%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP088-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 12:56:01 EDT 2022
% Result : Unsatisfiable 1.89s 2.10s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of clauses : 43 ( 39 unt; 0 nHn; 5 RR)
% Number of literals : 55 ( 54 equ; 16 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 : 95 ( 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('GRP088-1.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('GRP088-1.p',unknown),
[] ).
cnf(5,axiom,
divide(A,divide(B,divide(C,divide(A,B)))) = C,
file('GRP088-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP088-1.p',unknown),
[] ).
cnf(7,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP088-1.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(10,plain,
divide(divide(A,A),B) = divide(divide(C,C),B),
inference(para_into,[status(thm),theory(equality)],[7,7]),
[iquote('para_into,7.1.1,7.1.1')] ).
cnf(92,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[8,9]),
[iquote('para_into,8.1.1.2,9.1.1')] ).
cnf(93,plain,
divide(A,multiply(divide(B,B),C)) = multiply(A,divide(divide(D,D),C)),
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.2,8.1.1')] ).
cnf(99,plain,
multiply(A,divide(B,divide(A,divide(C,C)))) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,5])]),
[iquote('para_into,8.1.1,4.1.1,flip.1')] ).
cnf(105,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[92])]),
[iquote('copy,92,flip.1')] ).
cnf(106,plain,
multiply(A,divide(divide(B,B),C)) = divide(A,multiply(divide(D,D),C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[93])]),
[iquote('copy,93,flip.1')] ).
cnf(136,plain,
divide(A,A) = divide(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[10,5]),5]),
[iquote('para_from,10.1.1,4.1.1.2.2,demod,5')] ).
cnf(151,plain,
divide(A,divide(B,divide(C,C))) = divide(A,B),
inference(para_from,[status(thm),theory(equality)],[136,5]),
[iquote('para_from,136.1.1,4.1.1.2.2')] ).
cnf(153,plain,
divide(A,divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[136,5]),151]),
[iquote('para_from,136.1.1,4.1.1.2.2.2,demod,151')] ).
cnf(157,plain,
multiply(A,divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[99]),151]),
[iquote('back_demod,99,demod,151')] ).
cnf(180,plain,
multiply(divide(A,A),B) = B,
inference(para_into,[status(thm),theory(equality)],[153,8]),
[iquote('para_into,152.1.1,8.1.1')] ).
cnf(190,plain,
multiply(A,divide(divide(B,B),C)) = divide(A,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[106]),180]),
[iquote('back_demod,106,demod,180')] ).
cnf(193,plain,
multiply(divide(A,B),B) = A,
inference(para_into,[status(thm),theory(equality)],[157,153]),
[iquote('para_into,157.1.1.2,152.1.1')] ).
cnf(258,plain,
divide(multiply(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[193,8]),190]),
[iquote('para_into,193.1.1.1,8.1.1,demod,190')] ).
cnf(270,plain,
multiply(A,B) = multiply(B,A),
inference(para_from,[status(thm),theory(equality)],[258,157]),
[iquote('para_from,258.1.1,157.1.1.2')] ).
cnf(271,plain,
multiply(A,divide(B,C)) = divide(B,divide(C,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[258,5])]),
[iquote('para_from,258.1.1,4.1.1.2.2,flip.1')] ).
cnf(273,plain,
divide(multiply(A,B),A) = B,
inference(para_from,[status(thm),theory(equality)],[258,153]),
[iquote('para_from,258.1.1,152.1.1.2')] ).
cnf(290,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(para_from,[status(thm),theory(equality)],[270,2]),
[iquote('para_from,270.1.1,2.3.1')] ).
cnf(300,plain,
multiply(divide(A,B),C) = divide(A,divide(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[273,5])]),
[iquote('para_from,273.1.1,4.1.1.2.2,flip.1')] ).
cnf(307,plain,
multiply(multiply(inverse(A),B),A) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[92,273])]),
[iquote('para_into,92.1.1,273.1.1,flip.1')] ).
cnf(321,plain,
divide(A,multiply(A,B)) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[92,153]),
[iquote('para_from,92.1.1,152.1.1.2')] ).
cnf(340,plain,
multiply(A,B) = divide(B,inverse(A)),
inference(para_into,[status(thm),theory(equality)],[105,270]),
[iquote('para_into,105.1.1,270.1.1')] ).
cnf(342,plain,
divide(A,inverse(B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[340])]),
[iquote('copy,340,flip.1')] ).
cnf(396,plain,
multiply(inverse(A),B) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[307,258])]),
[iquote('para_from,307.1.1,258.1.1.1,flip.1')] ).
cnf(404,plain,
( divide(b1,b1) != divide(a1,a1)
| a2 != a2
| multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[290]),396,396,396,300,153]),
[iquote('back_demod,290,demod,396,396,396,300,153')] ).
cnf(468,plain,
divide(A,multiply(B,A)) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[321,270]),
[iquote('para_into,321.1.1.2,270.1.1')] ).
cnf(469,plain,
inverse(A) = divide(B,multiply(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[468])]),
[iquote('copy,468,flip.1')] ).
cnf(589,plain,
divide(A,divide(B,multiply(C,B))) = multiply(C,A),
inference(para_from,[status(thm),theory(equality)],[469,342]),
[iquote('para_from,469.1.1,342.1.1.2')] ).
cnf(590,plain,
divide(A,divide(B,multiply(C,B))) = multiply(A,C),
inference(para_from,[status(thm),theory(equality)],[469,92]),
[iquote('para_from,469.1.1,92.1.1.2')] ).
cnf(1034,plain,
multiply(A,B) = divide(multiply(C,B),divide(C,A)),
inference(para_into,[status(thm),theory(equality)],[271,273]),
[iquote('para_into,271.1.1.2,273.1.1')] ).
cnf(1054,plain,
divide(multiply(A,B),divide(A,C)) = multiply(C,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1034])]),
[iquote('copy,1034,flip.1')] ).
cnf(3097,plain,
multiply(multiply(A,B),C) = multiply(multiply(C,A),B),
inference(para_into,[status(thm),theory(equality)],[1054,590]),
[iquote('para_into,1054.1.1,590.1.1')] ).
cnf(3099,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1054,589])]),
[iquote('para_into,1054.1.1,589.1.1,flip.1')] ).
cnf(3103,plain,
multiply(A,multiply(B,C)) = multiply(B,multiply(C,A)),
inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3097])]),3099,3099]),
[iquote('copy,3097,flip.1,demod,3099,3099')] ).
cnf(3172,plain,
$false,
inference(hyper,[status(thm)],[3103,404,136,3,270]),
[iquote('hyper,3103,404,136,3,270')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP088-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 05:24:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.89/2.10 ----- Otter 3.3f, August 2004 -----
% 1.89/2.10 The process was started by sandbox2 on n018.cluster.edu,
% 1.89/2.10 Wed Jul 27 05:24:31 2022
% 1.89/2.10 The command was "./otter". The process ID is 12244.
% 1.89/2.10
% 1.89/2.10 set(prolog_style_variables).
% 1.89/2.10 set(auto).
% 1.89/2.10 dependent: set(auto1).
% 1.89/2.10 dependent: set(process_input).
% 1.89/2.10 dependent: clear(print_kept).
% 1.89/2.10 dependent: clear(print_new_demod).
% 1.89/2.10 dependent: clear(print_back_demod).
% 1.89/2.10 dependent: clear(print_back_sub).
% 1.89/2.10 dependent: set(control_memory).
% 1.89/2.10 dependent: assign(max_mem, 12000).
% 1.89/2.10 dependent: assign(pick_given_ratio, 4).
% 1.89/2.10 dependent: assign(stats_level, 1).
% 1.89/2.10 dependent: assign(max_seconds, 10800).
% 1.89/2.10 clear(print_given).
% 1.89/2.10
% 1.89/2.10 list(usable).
% 1.89/2.10 0 [] A=A.
% 1.89/2.10 0 [] divide(X,divide(Y,divide(Z,divide(X,Y))))=Z.
% 1.89/2.10 0 [] multiply(X,Y)=divide(X,divide(divide(Z,Z),Y)).
% 1.89/2.10 0 [] inverse(X)=divide(divide(Z,Z),X).
% 1.89/2.10 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).
% 1.89/2.10 end_of_list.
% 1.89/2.10
% 1.89/2.10 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.89/2.10
% 1.89/2.10 This is a Horn set with equality. The strategy will be
% 1.89/2.10 Knuth-Bendix and hyper_res, with positive clauses in
% 1.89/2.10 sos and nonpositive clauses in usable.
% 1.89/2.10
% 1.89/2.10 dependent: set(knuth_bendix).
% 1.89/2.10 dependent: set(anl_eq).
% 1.89/2.10 dependent: set(para_from).
% 1.89/2.10 dependent: set(para_into).
% 1.89/2.10 dependent: clear(para_from_right).
% 1.89/2.10 dependent: clear(para_into_right).
% 1.89/2.10 dependent: set(para_from_vars).
% 1.89/2.10 dependent: set(eq_units_both_ways).
% 1.89/2.10 dependent: set(dynamic_demod_all).
% 1.89/2.10 dependent: set(dynamic_demod).
% 1.89/2.10 dependent: set(order_eq).
% 1.89/2.10 dependent: set(back_demod).
% 1.89/2.10 dependent: set(lrpo).
% 1.89/2.10 dependent: set(hyper_res).
% 1.89/2.10 dependent: clear(order_hyper).
% 1.89/2.10
% 1.89/2.10 ------------> process usable:
% 1.89/2.10 ** 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).
% 1.89/2.10
% 1.89/2.10 ------------> process sos:
% 1.89/2.10 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.89/2.10 ** KEPT (pick-wt=11): 4 [] divide(A,divide(B,divide(C,divide(A,B))))=C.
% 1.89/2.10 ---> New Demodulator: 5 [new_demod,4] divide(A,divide(B,divide(C,divide(A,B))))=C.
% 1.89/2.10 ** KEPT (pick-wt=11): 6 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.89/2.10 ** KEPT (pick-wt=8): 7 [] inverse(A)=divide(divide(B,B),A).
% 1.89/2.10 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.89/2.10 >>>> Starting back demodulation with 5.
% 1.89/2.10 ** KEPT (pick-wt=11): 8 [copy,6,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.89/2.10 ** KEPT (pick-wt=8): 9 [copy,7,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.89/2.10 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.89/2.10 Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.89/2.10
% 1.89/2.10 ======= end of input processing =======
% 1.89/2.10
% 1.89/2.10 =========== start of search ===========
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Resetting weight limit to 12.
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Resetting weight limit to 12.
% 1.89/2.10
% 1.89/2.10 sos_size=1633
% 1.89/2.10
% 1.89/2.10 -------- PROOF --------
% 1.89/2.10
% 1.89/2.10 -----> EMPTY CLAUSE at 0.21 sec ----> 3172 [hyper,3103,404,136,3,270] $F.
% 1.89/2.10
% 1.89/2.10 Length of proof is 37. Level of proof is 13.
% 1.89/2.10
% 1.89/2.10 ---------------- PROOF ----------------
% 1.89/2.10 % SZS status Unsatisfiable
% 1.89/2.10 % SZS output start Refutation
% See solution above
% 1.89/2.10 ------------ end of proof -------------
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Search stopped by max_proofs option.
% 1.89/2.10
% 1.89/2.10
% 1.89/2.10 Search stopped by max_proofs option.
% 1.89/2.10
% 1.89/2.10 ============ end of search ============
% 1.89/2.10
% 1.89/2.10 -------------- statistics -------------
% 1.89/2.10 clauses given 175
% 1.89/2.10 clauses generated 18198
% 1.89/2.10 clauses kept 2548
% 1.89/2.10 clauses forward subsumed 14569
% 1.89/2.10 clauses back subsumed 2
% 1.89/2.10 Kbytes malloced 4882
% 1.89/2.10
% 1.89/2.10 ----------- times (seconds) -----------
% 1.89/2.10 user CPU time 0.21 (0 hr, 0 min, 0 sec)
% 1.89/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.89/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.89/2.10
% 1.89/2.10 That finishes the proof of the theorem.
% 1.89/2.10
% 1.89/2.10 Process 12244 finished Wed Jul 27 05:24:33 2022
% 1.89/2.10 Otter interrupted
% 1.89/2.10 PROOF FOUND
%------------------------------------------------------------------------------