TSTP Solution File: GRP510-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP510-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:57:09 EDT 2022
% Result : Unsatisfiable 1.74s 1.91s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 3 RR)
% Number of literals : 47 ( 46 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 143 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP510-1.p',unknown),
[] ).
cnf(4,axiom,
multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B,
file('GRP510-1.p',unknown),
[] ).
cnf(5,plain,
multiply(multiply(A,B),inverse(multiply(multiply(multiply(C,A),D),B))) = inverse(multiply(C,D)),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.1.1,3.1.1')] ).
cnf(7,plain,
multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) = C,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.1,3.1.1')] ).
cnf(9,plain,
multiply(multiply(multiply(multiply(multiply(A,B),C),D),inverse(multiply(A,C))),inverse(B)) = D,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.2.1,3.1.1')] ).
cnf(15,plain,
multiply(A,inverse(multiply(multiply(B,A),inverse(C)))) = inverse(multiply(multiply(D,B),inverse(multiply(D,C)))),
inference(para_into,[status(thm),theory(equality)],[7,7]),
[iquote('para_into,7.1.1.2.1.2.1,7.1.1')] ).
cnf(18,plain,
inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(D,inverse(multiply(multiply(B,D),inverse(C)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(23,plain,
multiply(multiply(A,B),inverse(multiply(C,B))) = inverse(multiply(multiply(D,C),inverse(multiply(D,A)))),
inference(para_from,[status(thm),theory(equality)],[7,4]),
[iquote('para_from,7.1.1,3.1.1.1.1')] ).
cnf(24,plain,
inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(multiply(C,D),inverse(multiply(B,D))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[23])]),
[iquote('copy,23,flip.1')] ).
cnf(31,plain,
multiply(multiply(inverse(multiply(multiply(A,B),inverse(multiply(A,C)))),D),inverse(multiply(multiply(C,E),D))) = inverse(multiply(B,E)),
inference(para_into,[status(thm),theory(equality)],[5,7]),
[iquote('para_into,5.1.1.2.1.1.1,7.1.1')] ).
cnf(34,plain,
multiply(multiply(A,B),inverse(multiply(C,B))) = inverse(multiply(D,inverse(multiply(multiply(E,multiply(D,A)),inverse(multiply(E,C)))))),
inference(para_into,[status(thm),theory(equality)],[5,7]),
[iquote('para_into,5.1.1.2.1.1,7.1.1')] ).
cnf(43,plain,
inverse(multiply(A,multiply(B,inverse(multiply(multiply(A,B),C))))) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,7])]),
[iquote('para_into,5.1.1,7.1.1,flip.1')] ).
cnf(44,plain,
inverse(multiply(A,B)) = multiply(multiply(inverse(multiply(multiply(C,A),inverse(multiply(C,D)))),E),inverse(multiply(multiply(D,B),E))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[31])]),
[iquote('copy,31,flip.1')] ).
cnf(62,plain,
inverse(multiply(multiply(A,multiply(B,C)),inverse(multiply(A,D)))) = inverse(multiply(B,multiply(C,inverse(D)))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[43,7])]),
[iquote('para_into,42.1.1.1.2.2.1,7.1.1,flip.1')] ).
cnf(73,plain,
multiply(multiply(A,B),inverse(multiply(C,B))) = inverse(multiply(D,inverse(multiply(D,multiply(A,inverse(C)))))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[34]),62]),
[iquote('back_demod,34,demod,62')] ).
cnf(80,plain,
multiply(multiply(multiply(A,B),multiply(C,inverse(multiply(multiply(A,C),D)))),D) = B,
inference(para_from,[status(thm),theory(equality)],[43,4]),
[iquote('para_from,42.1.1,3.1.1.2')] ).
cnf(94,plain,
multiply(multiply(A,inverse(B)),inverse(A)) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,9]),4]),
[iquote('para_into,9.1.1.1.1,9.1.1,demod,4')] ).
cnf(102,plain,
multiply(multiply(multiply(multiply(multiply(A,B),inverse(multiply(multiply(C,A),inverse(multiply(C,D))))),E),inverse(D)),inverse(B)) = E,
inference(para_into,[status(thm),theory(equality)],[9,7]),
[iquote('para_into,9.1.1.1.2.1,7.1.1')] ).
cnf(118,plain,
multiply(inverse(A),inverse(multiply(B,inverse(multiply(multiply(multiply(multiply(multiply(C,A),D),B),inverse(multiply(C,D))),E))))) = E,
inference(para_from,[status(thm),theory(equality)],[9,7]),
[iquote('para_from,9.1.1,7.1.1.2.1.1')] ).
cnf(127,plain,
multiply(multiply(A,B),inverse(A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[94,43]),43]),
[iquote('para_into,94.1.1.1.2,42.1.1,demod,43')] ).
cnf(133,plain,
inverse(multiply(multiply(A,B),inverse(multiply(A,C)))) = multiply(C,inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[94,7])]),
[iquote('para_into,94.1.1.1,7.1.1,flip.1')] ).
cnf(135,plain,
inverse(multiply(multiply(multiply(A,B),C),D)) = multiply(inverse(multiply(A,C)),inverse(multiply(B,D))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[94,5])]),
[iquote('para_into,94.1.1.1,5.1.1,flip.1')] ).
cnf(137,plain,
multiply(A,inverse(multiply(multiply(B,A),C))) = inverse(multiply(B,C)),
inference(para_into,[status(thm),theory(equality)],[94,4]),
[iquote('para_into,94.1.1.1,3.1.1')] ).
cnf(142,plain,
multiply(multiply(multiply(multiply(multiply(A,B),multiply(C,inverse(A))),D),inverse(C)),inverse(B)) = D,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[102]),133]),
[iquote('back_demod,102,demod,133')] ).
cnf(147,plain,
inverse(multiply(A,multiply(B,inverse(C)))) = multiply(C,inverse(multiply(A,B))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[62]),133])]),
[iquote('back_demod,61,demod,133,flip.1')] ).
cnf(150,plain,
inverse(multiply(A,B)) = multiply(multiply(multiply(C,inverse(A)),D),inverse(multiply(multiply(C,B),D))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),133]),
[iquote('back_demod,44,demod,133')] ).
cnf(155,plain,
multiply(multiply(A,B),inverse(multiply(C,B))) = multiply(A,inverse(C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[24]),133])]),
[iquote('back_demod,24,demod,133,flip.1')] ).
cnf(159,plain,
inverse(multiply(A,inverse(B))) = multiply(B,inverse(A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),133,137])]),
[iquote('back_demod,18,demod,133,137,flip.1')] ).
cnf(163,plain,
multiply(A,multiply(multiply(B,C),inverse(multiply(B,A)))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[7]),159]),
[iquote('back_demod,7,demod,159')] ).
cnf(167,plain,
multiply(inverse(A),multiply(multiply(B,C),multiply(A,inverse(B)))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[118]),135,155,127,147,159]),
[iquote('back_demod,118,demod,135,155,127,147,159')] ).
cnf(185,plain,
multiply(multiply(multiply(A,B),inverse(multiply(A,C))),C) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[80]),137]),
[iquote('back_demod,80,demod,137')] ).
cnf(193,plain,
multiply(multiply(A,B),inverse(multiply(A,C))) = multiply(B,inverse(C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[73]),155,147,147])]),
[iquote('back_demod,73,demod,155,147,147,flip.1')] ).
cnf(195,plain,
inverse(multiply(A,B)) = multiply(inverse(A),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[150])]),155,193])]),
[iquote('copy,150,flip.1,demod,155,193,flip.1')] ).
cnf(218,plain,
multiply(multiply(multiply(A,B),multiply(inverse(A),inverse(C))),C) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[185]),195]),
[iquote('back_demod,185,demod,195')] ).
cnf(222,plain,
multiply(A,multiply(multiply(B,C),multiply(inverse(B),inverse(A)))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[163]),195]),
[iquote('back_demod,163,demod,195')] ).
cnf(228,plain,
multiply(multiply(A,B),multiply(inverse(A),inverse(C))) = multiply(B,inverse(C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[193]),195]),
[iquote('back_demod,192,demod,195')] ).
cnf(271,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[222]),228]),
[iquote('back_demod,222,demod,228')] ).
cnf(275,plain,
multiply(multiply(A,inverse(B)),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[218]),228]),
[iquote('back_demod,218,demod,228')] ).
cnf(284,plain,
multiply(A,B) = multiply(B,A),
inference(para_into,[status(thm),theory(equality)],[275,127]),
[iquote('para_into,275.1.1.1,126.1.1')] ).
cnf(286,plain,
inverse(inverse(A)) = A,
inference(para_into,[status(thm),theory(equality)],[275,127]),
[iquote('para_into,275.1.1,126.1.1')] ).
cnf(326,plain,
multiply(multiply(multiply(A,B),multiply(inverse(B),inverse(A))),C) = C,
inference(para_into,[status(thm),theory(equality)],[142,275]),
[iquote('para_into,142.1.1,275.1.1')] ).
cnf(331,plain,
multiply(inverse(A),multiply(B,A)) = B,
inference(para_from,[status(thm),theory(equality)],[286,271]),
[iquote('para_from,285.1.1,271.1.1.2.2')] ).
cnf(340,plain,
multiply(multiply(b2,inverse(b2)),a2) != a2,
inference(para_from,[status(thm),theory(equality)],[284,1]),
[iquote('para_from,284.1.1,1.1.1.1')] ).
cnf(364,plain,
multiply(inverse(A),multiply(B,multiply(A,C))) = multiply(B,C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[167,331]),286]),
[iquote('para_into,167.1.1.2.1,331.1.1,demod,286')] ).
cnf(366,plain,
multiply(multiply(A,B),multiply(C,inverse(A))) = multiply(B,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[167,167]),286,364])]),
[iquote('para_into,167.1.1.2.1,167.1.1,demod,286,364,flip.1')] ).
cnf(377,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[326]),366]),
[iquote('back_demod,326,demod,366')] ).
cnf(379,plain,
$false,
inference(binary,[status(thm)],[377,340]),
[iquote('binary,377.1,340.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP510-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n022.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 05:05:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.74/1.91 ----- Otter 3.3f, August 2004 -----
% 1.74/1.91 The process was started by sandbox on n022.cluster.edu,
% 1.74/1.91 Wed Jul 27 05:05:35 2022
% 1.74/1.91 The command was "./otter". The process ID is 25078.
% 1.74/1.91
% 1.74/1.91 set(prolog_style_variables).
% 1.74/1.91 set(auto).
% 1.74/1.91 dependent: set(auto1).
% 1.74/1.91 dependent: set(process_input).
% 1.74/1.91 dependent: clear(print_kept).
% 1.74/1.91 dependent: clear(print_new_demod).
% 1.74/1.91 dependent: clear(print_back_demod).
% 1.74/1.91 dependent: clear(print_back_sub).
% 1.74/1.91 dependent: set(control_memory).
% 1.74/1.91 dependent: assign(max_mem, 12000).
% 1.74/1.91 dependent: assign(pick_given_ratio, 4).
% 1.74/1.91 dependent: assign(stats_level, 1).
% 1.74/1.91 dependent: assign(max_seconds, 10800).
% 1.74/1.91 clear(print_given).
% 1.74/1.91
% 1.74/1.91 list(usable).
% 1.74/1.91 0 [] A=A.
% 1.74/1.91 0 [] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C)))=B.
% 1.74/1.91 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.74/1.91 end_of_list.
% 1.74/1.91
% 1.74/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.74/1.91
% 1.74/1.91 All clauses are units, and equality is present; the
% 1.74/1.91 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.74/1.91
% 1.74/1.91 dependent: set(knuth_bendix).
% 1.74/1.91 dependent: set(anl_eq).
% 1.74/1.91 dependent: set(para_from).
% 1.74/1.91 dependent: set(para_into).
% 1.74/1.91 dependent: clear(para_from_right).
% 1.74/1.91 dependent: clear(para_into_right).
% 1.74/1.91 dependent: set(para_from_vars).
% 1.74/1.91 dependent: set(eq_units_both_ways).
% 1.74/1.91 dependent: set(dynamic_demod_all).
% 1.74/1.91 dependent: set(dynamic_demod).
% 1.74/1.91 dependent: set(order_eq).
% 1.74/1.91 dependent: set(back_demod).
% 1.74/1.91 dependent: set(lrpo).
% 1.74/1.91
% 1.74/1.91 ------------> process usable:
% 1.74/1.91 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.74/1.91
% 1.74/1.91 ------------> process sos:
% 1.74/1.91 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.74/1.91 ** KEPT (pick-wt=12): 3 [] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C)))=B.
% 1.74/1.91 ---> New Demodulator: 4 [new_demod,3] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C)))=B.
% 1.74/1.91 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.74/1.91 >>>> Starting back demodulation with 4.
% 1.74/1.91
% 1.74/1.91 ======= end of input processing =======
% 1.74/1.91
% 1.74/1.91 =========== start of search ===========
% 1.74/1.91
% 1.74/1.91 -------- PROOF --------
% 1.74/1.91
% 1.74/1.91 ----> UNIT CONFLICT at 0.01 sec ----> 379 [binary,377.1,340.1] $F.
% 1.74/1.91
% 1.74/1.91 Length of proof is 44. Level of proof is 13.
% 1.74/1.91
% 1.74/1.91 ---------------- PROOF ----------------
% 1.74/1.91 % SZS status Unsatisfiable
% 1.74/1.91 % SZS output start Refutation
% See solution above
% 1.74/1.91 ------------ end of proof -------------
% 1.74/1.91
% 1.74/1.91
% 1.74/1.91 Search stopped by max_proofs option.
% 1.74/1.91
% 1.74/1.91
% 1.74/1.91 Search stopped by max_proofs option.
% 1.74/1.91
% 1.74/1.91 ============ end of search ============
% 1.74/1.91
% 1.74/1.91 -------------- statistics -------------
% 1.74/1.91 clauses given 21
% 1.74/1.91 clauses generated 295
% 1.74/1.91 clauses kept 216
% 1.74/1.91 clauses forward subsumed 279
% 1.74/1.91 clauses back subsumed 2
% 1.74/1.91 Kbytes malloced 2929
% 1.74/1.91
% 1.74/1.91 ----------- times (seconds) -----------
% 1.74/1.91 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.74/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.91 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.74/1.91
% 1.74/1.91 That finishes the proof of the theorem.
% 1.74/1.91
% 1.74/1.91 Process 25078 finished Wed Jul 27 05:05:37 2022
% 1.74/1.91 Otter interrupted
% 1.74/1.91 PROOF FOUND
%------------------------------------------------------------------------------