%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP090-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13.52s 13.74s
% Output : Refutation 13.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 51 ( 45 unt; 0 nHn; 7 RR)
% Number of literals : 69 ( 68 equ; 24 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 115 ( 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('GRP090-1.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('GRP090-1.p',unknown),
[] ).
cnf(4,axiom,
divide(divide(A,divide(B,C)),divide(A,B)) = C,
file('GRP090-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP090-1.p',unknown),
[] ).
cnf(7,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP090-1.p',unknown),
[] ).
cnf(8,plain,
divide(A,divide(divide(B,B),C)) = multiply(A,C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(9,plain,
divide(divide(A,A),B) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(12,plain,
( multiply(divide(divide(A,A),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(para_from,[status(thm),theory(equality)],[7,2]),
[iquote('para_from,7.1.1,2.1.1.1')] ).
cnf(32,plain,
divide(divide(A,B),divide(A,divide(C,divide(D,B)))) = divide(C,D),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.2,4.1.1')] ).
cnf(42,plain,
divide(divide(divide(A,A),divide(B,C)),inverse(B)) = C,
inference(para_into,[status(thm),theory(equality)],[4,9]),
[iquote('para_into,4.1.1.2,9.1.1')] ).
cnf(44,plain,
divide(divide(divide(A,divide(B,C)),divide(divide(A,B),D)),C) = D,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.2,4.1.1')] ).
cnf(46,plain,
inverse(divide(divide(A,B),A)) = B,
inference(para_into,[status(thm),theory(equality)],[4,9]),
[iquote('para_into,4.1.1,9.1.1')] ).
cnf(55,plain,
inverse(inverse(A)) = A,
inference(para_into,[status(thm),theory(equality)],[46,9]),
[iquote('para_into,46.1.1.1,9.1.1')] ).
cnf(60,plain,
inverse(A) = divide(divide(B,A),B),
inference(para_into,[status(thm),theory(equality)],[55,46]),
[iquote('para_into,54.1.1.1,46.1.1')] ).
cnf(67,plain,
divide(divide(A,A),inverse(B)) = B,
inference(para_into,[status(thm),theory(equality)],[55,7]),
[iquote('para_into,54.1.1,7.1.1')] ).
cnf(69,plain,
divide(divide(A,B),A) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[60])]),
[iquote('copy,60,flip.1')] ).
cnf(71,plain,
divide(divide(A,inverse(B)),A) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[60,55])]),
[iquote('para_into,60.1.1,54.1.1,flip.1')] ).
cnf(106,plain,
divide(A,divide(B,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[69,67]),55]),
[iquote('para_into,69.1.1.1,67.1.1,demod,55')] ).
cnf(109,plain,
divide(A,divide(B,divide(C,A))) = inverse(divide(B,C)),
inference(para_into,[status(thm),theory(equality)],[69,4]),
[iquote('para_into,69.1.1.1,4.1.1')] ).
cnf(124,plain,
divide(A,divide(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[106,4])]),
[iquote('para_into,105.1.1,4.1.1,flip.1')] ).
cnf(135,plain,
inverse(divide(A,B)) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[124,69])]),
[iquote('para_from,124.1.1,69.1.1.1,flip.1')] ).
cnf(138,plain,
divide(divide(A,B),divide(A,C)) = divide(C,B),
inference(para_from,[status(thm),theory(equality)],[124,4]),
[iquote('para_from,124.1.1,4.1.1.1.2')] ).
cnf(140,plain,
divide(A,divide(B,divide(C,A))) = divide(C,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[109]),135]),
[iquote('back_demod,109,demod,135')] ).
cnf(146,plain,
multiply(A,divide(divide(B,B),C)) = divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,124])]),
[iquote('para_into,8.1.1.2,124.1.1,flip.1')] ).
cnf(157,plain,
multiply(divide(A,A),B) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,124])]),
[iquote('para_into,8.1.1,124.1.1,flip.1')] ).
cnf(170,plain,
divide(multiply(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[8,69]),135,106]),
[iquote('para_from,8.1.1,69.1.1.1,demod,135,106')] ).
cnf(187,plain,
divide(multiply(A,B),B) = A,
inference(para_from,[status(thm),theory(equality)],[170,124]),
[iquote('para_from,170.1.1,124.1.1.2')] ).
cnf(189,plain,
divide(A,multiply(B,A)) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[170,69]),
[iquote('para_from,170.1.1,69.1.1.1')] ).
cnf(196,plain,
inverse(A) = divide(B,multiply(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[189])]),
[iquote('copy,189,flip.1')] ).
cnf(202,plain,
multiply(divide(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[187,8]),146]),
[iquote('para_into,187.1.1,8.1.1,demod,146')] ).
cnf(203,plain,
( divide(A,A) != 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(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),202]),
[iquote('back_demod,12,demod,202')] ).
cnf(204,plain,
divide(A,multiply(A,B)) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[187,69]),
[iquote('para_from,187.1.1,69.1.1.1')] ).
cnf(212,plain,
multiply(A,B) = multiply(B,A),
inference(para_into,[status(thm),theory(equality)],[202,170]),
[iquote('para_into,201.1.1.1,170.1.1')] ).
cnf(216,plain,
multiply(inverse(A),B) = divide(B,A),
inference(para_into,[status(thm),theory(equality)],[202,69]),
[iquote('para_into,201.1.1.1,69.1.1')] ).
cnf(218,plain,
multiply(A,divide(B,C)) = divide(B,divide(C,A)),
inference(para_into,[status(thm),theory(equality)],[202,4]),
[iquote('para_into,201.1.1.1,4.1.1')] ).
cnf(219,plain,
( divide(A,A) != divide(a1,a1)
| a2 != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[203]),216,216,157]),
[iquote('back_demod,203,demod,216,216,157')] ).
cnf(237,plain,
multiply(A,B) = divide(B,inverse(A)),
inference(para_from,[status(thm),theory(equality)],[71,202]),
[iquote('para_from,71.1.1,201.1.1.1')] ).
cnf(247,plain,
divide(A,inverse(B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[237])]),
[iquote('copy,237,flip.1')] ).
cnf(372,plain,
divide(divide(A,B),inverse(C)) = divide(A,divide(B,C)),
inference(para_into,[status(thm),theory(equality)],[42,32]),
[iquote('para_into,42.1.1.1,32.1.1')] ).
cnf(472,plain,
divide(divide(A,divide(divide(B,C),D)),C) = multiply(divide(A,B),D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[44,204]),372]),
[iquote('para_into,44.1.1.1.2,204.1.1,demod,372')] ).
cnf(474,plain,
divide(divide(A,divide(divide(B,C),D)),C) = divide(A,divide(B,D)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[44,189]),372,218]),
[iquote('para_into,44.1.1.1.2,189.1.1,demod,372,218')] ).
cnf(483,plain,
multiply(divide(A,B),C) = divide(A,divide(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[472])]),474]),
[iquote('copy,472,flip.1,demod,474')] ).
cnf(554,plain,
divide(A,divide(B,multiply(C,B))) = multiply(C,A),
inference(para_into,[status(thm),theory(equality)],[247,196]),
[iquote('para_into,247.1.1.2,196.1.1')] ).
cnf(1022,plain,
divide(A,divide(B,C)) = divide(multiply(A,C),B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[138,204]),372]),
[iquote('para_into,138.1.1.2,204.1.1,demod,372')] ).
cnf(1064,plain,
divide(multiply(A,B),C) = divide(A,divide(C,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1022])]),
[iquote('copy,1022,flip.1')] ).
cnf(1697,plain,
( divide(A,A) != divide(a1,a1)
| a2 != a2
| divide(b3,divide(inverse(a3),c3)) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[219,237]),483]),
[iquote('para_into,219.3.1.1,237.1.1,demod,483')] ).
cnf(3044,plain,
divide(multiply(A,B),multiply(A,C)) = divide(B,C),
inference(para_from,[status(thm),theory(equality)],[554,140]),
[iquote('para_from,554.1.1,140.1.1.2')] ).
cnf(3609,plain,
multiply(A,multiply(B,C)) = divide(B,divide(inverse(A),C)),
inference(para_into,[status(thm),theory(equality)],[1064,247]),
[iquote('para_into,1064.1.1,247.1.1')] ).
cnf(3611,plain,
divide(A,divide(inverse(B),C)) = multiply(B,multiply(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3609])]),
[iquote('copy,3609,flip.1')] ).
cnf(3693,plain,
$false,
inference(hyper,[status(thm)],[1697,3044,3,3611,212]),
[iquote('hyper,1697,3044,3,3611,212')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP090-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 05:20:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 13.52/13.74 ----- Otter 3.3f, August 2004 -----
% 13.52/13.74 The process was started by sandbox2 on n012.cluster.edu,
% 13.52/13.74 Wed Jul 27 05:20:35 2022
% 13.52/13.74 The command was "./otter". The process ID is 18277.
% 13.52/13.74
% 13.52/13.74 set(prolog_style_variables).
% 13.52/13.74 set(auto).
% 13.52/13.74 dependent: set(auto1).
% 13.52/13.74 dependent: set(process_input).
% 13.52/13.74 dependent: clear(print_kept).
% 13.52/13.74 dependent: clear(print_new_demod).
% 13.52/13.74 dependent: clear(print_back_demod).
% 13.52/13.74 dependent: clear(print_back_sub).
% 13.52/13.74 dependent: set(control_memory).
% 13.52/13.74 dependent: assign(max_mem, 12000).
% 13.52/13.74 dependent: assign(pick_given_ratio, 4).
% 13.52/13.74 dependent: assign(stats_level, 1).
% 13.52/13.74 dependent: assign(max_seconds, 10800).
% 13.52/13.74 clear(print_given).
% 13.52/13.74
% 13.52/13.74 list(usable).
% 13.52/13.74 0 [] A=A.
% 13.52/13.74 0 [] divide(divide(X,divide(Y,Z)),divide(X,Y))=Z.
% 13.52/13.74 0 [] multiply(X,Y)=divide(X,divide(divide(Z,Z),Y)).
% 13.52/13.74 0 [] inverse(X)=divide(divide(Z,Z),X).
% 13.52/13.74 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).
% 13.52/13.74 end_of_list.
% 13.52/13.74
% 13.52/13.74 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 13.52/13.74
% 13.52/13.74 This is a Horn set with equality. The strategy will be
% 13.52/13.74 Knuth-Bendix and hyper_res, with positive clauses in
% 13.52/13.74 sos and nonpositive clauses in usable.
% 13.52/13.74
% 13.52/13.74 dependent: set(knuth_bendix).
% 13.52/13.74 dependent: set(anl_eq).
% 13.52/13.74 dependent: set(para_from).
% 13.52/13.74 dependent: set(para_into).
% 13.52/13.74 dependent: clear(para_from_right).
% 13.52/13.74 dependent: clear(para_into_right).
% 13.52/13.74 dependent: set(para_from_vars).
% 13.52/13.74 dependent: set(eq_units_both_ways).
% 13.52/13.74 dependent: set(dynamic_demod_all).
% 13.52/13.74 dependent: set(dynamic_demod).
% 13.52/13.74 dependent: set(order_eq).
% 13.52/13.74 dependent: set(back_demod).
% 13.52/13.74 dependent: set(lrpo).
% 13.52/13.74 dependent: set(hyper_res).
% 13.52/13.74 dependent: clear(order_hyper).
% 13.52/13.74
% 13.52/13.74 ------------> process usable:
% 13.52/13.74 ** 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).
% 13.52/13.74
% 13.52/13.74 ------------> process sos:
% 13.52/13.74 ** KEPT (pick-wt=3): 3 [] A=A.
% 13.52/13.74 ** KEPT (pick-wt=11): 4 [] divide(divide(A,divide(B,C)),divide(A,B))=C.
% 13.52/13.74 ---> New Demodulator: 5 [new_demod,4] divide(divide(A,divide(B,C)),divide(A,B))=C.
% 13.52/13.74 ** KEPT (pick-wt=11): 6 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 13.52/13.74 ** KEPT (pick-wt=8): 7 [] inverse(A)=divide(divide(B,B),A).
% 13.52/13.74 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 13.52/13.74 >>>> Starting back demodulation with 5.
% 13.52/13.74 ** KEPT (pick-wt=11): 8 [copy,6,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 13.52/13.74 ** KEPT (pick-wt=8): 9 [copy,7,flip.1] divide(divide(A,A),B)=inverse(B).
% 13.52/13.74 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 13.52/13.74 Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] inverse(A)=divide(divide(B,B),A).
% 13.52/13.74
% 13.52/13.74 ======= end of input processing =======
% 13.52/13.74
% 13.52/13.74 =========== start of search ===========
% 13.52/13.74
% 13.52/13.74
% 13.52/13.74 Resetting weight limit to 12.
% 13.52/13.74
% 13.52/13.74
% 13.52/13.74 Resetting weight limit to 12.
% 13.52/13.74
% 13.52/13.74 sos_size=2169
% 13.52/13.74
% 13.52/13.74 -- HEY sandbox2, WE HAVE A PROOF!! --
% 13.52/13.74
% 13.52/13.74 -----> EMPTY CLAUSE at 11.96 sec ----> 3693 [hyper,1697,3044,3,3611,212] $F.
% 13.52/13.74
% 13.52/13.74 Length of proof is 45. Level of proof is 15.
% 13.52/13.74
% 13.52/13.74 ---------------- PROOF ----------------
% 13.52/13.74 % SZS status Unsatisfiable
% 13.52/13.74 % SZS output start Refutation
% See solution above
% 13.52/13.74 ------------ end of proof -------------
% 13.52/13.74
% 13.52/13.74
% 13.52/13.74 Search stopped by max_proofs option.
% 13.52/13.74
% 13.52/13.74
% 13.52/13.74 Search stopped by max_proofs option.
% 13.52/13.74
% 13.52/13.74 ============ end of search ============
% 13.52/13.74
% 13.52/13.74 -------------- statistics -------------
% 13.52/13.74 clauses given 1256
% 13.52/13.74 clauses generated 2308819
% 13.52/13.74 clauses kept 2916
% 13.52/13.74 clauses forward subsumed 677862
% 13.52/13.74 clauses back subsumed 5
% 13.52/13.74 Kbytes malloced 4882
% 13.52/13.74
% 13.52/13.74 ----------- times (seconds) -----------
% 13.52/13.74 user CPU time 11.96 (0 hr, 0 min, 11 sec)
% 13.52/13.74 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 13.52/13.74 wall-clock time 14 (0 hr, 0 min, 14 sec)
% 13.52/13.74
% 13.52/13.74 That finishes the proof of the theorem.
% 13.52/13.74
% 13.52/13.74 Process 18277 finished Wed Jul 27 05:20:49 2022
% 13.52/13.74 Otter interrupted
% 13.52/13.74 PROOF FOUND
%------------------------------------------------------------------------------