TSTP Solution File: GRP603-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP603-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 12:57:20 EDT 2022
% Result : Unsatisfiable 1.68s 1.89s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of clauses : 38 ( 38 unt; 0 nHn; 2 RR)
% Number of literals : 38 ( 37 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 117 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP603-1.p',unknown),
[] ).
cnf(3,axiom,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B,
file('GRP603-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP603-1.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(A,multiply(multiply(double_divide(B,A),C),B)) = 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(multiply(double_divide(A,double_divide(B,C)),D),A) = multiply(C,multiply(D,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,8])]),
[iquote('para_into,8.1.1.2.1,8.1.1,flip.1')] ).
cnf(12,plain,
multiply(double_divide(A,B),multiply(B,multiply(C,A))) = C,
inference(para_from,[status(thm),theory(equality)],[10,8]),
[iquote('para_from,10.1.1,8.1.1.2')] ).
cnf(14,plain,
multiply(double_divide(multiply(A,multiply(B,C)),D),multiply(D,B)) = double_divide(C,A),
inference(para_into,[status(thm),theory(equality)],[12,12]),
[iquote('para_into,12.1.1.2.2,12.1.1')] ).
cnf(20,plain,
multiply(double_divide(multiply(A,B),double_divide(B,C)),A) = C,
inference(para_into,[status(thm),theory(equality)],[12,12]),
[iquote('para_into,12.1.1.2,12.1.1')] ).
cnf(56,plain,
double_divide(A,multiply(double_divide(multiply(B,A),C),B)) = C,
inference(para_into,[status(thm),theory(equality)],[20,14]),
[iquote('para_into,19.1.1,14.1.1')] ).
cnf(77,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)],[56,56])]),
[iquote('para_into,56.1.1.2.1,56.1.1,flip.1')] ).
cnf(78,plain,
double_divide(multiply(A,B),double_divide(B,multiply(C,A))) = C,
inference(para_into,[status(thm),theory(equality)],[56,14]),
[iquote('para_into,56.1.1.2,14.1.1')] ).
cnf(86,plain,
inverse(A) = multiply(multiply(double_divide(multiply(B,C),A),B),C),
inference(para_from,[status(thm),theory(equality)],[56,7]),
[iquote('para_from,56.1.1,6.1.1.1')] ).
cnf(90,plain,
multiply(multiply(double_divide(multiply(A,B),C),A),B) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[86])]),
[iquote('copy,86,flip.1')] ).
cnf(103,plain,
double_divide(multiply(multiply(A,multiply(B,C)),D),double_divide(D,B)) = double_divide(C,A),
inference(para_into,[status(thm),theory(equality)],[78,12]),
[iquote('para_into,78.1.1.2.2,12.1.1')] ).
cnf(114,plain,
inverse(A) = multiply(double_divide(B,multiply(A,C)),multiply(C,B)),
inference(para_from,[status(thm),theory(equality)],[78,7]),
[iquote('para_from,78.1.1,6.1.1.1')] ).
cnf(118,plain,
multiply(double_divide(A,multiply(B,C)),multiply(C,A)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[114])]),
[iquote('copy,114,flip.1')] ).
cnf(178,plain,
multiply(multiply(double_divide(A,B),double_divide(multiply(C,D),double_divide(D,A))),C) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[90,20]),
[iquote('para_into,90.1.1.1.1.1,19.1.1')] ).
cnf(186,plain,
inverse(A) = multiply(multiply(double_divide(B,A),double_divide(multiply(C,D),double_divide(D,B))),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[178])]),
[iquote('copy,178,flip.1')] ).
cnf(206,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)],[90,12]),77]),
[iquote('para_from,90.1.1,12.1.1.2,demod,77')] ).
cnf(222,plain,
multiply(double_divide(A,inverse(B)),multiply(multiply(C,D),A)) = multiply(multiply(B,C),D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[118,118]),7]),
[iquote('para_into,118.1.1.1.2,118.1.1,demod,7')] ).
cnf(223,plain,
multiply(double_divide(A,inverse(B)),multiply(C,A)) = inverse(multiply(double_divide(multiply(D,C),B),D)),
inference(para_into,[status(thm),theory(equality)],[118,90]),
[iquote('para_into,118.1.1.1.2,90.1.1')] ).
cnf(239,plain,
multiply(multiply(A,B),C) = multiply(double_divide(D,inverse(A)),multiply(multiply(B,C),D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[222])]),
[iquote('copy,222,flip.1')] ).
cnf(240,plain,
inverse(multiply(double_divide(multiply(A,B),C),A)) = multiply(double_divide(D,inverse(C)),multiply(B,D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[223])]),
[iquote('copy,223,flip.1')] ).
cnf(266,plain,
multiply(multiply(A,B),multiply(inverse(A),C)) = multiply(B,C),
inference(para_from,[status(thm),theory(equality)],[118,8]),
[iquote('para_from,118.1.1,8.1.1.2.1')] ).
cnf(297,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)],[206,56])]),
[iquote('para_from,206.1.1,56.1.1.2,flip.1')] ).
cnf(387,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)],[266,12]),7])]),
[iquote('para_into,266.1.1.1,12.1.1,demod,7,flip.1')] ).
cnf(437,plain,
double_divide(multiply(A,multiply(multiply(B,C),D)),double_divide(D,A)) = double_divide(C,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[103]),387]),
[iquote('back_demod,103,demod,387')] ).
cnf(476,plain,
double_divide(multiply(A,multiply(inverse(B),C)),double_divide(C,A)) = B,
inference(para_from,[status(thm),theory(equality)],[297,78]),
[iquote('para_from,297.1.1,78.1.1.2')] ).
cnf(478,plain,
double_divide(A,multiply(double_divide(A,B),inverse(C))) = multiply(C,B),
inference(para_from,[status(thm),theory(equality)],[297,56]),
[iquote('para_from,297.1.1,56.1.1.2.1')] ).
cnf(489,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)],[478,206])]),
[iquote('para_into,478.1.1.2,206.1.1,flip.1')] ).
cnf(497,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)],[489,489]),
[iquote('para_into,489.1.1.2.2,489.1.1')] ).
cnf(513,plain,
inverse(A) = multiply(double_divide(B,A),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[186]),497,20]),
[iquote('back_demod,186,demod,497,20')] ).
cnf(546,plain,
double_divide(A,double_divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[513,476]),437]),
[iquote('para_from,513.1.1,476.1.1.1.2.1,demod,437')] ).
cnf(589,plain,
multiply(double_divide(multiply(A,B),C),A) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[546,56])]),
[iquote('para_into,546.1.1.2,56.1.1,flip.1')] ).
cnf(600,plain,
multiply(double_divide(A,inverse(B)),multiply(C,A)) = multiply(B,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[240]),589,7])]),
[iquote('back_demod,240,demod,589,7,flip.1')] ).
cnf(616,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[239]),600]),
[iquote('back_demod,239,demod,600')] ).
cnf(618,plain,
$false,
inference(binary,[status(thm)],[616,1]),
[iquote('binary,616.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP603-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n003.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 05:31:56 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.68/1.89 ----- Otter 3.3f, August 2004 -----
% 1.68/1.89 The process was started by sandbox on n003.cluster.edu,
% 1.68/1.89 Wed Jul 27 05:31:56 2022
% 1.68/1.89 The command was "./otter". The process ID is 22858.
% 1.68/1.89
% 1.68/1.89 set(prolog_style_variables).
% 1.68/1.89 set(auto).
% 1.68/1.89 dependent: set(auto1).
% 1.68/1.89 dependent: set(process_input).
% 1.68/1.89 dependent: clear(print_kept).
% 1.68/1.89 dependent: clear(print_new_demod).
% 1.68/1.89 dependent: clear(print_back_demod).
% 1.68/1.89 dependent: clear(print_back_sub).
% 1.68/1.89 dependent: set(control_memory).
% 1.68/1.89 dependent: assign(max_mem, 12000).
% 1.68/1.89 dependent: assign(pick_given_ratio, 4).
% 1.68/1.89 dependent: assign(stats_level, 1).
% 1.68/1.89 dependent: assign(max_seconds, 10800).
% 1.68/1.89 clear(print_given).
% 1.68/1.89
% 1.68/1.89 list(usable).
% 1.68/1.89 0 [] A=A.
% 1.68/1.89 0 [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.68/1.89 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.68/1.89 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.68/1.89
% 1.68/1.89 All clauses are units, and equality is present; the
% 1.68/1.89 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.68/1.89
% 1.68/1.89 dependent: set(knuth_bendix).
% 1.68/1.89 dependent: set(anl_eq).
% 1.68/1.89 dependent: set(para_from).
% 1.68/1.89 dependent: set(para_into).
% 1.68/1.89 dependent: clear(para_from_right).
% 1.68/1.89 dependent: clear(para_into_right).
% 1.68/1.89 dependent: set(para_from_vars).
% 1.68/1.89 dependent: set(eq_units_both_ways).
% 1.68/1.89 dependent: set(dynamic_demod_all).
% 1.68/1.89 dependent: set(dynamic_demod).
% 1.68/1.89 dependent: set(order_eq).
% 1.68/1.89 dependent: set(back_demod).
% 1.68/1.89 dependent: set(lrpo).
% 1.68/1.89
% 1.68/1.89 ------------> process usable:
% 1.68/1.89 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.68/1.89
% 1.68/1.89 ------------> process sos:
% 1.68/1.89 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.68/1.89 ** KEPT (pick-wt=14): 3 [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.68/1.89 ---> New Demodulator: 4 [new_demod,3] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.68/1.89 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.68/1.89 ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 1.68/1.89 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.68/1.89 >>>> Starting back demodulation with 4.
% 1.68/1.89 >>>> Starting back demodulation with 7.
% 1.68/1.89 >> back demodulating 3 with 7.
% 1.68/1.89 >>>> Starting back demodulation with 9.
% 1.68/1.89
% 1.68/1.89 ======= end of input processing =======
% 1.68/1.89
% 1.68/1.89 =========== start of search ===========
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Resetting weight limit to 15.
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Resetting weight limit to 15.
% 1.68/1.89
% 1.68/1.89 sos_size=294
% 1.68/1.89
% 1.68/1.89 -------- PROOF --------
% 1.68/1.89
% 1.68/1.89 ----> UNIT CONFLICT at 0.02 sec ----> 618 [binary,616.1,1.1] $F.
% 1.68/1.89
% 1.68/1.89 Length of proof is 34. Level of proof is 18.
% 1.68/1.89
% 1.68/1.89 ---------------- PROOF ----------------
% 1.68/1.89 % SZS status Unsatisfiable
% 1.68/1.89 % SZS output start Refutation
% See solution above
% 1.68/1.89 ------------ end of proof -------------
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89 ============ end of search ============
% 1.68/1.89
% 1.68/1.89 -------------- statistics -------------
% 1.68/1.89 clauses given 24
% 1.68/1.89 clauses generated 567
% 1.68/1.89 clauses kept 440
% 1.68/1.89 clauses forward subsumed 353
% 1.68/1.89 clauses back subsumed 0
% 1.68/1.89 Kbytes malloced 4882
% 1.68/1.89
% 1.68/1.89 ----------- times (seconds) -----------
% 1.68/1.89 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.68/1.89 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.68/1.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.68/1.89
% 1.68/1.89 That finishes the proof of the theorem.
% 1.68/1.89
% 1.68/1.89 Process 22858 finished Wed Jul 27 05:31:58 2022
% 1.68/1.89 Otter interrupted
% 1.68/1.89 PROOF FOUND
%------------------------------------------------------------------------------