TSTP Solution File: GRP433-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP433-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 12:57:00 EDT 2022
% Result : Unsatisfiable 1.65s 1.91s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 4 RR)
% Number of literals : 47 ( 46 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 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 : 125 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP433-1.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(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = C,
file('GRP433-1.p',unknown),
[] ).
cnf(6,plain,
inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D)))) = multiply(E,inverse(E)),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.1.1.1,4.1.1')] ).
cnf(14,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(para_into,[status(thm),theory(equality)],[6,6]),
[iquote('para_into,6.1.1,6.1.1')] ).
cnf(28,plain,
inverse(multiply(multiply(multiply(inverse(multiply(A,inverse(A))),B),C),multiply(D,inverse(D)))) = inverse(multiply(B,C)),
inference(para_from,[status(thm),theory(equality)],[14,4]),
[iquote('para_from,14.1.1,4.1.1.1.1.1.1.1')] ).
cnf(29,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),B)),C),inverse(C)),multiply(D,inverse(D)))) = B,
inference(para_from,[status(thm),theory(equality)],[14,4]),
[iquote('para_from,14.1.1,4.1.1.1.1.1.1.1.1')] ).
cnf(39,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(C,inverse(C)))) = inverse(multiply(inverse(inverse(multiply(D,inverse(D)))),B)),
inference(para_into,[status(thm),theory(equality)],[28,14]),
[iquote('para_into,27.1.1.1.1.1,14.1.1')] ).
cnf(48,plain,
inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),B)) = inverse(multiply(multiply(multiply(C,inverse(C)),B),multiply(D,inverse(D)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[39])]),
[iquote('copy,39,flip.1')] ).
cnf(105,plain,
inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[29,14]),28]),
[iquote('para_into,29.1.1.1.1.1.1.1,14.1.1,demod,28')] ).
cnf(158,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(C,inverse(C)),
inference(para_from,[status(thm),theory(equality)],[105,14]),
[iquote('para_from,105.1.1,14.1.1.2')] ).
cnf(172,plain,
multiply(A,inverse(A)) = multiply(multiply(B,inverse(B)),inverse(multiply(C,inverse(C)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[158])]),
[iquote('copy,158,flip.1')] ).
cnf(203,plain,
inverse(multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(B))) = multiply(C,inverse(C)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[158,6]),28]),
[iquote('para_from,158.1.1,6.1.1.1.1.1.2.1.1,demod,28')] ).
cnf(221,plain,
inverse(multiply(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),inverse(inverse(inverse(multiply(multiply(C,inverse(C)),D))))),multiply(E,inverse(E)))) = D,
inference(para_from,[status(thm),theory(equality)],[172,29]),
[iquote('para_from,172.1.1,29.1.1.1.1.1')] ).
cnf(224,plain,
inverse(multiply(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),C),multiply(D,inverse(D)))) = inverse(multiply(inverse(inverse(multiply(E,inverse(E)))),C)),
inference(para_from,[status(thm),theory(equality)],[172,28]),
[iquote('para_from,172.1.1,27.1.1.1.1.1')] ).
cnf(236,plain,
inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),B)) = inverse(multiply(multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))),B),multiply(E,inverse(E)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[224])]),
[iquote('copy,224,flip.1')] ).
cnf(297,plain,
inverse(multiply(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),C),multiply(D,inverse(D)))) = inverse(C),
inference(para_from,[status(thm),theory(equality)],[203,4]),
[iquote('para_from,203.1.1,4.1.1.1.1.1.1')] ).
cnf(300,plain,
inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),B)) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[236]),297]),
[iquote('back_demod,236,demod,297')] ).
cnf(302,plain,
inverse(inverse(inverse(inverse(multiply(multiply(A,inverse(A)),B))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[221]),297]),
[iquote('back_demod,221,demod,297')] ).
cnf(305,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(C,inverse(C)))) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[48]),300])]),
[iquote('back_demod,48,demod,300,flip.1')] ).
cnf(333,plain,
inverse(inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(multiply(multiply(A,inverse(A)),B)))),B),C))))) = C,
inference(para_into,[status(thm),theory(equality)],[302,302]),
[iquote('para_into,301.1.1.1.1.1.1.1.2,301.1.1')] ).
cnf(335,plain,
inverse(inverse(inverse(inverse(multiply(multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),B),inverse(B)),C))))) = C,
inference(para_into,[status(thm),theory(equality)],[302,300]),
[iquote('para_into,301.1.1.1.1.1.1.1.2,299.1.1')] ).
cnf(344,plain,
multiply(inverse(inverse(inverse(multiply(multiply(A,inverse(A)),B)))),B) = multiply(C,inverse(C)),
inference(para_from,[status(thm),theory(equality)],[302,14]),
[iquote('para_from,301.1.1,14.1.1.2')] ).
cnf(351,plain,
multiply(A,inverse(A)) = multiply(inverse(inverse(inverse(multiply(multiply(B,inverse(B)),C)))),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[344])]),
[iquote('copy,344,flip.1')] ).
cnf(379,plain,
inverse(multiply(multiply(multiply(inverse(inverse(inverse(multiply(multiply(A,inverse(A)),B)))),B),C),multiply(D,inverse(D)))) = inverse(C),
inference(para_into,[status(thm),theory(equality)],[305,302]),
[iquote('para_into,305.1.1.1.1.1.2,301.1.1')] ).
cnf(388,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))))) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[305,105]),
[iquote('para_into,305.1.1.1.2.2,105.1.1')] ).
cnf(390,plain,
inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(A))))))) = multiply(B,inverse(B)),
inference(para_from,[status(thm),theory(equality)],[305,302]),
[iquote('para_from,305.1.1,301.1.1.1.1.1')] ).
cnf(433,plain,
inverse(inverse(multiply(A,inverse(A)))) = multiply(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[390,105]),302]),
[iquote('para_into,390.1.1.1.1.1.1.1.2,105.1.1,demod,302')] ).
cnf(471,plain,
inverse(multiply(multiply(A,inverse(A)),B)) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[433,300]),
[iquote('para_from,433.1.1,299.1.1.1.1')] ).
cnf(472,plain,
inverse(multiply(multiply(multiply(inverse(A),inverse(multiply(B,inverse(B)))),multiply(C,inverse(C))),multiply(D,inverse(D)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[433,29]),471]),
[iquote('para_from,433.1.1,29.1.1.1.1.2,demod,471')] ).
cnf(509,plain,
inverse(multiply(multiply(multiply(inverse(inverse(inverse(A))),A),B),multiply(C,inverse(C)))) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[379]),471]),
[iquote('back_demod,379,demod,471')] ).
cnf(521,plain,
multiply(A,inverse(A)) = multiply(inverse(inverse(inverse(B))),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[351]),471]),
[iquote('back_demod,351,demod,471')] ).
cnf(528,plain,
multiply(inverse(inverse(inverse(A))),A) = multiply(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[344]),471]),
[iquote('back_demod,344,demod,471')] ).
cnf(531,plain,
inverse(inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(A))),A),B))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[333]),471]),
[iquote('back_demod,333,demod,471')] ).
cnf(538,plain,
inverse(inverse(inverse(inverse(A)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[302]),471]),
[iquote('back_demod,301,demod,471')] ).
cnf(574,plain,
multiply(multiply(inverse(inverse(inverse(A))),A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[531]),538]),
[iquote('back_demod,531,demod,538')] ).
cnf(603,plain,
multiply(multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),B),inverse(B)),C) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[335]),538]),
[iquote('back_demod,335,demod,538')] ).
cnf(614,plain,
inverse(multiply(A,multiply(B,inverse(B)))) = inverse(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[509]),574]),
[iquote('back_demod,509,demod,574')] ).
cnf(629,plain,
inverse(multiply(inverse(A),inverse(multiply(B,inverse(B))))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[472]),614,614]),
[iquote('back_demod,472,demod,614,614')] ).
cnf(642,plain,
multiply(inverse(inverse(multiply(A,inverse(A)))),B) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[538,300]),538])]),
[iquote('para_into,537.1.1.1.1.1,299.1.1,demod,538,flip.1')] ).
cnf(644,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[603]),642]),
[iquote('back_demod,603,demod,642')] ).
cnf(662,plain,
inverse(multiply(A,inverse(multiply(B,inverse(B))))) = inverse(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[388]),644,644]),
[iquote('back_demod,388,demod,644,644')] ).
cnf(670,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[629]),662]),
[iquote('back_demod,629,demod,662')] ).
cnf(681,plain,
multiply(inverse(A),A) = multiply(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[528]),670]),
[iquote('back_demod,528,demod,670')] ).
cnf(683,plain,
multiply(A,inverse(A)) = multiply(inverse(B),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[521]),670]),
[iquote('back_demod,521,demod,670')] ).
cnf(687,plain,
multiply(A,inverse(A)) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[681,2]),
[iquote('para_from,681.1.1,2.1.1')] ).
cnf(688,plain,
$false,
inference(binary,[status(thm)],[687,683]),
[iquote('binary,687.1,683.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP433-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 05:12:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.65/1.91 ----- Otter 3.3f, August 2004 -----
% 1.65/1.91 The process was started by sandbox on n019.cluster.edu,
% 1.65/1.91 Wed Jul 27 05:12:52 2022
% 1.65/1.91 The command was "./otter". The process ID is 27911.
% 1.65/1.91
% 1.65/1.91 set(prolog_style_variables).
% 1.65/1.91 set(auto).
% 1.65/1.91 dependent: set(auto1).
% 1.65/1.91 dependent: set(process_input).
% 1.65/1.91 dependent: clear(print_kept).
% 1.65/1.91 dependent: clear(print_new_demod).
% 1.65/1.91 dependent: clear(print_back_demod).
% 1.65/1.91 dependent: clear(print_back_sub).
% 1.65/1.91 dependent: set(control_memory).
% 1.65/1.91 dependent: assign(max_mem, 12000).
% 1.65/1.91 dependent: assign(pick_given_ratio, 4).
% 1.65/1.91 dependent: assign(stats_level, 1).
% 1.65/1.91 dependent: assign(max_seconds, 10800).
% 1.65/1.91 clear(print_given).
% 1.65/1.91
% 1.65/1.91 list(usable).
% 1.65/1.91 0 [] A=A.
% 1.65/1.91 0 [] inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D))))=C.
% 1.65/1.91 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.65/1.91 end_of_list.
% 1.65/1.91
% 1.65/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.65/1.91
% 1.65/1.91 All clauses are units, and equality is present; the
% 1.65/1.91 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.65/1.91
% 1.65/1.91 dependent: set(knuth_bendix).
% 1.65/1.91 dependent: set(anl_eq).
% 1.65/1.91 dependent: set(para_from).
% 1.65/1.91 dependent: set(para_into).
% 1.65/1.91 dependent: clear(para_from_right).
% 1.65/1.91 dependent: clear(para_into_right).
% 1.65/1.91 dependent: set(para_from_vars).
% 1.65/1.91 dependent: set(eq_units_both_ways).
% 1.65/1.91 dependent: set(dynamic_demod_all).
% 1.65/1.91 dependent: set(dynamic_demod).
% 1.65/1.91 dependent: set(order_eq).
% 1.65/1.91 dependent: set(back_demod).
% 1.65/1.91 dependent: set(lrpo).
% 1.65/1.91
% 1.65/1.91 ------------> process usable:
% 1.65/1.91 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.65/1.91
% 1.65/1.91 ------------> process sos:
% 1.65/1.91 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.65/1.91 ** KEPT (pick-wt=18): 4 [] inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D))))=C.
% 1.65/1.91 ---> New Demodulator: 5 [new_demod,4] inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D))))=C.
% 1.65/1.91 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.65/1.91 >>>> Starting back demodulation with 5.
% 1.65/1.91
% 1.65/1.91 ======= end of input processing =======
% 1.65/1.91
% 1.65/1.91 =========== start of search ===========
% 1.65/1.91
% 1.65/1.91
% 1.65/1.91 Resetting weight limit to 22.
% 1.65/1.91
% 1.65/1.91
% 1.65/1.91 Resetting weight limit to 22.
% 1.65/1.91
% 1.65/1.91 sos_size=205
% 1.65/1.91
% 1.65/1.91 -------- PROOF --------
% 1.65/1.91
% 1.65/1.91 ----> UNIT CONFLICT at 0.04 sec ----> 688 [binary,687.1,683.1] $F.
% 1.65/1.91
% 1.65/1.91 Length of proof is 44. Level of proof is 20.
% 1.65/1.91
% 1.65/1.91 ---------------- PROOF ----------------
% 1.65/1.91 % SZS status Unsatisfiable
% 1.65/1.91 % SZS output start Refutation
% See solution above
% 1.65/1.92 ------------ end of proof -------------
% 1.65/1.92
% 1.65/1.92
% 1.65/1.92 Search stopped by max_proofs option.
% 1.65/1.92
% 1.65/1.92
% 1.65/1.92 Search stopped by max_proofs option.
% 1.65/1.92
% 1.65/1.92 ============ end of search ============
% 1.65/1.92
% 1.65/1.92 -------------- statistics -------------
% 1.65/1.92 clauses given 29
% 1.65/1.92 clauses generated 1050
% 1.65/1.92 clauses kept 544
% 1.65/1.92 clauses forward subsumed 749
% 1.65/1.92 clauses back subsumed 0
% 1.65/1.92 Kbytes malloced 6835
% 1.65/1.92
% 1.65/1.92 ----------- times (seconds) -----------
% 1.65/1.92 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.65/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.65/1.92
% 1.65/1.92 That finishes the proof of the theorem.
% 1.65/1.92
% 1.65/1.92 Process 27911 finished Wed Jul 27 05:12:53 2022
% 1.65/1.92 Otter interrupted
% 1.65/1.92 PROOF FOUND
%------------------------------------------------------------------------------