TSTP Solution File: GRP076-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP076-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 12:56:00 EDT 2022
% Result : Unsatisfiable 1.82s 2.00s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of clauses : 48 ( 43 unt; 0 nHn; 8 RR)
% Number of literals : 58 ( 57 equ; 15 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 78 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('GRP076-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP076-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = C,
file('GRP076-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP076-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP076-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP076-1.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(identity,identity) != identity
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),8,6,11,6,6,6,6,6])]),
[iquote('back_demod,1,demod,8,6,11,6,6,6,6,6,flip.3')] ).
cnf(13,plain,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),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(17,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,B),identity),
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.1.2.1,10.1.1')] ).
cnf(21,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),B),C),double_divide(B,identity)) = double_divide(double_divide(A,C),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,3])]),
[iquote('para_into,3.1.1.1.2,3.1.1,flip.1')] ).
cnf(24,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.1.2,10.1.1')] ).
cnf(25,plain,
double_divide(double_divide(A,B),double_divide(identity,identity)) = double_divide(double_divide(identity,B),double_divide(double_divide(double_divide(A,identity),identity),identity)),
inference(para_from,[status(thm),theory(equality)],[13,3]),
[iquote('para_from,13.1.1,3.1.1.1.2')] ).
cnf(28,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity))),double_divide(double_divide(B,C),double_divide(double_divide(identity,identity),identity))),double_divide(identity,identity)) = C,
inference(para_from,[status(thm),theory(equality)],[13,3]),
[iquote('para_from,13.1.1,3.1.1.1.2.1.1')] ).
cnf(30,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,identity),identity),identity)) = double_divide(double_divide(B,A),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[25])]),
[iquote('copy,25,flip.1')] ).
cnf(32,plain,
double_divide(identity,identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[24,3]),11,24])]),
[iquote('para_from,23.1.1,3.1.1.1.2.1,demod,11,24,flip.1')] ).
cnf(34,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[24,3]),32,32,32,32]),
[iquote('para_from,23.1.1,3.1.1.1.2.1.1,demod,32,32,32,32')] ).
cnf(35,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,identity),identity),identity)) = double_divide(double_divide(B,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[30]),32]),
[iquote('back_demod,30,demod,32')] ).
cnf(36,plain,
double_divide(double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity))),double_divide(double_divide(B,C),identity)),identity) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[28]),32,32,32]),
[iquote('back_demod,28,demod,32,32,32')] ).
cnf(40,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(identity,B),double_divide(double_divide(double_divide(A,identity),identity),identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),32]),
[iquote('back_demod,25,demod,32')] ).
cnf(41,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),B),C),double_divide(B,identity)) = double_divide(double_divide(A,C),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),32]),
[iquote('back_demod,21,demod,32')] ).
cnf(45,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),identity) = double_divide(double_divide(A,B),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),32]),
[iquote('back_demod,17,demod,32')] ).
cnf(50,plain,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),32]),
[iquote('back_demod,13,demod,32')] ).
cnf(51,plain,
( identity != identity
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),32]),
[iquote('back_demod,12,demod,32')] ).
cnf(54,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),A) = identity,
inference(para_from,[status(thm),theory(equality)],[34,11]),
[iquote('para_from,33.1.1,10.1.1.2')] ).
cnf(57,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)) = double_divide(double_divide(A,identity),identity),
inference(para_into,[status(thm),theory(equality)],[35,32]),
[iquote('para_into,35.1.1.1,31.1.1')] ).
cnf(58,plain,
double_divide(double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),B),identity) = double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,34])]),
[iquote('para_into,35.1.1.2.1.1,33.1.1,flip.1')] ).
cnf(60,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),identity),identity)),identity) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[54,35]),57]),
[iquote('para_into,54.1.1,35.1.1,demod,57')] ).
cnf(79,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[45,34]),34])]),
[iquote('para_from,45.1.1,33.1.1.1.2,demod,34,flip.1')] ).
cnf(83,plain,
double_divide(double_divide(double_divide(identity,A),B),identity) = double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[58]),79]),
[iquote('back_demod,58,demod,79')] ).
cnf(85,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[34]),79]),
[iquote('back_demod,33,demod,79')] ).
cnf(94,plain,
double_divide(double_divide(A,B),double_divide(double_divide(A,identity),identity)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[36,32]),32,85,83,79]),
[iquote('para_into,36.1.1.1.1.2.2.1,31.1.1,demod,32,85,83,79')] ).
cnf(103,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[36,60]),50])]),
[iquote('para_into,36.1.1.1.2,60.1.1,demod,50,flip.1')] ).
cnf(110,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(identity,B),double_divide(A,identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[40]),103]),
[iquote('back_demod,40,demod,103')] ).
cnf(111,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(double_divide(B,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[35]),103]),
[iquote('back_demod,35,demod,103')] ).
cnf(120,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),identity),identity)) = double_divide(double_divide(B,identity),identity),
inference(para_into,[status(thm),theory(equality)],[94,94]),
[iquote('para_into,94.1.1.1,94.1.1')] ).
cnf(124,plain,
double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) = double_divide(double_divide(identity,C),double_divide(double_divide(A,identity),identity)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[41,85]),83]),
[iquote('para_into,41.1.1.1.1.1,84.1.1,demod,83')] ).
cnf(135,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[103,85]),85]),
[iquote('para_into,102.1.1.1.1,84.1.1,demod,85')] ).
cnf(138,plain,
double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity)) = double_divide(double_divide(identity,C),A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[124]),135]),
[iquote('back_demod,124,demod,135')] ).
cnf(141,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[120]),135,135]),
[iquote('back_demod,120,demod,135,135')] ).
cnf(146,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[94]),135]),
[iquote('back_demod,94,demod,135')] ).
cnf(150,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[51]),135]),
[iquote('back_demod,51,demod,135')] ).
cnf(169,plain,
double_divide(double_divide(A,double_divide(B,identity)),identity) = double_divide(B,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[111,141])]),
[iquote('para_into,111.1.1.1,140.1.1,flip.1')] ).
cnf(174,plain,
double_divide(double_divide(double_divide(A,B),C),identity) = double_divide(double_divide(identity,C),double_divide(double_divide(identity,B),double_divide(A,identity))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[111,110])]),
[iquote('para_into,111.1.1.2,110.1.1,flip.1')] ).
cnf(176,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(b3,a3),double_divide(c3,identity)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[150]),174,32,141,169]),
[iquote('back_demod,150,demod,174,32,141,169')] ).
cnf(254,plain,
double_divide(double_divide(A,B),double_divide(C,identity)) = double_divide(double_divide(identity,B),double_divide(C,A)),
inference(para_into,[status(thm),theory(equality)],[138,146]),
[iquote('para_into,138.1.1.1.1,146.1.1')] ).
cnf(270,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(B,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[254])]),
[iquote('copy,254,flip.1')] ).
cnf(1420,plain,
$false,
inference(hyper,[status(thm)],[270,176,2,2]),
[iquote('hyper,270,176,2,2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP076-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 05:35:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.82/2.00 ----- Otter 3.3f, August 2004 -----
% 1.82/2.00 The process was started by sandbox on n027.cluster.edu,
% 1.82/2.00 Wed Jul 27 05:35:06 2022
% 1.82/2.00 The command was "./otter". The process ID is 1612.
% 1.82/2.00
% 1.82/2.00 set(prolog_style_variables).
% 1.82/2.00 set(auto).
% 1.82/2.00 dependent: set(auto1).
% 1.82/2.00 dependent: set(process_input).
% 1.82/2.00 dependent: clear(print_kept).
% 1.82/2.00 dependent: clear(print_new_demod).
% 1.82/2.00 dependent: clear(print_back_demod).
% 1.82/2.00 dependent: clear(print_back_sub).
% 1.82/2.00 dependent: set(control_memory).
% 1.82/2.00 dependent: assign(max_mem, 12000).
% 1.82/2.00 dependent: assign(pick_given_ratio, 4).
% 1.82/2.00 dependent: assign(stats_level, 1).
% 1.82/2.00 dependent: assign(max_seconds, 10800).
% 1.82/2.00 clear(print_given).
% 1.82/2.00
% 1.82/2.00 list(usable).
% 1.82/2.00 0 [] A=A.
% 1.82/2.00 0 [] double_divide(double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),double_divide(Y,identity))),double_divide(identity,identity))=Z.
% 1.82/2.00 0 [] multiply(X,Y)=double_divide(double_divide(Y,X),identity).
% 1.82/2.00 0 [] inverse(X)=double_divide(X,identity).
% 1.82/2.00 0 [] identity=double_divide(X,inverse(X)).
% 1.82/2.00 0 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.82/2.00 end_of_list.
% 1.82/2.00
% 1.82/2.00 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.82/2.00
% 1.82/2.00 This is a Horn set with equality. The strategy will be
% 1.82/2.00 Knuth-Bendix and hyper_res, with positive clauses in
% 1.82/2.00 sos and nonpositive clauses in usable.
% 1.82/2.00
% 1.82/2.00 dependent: set(knuth_bendix).
% 1.82/2.00 dependent: set(anl_eq).
% 1.82/2.00 dependent: set(para_from).
% 1.82/2.00 dependent: set(para_into).
% 1.82/2.00 dependent: clear(para_from_right).
% 1.82/2.00 dependent: clear(para_into_right).
% 1.82/2.00 dependent: set(para_from_vars).
% 1.82/2.00 dependent: set(eq_units_both_ways).
% 1.82/2.00 dependent: set(dynamic_demod_all).
% 1.82/2.00 dependent: set(dynamic_demod).
% 1.82/2.00 dependent: set(order_eq).
% 1.82/2.00 dependent: set(back_demod).
% 1.82/2.00 dependent: set(lrpo).
% 1.82/2.00 dependent: set(hyper_res).
% 1.82/2.00 dependent: clear(order_hyper).
% 1.82/2.00
% 1.82/2.00 ------------> process usable:
% 1.82/2.00 ** KEPT (pick-wt=22): 1 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.82/2.00
% 1.82/2.00 ------------> process sos:
% 1.82/2.00 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.82/2.00 ** KEPT (pick-wt=17): 3 [] double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.82/2.00 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.82/2.00 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.82/2.00 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.82/2.00 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 1.82/2.00 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 1.82/2.00 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.82/2.00 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 1.82/2.00 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.82/2.00 >>>> Starting back demodulation with 4.
% 1.82/2.00 >>>> Starting back demodulation with 6.
% 1.82/2.00 >> back demodulating 1 with 6.
% 1.82/2.00 >>>> Starting back demodulation with 8.
% 1.82/2.00 >>>> Starting back demodulation with 11.
% 1.82/2.00
% 1.82/2.00 ======= end of input processing =======
% 1.82/2.00
% 1.82/2.00 =========== start of search ===========
% 1.82/2.00
% 1.82/2.00 -------- PROOF --------
% 1.82/2.00
% 1.82/2.00 -----> EMPTY CLAUSE at 0.14 sec ----> 1420 [hyper,270,176,2,2] $F.
% 1.82/2.00
% 1.82/2.00 Length of proof is 41. Level of proof is 12.
% 1.82/2.00
% 1.82/2.00 ---------------- PROOF ----------------
% 1.82/2.00 % SZS status Unsatisfiable
% 1.82/2.00 % SZS output start Refutation
% See solution above
% 1.82/2.00 ------------ end of proof -------------
% 1.82/2.00
% 1.82/2.00
% 1.82/2.00 Search stopped by max_proofs option.
% 1.82/2.00
% 1.82/2.00
% 1.82/2.00 Search stopped by max_proofs option.
% 1.82/2.00
% 1.82/2.00 ============ end of search ============
% 1.82/2.00
% 1.82/2.00 -------------- statistics -------------
% 1.82/2.00 clauses given 102
% 1.82/2.00 clauses generated 8948
% 1.82/2.00 clauses kept 1104
% 1.82/2.00 clauses forward subsumed 8935
% 1.82/2.00 clauses back subsumed 63
% 1.82/2.00 Kbytes malloced 2929
% 1.82/2.00
% 1.82/2.00 ----------- times (seconds) -----------
% 1.82/2.00 user CPU time 0.14 (0 hr, 0 min, 0 sec)
% 1.82/2.00 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.00 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/2.00
% 1.82/2.00 That finishes the proof of the theorem.
% 1.82/2.00
% 1.82/2.00 Process 1612 finished Wed Jul 27 05:35:08 2022
% 1.82/2.00 Otter interrupted
% 1.82/2.00 PROOF FOUND
%------------------------------------------------------------------------------