TSTP Solution File: GRP576-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP576-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 1.66s 1.87s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of clauses : 39 ( 39 unt; 0 nHn; 6 RR)
% Number of literals : 39 ( 38 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP576-1.p',unknown),
[] ).
cnf(2,plain,
multiply(b,a) != multiply(a,b),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(3,axiom,
A = A,
file('GRP576-1.p',unknown),
[] ).
cnf(4,axiom,
double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B,
file('GRP576-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP576-1.p',unknown),
[] ).
cnf(9,axiom,
inverse(A) = double_divide(A,identity),
file('GRP576-1.p',unknown),
[] ).
cnf(10,axiom,
identity = double_divide(A,inverse(A)),
file('GRP576-1.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)],[10]),9])]),
[iquote('copy,10,demod,9,flip.1')] ).
cnf(13,plain,
double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),7,7])]),
[iquote('back_demod,2,demod,7,7,flip.1')] ).
cnf(14,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),double_divide(A,identity))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[4,11]),
[iquote('para_into,4.1.1.1.2.1.2,11.1.1')] ).
cnf(18,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(identity,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[4,11]),
[iquote('para_into,4.1.1.1.2.1,11.1.1')] ).
cnf(20,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(A,double_divide(C,B)),double_divide(C,identity))),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.2.1,4.1.1')] ).
cnf(21,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(double_divide(identity,double_divide(B,double_divide(identity,identity))),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
[iquote('copy,20,flip.1')] ).
cnf(25,plain,
double_divide(double_divide(double_divide(A,identity),A),double_divide(identity,identity)) = identity,
inference(para_from,[status(thm),theory(equality)],[18,4]),
[iquote('para_from,18.1.1,4.1.1.1.2')] ).
cnf(27,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(para_from,[status(thm),theory(equality)],[18,4]),
[iquote('para_from,18.1.1,4.1.1.1.2.1')] ).
cnf(30,plain,
double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),27]),
[iquote('back_demod,21,demod,27')] ).
cnf(33,plain,
double_divide(identity,identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,25]),25])]),
[iquote('para_into,14.1.1.1.2,24.1.1,demod,25,flip.1')] ).
cnf(35,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,11]),33]),
[iquote('para_into,14.1.1.1.2,11.1.1,demod,33')] ).
cnf(38,plain,
double_divide(double_divide(identity,double_divide(A,identity)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),33,33]),
[iquote('back_demod,26,demod,33,33')] ).
cnf(40,plain,
double_divide(double_divide(double_divide(A,identity),A),identity) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),33]),
[iquote('back_demod,24,demod,33')] ).
cnf(42,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),33]),
[iquote('back_demod,18,demod,33')] ).
cnf(62,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)],[35,40]),33,33,33])]),
[iquote('para_into,34.1.1.1.1.1,40.1.1,demod,33,33,33,flip.1')] ).
cnf(64,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),A) = identity,
inference(para_from,[status(thm),theory(equality)],[35,11]),
[iquote('para_from,34.1.1,11.1.1.2')] ).
cnf(69,plain,
double_divide(identity,double_divide(double_divide(A,B),B)) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[35,30]),35]),
[iquote('para_from,34.1.1,30.1.1.2.1.2,demod,35')] ).
cnf(70,plain,
double_divide(A,double_divide(double_divide(double_divide(A,identity),identity),identity)) = identity,
inference(para_into,[status(thm),theory(equality)],[62,35]),
[iquote('para_into,62.1.1.1,34.1.1')] ).
cnf(72,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(double_divide(A,B),identity)))) = double_divide(B,double_divide(identity,double_divide(A,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[62,30]),69])]),
[iquote('para_from,62.1.1,30.1.1.2.1,demod,69,flip.1')] ).
cnf(79,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(identity,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[38,35]),35]),
[iquote('para_into,38.1.1.1.2,34.1.1,demod,35')] ).
cnf(81,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[42]),79]),
[iquote('back_demod,42,demod,79')] ).
cnf(82,plain,
double_divide(A,B) = double_divide(B,double_divide(identity,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[72]),81]),
[iquote('back_demod,72,demod,81')] ).
cnf(83,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[82])]),
[iquote('copy,82,flip.1')] ).
cnf(86,plain,
double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[64,30]),35]),
[iquote('para_from,64.1.1,30.1.1.2.1.2,demod,35')] ).
cnf(89,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[70,30]),86,86,81])]),
[iquote('para_from,70.1.1,30.1.1.2.1,demod,86,86,81,flip.1')] ).
cnf(93,plain,
double_divide(A,double_divide(double_divide(B,identity),A)) = double_divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[86]),89]),
[iquote('back_demod,85,demod,89')] ).
cnf(95,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[81]),89]),
[iquote('back_demod,80,demod,89')] ).
cnf(110,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[89]),95]),
[iquote('back_demod,88,demod,95')] ).
cnf(115,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[110,35]),93])]),
[iquote('para_into,110.1.1,34.1.1,demod,93,flip.1')] ).
cnf(116,plain,
double_divide(A,B) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[83]),115]),
[iquote('back_demod,83,demod,115')] ).
cnf(136,plain,
double_divide(double_divide(a,b),identity) != double_divide(double_divide(a,b),identity),
inference(para_from,[status(thm),theory(equality)],[116,13]),
[iquote('para_from,116.1.1,13.1.1.1')] ).
cnf(137,plain,
$false,
inference(binary,[status(thm)],[136,3]),
[iquote('binary,136.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP576-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 05:06:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.87 ----- Otter 3.3f, August 2004 -----
% 1.66/1.87 The process was started by sandbox on n003.cluster.edu,
% 1.66/1.87 Wed Jul 27 05:06:26 2022
% 1.66/1.87 The command was "./otter". The process ID is 19005.
% 1.66/1.87
% 1.66/1.87 set(prolog_style_variables).
% 1.66/1.87 set(auto).
% 1.66/1.87 dependent: set(auto1).
% 1.66/1.87 dependent: set(process_input).
% 1.66/1.87 dependent: clear(print_kept).
% 1.66/1.87 dependent: clear(print_new_demod).
% 1.66/1.87 dependent: clear(print_back_demod).
% 1.66/1.87 dependent: clear(print_back_sub).
% 1.66/1.87 dependent: set(control_memory).
% 1.66/1.87 dependent: assign(max_mem, 12000).
% 1.66/1.87 dependent: assign(pick_given_ratio, 4).
% 1.66/1.87 dependent: assign(stats_level, 1).
% 1.66/1.87 dependent: assign(max_seconds, 10800).
% 1.66/1.87 clear(print_given).
% 1.66/1.87
% 1.66/1.87 list(usable).
% 1.66/1.87 0 [] A=A.
% 1.66/1.87 0 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 1.66/1.87 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.66/1.87 0 [] inverse(A)=double_divide(A,identity).
% 1.66/1.87 0 [] identity=double_divide(A,inverse(A)).
% 1.66/1.87 0 [] multiply(a,b)!=multiply(b,a).
% 1.66/1.87 end_of_list.
% 1.66/1.87
% 1.66/1.87 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.66/1.87
% 1.66/1.87 All clauses are units, and equality is present; the
% 1.66/1.87 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.66/1.87
% 1.66/1.87 dependent: set(knuth_bendix).
% 1.66/1.87 dependent: set(anl_eq).
% 1.66/1.87 dependent: set(para_from).
% 1.66/1.87 dependent: set(para_into).
% 1.66/1.87 dependent: clear(para_from_right).
% 1.66/1.87 dependent: clear(para_into_right).
% 1.66/1.87 dependent: set(para_from_vars).
% 1.66/1.87 dependent: set(eq_units_both_ways).
% 1.66/1.87 dependent: set(dynamic_demod_all).
% 1.66/1.87 dependent: set(dynamic_demod).
% 1.66/1.87 dependent: set(order_eq).
% 1.66/1.87 dependent: set(back_demod).
% 1.66/1.87 dependent: set(lrpo).
% 1.66/1.87
% 1.66/1.87 ------------> process usable:
% 1.66/1.87 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.66/1.87
% 1.66/1.87 ------------> process sos:
% 1.66/1.87 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.66/1.87 ** KEPT (pick-wt=17): 4 [] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 1.66/1.87 ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity))=B.
% 1.66/1.87 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.66/1.87 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.66/1.87 ** KEPT (pick-wt=6): 8 [] inverse(A)=double_divide(A,identity).
% 1.66/1.87 ---> New Demodulator: 9 [new_demod,8] inverse(A)=double_divide(A,identity).
% 1.66/1.87 ** KEPT (pick-wt=7): 11 [copy,10,demod,9,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.66/1.87 ---> New Demodulator: 12 [new_demod,11] double_divide(A,double_divide(A,identity))=identity.
% 1.66/1.87 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.66/1.87 >>>> Starting back demodulation with 5.
% 1.66/1.87 >>>> Starting back demodulation with 7.
% 1.66/1.87 >> back demodulating 2 with 7.
% 1.66/1.87 >>>> Starting back demodulation with 9.
% 1.66/1.87 >>>> Starting back demodulation with 12.
% 1.66/1.87
% 1.66/1.87 ======= end of input processing =======
% 1.66/1.87
% 1.66/1.87 =========== start of search ===========
% 1.66/1.87
% 1.66/1.87 -------- PROOF --------
% 1.66/1.87
% 1.66/1.87 ----> UNIT CONFLICT at 0.00 sec ----> 137 [binary,136.1,3.1] $F.
% 1.66/1.87
% 1.66/1.87 Length of proof is 32. Level of proof is 13.
% 1.66/1.87
% 1.66/1.87 ---------------- PROOF ----------------
% 1.66/1.87 % SZS status Unsatisfiable
% 1.66/1.87 % SZS output start Refutation
% See solution above
% 1.66/1.87 ------------ end of proof -------------
% 1.66/1.87
% 1.66/1.87
% 1.66/1.87 Search stopped by max_proofs option.
% 1.66/1.87
% 1.66/1.87
% 1.66/1.87 Search stopped by max_proofs option.
% 1.66/1.87
% 1.66/1.87 ============ end of search ============
% 1.66/1.87
% 1.66/1.87 -------------- statistics -------------
% 1.66/1.87 clauses given 24
% 1.66/1.87 clauses generated 194
% 1.66/1.87 clauses kept 74
% 1.66/1.87 clauses forward subsumed 184
% 1.66/1.87 clauses back subsumed 2
% 1.66/1.87 Kbytes malloced 976
% 1.66/1.87
% 1.66/1.87 ----------- times (seconds) -----------
% 1.66/1.87 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.87 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.87 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.66/1.87
% 1.66/1.87 That finishes the proof of the theorem.
% 1.66/1.87
% 1.66/1.87 Process 19005 finished Wed Jul 27 05:06:28 2022
% 1.66/1.87 Otter interrupted
% 1.66/1.87 PROOF FOUND
%------------------------------------------------------------------------------