TSTP Solution File: GRP548-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP548-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:57:13 EDT 2022
% Result : Unsatisfiable 1.91s 2.09s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 5 RR)
% Number of literals : 22 ( 21 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP548-1.p',unknown),
[] ).
cnf(2,plain,
multiply(b,a) != multiply(a,b),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C,
file('GRP548-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = divide(A,divide(identity,B)),
file('GRP548-1.p',unknown),
[] ).
cnf(10,axiom,
identity = divide(A,A),
file('GRP548-1.p',unknown),
[] ).
cnf(12,plain,
divide(A,A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(13,plain,
divide(a,divide(identity,b)) != divide(b,divide(identity,a)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),7,7])]),
[iquote('back_demod,2,demod,7,7,flip.1')] ).
cnf(15,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,12]),12]),
[iquote('para_into,4.1.1.1.2,11.1.1,demod,12')] ).
cnf(22,plain,
divide(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,12]),15]),
[iquote('para_into,4.1.1.2,11.1.1,demod,15')] ).
cnf(23,plain,
divide(divide(identity,divide(divide(A,B),C)),B) = divide(C,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,4]),22]),
[iquote('para_into,4.1.1.2,4.1.1,demod,22')] ).
cnf(26,plain,
divide(divide(identity,divide(identity,A)),divide(A,B)) = B,
inference(para_from,[status(thm),theory(equality)],[22,4]),
[iquote('para_from,21.1.1,4.1.1.2')] ).
cnf(32,plain,
divide(divide(A,B),A) = divide(identity,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,15]),22])]),
[iquote('para_into,14.1.1.2.1,14.1.1,demod,22,flip.1')] ).
cnf(35,plain,
divide(identity,divide(identity,A)) = A,
inference(para_into,[status(thm),theory(equality)],[15,12]),
[iquote('para_into,14.1.1.2.1,11.1.1')] ).
cnf(37,plain,
divide(A,divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),35]),
[iquote('back_demod,26,demod,35')] ).
cnf(46,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(para_into,[status(thm),theory(equality)],[32,37]),
[iquote('para_into,32.1.1.1,37.1.1')] ).
cnf(47,plain,
divide(divide(identity,A),divide(B,A)) = divide(identity,B),
inference(para_into,[status(thm),theory(equality)],[32,32]),
[iquote('para_into,32.1.1.1,32.1.1')] ).
cnf(50,plain,
divide(divide(A,B),divide(identity,B)) = A,
inference(para_from,[status(thm),theory(equality)],[32,37]),
[iquote('para_from,32.1.1,37.1.1.2')] ).
cnf(88,plain,
divide(identity,divide(divide(identity,b),a)) != divide(b,divide(identity,a)),
inference(para_from,[status(thm),theory(equality)],[46,13]),
[iquote('para_from,46.1.1,13.1.1')] ).
cnf(103,plain,
divide(divide(identity,divide(A,B)),divide(identity,C)) = divide(B,divide(A,C)),
inference(para_into,[status(thm),theory(equality)],[23,50]),
[iquote('para_into,23.1.1.1.2.1,50.1.1')] ).
cnf(140,plain,
divide(divide(identity,A),divide(identity,B)) = divide(identity,divide(A,B)),
inference(para_into,[status(thm),theory(equality)],[47,32]),
[iquote('para_into,47.1.1.2,32.1.1')] ).
cnf(142,plain,
divide(identity,divide(divide(A,B),C)) = divide(B,divide(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[103]),140]),
[iquote('back_demod,103,demod,140')] ).
cnf(144,plain,
$false,
inference(binary,[status(thm)],[142,88]),
[iquote('binary,142.1,88.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP548-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.14/0.33 % Computer : n026.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Wed Jul 27 05:42:39 EDT 2022
% 0.14/0.33 % CPUTime :
% 1.91/2.09 ----- Otter 3.3f, August 2004 -----
% 1.91/2.09 The process was started by sandbox on n026.cluster.edu,
% 1.91/2.09 Wed Jul 27 05:42:39 2022
% 1.91/2.09 The command was "./otter". The process ID is 30629.
% 1.91/2.09
% 1.91/2.09 set(prolog_style_variables).
% 1.91/2.09 set(auto).
% 1.91/2.09 dependent: set(auto1).
% 1.91/2.09 dependent: set(process_input).
% 1.91/2.09 dependent: clear(print_kept).
% 1.91/2.09 dependent: clear(print_new_demod).
% 1.91/2.09 dependent: clear(print_back_demod).
% 1.91/2.09 dependent: clear(print_back_sub).
% 1.91/2.09 dependent: set(control_memory).
% 1.91/2.09 dependent: assign(max_mem, 12000).
% 1.91/2.09 dependent: assign(pick_given_ratio, 4).
% 1.91/2.09 dependent: assign(stats_level, 1).
% 1.91/2.09 dependent: assign(max_seconds, 10800).
% 1.91/2.09 clear(print_given).
% 1.91/2.09
% 1.91/2.09 list(usable).
% 1.91/2.09 0 [] A=A.
% 1.91/2.09 0 [] divide(divide(identity,divide(A,B)),divide(divide(B,C),A))=C.
% 1.91/2.09 0 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.91/2.09 0 [] inverse(A)=divide(identity,A).
% 1.91/2.09 0 [] identity=divide(A,A).
% 1.91/2.09 0 [] multiply(a,b)!=multiply(b,a).
% 1.91/2.09 end_of_list.
% 1.91/2.09
% 1.91/2.09 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.91/2.09
% 1.91/2.09 All clauses are units, and equality is present; the
% 1.91/2.09 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.91/2.09
% 1.91/2.09 dependent: set(knuth_bendix).
% 1.91/2.09 dependent: set(anl_eq).
% 1.91/2.09 dependent: set(para_from).
% 1.91/2.09 dependent: set(para_into).
% 1.91/2.09 dependent: clear(para_from_right).
% 1.91/2.09 dependent: clear(para_into_right).
% 1.91/2.09 dependent: set(para_from_vars).
% 1.91/2.09 dependent: set(eq_units_both_ways).
% 1.91/2.09 dependent: set(dynamic_demod_all).
% 1.91/2.09 dependent: set(dynamic_demod).
% 1.91/2.09 dependent: set(order_eq).
% 1.91/2.09 dependent: set(back_demod).
% 1.91/2.09 dependent: set(lrpo).
% 1.91/2.09
% 1.91/2.09 ------------> process usable:
% 1.91/2.09 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.91/2.09
% 1.91/2.09 ------------> process sos:
% 1.91/2.09 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.91/2.09 ** KEPT (pick-wt=13): 4 [] divide(divide(identity,divide(A,B)),divide(divide(B,C),A))=C.
% 1.91/2.09 ---> New Demodulator: 5 [new_demod,4] divide(divide(identity,divide(A,B)),divide(divide(B,C),A))=C.
% 1.91/2.09 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.91/2.09 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=divide(A,divide(identity,B)).
% 1.91/2.09 ** KEPT (pick-wt=6): 8 [] inverse(A)=divide(identity,A).
% 1.91/2.09 ---> New Demodulator: 9 [new_demod,8] inverse(A)=divide(identity,A).
% 1.91/2.09 ** KEPT (pick-wt=5): 11 [copy,10,flip.1] divide(A,A)=identity.
% 1.91/2.09 ---> New Demodulator: 12 [new_demod,11] divide(A,A)=identity.
% 1.91/2.09 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.91/2.09 >>>> Starting back demodulation with 5.
% 1.91/2.09 >>>> Starting back demodulation with 7.
% 1.91/2.09 >> back demodulating 2 with 7.
% 1.91/2.09 >>>> Starting back demodulation with 9.
% 1.91/2.09 >>>> Starting back demodulation with 12.
% 1.91/2.09
% 1.91/2.09 ======= end of input processing =======
% 1.91/2.09
% 1.91/2.09 =========== start of search ===========
% 1.91/2.09
% 1.91/2.09 -------- PROOF --------
% 1.91/2.09
% 1.91/2.09 ----> UNIT CONFLICT at 0.01 sec ----> 144 [binary,142.1,88.1] $F.
% 1.91/2.09
% 1.91/2.09 Length of proof is 17. Level of proof is 8.
% 1.91/2.09
% 1.91/2.09 ---------------- PROOF ----------------
% 1.91/2.09 % SZS status Unsatisfiable
% 1.91/2.09 % SZS output start Refutation
% See solution above
% 1.91/2.09 ------------ end of proof -------------
% 1.91/2.09
% 1.91/2.09
% 1.91/2.09 Search stopped by max_proofs option.
% 1.91/2.09
% 1.91/2.09
% 1.91/2.09 Search stopped by max_proofs option.
% 1.91/2.09
% 1.91/2.09 ============ end of search ============
% 1.91/2.09
% 1.91/2.09 -------------- statistics -------------
% 1.91/2.09 clauses given 17
% 1.91/2.09 clauses generated 218
% 1.91/2.09 clauses kept 88
% 1.91/2.09 clauses forward subsumed 193
% 1.91/2.09 clauses back subsumed 0
% 1.91/2.09 Kbytes malloced 976
% 1.91/2.09
% 1.91/2.09 ----------- times (seconds) -----------
% 1.91/2.09 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.91/2.09 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.09 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.91/2.09
% 1.91/2.09 That finishes the proof of the theorem.
% 1.91/2.09
% 1.91/2.09 Process 30629 finished Wed Jul 27 05:42:40 2022
% 1.91/2.09 Otter interrupted
% 1.91/2.09 PROOF FOUND
%------------------------------------------------------------------------------