TSTP Solution File: GRP568-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 12:57:16 EDT 2022
% Result : Unsatisfiable 1.68s 1.88s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 6 RR)
% Number of literals : 27 ( 26 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP568-1.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(4,axiom,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity)) = B,
file('GRP568-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP568-1.p',unknown),
[] ).
cnf(9,axiom,
inverse(A) = double_divide(A,identity),
file('GRP568-1.p',unknown),
[] ).
cnf(10,axiom,
identity = double_divide(A,inverse(A)),
file('GRP568-1.p',unknown),
[] ).
cnf(12,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10]),9])]),
[iquote('copy,10,demod,9,flip.1')] ).
cnf(13,plain,
double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),7,7])]),
[iquote('back_demod,2,demod,7,7,flip.1')] ).
cnf(19,plain,
double_divide(double_divide(A,identity),double_divide(identity,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,12]),12]),
[iquote('para_into,4.1.1.1.2.1,11.1.1,demod,12')] ).
cnf(20,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(B,C)),double_divide(identity,C))),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.2.1,4.1.1')] ).
cnf(23,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))) = double_divide(double_divide(identity,double_divide(B,double_divide(identity,identity))),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
[iquote('copy,20,flip.1')] ).
cnf(25,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(A,identity),
inference(para_from,[status(thm),theory(equality)],[19,4]),
[iquote('para_from,18.1.1,4.1.1.1.2.1')] ).
cnf(28,plain,
double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[23]),25]),
[iquote('back_demod,23,demod,25')] ).
cnf(32,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(double_divide(A,identity),identity),
inference(para_into,[status(thm),theory(equality)],[25,19]),
[iquote('para_into,24.1.1.1.2,18.1.1')] ).
cnf(34,plain,
double_divide(identity,identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,12]),19])]),
[iquote('para_into,24.1.1.1.2,11.1.1,demod,19,flip.1')] ).
cnf(35,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(identity,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[32])]),34]),
[iquote('copy,32,flip.1,demod,34')] ).
cnf(44,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),34]),
[iquote('back_demod,18,demod,34')] ).
cnf(47,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[35])]),44]),
[iquote('copy,35,flip.1,demod,44')] ).
cnf(51,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,A),identity)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,44]),34]),
[iquote('para_into,28.1.1.2.1.2,43.1.1,demod,34')] ).
cnf(53,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,34]),34,44]),
[iquote('para_into,28.1.1.2.1.2,33.1.1,demod,34,44')] ).
cnf(64,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[53])]),
[iquote('copy,53,flip.1')] ).
cnf(86,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[64,47])]),
[iquote('para_into,64.1.1,47.1.1,flip.1')] ).
cnf(91,plain,
double_divide(double_divide(a,b),identity) != double_divide(identity,double_divide(b,a)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[64,13])]),
[iquote('para_from,64.1.1,13.1.1,flip.1')] ).
cnf(94,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[51,51]),44,44,44]),
[iquote('para_into,51.1.1.2.1,51.1.1,demod,44,44,44')] ).
cnf(104,plain,
double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(A,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[86,28]),86]),
[iquote('para_from,85.1.1,28.1.1.2.1.2,demod,86')] ).
cnf(194,plain,
double_divide(double_divide(A,B),identity) = double_divide(identity,double_divide(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[104,94])]),
[iquote('para_into,104.1.1.2.1,94.1.1,flip.1')] ).
cnf(196,plain,
$false,
inference(binary,[status(thm)],[194,91]),
[iquote('binary,194.1,91.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP568-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 05:14:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.88 ----- Otter 3.3f, August 2004 -----
% 1.68/1.88 The process was started by sandbox2 on n012.cluster.edu,
% 1.68/1.88 Wed Jul 27 05:14:35 2022
% 1.68/1.88 The command was "./otter". The process ID is 11368.
% 1.68/1.88
% 1.68/1.88 set(prolog_style_variables).
% 1.68/1.88 set(auto).
% 1.68/1.88 dependent: set(auto1).
% 1.68/1.88 dependent: set(process_input).
% 1.68/1.88 dependent: clear(print_kept).
% 1.68/1.88 dependent: clear(print_new_demod).
% 1.68/1.88 dependent: clear(print_back_demod).
% 1.68/1.88 dependent: clear(print_back_sub).
% 1.68/1.88 dependent: set(control_memory).
% 1.68/1.88 dependent: assign(max_mem, 12000).
% 1.68/1.88 dependent: assign(pick_given_ratio, 4).
% 1.68/1.88 dependent: assign(stats_level, 1).
% 1.68/1.88 dependent: assign(max_seconds, 10800).
% 1.68/1.88 clear(print_given).
% 1.68/1.88
% 1.68/1.88 list(usable).
% 1.68/1.88 0 [] A=A.
% 1.68/1.88 0 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity))=B.
% 1.68/1.88 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.68/1.88 0 [] inverse(A)=double_divide(A,identity).
% 1.68/1.88 0 [] identity=double_divide(A,inverse(A)).
% 1.68/1.88 0 [] multiply(a,b)!=multiply(b,a).
% 1.68/1.88 end_of_list.
% 1.68/1.88
% 1.68/1.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.68/1.88
% 1.68/1.88 All clauses are units, and equality is present; the
% 1.68/1.88 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.68/1.88
% 1.68/1.88 dependent: set(knuth_bendix).
% 1.68/1.88 dependent: set(anl_eq).
% 1.68/1.88 dependent: set(para_from).
% 1.68/1.88 dependent: set(para_into).
% 1.68/1.88 dependent: clear(para_from_right).
% 1.68/1.88 dependent: clear(para_into_right).
% 1.68/1.88 dependent: set(para_from_vars).
% 1.68/1.88 dependent: set(eq_units_both_ways).
% 1.68/1.88 dependent: set(dynamic_demod_all).
% 1.68/1.88 dependent: set(dynamic_demod).
% 1.68/1.88 dependent: set(order_eq).
% 1.68/1.88 dependent: set(back_demod).
% 1.68/1.88 dependent: set(lrpo).
% 1.68/1.88
% 1.68/1.88 ------------> process usable:
% 1.68/1.88 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.68/1.88
% 1.68/1.88 ------------> process sos:
% 1.68/1.88 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.68/1.88 ** KEPT (pick-wt=17): 4 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity))=B.
% 1.68/1.88 ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(A,C)),double_divide(identity,C))),double_divide(identity,identity))=B.
% 1.68/1.88 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.68/1.88 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.68/1.88 ** KEPT (pick-wt=6): 8 [] inverse(A)=double_divide(A,identity).
% 1.68/1.88 ---> New Demodulator: 9 [new_demod,8] inverse(A)=double_divide(A,identity).
% 1.68/1.88 ** KEPT (pick-wt=7): 11 [copy,10,demod,9,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.68/1.88 ---> New Demodulator: 12 [new_demod,11] double_divide(A,double_divide(A,identity))=identity.
% 1.68/1.88 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.68/1.88 >>>> Starting back demodulation with 5.
% 1.68/1.88 >>>> Starting back demodulation with 7.
% 1.68/1.88 >> back demodulating 2 with 7.
% 1.68/1.88 >>>> Starting back demodulation with 9.
% 1.68/1.88 >>>> Starting back demodulation with 12.
% 1.68/1.88
% 1.68/1.88 ======= end of input processing =======
% 1.68/1.88
% 1.68/1.88 =========== start of search ===========
% 1.68/1.88
% 1.68/1.88 -------- PROOF --------
% 1.68/1.88
% 1.68/1.88 ----> UNIT CONFLICT at 0.01 sec ----> 196 [binary,194.1,91.1] $F.
% 1.68/1.88
% 1.68/1.88 Length of proof is 21. Level of proof is 10.
% 1.68/1.88
% 1.68/1.88 ---------------- PROOF ----------------
% 1.68/1.88 % SZS status Unsatisfiable
% 1.68/1.88 % SZS output start Refutation
% See solution above
% 1.68/1.88 ------------ end of proof -------------
% 1.68/1.88
% 1.68/1.88
% 1.68/1.88 Search stopped by max_proofs option.
% 1.68/1.88
% 1.68/1.88
% 1.68/1.88 Search stopped by max_proofs option.
% 1.68/1.88
% 1.68/1.88 ============ end of search ============
% 1.68/1.88
% 1.68/1.88 -------------- statistics -------------
% 1.68/1.88 clauses given 25
% 1.68/1.88 clauses generated 326
% 1.68/1.88 clauses kept 106
% 1.68/1.88 clauses forward subsumed 291
% 1.68/1.88 clauses back subsumed 0
% 1.68/1.88 Kbytes malloced 1953
% 1.68/1.88
% 1.68/1.88 ----------- times (seconds) -----------
% 1.68/1.88 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.68/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.88 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.68/1.88
% 1.68/1.88 That finishes the proof of the theorem.
% 1.68/1.88
% 1.68/1.88 Process 11368 finished Wed Jul 27 05:14:37 2022
% 1.68/1.88 Otter interrupted
% 1.68/1.88 PROOF FOUND
%------------------------------------------------------------------------------