TSTP Solution File: GRP495-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP495-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:57:07 EDT 2022
% Result : Unsatisfiable 2.11s 2.26s
% Output : Refutation 2.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 5
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 7 RR)
% Number of literals : 43 ( 42 equ; 5 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP495-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B,
file('GRP495-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP495-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP495-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP495-1.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(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]),6,6,6,6])]),
[iquote('back_demod,1,demod,6,6,6,6,flip.1')] ).
cnf(15,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,double_divide(B,identity)))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,11]),11]),
[iquote('para_into,3.1.1.2.1.1,10.1.1,demod,11')] ).
cnf(17,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,double_divide(identity,identity)),double_divide(A,double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(D,C))))) = double_divide(identity,D),
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.2.1.1,3.1.1')] ).
cnf(19,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,double_divide(A,identity)),double_divide(identity,identity)),identity)) = B,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.2.2,10.1.1')] ).
cnf(23,plain,
double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(identity,identity))),identity) = A,
inference(para_into,[status(thm),theory(equality)],[3,11]),
[iquote('para_into,3.1.1.2,10.1.1')] ).
cnf(25,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,identity),double_divide(A,identity)))) = A,
inference(para_into,[status(thm),theory(equality)],[15,11]),
[iquote('para_into,15.1.1.1,10.1.1')] ).
cnf(27,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[15,11]),
[iquote('para_into,15.1.1.2.2,10.1.1')] ).
cnf(31,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,double_divide(identity,identity)),double_divide(A,double_divide(identity,double_divide(C,double_divide(B,identity)))))) = double_divide(identity,C),
inference(para_from,[status(thm),theory(equality)],[15,3]),
[iquote('para_from,15.1.1,3.1.1.2.1.1')] ).
cnf(34,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)],[27,11]),11])]),
[iquote('para_into,27.1.1.1,10.1.1,demod,11,flip.1')] ).
cnf(35,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,identity),double_divide(A,double_divide(identity,double_divide(C,double_divide(B,identity)))))) = double_divide(identity,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[31]),34]),
[iquote('back_demod,31,demod,34')] ).
cnf(40,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),34]),
[iquote('back_demod,27,demod,34')] ).
cnf(41,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)],[25]),34]),
[iquote('back_demod,25,demod,34')] ).
cnf(44,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[23]),34,40]),
[iquote('back_demod,23,demod,34,40')] ).
cnf(48,plain,
double_divide(double_divide(identity,A),double_divide(B,double_divide(A,identity))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),34,44]),
[iquote('back_demod,19,demod,34,44')] ).
cnf(49,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,identity),double_divide(A,double_divide(double_divide(double_divide(B,C),identity),double_divide(D,C))))) = double_divide(identity,D),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),34,34]),
[iquote('back_demod,17,demod,34,34')] ).
cnf(56,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,B))) = double_divide(identity,B),
inference(para_from,[status(thm),theory(equality)],[40,15]),
[iquote('para_from,39.1.1,15.1.1.2.2.2')] ).
cnf(57,plain,
double_divide(double_divide(identity,A),A) = identity,
inference(para_from,[status(thm),theory(equality)],[40,11]),
[iquote('para_from,39.1.1,10.1.1.2')] ).
cnf(60,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),56]),
[iquote('back_demod,15,demod,56')] ).
cnf(62,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),60]),
[iquote('back_demod,41,demod,60')] ).
cnf(71,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,11]),34,48]),
[iquote('para_into,35.1.1.2.2.2.2,10.1.1,demod,34,48')] ).
cnf(72,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[71])]),
[iquote('copy,71,flip.1')] ).
cnf(78,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,62]),40]),
[iquote('para_into,47.1.1.1,61.1.1,demod,40')] ).
cnf(79,plain,
double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),a3)) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(para_from,[status(thm),theory(equality)],[71,12]),
[iquote('para_from,71.1.1,12.1.1')] ).
cnf(81,plain,
double_divide(double_divide(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[78,78]),
[iquote('para_into,77.1.1.2,77.1.1')] ).
cnf(117,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,identity),double_divide(A,double_divide(B,C)))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,57]),44,62]),
[iquote('para_into,49.1.1.2.2.2.2,57.1.1,demod,44,62')] ).
cnf(130,plain,
double_divide(A,double_divide(identity,B)) = double_divide(A,double_divide(B,identity)),
inference(para_into,[status(thm),theory(equality)],[81,48]),
[iquote('para_into,81.1.1.1,47.1.1')] ).
cnf(132,plain,
double_divide(A,double_divide(B,identity)) = double_divide(A,double_divide(identity,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[130])]),
[iquote('copy,130,flip.1')] ).
cnf(136,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,identity),double_divide(A,double_divide(double_divide(double_divide(B,C),identity),D)))) = double_divide(identity,double_divide(C,D)),
inference(para_from,[status(thm),theory(equality)],[81,49]),
[iquote('para_from,81.1.1,49.1.1.2.2.2.2')] ).
cnf(147,plain,
double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,A))) = B,
inference(para_from,[status(thm),theory(equality)],[132,78]),
[iquote('para_from,132.1.1,77.1.1.2')] ).
cnf(230,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(identity,A))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[56,147]),78]),
[iquote('para_into,55.1.1.2.2,147.1.1,demod,78')] ).
cnf(238,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[56,48]),62]),
[iquote('para_into,55.1.1.2.2,47.1.1,demod,62')] ).
cnf(243,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(identity,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[238])]),
[iquote('copy,238,flip.1')] ).
cnf(500,plain,
double_divide(double_divide(A,double_divide(B,identity)),identity) = double_divide(B,double_divide(identity,A)),
inference(para_into,[status(thm),theory(equality)],[243,72]),
[iquote('para_into,243.1.1,72.1.1')] ).
cnf(512,plain,
double_divide(identity,double_divide(double_divide(double_divide(c3,b3),identity),a3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[79]),500]),
[iquote('back_demod,79,demod,500')] ).
cnf(1512,plain,
double_divide(double_divide(double_divide(A,B),identity),C) = double_divide(A,double_divide(identity,double_divide(B,C))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[136,117]),78])]),
[iquote('para_from,136.1.1,117.1.1.2,demod,78,flip.1')] ).
cnf(1547,plain,
double_divide(double_divide(b3,a3),double_divide(identity,c3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[512]),1512])]),
[iquote('back_demod,512,demod,1512,flip.1')] ).
cnf(1548,plain,
$false,
inference(binary,[status(thm)],[1547,230]),
[iquote('binary,1547.1,230.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP495-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n026.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 05:48:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.11/2.26 ----- Otter 3.3f, August 2004 -----
% 2.11/2.26 The process was started by sandbox on n026.cluster.edu,
% 2.11/2.26 Wed Jul 27 05:48:24 2022
% 2.11/2.26 The command was "./otter". The process ID is 7003.
% 2.11/2.26
% 2.11/2.26 set(prolog_style_variables).
% 2.11/2.26 set(auto).
% 2.11/2.26 dependent: set(auto1).
% 2.11/2.26 dependent: set(process_input).
% 2.11/2.26 dependent: clear(print_kept).
% 2.11/2.26 dependent: clear(print_new_demod).
% 2.11/2.26 dependent: clear(print_back_demod).
% 2.11/2.26 dependent: clear(print_back_sub).
% 2.11/2.26 dependent: set(control_memory).
% 2.11/2.26 dependent: assign(max_mem, 12000).
% 2.11/2.26 dependent: assign(pick_given_ratio, 4).
% 2.11/2.26 dependent: assign(stats_level, 1).
% 2.11/2.26 dependent: assign(max_seconds, 10800).
% 2.11/2.26 clear(print_given).
% 2.11/2.26
% 2.11/2.26 list(usable).
% 2.11/2.26 0 [] A=A.
% 2.11/2.26 0 [] double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)))=B.
% 2.11/2.26 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.11/2.26 0 [] inverse(A)=double_divide(A,identity).
% 2.11/2.26 0 [] identity=double_divide(A,inverse(A)).
% 2.11/2.26 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.11/2.26 end_of_list.
% 2.11/2.26
% 2.11/2.26 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 2.11/2.26
% 2.11/2.26 All clauses are units, and equality is present; the
% 2.11/2.26 strategy will be Knuth-Bendix with positive clauses in sos.
% 2.11/2.26
% 2.11/2.26 dependent: set(knuth_bendix).
% 2.11/2.26 dependent: set(anl_eq).
% 2.11/2.26 dependent: set(para_from).
% 2.11/2.26 dependent: set(para_into).
% 2.11/2.26 dependent: clear(para_from_right).
% 2.11/2.26 dependent: clear(para_into_right).
% 2.11/2.26 dependent: set(para_from_vars).
% 2.11/2.26 dependent: set(eq_units_both_ways).
% 2.11/2.26 dependent: set(dynamic_demod_all).
% 2.11/2.26 dependent: set(dynamic_demod).
% 2.11/2.26 dependent: set(order_eq).
% 2.11/2.26 dependent: set(back_demod).
% 2.11/2.26 dependent: set(lrpo).
% 2.11/2.26
% 2.11/2.26 ------------> process usable:
% 2.11/2.26 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.11/2.26
% 2.11/2.26 ------------> process sos:
% 2.11/2.26 ** KEPT (pick-wt=3): 2 [] A=A.
% 2.11/2.26 ** KEPT (pick-wt=17): 3 [] double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)))=B.
% 2.11/2.26 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C)))=B.
% 2.11/2.26 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.11/2.26 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.11/2.26 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 2.11/2.26 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 2.11/2.26 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 2.11/2.26 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 2.11/2.26 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.11/2.26 >>>> Starting back demodulation with 4.
% 2.11/2.26 >>>> Starting back demodulation with 6.
% 2.11/2.26 >> back demodulating 1 with 6.
% 2.11/2.26 >>>> Starting back demodulation with 8.
% 2.11/2.26 >>>> Starting back demodulation with 11.
% 2.11/2.26
% 2.11/2.26 ======= end of input processing =======
% 2.11/2.26
% 2.11/2.26 =========== start of search ===========
% 2.11/2.26
% 2.11/2.26 -------- PROOF --------
% 2.11/2.26
% 2.11/2.26 ----> UNIT CONFLICT at 0.10 sec ----> 1548 [binary,1547.1,230.1] $F.
% 2.11/2.26
% 2.11/2.26 Length of proof is 37. Level of proof is 14.
% 2.11/2.26
% 2.11/2.26 ---------------- PROOF ----------------
% 2.11/2.26 % SZS status Unsatisfiable
% 2.11/2.26 % SZS output start Refutation
% See solution above
% 2.11/2.26 ------------ end of proof -------------
% 2.11/2.26
% 2.11/2.26
% 2.11/2.26 Search stopped by max_proofs option.
% 2.11/2.26
% 2.11/2.26
% 2.11/2.26 Search stopped by max_proofs option.
% 2.11/2.26
% 2.11/2.26 ============ end of search ============
% 2.11/2.26
% 2.11/2.26 -------------- statistics -------------
% 2.11/2.26 clauses given 76
% 2.11/2.26 clauses generated 5350
% 2.11/2.26 clauses kept 993
% 2.11/2.26 clauses forward subsumed 5073
% 2.11/2.26 clauses back subsumed 10
% 2.11/2.26 Kbytes malloced 2929
% 2.11/2.26
% 2.11/2.26 ----------- times (seconds) -----------
% 2.11/2.26 user CPU time 0.10 (0 hr, 0 min, 0 sec)
% 2.11/2.26 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.11/2.26 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.11/2.26
% 2.11/2.26 That finishes the proof of the theorem.
% 2.11/2.26
% 2.11/2.26 Process 7003 finished Wed Jul 27 05:48:26 2022
% 2.11/2.26 Otter interrupted
% 2.11/2.26 PROOF FOUND
%------------------------------------------------------------------------------