_e_2]) ).
cnf(34,plain,
~ product(e_1,e_1,e_4),
inference('UR-RESOLVE',[status(thm)],[no_redundancy,e_1_then_e_2,e_4_greater_e_2]) ).
cnf(35,plain,
( product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_4,element_4]) ).
cnf(37,plain,
( product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_4,element_2]) ).
cnf(38,plain,
( product(e_4,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_4,element_1]) ).
cnf(40,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3)
| product(e_3,e_3,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_3,element_3]) ).
cnf(41,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_3,element_2]) ).
cnf(42,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_3,element_1]) ).
cnf(45,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_2,element_2]) ).
cnf(46,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_2,element_1]),32]) ).
cnf(47,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_4]) ).
cnf(48,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_3]) ).
cnf(49,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_2]) ).
cnf(50,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_1,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function1,element_1,element_1]),34,33]) ).
cnf(89,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,42,40]),e_1_is_not_e_3]) ).
cnf(90,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,42,41]),e_1_is_not_e_2]) ).
cnf(108,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,47,35]),e_1_is_not_e_4]) ).
cnf(115,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_2,e_4) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,48,46]) ).
cnf(124,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,49,37]),e_1_is_not_e_4]) ).
cnf(125,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,49,41]),e_1_is_not_e_3]) ).
cnf(126,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,49,45]),e_1_is_not_e_2]) ).
cnf(191,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_3,e_1)
| product(e_3,e_3,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,90,89]),e_2_is_not_e_3]) ).
cnf(255,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_4,e_4,e_1)
| product(e_4,e_4,e_2)
| product(e_4,e_1,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,108,47]) ).
cnf(290,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,115,42]),e_2_is_not_e_1]) ).
cnf(340,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_4,e_2,e_1)
| product(e_4,e_2,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,126,124]),e_2_is_not_e_4]) ).
cnf(341,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,126,125]),e_2_is_not_e_3]) ).
cnf(410,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_4,e_4,e_1)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,255,47]) ).
cnf(421,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,410,47]) ).
cnf(452,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| product(e_4,e_4,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,421,38]) ).
cnf(497,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,452,421]),e_4_is_not_e_1]) ).
cnf(498,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,497,46]),e_4_is_not_e_2]) ).
cnf(597,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_3,e_1)
| product(e_2,e_3,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,191,90]) ).
cnf(754,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_4,e_2,e_1)
| product(e_2,e_4,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,340,126]) ).
cnf(762,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_3,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,341,126]) ).
cnf(791,plain,
( product(e_1,e_4,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,498,50]),e_4_is_not_e_1]) ).
cnf(793,plain,
( product(e_1,e_4,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_4,e_2) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,498,38]) ).
cnf(853,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_3,e_1) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,597,191]) ).
cnf(855,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_3,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,853,46]),e_3_is_not_e_2]) ).
cnf(973,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,754,126]),e_4_is_not_e_2]) ).
cnf(985,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,762,126]),e_3_is_not_e_2]) ).
cnf(986,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,985,973]),e_3_is_not_e_4]) ).
cnf(999,plain,
( product(e_1,e_4,e_1)
| product(e_4,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,791,50]),e_4_is_not_e_1]) ).
cnf(1000,plain,
( product(e_1,e_4,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_1,e_4,e_2) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,999,50]) ).
cnf(1001,plain,
( product(e_4,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[qg3,999,38]),34]) ).
cnf(1013,plain,
( product(e_1,e_4,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,1000,50]),e_4_is_not_e_1]) ).
cnf(1296,plain,
( product(e_4,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_1)
| product(e_4,e_1,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,1001,46]),e_4_is_not_e_2]) ).
cnf(1297,plain,
( product(e_4,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,1296,50]),e_4_is_not_e_1]) ).
cnf(1298,plain,
( product(e_2,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,1297,1013]) ).
cnf(1299,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_1) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,1298,50]),e_2_is_not_e_1]) ).
cnf(1300,plain,
( product(e_1,e_1,e_1)
| product(e_1,e_2,e_2) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,1299,50]) ).
cnf(1303,plain,
product(e_1,e_1,e_1),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_right_cancellation,1300,50]),e_2_is_not_e_1]) ).
cnf(1305,plain,
~ product(e_2,e_1,e_1),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,1303,e_1_is_not_e_2]) ).
cnf(1306,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference('REWRITE',[status(thm)],[46,1305]) ).
cnf(1314,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference('REWRITE',[status(thm)],[290,1305]) ).
cnf(1318,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[498,1305]) ).
cnf(1369,plain,
( product(e_1,e_4,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1)
| product(e_2,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_4,e_2) ),
inference('REWRITE',[status(thm)],[793,1305]) ).
cnf(1399,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_3,e_1)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[855,1305]) ).
cnf(1491,plain,
~ product(e_3,e_1,e_1),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,1303,e_1_is_not_e_3]) ).
cnf(1603,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference('REWRITE',[status(thm)],[1314,1491]) ).
cnf(1617,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_3,e_1)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[1399,1491]) ).
cnf(1639,plain,
~ product(e_4,e_1,e_1),
inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,1303,e_1_is_not_e_4]) ).
cnf(1755,plain,
( product(e_1,e_4,e_1)
| product(e_1,e_4,e_2)
| product(e_4,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[1318,1639]) ).
cnf(1758,plain,
( product(e_1,e_4,e_1)
| product(e_4,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_4,e_2) ),
inference('REWRITE',[status(thm)],[1369,1639]) ).
cnf(1843,plain,
~ product(e_1,e_2,e_1),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,1303,e_1_is_not_e_2]) ).
cnf(1895,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_2) ),
inference('REWRITE',[status(thm)],[986,1843]) ).
cnf(1961,plain,
~ product(e_1,e_3,e_1),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,1303,e_1_is_not_e_3]) ).
cnf(2079,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference('REWRITE',[status(thm)],[1603,1961]) ).
cnf(2139,plain,
~ product(e_1,e_4,e_1),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,1303,e_1_is_not_e_4]) ).
cnf(2230,plain,
( product(e_1,e_4,e_2)
| product(e_4,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[1755,2139]) ).
cnf(2231,plain,
( product(e_4,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_4,e_2) ),
inference('REWRITE',[status(thm)],[1758,2139]) ).
cnf(2334,plain,
( product(e_1,e_3,e_2)
| product(e_1,e_3,e_3)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,2079,1306]),e_3_is_not_e_2]) ).
cnf(2335,plain,
( product(e_1,e_3,e_2)
| product(e_2,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_3,e_2,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,2334,1306]) ).
cnf(2357,plain,
( product(e_4,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,2231,2230]),e_4_is_not_e_1]) ).
cnf(2358,plain,
( product(e_4,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,2357,1306]),e_4_is_not_e_2]) ).
cnf(2370,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[qg3,1617,2334]),1491]) ).
cnf(2377,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_2,e_1)
| product(e_2,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function2,2370,2335]),e_2_is_not_e_3]) ).
cnf(2378,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_total_function2,2377,2335]),e_1_is_not_e_3]) ).
cnf(2380,plain,
( product(e_2,e_1,e_2)
| product(e_1,e_3,e_2) ),
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[product_left_cancellation,2378,2358]),e_3_is_not_e_4]) ).
cnf(2381,plain,
( product(e_2,e_1,e_2)
| product(e_3,e_2,e_2) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,2380,1306]) ).
cnf(2383,plain,
product(e_2,e_1,e_2),
inference('HYPERRESOLVE',[status(thm)],[qg3,2381,2380]) ).
cnf(2628,plain,
~ product(e_2,e_2,e_2),
inference('UR-RESOLVE',[status(thm)],[product_right_cancellation,2383,e_1_is_not_e_2]) ).
cnf(2660,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_3)
| product(e_2,e_2,e_1) ),
inference('REWRITE',[status(thm)],[1895,2628]) ).
cnf(2916,plain,
~ product(e_1,e_2,e_2),
inference('UR-RESOLVE',[status(thm)],[qg3,2628,2383]) ).
cnf(2949,plain,
( product(e_1,e_2,e_3)
| product(e_2,e_2,e_1) ),
inference('REWRITE',[status(thm)],[2660,2916]) ).
cnf(2982,plain,
( product(e_2,e_2,e_1)
| product(e_2,e_2,e_3) ),
inference('HYPERRESOLVE',[status(thm)],[qg3,2949,2383]) ).
cnf(2991,plain,
~ product(e_2,e_2,e_1),
inference('UR-RESOLVE',[status(thm)],[qg3,2916,2383]) ).
cnf(2992,plain,
product(e_1,e_2,e_3),
inference('REWRITE',[status(thm)],[2949,2991]) ).
cnf(3001,plain,
product(e_2,e_2,e_3),
inference('REWRITE',[status(thm)],[2982,2991]) ).
cnf(3010,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[product_left_cancellation,2992,e_1_is_not_e_2]),3001]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP129-2.004 : TPTP v8.1.0. Released v1.2.0.
% 0.06/0.13 % Command : run-snark %s %d
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 08:42:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.46 *
% 0.19/0.46 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46 (USE-FACTORING :POS)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46 *
% 0.19/0.46 "."
% 0.19/0.46 *
% 0.19/0.46 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T08:42:39
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n028.cluster.edu at 2022-06-14T08:42:39
% 5.54/5.74
% 5.54/5.74
% 5.54/5.74 #||
% 5.54/5.74 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.54/5.74 % SZS output start Refutation
% See solution above
% 5.58/5.75 ||#
% 5.58/5.75
% 5.58/5.75 ; Summary of computation:
% 5.58/5.75 ; 18506 formulas have been input or derived (from 333 formulas).
% 5.58/5.75 ; 3010 (16%) were retained. Of these,
% 5.58/5.75 ; 2815 (94%) were simplified or subsumed later,
% 5.58/5.75 ; 195 ( 6%) are still being kept.
% 5.58/5.75 ;
% 5.58/5.75 ; Run time in seconds excluding printing time:
% 5.58/5.75 ; 0.004 0% Read assertion file (1 call)
% 5.58/5.75 ; 0.000 0% Assert (31 calls)
% 5.58/5.75 ; 0.341 6% Process new row (17,521 calls)
% 5.58/5.75 ; 0.443 8% Resolution (664 calls)
% 5.58/5.75 ; 0.000 0% Paramodulation (332 calls)
% 5.58/5.75 ; 0.002 0% Factoring (274 calls)
% 5.58/5.75 ; 0.020 0% Condensing (10,754 calls)
% 5.58/5.75 ; 2.295 44% Forward subsumption (10,754 calls)
% 5.58/5.75 ; 0.663 13% Backward subsumption (2,954 calls)
% 5.58/5.75 ; 0.694 13% Clause clause subsumption (351,169 calls)
% 5.58/5.75 ; 0.582 11% Forward simplification (14,204 calls)
% 5.58/5.75 ; 0.099 2% Backward simplification (3,010 calls)
% 5.58/5.75 ; 0.044 1% Ordering (31,906 calls)
% 5.58/5.75 ; 0.001 0% Sortal reasoning (32 calls)
% 5.58/5.75 ; 0.000 0% Purity testing (1 call)
% 5.58/5.75 ; 0.084 2% Other
% 5.58/5.75 ; 5.272 Total
% 5.58/5.75 ; 5.285 Real time
% 5.58/5.75 ;
% 5.58/5.75 ; Term-hash-array has 114 terms in all.
% 5.58/5.75 ; Feature-vector-row-index has 139 entries (802 at peak, 2,954 added, 2,815 deleted).
% 5.58/5.75 ; Feature-vector-row-index has 684 nodes (3,017 at peak, 9,519 added, 8,835 deleted).
% 5.58/5.75 ; Retrieved 463,569 possibly forward subsuming rows in 10,754 calls.
% 5.58/5.75 ; Retrieved 138,189 possibly backward subsumed rows in 2,954 calls.
% 5.58/5.75 ; Path-index has 116 entries (118 at peak, 126 added, 10 deleted).
% 5.58/5.75 ; Path-index has 67 nodes (67 at peak, 67 added, 0 deleted).
% 5.58/5.75 ; Trie-index has 116 entries (118 at peak, 126 added, 10 deleted).
% 5.58/5.75 ; Trie-index has 151 nodes (153 at peak, 161 added, 10 deleted).
% 5.58/5.75 ; Retrieved 9,893 generalization terms in 125,810 calls.
% 5.58/5.75 ; Retrieved 55 instance terms in 55 calls.
% 5.58/5.75 ; Retrieved 22,978 unifiable terms in 4,562 calls.
% 5.58/5.75 ;
% 5.58/5.75 ; The agenda of rows to process has 22 entries:
% 5.58/5.75 ; 17 with value 12 2 with value 21 1 with value 24
% 5.58/5.75 ; 1 with value 20 1 with value 22
% 5.58/5.75 ; The agenda of rows to give has 117 entries:
% 5.58/5.75 ; 1 with value (4 14) 11 with value (4 33) 6 with value (4 44)
% 5.58/5.75 ; 3 with value (4 20) 2 with value (4 34) 8 with value (4 45)
% 5.58/5.75 ; 9 with value (4 22) 3 with value (4 35) 2 with value (4 47)
% 5.58/5.75 ; 2 with value (4 23) 2 with value (4 36) 4 with value (4 48)
% 5.58/5.75 ; 1 with value (4 25) 3 with value (4 37) 4 with value (4 49)
% 5.58/5.75 ; 8 with value (4 27) 6 with value (4 38) 6 with value (4 50)
% 5.58/5.75 ; 5 with value (4 28) 3 with value (4 39) 2 with value (4 53)
% 5.58/5.75 ; 2 with value (4 29) 5 with value (4 40) 2 with value (4 54)
% 5.58/5.75 ; 3 with value (4 30) 1 with value (4 41) 1 with value (4 55)
% 5.58/5.75 ; 2 with value (4 32) 10 with value (4 43)
% 5.58/5.75 Evaluation took:
% 5.58/5.75 5.286 seconds of real time
% 5.58/5.75 4.722709 seconds of user run time
% 5.58/5.75 0.563077 seconds of system run time
% 5.58/5.75 [Run times include 0.23 seconds GC run time.]
% 5.58/5.75 0 calls to %EVAL
% 5.58/5.75 0 page faults and
% 5.58/5.75 694,261,200 bytes consed.
% 5.58/5.75 :PROOF-FOUND
% 5.58/5.75 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-14T08:42:44
% 5.58/5.75 :PROOF-FOUND
% 5.58/5.75 *
%------------------------------------------------------------------------------