TSTP Solution File: GRP512-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP512-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 12:57:09 EDT 2022
% Result : Unsatisfiable 1.59s 1.77s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of clauses : 30 ( 30 unt; 0 nHn; 3 RR)
% Number of literals : 30 ( 29 equ; 2 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP512-1.p',unknown),
[] ).
cnf(2,plain,
multiply(b,a) != multiply(a,b),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(5,axiom,
multiply(multiply(multiply(A,B),C),inverse(multiply(A,C))) = B,
file('GRP512-1.p',unknown),
[] ).
cnf(6,plain,
multiply(multiply(A,B),inverse(multiply(multiply(multiply(C,A),D),B))) = inverse(multiply(C,D)),
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.1.1,4.1.1')] ).
cnf(8,plain,
multiply(A,inverse(multiply(multiply(B,A),inverse(multiply(B,C))))) = C,
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.1,4.1.1')] ).
cnf(10,plain,
multiply(multiply(multiply(multiply(multiply(A,B),C),D),inverse(multiply(A,C))),inverse(B)) = D,
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.2.1,4.1.1')] ).
cnf(24,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)],[8,5]),
[iquote('para_from,8.1.1,4.1.1.1.1')] ).
cnf(25,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)],[24])]),
[iquote('copy,24,flip.1')] ).
cnf(32,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)],[6,8]),
[iquote('para_into,6.1.1.2.1.1.1,8.1.1')] ).
cnf(35,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)],[6,8]),
[iquote('para_into,6.1.1.2.1.1,8.1.1')] ).
cnf(44,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)],[6,8])]),
[iquote('para_into,6.1.1,8.1.1,flip.1')] ).
cnf(45,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)],[32])]),
[iquote('copy,32,flip.1')] ).
cnf(63,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)],[44,8])]),
[iquote('para_into,43.1.1.1.2.2.1,8.1.1,flip.1')] ).
cnf(74,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)],[35]),63]),
[iquote('back_demod,35,demod,63')] ).
cnf(81,plain,
multiply(multiply(multiply(A,B),multiply(C,inverse(multiply(multiply(A,C),D)))),D) = B,
inference(para_from,[status(thm),theory(equality)],[44,5]),
[iquote('para_from,43.1.1,4.1.1.2')] ).
cnf(95,plain,
multiply(multiply(A,inverse(B)),inverse(A)) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,10]),5]),
[iquote('para_into,10.1.1.1.1,10.1.1,demod,5')] ).
cnf(127,plain,
multiply(multiply(A,B),inverse(A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[95,44]),44]),
[iquote('para_into,95.1.1.1.2,43.1.1,demod,44')] ).
cnf(134,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)],[95,8])]),
[iquote('para_into,95.1.1.1,8.1.1,flip.1')] ).
cnf(138,plain,
multiply(A,inverse(multiply(multiply(B,A),C))) = inverse(multiply(B,C)),
inference(para_into,[status(thm),theory(equality)],[95,5]),
[iquote('para_into,95.1.1.1,4.1.1')] ).
cnf(148,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)],[63]),134])]),
[iquote('back_demod,62,demod,134,flip.1')] ).
cnf(151,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)],[45]),134]),
[iquote('back_demod,45,demod,134')] ).
cnf(156,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)],[25]),134])]),
[iquote('back_demod,25,demod,134,flip.1')] ).
cnf(186,plain,
multiply(multiply(multiply(A,B),inverse(multiply(A,C))),C) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[81]),138]),
[iquote('back_demod,81,demod,138')] ).
cnf(194,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)],[74]),156,148,148])]),
[iquote('back_demod,74,demod,156,148,148,flip.1')] ).
cnf(196,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)],[151])]),156,194])]),
[iquote('copy,151,flip.1,demod,156,194,flip.1')] ).
cnf(219,plain,
multiply(multiply(multiply(A,B),multiply(inverse(A),inverse(C))),C) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[186]),196]),
[iquote('back_demod,186,demod,196')] ).
cnf(229,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)],[194]),196]),
[iquote('back_demod,193,demod,196')] ).
cnf(276,plain,
multiply(multiply(A,inverse(B)),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[219]),229]),
[iquote('back_demod,219,demod,229')] ).
cnf(285,plain,
multiply(A,B) = multiply(B,A),
inference(para_into,[status(thm),theory(equality)],[276,127]),
[iquote('para_into,276.1.1.1,127.1.1')] ).
cnf(286,plain,
$false,
inference(binary,[status(thm)],[285,2]),
[iquote('binary,285.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP512-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:01:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.59/1.77 ----- Otter 3.3f, August 2004 -----
% 1.59/1.77 The process was started by sandbox2 on n019.cluster.edu,
% 1.59/1.77 Wed Jul 27 05:01:37 2022
% 1.59/1.77 The command was "./otter". The process ID is 8555.
% 1.59/1.77
% 1.59/1.77 set(prolog_style_variables).
% 1.59/1.77 set(auto).
% 1.59/1.77 dependent: set(auto1).
% 1.59/1.77 dependent: set(process_input).
% 1.59/1.77 dependent: clear(print_kept).
% 1.59/1.77 dependent: clear(print_new_demod).
% 1.59/1.77 dependent: clear(print_back_demod).
% 1.59/1.77 dependent: clear(print_back_sub).
% 1.59/1.77 dependent: set(control_memory).
% 1.59/1.77 dependent: assign(max_mem, 12000).
% 1.59/1.77 dependent: assign(pick_given_ratio, 4).
% 1.59/1.77 dependent: assign(stats_level, 1).
% 1.59/1.77 dependent: assign(max_seconds, 10800).
% 1.59/1.77 clear(print_given).
% 1.59/1.77
% 1.59/1.77 list(usable).
% 1.59/1.77 0 [] A=A.
% 1.59/1.77 0 [] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C)))=B.
% 1.59/1.77 0 [] multiply(a,b)!=multiply(b,a).
% 1.59/1.77 end_of_list.
% 1.59/1.77
% 1.59/1.77 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.59/1.77
% 1.59/1.77 All clauses are units, and equality is present; the
% 1.59/1.77 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.59/1.77
% 1.59/1.77 dependent: set(knuth_bendix).
% 1.59/1.77 dependent: set(anl_eq).
% 1.59/1.77 dependent: set(para_from).
% 1.59/1.77 dependent: set(para_into).
% 1.59/1.77 dependent: clear(para_from_right).
% 1.59/1.77 dependent: clear(para_into_right).
% 1.59/1.77 dependent: set(para_from_vars).
% 1.59/1.77 dependent: set(eq_units_both_ways).
% 1.59/1.77 dependent: set(dynamic_demod_all).
% 1.59/1.77 dependent: set(dynamic_demod).
% 1.59/1.77 dependent: set(order_eq).
% 1.59/1.77 dependent: set(back_demod).
% 1.59/1.77 dependent: set(lrpo).
% 1.59/1.77
% 1.59/1.77 ------------> process usable:
% 1.59/1.77 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.59/1.77
% 1.59/1.77 ------------> process sos:
% 1.59/1.77 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.59/1.77 ** KEPT (pick-wt=12): 4 [] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C)))=B.
% 1.59/1.77 ---> New Demodulator: 5 [new_demod,4] multiply(multiply(multiply(A,B),C),inverse(multiply(A,C)))=B.
% 1.59/1.77 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.59/1.77 >>>> Starting back demodulation with 5.
% 1.59/1.77
% 1.59/1.77 ======= end of input processing =======
% 1.59/1.77
% 1.59/1.77 =========== start of search ===========
% 1.59/1.77
% 1.59/1.77 -------- PROOF --------
% 1.59/1.77
% 1.59/1.77 ----> UNIT CONFLICT at 0.01 sec ----> 286 [binary,285.1,2.1] $F.
% 1.59/1.77
% 1.59/1.77 Length of proof is 27. Level of proof is 9.
% 1.59/1.77
% 1.59/1.77 ---------------- PROOF ----------------
% 1.59/1.77 % SZS status Unsatisfiable
% 1.59/1.77 % SZS output start Refutation
% See solution above
% 1.59/1.77 ------------ end of proof -------------
% 1.59/1.77
% 1.59/1.77
% 1.59/1.77 Search stopped by max_proofs option.
% 1.59/1.77
% 1.59/1.77
% 1.59/1.77 Search stopped by max_proofs option.
% 1.59/1.77
% 1.59/1.77 ============ end of search ============
% 1.59/1.77
% 1.59/1.77 -------------- statistics -------------
% 1.59/1.77 clauses given 10
% 1.59/1.77 clauses generated 113
% 1.59/1.77 clauses kept 165
% 1.59/1.77 clauses forward subsumed 115
% 1.59/1.77 clauses back subsumed 2
% 1.59/1.77 Kbytes malloced 2929
% 1.59/1.77
% 1.59/1.77 ----------- times (seconds) -----------
% 1.59/1.77 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.59/1.77 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.59/1.77 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.59/1.77
% 1.59/1.77 That finishes the proof of the theorem.
% 1.59/1.77
% 1.59/1.77 Process 8555 finished Wed Jul 27 05:01:38 2022
% 1.59/1.77 Otter interrupted
% 1.59/1.77 PROOF FOUND
%------------------------------------------------------------------------------