TSTP Solution File: GRP613-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP613-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 12:57:22 EDT 2022
% Result : Unsatisfiable 1.67s 1.90s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 4 RR)
% Number of literals : 32 ( 31 equ; 3 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP613-1.p',unknown),
[] ).
cnf(2,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,C)) = B,
file('GRP613-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP613-1.p',unknown),
[] ).
cnf(8,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(10,plain,
double_divide(multiply(A,multiply(inverse(B),C)),double_divide(C,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),8,8]),
[iquote('back_demod,4,demod,8,8')] ).
cnf(13,plain,
double_divide(multiply(double_divide(A,B),multiply(inverse(C),multiply(B,multiply(inverse(D),A)))),D) = C,
inference(para_into,[status(thm),theory(equality)],[10,10]),
[iquote('para_into,9.1.1.2,9.1.1')] ).
cnf(15,plain,
multiply(double_divide(A,B),multiply(B,multiply(inverse(C),A))) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[10,8])]),
[iquote('para_from,9.1.1,7.1.1.1,flip.1')] ).
cnf(17,plain,
multiply(A,multiply(double_divide(B,C),multiply(inverse(D),multiply(C,multiply(inverse(A),B))))) = inverse(D),
inference(para_into,[status(thm),theory(equality)],[15,10]),
[iquote('para_into,15.1.1.1,9.1.1')] ).
cnf(97,plain,
multiply(A,multiply(inverse(B),inverse(A))) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,17]),10]),
[iquote('para_into,17.1.1.2.2,17.1.1,demod,10')] ).
cnf(109,plain,
double_divide(multiply(inverse(A),inverse(B)),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[17,13]),10]),
[iquote('para_from,17.1.1,13.1.1.1.2,demod,10')] ).
cnf(119,plain,
double_divide(multiply(inverse(A),multiply(B,C)),double_divide(C,B)) = A,
inference(para_into,[status(thm),theory(equality)],[109,8]),
[iquote('para_into,109.1.1.1.2,7.1.1')] ).
cnf(165,plain,
double_divide(inverse(A),double_divide(inverse(B),B)) = A,
inference(para_from,[status(thm),theory(equality)],[97,10]),
[iquote('para_from,97.1.1,9.1.1.1')] ).
cnf(169,plain,
double_divide(multiply(A,B),double_divide(inverse(C),C)) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[165,8]),
[iquote('para_into,165.1.1.1,7.1.1')] ).
cnf(317,plain,
double_divide(multiply(A,inverse(A)),inverse(B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[169,119])]),
[iquote('para_into,169.1.1,119.1.1,flip.1')] ).
cnf(340,plain,
double_divide(multiply(inverse(A),multiply(inverse(B),multiply(C,inverse(C)))),A) = B,
inference(para_from,[status(thm),theory(equality)],[317,10]),
[iquote('para_from,317.1.1,9.1.1.2')] ).
cnf(349,plain,
multiply(inverse(A),multiply(B,inverse(B))) = inverse(A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[317,8])]),
[iquote('para_from,317.1.1,7.1.1.1,flip.1')] ).
cnf(355,plain,
double_divide(multiply(inverse(A),inverse(B)),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[340]),349]),
[iquote('back_demod,340,demod,349')] ).
cnf(369,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[355,317])]),
[iquote('para_into,355.1.1,317.1.1,flip.1')] ).
cnf(495,plain,
multiply(A,multiply(B,multiply(inverse(C),multiply(D,multiply(inverse(A),multiply(inverse(D),inverse(B))))))) = inverse(C),
inference(para_from,[status(thm),theory(equality)],[355,17]),
[iquote('para_from,355.1.1,17.1.1.2.1')] ).
cnf(553,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[369,97]),369]),
[iquote('para_from,368.1.1,97.1.1.2.1,demod,369')] ).
cnf(643,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[553,119]),369]),
[iquote('para_from,553.1.1,119.1.1.1,demod,369')] ).
cnf(657,plain,
double_divide(double_divide(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[643,643]),
[iquote('para_into,643.1.1.2,643.1.1')] ).
cnf(659,plain,
multiply(inverse(A),inverse(B)) = double_divide(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[643,355])]),
[iquote('para_into,643.1.1.2,355.1.1,flip.1')] ).
cnf(666,plain,
double_divide(A,B) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[643,109]),659]),
[iquote('para_into,643.1.1.2,109.1.1,demod,659')] ).
cnf(672,plain,
multiply(A,multiply(inverse(B),C)) = double_divide(double_divide(C,A),B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[643,10])]),
[iquote('para_into,643.1.1.2,9.1.1,flip.1')] ).
cnf(682,plain,
multiply(A,double_divide(A,B)) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[495]),659,672,657,672,657]),
[iquote('back_demod,495,demod,659,672,657,672,657')] ).
cnf(832,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[666,8]),8]),
[iquote('para_from,666.1.1,7.1.1.1,demod,8')] ).
cnf(844,plain,
multiply(b1,inverse(b1)) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[832,2]),
[iquote('para_from,832.1.1,2.1.1')] ).
cnf(851,plain,
multiply(inverse(A),A) = multiply(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[682,165]),8]),
[iquote('para_into,682.1.1.2,165.1.1,demod,8')] ).
cnf(853,plain,
multiply(A,inverse(A)) = multiply(inverse(B),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[851])]),
[iquote('copy,851,flip.1')] ).
cnf(854,plain,
$false,
inference(binary,[status(thm)],[853,844]),
[iquote('binary,853.1,844.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP613-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 05:02:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.90 ----- Otter 3.3f, August 2004 -----
% 1.67/1.90 The process was started by sandbox2 on n014.cluster.edu,
% 1.67/1.90 Wed Jul 27 05:02:39 2022
% 1.67/1.90 The command was "./otter". The process ID is 6688.
% 1.67/1.90
% 1.67/1.90 set(prolog_style_variables).
% 1.67/1.90 set(auto).
% 1.67/1.90 dependent: set(auto1).
% 1.67/1.90 dependent: set(process_input).
% 1.67/1.90 dependent: clear(print_kept).
% 1.67/1.90 dependent: clear(print_new_demod).
% 1.67/1.90 dependent: clear(print_back_demod).
% 1.67/1.90 dependent: clear(print_back_sub).
% 1.67/1.90 dependent: set(control_memory).
% 1.67/1.90 dependent: assign(max_mem, 12000).
% 1.67/1.90 dependent: assign(pick_given_ratio, 4).
% 1.67/1.90 dependent: assign(stats_level, 1).
% 1.67/1.90 dependent: assign(max_seconds, 10800).
% 1.67/1.90 clear(print_given).
% 1.67/1.90
% 1.67/1.90 list(usable).
% 1.67/1.90 0 [] A=A.
% 1.67/1.90 0 [] double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,C))=B.
% 1.67/1.90 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.67/1.90 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.67/1.90 end_of_list.
% 1.67/1.90
% 1.67/1.90 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.67/1.90
% 1.67/1.90 All clauses are units, and equality is present; the
% 1.67/1.90 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.67/1.90
% 1.67/1.90 dependent: set(knuth_bendix).
% 1.67/1.90 dependent: set(anl_eq).
% 1.67/1.90 dependent: set(para_from).
% 1.67/1.90 dependent: set(para_into).
% 1.67/1.90 dependent: clear(para_from_right).
% 1.67/1.90 dependent: clear(para_into_right).
% 1.67/1.90 dependent: set(para_from_vars).
% 1.67/1.90 dependent: set(eq_units_both_ways).
% 1.67/1.90 dependent: set(dynamic_demod_all).
% 1.67/1.90 dependent: set(dynamic_demod).
% 1.67/1.90 dependent: set(order_eq).
% 1.67/1.90 dependent: set(back_demod).
% 1.67/1.90 dependent: set(lrpo).
% 1.67/1.90
% 1.67/1.90 ------------> process usable:
% 1.67/1.90 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.67/1.90
% 1.67/1.90 ------------> process sos:
% 1.67/1.90 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.67/1.90 ** KEPT (pick-wt=14): 4 [] double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,C))=B.
% 1.67/1.90 ---> New Demodulator: 5 [new_demod,4] double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,C))=B.
% 1.67/1.90 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.67/1.90 ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.67/1.90 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.67/1.90 >>>> Starting back demodulation with 5.
% 1.67/1.90 >>>> Starting back demodulation with 8.
% 1.67/1.90 >> back demodulating 4 with 8.
% 1.67/1.90 >>>> Starting back demodulation with 10.
% 1.67/1.90
% 1.67/1.90 ======= end of input processing =======
% 1.67/1.90
% 1.67/1.90 =========== start of search ===========
% 1.67/1.90
% 1.67/1.90
% 1.67/1.90 Resetting weight limit to 9.
% 1.67/1.90
% 1.67/1.90
% 1.67/1.90 Resetting weight limit to 9.
% 1.67/1.90
% 1.67/1.90 sos_size=199
% 1.67/1.90
% 1.67/1.90 -------- PROOF --------
% 1.67/1.90
% 1.67/1.90 ----> UNIT CONFLICT at 0.03 sec ----> 854 [binary,853.1,844.1] $F.
% 1.67/1.90
% 1.67/1.90 Length of proof is 28. Level of proof is 17.
% 1.67/1.90
% 1.67/1.90 ---------------- PROOF ----------------
% 1.67/1.90 % SZS status Unsatisfiable
% 1.67/1.90 % SZS output start Refutation
% See solution above
% 1.67/1.91 ------------ end of proof -------------
% 1.67/1.91
% 1.67/1.91
% 1.67/1.91 Search stopped by max_proofs option.
% 1.67/1.91
% 1.67/1.91
% 1.67/1.91 Search stopped by max_proofs option.
% 1.67/1.91
% 1.67/1.91 ============ end of search ============
% 1.67/1.91
% 1.67/1.91 -------------- statistics -------------
% 1.67/1.91 clauses given 40
% 1.67/1.91 clauses generated 726
% 1.67/1.91 clauses kept 496
% 1.67/1.91 clauses forward subsumed 582
% 1.67/1.91 clauses back subsumed 4
% 1.67/1.91 Kbytes malloced 4882
% 1.67/1.91
% 1.67/1.91 ----------- times (seconds) -----------
% 1.67/1.91 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.67/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.91 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.91
% 1.67/1.91 That finishes the proof of the theorem.
% 1.67/1.91
% 1.67/1.91 Process 6688 finished Wed Jul 27 05:02:40 2022
% 1.67/1.91 Otter interrupted
% 1.67/1.91 PROOF FOUND
%------------------------------------------------------------------------------