TSTP Solution File: GRP614-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP614-1 : 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 12:57:22 EDT 2022
% Result : Unsatisfiable 1.66s 1.91s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of clauses : 28 ( 28 unt; 0 nHn; 3 RR)
% Number of literals : 28 ( 27 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 : 59 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP614-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP614-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,C)) = B,
file('GRP614-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP614-1.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(9,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)],[3]),7,7]),
[iquote('back_demod,3,demod,7,7')] ).
cnf(12,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)],[9,9]),
[iquote('para_into,8.1.1.2,8.1.1')] ).
cnf(14,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)],[9,7])]),
[iquote('para_from,8.1.1,6.1.1.1,flip.1')] ).
cnf(16,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)],[14,9]),
[iquote('para_into,14.1.1.1,8.1.1')] ).
cnf(96,plain,
multiply(A,multiply(inverse(B),inverse(A))) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,16]),9]),
[iquote('para_into,16.1.1.2.2,16.1.1,demod,9')] ).
cnf(108,plain,
double_divide(multiply(inverse(A),inverse(B)),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[16,12]),9]),
[iquote('para_from,16.1.1,12.1.1.1.2,demod,9')] ).
cnf(118,plain,
double_divide(multiply(inverse(A),multiply(B,C)),double_divide(C,B)) = A,
inference(para_into,[status(thm),theory(equality)],[108,7]),
[iquote('para_into,108.1.1.1.2,6.1.1')] ).
cnf(164,plain,
double_divide(inverse(A),double_divide(inverse(B),B)) = A,
inference(para_from,[status(thm),theory(equality)],[96,9]),
[iquote('para_from,96.1.1,8.1.1.1')] ).
cnf(168,plain,
double_divide(multiply(A,B),double_divide(inverse(C),C)) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[164,7]),
[iquote('para_into,164.1.1.1,6.1.1')] ).
cnf(316,plain,
double_divide(multiply(A,inverse(A)),inverse(B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[168,118])]),
[iquote('para_into,168.1.1,118.1.1,flip.1')] ).
cnf(339,plain,
double_divide(multiply(inverse(A),multiply(inverse(B),multiply(C,inverse(C)))),A) = B,
inference(para_from,[status(thm),theory(equality)],[316,9]),
[iquote('para_from,316.1.1,8.1.1.2')] ).
cnf(348,plain,
multiply(inverse(A),multiply(B,inverse(B))) = inverse(A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[316,7])]),
[iquote('para_from,316.1.1,6.1.1.1,flip.1')] ).
cnf(354,plain,
double_divide(multiply(inverse(A),inverse(B)),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[339]),348]),
[iquote('back_demod,339,demod,348')] ).
cnf(368,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[354,316])]),
[iquote('para_into,354.1.1,316.1.1,flip.1')] ).
cnf(552,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[368,96]),368]),
[iquote('para_from,367.1.1,96.1.1.2.1,demod,368')] ).
cnf(642,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[552,118]),368]),
[iquote('para_from,552.1.1,118.1.1.1,demod,368')] ).
cnf(656,plain,
double_divide(double_divide(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[642,642]),
[iquote('para_into,642.1.1.2,642.1.1')] ).
cnf(658,plain,
multiply(inverse(A),inverse(B)) = double_divide(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[642,354])]),
[iquote('para_into,642.1.1.2,354.1.1,flip.1')] ).
cnf(665,plain,
double_divide(A,B) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[642,108]),658]),
[iquote('para_into,642.1.1.2,108.1.1,demod,658')] ).
cnf(671,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)],[642,9])]),
[iquote('para_into,642.1.1.2,8.1.1,flip.1')] ).
cnf(831,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[665,7]),7]),
[iquote('para_from,665.1.1,6.1.1.1,demod,7')] ).
cnf(843,plain,
a2 != a2,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[831,1]),671,656]),
[iquote('para_from,831.1.1,1.1.1,demod,671,656')] ).
cnf(844,plain,
$false,
inference(binary,[status(thm)],[843,2]),
[iquote('binary,843.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP614-1 : TPTP v8.1.0. Released v2.6.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 05:10:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.91 ----- Otter 3.3f, August 2004 -----
% 1.66/1.91 The process was started by sandbox2 on n005.cluster.edu,
% 1.66/1.91 Wed Jul 27 05:10:05 2022
% 1.66/1.91 The command was "./otter". The process ID is 21099.
% 1.66/1.91
% 1.66/1.91 set(prolog_style_variables).
% 1.66/1.91 set(auto).
% 1.66/1.91 dependent: set(auto1).
% 1.66/1.91 dependent: set(process_input).
% 1.66/1.91 dependent: clear(print_kept).
% 1.66/1.91 dependent: clear(print_new_demod).
% 1.66/1.91 dependent: clear(print_back_demod).
% 1.66/1.91 dependent: clear(print_back_sub).
% 1.66/1.91 dependent: set(control_memory).
% 1.66/1.91 dependent: assign(max_mem, 12000).
% 1.66/1.91 dependent: assign(pick_given_ratio, 4).
% 1.66/1.91 dependent: assign(stats_level, 1).
% 1.66/1.91 dependent: assign(max_seconds, 10800).
% 1.66/1.91 clear(print_given).
% 1.66/1.91
% 1.66/1.91 list(usable).
% 1.66/1.91 0 [] A=A.
% 1.66/1.91 0 [] double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,C))=B.
% 1.66/1.91 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.66/1.91 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.66/1.91 end_of_list.
% 1.66/1.91
% 1.66/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.66/1.91
% 1.66/1.91 All clauses are units, and equality is present; the
% 1.66/1.91 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.66/1.91
% 1.66/1.91 dependent: set(knuth_bendix).
% 1.66/1.91 dependent: set(anl_eq).
% 1.66/1.91 dependent: set(para_from).
% 1.66/1.91 dependent: set(para_into).
% 1.66/1.91 dependent: clear(para_from_right).
% 1.66/1.91 dependent: clear(para_into_right).
% 1.66/1.91 dependent: set(para_from_vars).
% 1.66/1.91 dependent: set(eq_units_both_ways).
% 1.66/1.91 dependent: set(dynamic_demod_all).
% 1.66/1.91 dependent: set(dynamic_demod).
% 1.66/1.91 dependent: set(order_eq).
% 1.66/1.91 dependent: set(back_demod).
% 1.66/1.91 dependent: set(lrpo).
% 1.66/1.91
% 1.66/1.91 ------------> process usable:
% 1.66/1.91 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.66/1.91
% 1.66/1.91 ------------> process sos:
% 1.66/1.91 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.66/1.91 ** KEPT (pick-wt=14): 3 [] double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,C))=B.
% 1.66/1.91 ---> New Demodulator: 4 [new_demod,3] double_divide(inverse(double_divide(inverse(double_divide(A,inverse(B))),C)),double_divide(A,C))=B.
% 1.66/1.91 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.66/1.91 ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 1.66/1.91 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.66/1.91 >>>> Starting back demodulation with 4.
% 1.66/1.91 >>>> Starting back demodulation with 7.
% 1.66/1.91 >> back demodulating 3 with 7.
% 1.66/1.91 >>>> Starting back demodulation with 9.
% 1.66/1.91
% 1.66/1.91 ======= end of input processing =======
% 1.66/1.91
% 1.66/1.91 =========== start of search ===========
% 1.66/1.91
% 1.66/1.91
% 1.66/1.91 Resetting weight limit to 9.
% 1.66/1.91
% 1.66/1.91
% 1.66/1.91 Resetting weight limit to 9.
% 1.66/1.91
% 1.66/1.91 sos_size=199
% 1.66/1.91
% 1.66/1.91 -------- PROOF --------
% 1.66/1.91
% 1.66/1.91 ----> UNIT CONFLICT at 0.03 sec ----> 844 [binary,843.1,2.1] $F.
% 1.66/1.91
% 1.66/1.91 Length of proof is 23. Level of proof is 17.
% 1.66/1.91
% 1.66/1.91 ---------------- PROOF ----------------
% 1.66/1.91 % SZS status Unsatisfiable
% 1.66/1.91 % SZS output start Refutation
% See solution above
% 1.66/1.91 ------------ end of proof -------------
% 1.66/1.91
% 1.66/1.91
% 1.66/1.91 Search stopped by max_proofs option.
% 1.66/1.91
% 1.66/1.91
% 1.66/1.91 Search stopped by max_proofs option.
% 1.66/1.91
% 1.66/1.91 ============ end of search ============
% 1.66/1.91
% 1.66/1.91 -------------- statistics -------------
% 1.66/1.91 clauses given 37
% 1.66/1.91 clauses generated 669
% 1.66/1.91 clauses kept 489
% 1.66/1.91 clauses forward subsumed 541
% 1.66/1.91 clauses back subsumed 4
% 1.66/1.91 Kbytes malloced 4882
% 1.66/1.91
% 1.66/1.91 ----------- times (seconds) -----------
% 1.66/1.91 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.66/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.91 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.66/1.91
% 1.66/1.91 That finishes the proof of the theorem.
% 1.66/1.91
% 1.66/1.91 Process 21099 finished Wed Jul 27 05:10:07 2022
% 1.66/1.91 Otter interrupted
% 1.66/1.91 PROOF FOUND
%------------------------------------------------------------------------------