TSTP Solution File: GRP002-2 by SNARK---20120808r022
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%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:35:09 EDT 2022
% Result : Unsatisfiable 0.46s 0.65s
% Output : Refutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 22 RR)
% Number of literals : 49 ( 48 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 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 : 41 ( 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(right_identity,axiom,
multiply(X,identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(right_inverse,axiom,
multiply(X,inverse(X)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(x_cubed_is_identity,hypothesis,
multiply(X,multiply(X,X)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_cubed_is_identity) ).
cnf(a_times_b_is_c,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(c_times_inverse_a_is_d,negated_conjecture,
multiply(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,
multiply(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,
multiply(h,b) = j,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',h_times_b_is_j) ).
cnf(j_times_inverse_h_is_k,negated_conjecture,
multiply(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,
multiply(k,inverse(b)) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
cnf(15,plain,
multiply(c,X) = multiply(a,multiply(b,X)),
inference('PARAMODULATE',[status(thm)],[associativity,a_times_b_is_c,theory(equality)]) ).
cnf(17,plain,
multiply(multiply(X,a),b) = multiply(X,c),
inference('PARAMODULATE',[status(thm)],[associativity,a_times_b_is_c,theory(equality)]) ).
cnf(19,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(22,plain,
multiply(multiply(X,c),inverse(a)) = multiply(X,d),
inference('PARAMODULATE',[status(thm)],[associativity,c_times_inverse_a_is_d,theory(equality)]) ).
cnf(23,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,right_inverse,theory(equality)]),right_identity,theory(equality)]) ).
cnf(26,plain,
multiply(d,X) = multiply(c,multiply(inverse(a),X)),
inference('PARAMODULATE',[status(thm)],[associativity,c_times_inverse_a_is_d,theory(equality)]) ).
cnf(27,plain,
X = multiply(Y,multiply(inverse(Y),X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity,right_inverse,theory(equality)]),left_identity,theory(equality)]) ).
cnf(39,plain,
b = multiply(inverse(a),c),
inference('PARAMODULATE',[status(thm)],[19,a_times_b_is_c,theory(equality)]) ).
cnf(40,plain,
b = multiply(inverse(h),j),
inference('PARAMODULATE',[status(thm)],[19,h_times_b_is_j,theory(equality)]) ).
cnf(44,plain,
X = inverse(inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[19,left_inverse,theory(equality)]),right_identity,theory(equality)]) ).
cnf(45,plain,
multiply(X,X) = inverse(X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[19,x_cubed_is_identity,theory(equality)]),right_identity,theory(equality)]) ).
cnf(48,plain,
multiply(inverse(X),Y) = multiply(X,multiply(X,Y)),
inference('PARAMODULATE',[status(thm)],[associativity,45,theory(equality)]) ).
cnf(50,plain,
multiply(b,X) = multiply(inverse(a),multiply(c,X)),
inference('PARAMODULATE',[status(thm)],[associativity,39,theory(equality)]) ).
cnf(56,plain,
multiply(b,inverse(j)) = inverse(h),
inference('PARAMODULATE',[status(thm)],[23,40,theory(equality)]) ).
cnf(58,plain,
multiply(k,h) = j,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[23,j_times_inverse_h_is_k,theory(equality)]),44,theory(equality)]) ).
cnf(59,plain,
j = d,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[23,d_times_inverse_b_is_h,theory(equality)]),h_times_b_is_j,44,theory(equality)]) ).
cnf(70,plain,
multiply(b,inverse(d)) = inverse(h),
inference('REWRITE',[status(thm)],[56,59,theory(equality)]) ).
cnf(71,plain,
multiply(k,h) = d,
inference('REWRITE',[status(thm)],[58,59,theory(equality)]) ).
cnf(73,plain,
inverse(X) = multiply(inverse(multiply(Y,X)),Y),
inference('PARAMODULATE',[status(thm)],[19,23,theory(equality)]) ).
cnf(74,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference('PARAMODULATE',[status(thm)],[23,19,theory(equality)]) ).
cnf(77,plain,
h = multiply(inverse(k),d),
inference('PARAMODULATE',[status(thm)],[19,71,theory(equality)]) ).
cnf(95,plain,
multiply(h,inverse(d)) = inverse(k),
inference('PARAMODULATE',[status(thm)],[23,77,theory(equality)]) ).
cnf(103,plain,
multiply(multiply(X,a),multiply(b,Y)) = multiply(X,multiply(c,Y)),
inference('PARAMODULATE',[status(thm)],[associativity,15,theory(equality)]) ).
cnf(105,plain,
multiply(inverse(a),b) = multiply(a,c),
inference('PARAMODULATE',[status(thm)],[17,45,theory(equality)]) ).
cnf(126,plain,
multiply(multiply(X,b),inverse(d)) = multiply(X,inverse(h)),
inference('PARAMODULATE',[status(thm)],[associativity,70,theory(equality)]) ).
cnf(136,plain,
multiply(inverse(c),inverse(a)) = multiply(c,d),
inference('PARAMODULATE',[status(thm)],[22,45,theory(equality)]) ).
cnf(158,plain,
multiply(multiply(a,c),X) = multiply(inverse(a),multiply(b,X)),
inference('PARAMODULATE',[status(thm)],[associativity,105,theory(equality)]) ).
cnf(178,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[23,73,theory(equality)]) ).
cnf(181,plain,
inverse(multiply(a,c)) = multiply(c,d),
inference('REWRITE',[status(thm)],[136,178,theory(equality)]) ).
cnf(200,plain,
inverse(multiply(X,inverse(Y))) = multiply(Y,inverse(X)),
inference('PARAMODULATE',[status(thm)],[27,74,theory(equality)]) ).
cnf(236,plain,
inverse(multiply(X,multiply(Y,X))) = multiply(multiply(Y,X),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[48,23,theory(equality)]),178,theory(equality)]) ).
cnf(240,plain,
multiply(multiply(X,Y),multiply(Y,Z)) = multiply(X,multiply(inverse(Y),Z)),
inference('PARAMODULATE',[status(thm)],[associativity,48,theory(equality)]) ).
cnf(241,plain,
multiply(d,X) = multiply(multiply(c,a),multiply(a,X)),
inference('REWRITE',[status(thm)],[26,240,theory(equality)]) ).
cnf(263,plain,
multiply(d,b) = inverse(multiply(inverse(a),multiply(b,a))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[241,a_times_b_is_c,theory(equality)]),45,103,236,theory(equality)]) ).
cnf(317,plain,
multiply(b,d) = multiply(d,b),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[50,181,theory(equality)]),263,158,178,theory(equality)]) ).
cnf(320,plain,
k = b,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[23,317,theory(equality)]),44,95,200,126,theory(equality)]) ).
cnf(321,plain,
$false,
inference('REWRITE',[status(thm)],[prove_k_times_inverse_b_is_e,right_inverse,320,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP002-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.04/0.14 % Command : run-snark %s %d
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 13 06:20:07 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.48 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.49 *
% 0.21/0.49 *
% 0.21/0.50 #<PACKAGE "SNARK-USER">
% 0.21/0.50 *
% 0.21/0.50 SNARK-TPTP-OPTIONS
% 0.21/0.50 *
% 0.21/0.50 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.21/0.50 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.21/0.50 (USE-FACTORING :POS)
% 0.21/0.50 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.21/0.50 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.21/0.50 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.21/0.50 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.21/0.50 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.21/0.50 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.21/0.50 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.21/0.50 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.21/0.50 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.21/0.50 (DECLARE-TPTP-SYMBOLS2))
% 0.21/0.50 *
% 0.21/0.50 "."
% 0.21/0.50 *
% 0.21/0.50 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T06:20:08
% 0.21/0.50 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n017.cluster.edu at 2022-06-13T06:20:08
% 0.21/0.51
% 0.21/0.51 ; Recognized left identity assertion (= (|multiply| |identity| ?X) ?X).
% 0.21/0.51 ; Recognized possible left inverse assertion (= (|multiply| (|inverse| ?X) ?X) |identity|).
% 0.21/0.51 ; Recognized associativity assertion (= (|multiply| (|multiply| ?X ?Y) ?Z) (|multiply| ?X (|multiply| ?Y ?Z))).
% 0.21/0.51 ; Recognized right identity assertion (= (|multiply| ?X |identity|) ?X).
% 0.46/0.65 ; Recognized possible right inverse assertion (= (|multiply| ?X (|inverse| ?X)) |identity|).
% 0.46/0.65
% 0.46/0.65 #||
% 0.46/0.65 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.65 % SZS output start Refutation
% See solution above
% 0.46/0.65 ||#
% 0.46/0.65
% 0.46/0.65 ; Summary of computation:
% 0.46/0.65 ; 1102 formulas have been input or derived (from 83 formulas).
% 0.46/0.65 ; 321 (29%) were retained. Of these,
% 0.46/0.65 ; 161 (50%) were simplified or subsumed later,
% 0.46/0.65 ; 160 (50%) are still being kept.
% 0.46/0.65 ;
% 0.46/0.65 ; Run time in seconds excluding printing time:
% 0.46/0.65 ; 0.002 1% Read assertion file (1 call)
% 0.46/0.65 ; 0.001 1% Assert (12 calls)
% 0.46/0.65 ; 0.031 21% Process new row (1,029 calls)
% 0.46/0.65 ; 0.006 4% Resolution (164 calls)
% 0.46/0.65 ; 0.013 9% Paramodulation (82 calls)
% 0.46/0.65 ; 0.035 23% Forward simplification (942 calls)
% 0.46/0.65 ; 0.012 8% Backward simplification (321 calls)
% 0.46/0.65 ; 0.021 14% Ordering (3,588 calls)
% 0.46/0.65 ; 0.000 0% Sortal reasoning (32 calls)
% 0.46/0.65 ; 0.000 0% Purity testing (1 call)
% 0.46/0.65 ; 0.028 19% Other
% 0.46/0.65 ; 0.149 Total
% 0.46/0.65 ; 0.154 Real time
% 0.46/0.65 ;
% 0.46/0.65 ; Term-hash-array has 827 terms in all.
% 0.46/0.65 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 0.46/0.65 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 0.46/0.65 ; Path-index has 468 entries (608 at peak, 870 added, 402 deleted).
% 0.46/0.65 ; Path-index has 395 nodes (456 at peak, 521 added, 126 deleted).
% 0.46/0.65 ; Trie-index has 468 entries (608 at peak, 870 added, 402 deleted).
% 0.46/0.65 ; Trie-index has 1,669 nodes (2,143 at peak, 2,955 added, 1,286 deleted).
% 0.46/0.65 ; Retrieved 5,906 generalization terms in 5,423 calls.
% 0.46/0.65 ; Retrieved 1,000 instance terms in 386 calls.
% 0.46/0.65 ; Retrieved 2,050 unifiable terms in 545 calls.
% 0.46/0.65 ;
% 0.46/0.65 ; The agenda of backward simplifiable rows to process has 49 entries:
% 0.46/0.65 ; 49 with value 0
% 0.46/0.65 ; The agenda of rows to process has 18 entries:
% 0.46/0.65 ; 3 with value 16 6 with value 18 6 with value 19
% 0.46/0.65 ; 3 with value 17
% 0.46/0.65 ; The agenda of rows to give has 117 entries:
% 0.46/0.65 ; 1 with value (4 9) 18 with value (4 19) 10 with value (4 22)
% 0.46/0.65 ; 11 with value (4 16) 22 with value (4 20) 6 with value (4 23)
% 0.46/0.65 ; 11 with value (4 17) 10 with value (4 21) 8 with value (4 24)
% 0.46/0.65 ; 20 with value (4 18)
% 0.46/0.65 Evaluation took:
% 0.46/0.65 0.154 seconds of real time
% 0.46/0.65 0.127803 seconds of user run time
% 0.46/0.65 0.025884 seconds of system run time
% 0.46/0.65 0 calls to %EVAL
% 0.46/0.65 0 page faults and
% 0.46/0.65 10,290,248 bytes consed.
% 0.46/0.65 :PROOF-FOUND
% 0.46/0.65 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-13T06:20:08
% 0.46/0.65 :PROOF-FOUND
% 0.46/0.65 *
%------------------------------------------------------------------------------