TSTP Solution File: GRP589-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP589-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 1.87s 2.09s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 3 RR)
% Number of literals : 16 ( 15 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 : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP589-1.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(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B) = C,
file('GRP589-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP589-1.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(9,plain,
double_divide(multiply(multiply(inverse(A),B),double_divide(B,C)),C) = A,
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(multiply(inverse(A),multiply(multiply(inverse(B),C),double_divide(C,D))),B),D) = A,
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.1.2,9.1.1')] ).
cnf(15,plain,
multiply(A,multiply(multiply(inverse(B),C),double_divide(C,A))) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[9,8])]),
[iquote('para_from,9.1.1,7.1.1.1,flip.1')] ).
cnf(43,plain,
double_divide(multiply(inverse(A),A),inverse(B)) = B,
inference(para_into,[status(thm),theory(equality)],[13,15]),
[iquote('para_into,13.1.1.1.1,15.1.1')] ).
cnf(59,plain,
double_divide(multiply(multiply(inverse(A),multiply(inverse(B),B)),C),inverse(C)) = A,
inference(para_from,[status(thm),theory(equality)],[43,9]),
[iquote('para_from,43.1.1,9.1.1.1.2')] ).
cnf(62,plain,
multiply(inverse(A),multiply(inverse(B),B)) = inverse(A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[43,8])]),
[iquote('para_from,43.1.1,7.1.1.1,flip.1')] ).
cnf(63,plain,
double_divide(multiply(inverse(A),B),inverse(B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[59]),62]),
[iquote('back_demod,59,demod,62')] ).
cnf(87,plain,
double_divide(inverse(multiply(inverse(A),A)),inverse(B)) = B,
inference(para_from,[status(thm),theory(equality)],[62,43]),
[iquote('para_from,61.1.1,43.1.1.1')] ).
cnf(93,plain,
double_divide(inverse(A),inverse(multiply(inverse(B),B))) = A,
inference(para_from,[status(thm),theory(equality)],[62,63]),
[iquote('para_from,61.1.1,63.1.1.1')] ).
cnf(153,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(para_into,[status(thm),theory(equality)],[93,87]),
[iquote('para_into,93.1.1,87.1.1')] ).
cnf(154,plain,
$false,
inference(binary,[status(thm)],[153,2]),
[iquote('binary,153.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP589-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 05:16:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.87/2.09 ----- Otter 3.3f, August 2004 -----
% 1.87/2.09 The process was started by sandbox2 on n025.cluster.edu,
% 1.87/2.09 Wed Jul 27 05:16:30 2022
% 1.87/2.09 The command was "./otter". The process ID is 14571.
% 1.87/2.09
% 1.87/2.09 set(prolog_style_variables).
% 1.87/2.09 set(auto).
% 1.87/2.09 dependent: set(auto1).
% 1.87/2.09 dependent: set(process_input).
% 1.87/2.09 dependent: clear(print_kept).
% 1.87/2.09 dependent: clear(print_new_demod).
% 1.87/2.09 dependent: clear(print_back_demod).
% 1.87/2.09 dependent: clear(print_back_sub).
% 1.87/2.09 dependent: set(control_memory).
% 1.87/2.09 dependent: assign(max_mem, 12000).
% 1.87/2.09 dependent: assign(pick_given_ratio, 4).
% 1.87/2.09 dependent: assign(stats_level, 1).
% 1.87/2.09 dependent: assign(max_seconds, 10800).
% 1.87/2.09 clear(print_given).
% 1.87/2.09
% 1.87/2.09 list(usable).
% 1.87/2.09 0 [] A=A.
% 1.87/2.09 0 [] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.87/2.09 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.87/2.09 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.87/2.09 end_of_list.
% 1.87/2.09
% 1.87/2.09 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.87/2.09
% 1.87/2.09 All clauses are units, and equality is present; the
% 1.87/2.09 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.87/2.09
% 1.87/2.09 dependent: set(knuth_bendix).
% 1.87/2.09 dependent: set(anl_eq).
% 1.87/2.09 dependent: set(para_from).
% 1.87/2.09 dependent: set(para_into).
% 1.87/2.09 dependent: clear(para_from_right).
% 1.87/2.09 dependent: clear(para_into_right).
% 1.87/2.09 dependent: set(para_from_vars).
% 1.87/2.09 dependent: set(eq_units_both_ways).
% 1.87/2.09 dependent: set(dynamic_demod_all).
% 1.87/2.09 dependent: set(dynamic_demod).
% 1.87/2.09 dependent: set(order_eq).
% 1.87/2.09 dependent: set(back_demod).
% 1.87/2.09 dependent: set(lrpo).
% 1.87/2.09
% 1.87/2.09 ------------> process usable:
% 1.87/2.09 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.87/2.09
% 1.87/2.09 ------------> process sos:
% 1.87/2.09 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.87/2.09 ** KEPT (pick-wt=14): 4 [] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.87/2.09 ---> New Demodulator: 5 [new_demod,4] double_divide(inverse(double_divide(double_divide(A,B),inverse(double_divide(A,inverse(C))))),B)=C.
% 1.87/2.09 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.87/2.09 ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.87/2.09 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.87/2.09 >>>> Starting back demodulation with 5.
% 1.87/2.09 >>>> Starting back demodulation with 8.
% 1.87/2.09 >> back demodulating 4 with 8.
% 1.87/2.09 >>>> Starting back demodulation with 10.
% 1.87/2.09
% 1.87/2.09 ======= end of input processing =======
% 1.87/2.09
% 1.87/2.09 =========== start of search ===========
% 1.87/2.09
% 1.87/2.09 -------- PROOF --------
% 1.87/2.09
% 1.87/2.09 ----> UNIT CONFLICT at 0.00 sec ----> 154 [binary,153.1,2.1] $F.
% 1.87/2.09
% 1.87/2.09 Length of proof is 12. Level of proof is 8.
% 1.87/2.09
% 1.87/2.09 ---------------- PROOF ----------------
% 1.87/2.09 % SZS status Unsatisfiable
% 1.87/2.09 % SZS output start Refutation
% See solution above
% 1.87/2.09 ------------ end of proof -------------
% 1.87/2.09
% 1.87/2.09
% 1.87/2.09 Search stopped by max_proofs option.
% 1.87/2.09
% 1.87/2.09
% 1.87/2.09 Search stopped by max_proofs option.
% 1.87/2.09
% 1.87/2.09 ============ end of search ============
% 1.87/2.09
% 1.87/2.09 -------------- statistics -------------
% 1.87/2.09 clauses given 13
% 1.87/2.09 clauses generated 125
% 1.87/2.09 clauses kept 78
% 1.87/2.09 clauses forward subsumed 59
% 1.87/2.09 clauses back subsumed 0
% 1.87/2.09 Kbytes malloced 1953
% 1.87/2.09
% 1.87/2.09 ----------- times (seconds) -----------
% 1.87/2.09 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.09 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.87/2.09
% 1.87/2.09 That finishes the proof of the theorem.
% 1.87/2.09
% 1.87/2.09 Process 14571 finished Wed Jul 27 05:16:32 2022
% 1.87/2.09 Otter interrupted
% 1.87/2.09 PROOF FOUND
%------------------------------------------------------------------------------