TSTP Solution File: GRP593-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP593-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% 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 : 300s
% DateTime : Wed Jul 27 12:57:19 EDT 2022
% Result : Unsatisfiable 1.93s 2.17s
% Output : Refutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 4 RR)
% Number of literals : 49 ( 48 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 133 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP593-1.p',unknown),
[] ).
cnf(2,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B)))))) = C,
file('GRP593-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP593-1.p',unknown),
[] ).
cnf(8,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(9,plain,
multiply(multiply(multiply(A,B),C),double_divide(C,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),8,8,8]),
[iquote('back_demod,4,demod,8,8,8')] ).
cnf(11,plain,
multiply(multiply(A,B),double_divide(B,multiply(multiply(C,A),D))) = double_divide(D,C),
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.1.1,9.1.1')] ).
cnf(13,plain,
multiply(A,double_divide(double_divide(B,C),multiply(C,A))) = B,
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.1,9.1.1')] ).
cnf(17,plain,
multiply(double_divide(A,B),double_divide(double_divide(C,multiply(multiply(B,D),A)),D)) = C,
inference(para_into,[status(thm),theory(equality)],[13,9]),
[iquote('para_into,13.1.1.2.2,9.1.1')] ).
cnf(36,plain,
double_divide(multiply(A,double_divide(B,multiply(C,A))),C) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,13])]),
[iquote('para_into,11.1.1,13.1.1,flip.1')] ).
cnf(67,plain,
double_divide(double_divide(multiply(A,B),C),multiply(C,A)) = B,
inference(para_into,[status(thm),theory(equality)],[36,11]),
[iquote('para_into,36.1.1.1,11.1.1')] ).
cnf(77,plain,
inverse(A) = multiply(B,multiply(C,double_divide(A,multiply(B,C)))),
inference(para_from,[status(thm),theory(equality)],[36,8]),
[iquote('para_from,36.1.1,7.1.1.1')] ).
cnf(79,plain,
multiply(A,multiply(B,double_divide(C,multiply(A,B)))) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[77])]),
[iquote('copy,77,flip.1')] ).
cnf(103,plain,
inverse(A) = multiply(multiply(B,C),double_divide(multiply(C,A),B)),
inference(para_from,[status(thm),theory(equality)],[67,8]),
[iquote('para_from,66.1.1,7.1.1.1')] ).
cnf(104,plain,
multiply(multiply(A,B),double_divide(multiply(B,C),A)) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[103])]),
[iquote('copy,103,flip.1')] ).
cnf(161,plain,
multiply(double_divide(A,B),double_divide(C,D)) = double_divide(multiply(A,C),multiply(B,D)),
inference(para_into,[status(thm),theory(equality)],[17,67]),
[iquote('para_into,17.1.1.2.1,66.1.1')] ).
cnf(215,plain,
multiply(inverse(A),double_divide(double_divide(multiply(B,A),C),C)) = B,
inference(para_from,[status(thm),theory(equality)],[104,9]),
[iquote('para_from,104.1.1,9.1.1.1')] ).
cnf(244,plain,
multiply(multiply(A,inverse(B)),multiply(C,B)) = multiply(A,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[215,79]),8])]),
[iquote('para_from,215.1.1,79.1.1.2,demod,8,flip.1')] ).
cnf(246,plain,
double_divide(multiply(A,B),multiply(C,inverse(B))) = double_divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[215,36])]),
[iquote('para_from,215.1.1,36.1.1.1,flip.1')] ).
cnf(359,plain,
double_divide(double_divide(A,B),multiply(multiply(B,inverse(C)),A)) = C,
inference(para_from,[status(thm),theory(equality)],[246,67]),
[iquote('para_from,246.1.1,66.1.1.1')] ).
cnf(361,plain,
double_divide(multiply(inverse(A),double_divide(B,C)),C) = multiply(B,A),
inference(para_from,[status(thm),theory(equality)],[246,36]),
[iquote('para_from,246.1.1,36.1.1.1.2')] ).
cnf(378,plain,
double_divide(A,multiply(multiply(B,inverse(C)),multiply(D,double_divide(A,multiply(B,D))))) = C,
inference(para_into,[status(thm),theory(equality)],[359,36]),
[iquote('para_into,359.1.1.1,36.1.1')] ).
cnf(406,plain,
double_divide(multiply(multiply(multiply(A,B),double_divide(multiply(B,C),A)),double_divide(D,E)),E) = multiply(D,C),
inference(para_into,[status(thm),theory(equality)],[361,103]),
[iquote('para_into,361.1.1.1.1,103.1.1')] ).
cnf(414,plain,
multiply(double_divide(multiply(A,B),C),B) = double_divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[361,215])]),
[iquote('para_into,361.1.1.1,215.1.1,flip.1')] ).
cnf(419,plain,
multiply(A,B) = double_divide(multiply(multiply(multiply(C,D),double_divide(multiply(D,B),C)),double_divide(A,E)),E),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[406])]),
[iquote('copy,406,flip.1')] ).
cnf(443,plain,
multiply(double_divide(double_divide(A,B),C),D) = double_divide(double_divide(multiply(A,D),B),C),
inference(para_into,[status(thm),theory(equality)],[414,414]),
[iquote('para_into,414.1.1.1.1,414.1.1')] ).
cnf(456,plain,
multiply(A,double_divide(A,multiply(B,C))) = double_divide(C,B),
inference(para_into,[status(thm),theory(equality)],[414,36]),
[iquote('para_into,414.1.1.1,36.1.1')] ).
cnf(493,plain,
multiply(multiply(A,inverse(B)),double_divide(C,D)) = multiply(A,double_divide(multiply(C,B),D)),
inference(para_from,[status(thm),theory(equality)],[414,244]),
[iquote('para_from,414.1.1,244.1.1.2')] ).
cnf(518,plain,
multiply(A,double_divide(multiply(B,C),D)) = multiply(multiply(A,inverse(C)),double_divide(B,D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[493])]),
[iquote('copy,493,flip.1')] ).
cnf(539,plain,
inverse(multiply(A,B)) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[456,104]),
[iquote('para_into,456.1.1,104.1.1')] ).
cnf(541,plain,
double_divide(double_divide(A,B),B) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[456,13])]),
[iquote('para_into,456.1.1,13.1.1,flip.1')] ).
cnf(583,plain,
multiply(inverse(A),multiply(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[215]),541]),
[iquote('back_demod,215,demod,541')] ).
cnf(597,plain,
multiply(A,double_divide(B,A)) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[456,79]),
[iquote('para_from,456.1.1,79.1.1.2')] ).
cnf(623,plain,
multiply(A,double_divide(B,multiply(C,A))) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[541,36])]),
[iquote('para_into,540.1.1.1,36.1.1,flip.1')] ).
cnf(638,plain,
double_divide(A,multiply(multiply(B,inverse(C)),double_divide(A,B))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[378]),623]),
[iquote('back_demod,378,demod,623')] ).
cnf(768,plain,
multiply(multiply(A,inverse(B)),double_divide(C,A)) = double_divide(B,C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[583,104]),539]),
[iquote('para_from,583.1.1,104.1.1.2.1,demod,539')] ).
cnf(776,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[638]),768]),
[iquote('back_demod,638,demod,768')] ).
cnf(788,plain,
double_divide(double_divide(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[776,776]),
[iquote('para_into,776.1.1.2,776.1.1')] ).
cnf(824,plain,
multiply(multiply(A,inverse(B)),C) = double_divide(B,double_divide(C,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[788,359])]),
[iquote('para_into,788.1.1.1,359.1.1,flip.1')] ).
cnf(830,plain,
multiply(A,double_divide(multiply(B,C),D)) = double_divide(C,double_divide(double_divide(B,D),A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[518]),824]),
[iquote('back_demod,518,demod,824')] ).
cnf(853,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[419]),830,161,443,67,541]),
[iquote('back_demod,419,demod,830,161,443,67,541')] ).
cnf(934,plain,
multiply(multiply(A,B),inverse(B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[853,583])]),
[iquote('para_into,853.1.1,583.1.1,flip.1')] ).
cnf(948,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(para_from,[status(thm),theory(equality)],[853,583]),
[iquote('para_from,853.1.1,583.1.1.2')] ).
cnf(966,plain,
multiply(b1,inverse(b1)) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[853,2]),
[iquote('para_from,853.1.1,2.1.1')] ).
cnf(1001,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[597,67]),8]),
[iquote('para_into,597.1.1.2,66.1.1,demod,8')] ).
cnf(1026,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[934]),1001]),
[iquote('back_demod,934,demod,1001')] ).
cnf(1226,plain,
multiply(inverse(A),A) = multiply(B,inverse(B)),
inference(para_from,[status(thm),theory(equality)],[1026,948]),
[iquote('para_from,1026.1.1,948.1.1.2')] ).
cnf(1227,plain,
multiply(A,inverse(A)) = multiply(inverse(B),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1226])]),
[iquote('copy,1226,flip.1')] ).
cnf(1228,plain,
$false,
inference(binary,[status(thm)],[1227,966]),
[iquote('binary,1227.1,966.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP593-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 05:26:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.93/2.17 ----- Otter 3.3f, August 2004 -----
% 1.93/2.17 The process was started by sandbox2 on n011.cluster.edu,
% 1.93/2.17 Wed Jul 27 05:26:55 2022
% 1.93/2.17 The command was "./otter". The process ID is 32662.
% 1.93/2.17
% 1.93/2.17 set(prolog_style_variables).
% 1.93/2.17 set(auto).
% 1.93/2.17 dependent: set(auto1).
% 1.93/2.17 dependent: set(process_input).
% 1.93/2.17 dependent: clear(print_kept).
% 1.93/2.17 dependent: clear(print_new_demod).
% 1.93/2.17 dependent: clear(print_back_demod).
% 1.93/2.17 dependent: clear(print_back_sub).
% 1.93/2.17 dependent: set(control_memory).
% 1.93/2.17 dependent: assign(max_mem, 12000).
% 1.93/2.17 dependent: assign(pick_given_ratio, 4).
% 1.93/2.17 dependent: assign(stats_level, 1).
% 1.93/2.17 dependent: assign(max_seconds, 10800).
% 1.93/2.17 clear(print_given).
% 1.93/2.17
% 1.93/2.17 list(usable).
% 1.93/2.17 0 [] A=A.
% 1.93/2.17 0 [] inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B))))))=C.
% 1.93/2.17 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.93/2.17 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.93/2.17 end_of_list.
% 1.93/2.17
% 1.93/2.17 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.93/2.17
% 1.93/2.17 All clauses are units, and equality is present; the
% 1.93/2.17 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.93/2.17
% 1.93/2.17 dependent: set(knuth_bendix).
% 1.93/2.17 dependent: set(anl_eq).
% 1.93/2.17 dependent: set(para_from).
% 1.93/2.17 dependent: set(para_into).
% 1.93/2.17 dependent: clear(para_from_right).
% 1.93/2.17 dependent: clear(para_into_right).
% 1.93/2.17 dependent: set(para_from_vars).
% 1.93/2.17 dependent: set(eq_units_both_ways).
% 1.93/2.17 dependent: set(dynamic_demod_all).
% 1.93/2.17 dependent: set(dynamic_demod).
% 1.93/2.17 dependent: set(order_eq).
% 1.93/2.17 dependent: set(back_demod).
% 1.93/2.17 dependent: set(lrpo).
% 1.93/2.17
% 1.93/2.17 ------------> process usable:
% 1.93/2.17 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.93/2.17
% 1.93/2.17 ------------> process sos:
% 1.93/2.17 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.93/2.17 ** KEPT (pick-wt=14): 4 [] inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B))))))=C.
% 1.93/2.17 ---> New Demodulator: 5 [new_demod,4] inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B))))))=C.
% 1.93/2.17 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.93/2.17 ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.93/2.17 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.93/2.17 >>>> Starting back demodulation with 5.
% 1.93/2.17 >>>> Starting back demodulation with 8.
% 1.93/2.17 >> back demodulating 4 with 8.
% 1.93/2.17 >>>> Starting back demodulation with 10.
% 1.93/2.17
% 1.93/2.17 ======= end of input processing =======
% 1.93/2.17
% 1.93/2.17 =========== start of search ===========
% 1.93/2.17
% 1.93/2.17
% 1.93/2.17 Resetting weight limit to 15.
% 1.93/2.17
% 1.93/2.17
% 1.93/2.17 Resetting weight limit to 15.
% 1.93/2.17
% 1.93/2.17 sos_size=294
% 1.93/2.17
% 1.93/2.17
% 1.93/2.17 Resetting weight limit to 9.
% 1.93/2.17
% 1.93/2.17
% 1.93/2.17 Resetting weight limit to 9.
% 1.93/2.17
% 1.93/2.17 sos_size=368
% 1.93/2.17
% 1.93/2.17 -------- PROOF --------
% 1.93/2.17
% 1.93/2.17 ----> UNIT CONFLICT at 0.05 sec ----> 1228 [binary,1227.1,966.1] $F.
% 1.93/2.17
% 1.93/2.17 Length of proof is 45. Level of proof is 24.
% 1.93/2.17
% 1.93/2.17 ---------------- PROOF ----------------
% 1.93/2.17 % SZS status Unsatisfiable
% 1.93/2.17 % SZS output start Refutation
% See solution above
% 1.93/2.17 ------------ end of proof -------------
% 1.93/2.17
% 1.93/2.17
% 1.93/2.17 Search stopped by max_proofs option.
% 1.93/2.17
% 1.93/2.17
% 1.93/2.17 Search stopped by max_proofs option.
% 1.93/2.17
% 1.93/2.17 ============ end of search ============
% 1.93/2.17
% 1.93/2.17 -------------- statistics -------------
% 1.93/2.17 clauses given 54
% 1.93/2.17 clauses generated 1476
% 1.93/2.17 clauses kept 872
% 1.93/2.17 clauses forward subsumed 1034
% 1.93/2.17 clauses back subsumed 0
% 1.93/2.17 Kbytes malloced 4882
% 1.93/2.17
% 1.93/2.17 ----------- times (seconds) -----------
% 1.93/2.17 user CPU time 0.05 (0 hr, 0 min, 0 sec)
% 1.93/2.17 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.17 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.93/2.17
% 1.93/2.17 That finishes the proof of the theorem.
% 1.93/2.17
% 1.93/2.17 Process 32662 finished Wed Jul 27 05:26:57 2022
% 1.93/2.17 Otter interrupted
% 1.93/2.17 PROOF FOUND
%------------------------------------------------------------------------------