TSTP Solution File: GRP597-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP597-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 1.79s 1.94s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 4 RR)
% Number of literals : 31 ( 30 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 : 66 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP597-1.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(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B))))) = C,
file('GRP597-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP597-1.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(double_divide(A,B),multiply(multiply(B,inverse(C)),A)) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),8,8]),
[iquote('back_demod,4,demod,8,8')] ).
cnf(11,plain,
double_divide(A,multiply(multiply(multiply(multiply(B,inverse(A)),C),inverse(D)),double_divide(C,B))) = D,
inference(para_into,[status(thm),theory(equality)],[10,10]),
[iquote('para_into,9.1.1.1,9.1.1')] ).
cnf(15,plain,
multiply(multiply(multiply(A,inverse(B)),C),double_divide(C,A)) = inverse(B),
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(21,plain,
multiply(multiply(multiply(multiply(multiply(A,inverse(B)),C),inverse(D)),double_divide(C,A)),B) = inverse(D),
inference(para_into,[status(thm),theory(equality)],[15,10]),
[iquote('para_into,15.1.1.2,9.1.1')] ).
cnf(89,plain,
multiply(multiply(inverse(A),inverse(B)),A) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[21,21]),10]),
[iquote('para_into,21.1.1.1.1,21.1.1,demod,10')] ).
cnf(109,plain,
double_divide(A,multiply(inverse(A),inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[21,11]),10]),
[iquote('para_from,21.1.1,11.1.1.2.1,demod,10')] ).
cnf(117,plain,
double_divide(double_divide(A,B),multiply(multiply(B,A),inverse(C))) = C,
inference(para_into,[status(thm),theory(equality)],[109,8]),
[iquote('para_into,109.1.1.2.1,7.1.1')] ).
cnf(163,plain,
double_divide(double_divide(A,inverse(A)),inverse(B)) = B,
inference(para_from,[status(thm),theory(equality)],[89,10]),
[iquote('para_from,89.1.1,9.1.1.2')] ).
cnf(171,plain,
double_divide(double_divide(A,inverse(A)),multiply(B,C)) = double_divide(C,B),
inference(para_into,[status(thm),theory(equality)],[163,8]),
[iquote('para_into,163.1.1.2,7.1.1')] ).
cnf(337,plain,
double_divide(inverse(A),multiply(inverse(B),B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[171,117])]),
[iquote('para_into,171.1.1,117.1.1,flip.1')] ).
cnf(364,plain,
double_divide(A,multiply(multiply(multiply(inverse(B),B),inverse(C)),inverse(A))) = C,
inference(para_from,[status(thm),theory(equality)],[337,10]),
[iquote('para_from,337.1.1,9.1.1.1')] ).
cnf(367,plain,
multiply(multiply(inverse(A),A),inverse(B)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[337,8])]),
[iquote('para_from,337.1.1,7.1.1.1,flip.1')] ).
cnf(369,plain,
double_divide(A,multiply(inverse(B),inverse(A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[364]),367]),
[iquote('back_demod,364,demod,367')] ).
cnf(387,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[369,337])]),
[iquote('para_into,369.1.1,337.1.1,flip.1')] ).
cnf(529,plain,
multiply(multiply(multiply(multiply(multiply(multiply(inverse(A),inverse(B)),inverse(C)),B),inverse(D)),A),C) = inverse(D),
inference(para_from,[status(thm),theory(equality)],[369,21]),
[iquote('para_from,369.1.1,21.1.1.1.2')] ).
cnf(585,plain,
multiply(multiply(inverse(A),B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[387,89]),387]),
[iquote('para_from,386.1.1,89.1.1.1.2,demod,387')] ).
cnf(682,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[585,117]),387]),
[iquote('para_from,585.1.1,117.1.1.2,demod,387')] ).
cnf(700,plain,
double_divide(A,double_divide(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[682,682]),
[iquote('para_into,682.1.1.1,682.1.1')] ).
cnf(702,plain,
multiply(inverse(A),inverse(B)) = double_divide(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[682,369])]),
[iquote('para_into,682.1.1.1,369.1.1,flip.1')] ).
cnf(711,plain,
double_divide(A,B) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[682,109]),702]),
[iquote('para_into,682.1.1.1,109.1.1,demod,702')] ).
cnf(717,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)],[682,10])]),
[iquote('para_into,682.1.1.1,9.1.1,flip.1')] ).
cnf(757,plain,
multiply(double_divide(A,B),B) = inverse(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[529]),702,717,700,717,700]),
[iquote('back_demod,529,demod,702,717,700,717,700')] ).
cnf(931,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[711,8]),8]),
[iquote('para_from,711.1.1,7.1.1.1,demod,8')] ).
cnf(941,plain,
multiply(b1,inverse(b1)) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[931,2]),
[iquote('para_from,931.1.1,2.1.1')] ).
cnf(950,plain,
multiply(A,inverse(A)) = multiply(inverse(B),B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[757,163]),8]),
[iquote('para_into,757.1.1.1,163.1.1,demod,8')] ).
cnf(951,plain,
$false,
inference(binary,[status(thm)],[950,941]),
[iquote('binary,950.1,941.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP597-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 05:00:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.79/1.94 ----- Otter 3.3f, August 2004 -----
% 1.79/1.94 The process was started by sandbox2 on n008.cluster.edu,
% 1.79/1.94 Wed Jul 27 05:00:38 2022
% 1.79/1.94 The command was "./otter". The process ID is 29357.
% 1.79/1.94
% 1.79/1.94 set(prolog_style_variables).
% 1.79/1.94 set(auto).
% 1.79/1.94 dependent: set(auto1).
% 1.79/1.94 dependent: set(process_input).
% 1.79/1.94 dependent: clear(print_kept).
% 1.79/1.94 dependent: clear(print_new_demod).
% 1.79/1.94 dependent: clear(print_back_demod).
% 1.79/1.94 dependent: clear(print_back_sub).
% 1.79/1.94 dependent: set(control_memory).
% 1.79/1.94 dependent: assign(max_mem, 12000).
% 1.79/1.94 dependent: assign(pick_given_ratio, 4).
% 1.79/1.94 dependent: assign(stats_level, 1).
% 1.79/1.94 dependent: assign(max_seconds, 10800).
% 1.79/1.94 clear(print_given).
% 1.79/1.94
% 1.79/1.94 list(usable).
% 1.79/1.94 0 [] A=A.
% 1.79/1.94 0 [] double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B)))))=C.
% 1.79/1.94 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.79/1.94 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.79/1.94 end_of_list.
% 1.79/1.94
% 1.79/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.79/1.94
% 1.79/1.94 All clauses are units, and equality is present; the
% 1.79/1.94 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.79/1.94
% 1.79/1.94 dependent: set(knuth_bendix).
% 1.79/1.94 dependent: set(anl_eq).
% 1.79/1.94 dependent: set(para_from).
% 1.79/1.94 dependent: set(para_into).
% 1.79/1.94 dependent: clear(para_from_right).
% 1.79/1.94 dependent: clear(para_into_right).
% 1.79/1.94 dependent: set(para_from_vars).
% 1.79/1.94 dependent: set(eq_units_both_ways).
% 1.79/1.94 dependent: set(dynamic_demod_all).
% 1.79/1.94 dependent: set(dynamic_demod).
% 1.79/1.94 dependent: set(order_eq).
% 1.79/1.94 dependent: set(back_demod).
% 1.79/1.94 dependent: set(lrpo).
% 1.79/1.94
% 1.79/1.94 ------------> process usable:
% 1.79/1.94 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.79/1.94
% 1.79/1.94 ------------> process sos:
% 1.79/1.94 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.79/1.94 ** KEPT (pick-wt=14): 4 [] double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B)))))=C.
% 1.79/1.94 ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,B),inverse(double_divide(A,inverse(double_divide(inverse(C),B)))))=C.
% 1.79/1.94 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.79/1.94 ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.79/1.94 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.79/1.94 >>>> Starting back demodulation with 5.
% 1.79/1.94 >>>> Starting back demodulation with 8.
% 1.79/1.94 >> back demodulating 4 with 8.
% 1.79/1.94 >>>> Starting back demodulation with 10.
% 1.79/1.94
% 1.79/1.94 ======= end of input processing =======
% 1.79/1.94
% 1.79/1.94 =========== start of search ===========
% 1.79/1.94
% 1.79/1.94
% 1.79/1.94 Resetting weight limit to 9.
% 1.79/1.94
% 1.79/1.94
% 1.79/1.94 Resetting weight limit to 9.
% 1.79/1.94
% 1.79/1.94 sos_size=237
% 1.79/1.94
% 1.79/1.94 -------- PROOF --------
% 1.79/1.94
% 1.79/1.94 ----> UNIT CONFLICT at 0.04 sec ----> 951 [binary,950.1,941.1] $F.
% 1.79/1.94
% 1.79/1.94 Length of proof is 27. Level of proof is 17.
% 1.79/1.94
% 1.79/1.94 ---------------- PROOF ----------------
% 1.79/1.94 % SZS status Unsatisfiable
% 1.79/1.94 % SZS output start Refutation
% See solution above
% 1.79/1.94 ------------ end of proof -------------
% 1.79/1.94
% 1.79/1.94
% 1.79/1.94 Search stopped by max_proofs option.
% 1.79/1.94
% 1.79/1.94
% 1.79/1.94 Search stopped by max_proofs option.
% 1.79/1.94
% 1.79/1.94 ============ end of search ============
% 1.79/1.94
% 1.79/1.94 -------------- statistics -------------
% 1.79/1.94 clauses given 39
% 1.79/1.94 clauses generated 762
% 1.79/1.94 clauses kept 554
% 1.79/1.94 clauses forward subsumed 601
% 1.79/1.94 clauses back subsumed 4
% 1.79/1.94 Kbytes malloced 4882
% 1.79/1.94
% 1.79/1.94 ----------- times (seconds) -----------
% 1.79/1.94 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.79/1.94 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.79/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.79/1.94
% 1.79/1.94 That finishes the proof of the theorem.
% 1.79/1.94
% 1.79/1.94 Process 29357 finished Wed Jul 27 05:00:40 2022
% 1.79/1.94 Otter interrupted
% 1.79/1.94 PROOF FOUND
%------------------------------------------------------------------------------