TSTP Solution File: GRP497-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP497-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 1.71s 1.92s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of clauses : 36 ( 36 unt; 0 nHn; 5 RR)
% Number of literals : 36 ( 35 equ; 3 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 : 60 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(identity,a2) != a2,
file('GRP497-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity)) = C,
file('GRP497-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP497-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP497-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP497-1.p',unknown),
[] ).
cnf(10,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(identity,identity),double_divide(double_divide(A,double_divide(B,A)),identity)) = B,
inference(para_into,[status(thm),theory(equality)],[3,10]),
[iquote('para_into,3.1.1.1.2,10.1.1')] ).
cnf(15,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,double_divide(A,C)),double_divide(D,double_divide(identity,double_divide(C,double_divide(B,identity))))),identity)) = D,
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.1.2,3.1.1')] ).
cnf(19,plain,
double_divide(double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,C)),identity),double_divide(D,identity))),double_divide(double_divide(D,B),identity)) = double_divide(identity,double_divide(C,double_divide(A,identity))),
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.2.1.2,3.1.1')] ).
cnf(21,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)],[3,10]),
[iquote('para_into,3.1.1.2.1,10.1.1')] ).
cnf(25,plain,
double_divide(identity,identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,10])]),
[iquote('para_into,3.1.1,10.1.1,flip.1')] ).
cnf(27,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)],[21]),25]),
[iquote('back_demod,21,demod,25')] ).
cnf(29,plain,
double_divide(identity,double_divide(double_divide(A,double_divide(B,A)),identity)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),25]),
[iquote('back_demod,13,demod,25')] ).
cnf(36,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(para_into,[status(thm),theory(equality)],[27,27]),
[iquote('para_into,27.1.1.1.2.2,27.1.1')] ).
cnf(37,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),36]),
[iquote('back_demod,27,demod,36')] ).
cnf(41,plain,
double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)) = A,
inference(para_into,[status(thm),theory(equality)],[29,10]),
[iquote('para_into,29.1.1.2.1.2,10.1.1')] ).
cnf(91,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,identity)) = double_divide(double_divide(C,double_divide(A,D)),double_divide(B,double_divide(identity,double_divide(D,double_divide(C,identity))))),
inference(para_from,[status(thm),theory(equality)],[15,3]),
[iquote('para_from,15.1.1,3.1.1.2.1')] ).
cnf(92,plain,
double_divide(double_divide(A,double_divide(B,C)),double_divide(D,double_divide(identity,double_divide(C,double_divide(A,identity))))) = double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,B),identity))),double_divide(D,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[91])]),
[iquote('copy,91,flip.1')] ).
cnf(93,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(para_from,[status(thm),theory(equality)],[41,37]),
[iquote('para_from,41.1.1,37.1.1.2')] ).
cnf(103,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[41,29])]),
[iquote('para_from,41.1.1,29.1.1.2.1,flip.1')] ).
cnf(104,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[93])]),
[iquote('copy,93,flip.1')] ).
cnf(119,plain,
double_divide(identity,double_divide(a2,identity)) != a2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),103]),
[iquote('back_demod,12,demod,103')] ).
cnf(128,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(double_divide(B,double_divide(A,C)),double_divide(D,double_divide(identity,double_divide(C,double_divide(B,identity))))),identity)) = D,
inference(para_from,[status(thm),theory(equality)],[93,15]),
[iquote('para_from,93.1.1,15.1.1.1')] ).
cnf(142,plain,
double_divide(A,double_divide(identity,A)) = identity,
inference(para_from,[status(thm),theory(equality)],[104,10]),
[iquote('para_from,104.1.1,10.1.1.2')] ).
cnf(146,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(double_divide(A,double_divide(identity,B)),identity)) = B,
inference(para_from,[status(thm),theory(equality)],[104,3]),
[iquote('para_from,104.1.1,3.1.1.2.1.2')] ).
cnf(157,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,double_divide(A,identity)),double_divide(B,identity))),double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,25]),103,103]),
[iquote('para_into,19.1.1.1.2.1.1.2,24.1.1,demod,103,103')] ).
cnf(171,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),double_divide(double_divide(A,B),identity)) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,10]),25]),
[iquote('para_into,19.1.1.1.2.1.1,10.1.1,demod,25')] ).
cnf(206,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[146]),171]),
[iquote('back_demod,146,demod,171')] ).
cnf(213,plain,
double_divide(double_divide(A,double_divide(B,C)),double_divide(D,double_divide(identity,double_divide(C,double_divide(A,identity))))) = double_divide(B,double_divide(D,identity)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[92]),206]),
[iquote('back_demod,92,demod,206')] ).
cnf(224,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(A,double_divide(B,identity)),identity)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[128]),213]),
[iquote('back_demod,128,demod,213')] ).
cnf(248,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),double_divide(B,identity))),double_divide(identity,double_divide(B,identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[142,3]),103]),
[iquote('para_from,142.1.1,3.1.1.2.1.2,demod,103')] ).
cnf(251,plain,
double_divide(identity,double_divide(identity,double_divide(A,identity))) = double_divide(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[157]),248])]),
[iquote('back_demod,157,demod,248,flip.1')] ).
cnf(261,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(A,B),identity)) = double_divide(B,identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[171]),251,251]),
[iquote('back_demod,170,demod,251,251')] ).
cnf(290,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[224]),261,103]),
[iquote('back_demod,224,demod,261,103')] ).
cnf(292,plain,
$false,
inference(binary,[status(thm)],[290,119]),
[iquote('binary,290.1,119.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP497-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:24:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.71/1.92 ----- Otter 3.3f, August 2004 -----
% 1.71/1.92 The process was started by sandbox on n021.cluster.edu,
% 1.71/1.92 Wed Jul 27 05:24:08 2022
% 1.71/1.92 The command was "./otter". The process ID is 14563.
% 1.71/1.92
% 1.71/1.92 set(prolog_style_variables).
% 1.71/1.92 set(auto).
% 1.71/1.92 dependent: set(auto1).
% 1.71/1.92 dependent: set(process_input).
% 1.71/1.92 dependent: clear(print_kept).
% 1.71/1.92 dependent: clear(print_new_demod).
% 1.71/1.92 dependent: clear(print_back_demod).
% 1.71/1.92 dependent: clear(print_back_sub).
% 1.71/1.92 dependent: set(control_memory).
% 1.71/1.92 dependent: assign(max_mem, 12000).
% 1.71/1.92 dependent: assign(pick_given_ratio, 4).
% 1.71/1.92 dependent: assign(stats_level, 1).
% 1.71/1.92 dependent: assign(max_seconds, 10800).
% 1.71/1.92 clear(print_given).
% 1.71/1.92
% 1.71/1.92 list(usable).
% 1.71/1.92 0 [] A=A.
% 1.71/1.92 0 [] double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))=C.
% 1.71/1.92 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.71/1.92 0 [] inverse(A)=double_divide(A,identity).
% 1.71/1.92 0 [] identity=double_divide(A,inverse(A)).
% 1.71/1.92 0 [] multiply(identity,a2)!=a2.
% 1.71/1.92 end_of_list.
% 1.71/1.92
% 1.71/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.71/1.92
% 1.71/1.92 All clauses are units, and equality is present; the
% 1.71/1.92 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.71/1.92
% 1.71/1.92 dependent: set(knuth_bendix).
% 1.71/1.92 dependent: set(anl_eq).
% 1.71/1.92 dependent: set(para_from).
% 1.71/1.92 dependent: set(para_into).
% 1.71/1.92 dependent: clear(para_from_right).
% 1.71/1.92 dependent: clear(para_into_right).
% 1.71/1.92 dependent: set(para_from_vars).
% 1.71/1.92 dependent: set(eq_units_both_ways).
% 1.71/1.92 dependent: set(dynamic_demod_all).
% 1.71/1.92 dependent: set(dynamic_demod).
% 1.71/1.92 dependent: set(order_eq).
% 1.71/1.92 dependent: set(back_demod).
% 1.71/1.92 dependent: set(lrpo).
% 1.71/1.92
% 1.71/1.92 ------------> process usable:
% 1.71/1.92 ** KEPT (pick-wt=5): 1 [] multiply(identity,a2)!=a2.
% 1.71/1.92
% 1.71/1.92 ------------> process sos:
% 1.71/1.92 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.71/1.92 ** KEPT (pick-wt=17): 3 [] double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))=C.
% 1.71/1.92 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(identity,double_divide(A,double_divide(B,identity))),double_divide(double_divide(B,double_divide(C,A)),identity))=C.
% 1.71/1.92 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.71/1.92 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.71/1.92 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 1.71/1.92 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 1.71/1.92 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.71/1.92 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 1.71/1.92 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.71/1.92 >>>> Starting back demodulation with 4.
% 1.71/1.92 >>>> Starting back demodulation with 6.
% 1.71/1.92 >> back demodulating 1 with 6.
% 1.71/1.92 >>>> Starting back demodulation with 8.
% 1.71/1.92 >>>> Starting back demodulation with 11.
% 1.71/1.92
% 1.71/1.92 ======= end of input processing =======
% 1.71/1.92
% 1.71/1.92 =========== start of search ===========
% 1.71/1.92
% 1.71/1.92 -------- PROOF --------
% 1.71/1.92
% 1.71/1.92 ----> UNIT CONFLICT at 0.01 sec ----> 292 [binary,290.1,119.1] $F.
% 1.71/1.92
% 1.71/1.92 Length of proof is 30. Level of proof is 12.
% 1.71/1.92
% 1.71/1.92 ---------------- PROOF ----------------
% 1.71/1.92 % SZS status Unsatisfiable
% 1.71/1.92 % SZS output start Refutation
% See solution above
% 1.71/1.92 ------------ end of proof -------------
% 1.71/1.92
% 1.71/1.92
% 1.71/1.92 Search stopped by max_proofs option.
% 1.71/1.92
% 1.71/1.92
% 1.71/1.92 Search stopped by max_proofs option.
% 1.71/1.92
% 1.71/1.92 ============ end of search ============
% 1.71/1.92
% 1.71/1.92 -------------- statistics -------------
% 1.71/1.92 clauses given 17
% 1.71/1.92 clauses generated 191
% 1.71/1.92 clauses kept 166
% 1.71/1.92 clauses forward subsumed 140
% 1.71/1.92 clauses back subsumed 1
% 1.71/1.92 Kbytes malloced 1953
% 1.71/1.92
% 1.71/1.92 ----------- times (seconds) -----------
% 1.71/1.92 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.71/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.71/1.92
% 1.71/1.92 That finishes the proof of the theorem.
% 1.71/1.92
% 1.71/1.92 Process 14563 finished Wed Jul 27 05:24:09 2022
% 1.71/1.92 Otter interrupted
% 1.71/1.92 PROOF FOUND
%------------------------------------------------------------------------------