TSTP Solution File: GRP578-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP578-1 : 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 12:57:17 EDT 2022
% Result : Unsatisfiable 1.73s 1.92s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 8 RR)
% Number of literals : 31 ( 30 equ; 4 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 : 38 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(identity,a2) != a2,
file('GRP578-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity)) = C,
file('GRP578-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP578-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP578-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP578-1.p',unknown),
[] ).
cnf(11,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9]),8])]),
[iquote('copy,9,demod,8,flip.1')] ).
cnf(12,plain,
double_divide(double_divide(a2,identity),identity) != a2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),6]),
[iquote('back_demod,1,demod,6')] ).
cnf(13,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,B),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.1.2.1.1,10.1.1')] ).
cnf(25,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),double_divide(identity,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.1.2,10.1.1')] ).
cnf(33,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(para_into,[status(thm),theory(equality)],[25,11]),
[iquote('para_into,25.1.1.1.1.1,10.1.1')] ).
cnf(37,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),double_divide(identity,identity)) = B,
inference(para_from,[status(thm),theory(equality)],[25,3]),
[iquote('para_from,25.1.1,3.1.1.1.2.1.1')] ).
cnf(40,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[33,3]),11]),
[iquote('para_from,33.1.1,3.1.1.1.2.1,demod,11')] ).
cnf(44,plain,
double_divide(identity,identity) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[40,13]),40,40]),
[iquote('para_from,39.1.1,13.1.1.1.2,demod,40,40')] ).
cnf(47,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[37]),44,44]),
[iquote('back_demod,37,demod,44,44')] ).
cnf(58,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),identity),identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),44]),
[iquote('back_demod,25,demod,44')] ).
cnf(73,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),58]),
[iquote('back_demod,47,demod,58')] ).
cnf(79,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(A,identity),
inference(para_into,[status(thm),theory(equality)],[73,11]),
[iquote('para_into,73.1.1.1.2.1,10.1.1')] ).
cnf(81,plain,
double_divide(double_divide(identity,A),identity) = double_divide(double_divide(B,A),B),
inference(para_into,[status(thm),theory(equality)],[73,73]),
[iquote('para_into,73.1.1.1.2,73.1.1')] ).
cnf(83,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(B,A),B),
inference(para_from,[status(thm),theory(equality)],[73,58]),
[iquote('para_from,73.1.1,57.1.1.1.1')] ).
cnf(84,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,B),A)),B) = identity,
inference(para_from,[status(thm),theory(equality)],[73,11]),
[iquote('para_from,73.1.1,10.1.1.2')] ).
cnf(86,plain,
double_divide(double_divide(A,B),A) = double_divide(double_divide(B,identity),identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[83])]),
[iquote('copy,83,flip.1')] ).
cnf(94,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(identity,A),
inference(para_from,[status(thm),theory(equality)],[79,58]),
[iquote('para_from,79.1.1,57.1.1.1.1')] ).
cnf(100,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[58]),94]),
[iquote('back_demod,57,demod,94')] ).
cnf(107,plain,
double_divide(double_divide(A,identity),A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[81,44]),44])]),
[iquote('para_into,81.1.1.1,43.1.1,demod,44,flip.1')] ).
cnf(110,plain,
double_divide(double_divide(A,double_divide(double_divide(B,C),B)),A) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[81,73])]),
[iquote('para_into,81.1.1,73.1.1,flip.1')] ).
cnf(114,plain,
double_divide(double_divide(A,a2),A) != a2,
inference(para_from,[status(thm),theory(equality)],[83,12]),
[iquote('para_from,83.1.1,12.1.1')] ).
cnf(133,plain,
double_divide(identity,double_divide(a2,identity)) != a2,
inference(para_into,[status(thm),theory(equality)],[114,107]),
[iquote('para_into,114.1.1.1,107.1.1')] ).
cnf(140,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[86,107])]),
[iquote('para_into,86.1.1.1,107.1.1,flip.1')] ).
cnf(145,plain,
double_divide(double_divide(A,B),A) = double_divide(identity,double_divide(B,identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[86,84]),100,140]),
[iquote('para_into,86.1.1.1,84.1.1,demod,100,140')] ).
cnf(163,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[110]),145,145,145,140,100]),
[iquote('back_demod,110,demod,145,145,145,140,100')] ).
cnf(165,plain,
$false,
inference(binary,[status(thm)],[163,133]),
[iquote('binary,163.1,133.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP578-1 : 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 05:19:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.73/1.92 ----- Otter 3.3f, August 2004 -----
% 1.73/1.92 The process was started by sandbox on n014.cluster.edu,
% 1.73/1.92 Wed Jul 27 05:19:54 2022
% 1.73/1.92 The command was "./otter". The process ID is 1386.
% 1.73/1.92
% 1.73/1.92 set(prolog_style_variables).
% 1.73/1.92 set(auto).
% 1.73/1.92 dependent: set(auto1).
% 1.73/1.92 dependent: set(process_input).
% 1.73/1.92 dependent: clear(print_kept).
% 1.73/1.92 dependent: clear(print_new_demod).
% 1.73/1.92 dependent: clear(print_back_demod).
% 1.73/1.92 dependent: clear(print_back_sub).
% 1.73/1.92 dependent: set(control_memory).
% 1.73/1.92 dependent: assign(max_mem, 12000).
% 1.73/1.92 dependent: assign(pick_given_ratio, 4).
% 1.73/1.92 dependent: assign(stats_level, 1).
% 1.73/1.92 dependent: assign(max_seconds, 10800).
% 1.73/1.92 clear(print_given).
% 1.73/1.92
% 1.73/1.92 list(usable).
% 1.73/1.92 0 [] A=A.
% 1.73/1.92 0 [] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.73/1.92 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.73/1.92 0 [] inverse(A)=double_divide(A,identity).
% 1.73/1.92 0 [] identity=double_divide(A,inverse(A)).
% 1.73/1.92 0 [] multiply(identity,a2)!=a2.
% 1.73/1.92 end_of_list.
% 1.73/1.92
% 1.73/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.73/1.92
% 1.73/1.92 All clauses are units, and equality is present; the
% 1.73/1.92 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.73/1.92
% 1.73/1.92 dependent: set(knuth_bendix).
% 1.73/1.92 dependent: set(anl_eq).
% 1.73/1.92 dependent: set(para_from).
% 1.73/1.92 dependent: set(para_into).
% 1.73/1.92 dependent: clear(para_from_right).
% 1.73/1.92 dependent: clear(para_into_right).
% 1.73/1.92 dependent: set(para_from_vars).
% 1.73/1.92 dependent: set(eq_units_both_ways).
% 1.73/1.92 dependent: set(dynamic_demod_all).
% 1.73/1.92 dependent: set(dynamic_demod).
% 1.73/1.92 dependent: set(order_eq).
% 1.73/1.92 dependent: set(back_demod).
% 1.73/1.92 dependent: set(lrpo).
% 1.73/1.92
% 1.73/1.92 ------------> process usable:
% 1.73/1.92 ** KEPT (pick-wt=5): 1 [] multiply(identity,a2)!=a2.
% 1.73/1.92
% 1.73/1.92 ------------> process sos:
% 1.73/1.92 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.73/1.92 ** KEPT (pick-wt=17): 3 [] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.73/1.92 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(A,double_divide(double_divide(double_divide(B,A),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.73/1.92 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.73/1.92 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.73/1.92 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 1.73/1.92 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 1.73/1.92 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.73/1.92 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 1.73/1.92 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.73/1.92 >>>> Starting back demodulation with 4.
% 1.73/1.92 >>>> Starting back demodulation with 6.
% 1.73/1.92 >> back demodulating 1 with 6.
% 1.73/1.92 >>>> Starting back demodulation with 8.
% 1.73/1.92 >>>> Starting back demodulation with 11.
% 1.73/1.92
% 1.73/1.92 ======= end of input processing =======
% 1.73/1.92
% 1.73/1.92 =========== start of search ===========
% 1.73/1.92
% 1.73/1.92 -------- PROOF --------
% 1.73/1.92
% 1.73/1.92 ----> UNIT CONFLICT at 0.00 sec ----> 165 [binary,163.1,133.1] $F.
% 1.73/1.92
% 1.73/1.92 Length of proof is 25. Level of proof is 13.
% 1.73/1.92
% 1.73/1.92 ---------------- PROOF ----------------
% 1.73/1.92 % SZS status Unsatisfiable
% 1.73/1.92 % SZS output start Refutation
% See solution above
% 1.73/1.92 ------------ end of proof -------------
% 1.73/1.92
% 1.73/1.92
% 1.73/1.92 Search stopped by max_proofs option.
% 1.73/1.92
% 1.73/1.92
% 1.73/1.92 Search stopped by max_proofs option.
% 1.73/1.92
% 1.73/1.92 ============ end of search ============
% 1.73/1.92
% 1.73/1.92 -------------- statistics -------------
% 1.73/1.92 clauses given 25
% 1.73/1.92 clauses generated 187
% 1.73/1.92 clauses kept 93
% 1.73/1.92 clauses forward subsumed 169
% 1.73/1.92 clauses back subsumed 3
% 1.73/1.92 Kbytes malloced 1953
% 1.73/1.92
% 1.73/1.92 ----------- times (seconds) -----------
% 1.73/1.92 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.73/1.92
% 1.73/1.92 That finishes the proof of the theorem.
% 1.73/1.92
% 1.73/1.92 Process 1386 finished Wed Jul 27 05:19:55 2022
% 1.73/1.92 Otter interrupted
% 1.73/1.92 PROOF FOUND
%------------------------------------------------------------------------------