TSTP Solution File: GRP097-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP097-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 12:56:03 EDT 2022
% Result : Unsatisfiable 1.82s 2.03s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of clauses : 44 ( 39 unt; 0 nHn; 6 RR)
% Number of literals : 59 ( 58 equ; 20 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 : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 92 ( 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('GRP097-1.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('GRP097-1.p',unknown),
[] ).
cnf(4,axiom,
divide(A,inverse(divide(divide(B,C),divide(A,C)))) = B,
file('GRP097-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,inverse(B)),
file('GRP097-1.p',unknown),
[] ).
cnf(7,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(11,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| divide(multiply(inverse(b2),b2),inverse(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)],[6,2]),
[iquote('para_from,6.1.1,2.2.1')] ).
cnf(22,plain,
multiply(A,divide(divide(B,C),divide(A,C))) = B,
inference(para_into,[status(thm),theory(equality)],[4,7]),
[iquote('para_into,4.1.1,7.1.1')] ).
cnf(24,plain,
multiply(A,divide(multiply(B,C),divide(A,inverse(C)))) = B,
inference(para_into,[status(thm),theory(equality)],[22,7]),
[iquote('para_into,22.1.1.2.1,7.1.1')] ).
cnf(39,plain,
multiply(A,divide(multiply(B,C),multiply(A,C))) = B,
inference(para_into,[status(thm),theory(equality)],[24,7]),
[iquote('para_into,24.1.1.2.2,7.1.1')] ).
cnf(41,plain,
multiply(A,divide(multiply(B,divide(divide(C,D),divide(A,D))),C)) = B,
inference(para_into,[status(thm),theory(equality)],[24,4]),
[iquote('para_into,24.1.1.2.2,4.1.1')] ).
cnf(53,plain,
divide(A,inverse(divide(multiply(B,C),multiply(A,C)))) = B,
inference(para_into,[status(thm),theory(equality)],[39,6]),
[iquote('para_into,39.1.1,6.1.1')] ).
cnf(118,plain,
multiply(A,divide(B,B)) = A,
inference(para_into,[status(thm),theory(equality)],[41,22]),
[iquote('para_into,41.1.1.2.1,22.1.1')] ).
cnf(139,plain,
divide(A,inverse(divide(B,B))) = A,
inference(para_into,[status(thm),theory(equality)],[118,6]),
[iquote('para_into,117.1.1,6.1.1')] ).
cnf(141,plain,
multiply(A,divide(B,A)) = B,
inference(para_from,[status(thm),theory(equality)],[118,41]),
[iquote('para_from,117.1.1,41.1.1.2.1')] ).
cnf(143,plain,
divide(A,inverse(divide(B,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[118,53]),118]),
[iquote('para_from,117.1.1,53.1.1.2.1.2,demod,118')] ).
cnf(154,plain,
multiply(inverse(A),multiply(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[141,7]),
[iquote('para_into,141.1.1.2,7.1.1')] ).
cnf(185,plain,
multiply(inverse(divide(A,A)),B) = B,
inference(para_from,[status(thm),theory(equality)],[139,141]),
[iquote('para_from,139.1.1,141.1.1.2')] ).
cnf(190,plain,
divide(inverse(divide(A,A)),inverse(B)) = B,
inference(para_into,[status(thm),theory(equality)],[143,139]),
[iquote('para_into,143.1.1.2.1,139.1.1')] ).
cnf(241,plain,
divide(multiply(A,B),B) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[185,39]),185])]),
[iquote('para_into,184.1.1,39.1.1,demod,185,flip.1')] ).
cnf(259,plain,
divide(A,multiply(A,B)) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[241,154]),
[iquote('para_into,241.1.1.1,154.1.1')] ).
cnf(260,plain,
divide(A,divide(A,B)) = B,
inference(para_into,[status(thm),theory(equality)],[241,141]),
[iquote('para_into,241.1.1.1,141.1.1')] ).
cnf(278,plain,
inverse(A) = divide(B,multiply(B,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[259])]),
[iquote('copy,259,flip.1')] ).
cnf(279,plain,
divide(A,inverse(B)) = multiply(B,A),
inference(para_from,[status(thm),theory(equality)],[241,143]),
[iquote('para_from,241.1.1,143.1.1.2.1')] ).
cnf(280,plain,
multiply(A,B) = multiply(B,A),
inference(para_from,[status(thm),theory(equality)],[241,141]),
[iquote('para_from,241.1.1,141.1.1.2')] ).
cnf(298,plain,
divide(A,inverse(divide(B,divide(A,C)))) = multiply(B,C),
inference(para_from,[status(thm),theory(equality)],[241,4]),
[iquote('para_from,241.1.1,4.1.1.2.1.1')] ).
cnf(322,plain,
multiply(divide(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),298]),
[iquote('back_demod,4,demod,298')] ).
cnf(325,plain,
divide(multiply(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[260,241]),
[iquote('para_into,260.1.1.2,241.1.1')] ).
cnf(328,plain,
inverse(divide(A,B)) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[260,143])]),
[iquote('para_into,260.1.1.2,143.1.1,flip.1')] ).
cnf(329,plain,
divide(A,A) = divide(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[260,139]),328]),
[iquote('para_into,260.1.1.2,139.1.1,demod,328')] ).
cnf(332,plain,
divide(A,divide(divide(A,B),C)) = multiply(C,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[298]),328]),
[iquote('back_demod,297,demod,328')] ).
cnf(369,plain,
divide(divide(A,A),inverse(B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[190]),328]),
[iquote('back_demod,190,demod,328')] ).
cnf(480,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| divide(multiply(inverse(b2),b2),inverse(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)],[280,11]),
[iquote('para_from,280.1.1,11.3.1')] ).
cnf(485,plain,
multiply(inverse(A),B) = divide(B,A),
inference(para_from,[status(thm),theory(equality)],[322,154]),
[iquote('para_from,322.1.1,154.1.1.2')] ).
cnf(496,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)],[480]),485,485,485,369]),
[iquote('back_demod,480,demod,485,485,485,369')] ).
cnf(673,plain,
divide(A,divide(B,multiply(B,C))) = multiply(A,C),
inference(para_from,[status(thm),theory(equality)],[278,7]),
[iquote('para_from,278.1.1,7.1.1.2')] ).
cnf(675,plain,
divide(A,divide(B,multiply(B,C))) = multiply(C,A),
inference(para_into,[status(thm),theory(equality)],[279,278]),
[iquote('para_into,279.1.1.2,278.1.1')] ).
cnf(734,plain,
divide(multiply(A,B),divide(B,C)) = multiply(C,A),
inference(para_into,[status(thm),theory(equality)],[332,325]),
[iquote('para_into,332.1.1.2.1,325.1.1')] ).
cnf(738,plain,
divide(multiply(A,B),divide(A,C)) = multiply(C,B),
inference(para_into,[status(thm),theory(equality)],[332,241]),
[iquote('para_into,332.1.1.2.1,241.1.1')] ).
cnf(1151,plain,
multiply(multiply(A,B),C) = multiply(multiply(B,C),A),
inference(para_into,[status(thm),theory(equality)],[734,673]),
[iquote('para_into,734.1.1,673.1.1')] ).
cnf(1154,plain,
multiply(multiply(A,B),C) = multiply(multiply(C,A),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1151])]),
[iquote('copy,1151,flip.1')] ).
cnf(1159,plain,
multiply(multiply(A,B),C) = multiply(B,multiply(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[738,675])]),
[iquote('para_into,738.1.1,675.1.1,flip.1')] ).
cnf(1163,plain,
multiply(A,multiply(B,C)) = multiply(B,multiply(C,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1154]),1159,1159]),
[iquote('back_demod,1154,demod,1159,1159')] ).
cnf(1175,plain,
$false,
inference(hyper,[status(thm)],[1163,496,329,3,280]),
[iquote('hyper,1163,496,329,3,280')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP097-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 04:59:06 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.82/2.03 ----- Otter 3.3f, August 2004 -----
% 1.82/2.03 The process was started by sandbox on n004.cluster.edu,
% 1.82/2.03 Wed Jul 27 04:59:06 2022
% 1.82/2.03 The command was "./otter". The process ID is 12369.
% 1.82/2.03
% 1.82/2.03 set(prolog_style_variables).
% 1.82/2.03 set(auto).
% 1.82/2.03 dependent: set(auto1).
% 1.82/2.03 dependent: set(process_input).
% 1.82/2.03 dependent: clear(print_kept).
% 1.82/2.03 dependent: clear(print_new_demod).
% 1.82/2.03 dependent: clear(print_back_demod).
% 1.82/2.03 dependent: clear(print_back_sub).
% 1.82/2.03 dependent: set(control_memory).
% 1.82/2.03 dependent: assign(max_mem, 12000).
% 1.82/2.03 dependent: assign(pick_given_ratio, 4).
% 1.82/2.03 dependent: assign(stats_level, 1).
% 1.82/2.03 dependent: assign(max_seconds, 10800).
% 1.82/2.03 clear(print_given).
% 1.82/2.03
% 1.82/2.03 list(usable).
% 1.82/2.03 0 [] A=A.
% 1.82/2.03 0 [] divide(X,inverse(divide(divide(Y,Z),divide(X,Z))))=Y.
% 1.82/2.03 0 [] multiply(X,Y)=divide(X,inverse(Y)).
% 1.82/2.03 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).
% 1.82/2.03 end_of_list.
% 1.82/2.03
% 1.82/2.03 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.82/2.03
% 1.82/2.03 This is a Horn set with equality. The strategy will be
% 1.82/2.03 Knuth-Bendix and hyper_res, with positive clauses in
% 1.82/2.03 sos and nonpositive clauses in usable.
% 1.82/2.03
% 1.82/2.03 dependent: set(knuth_bendix).
% 1.82/2.03 dependent: set(anl_eq).
% 1.82/2.03 dependent: set(para_from).
% 1.82/2.03 dependent: set(para_into).
% 1.82/2.03 dependent: clear(para_from_right).
% 1.82/2.03 dependent: clear(para_into_right).
% 1.82/2.03 dependent: set(para_from_vars).
% 1.82/2.03 dependent: set(eq_units_both_ways).
% 1.82/2.03 dependent: set(dynamic_demod_all).
% 1.82/2.03 dependent: set(dynamic_demod).
% 1.82/2.03 dependent: set(order_eq).
% 1.82/2.03 dependent: set(back_demod).
% 1.82/2.03 dependent: set(lrpo).
% 1.82/2.03 dependent: set(hyper_res).
% 1.82/2.03 dependent: clear(order_hyper).
% 1.82/2.03
% 1.82/2.03 ------------> process usable:
% 1.82/2.03 ** 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).
% 1.82/2.03
% 1.82/2.03 ------------> process sos:
% 1.82/2.03 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.82/2.03 ** KEPT (pick-wt=12): 4 [] divide(A,inverse(divide(divide(B,C),divide(A,C))))=B.
% 1.82/2.03 ---> New Demodulator: 5 [new_demod,4] divide(A,inverse(divide(divide(B,C),divide(A,C))))=B.
% 1.82/2.03 ** KEPT (pick-wt=8): 6 [] multiply(A,B)=divide(A,inverse(B)).
% 1.82/2.03 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.82/2.03 >>>> Starting back demodulation with 5.
% 1.82/2.03 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] divide(A,inverse(B))=multiply(A,B).
% 1.82/2.03 Following clause subsumed by 6 during input processing: 0 [copy,7,flip.1] multiply(A,B)=divide(A,inverse(B)).
% 1.82/2.03
% 1.82/2.03 ======= end of input processing =======
% 1.82/2.03
% 1.82/2.03 =========== start of search ===========
% 1.82/2.03
% 1.82/2.03
% 1.82/2.03 Resetting weight limit to 11.
% 1.82/2.03
% 1.82/2.03
% 1.82/2.03 Resetting weight limit to 11.
% 1.82/2.03
% 1.82/2.03 sos_size=376
% 1.82/2.03
% 1.82/2.03 -------- PROOF --------
% 1.82/2.03
% 1.82/2.03 -----> EMPTY CLAUSE at 0.10 sec ----> 1175 [hyper,1163,496,329,3,280] $F.
% 1.82/2.03
% 1.82/2.03 Length of proof is 39. Level of proof is 15.
% 1.82/2.03
% 1.82/2.03 ---------------- PROOF ----------------
% 1.82/2.03 % SZS status Unsatisfiable
% 1.82/2.03 % SZS output start Refutation
% See solution above
% 1.82/2.03 ------------ end of proof -------------
% 1.82/2.03
% 1.82/2.03
% 1.82/2.03 Search stopped by max_proofs option.
% 1.82/2.03
% 1.82/2.03
% 1.82/2.03 Search stopped by max_proofs option.
% 1.82/2.03
% 1.82/2.03 ============ end of search ============
% 1.82/2.03
% 1.82/2.03 -------------- statistics -------------
% 1.82/2.03 clauses given 195
% 1.82/2.03 clauses generated 26387
% 1.82/2.03 clauses kept 785
% 1.82/2.03 clauses forward subsumed 11839
% 1.82/2.03 clauses back subsumed 0
% 1.82/2.03 Kbytes malloced 4882
% 1.82/2.03
% 1.82/2.03 ----------- times (seconds) -----------
% 1.82/2.03 user CPU time 0.10 (0 hr, 0 min, 0 sec)
% 1.82/2.03 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.03 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/2.03
% 1.82/2.03 That finishes the proof of the theorem.
% 1.82/2.03
% 1.82/2.03 Process 12369 finished Wed Jul 27 04:59:08 2022
% 1.82/2.03 Otter interrupted
% 1.82/2.03 PROOF FOUND
%------------------------------------------------------------------------------