TSTP Solution File: GRP095-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP095-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 12:56:02 EDT 2022
% Result : Unsatisfiable 1.65s 1.91s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of clauses : 54 ( 48 unt; 0 nHn; 7 RR)
% Number of literals : 72 ( 71 equ; 24 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
file('GRP095-1.p',unknown),
[] ).
cnf(2,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])])]),
[iquote('copy,1,flip.1,flip.4')] ).
cnf(3,axiom,
A = A,
file('GRP095-1.p',unknown),
[] ).
cnf(4,axiom,
divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C,
file('GRP095-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = divide(A,divide(identity,B)),
file('GRP095-1.p',unknown),
[] ).
cnf(9,axiom,
inverse(A) = divide(identity,A),
file('GRP095-1.p',unknown),
[] ).
cnf(10,axiom,
identity = divide(A,A),
file('GRP095-1.p',unknown),
[] ).
cnf(12,plain,
divide(A,A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(13,plain,
( identity != identity
| divide(identity,divide(identity,a2)) != a2
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),9,7,12,9,7,12,9,7,12,7,7,7,7,7,7,7])]),
[iquote('back_demod,2,demod,9,7,12,9,7,12,9,7,12,7,7,7,7,7,7,7,flip.4')] ).
cnf(14,plain,
divide(identity,divide(divide(divide(A,identity),B),A)) = B,
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1,11.1.1')] ).
cnf(16,plain,
divide(divide(identity,A),divide(divide(identity,B),A)) = B,
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.2.1.1,11.1.1')] ).
cnf(18,plain,
divide(divide(identity,divide(divide(divide(A,B),C),A)),divide(divide(C,D),divide(identity,B))) = D,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.2.1.1,4.1.1')] ).
cnf(20,plain,
divide(divide(identity,A),divide(identity,B)) = divide(B,A),
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.2.1,11.1.1')] ).
cnf(22,plain,
divide(divide(divide(A,B),C),A) = divide(divide(identity,B),divide(C,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,4])]),
[iquote('para_into,4.1.1.2.1,4.1.1,flip.1')] ).
cnf(24,plain,
divide(divide(identity,divide(divide(identity,A),divide(B,identity))),divide(divide(B,C),divide(identity,A))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),22]),
[iquote('back_demod,18,demod,22')] ).
cnf(26,plain,
divide(identity,divide(identity,divide(A,identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[14]),22,12]),
[iquote('back_demod,14,demod,22,12')] ).
cnf(30,plain,
divide(A,divide(divide(identity,B),divide(identity,divide(A,identity)))) = B,
inference(para_into,[status(thm),theory(equality)],[16,26]),
[iquote('para_into,16.1.1.1,26.1.1')] ).
cnf(32,plain,
divide(identity,divide(divide(identity,A),identity)) = A,
inference(para_into,[status(thm),theory(equality)],[16,12]),
[iquote('para_into,16.1.1.1,11.1.1')] ).
cnf(35,plain,
divide(divide(identity,divide(divide(identity,A),B)),A) = B,
inference(para_into,[status(thm),theory(equality)],[16,16]),
[iquote('para_into,16.1.1.2,16.1.1')] ).
cnf(41,plain,
divide(divide(identity,A),identity) = divide(identity,divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,32])]),
[iquote('para_into,32.1.1.2.1,32.1.1,flip.1')] ).
cnf(42,plain,
divide(A,divide(identity,B)) = divide(B,divide(identity,divide(A,identity))),
inference(para_into,[status(thm),theory(equality)],[20,26]),
[iquote('para_into,20.1.1.1,26.1.1')] ).
cnf(43,plain,
divide(identity,divide(identity,A)) = divide(A,identity),
inference(para_into,[status(thm),theory(equality)],[20,12]),
[iquote('para_into,20.1.1.1,11.1.1')] ).
cnf(46,plain,
divide(identity,divide(A,identity)) = divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,12]),41]),
[iquote('para_into,20.1.1.2,11.1.1,demod,41')] ).
cnf(47,plain,
divide(A,divide(identity,B)) = divide(B,divide(identity,A)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[42])]),46]),
[iquote('copy,42,flip.1,demod,46')] ).
cnf(48,plain,
divide(A,identity) = divide(identity,divide(identity,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[43])]),
[iquote('copy,43,flip.1')] ).
cnf(54,plain,
divide(A,divide(divide(identity,B),divide(identity,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[30]),46]),
[iquote('back_demod,30,demod,46')] ).
cnf(57,plain,
divide(identity,divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),46]),
[iquote('back_demod,26,demod,46')] ).
cnf(59,plain,
divide(A,identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[48])]),57])]),
[iquote('copy,48,flip.1,demod,57,flip.1')] ).
cnf(60,plain,
( identity != identity
| a2 != a2
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),57]),
[iquote('back_demod,13,demod,57')] ).
cnf(63,plain,
divide(divide(identity,divide(divide(identity,A),B)),divide(divide(B,C),divide(identity,A))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[24]),59]),
[iquote('back_demod,24,demod,59')] ).
cnf(74,plain,
divide(A,divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,20]),57]),
[iquote('para_into,35.1.1,20.1.1,demod,57')] ).
cnf(75,plain,
divide(A,divide(B,divide(identity,A))) = divide(identity,B),
inference(para_from,[status(thm),theory(equality)],[47,74]),
[iquote('para_from,47.1.1,73.1.1.2')] ).
cnf(76,plain,
divide(identity,A) = divide(B,divide(A,divide(identity,B))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[75])]),
[iquote('copy,75,flip.1')] ).
cnf(78,plain,
( identity != identity
| a2 != a2
| divide(a3,divide(identity,divide(b3,divide(identity,c3)))) != divide(c3,divide(identity,divide(a3,divide(identity,b3))))
| divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[60,47])]),
[iquote('para_into,60.3.1,47.1.1,flip.3')] ).
cnf(121,plain,
divide(A,divide(divide(divide(A,B),C),divide(identity,B))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[63,75]),74,74]),
[iquote('para_into,63.1.1.1.2,75.1.1,demod,74,74')] ).
cnf(143,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[63,75]),74,12,59]),
[iquote('para_into,63.1.1.2,75.1.1,demod,74,12,59')] ).
cnf(151,plain,
divide(divide(A,B),A) = divide(identity,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[143,143]),59])]),
[iquote('para_into,143.1.1.2.1,143.1.1,demod,59,flip.1')] ).
cnf(154,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(para_into,[status(thm),theory(equality)],[143,74]),
[iquote('para_into,143.1.1.2.1,73.1.1')] ).
cnf(158,plain,
divide(divide(identity,A),divide(identity,B)) = divide(identity,divide(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[143,54])]),
[iquote('para_into,143.1.1.2.1,54.1.1,flip.1')] ).
cnf(165,plain,
divide(A,divide(identity,divide(B,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[143,76]),151,158]),
[iquote('para_into,143.1.1,76.1.1,demod,151,158')] ).
cnf(181,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[154])]),
[iquote('copy,154,flip.1')] ).
cnf(183,plain,
divide(divide(identity,A),B) = divide(identity,divide(A,divide(identity,B))),
inference(para_into,[status(thm),theory(equality)],[151,75]),
[iquote('para_into,150.1.1.1,75.1.1')] ).
cnf(206,plain,
divide(divide(A,B),divide(identity,B)) = A,
inference(para_from,[status(thm),theory(equality)],[151,74]),
[iquote('para_from,150.1.1,73.1.1.2')] ).
cnf(210,plain,
divide(A,divide(B,C)) = divide(divide(C,B),divide(identity,A)),
inference(para_from,[status(thm),theory(equality)],[154,47]),
[iquote('para_from,154.1.1,47.1.1.2')] ).
cnf(215,plain,
divide(divide(A,B),divide(identity,C)) = divide(C,divide(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[210])]),
[iquote('copy,210,flip.1')] ).
cnf(234,plain,
( identity != identity
| a2 != a2
| divide(a3,divide(identity,divide(c3,divide(identity,b3)))) != divide(c3,divide(identity,divide(a3,divide(identity,b3))))
| divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[78,181]),183,74]),
[iquote('para_into,78.3.1.2.2,181.1.1,demod,183,74')] ).
cnf(240,plain,
divide(divide(A,B),divide(divide(A,C),B)) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[121,206]),74]),
[iquote('para_into,121.1.1.2.1.1,206.1.1,demod,74')] ).
cnf(306,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(para_into,[status(thm),theory(equality)],[240,74]),
[iquote('para_into,240.1.1.2.1,73.1.1')] ).
cnf(308,plain,
divide(divide(A,divide(divide(A,B),C)),B) = C,
inference(para_into,[status(thm),theory(equality)],[240,240]),
[iquote('para_into,240.1.1.2,240.1.1')] ).
cnf(371,plain,
divide(divide(A,B),divide(identity,C)) = divide(A,divide(B,C)),
inference(para_into,[status(thm),theory(equality)],[306,151]),
[iquote('para_into,306.1.1.2,150.1.1')] ).
cnf(394,plain,
divide(A,divide(B,C)) = divide(C,divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[215]),371]),
[iquote('back_demod,215,demod,371')] ).
cnf(432,plain,
divide(divide(A,B),C) = divide(identity,divide(B,divide(A,C))),
inference(para_into,[status(thm),theory(equality)],[308,165]),
[iquote('para_into,308.1.1.1.2,165.1.1')] ).
cnf(615,plain,
divide(A,divide(B,divide(C,D))) = divide(C,divide(B,divide(A,D))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[432,394]),432,432,74,432,74]),
[iquote('para_into,431.1.1.1,394.1.1,demod,432,432,74,432,74')] ).
cnf(1415,plain,
$false,
inference(hyper,[status(thm)],[615,234,3,3,394]),
[iquote('hyper,615,234,3,3,394')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP095-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 05:31:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.65/1.91 ----- Otter 3.3f, August 2004 -----
% 1.65/1.91 The process was started by sandbox2 on n005.cluster.edu,
% 1.65/1.91 Wed Jul 27 05:31:05 2022
% 1.65/1.91 The command was "./otter". The process ID is 18784.
% 1.65/1.91
% 1.65/1.91 set(prolog_style_variables).
% 1.65/1.91 set(auto).
% 1.65/1.91 dependent: set(auto1).
% 1.65/1.91 dependent: set(process_input).
% 1.65/1.91 dependent: clear(print_kept).
% 1.65/1.91 dependent: clear(print_new_demod).
% 1.65/1.91 dependent: clear(print_back_demod).
% 1.65/1.91 dependent: clear(print_back_sub).
% 1.65/1.91 dependent: set(control_memory).
% 1.65/1.91 dependent: assign(max_mem, 12000).
% 1.65/1.91 dependent: assign(pick_given_ratio, 4).
% 1.65/1.91 dependent: assign(stats_level, 1).
% 1.65/1.91 dependent: assign(max_seconds, 10800).
% 1.65/1.91 clear(print_given).
% 1.65/1.91
% 1.65/1.91 list(usable).
% 1.65/1.91 0 [] A=A.
% 1.65/1.91 0 [] divide(divide(identity,X),divide(divide(divide(Y,X),Z),Y))=Z.
% 1.65/1.91 0 [] multiply(X,Y)=divide(X,divide(identity,Y)).
% 1.65/1.91 0 [] inverse(X)=divide(identity,X).
% 1.65/1.91 0 [] identity=divide(X,X).
% 1.65/1.91 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1)|multiply(multiply(inverse(b2),b2),a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3))|multiply(a4,b4)!=multiply(b4,a4).
% 1.65/1.91 end_of_list.
% 1.65/1.91
% 1.65/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.65/1.91
% 1.65/1.91 This is a Horn set with equality. The strategy will be
% 1.65/1.91 Knuth-Bendix and hyper_res, with positive clauses in
% 1.65/1.91 sos and nonpositive clauses in usable.
% 1.65/1.91
% 1.65/1.91 dependent: set(knuth_bendix).
% 1.65/1.91 dependent: set(anl_eq).
% 1.65/1.91 dependent: set(para_from).
% 1.65/1.91 dependent: set(para_into).
% 1.65/1.91 dependent: clear(para_from_right).
% 1.65/1.91 dependent: clear(para_into_right).
% 1.65/1.91 dependent: set(para_from_vars).
% 1.65/1.91 dependent: set(eq_units_both_ways).
% 1.65/1.91 dependent: set(dynamic_demod_all).
% 1.65/1.91 dependent: set(dynamic_demod).
% 1.65/1.91 dependent: set(order_eq).
% 1.65/1.91 dependent: set(back_demod).
% 1.65/1.91 dependent: set(lrpo).
% 1.65/1.91 dependent: set(hyper_res).
% 1.65/1.91 dependent: clear(order_hyper).
% 1.65/1.91
% 1.65/1.91 ------------> process usable:
% 1.65/1.91 ** KEPT (pick-wt=35): 2 [copy,1,flip.1,flip.4] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1)|multiply(multiply(inverse(b2),b2),a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3))|multiply(b4,a4)!=multiply(a4,b4).
% 1.65/1.91
% 1.65/1.91 ------------> process sos:
% 1.65/1.91 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.65/1.91 ** KEPT (pick-wt=13): 4 [] divide(divide(identity,A),divide(divide(divide(B,A),C),B))=C.
% 1.65/1.91 ---> New Demodulator: 5 [new_demod,4] divide(divide(identity,A),divide(divide(divide(B,A),C),B))=C.
% 1.65/1.91 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.65/1.91 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=divide(A,divide(identity,B)).
% 1.65/1.91 ** KEPT (pick-wt=6): 8 [] inverse(A)=divide(identity,A).
% 1.65/1.91 ---> New Demodulator: 9 [new_demod,8] inverse(A)=divide(identity,A).
% 1.65/1.91 ** KEPT (pick-wt=5): 11 [copy,10,flip.1] divide(A,A)=identity.
% 1.65/1.91 ---> New Demodulator: 12 [new_demod,11] divide(A,A)=identity.
% 1.65/1.91 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.65/1.91 >>>> Starting back demodulation with 5.
% 1.65/1.91 >>>> Starting back demodulation with 7.
% 1.65/1.91 >> back demodulating 2 with 7.
% 1.65/1.91 >>>> Starting back demodulation with 9.
% 1.65/1.91 >>>> Starting back demodulation with 12.
% 1.65/1.91
% 1.65/1.91 ======= end of input processing =======
% 1.65/1.91
% 1.65/1.91 =========== start of search ===========
% 1.65/1.91
% 1.65/1.91 -------- PROOF --------
% 1.65/1.91
% 1.65/1.91 -----> EMPTY CLAUSE at 0.12 sec ----> 1415 [hyper,615,234,3,3,394] $F.
% 1.65/1.91
% 1.65/1.91 Length of proof is 47. Level of proof is 16.
% 1.65/1.91
% 1.65/1.91 ---------------- PROOF ----------------
% 1.65/1.91 % SZS status Unsatisfiable
% 1.65/1.91 % SZS output start Refutation
% See solution above
% 1.65/1.91 ------------ end of proof -------------
% 1.65/1.91
% 1.65/1.91
% 1.65/1.91 Search stopped by max_proofs option.
% 1.65/1.91
% 1.65/1.91
% 1.65/1.91 Search stopped by max_proofs option.
% 1.65/1.91
% 1.65/1.91 ============ end of search ============
% 1.65/1.91
% 1.65/1.91 -------------- statistics -------------
% 1.65/1.91 clauses given 78
% 1.65/1.91 clauses generated 4708
% 1.65/1.91 clauses kept 1168
% 1.65/1.91 clauses forward subsumed 4613
% 1.65/1.91 clauses back subsumed 149
% 1.65/1.91 Kbytes malloced 2929
% 1.65/1.91
% 1.65/1.91 ----------- times (seconds) -----------
% 1.65/1.91 user CPU time 0.12 (0 hr, 0 min, 0 sec)
% 1.65/1.91 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.65/1.91 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.65/1.91
% 1.65/1.91 That finishes the proof of the theorem.
% 1.65/1.91
% 1.65/1.91 Process 18784 finished Wed Jul 27 05:31:07 2022
% 1.65/1.91 Otter interrupted
% 1.65/1.91 PROOF FOUND
%------------------------------------------------------------------------------