TSTP Solution File: GRP594-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP594-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 12:57:19 EDT 2022
% Result : Unsatisfiable 1.65s 1.86s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 4
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 3 RR)
% Number of literals : 42 ( 41 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 119 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP594-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP594-1.p',unknown),
[] ).
cnf(3,axiom,
inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B)))))) = C,
file('GRP594-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP594-1.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(multiply(multiply(A,B),C),double_divide(C,A)) = B,
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(A,B),double_divide(B,multiply(multiply(C,A),D))) = double_divide(D,C),
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.1.1,8.1.1')] ).
cnf(12,plain,
multiply(A,double_divide(double_divide(B,C),multiply(C,A))) = B,
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.1,8.1.1')] ).
cnf(16,plain,
multiply(double_divide(A,B),double_divide(double_divide(C,multiply(multiply(B,D),A)),D)) = C,
inference(para_into,[status(thm),theory(equality)],[12,8]),
[iquote('para_into,12.1.1.2.2,8.1.1')] ).
cnf(35,plain,
double_divide(multiply(A,double_divide(B,multiply(C,A))),C) = B,
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(66,plain,
double_divide(double_divide(multiply(A,B),C),multiply(C,A)) = B,
inference(para_into,[status(thm),theory(equality)],[35,10]),
[iquote('para_into,35.1.1.1,10.1.1')] ).
cnf(76,plain,
inverse(A) = multiply(B,multiply(C,double_divide(A,multiply(B,C)))),
inference(para_from,[status(thm),theory(equality)],[35,7]),
[iquote('para_from,35.1.1,6.1.1.1')] ).
cnf(78,plain,
multiply(A,multiply(B,double_divide(C,multiply(A,B)))) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[76])]),
[iquote('copy,76,flip.1')] ).
cnf(102,plain,
inverse(A) = multiply(multiply(B,C),double_divide(multiply(C,A),B)),
inference(para_from,[status(thm),theory(equality)],[66,7]),
[iquote('para_from,65.1.1,6.1.1.1')] ).
cnf(103,plain,
multiply(multiply(A,B),double_divide(multiply(B,C),A)) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[102])]),
[iquote('copy,102,flip.1')] ).
cnf(159,plain,
multiply(double_divide(A,B),double_divide(C,D)) = double_divide(multiply(A,C),multiply(B,D)),
inference(para_into,[status(thm),theory(equality)],[16,66]),
[iquote('para_into,16.1.1.2.1,65.1.1')] ).
cnf(212,plain,
multiply(inverse(A),double_divide(double_divide(multiply(B,A),C),C)) = B,
inference(para_from,[status(thm),theory(equality)],[103,8]),
[iquote('para_from,103.1.1,8.1.1.1')] ).
cnf(241,plain,
multiply(multiply(A,inverse(B)),multiply(C,B)) = multiply(A,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[212,78]),7])]),
[iquote('para_from,212.1.1,78.1.1.2,demod,7,flip.1')] ).
cnf(243,plain,
double_divide(multiply(A,B),multiply(C,inverse(B))) = double_divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[212,35])]),
[iquote('para_from,212.1.1,35.1.1.1,flip.1')] ).
cnf(356,plain,
double_divide(double_divide(A,B),multiply(multiply(B,inverse(C)),A)) = C,
inference(para_from,[status(thm),theory(equality)],[243,66]),
[iquote('para_from,243.1.1,65.1.1.1')] ).
cnf(358,plain,
double_divide(multiply(inverse(A),double_divide(B,C)),C) = multiply(B,A),
inference(para_from,[status(thm),theory(equality)],[243,35]),
[iquote('para_from,243.1.1,35.1.1.1.2')] ).
cnf(375,plain,
double_divide(A,multiply(multiply(B,inverse(C)),multiply(D,double_divide(A,multiply(B,D))))) = C,
inference(para_into,[status(thm),theory(equality)],[356,35]),
[iquote('para_into,356.1.1.1,35.1.1')] ).
cnf(403,plain,
double_divide(multiply(multiply(multiply(A,B),double_divide(multiply(B,C),A)),double_divide(D,E)),E) = multiply(D,C),
inference(para_into,[status(thm),theory(equality)],[358,102]),
[iquote('para_into,358.1.1.1.1,102.1.1')] ).
cnf(411,plain,
multiply(double_divide(multiply(A,B),C),B) = double_divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[358,212])]),
[iquote('para_into,358.1.1.1,212.1.1,flip.1')] ).
cnf(416,plain,
multiply(A,B) = double_divide(multiply(multiply(multiply(C,D),double_divide(multiply(D,B),C)),double_divide(A,E)),E),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[403])]),
[iquote('copy,403,flip.1')] ).
cnf(440,plain,
multiply(double_divide(double_divide(A,B),C),D) = double_divide(double_divide(multiply(A,D),B),C),
inference(para_into,[status(thm),theory(equality)],[411,411]),
[iquote('para_into,411.1.1.1.1,411.1.1')] ).
cnf(453,plain,
multiply(A,double_divide(A,multiply(B,C))) = double_divide(C,B),
inference(para_into,[status(thm),theory(equality)],[411,35]),
[iquote('para_into,411.1.1.1,35.1.1')] ).
cnf(490,plain,
multiply(multiply(A,inverse(B)),double_divide(C,D)) = multiply(A,double_divide(multiply(C,B),D)),
inference(para_from,[status(thm),theory(equality)],[411,241]),
[iquote('para_from,411.1.1,241.1.1.2')] ).
cnf(515,plain,
multiply(A,double_divide(multiply(B,C),D)) = multiply(multiply(A,inverse(C)),double_divide(B,D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[490])]),
[iquote('copy,490,flip.1')] ).
cnf(536,plain,
inverse(multiply(A,B)) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[453,103]),
[iquote('para_into,453.1.1,103.1.1')] ).
cnf(538,plain,
double_divide(double_divide(A,B),B) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[453,12])]),
[iquote('para_into,453.1.1,12.1.1,flip.1')] ).
cnf(580,plain,
multiply(inverse(A),multiply(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[212]),538]),
[iquote('back_demod,212,demod,538')] ).
cnf(620,plain,
multiply(A,double_divide(B,multiply(C,A))) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[538,35])]),
[iquote('para_into,537.1.1.1,35.1.1,flip.1')] ).
cnf(635,plain,
double_divide(A,multiply(multiply(B,inverse(C)),double_divide(A,B))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[375]),620]),
[iquote('back_demod,375,demod,620')] ).
cnf(764,plain,
multiply(multiply(A,inverse(B)),double_divide(C,A)) = double_divide(B,C),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[580,103]),536]),
[iquote('para_from,580.1.1,103.1.1.2.1,demod,536')] ).
cnf(773,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[635]),764]),
[iquote('back_demod,635,demod,764')] ).
cnf(784,plain,
double_divide(double_divide(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[773,773]),
[iquote('para_into,772.1.1.2,772.1.1')] ).
cnf(820,plain,
multiply(multiply(A,inverse(B)),C) = double_divide(B,double_divide(C,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[784,356])]),
[iquote('para_into,784.1.1.1,356.1.1,flip.1')] ).
cnf(826,plain,
multiply(A,double_divide(multiply(B,C),D)) = double_divide(C,double_divide(double_divide(B,D),A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[515]),820]),
[iquote('back_demod,515,demod,820')] ).
cnf(849,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[416]),826,159,440,66,538]),
[iquote('back_demod,416,demod,826,159,440,66,538')] ).
cnf(964,plain,
a2 != a2,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[849,1]),820,773]),
[iquote('para_from,849.1.1,1.1.1.1,demod,820,773')] ).
cnf(965,plain,
$false,
inference(binary,[status(thm)],[964,2]),
[iquote('binary,964.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP594-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n005.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 05:00:50 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.65/1.86 ----- Otter 3.3f, August 2004 -----
% 1.65/1.86 The process was started by sandbox on n005.cluster.edu,
% 1.65/1.86 Wed Jul 27 05:00:50 2022
% 1.65/1.86 The command was "./otter". The process ID is 14748.
% 1.65/1.86
% 1.65/1.86 set(prolog_style_variables).
% 1.65/1.86 set(auto).
% 1.65/1.86 dependent: set(auto1).
% 1.65/1.86 dependent: set(process_input).
% 1.65/1.86 dependent: clear(print_kept).
% 1.65/1.86 dependent: clear(print_new_demod).
% 1.65/1.86 dependent: clear(print_back_demod).
% 1.65/1.86 dependent: clear(print_back_sub).
% 1.65/1.86 dependent: set(control_memory).
% 1.65/1.86 dependent: assign(max_mem, 12000).
% 1.65/1.86 dependent: assign(pick_given_ratio, 4).
% 1.65/1.86 dependent: assign(stats_level, 1).
% 1.65/1.86 dependent: assign(max_seconds, 10800).
% 1.65/1.86 clear(print_given).
% 1.65/1.86
% 1.65/1.86 list(usable).
% 1.65/1.86 0 [] A=A.
% 1.65/1.86 0 [] inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B))))))=C.
% 1.65/1.86 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.65/1.86 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.65/1.86 end_of_list.
% 1.65/1.86
% 1.65/1.86 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.65/1.86
% 1.65/1.86 All clauses are units, and equality is present; the
% 1.65/1.86 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.65/1.86
% 1.65/1.86 dependent: set(knuth_bendix).
% 1.65/1.86 dependent: set(anl_eq).
% 1.65/1.86 dependent: set(para_from).
% 1.65/1.86 dependent: set(para_into).
% 1.65/1.86 dependent: clear(para_from_right).
% 1.65/1.86 dependent: clear(para_into_right).
% 1.65/1.86 dependent: set(para_from_vars).
% 1.65/1.86 dependent: set(eq_units_both_ways).
% 1.65/1.86 dependent: set(dynamic_demod_all).
% 1.65/1.86 dependent: set(dynamic_demod).
% 1.65/1.86 dependent: set(order_eq).
% 1.65/1.86 dependent: set(back_demod).
% 1.65/1.86 dependent: set(lrpo).
% 1.65/1.86
% 1.65/1.86 ------------> process usable:
% 1.65/1.86 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.65/1.86
% 1.65/1.86 ------------> process sos:
% 1.65/1.86 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.65/1.86 ** KEPT (pick-wt=14): 3 [] inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B))))))=C.
% 1.65/1.86 ---> New Demodulator: 4 [new_demod,3] inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(C,B))))))=C.
% 1.65/1.86 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.65/1.86 ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 1.65/1.86 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.65/1.86 >>>> Starting back demodulation with 4.
% 1.65/1.86 >>>> Starting back demodulation with 7.
% 1.65/1.86 >> back demodulating 3 with 7.
% 1.65/1.86 >>>> Starting back demodulation with 9.
% 1.65/1.86
% 1.65/1.86 ======= end of input processing =======
% 1.65/1.86
% 1.65/1.86 =========== start of search ===========
% 1.65/1.86
% 1.65/1.86
% 1.65/1.86 Resetting weight limit to 15.
% 1.65/1.86
% 1.65/1.86
% 1.65/1.86 Resetting weight limit to 15.
% 1.65/1.86
% 1.65/1.86 sos_size=292
% 1.65/1.86
% 1.65/1.86 -------- PROOF --------
% 1.65/1.86
% 1.65/1.86 ----> UNIT CONFLICT at 0.02 sec ----> 965 [binary,964.1,2.1] $F.
% 1.65/1.86
% 1.65/1.86 Length of proof is 37. Level of proof is 21.
% 1.65/1.86
% 1.65/1.86 ---------------- PROOF ----------------
% 1.65/1.86 % SZS status Unsatisfiable
% 1.65/1.86 % SZS output start Refutation
% See solution above
% 1.65/1.86 ------------ end of proof -------------
% 1.65/1.86
% 1.65/1.86
% 1.65/1.86 Search stopped by max_proofs option.
% 1.65/1.86
% 1.65/1.86
% 1.65/1.86 Search stopped by max_proofs option.
% 1.65/1.86
% 1.65/1.86 ============ end of search ============
% 1.65/1.86
% 1.65/1.86 -------------- statistics -------------
% 1.65/1.86 clauses given 34
% 1.65/1.86 clauses generated 784
% 1.65/1.86 clauses kept 677
% 1.65/1.86 clauses forward subsumed 588
% 1.65/1.86 clauses back subsumed 0
% 1.65/1.86 Kbytes malloced 4882
% 1.65/1.86
% 1.65/1.86 ----------- times (seconds) -----------
% 1.65/1.86 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.65/1.86 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.86 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.65/1.86
% 1.65/1.86 That finishes the proof of the theorem.
% 1.65/1.86
% 1.65/1.86 Process 14748 finished Wed Jul 27 05:00:52 2022
% 1.65/1.86 Otter interrupted
% 1.65/1.86 PROOF FOUND
%------------------------------------------------------------------------------