TSTP Solution File: GRP002-3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP002-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 12:55:49 EDT 2022
% Result : Unsatisfiable 1.75s 1.94s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 2 RR)
% Number of literals : 42 ( 41 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 81 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
commutator(commutator(a,b),b) != identity,
file('GRP002-3.p',unknown),
[] ).
cnf(4,axiom,
multiply(identity,A) = A,
file('GRP002-3.p',unknown),
[] ).
cnf(5,axiom,
multiply(inverse(A),A) = identity,
file('GRP002-3.p',unknown),
[] ).
cnf(8,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP002-3.p',unknown),
[] ).
cnf(9,axiom,
commutator(A,B) = multiply(A,multiply(B,multiply(inverse(A),inverse(B)))),
file('GRP002-3.p',unknown),
[] ).
cnf(10,plain,
multiply(A,multiply(B,multiply(inverse(A),inverse(B)))) = commutator(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(13,axiom,
multiply(A,multiply(A,A)) = identity,
file('GRP002-3.p',unknown),
[] ).
cnf(15,plain,
multiply(A,multiply(A,multiply(A,B))) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,13]),4,8])]),
[iquote('para_into,7.1.1.1,12.1.1,demod,4,8,flip.1')] ).
cnf(16,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,5]),4])]),
[iquote('para_into,7.1.1.1,5.1.1,demod,4,flip.1')] ).
cnf(18,plain,
multiply(A,multiply(B,multiply(A,multiply(B,multiply(A,B))))) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,13]),8])]),
[iquote('para_into,7.1.1,12.1.1,demod,8,flip.1')] ).
cnf(22,plain,
multiply(A,multiply(B,multiply(C,multiply(inverse(A),inverse(multiply(B,C)))))) = commutator(A,multiply(B,C)),
inference(para_into,[status(thm),theory(equality)],[10,8]),
[iquote('para_into,10.1.1.2,7.1.1')] ).
cnf(26,plain,
multiply(A,multiply(B,multiply(C,multiply(inverse(multiply(A,B)),inverse(C))))) = commutator(multiply(A,B),C),
inference(para_into,[status(thm),theory(equality)],[10,8]),
[iquote('para_into,10.1.1,7.1.1')] ).
cnf(30,plain,
multiply(commutator(A,B),C) = multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),C)))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[10,8]),8,8]),
[iquote('para_from,10.1.1,7.1.1.1,demod,8,8')] ).
cnf(31,plain,
multiply(A,multiply(B,multiply(inverse(A),multiply(inverse(B),C)))) = multiply(commutator(A,B),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[30])]),
[iquote('copy,30,flip.1')] ).
cnf(33,plain,
multiply(inverse(inverse(A)),B) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[16,16]),
[iquote('para_into,16.1.1.2,16.1.1')] ).
cnf(35,plain,
multiply(inverse(A),identity) = multiply(A,A),
inference(para_into,[status(thm),theory(equality)],[16,13]),
[iquote('para_into,16.1.1.2,12.1.1')] ).
cnf(36,plain,
multiply(inverse(A),commutator(A,B)) = multiply(B,multiply(inverse(A),inverse(B))),
inference(para_into,[status(thm),theory(equality)],[16,10]),
[iquote('para_into,16.1.1.2,10.1.1')] ).
cnf(39,plain,
multiply(inverse(A),inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,5]),35]),
[iquote('para_into,16.1.1.2,5.1.1,demod,35')] ).
cnf(43,plain,
multiply(A,multiply(inverse(B),inverse(A))) = multiply(inverse(B),commutator(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[36])]),
[iquote('copy,36,flip.1')] ).
cnf(59,plain,
inverse(A) = multiply(A,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[39,16]),33])]),
[iquote('para_from,39.1.1,16.1.1.2,demod,33,flip.1')] ).
cnf(64,plain,
multiply(A,multiply(B,multiply(B,multiply(A,A)))) = multiply(B,multiply(B,commutator(B,A))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[43]),59,59,8,59,8]),
[iquote('back_demod,43,demod,59,59,8,59,8')] ).
cnf(66,plain,
multiply(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[39]),59,59,8,13]),
[iquote('back_demod,39,demod,59,59,8,13')] ).
cnf(71,plain,
multiply(commutator(A,B),C) = multiply(A,multiply(B,multiply(A,multiply(A,multiply(B,multiply(B,C)))))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[31]),59,59,8,8])]),
[iquote('back_demod,31,demod,59,59,8,8,flip.1')] ).
cnf(72,plain,
multiply(A,multiply(B,multiply(C,multiply(A,multiply(B,multiply(A,multiply(B,multiply(C,C)))))))) = commutator(multiply(A,B),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),59,8,59,8,8,8]),
[iquote('back_demod,26,demod,59,8,59,8,8,8')] ).
cnf(74,plain,
multiply(A,multiply(B,multiply(C,multiply(A,multiply(A,multiply(B,multiply(C,multiply(B,C)))))))) = commutator(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[22]),59,59,8,8]),
[iquote('back_demod,22,demod,59,59,8,8')] ).
cnf(79,plain,
multiply(A,multiply(B,multiply(A,multiply(A,multiply(B,B))))) = commutator(A,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[10]),59,59,8]),
[iquote('back_demod,10,demod,59,59,8')] ).
cnf(82,plain,
multiply(A,multiply(B,multiply(A,multiply(B,A)))) = multiply(B,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[18,15]),66])]),
[iquote('para_from,18.1.1,14.1.1.2.2,demod,66,flip.1')] ).
cnf(88,plain,
multiply(A,multiply(A,multiply(B,B))) = multiply(B,multiply(A,multiply(B,A))),
inference(para_from,[status(thm),theory(equality)],[82,15]),
[iquote('para_from,82.1.1,14.1.1.2.2')] ).
cnf(91,plain,
multiply(A,multiply(B,multiply(A,B))) = multiply(B,multiply(B,multiply(A,A))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[88])]),
[iquote('copy,88,flip.1')] ).
cnf(101,plain,
multiply(A,multiply(B,multiply(B,multiply(A,multiply(A,commutator(A,B)))))) = multiply(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[64,82]),8,8,8,8,8,8,15,15]),
[iquote('para_from,64.1.1,82.1.1.2.2.2,demod,8,8,8,8,8,8,15,15')] ).
cnf(127,plain,
multiply(A,multiply(B,multiply(B,multiply(A,multiply(B,A))))) = commutator(A,B),
inference(para_from,[status(thm),theory(equality)],[88,79]),
[iquote('para_from,88.1.1,78.1.1.2.2')] ).
cnf(168,plain,
multiply(A,multiply(B,commutator(B,A))) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[91,88]),8,8,15,15,8,8,8,8,79])]),
[iquote('para_into,91.1.1.2.2,88.1.1,demod,8,8,15,15,8,8,8,8,79,flip.1')] ).
cnf(224,plain,
multiply(A,multiply(A,multiply(B,A))) = multiply(B,commutator(B,A)),
inference(para_from,[status(thm),theory(equality)],[168,15]),
[iquote('para_from,168.1.1,14.1.1.2.2')] ).
cnf(227,plain,
multiply(A,commutator(A,B)) = multiply(B,multiply(B,multiply(A,B))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[224])]),
[iquote('copy,224,flip.1')] ).
cnf(292,plain,
multiply(A,multiply(A,multiply(B,multiply(B,multiply(A,B))))) = commutator(A,B),
inference(para_from,[status(thm),theory(equality)],[227,15]),
[iquote('para_from,227.1.1,14.1.1.2.2')] ).
cnf(296,plain,
commutator(commutator(A,B),A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[127,227]),71,15,127,15,71,101,13])]),
[iquote('para_into,126.1.1.2.2.2.2,227.1.1,demod,71,15,127,15,71,101,13,flip.1')] ).
cnf(367,plain,
commutator(multiply(A,B),B) = commutator(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[72,13]),66,127])]),
[iquote('para_into,72.1.1.2.2.2.2.2.2,12.1.1,demod,66,127,flip.1')] ).
cnf(457,plain,
commutator(commutator(A,B),multiply(A,B)) = identity,
inference(para_from,[status(thm),theory(equality)],[367,296]),
[iquote('para_from,367.1.1,296.1.1.1')] ).
cnf(491,plain,
commutator(commutator(A,multiply(A,multiply(A,B))),B) = identity,
inference(para_into,[status(thm),theory(equality)],[457,15]),
[iquote('para_into,457.1.1.2,14.1.1')] ).
cnf(544,plain,
commutator(A,multiply(A,B)) = commutator(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[74,15]),292])]),
[iquote('para_into,74.1.1.2.2.2,14.1.1,demod,292,flip.1')] ).
cnf(551,plain,
commutator(commutator(A,B),B) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[491]),544,544]),
[iquote('back_demod,491,demod,544,544')] ).
cnf(553,plain,
$false,
inference(binary,[status(thm)],[551,1]),
[iquote('binary,551.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP002-3 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 05:16:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.75/1.94 ----- Otter 3.3f, August 2004 -----
% 1.75/1.94 The process was started by sandbox on n009.cluster.edu,
% 1.75/1.94 Wed Jul 27 05:16:36 2022
% 1.75/1.94 The command was "./otter". The process ID is 12614.
% 1.75/1.94
% 1.75/1.94 set(prolog_style_variables).
% 1.75/1.94 set(auto).
% 1.75/1.94 dependent: set(auto1).
% 1.75/1.94 dependent: set(process_input).
% 1.75/1.94 dependent: clear(print_kept).
% 1.75/1.94 dependent: clear(print_new_demod).
% 1.75/1.94 dependent: clear(print_back_demod).
% 1.75/1.94 dependent: clear(print_back_sub).
% 1.75/1.94 dependent: set(control_memory).
% 1.75/1.94 dependent: assign(max_mem, 12000).
% 1.75/1.94 dependent: assign(pick_given_ratio, 4).
% 1.75/1.94 dependent: assign(stats_level, 1).
% 1.75/1.94 dependent: assign(max_seconds, 10800).
% 1.75/1.94 clear(print_given).
% 1.75/1.94
% 1.75/1.94 list(usable).
% 1.75/1.94 0 [] A=A.
% 1.75/1.94 0 [] multiply(identity,X)=X.
% 1.75/1.94 0 [] multiply(inverse(X),X)=identity.
% 1.75/1.94 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.75/1.94 0 [] commutator(X,Y)=multiply(X,multiply(Y,multiply(inverse(X),inverse(Y)))).
% 1.75/1.94 0 [] multiply(X,multiply(X,X))=identity.
% 1.75/1.94 0 [] commutator(commutator(a,b),b)!=identity.
% 1.75/1.94 end_of_list.
% 1.75/1.94
% 1.75/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.75/1.94
% 1.75/1.94 All clauses are units, and equality is present; the
% 1.75/1.94 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.75/1.94
% 1.75/1.94 dependent: set(knuth_bendix).
% 1.75/1.94 dependent: set(anl_eq).
% 1.75/1.94 dependent: set(para_from).
% 1.75/1.94 dependent: set(para_into).
% 1.75/1.94 dependent: clear(para_from_right).
% 1.75/1.94 dependent: clear(para_into_right).
% 1.75/1.94 dependent: set(para_from_vars).
% 1.75/1.94 dependent: set(eq_units_both_ways).
% 1.75/1.94 dependent: set(dynamic_demod_all).
% 1.75/1.94 dependent: set(dynamic_demod).
% 1.75/1.94 dependent: set(order_eq).
% 1.75/1.94 dependent: set(back_demod).
% 1.75/1.94 dependent: set(lrpo).
% 1.75/1.94
% 1.75/1.94 ------------> process usable:
% 1.75/1.94 ** KEPT (pick-wt=7): 1 [] commutator(commutator(a,b),b)!=identity.
% 1.75/1.94
% 1.75/1.94 ------------> process sos:
% 1.75/1.94 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.75/1.94 ** KEPT (pick-wt=5): 3 [] multiply(identity,A)=A.
% 1.75/1.94 ---> New Demodulator: 4 [new_demod,3] multiply(identity,A)=A.
% 1.75/1.94 ** KEPT (pick-wt=6): 5 [] multiply(inverse(A),A)=identity.
% 1.75/1.94 ---> New Demodulator: 6 [new_demod,5] multiply(inverse(A),A)=identity.
% 1.75/1.94 ** KEPT (pick-wt=11): 7 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.75/1.94 ---> New Demodulator: 8 [new_demod,7] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.75/1.94 ** KEPT (pick-wt=13): 10 [copy,9,flip.1] multiply(A,multiply(B,multiply(inverse(A),inverse(B))))=commutator(A,B).
% 1.75/1.94 ---> New Demodulator: 11 [new_demod,10] multiply(A,multiply(B,multiply(inverse(A),inverse(B))))=commutator(A,B).
% 1.75/1.94 ** KEPT (pick-wt=7): 12 [] multiply(A,multiply(A,A))=identity.
% 1.75/1.94 ---> New Demodulator: 13 [new_demod,12] multiply(A,multiply(A,A))=identity.
% 1.75/1.94 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.75/1.94 >>>> Starting back demodulation with 4.
% 1.75/1.94 >>>> Starting back demodulation with 6.
% 1.75/1.94 >>>> Starting back demodulation with 8.
% 1.75/1.94 >>>> Starting back demodulation with 11.
% 1.75/1.94 >>>> Starting back demodulation with 13.
% 1.75/1.94
% 1.75/1.94 ======= end of input processing =======
% 1.75/1.94
% 1.75/1.94 =========== start of search ===========
% 1.75/1.94
% 1.75/1.94 -------- PROOF --------
% 1.75/1.94
% 1.75/1.94 ----> UNIT CONFLICT at 0.03 sec ----> 553 [binary,551.1,1.1] $F.
% 1.75/1.94
% 1.75/1.94 Length of proof is 35. Level of proof is 15.
% 1.75/1.94
% 1.75/1.94 ---------------- PROOF ----------------
% 1.75/1.94 % SZS status Unsatisfiable
% 1.75/1.94 % SZS output start Refutation
% See solution above
% 1.75/1.94 ------------ end of proof -------------
% 1.75/1.94
% 1.75/1.94
% 1.75/1.94 Search stopped by max_proofs option.
% 1.75/1.94
% 1.75/1.94
% 1.75/1.94 Search stopped by max_proofs option.
% 1.75/1.94
% 1.75/1.94 ============ end of search ============
% 1.75/1.94
% 1.75/1.94 -------------- statistics -------------
% 1.75/1.94 clauses given 41
% 1.75/1.94 clauses generated 938
% 1.75/1.94 clauses kept 324
% 1.75/1.94 clauses forward subsumed 812
% 1.75/1.94 clauses back subsumed 0
% 1.75/1.94 Kbytes malloced 2929
% 1.75/1.94
% 1.75/1.94 ----------- times (seconds) -----------
% 1.75/1.94 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.75/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.75/1.94
% 1.75/1.94 That finishes the proof of the theorem.
% 1.75/1.94
% 1.75/1.94 Process 12614 finished Wed Jul 27 05:16:37 2022
% 1.75/1.94 Otter interrupted
% 1.75/1.94 PROOF FOUND
%------------------------------------------------------------------------------