TSTP Solution File: GRP522-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP522-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 12:57:10 EDT 2022
% Result : Unsatisfiable 1.68s 1.88s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 4 RR)
% Number of literals : 24 ( 23 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 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 : 48 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP522-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP522-1.p',unknown),
[] ).
cnf(4,axiom,
divide(A,divide(B,divide(C,divide(A,B)))) = C,
file('GRP522-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP522-1.p',unknown),
[] ).
cnf(6,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP522-1.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(9,plain,
divide(divide(A,A),B) = divide(divide(C,C),B),
inference(para_into,[status(thm),theory(equality)],[6,6]),
[iquote('para_into,6.1.1,6.1.1')] ).
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(14,plain,
divide(inverse(inverse(divide(A,A))),B) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[11,8]),
[iquote('para_into,11.1.1.1.1,8.1.1')] ).
cnf(17,plain,
inverse(A) = divide(inverse(inverse(divide(B,B))),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[14])]),
[iquote('copy,14,flip.1')] ).
cnf(73,plain,
multiply(multiply(divide(inverse(inverse(divide(A,A))),b2),b2),a2) != a2,
inference(para_from,[status(thm),theory(equality)],[17,1]),
[iquote('para_from,17.1.1,1.1.1.1.1')] ).
cnf(88,plain,
inverse(divide(divide(A,A),B)) = multiply(inverse(inverse(divide(C,C))),B),
inference(para_into,[status(thm),theory(equality)],[7,14]),
[iquote('para_into,7.1.1,14.1.1')] ).
cnf(91,plain,
multiply(A,divide(B,divide(A,divide(C,C)))) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,4])]),
[iquote('para_into,7.1.1,3.1.1,flip.1')] ).
cnf(99,plain,
multiply(inverse(inverse(divide(A,A))),B) = inverse(divide(divide(C,C),B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[88])]),
[iquote('copy,88,flip.1')] ).
cnf(128,plain,
divide(A,A) = divide(B,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[9,4]),4]),
[iquote('para_from,9.1.1,3.1.1.2.2,demod,4')] ).
cnf(143,plain,
divide(A,divide(B,divide(C,C))) = divide(A,B),
inference(para_from,[status(thm),theory(equality)],[128,4]),
[iquote('para_from,128.1.1,3.1.1.2.2')] ).
cnf(144,plain,
divide(A,divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[128,4]),143]),
[iquote('para_from,128.1.1,3.1.1.2.2.2,demod,143')] ).
cnf(149,plain,
multiply(A,divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[91]),143]),
[iquote('back_demod,91,demod,143')] ).
cnf(170,plain,
inverse(divide(divide(A,A),B)) = B,
inference(para_into,[status(thm),theory(equality)],[144,8]),
[iquote('para_into,144.1.1,8.1.1')] ).
cnf(180,plain,
multiply(inverse(inverse(divide(A,A))),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[99]),170]),
[iquote('back_demod,99,demod,170')] ).
cnf(186,plain,
multiply(divide(A,B),B) = A,
inference(para_into,[status(thm),theory(equality)],[149,144]),
[iquote('para_into,149.1.1.2,144.1.1')] ).
cnf(194,plain,
a2 != a2,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[73]),186,180]),
[iquote('back_demod,73,demod,186,180')] ).
cnf(195,plain,
$false,
inference(binary,[status(thm)],[194,2]),
[iquote('binary,194.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP522-1 : TPTP v8.1.0. Released v2.6.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 05:25:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.88 ----- Otter 3.3f, August 2004 -----
% 1.68/1.88 The process was started by sandbox2 on n003.cluster.edu,
% 1.68/1.88 Wed Jul 27 05:25:26 2022
% 1.68/1.88 The command was "./otter". The process ID is 13885.
% 1.68/1.88
% 1.68/1.88 set(prolog_style_variables).
% 1.68/1.88 set(auto).
% 1.68/1.88 dependent: set(auto1).
% 1.68/1.88 dependent: set(process_input).
% 1.68/1.88 dependent: clear(print_kept).
% 1.68/1.88 dependent: clear(print_new_demod).
% 1.68/1.88 dependent: clear(print_back_demod).
% 1.68/1.88 dependent: clear(print_back_sub).
% 1.68/1.88 dependent: set(control_memory).
% 1.68/1.88 dependent: assign(max_mem, 12000).
% 1.68/1.88 dependent: assign(pick_given_ratio, 4).
% 1.68/1.88 dependent: assign(stats_level, 1).
% 1.68/1.88 dependent: assign(max_seconds, 10800).
% 1.68/1.88 clear(print_given).
% 1.68/1.88
% 1.68/1.88 list(usable).
% 1.68/1.88 0 [] A=A.
% 1.68/1.88 0 [] divide(A,divide(B,divide(C,divide(A,B))))=C.
% 1.68/1.88 0 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.68/1.88 0 [] inverse(A)=divide(divide(B,B),A).
% 1.68/1.88 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.68/1.88 end_of_list.
% 1.68/1.88
% 1.68/1.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.68/1.88
% 1.68/1.88 All clauses are units, and equality is present; the
% 1.68/1.88 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.68/1.88
% 1.68/1.88 dependent: set(knuth_bendix).
% 1.68/1.88 dependent: set(anl_eq).
% 1.68/1.88 dependent: set(para_from).
% 1.68/1.88 dependent: set(para_into).
% 1.68/1.88 dependent: clear(para_from_right).
% 1.68/1.88 dependent: clear(para_into_right).
% 1.68/1.88 dependent: set(para_from_vars).
% 1.68/1.88 dependent: set(eq_units_both_ways).
% 1.68/1.88 dependent: set(dynamic_demod_all).
% 1.68/1.88 dependent: set(dynamic_demod).
% 1.68/1.88 dependent: set(order_eq).
% 1.68/1.88 dependent: set(back_demod).
% 1.68/1.88 dependent: set(lrpo).
% 1.68/1.88
% 1.68/1.88 ------------> process usable:
% 1.68/1.88 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.68/1.88
% 1.68/1.88 ------------> process sos:
% 1.68/1.88 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.68/1.88 ** KEPT (pick-wt=11): 3 [] divide(A,divide(B,divide(C,divide(A,B))))=C.
% 1.68/1.88 ---> New Demodulator: 4 [new_demod,3] divide(A,divide(B,divide(C,divide(A,B))))=C.
% 1.68/1.88 ** KEPT (pick-wt=11): 5 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.68/1.88 ** KEPT (pick-wt=8): 6 [] inverse(A)=divide(divide(B,B),A).
% 1.68/1.88 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.68/1.88 >>>> Starting back demodulation with 4.
% 1.68/1.88 ** KEPT (pick-wt=11): 7 [copy,5,flip.1] divide(A,divide(divide(B,B),C))=multiply(A,C).
% 1.68/1.88 ** KEPT (pick-wt=8): 8 [copy,6,flip.1] divide(divide(A,A),B)=inverse(B).
% 1.68/1.88 Following clause subsumed by 5 during input processing: 0 [copy,7,flip.1] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.68/1.88 Following clause subsumed by 6 during input processing: 0 [copy,8,flip.1] inverse(A)=divide(divide(B,B),A).
% 1.68/1.88
% 1.68/1.88 ======= end of input processing =======
% 1.68/1.88
% 1.68/1.88 =========== start of search ===========
% 1.68/1.88
% 1.68/1.88 -------- PROOF --------
% 1.68/1.88
% 1.68/1.88 ----> UNIT CONFLICT at 0.00 sec ----> 195 [binary,194.1,2.1] $F.
% 1.68/1.88
% 1.68/1.88 Length of proof is 18. Level of proof is 7.
% 1.68/1.88
% 1.68/1.88 ---------------- PROOF ----------------
% 1.68/1.88 % SZS status Unsatisfiable
% 1.68/1.88 % SZS output start Refutation
% See solution above
% 1.68/1.88 ------------ end of proof -------------
% 1.68/1.88
% 1.68/1.88
% 1.68/1.88 Search stopped by max_proofs option.
% 1.68/1.88
% 1.68/1.88
% 1.68/1.88 Search stopped by max_proofs option.
% 1.68/1.88
% 1.68/1.88 ============ end of search ============
% 1.68/1.88
% 1.68/1.88 -------------- statistics -------------
% 1.68/1.88 clauses given 14
% 1.68/1.88 clauses generated 171
% 1.68/1.88 clauses kept 154
% 1.68/1.88 clauses forward subsumed 189
% 1.68/1.88 clauses back subsumed 0
% 1.68/1.88 Kbytes malloced 1953
% 1.68/1.88
% 1.68/1.88 ----------- times (seconds) -----------
% 1.68/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.88 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.68/1.88
% 1.68/1.88 That finishes the proof of the theorem.
% 1.68/1.88
% 1.68/1.88 Process 13885 finished Wed Jul 27 05:25:28 2022
% 1.68/1.88 Otter interrupted
% 1.68/1.88 PROOF FOUND
%------------------------------------------------------------------------------