TSTP Solution File: GRP523-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP523-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 12:57:10 EDT 2022
% Result : Unsatisfiable 1.69s 1.87s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 3 RR)
% Number of literals : 32 ( 31 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP523-1.p',unknown),
[] ).
cnf(4,axiom,
divide(A,divide(B,divide(C,divide(A,B)))) = C,
file('GRP523-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP523-1.p',unknown),
[] ).
cnf(6,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP523-1.p',unknown),
[] ).
cnf(7,plain,
divide(A,divide(divide(B,B),C)) = multiply(A,C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(8,plain,
divide(divide(A,A),B) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(9,plain,
divide(divide(A,A),B) = divide(divide(C,C),B),
inference(para_into,[status(thm),theory(equality)],[6,6]),
[iquote('para_into,6.1.1,6.1.1')] ).
cnf(35,plain,
divide(A,inverse(divide(B,divide(A,divide(C,C))))) = B,
inference(para_into,[status(thm),theory(equality)],[4,8]),
[iquote('para_into,3.1.1.2,8.1.1')] ).
cnf(82,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[7,8]),
[iquote('para_into,7.1.1.2,8.1.1')] ).
cnf(83,plain,
divide(A,multiply(divide(B,B),C)) = multiply(A,divide(divide(D,D),C)),
inference(para_into,[status(thm),theory(equality)],[7,7]),
[iquote('para_into,7.1.1.2,7.1.1')] ).
cnf(89,plain,
multiply(A,divide(B,divide(A,divide(C,C)))) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,4])]),
[iquote('para_into,7.1.1,3.1.1,flip.1')] ).
cnf(95,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[82])]),
[iquote('copy,82,flip.1')] ).
cnf(96,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)],[83])]),
[iquote('copy,83,flip.1')] ).
cnf(126,plain,
divide(A,A) = divide(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[9,4]),4]),
[iquote('para_from,9.1.1,3.1.1.2.2,demod,4')] ).
cnf(141,plain,
divide(A,divide(B,divide(C,C))) = divide(A,B),
inference(para_from,[status(thm),theory(equality)],[126,4]),
[iquote('para_from,126.1.1,3.1.1.2.2')] ).
cnf(142,plain,
divide(A,divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[126,4]),141]),
[iquote('para_from,126.1.1,3.1.1.2.2.2,demod,141')] ).
cnf(147,plain,
multiply(A,divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[89]),141]),
[iquote('back_demod,89,demod,141')] ).
cnf(149,plain,
divide(A,inverse(divide(B,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[35]),141]),
[iquote('back_demod,35,demod,141')] ).
cnf(170,plain,
multiply(divide(A,A),B) = B,
inference(para_into,[status(thm),theory(equality)],[142,7]),
[iquote('para_into,142.1.1,7.1.1')] ).
cnf(180,plain,
multiply(A,divide(divide(B,B),C)) = divide(A,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[96]),170]),
[iquote('back_demod,96,demod,170')] ).
cnf(183,plain,
multiply(divide(A,B),B) = A,
inference(para_into,[status(thm),theory(equality)],[147,142]),
[iquote('para_into,147.1.1.2,142.1.1')] ).
cnf(244,plain,
divide(multiply(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[183,7]),180]),
[iquote('para_into,183.1.1.1,7.1.1,demod,180')] ).
cnf(256,plain,
multiply(A,B) = multiply(B,A),
inference(para_from,[status(thm),theory(equality)],[244,147]),
[iquote('para_from,244.1.1,147.1.1.2')] ).
cnf(259,plain,
divide(multiply(A,B),A) = B,
inference(para_from,[status(thm),theory(equality)],[244,142]),
[iquote('para_from,244.1.1,142.1.1.2')] ).
cnf(281,plain,
multiply(divide(A,B),C) = divide(A,divide(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[259,4])]),
[iquote('para_from,259.1.1,3.1.1.2.2,flip.1')] ).
cnf(320,plain,
multiply(A,B) = divide(B,inverse(A)),
inference(para_into,[status(thm),theory(equality)],[95,256]),
[iquote('para_into,95.1.1,256.1.1')] ).
cnf(322,plain,
divide(A,inverse(B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[320])]),
[iquote('copy,320,flip.1')] ).
cnf(329,plain,
divide(a3,divide(inverse(b3),c3)) != multiply(a3,multiply(b3,c3)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[95,1]),281]),
[iquote('para_from,95.1.1,1.1.1.1,demod,281')] ).
cnf(342,plain,
inverse(divide(A,B)) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[149,142])]),
[iquote('para_from,149.1.1,142.1.1.2,flip.1')] ).
cnf(502,plain,
inverse(multiply(A,B)) = divide(inverse(A),B),
inference(para_into,[status(thm),theory(equality)],[342,322]),
[iquote('para_into,342.1.1.1,322.1.1')] ).
cnf(696,plain,
divide(A,divide(inverse(B),C)) = multiply(A,multiply(B,C)),
inference(para_from,[status(thm),theory(equality)],[502,82]),
[iquote('para_from,502.1.1,82.1.1.2')] ).
cnf(697,plain,
$false,
inference(binary,[status(thm)],[696,329]),
[iquote('binary,696.1,329.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP523-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n016.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 05:51:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.87 ----- Otter 3.3f, August 2004 -----
% 1.69/1.87 The process was started by sandbox2 on n016.cluster.edu,
% 1.69/1.87 Wed Jul 27 05:51:22 2022
% 1.69/1.87 The command was "./otter". The process ID is 14361.
% 1.69/1.87
% 1.69/1.87 set(prolog_style_variables).
% 1.69/1.87 set(auto).
% 1.69/1.87 dependent: set(auto1).
% 1.69/1.87 dependent: set(process_input).
% 1.69/1.87 dependent: clear(print_kept).
% 1.69/1.87 dependent: clear(print_new_demod).
% 1.69/1.87 dependent: clear(print_back_demod).
% 1.69/1.87 dependent: clear(print_back_sub).
% 1.69/1.87 dependent: set(control_memory).
% 1.69/1.87 dependent: assign(max_mem, 12000).
% 1.69/1.87 dependent: assign(pick_given_ratio, 4).
% 1.69/1.87 dependent: assign(stats_level, 1).
% 1.69/1.87 dependent: assign(max_seconds, 10800).
% 1.69/1.87 clear(print_given).
% 1.69/1.87
% 1.69/1.87 list(usable).
% 1.69/1.87 0 [] A=A.
% 1.69/1.87 0 [] divide(A,divide(B,divide(C,divide(A,B))))=C.
% 1.69/1.87 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.69/1.87 0 [] inverse(A)=divide(divide(B,B),A).
% 1.69/1.87 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.69/1.87 end_of_list.
% 1.69/1.87
% 1.69/1.87 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.69/1.87
% 1.69/1.87 All clauses are units, and equality is present; the
% 1.69/1.87 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.69/1.87
% 1.69/1.87 dependent: set(knuth_bendix).
% 1.69/1.87 dependent: set(anl_eq).
% 1.69/1.87 dependent: set(para_from).
% 1.69/1.87 dependent: set(para_into).
% 1.69/1.87 dependent: clear(para_from_right).
% 1.69/1.87 dependent: clear(para_into_right).
% 1.69/1.87 dependent: set(para_from_vars).
% 1.69/1.87 dependent: set(eq_units_both_ways).
% 1.69/1.87 dependent: set(dynamic_demod_all).
% 1.69/1.87 dependent: set(dynamic_demod).
% 1.69/1.87 dependent: set(order_eq).
% 1.69/1.87 dependent: set(back_demod).
% 1.69/1.87 dependent: set(lrpo).
% 1.69/1.87
% 1.69/1.87 ------------> process usable:
% 1.69/1.87 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.69/1.87
% 1.69/1.87 ------------> process sos:
% 1.69/1.87 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.69/1.87 ** KEPT (pick-wt=11): 3 [] divide(A,divide(B,divide(C,divide(A,B))))=C.
% 1.69/1.87 ---> New Demodulator: 4 [new_demod,3] divide(A,divide(B,divide(C,divide(A,B))))=C.
% 1.69/1.87 ** KEPT (pick-wt=11): 5 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.69/1.87 ** KEPT (pick-wt=8): 6 [] inverse(A)=divide(divide(B,B),A).
% 1.69/1.87 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.69/1.87 >>>> Starting back demodulation with 4.
% 1.69/1.87 ** KEPT (pick-wt=11): 7 [copy,5,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.69/1.87 ** KEPT (pick-wt=8): 8 [copy,6,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.69/1.87 Following clause subsumed by 5 during input processing: 0 [copy,7,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.69/1.87 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.69/1.87
% 1.69/1.87 ======= end of input processing =======
% 1.69/1.87
% 1.69/1.87 =========== start of search ===========
% 1.69/1.87
% 1.69/1.87 -------- PROOF --------
% 1.69/1.87
% 1.69/1.87 ----> UNIT CONFLICT at 0.02 sec ----> 697 [binary,696.1,329.1] $F.
% 1.69/1.87
% 1.69/1.87 Length of proof is 27. Level of proof is 12.
% 1.69/1.87
% 1.69/1.87 ---------------- PROOF ----------------
% 1.69/1.87 % SZS status Unsatisfiable
% 1.69/1.87 % SZS output start Refutation
% See solution above
% 1.69/1.87 ------------ end of proof -------------
% 1.69/1.87
% 1.69/1.87
% 1.69/1.87 Search stopped by max_proofs option.
% 1.69/1.87
% 1.69/1.87
% 1.69/1.87 Search stopped by max_proofs option.
% 1.69/1.87
% 1.69/1.87 ============ end of search ============
% 1.69/1.87
% 1.69/1.87 -------------- statistics -------------
% 1.69/1.87 clauses given 62
% 1.69/1.87 clauses generated 1502
% 1.69/1.87 clauses kept 521
% 1.69/1.87 clauses forward subsumed 1540
% 1.69/1.87 clauses back subsumed 0
% 1.69/1.87 Kbytes malloced 2929
% 1.69/1.87
% 1.69/1.87 ----------- times (seconds) -----------
% 1.69/1.87 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.69/1.87 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.87 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.69/1.87
% 1.69/1.87 That finishes the proof of the theorem.
% 1.69/1.87
% 1.69/1.87 Process 14361 finished Wed Jul 27 05:51:23 2022
% 1.69/1.87 Otter interrupted
% 1.69/1.87 PROOF FOUND
%------------------------------------------------------------------------------