TSTP Solution File: GRP610-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP610-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:57:21 EDT 2022
% Result : Unsatisfiable 1.69s 1.91s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 4 RR)
% Number of literals : 33 ( 32 equ; 3 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP610-1.p',unknown),
[] ).
cnf(3,axiom,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B,
file('GRP610-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP610-1.p',unknown),
[] ).
cnf(7,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(8,plain,
multiply(double_divide(A,B),multiply(B,multiply(C,A))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),7,7,7]),
[iquote('back_demod,3,demod,7,7,7')] ).
cnf(10,plain,
multiply(double_divide(multiply(A,multiply(B,C)),D),multiply(D,B)) = double_divide(C,A),
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.2.2,8.1.1')] ).
cnf(12,plain,
multiply(double_divide(multiply(A,B),double_divide(B,C)),A) = C,
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.2,8.1.1')] ).
cnf(34,plain,
double_divide(A,multiply(double_divide(multiply(B,A),C),B)) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,12])]),
[iquote('para_into,10.1.1,12.1.1,flip.1')] ).
cnf(65,plain,
multiply(double_divide(multiply(A,multiply(B,C)),D),A) = double_divide(C,multiply(D,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,34])]),
[iquote('para_into,34.1.1.2.1,34.1.1,flip.1')] ).
cnf(66,plain,
double_divide(multiply(A,B),double_divide(B,multiply(C,A))) = C,
inference(para_into,[status(thm),theory(equality)],[34,10]),
[iquote('para_into,34.1.1.2,10.1.1')] ).
cnf(76,plain,
inverse(A) = multiply(multiply(double_divide(multiply(B,C),A),B),C),
inference(para_from,[status(thm),theory(equality)],[34,7]),
[iquote('para_from,34.1.1,6.1.1.1')] ).
cnf(78,plain,
multiply(multiply(double_divide(multiply(A,B),C),A),B) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[76])]),
[iquote('copy,76,flip.1')] ).
cnf(100,plain,
inverse(A) = multiply(double_divide(B,multiply(A,C)),multiply(C,B)),
inference(para_from,[status(thm),theory(equality)],[66,7]),
[iquote('para_from,66.1.1,6.1.1.1')] ).
cnf(101,plain,
multiply(double_divide(A,multiply(B,C)),multiply(C,A)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[100])]),
[iquote('copy,100,flip.1')] ).
cnf(129,plain,
multiply(double_divide(A,double_divide(A,multiply(B,C))),inverse(B)) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[78,8]),65]),
[iquote('para_from,78.1.1,8.1.1.2,demod,65')] ).
cnf(181,plain,
multiply(multiply(multiply(double_divide(A,multiply(b2,B)),multiply(B,A)),b2),a2) != a2,
inference(para_from,[status(thm),theory(equality)],[100,1]),
[iquote('para_from,100.1.1,1.1.1.1.1')] ).
cnf(227,plain,
multiply(double_divide(A,double_divide(A,multiply(double_divide(B,C),D))),multiply(C,B)) = D,
inference(para_into,[status(thm),theory(equality)],[129,7]),
[iquote('para_into,129.1.1.2,6.1.1')] ).
cnf(231,plain,
multiply(multiply(A,B),multiply(inverse(A),C)) = multiply(B,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[129,78]),7])]),
[iquote('para_from,129.1.1,78.1.1.1,demod,7,flip.1')] ).
cnf(233,plain,
double_divide(multiply(inverse(A),B),multiply(A,C)) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[129,34])]),
[iquote('para_from,129.1.1,34.1.1.2,flip.1')] ).
cnf(258,plain,
multiply(multiply(A,multiply(B,C)),D) = multiply(B,multiply(multiply(A,C),D)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[231,8]),7])]),
[iquote('para_into,231.1.1.1,8.1.1,demod,7,flip.1')] ).
cnf(270,plain,
multiply(multiply(double_divide(A,multiply(b2,B)),A),multiply(multiply(B,b2),a2)) != a2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[181]),258,258]),
[iquote('back_demod,181,demod,258,258')] ).
cnf(356,plain,
double_divide(multiply(A,multiply(inverse(B),C)),double_divide(C,A)) = B,
inference(para_from,[status(thm),theory(equality)],[233,66]),
[iquote('para_from,233.1.1,66.1.1.2')] ).
cnf(358,plain,
double_divide(A,multiply(double_divide(A,B),inverse(C))) = multiply(C,B),
inference(para_from,[status(thm),theory(equality)],[233,34]),
[iquote('para_from,233.1.1,34.1.1.2.1')] ).
cnf(370,plain,
double_divide(inverse(A),double_divide(B,double_divide(B,multiply(A,inverse(C))))) = C,
inference(para_into,[status(thm),theory(equality)],[356,101]),
[iquote('para_into,356.1.1.1,101.1.1')] ).
cnf(402,plain,
multiply(A,double_divide(B,multiply(A,C))) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[358,129])]),
[iquote('para_into,358.1.1.2,129.1.1,flip.1')] ).
cnf(431,plain,
multiply(A,double_divide(B,double_divide(C,D))) = double_divide(B,double_divide(C,multiply(A,D))),
inference(para_into,[status(thm),theory(equality)],[402,402]),
[iquote('para_into,402.1.1.2.2,402.1.1')] ).
cnf(442,plain,
double_divide(A,double_divide(B,double_divide(B,multiply(C,D)))) = double_divide(A,multiply(C,D)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[402,10]),431,65]),
[iquote('para_into,402.1.1.2.2,10.1.1,demod,431,65')] ).
cnf(474,plain,
double_divide(inverse(A),multiply(A,inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[370]),442]),
[iquote('back_demod,370,demod,442')] ).
cnf(528,plain,
double_divide(multiply(inverse(A),inverse(B)),A) = B,
inference(para_from,[status(thm),theory(equality)],[474,66]),
[iquote('para_from,474.1.1,66.1.1.2')] ).
cnf(580,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[528,12]),7]),
[iquote('para_from,528.1.1,12.1.1.1,demod,7')] ).
cnf(589,plain,
double_divide(A,double_divide(A,multiply(B,C))) = multiply(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[580,129])]),
[iquote('para_into,580.1.1.2,129.1.1,flip.1')] ).
cnf(598,plain,
multiply(multiply(double_divide(A,B),C),multiply(B,A)) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[227]),589]),
[iquote('back_demod,227,demod,589')] ).
cnf(600,plain,
$false,
inference(binary,[status(thm)],[598,270]),
[iquote('binary,598.1,270.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP610-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n022.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 05:01:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.69/1.91 ----- Otter 3.3f, August 2004 -----
% 1.69/1.91 The process was started by sandbox2 on n022.cluster.edu,
% 1.69/1.91 Wed Jul 27 05:01:05 2022
% 1.69/1.91 The command was "./otter". The process ID is 21496.
% 1.69/1.91
% 1.69/1.91 set(prolog_style_variables).
% 1.69/1.91 set(auto).
% 1.69/1.91 dependent: set(auto1).
% 1.69/1.91 dependent: set(process_input).
% 1.69/1.91 dependent: clear(print_kept).
% 1.69/1.91 dependent: clear(print_new_demod).
% 1.69/1.91 dependent: clear(print_back_demod).
% 1.69/1.91 dependent: clear(print_back_sub).
% 1.69/1.91 dependent: set(control_memory).
% 1.69/1.91 dependent: assign(max_mem, 12000).
% 1.69/1.91 dependent: assign(pick_given_ratio, 4).
% 1.69/1.91 dependent: assign(stats_level, 1).
% 1.69/1.91 dependent: assign(max_seconds, 10800).
% 1.69/1.91 clear(print_given).
% 1.69/1.91
% 1.69/1.91 list(usable).
% 1.69/1.91 0 [] A=A.
% 1.69/1.91 0 [] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.69/1.91 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.69/1.91 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.69/1.91 end_of_list.
% 1.69/1.91
% 1.69/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.69/1.91
% 1.69/1.91 All clauses are units, and equality is present; the
% 1.69/1.91 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.69/1.91
% 1.69/1.91 dependent: set(knuth_bendix).
% 1.69/1.91 dependent: set(anl_eq).
% 1.69/1.91 dependent: set(para_from).
% 1.69/1.91 dependent: set(para_into).
% 1.69/1.91 dependent: clear(para_from_right).
% 1.69/1.91 dependent: clear(para_into_right).
% 1.69/1.91 dependent: set(para_from_vars).
% 1.69/1.91 dependent: set(eq_units_both_ways).
% 1.69/1.91 dependent: set(dynamic_demod_all).
% 1.69/1.91 dependent: set(dynamic_demod).
% 1.69/1.91 dependent: set(order_eq).
% 1.69/1.91 dependent: set(back_demod).
% 1.69/1.91 dependent: set(lrpo).
% 1.69/1.91
% 1.69/1.91 ------------> process usable:
% 1.69/1.91 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.69/1.91
% 1.69/1.91 ------------> process sos:
% 1.69/1.91 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.69/1.91 ** KEPT (pick-wt=14): 3 [] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.69/1.91 ---> New Demodulator: 4 [new_demod,3] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.69/1.91 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.69/1.91 ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 1.69/1.91 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.69/1.91 >>>> Starting back demodulation with 4.
% 1.69/1.91 >>>> Starting back demodulation with 7.
% 1.69/1.91 >> back demodulating 3 with 7.
% 1.69/1.91 >>>> Starting back demodulation with 9.
% 1.69/1.91
% 1.69/1.91 ======= end of input processing =======
% 1.69/1.91
% 1.69/1.91 =========== start of search ===========
% 1.69/1.91
% 1.69/1.91
% 1.69/1.91 Resetting weight limit to 13.
% 1.69/1.91
% 1.69/1.91
% 1.69/1.91 Resetting weight limit to 13.
% 1.69/1.91
% 1.69/1.91 sos_size=275
% 1.69/1.91
% 1.69/1.91 -------- PROOF --------
% 1.69/1.91
% 1.69/1.91 ----> UNIT CONFLICT at 0.01 sec ----> 600 [binary,598.1,270.1] $F.
% 1.69/1.91
% 1.69/1.91 Length of proof is 29. Level of proof is 17.
% 1.69/1.91
% 1.69/1.91 ---------------- PROOF ----------------
% 1.69/1.91 % SZS status Unsatisfiable
% 1.69/1.91 % SZS output start Refutation
% See solution above
% 1.69/1.91 ------------ end of proof -------------
% 1.69/1.91
% 1.69/1.91
% 1.69/1.91 Search stopped by max_proofs option.
% 1.69/1.91
% 1.69/1.91
% 1.69/1.91 Search stopped by max_proofs option.
% 1.69/1.91
% 1.69/1.91 ============ end of search ============
% 1.69/1.91
% 1.69/1.91 -------------- statistics -------------
% 1.69/1.91 clauses given 25
% 1.69/1.91 clauses generated 497
% 1.69/1.91 clauses kept 407
% 1.69/1.91 clauses forward subsumed 286
% 1.69/1.91 clauses back subsumed 0
% 1.69/1.91 Kbytes malloced 4882
% 1.69/1.91
% 1.69/1.91 ----------- times (seconds) -----------
% 1.69/1.91 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.69/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.91 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.69/1.91
% 1.69/1.91 That finishes the proof of the theorem.
% 1.69/1.91
% 1.69/1.91 Process 21496 finished Wed Jul 27 05:01:07 2022
% 1.69/1.91 Otter interrupted
% 1.69/1.91 PROOF FOUND
%------------------------------------------------------------------------------