%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP526-1 : 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 12:57:11 EDT 2022
% Result : Unsatisfiable 1.80s 2.03s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 3 RR)
% Number of literals : 18 ( 17 equ; 2 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; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP526-1.p',unknown),
[] ).
cnf(3,axiom,
divide(A,divide(divide(A,B),divide(C,B))) = C,
file('GRP526-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP526-1.p',unknown),
[] ).
cnf(6,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP526-1.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(10,plain,
multiply(multiply(divide(divide(A,A),b2),b2),a2) != a2,
inference(para_from,[status(thm),theory(equality)],[6,1]),
[iquote('para_from,6.1.1,1.1.1.1.1')] ).
cnf(11,plain,
divide(inverse(divide(A,A)),B) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.1,8.1.1')] ).
cnf(35,plain,
divide(A,inverse(divide(B,A))) = B,
inference(para_into,[status(thm),theory(equality)],[3,8]),
[iquote('para_into,3.1.1.2,8.1.1')] ).
cnf(45,plain,
divide(inverse(divide(A,B)),inverse(A)) = B,
inference(para_into,[status(thm),theory(equality)],[35,35]),
[iquote('para_into,35.1.1.2.1,35.1.1')] ).
cnf(57,plain,
inverse(inverse(divide(A,divide(B,B)))) = A,
inference(para_into,[status(thm),theory(equality)],[35,8]),
[iquote('para_into,35.1.1,8.1.1')] ).
cnf(68,plain,
inverse(divide(A,B)) = divide(inverse(A),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[45,35])]),
[iquote('para_into,45.1.1.1.1,35.1.1,flip.1')] ).
cnf(83,plain,
inverse(inverse(A)) = A,
inference(para_into,[status(thm),theory(equality)],[45,11]),
[iquote('para_into,45.1.1,11.1.1')] ).
cnf(90,plain,
divide(A,divide(B,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[57]),68,68,68,83,68,83,83]),
[iquote('back_demod,57,demod,68,68,68,83,68,83,83')] ).
cnf(108,plain,
divide(A,divide(A,B)) = B,
inference(para_from,[status(thm),theory(equality)],[90,3]),
[iquote('para_from,90.1.1,3.1.1.2')] ).
cnf(137,plain,
multiply(divide(A,A),B) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,108])]),
[iquote('para_into,7.1.1,108.1.1,flip.1')] ).
cnf(155,plain,
multiply(multiply(divide(divide(A,A),B),B),C) = C,
inference(para_into,[status(thm),theory(equality)],[137,7]),
[iquote('para_into,137.1.1.1,7.1.1')] ).
cnf(157,plain,
$false,
inference(binary,[status(thm)],[155,10]),
[iquote('binary,155.1,10.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : GRP526-1 : TPTP v8.1.0. Released v2.6.0.
% 0.08/0.12 % 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 05:37:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.80/2.03 ----- Otter 3.3f, August 2004 -----
% 1.80/2.03 The process was started by sandbox on n025.cluster.edu,
% 1.80/2.03 Wed Jul 27 05:37:30 2022
% 1.80/2.03 The command was "./otter". The process ID is 2812.
% 1.80/2.03
% 1.80/2.03 set(prolog_style_variables).
% 1.80/2.03 set(auto).
% 1.80/2.03 dependent: set(auto1).
% 1.80/2.03 dependent: set(process_input).
% 1.80/2.03 dependent: clear(print_kept).
% 1.80/2.03 dependent: clear(print_new_demod).
% 1.80/2.03 dependent: clear(print_back_demod).
% 1.80/2.03 dependent: clear(print_back_sub).
% 1.80/2.03 dependent: set(control_memory).
% 1.80/2.03 dependent: assign(max_mem, 12000).
% 1.80/2.03 dependent: assign(pick_given_ratio, 4).
% 1.80/2.03 dependent: assign(stats_level, 1).
% 1.80/2.03 dependent: assign(max_seconds, 10800).
% 1.80/2.03 clear(print_given).
% 1.80/2.03
% 1.80/2.03 list(usable).
% 1.80/2.03 0 [] A=A.
% 1.80/2.03 0 [] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.80/2.03 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.80/2.03 0 [] inverse(A)=divide(divide(B,B),A).
% 1.80/2.03 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.80/2.03 end_of_list.
% 1.80/2.03
% 1.80/2.03 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.80/2.03
% 1.80/2.03 All clauses are units, and equality is present; the
% 1.80/2.03 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.80/2.03
% 1.80/2.03 dependent: set(knuth_bendix).
% 1.80/2.03 dependent: set(anl_eq).
% 1.80/2.03 dependent: set(para_from).
% 1.80/2.03 dependent: set(para_into).
% 1.80/2.03 dependent: clear(para_from_right).
% 1.80/2.03 dependent: clear(para_into_right).
% 1.80/2.03 dependent: set(para_from_vars).
% 1.80/2.03 dependent: set(eq_units_both_ways).
% 1.80/2.03 dependent: set(dynamic_demod_all).
% 1.80/2.03 dependent: set(dynamic_demod).
% 1.80/2.03 dependent: set(order_eq).
% 1.80/2.03 dependent: set(back_demod).
% 1.80/2.03 dependent: set(lrpo).
% 1.80/2.03
% 1.80/2.03 ------------> process usable:
% 1.80/2.03 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.80/2.03
% 1.80/2.03 ------------> process sos:
% 1.80/2.03 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.80/2.03 ** KEPT (pick-wt=11): 3 [] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.80/2.03 ---> New Demodulator: 4 [new_demod,3] divide(A,divide(divide(A,B),divide(C,B)))=C.
% 1.80/2.03 ** KEPT (pick-wt=11): 5 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.80/2.03 ** KEPT (pick-wt=8): 6 [] inverse(A)=divide(divide(B,B),A).
% 1.80/2.03 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.80/2.03 >>>> Starting back demodulation with 4.
% 1.80/2.03 ** KEPT (pick-wt=11): 7 [copy,5,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.80/2.03 ** KEPT (pick-wt=8): 8 [copy,6,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.80/2.03 Following clause subsumed by 5 during input processing: 0 [copy,7,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.80/2.03 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.80/2.03
% 1.80/2.03 ======= end of input processing =======
% 1.80/2.03
% 1.80/2.03 =========== start of search ===========
% 1.80/2.03
% 1.80/2.03 -------- PROOF --------
% 1.80/2.03
% 1.80/2.03 ----> UNIT CONFLICT at 0.00 sec ----> 157 [binary,155.1,10.1] $F.
% 1.80/2.03
% 1.80/2.03 Length of proof is 13. Level of proof is 8.
% 1.80/2.03
% 1.80/2.03 ---------------- PROOF ----------------
% 1.80/2.03 % SZS status Unsatisfiable
% 1.80/2.03 % SZS output start Refutation
% See solution above
% 1.80/2.03 ------------ end of proof -------------
% 1.80/2.03
% 1.80/2.03
% 1.80/2.03 Search stopped by max_proofs option.
% 1.80/2.03
% 1.80/2.03
% 1.80/2.03 Search stopped by max_proofs option.
% 1.80/2.03
% 1.80/2.03 ============ end of search ============
% 1.80/2.03
% 1.80/2.03 -------------- statistics -------------
% 1.80/2.03 clauses given 18
% 1.80/2.03 clauses generated 176
% 1.80/2.03 clauses kept 105
% 1.80/2.03 clauses forward subsumed 172
% 1.80/2.03 clauses back subsumed 2
% 1.80/2.03 Kbytes malloced 1953
% 1.80/2.03
% 1.80/2.03 ----------- times (seconds) -----------
% 1.80/2.03 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/2.03 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/2.03 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.80/2.03
% 1.80/2.03 That finishes the proof of the theorem.
% 1.80/2.03
% 1.80/2.03 Process 2812 finished Wed Jul 27 05:37:32 2022
% 1.80/2.03 Otter interrupted
% 1.80/2.03 PROOF FOUND
%------------------------------------------------------------------------------