%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP532-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 12:57:12 EDT 2022
% Result : Unsatisfiable 1.81s 2.04s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 3 RR)
% Number of literals : 21 ( 20 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 39 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP532-1.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(A,divide(B,C)),divide(A,B)) = C,
file('GRP532-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP532-1.p',unknown),
[] ).
cnf(7,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP532-1.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(42,plain,
inverse(divide(divide(A,B),A)) = B,
inference(para_into,[status(thm),theory(equality)],[4,9]),
[iquote('para_into,4.1.1,9.1.1')] ).
cnf(51,plain,
inverse(inverse(A)) = A,
inference(para_into,[status(thm),theory(equality)],[42,9]),
[iquote('para_into,42.1.1.1,9.1.1')] ).
cnf(56,plain,
inverse(A) = divide(divide(B,A),B),
inference(para_into,[status(thm),theory(equality)],[51,42]),
[iquote('para_into,50.1.1.1,42.1.1')] ).
cnf(63,plain,
divide(divide(A,A),inverse(B)) = B,
inference(para_into,[status(thm),theory(equality)],[51,7]),
[iquote('para_into,50.1.1,7.1.1')] ).
cnf(65,plain,
divide(divide(A,B),A) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[56])]),
[iquote('copy,56,flip.1')] ).
cnf(96,plain,
divide(A,divide(B,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[65,63]),51]),
[iquote('para_into,65.1.1.1,63.1.1,demod,51')] ).
cnf(114,plain,
divide(A,divide(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[96,4])]),
[iquote('para_into,95.1.1,4.1.1,flip.1')] ).
cnf(125,plain,
inverse(divide(A,B)) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[114,65])]),
[iquote('para_from,114.1.1,65.1.1.1,flip.1')] ).
cnf(136,plain,
multiply(A,divide(divide(B,B),C)) = divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,114])]),
[iquote('para_into,8.1.1.2,114.1.1,flip.1')] ).
cnf(160,plain,
divide(multiply(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[8,65]),125,96]),
[iquote('para_from,8.1.1,65.1.1.1,demod,125,96')] ).
cnf(176,plain,
divide(multiply(A,B),B) = A,
inference(para_from,[status(thm),theory(equality)],[160,114]),
[iquote('para_from,160.1.1,114.1.1.2')] ).
cnf(190,plain,
multiply(divide(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[176,8]),136]),
[iquote('para_into,176.1.1,8.1.1,demod,136')] ).
cnf(200,plain,
multiply(A,B) = multiply(B,A),
inference(para_into,[status(thm),theory(equality)],[190,160]),
[iquote('para_into,190.1.1.1,160.1.1')] ).
cnf(201,plain,
$false,
inference(binary,[status(thm)],[200,2]),
[iquote('binary,200.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : GRP532-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 05:28:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.81/2.04 ----- Otter 3.3f, August 2004 -----
% 1.81/2.04 The process was started by sandbox2 on n015.cluster.edu,
% 1.81/2.04 Wed Jul 27 05:28:56 2022
% 1.81/2.04 The command was "./otter". The process ID is 29510.
% 1.81/2.04
% 1.81/2.04 set(prolog_style_variables).
% 1.81/2.04 set(auto).
% 1.81/2.04 dependent: set(auto1).
% 1.81/2.04 dependent: set(process_input).
% 1.81/2.04 dependent: clear(print_kept).
% 1.81/2.04 dependent: clear(print_new_demod).
% 1.81/2.04 dependent: clear(print_back_demod).
% 1.81/2.04 dependent: clear(print_back_sub).
% 1.81/2.04 dependent: set(control_memory).
% 1.81/2.04 dependent: assign(max_mem, 12000).
% 1.81/2.04 dependent: assign(pick_given_ratio, 4).
% 1.81/2.04 dependent: assign(stats_level, 1).
% 1.81/2.04 dependent: assign(max_seconds, 10800).
% 1.81/2.04 clear(print_given).
% 1.81/2.04
% 1.81/2.04 list(usable).
% 1.81/2.04 0 [] A=A.
% 1.81/2.04 0 [] divide(divide(A,divide(B,C)),divide(A,B))=C.
% 1.81/2.04 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.81/2.04 0 [] inverse(A)=divide(divide(B,B),A).
% 1.81/2.04 0 [] multiply(a,b)!=multiply(b,a).
% 1.81/2.04 end_of_list.
% 1.81/2.04
% 1.81/2.04 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.81/2.04
% 1.81/2.04 All clauses are units, and equality is present; the
% 1.81/2.04 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.81/2.04
% 1.81/2.04 dependent: set(knuth_bendix).
% 1.81/2.04 dependent: set(anl_eq).
% 1.81/2.04 dependent: set(para_from).
% 1.81/2.04 dependent: set(para_into).
% 1.81/2.04 dependent: clear(para_from_right).
% 1.81/2.04 dependent: clear(para_into_right).
% 1.81/2.04 dependent: set(para_from_vars).
% 1.81/2.04 dependent: set(eq_units_both_ways).
% 1.81/2.04 dependent: set(dynamic_demod_all).
% 1.81/2.04 dependent: set(dynamic_demod).
% 1.81/2.04 dependent: set(order_eq).
% 1.81/2.04 dependent: set(back_demod).
% 1.81/2.04 dependent: set(lrpo).
% 1.81/2.04
% 1.81/2.04 ------------> process usable:
% 1.81/2.04 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.81/2.04
% 1.81/2.04 ------------> process sos:
% 1.81/2.04 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.81/2.04 ** KEPT (pick-wt=11): 4 [] divide(divide(A,divide(B,C)),divide(A,B))=C.
% 1.81/2.04 ---> New Demodulator: 5 [new_demod,4] divide(divide(A,divide(B,C)),divide(A,B))=C.
% 1.81/2.04 ** KEPT (pick-wt=11): 6 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.81/2.04 ** KEPT (pick-wt=8): 7 [] inverse(A)=divide(divide(B,B),A).
% 1.81/2.04 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.81/2.04 >>>> Starting back demodulation with 5.
% 1.81/2.04 ** KEPT (pick-wt=11): 8 [copy,6,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.81/2.04 ** KEPT (pick-wt=8): 9 [copy,7,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.81/2.04 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.81/2.04 Following clause subsumed by 7 during input processing: 0 [copy,9,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.81/2.04
% 1.81/2.04 ======= end of input processing =======
% 1.81/2.04
% 1.81/2.04 =========== start of search ===========
% 1.81/2.04
% 1.81/2.04 -------- PROOF --------
% 1.81/2.04
% 1.81/2.04 ----> UNIT CONFLICT at 0.01 sec ----> 201 [binary,200.1,2.1] $F.
% 1.81/2.04
% 1.81/2.04 Length of proof is 16. Level of proof is 12.
% 1.81/2.04
% 1.81/2.04 ---------------- PROOF ----------------
% 1.81/2.04 % SZS status Unsatisfiable
% 1.81/2.04 % SZS output start Refutation
% See solution above
% 1.81/2.04 ------------ end of proof -------------
% 1.81/2.04
% 1.81/2.04
% 1.81/2.04 Search stopped by max_proofs option.
% 1.81/2.04
% 1.81/2.04
% 1.81/2.04 Search stopped by max_proofs option.
% 1.81/2.04
% 1.81/2.04 ============ end of search ============
% 1.81/2.04
% 1.81/2.04 -------------- statistics -------------
% 1.81/2.04 clauses given 23
% 1.81/2.04 clauses generated 304
% 1.81/2.04 clauses kept 134
% 1.81/2.04 clauses forward subsumed 298
% 1.81/2.04 clauses back subsumed 2
% 1.81/2.04 Kbytes malloced 1953
% 1.81/2.04
% 1.81/2.04 ----------- times (seconds) -----------
% 1.81/2.04 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.81/2.04 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.04 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.81/2.04
% 1.81/2.04 That finishes the proof of the theorem.
% 1.81/2.04
% 1.81/2.04 Process 29510 finished Wed Jul 27 05:28:58 2022
% 1.81/2.04 Otter interrupted
% 1.81/2.04 PROOF FOUND
%------------------------------------------------------------------------------