TSTP Solution File: GRP403-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP403-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 12:56:57 EDT 2022
% Result : Unsatisfiable 1.79s 2.04s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of clauses : 26 ( 26 unt; 0 nHn; 4 RR)
% Number of literals : 26 ( 25 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 14 ( 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 : 100 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP403-1.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(5,axiom,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B)))))) = C,
file('GRP403-1.p',unknown),
[] ).
cnf(6,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(B),C)),inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D))))),multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D)))))),inverse(multiply(inverse(multiply(inverse(multiply(A,D)),B)),inverse(multiply(D,multiply(inverse(D),D))))))))))) = C,
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.2.1.1.1.1.1,4.1.1')] ).
cnf(8,plain,
inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),D)),inverse(multiply(C,multiply(inverse(C),C))))) = multiply(A,inverse(multiply(inverse(D),inverse(multiply(B,multiply(inverse(B),B)))))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,5])]),
[iquote('para_into,4.1.1.2.1.1.1,4.1.1,flip.1')] ).
cnf(22,plain,
multiply(inverse(multiply(A,B)),multiply(A,inverse(multiply(inverse(C),inverse(multiply(B,multiply(inverse(B),B))))))) = C,
inference(para_from,[status(thm),theory(equality)],[8,5]),
[iquote('para_from,8.1.1,4.1.1.2')] ).
cnf(37,plain,
multiply(inverse(multiply(A,B)),multiply(A,multiply(C,inverse(multiply(inverse(D),inverse(multiply(E,multiply(inverse(E),E)))))))) = multiply(inverse(multiply(inverse(multiply(C,E)),B)),D),
inference(para_into,[status(thm),theory(equality)],[22,8]),
[iquote('para_into,22.1.1.2.2,8.1.1')] ).
cnf(102,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(inverse(D),B)),multiply(inverse(D),C)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[6,37]),5]),
[iquote('para_from,6.1.1,37.1.1.2.2,demod,5')] ).
cnf(107,plain,
multiply(inverse(multiply(inverse(A),B)),multiply(inverse(A),C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[102])]),
[iquote('copy,102,flip.1')] ).
cnf(141,plain,
multiply(inverse(multiply(A,B)),multiply(A,C)) = multiply(inverse(multiply(D,B)),multiply(D,C)),
inference(para_into,[status(thm),theory(equality)],[107,107]),
[iquote('para_into,107.1.1,107.1.1')] ).
cnf(157,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,C))),inverse(multiply(B,multiply(inverse(B),B))))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[141,8]),5]),
[iquote('para_from,141.1.1,8.1.1.1.1.1,demod,5')] ).
cnf(159,plain,
multiply(inverse(multiply(A,multiply(B,C))),multiply(A,inverse(multiply(inverse(D),inverse(multiply(multiply(B,C),multiply(inverse(multiply(E,C)),multiply(E,C)))))))) = D,
inference(para_from,[status(thm),theory(equality)],[141,22]),
[iquote('para_from,141.1.1,22.1.1.2.2.1.2.1.2')] ).
cnf(161,plain,
multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),D)),inverse(multiply(multiply(B,C),multiply(inverse(multiply(E,C)),multiply(E,C))))))) = D,
inference(para_from,[status(thm),theory(equality)],[141,5]),
[iquote('para_from,141.1.1,4.1.1.2.1.2.1.2')] ).
cnf(173,plain,
inverse(multiply(inverse(multiply(inverse(multiply(A,multiply(B,C))),multiply(A,D))),inverse(multiply(multiply(B,C),multiply(inverse(multiply(E,C)),multiply(E,C)))))) = D,
inference(para_into,[status(thm),theory(equality)],[157,141]),
[iquote('para_into,157.1.1.1.2.1.2,141.1.1')] ).
cnf(177,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(inverse(multiply(E,inverse(multiply(C,multiply(inverse(C),C))))),multiply(E,D)),
inference(para_from,[status(thm),theory(equality)],[157,141]),
[iquote('para_from,157.1.1,141.1.1.1')] ).
cnf(181,plain,
multiply(inverse(multiply(A,inverse(multiply(B,multiply(inverse(B),B))))),multiply(A,C)) = multiply(D,multiply(inverse(multiply(inverse(multiply(E,B)),multiply(E,D))),C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[177])]),
[iquote('copy,177,flip.1')] ).
cnf(286,plain,
multiply(inverse(multiply(A,B)),inverse(multiply(C,inverse(multiply(multiply(A,C),multiply(inverse(multiply(D,C)),multiply(D,C))))))) = inverse(multiply(B,multiply(inverse(B),B))),
inference(para_into,[status(thm),theory(equality)],[161,157]),
[iquote('para_into,161.1.1.2.1.1,157.1.1')] ).
cnf(291,plain,
multiply(inverse(multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(B,multiply(C,D))),E)),inverse(multiply(multiply(C,D),multiply(inverse(multiply(F,D)),multiply(F,D)))))))),multiply(A,G)) = multiply(inverse(E),multiply(B,G)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[161,141])]),
[iquote('para_from,161.1.1,141.1.1.1.1,flip.1')] ).
cnf(311,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),D)) = multiply(E,multiply(inverse(multiply(inverse(multiply(F,C)),multiply(F,E))),D)),
inference(para_into,[status(thm),theory(equality)],[181,157]),
[iquote('para_into,181.1.1.1,157.1.1')] ).
cnf(314,plain,
multiply(A,multiply(inverse(multiply(inverse(B),multiply(C,A))),D)) = multiply(E,multiply(inverse(multiply(inverse(B),multiply(C,E))),D)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[311,161]),291]),
[iquote('para_into,311.1.1.2.1.1.1.1,161.1.1,demod,291')] ).
cnf(315,plain,
multiply(A,multiply(inverse(multiply(B,multiply(C,A))),D)) = multiply(E,multiply(inverse(multiply(B,multiply(C,E))),D)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[314,173]),173]),
[iquote('para_into,314.1.1.2.1.1.1,172.1.1,demod,173')] ).
cnf(323,plain,
multiply(inverse(multiply(inverse(multiply(A,B)),multiply(A,inverse(C)))),inverse(multiply(B,multiply(inverse(B),B)))) = C,
inference(para_from,[status(thm),theory(equality)],[286,159]),
[iquote('para_from,286.1.1,159.1.1.2')] ).
cnf(329,plain,
multiply(inverse(A),A) = multiply(B,multiply(inverse(multiply(inverse(multiply(C,D)),multiply(C,B))),inverse(multiply(D,multiply(inverse(D),D))))),
inference(para_from,[status(thm),theory(equality)],[323,315]),
[iquote('para_from,323.1.1,315.1.1.2')] ).
cnf(331,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),inverse(multiply(C,multiply(inverse(C),C))))) = multiply(inverse(D),D),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[329])]),
[iquote('copy,329,flip.1')] ).
cnf(333,plain,
multiply(A,multiply(inverse(multiply(inverse(multiply(B,C)),multiply(B,A))),inverse(multiply(C,multiply(inverse(C),C))))) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[329,2]),
[iquote('para_from,329.1.1,2.1.1')] ).
cnf(334,plain,
$false,
inference(binary,[status(thm)],[333,331]),
[iquote('binary,333.1,331.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP403-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n010.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 05:23:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.79/2.04 ----- Otter 3.3f, August 2004 -----
% 1.79/2.04 The process was started by sandbox2 on n010.cluster.edu,
% 1.79/2.04 Wed Jul 27 05:23:40 2022
% 1.79/2.04 The command was "./otter". The process ID is 27779.
% 1.79/2.04
% 1.79/2.04 set(prolog_style_variables).
% 1.79/2.04 set(auto).
% 1.79/2.04 dependent: set(auto1).
% 1.79/2.04 dependent: set(process_input).
% 1.79/2.04 dependent: clear(print_kept).
% 1.79/2.04 dependent: clear(print_new_demod).
% 1.79/2.04 dependent: clear(print_back_demod).
% 1.79/2.04 dependent: clear(print_back_sub).
% 1.79/2.04 dependent: set(control_memory).
% 1.79/2.04 dependent: assign(max_mem, 12000).
% 1.79/2.04 dependent: assign(pick_given_ratio, 4).
% 1.79/2.04 dependent: assign(stats_level, 1).
% 1.79/2.04 dependent: assign(max_seconds, 10800).
% 1.79/2.04 clear(print_given).
% 1.79/2.04
% 1.79/2.04 list(usable).
% 1.79/2.04 0 [] A=A.
% 1.79/2.04 0 [] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B))))))=C.
% 1.79/2.04 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.79/2.04 end_of_list.
% 1.79/2.04
% 1.79/2.04 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.79/2.04
% 1.79/2.04 All clauses are units, and equality is present; the
% 1.79/2.04 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.79/2.04
% 1.79/2.04 dependent: set(knuth_bendix).
% 1.79/2.04 dependent: set(anl_eq).
% 1.79/2.04 dependent: set(para_from).
% 1.79/2.04 dependent: set(para_into).
% 1.79/2.04 dependent: clear(para_from_right).
% 1.79/2.04 dependent: clear(para_into_right).
% 1.79/2.04 dependent: set(para_from_vars).
% 1.79/2.04 dependent: set(eq_units_both_ways).
% 1.79/2.04 dependent: set(dynamic_demod_all).
% 1.79/2.04 dependent: set(dynamic_demod).
% 1.79/2.04 dependent: set(order_eq).
% 1.79/2.04 dependent: set(back_demod).
% 1.79/2.04 dependent: set(lrpo).
% 1.79/2.04
% 1.79/2.04 ------------> process usable:
% 1.79/2.04 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.79/2.04
% 1.79/2.04 ------------> process sos:
% 1.79/2.04 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.79/2.04 ** KEPT (pick-wt=20): 4 [] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B))))))=C.
% 1.79/2.04 ---> New Demodulator: 5 [new_demod,4] multiply(A,inverse(multiply(inverse(multiply(inverse(multiply(A,B)),C)),inverse(multiply(B,multiply(inverse(B),B))))))=C.
% 1.79/2.04 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.79/2.04 >>>> Starting back demodulation with 5.
% 1.79/2.04
% 1.79/2.04 ======= end of input processing =======
% 1.79/2.04
% 1.79/2.04 =========== start of search ===========
% 1.79/2.04
% 1.79/2.04
% 1.79/2.04 Resetting weight limit to 38.
% 1.79/2.04
% 1.79/2.04
% 1.79/2.04 Resetting weight limit to 38.
% 1.79/2.04
% 1.79/2.04 sos_size=64
% 1.79/2.04
% 1.79/2.04
% 1.79/2.04 Resetting weight limit to 30.
% 1.79/2.04
% 1.79/2.04
% 1.79/2.04 Resetting weight limit to 30.
% 1.79/2.04
% 1.79/2.04 sos_size=159
% 1.79/2.04
% 1.79/2.04 -------- PROOF --------
% 1.79/2.04
% 1.79/2.04 ----> UNIT CONFLICT at 0.18 sec ----> 334 [binary,333.1,331.1] $F.
% 1.79/2.04
% 1.79/2.04 Length of proof is 23. Level of proof is 14.
% 1.79/2.04
% 1.79/2.04 ---------------- PROOF ----------------
% 1.79/2.04 % SZS status Unsatisfiable
% 1.79/2.04 % SZS output start Refutation
% See solution above
% 1.79/2.04 ------------ end of proof -------------
% 1.79/2.04
% 1.79/2.04
% 1.79/2.04 Search stopped by max_proofs option.
% 1.79/2.04
% 1.79/2.04
% 1.79/2.04 Search stopped by max_proofs option.
% 1.79/2.04
% 1.79/2.04 ============ end of search ============
% 1.79/2.04
% 1.79/2.04 -------------- statistics -------------
% 1.79/2.04 clauses given 39
% 1.79/2.04 clauses generated 4645
% 1.79/2.04 clauses kept 268
% 1.79/2.04 clauses forward subsumed 811
% 1.79/2.04 clauses back subsumed 44
% 1.79/2.04 Kbytes malloced 6835
% 1.79/2.04
% 1.79/2.04 ----------- times (seconds) -----------
% 1.79/2.04 user CPU time 0.18 (0 hr, 0 min, 0 sec)
% 1.79/2.04 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.79/2.04 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.79/2.04
% 1.79/2.04 That finishes the proof of the theorem.
% 1.79/2.04
% 1.79/2.04 Process 27779 finished Wed Jul 27 05:23:41 2022
% 1.79/2.04 Otter interrupted
% 1.79/2.04 PROOF FOUND
%------------------------------------------------------------------------------