TSTP Solution File: GRP486-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP486-1 : 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 12:57:06 EDT 2022
% Result : Unsatisfiable 1.69s 1.89s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 46 ( 46 unt; 0 nHn; 7 RR)
% Number of literals : 46 ( 45 equ; 4 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 : 77 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP486-1.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('GRP486-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP486-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP486-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP486-1.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(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(53,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(56,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(57,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(59,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)],[53,35]),56]),
[iquote('para_into,53.1.1,35.1.1,demod,56')] ).
cnf(78,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(82,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)],[57]),78]),
[iquote('back_demod,57,demod,78')] ).
cnf(84,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[34]),78]),
[iquote('back_demod,33,demod,78')] ).
cnf(93,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]),32,84,82,78]),
[iquote('para_into,36.1.1.1.1.2.2.1,31.1.1,demod,32,84,82,78')] ).
cnf(102,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)],[36,59]),50])]),
[iquote('para_into,36.1.1.1.2,59.1.1,demod,50,flip.1')] ).
cnf(109,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]),102]),
[iquote('back_demod,40,demod,102')] ).
cnf(110,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]),102]),
[iquote('back_demod,35,demod,102')] ).
cnf(119,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)],[93,93]),
[iquote('para_into,93.1.1.1,93.1.1')] ).
cnf(123,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)],[41,84]),82]),
[iquote('para_into,41.1.1.1.1.1,83.1.1,demod,82')] ).
cnf(134,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[102,84]),84]),
[iquote('para_into,101.1.1.1.1,83.1.1,demod,84')] ).
cnf(137,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)],[123]),134]),
[iquote('back_demod,123,demod,134')] ).
cnf(140,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[119]),134,134]),
[iquote('back_demod,119,demod,134,134')] ).
cnf(146,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[93]),134]),
[iquote('back_demod,93,demod,134')] ).
cnf(156,plain,
double_divide(double_divide(double_divide(double_divide(identity,b3),double_divide(c3,identity)),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(para_from,[status(thm),theory(equality)],[109,12]),
[iquote('para_from,109.1.1,12.1.1.1.1')] ).
cnf(170,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)],[110,140])]),
[iquote('para_into,110.1.1.1,139.1.1,flip.1')] ).
cnf(175,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)],[110,109])]),
[iquote('para_into,110.1.1.2,109.1.1,flip.1')] ).
cnf(178,plain,
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)],[156]),175,140,146,170]),
[iquote('back_demod,156,demod,175,140,146,170')] ).
cnf(256,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)],[137,146]),
[iquote('para_into,137.1.1.1.1,145.1.1')] ).
cnf(272,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)],[256])]),
[iquote('copy,256,flip.1')] ).
cnf(273,plain,
$false,
inference(binary,[status(thm)],[272,178]),
[iquote('binary,272.1,178.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP486-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.12 % 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 05:05:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.89 ----- Otter 3.3f, August 2004 -----
% 1.69/1.89 The process was started by sandbox on n014.cluster.edu,
% 1.69/1.89 Wed Jul 27 05:05:24 2022
% 1.69/1.89 The command was "./otter". The process ID is 11168.
% 1.69/1.89
% 1.69/1.89 set(prolog_style_variables).
% 1.69/1.89 set(auto).
% 1.69/1.89 dependent: set(auto1).
% 1.69/1.89 dependent: set(process_input).
% 1.69/1.89 dependent: clear(print_kept).
% 1.69/1.89 dependent: clear(print_new_demod).
% 1.69/1.89 dependent: clear(print_back_demod).
% 1.69/1.89 dependent: clear(print_back_sub).
% 1.69/1.89 dependent: set(control_memory).
% 1.69/1.89 dependent: assign(max_mem, 12000).
% 1.69/1.89 dependent: assign(pick_given_ratio, 4).
% 1.69/1.89 dependent: assign(stats_level, 1).
% 1.69/1.89 dependent: assign(max_seconds, 10800).
% 1.69/1.89 clear(print_given).
% 1.69/1.89
% 1.69/1.89 list(usable).
% 1.69/1.89 0 [] A=A.
% 1.69/1.89 0 [] double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity))=C.
% 1.69/1.89 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.69/1.89 0 [] inverse(A)=double_divide(A,identity).
% 1.69/1.89 0 [] identity=double_divide(A,inverse(A)).
% 1.69/1.89 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.69/1.89 end_of_list.
% 1.69/1.89
% 1.69/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.69/1.89
% 1.69/1.89 All clauses are units, and equality is present; the
% 1.69/1.89 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.69/1.89
% 1.69/1.89 dependent: set(knuth_bendix).
% 1.69/1.89 dependent: set(anl_eq).
% 1.69/1.89 dependent: set(para_from).
% 1.69/1.89 dependent: set(para_into).
% 1.69/1.89 dependent: clear(para_from_right).
% 1.69/1.89 dependent: clear(para_into_right).
% 1.69/1.89 dependent: set(para_from_vars).
% 1.69/1.89 dependent: set(eq_units_both_ways).
% 1.69/1.89 dependent: set(dynamic_demod_all).
% 1.69/1.89 dependent: set(dynamic_demod).
% 1.69/1.89 dependent: set(order_eq).
% 1.69/1.89 dependent: set(back_demod).
% 1.69/1.89 dependent: set(lrpo).
% 1.69/1.89
% 1.69/1.89 ------------> process usable:
% 1.69/1.89 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.69/1.89
% 1.69/1.89 ------------> process sos:
% 1.69/1.89 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.69/1.89 ** 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.
% 1.69/1.89 ---> 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.
% 1.69/1.89 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.69/1.89 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.69/1.89 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 1.69/1.89 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 1.69/1.89 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.69/1.89 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 1.69/1.89 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.69/1.89 >>>> Starting back demodulation with 4.
% 1.69/1.89 >>>> Starting back demodulation with 6.
% 1.69/1.89 >> back demodulating 1 with 6.
% 1.69/1.89 >>>> Starting back demodulation with 8.
% 1.69/1.89 >>>> Starting back demodulation with 11.
% 1.69/1.89
% 1.69/1.89 ======= end of input processing =======
% 1.69/1.89
% 1.69/1.89 =========== start of search ===========
% 1.69/1.89
% 1.69/1.89 -------- PROOF --------
% 1.69/1.89
% 1.69/1.89 ----> UNIT CONFLICT at 0.01 sec ----> 273 [binary,272.1,178.1] $F.
% 1.69/1.89
% 1.69/1.89 Length of proof is 40. Level of proof is 12.
% 1.69/1.89
% 1.69/1.89 ---------------- PROOF ----------------
% 1.69/1.89 % SZS status Unsatisfiable
% 1.69/1.89 % SZS output start Refutation
% See solution above
% 1.69/1.89 ------------ end of proof -------------
% 1.69/1.89
% 1.69/1.89
% 1.69/1.89 Search stopped by max_proofs option.
% 1.69/1.89
% 1.69/1.89
% 1.69/1.89 Search stopped by max_proofs option.
% 1.69/1.89
% 1.69/1.89 ============ end of search ============
% 1.69/1.89
% 1.69/1.89 -------------- statistics -------------
% 1.69/1.89 clauses given 36
% 1.69/1.89 clauses generated 526
% 1.69/1.89 clauses kept 164
% 1.69/1.89 clauses forward subsumed 487
% 1.69/1.89 clauses back subsumed 0
% 1.69/1.89 Kbytes malloced 1953
% 1.69/1.89
% 1.69/1.89 ----------- times (seconds) -----------
% 1.69/1.89 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.69/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.89
% 1.69/1.89 That finishes the proof of the theorem.
% 1.69/1.89
% 1.69/1.89 Process 11168 finished Wed Jul 27 05:05:25 2022
% 1.69/1.89 Otter interrupted
% 1.69/1.89 PROOF FOUND
%------------------------------------------------------------------------------