%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n011.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 11:35:09 EDT 2022
% Result : Unsatisfiable 67.11s 67.33s
% Output : Refutation 67.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 15
% Syntax : Number of clauses : 40 ( 36 unt; 0 nHn; 28 RR)
% Number of literals : 49 ( 3 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
product(identity,X,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_identity) ).
cnf(right_identity,axiom,
product(X,identity,X),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',left_inverse) ).
cnf(right_inverse,axiom,
product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',right_inverse) ).
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function1) ).
cnf(total_function2,axiom,
( ~ product(X,Y,Z)
| ~ product(X,Y,U)
| Z = U ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',total_function2) ).
cnf(associativity1,axiom,
( ~ product(X,Y,Z)
| ~ product(Y,U,V)
| ~ product(Z,U,W)
| product(X,V,W) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity1) ).
cnf(associativity2,axiom,
( ~ product(X,Y,Z)
| ~ product(Y,U,V)
| ~ product(X,V,W)
| product(Z,U,W) ),
file('/export/starexec/sandbox/benchmark/Axioms/GRP003-0.ax',associativity2) ).
cnf(x_cubed_is_identity_2,hypothesis,
( ~ product(X,X,Y)
| product(Y,X,identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_identity_2) ).
cnf(a_times_b_is_c,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(c_times_inverse_a_is_d,negated_conjecture,
product(c,inverse(a),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
cnf(d_times_inverse_b_is_h,negated_conjecture,
product(d,inverse(b),h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
cnf(h_times_b_is_j,negated_conjecture,
product(h,b,j),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_b_is_j) ).
cnf(j_times_inverse_h_is_k,negated_conjecture,
product(j,inverse(h),k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
cnf(prove_k_times_inverse_b_is_e,negated_conjecture,
~ product(k,inverse(b),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
cnf(19,plain,
product(multiply(X,X),X,identity),
inference('HYPERRESOLVE',[status(thm)],[x_cubed_is_identity_2,total_function1]) ).
cnf(31,plain,
product(d,identity,j),
inference('HYPERRESOLVE',[status(thm)],[associativity1,d_times_inverse_b_is_h,left_inverse,h_times_b_is_j]) ).
cnf(32,plain,
~ product(k,identity,b),
inference('UR-RESOLVE',[status(thm)],[associativity1,left_identity,right_inverse,prove_k_times_inverse_b_is_e]) ).
cnf(34,plain,
product(inverse(a),c,b),
inference('HYPERRESOLVE',[status(thm)],[associativity1,left_inverse,a_times_b_is_c,left_identity]) ).
cnf(43,plain,
product(inverse(X),multiply(X,Y),Y),
inference('HYPERRESOLVE',[status(thm)],[associativity1,left_inverse,total_function1,left_identity]) ).
cnf(76,plain,
product(k,h,j),
inference('HYPERRESOLVE',[status(thm)],[associativity2,j_times_inverse_h_is_k,left_inverse,right_identity]) ).
cnf(77,plain,
product(h,b,d),
inference('HYPERRESOLVE',[status(thm)],[associativity2,d_times_inverse_b_is_h,left_inverse,right_identity]) ).
cnf(78,plain,
product(d,a,c),
inference('HYPERRESOLVE',[status(thm)],[associativity2,c_times_inverse_a_is_d,left_inverse,right_identity]) ).
cnf(82,plain,
product(c,inverse(b),a),
inference('HYPERRESOLVE',[status(thm)],[associativity2,a_times_b_is_c,right_inverse,right_identity]) ).
cnf(90,plain,
product(multiply(X,Y),inverse(Y),X),
inference('HYPERRESOLVE',[status(thm)],[associativity2,total_function1,right_inverse,right_identity]) ).
cnf(122,plain,
j = d,
inference('HYPERRESOLVE',[status(thm)],[total_function2,31,right_identity]) ).
cnf(136,plain,
product(k,h,d),
inference('REWRITE',[status(thm)],[76,122,theory(equality)]) ).
cnf(159,plain,
product(h,multiply(b,a),c),
inference('HYPERRESOLVE',[status(thm)],[associativity1,78,77,total_function1]) ).
cnf(208,plain,
product(b,inverse(c),inverse(a)),
inference('HYPERRESOLVE',[status(thm)],[associativity2,34,right_inverse,right_identity]) ).
cnf(233,plain,
product(multiply(X,c),inverse(b),multiply(X,a)),
inference('HYPERRESOLVE',[status(thm)],[associativity2,82,total_function1,total_function1]) ).
cnf(698,plain,
product(X,X,inverse(X)),
inference('HYPERRESOLVE',[status(thm)],[associativity2,43,19,right_identity]) ).
cnf(740,plain,
product(X,inverse(multiply(Y,X)),inverse(Y)),
inference('HYPERRESOLVE',[status(thm)],[associativity2,43,right_inverse,right_identity]) ).
cnf(889,plain,
product(inverse(X),inverse(X),X),
inference('HYPERRESOLVE',[status(thm)],[associativity2,698,right_inverse,right_identity]) ).
cnf(1177,plain,
~ product(k,X,multiply(b,X)),
inference('UR-RESOLVE',[status(thm)],[associativity1,90,right_inverse,32]) ).
cnf(1706,plain,
product(multiply(b,c),c,inverse(a)),
inference('HYPERRESOLVE',[status(thm)],[associativity2,208,total_function1,698]) ).
cnf(2477,plain,
~ product(d,multiply(b,a),multiply(b,c)),
inference('UR-RESOLVE',[status(thm)],[associativity1,1177,136,159]) ).
cnf(32773,plain,
product(multiply(b,c),d,a),
inference('HYPERRESOLVE',[status(thm)],[associativity1,1706,c_times_inverse_a_is_d,889]) ).
cnf(44730,plain,
a = multiply(multiply(b,c),d),
inference('HYPERRESOLVE',[status(thm)],[total_function2,32773,total_function1]) ).
cnf(50658,plain,
product(inverse(a),inverse(multiply(b,c)),multiply(b,a)),
inference('HYPERRESOLVE',[status(thm)],[associativity2,740,1706,233]) ).
cnf(84079,plain,
$false,
inference('REWRITE',[status(thm)],[inference('UR-RESOLVE',[status(thm)],[associativity1,2477,740,889]),50658,44730,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : run-snark %s %d
% 0.14/0.33 % Computer : n011.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Tue Jun 14 05:19:04 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.19/0.45 /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p 2022-06-14T05:19:04
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n011.cluster.edu at 2022-06-14T05:19:04
% 0.19/0.48
% 0.19/0.48 ; Recognized possible left identity assertion (|product| |identity| ?X ?X).
% 0.19/0.48 ; Recognized possible right identity assertion (|product| ?X |identity| ?X).
% 0.19/0.48 ; Recognized possible left inverse assertion (|product| (|inverse| ?X) ?X |identity|).
% 0.19/0.48 ; Recognized possible right inverse assertion (|product| ?X (|inverse| ?X) |identity|).
% 0.19/0.48 ; Recognized relation function assertion (|product| ?X ?Y (|multiply| ?X ?Y)).
% 0.19/0.48 ; Recognized relation functionality assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?X ?Y ?U)) (= ?Z ?U)).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?Z ?U ?W)) (|product| ?X ?V ?W)).
% 67.11/67.33 ; Recognized possible associativity assertion (OR (NOT (|product| ?X ?Y ?Z)) (NOT (|product| ?Y ?U ?V)) (NOT (|product| ?X ?V ?W)) (|product| ?Z ?U ?W)).
% 67.11/67.33
% 67.11/67.33 #||
% 67.11/67.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 67.11/67.33 % SZS output start Refutation
% See solution above
% 67.11/67.33 ||#
% 67.11/67.33
% 67.11/67.33 ; Summary of computation:
% 67.11/67.33 ; 323686 formulas have been input or derived (from 923 formulas).
% 67.11/67.33 ; 84079 (26%) were retained. Of these,
% 67.11/67.33 ; 8095 (10%) were simplified or subsumed later,
% 67.11/67.33 ; 75984 (90%) are still being kept.
% 67.11/67.33 ;
% 67.11/67.33 ; Run time in seconds excluding printing time:
% 67.11/67.33 ; 0.003 0% Read assertion file (1 call)
% 67.11/67.33 ; 0.000 0% Assert (16 calls)
% 67.11/67.33 ; 7.589 11% Process new row (317,926 calls)
% 67.11/67.33 ; 48.762 73% Resolution (1,844 calls)
% 67.11/67.33 ; 0.115 0% Paramodulation (922 calls)
% 67.11/67.33 ; 0.000 0% Condensing (5 calls)
% 67.11/67.33 ; 0.000 0% Forward subsumption (5 calls)
% 67.11/67.33 ; 0.000 0% Backward subsumption (5 calls)
% 67.11/67.33 ; 0.000 0% Clause clause subsumption (4 calls)
% 67.11/67.33 ; 6.988 10% Forward simplification (311,058 calls)
% 67.11/67.33 ; 2.411 4% Backward simplification (84,079 calls)
% 67.11/67.33 ; 0.002 0% Ordering (1,332 calls)
% 67.11/67.33 ; 0.000 0% Sortal reasoning (32 calls)
% 67.11/67.33 ; 0.000 0% Purity testing (1 call)
% 67.11/67.33 ; 0.988 1% Other
% 67.11/67.33 ; 66.858 Total
% 67.11/67.33 ; 66.868 Real time
% 67.11/67.34 ;
% 67.11/67.34 ; Term-hash-array has 98,527 terms in all.
% 67.11/67.34 ; Feature-vector-row-index has 5 entries (5 at peak, 5 added, 0 deleted).
% 67.11/67.34 ; Feature-vector-row-index has 7 nodes (7 at peak, 7 added, 0 deleted).
% 67.11/67.34 ; Retrieved 2 possibly forward subsuming rows in 5 calls.
% 67.11/67.34 ; Retrieved 2 possibly backward subsumed rows in 5 calls.
% 67.11/67.34 ; Path-index has 89,596 entries (89,596 at peak, 98,550 added, 8,954 deleted).
% 67.11/67.34 ; Path-index has 2,829 nodes (2,829 at peak, 3,115 added, 286 deleted).
% 67.11/67.34 ; Trie-index has 89,596 entries (89,596 at peak, 98,550 added, 8,954 deleted).
% 67.11/67.34 ; Trie-index has 250,593 nodes (250,593 at peak, 272,380 added, 21,787 deleted).
% 67.11/67.34 ; Retrieved 1,624,253 generalization terms in 1,459,394 calls.
% 67.11/67.34 ; Retrieved 161,987 instance terms in 84,073 calls.
% 67.11/67.34 ; Retrieved 22,739,665 unifiable terms in 181,240 calls.
% 67.11/67.34 ;
% 67.11/67.34 ; The agenda of rows to process has 28 entries:
% 67.11/67.34 ; 18 with value 23 7 with value 24 3 with value 25
% 67.11/67.34 ; The agenda of rows to give has 75115 entries:
% 67.11/67.34 ; 434 with value (4 13) 12080 with value (4 19) 1075 with value (4 24)
% 67.11/67.34 ; 1307 with value (4 14) 12438 with value (4 20) 192 with value (4 25)
% 67.11/67.34 ; 2584 with value (4 15) 11277 with value (4 21) 25 with value (4 26)
% 67.11/67.34 ; 4545 with value (4 16) 8594 with value (4 22) 21 with value (4 27)
% 67.11/67.34 ; 7005 with value (4 17) 3974 with value (4 23) 4 with value (4 28)
% 67.11/67.34 ; 9560 with value (4 18)
% 67.11/67.34 Evaluation took:
% 67.11/67.34 66.872 seconds of real time
% 67.11/67.34 64.84745 seconds of user run time
% 67.11/67.34 2.01793 seconds of system run time
% 67.11/67.34 [Run times include 7.022 seconds GC run time.]
% 67.11/67.34 0 calls to %EVAL
% 67.11/67.34 0 page faults and
% 67.11/67.34 1,442,139,568 bytes consed.
% 67.11/67.34 :PROOF-FOUND
% 67.11/67.34 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-14T05:20:11
% 67.11/67.34 :PROOF-FOUND
% 67.11/67.34 *
%------------------------------------------------------------------------------