TSTP Solution File: GRP558-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP558-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 12:57:15 EDT 2022
% Result : Unsatisfiable 1.66s 1.88s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of clauses : 22 ( 22 unt; 0 nHn; 3 RR)
% Number of literals : 22 ( 21 equ; 2 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 : 47 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP558-1.p',unknown),
[] ).
cnf(3,axiom,
divide(A,inverse(divide(divide(B,C),divide(A,C)))) = B,
file('GRP558-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = divide(A,inverse(B)),
file('GRP558-1.p',unknown),
[] ).
cnf(6,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(8,plain,
multiply(divide(inverse(b2),inverse(b2)),a2) != a2,
inference(para_from,[status(thm),theory(equality)],[5,1]),
[iquote('para_from,5.1.1,1.1.1.1')] ).
cnf(12,plain,
divide(A,inverse(divide(B,divide(A,inverse(divide(divide(B,C),divide(D,C))))))) = D,
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.2.1.1,3.1.1')] ).
cnf(18,plain,
multiply(A,divide(divide(B,C),divide(A,C))) = B,
inference(para_into,[status(thm),theory(equality)],[3,6]),
[iquote('para_into,3.1.1,6.1.1')] ).
cnf(20,plain,
multiply(A,divide(multiply(B,C),divide(A,inverse(C)))) = B,
inference(para_into,[status(thm),theory(equality)],[18,6]),
[iquote('para_into,18.1.1.2.1,6.1.1')] ).
cnf(30,plain,
multiply(A,divide(multiply(B,C),multiply(A,C))) = B,
inference(para_into,[status(thm),theory(equality)],[20,6]),
[iquote('para_into,20.1.1.2.2,6.1.1')] ).
cnf(32,plain,
multiply(A,divide(multiply(B,divide(divide(C,D),divide(A,D))),C)) = B,
inference(para_into,[status(thm),theory(equality)],[20,3]),
[iquote('para_into,20.1.1.2.2,3.1.1')] ).
cnf(44,plain,
divide(A,inverse(divide(multiply(B,C),multiply(A,C)))) = B,
inference(para_into,[status(thm),theory(equality)],[30,5]),
[iquote('para_into,30.1.1,5.1.1')] ).
cnf(105,plain,
multiply(A,divide(B,B)) = A,
inference(para_into,[status(thm),theory(equality)],[32,18]),
[iquote('para_into,32.1.1.2.1,18.1.1')] ).
cnf(144,plain,
divide(A,inverse(divide(B,B))) = A,
inference(para_into,[status(thm),theory(equality)],[12,3]),
[iquote('para_into,12.1.1.2.1.2,3.1.1')] ).
cnf(164,plain,
multiply(A,divide(B,A)) = B,
inference(para_from,[status(thm),theory(equality)],[105,32]),
[iquote('para_from,104.1.1,32.1.1.2.1')] ).
cnf(166,plain,
divide(A,inverse(divide(B,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[105,44]),105]),
[iquote('para_from,104.1.1,44.1.1.2.1.2,demod,105')] ).
cnf(203,plain,
multiply(inverse(divide(A,A)),B) = B,
inference(para_from,[status(thm),theory(equality)],[144,164]),
[iquote('para_from,144.1.1,164.1.1.2')] ).
cnf(314,plain,
multiply(inverse(inverse(divide(A,A))),B) = B,
inference(para_into,[status(thm),theory(equality)],[203,144]),
[iquote('para_into,202.1.1.1.1,144.1.1')] ).
cnf(320,plain,
divide(multiply(A,B),B) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[203,30]),203])]),
[iquote('para_into,202.1.1,30.1.1,demod,203,flip.1')] ).
cnf(339,plain,
divide(A,divide(A,B)) = B,
inference(para_into,[status(thm),theory(equality)],[320,164]),
[iquote('para_into,320.1.1.1,164.1.1')] ).
cnf(462,plain,
inverse(divide(A,B)) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[339,166])]),
[iquote('para_into,339.1.1.2,166.1.1,flip.1')] ).
cnf(514,plain,
multiply(divide(A,A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[314]),462,462]),
[iquote('back_demod,314,demod,462,462')] ).
cnf(516,plain,
$false,
inference(binary,[status(thm)],[514,8]),
[iquote('binary,514.1,8.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP558-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n019.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 05:13:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.88 ----- Otter 3.3f, August 2004 -----
% 1.66/1.88 The process was started by sandbox on n019.cluster.edu,
% 1.66/1.88 Wed Jul 27 05:13:07 2022
% 1.66/1.88 The command was "./otter". The process ID is 28786.
% 1.66/1.88
% 1.66/1.88 set(prolog_style_variables).
% 1.66/1.88 set(auto).
% 1.66/1.88 dependent: set(auto1).
% 1.66/1.88 dependent: set(process_input).
% 1.66/1.88 dependent: clear(print_kept).
% 1.66/1.88 dependent: clear(print_new_demod).
% 1.66/1.88 dependent: clear(print_back_demod).
% 1.66/1.88 dependent: clear(print_back_sub).
% 1.66/1.88 dependent: set(control_memory).
% 1.66/1.88 dependent: assign(max_mem, 12000).
% 1.66/1.88 dependent: assign(pick_given_ratio, 4).
% 1.66/1.88 dependent: assign(stats_level, 1).
% 1.66/1.88 dependent: assign(max_seconds, 10800).
% 1.66/1.88 clear(print_given).
% 1.66/1.88
% 1.66/1.88 list(usable).
% 1.66/1.88 0 [] A=A.
% 1.66/1.88 0 [] divide(A,inverse(divide(divide(B,C),divide(A,C))))=B.
% 1.66/1.88 0 [] multiply(A,B)=divide(A,inverse(B)).
% 1.66/1.88 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.66/1.88
% 1.66/1.88 All clauses are units, and equality is present; the
% 1.66/1.88 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.66/1.88
% 1.66/1.88 dependent: set(knuth_bendix).
% 1.66/1.88 dependent: set(anl_eq).
% 1.66/1.88 dependent: set(para_from).
% 1.66/1.88 dependent: set(para_into).
% 1.66/1.88 dependent: clear(para_from_right).
% 1.66/1.88 dependent: clear(para_into_right).
% 1.66/1.88 dependent: set(para_from_vars).
% 1.66/1.88 dependent: set(eq_units_both_ways).
% 1.66/1.88 dependent: set(dynamic_demod_all).
% 1.66/1.88 dependent: set(dynamic_demod).
% 1.66/1.88 dependent: set(order_eq).
% 1.66/1.88 dependent: set(back_demod).
% 1.66/1.88 dependent: set(lrpo).
% 1.66/1.88
% 1.66/1.88 ------------> process usable:
% 1.66/1.88 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.66/1.88
% 1.66/1.88 ------------> process sos:
% 1.66/1.88 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.66/1.88 ** KEPT (pick-wt=12): 3 [] divide(A,inverse(divide(divide(B,C),divide(A,C))))=B.
% 1.66/1.88 ---> New Demodulator: 4 [new_demod,3] divide(A,inverse(divide(divide(B,C),divide(A,C))))=B.
% 1.66/1.88 ** KEPT (pick-wt=8): 5 [] multiply(A,B)=divide(A,inverse(B)).
% 1.66/1.88 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.66/1.88 >>>> Starting back demodulation with 4.
% 1.66/1.88 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] divide(A,inverse(B))=multiply(A,B).
% 1.66/1.88 Following clause subsumed by 5 during input processing: 0 [copy,6,flip.1] multiply(A,B)=divide(A,inverse(B)).
% 1.66/1.88
% 1.66/1.88 ======= end of input processing =======
% 1.66/1.88
% 1.66/1.88 =========== start of search ===========
% 1.66/1.88
% 1.66/1.88 -------- PROOF --------
% 1.66/1.88
% 1.66/1.88 ----> UNIT CONFLICT at 0.01 sec ----> 516 [binary,514.1,8.1] $F.
% 1.66/1.88
% 1.66/1.88 Length of proof is 18. Level of proof is 11.
% 1.66/1.88
% 1.66/1.88 ---------------- PROOF ----------------
% 1.66/1.88 % SZS status Unsatisfiable
% 1.66/1.88 % SZS output start Refutation
% See solution above
% 1.66/1.89 ------------ end of proof -------------
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89 ============ end of search ============
% 1.66/1.89
% 1.66/1.89 -------------- statistics -------------
% 1.66/1.89 clauses given 27
% 1.66/1.89 clauses generated 465
% 1.66/1.89 clauses kept 283
% 1.66/1.89 clauses forward subsumed 314
% 1.66/1.89 clauses back subsumed 0
% 1.66/1.89 Kbytes malloced 4882
% 1.66/1.89
% 1.66/1.89 ----------- times (seconds) -----------
% 1.66/1.89 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.66/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.66/1.89
% 1.66/1.89 That finishes the proof of the theorem.
% 1.66/1.89
% 1.66/1.89 Process 28786 finished Wed Jul 27 05:13:08 2022
% 1.66/1.89 Otter interrupted
% 1.66/1.89 PROOF FOUND
%------------------------------------------------------------------------------