TSTP Solution File: GRP445-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP445-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 12:57:02 EDT 2022
% Result : Unsatisfiable 1.96s 2.13s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 5 RR)
% Number of literals : 20 ( 19 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP445-1.p',unknown),
[] ).
cnf(2,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(divide(A,A),A),C))) = B,
file('GRP445-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP445-1.p',unknown),
[] ).
cnf(7,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP445-1.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(13,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.1,9.1.1')] ).
cnf(14,plain,
inverse(A) = divide(inverse(divide(B,B)),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(22,plain,
divide(divide(A,A),B) = divide(inverse(divide(C,C)),B),
inference(para_into,[status(thm),theory(equality)],[14,7]),
[iquote('para_into,14.1.1,7.1.1')] ).
cnf(27,plain,
divide(inverse(divide(A,A)),divide(divide(divide(inverse(inverse(divide(A,A))),B),C),divide(divide(divide(inverse(divide(A,A)),inverse(divide(A,A))),inverse(divide(A,A))),C))) = B,
inference(para_into,[status(thm),theory(equality)],[4,13]),
[iquote('para_into,4.1.1.2.1.1.1,13.1.1')] ).
cnf(32,plain,
divide(A,divide(divide(inverse(B),C),divide(divide(divide(A,A),A),C))) = B,
inference(para_into,[status(thm),theory(equality)],[4,9]),
[iquote('para_into,4.1.1.2.1.1,9.1.1')] ).
cnf(89,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(102,plain,
multiply(A,B) = divide(A,inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[89])]),
[iquote('copy,89,flip.1')] ).
cnf(173,plain,
divide(inverse(b1),inverse(b1)) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[102,2]),
[iquote('para_from,102.1.1,2.1.1')] ).
cnf(351,plain,
divide(A,A) = inverse(inverse(divide(B,B))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,22]),32]),
[iquote('para_into,27.1.1.2.1,22.1.1,demod,32')] ).
cnf(356,plain,
multiply(inverse(A),A) = inverse(inverse(divide(B,B))),
inference(para_into,[status(thm),theory(equality)],[351,89]),
[iquote('para_into,351.1.1,89.1.1')] ).
cnf(361,plain,
inverse(inverse(divide(A,A))) = multiply(inverse(B),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[356])]),
[iquote('copy,356,flip.1')] ).
cnf(364,plain,
inverse(inverse(divide(A,A))) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[351,173]),
[iquote('para_from,351.1.1,173.1.1')] ).
cnf(365,plain,
$false,
inference(binary,[status(thm)],[364,361]),
[iquote('binary,364.1,361.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP445-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 05:16:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.96/2.13 ----- Otter 3.3f, August 2004 -----
% 1.96/2.13 The process was started by sandbox2 on n025.cluster.edu,
% 1.96/2.13 Wed Jul 27 05:16:00 2022
% 1.96/2.13 The command was "./otter". The process ID is 12788.
% 1.96/2.13
% 1.96/2.13 set(prolog_style_variables).
% 1.96/2.13 set(auto).
% 1.96/2.13 dependent: set(auto1).
% 1.96/2.13 dependent: set(process_input).
% 1.96/2.13 dependent: clear(print_kept).
% 1.96/2.13 dependent: clear(print_new_demod).
% 1.96/2.13 dependent: clear(print_back_demod).
% 1.96/2.13 dependent: clear(print_back_sub).
% 1.96/2.13 dependent: set(control_memory).
% 1.96/2.13 dependent: assign(max_mem, 12000).
% 1.96/2.13 dependent: assign(pick_given_ratio, 4).
% 1.96/2.13 dependent: assign(stats_level, 1).
% 1.96/2.13 dependent: assign(max_seconds, 10800).
% 1.96/2.13 clear(print_given).
% 1.96/2.13
% 1.96/2.13 list(usable).
% 1.96/2.13 0 [] A=A.
% 1.96/2.13 0 [] divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(divide(A,A),A),C)))=B.
% 1.96/2.13 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.96/2.13 0 [] inverse(A)=divide(divide(B,B),A).
% 1.96/2.13 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.96/2.13 end_of_list.
% 1.96/2.13
% 1.96/2.13 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.96/2.13
% 1.96/2.13 All clauses are units, and equality is present; the
% 1.96/2.13 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.96/2.13
% 1.96/2.13 dependent: set(knuth_bendix).
% 1.96/2.13 dependent: set(anl_eq).
% 1.96/2.13 dependent: set(para_from).
% 1.96/2.13 dependent: set(para_into).
% 1.96/2.13 dependent: clear(para_from_right).
% 1.96/2.13 dependent: clear(para_into_right).
% 1.96/2.13 dependent: set(para_from_vars).
% 1.96/2.13 dependent: set(eq_units_both_ways).
% 1.96/2.13 dependent: set(dynamic_demod_all).
% 1.96/2.13 dependent: set(dynamic_demod).
% 1.96/2.13 dependent: set(order_eq).
% 1.96/2.13 dependent: set(back_demod).
% 1.96/2.13 dependent: set(lrpo).
% 1.96/2.13
% 1.96/2.13 ------------> process usable:
% 1.96/2.13 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.96/2.13
% 1.96/2.13 ------------> process sos:
% 1.96/2.13 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.96/2.13 ** KEPT (pick-wt=19): 4 [] divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(divide(A,A),A),C)))=B.
% 1.96/2.13 ---> New Demodulator: 5 [new_demod,4] divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(divide(A,A),A),C)))=B.
% 1.96/2.13 ** KEPT (pick-wt=11): 6 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.96/2.13 ** KEPT (pick-wt=8): 7 [] inverse(A)=divide(divide(B,B),A).
% 1.96/2.13 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.96/2.13 >>>> Starting back demodulation with 5.
% 1.96/2.13 ** KEPT (pick-wt=11): 8 [copy,6,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.96/2.13 ** KEPT (pick-wt=8): 9 [copy,7,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.96/2.13 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.96/2.13 Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.96/2.13
% 1.96/2.13 ======= end of input processing =======
% 1.96/2.13
% 1.96/2.13 =========== start of search ===========
% 1.96/2.13
% 1.96/2.13
% 1.96/2.13 Resetting weight limit to 12.
% 1.96/2.13
% 1.96/2.13
% 1.96/2.13 Resetting weight limit to 12.
% 1.96/2.13
% 1.96/2.13 sos_size=275
% 1.96/2.13
% 1.96/2.13 -------- PROOF --------
% 1.96/2.13
% 1.96/2.13 ----> UNIT CONFLICT at 0.03 sec ----> 365 [binary,364.1,361.1] $F.
% 1.96/2.13
% 1.96/2.13 Length of proof is 15. Level of proof is 7.
% 1.96/2.13
% 1.96/2.13 ---------------- PROOF ----------------
% 1.96/2.13 % SZS status Unsatisfiable
% 1.96/2.13 % SZS output start Refutation
% See solution above
% 1.96/2.13 ------------ end of proof -------------
% 1.96/2.13
% 1.96/2.13
% 1.96/2.13 Search stopped by max_proofs option.
% 1.96/2.13
% 1.96/2.13
% 1.96/2.13 Search stopped by max_proofs option.
% 1.96/2.13
% 1.96/2.13 ============ end of search ============
% 1.96/2.13
% 1.96/2.13 -------------- statistics -------------
% 1.96/2.13 clauses given 62
% 1.96/2.13 clauses generated 2578
% 1.96/2.13 clauses kept 333
% 1.96/2.13 clauses forward subsumed 440
% 1.96/2.13 clauses back subsumed 0
% 1.96/2.13 Kbytes malloced 4882
% 1.96/2.13
% 1.96/2.13 ----------- times (seconds) -----------
% 1.96/2.13 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.96/2.13 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.96/2.13 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.96/2.13
% 1.96/2.13 That finishes the proof of the theorem.
% 1.96/2.13
% 1.96/2.13 Process 12788 finished Wed Jul 27 05:16:02 2022
% 1.96/2.13 Otter interrupted
% 1.96/2.13 PROOF FOUND
%------------------------------------------------------------------------------