TSTP Solution File: BOO072-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO072-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 12:47:41 EDT 2022
% Result : Unsatisfiable 1.98s 2.16s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 2
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 2 RR)
% Number of literals : 55 ( 54 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 94 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
add(b,a) != add(a,b),
file('BOO072-1.p',unknown),
[] ).
cnf(3,axiom,
inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,D)))))))) = C,
file('BOO072-1.p',unknown),
[] ).
cnf(13,plain,
inverse(add(inverse(add(inverse(add(inverse(add(inverse(add(inverse(inverse(A)),B)),A)),C)),inverse(A))),A)) = inverse(A),
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.1.2,3.1.1')] ).
cnf(19,plain,
inverse(add(inverse(add(A,inverse(A))),A)) = inverse(A),
inference(para_into,[status(thm),theory(equality)],[13,3]),
[iquote('para_into,13.1.1.1.1.1.1,3.1.1')] ).
cnf(41,plain,
inverse(add(inverse(A),inverse(add(A,inverse(add(inverse(A),inverse(add(A,B)))))))) = A,
inference(para_from,[status(thm),theory(equality)],[19,3]),
[iquote('para_from,19.1.1,3.1.1.1.1')] ).
cnf(61,plain,
inverse(add(inverse(A),inverse(add(A,A)))) = A,
inference(para_into,[status(thm),theory(equality)],[41,41]),
[iquote('para_into,41.1.1.1.2.1.2,41.1.1')] ).
cnf(72,plain,
inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,C)))) = C,
inference(para_from,[status(thm),theory(equality)],[41,3]),
[iquote('para_from,41.1.1,3.1.1.1.2.1.2')] ).
cnf(140,plain,
inverse(add(inverse(add(A,B)),inverse(add(inverse(A),B)))) = B,
inference(para_into,[status(thm),theory(equality)],[72,61]),
[iquote('para_into,71.1.1.1.1.1.1,61.1.1')] ).
cnf(143,plain,
inverse(add(A,inverse(add(inverse(add(B,C)),inverse(add(B,A)))))) = inverse(add(B,A)),
inference(para_into,[status(thm),theory(equality)],[72,72]),
[iquote('para_into,71.1.1.1.1,71.1.1')] ).
cnf(216,plain,
inverse(add(inverse(add(add(A,inverse(A)),A)),inverse(A))) = A,
inference(para_into,[status(thm),theory(equality)],[140,19]),
[iquote('para_into,139.1.1.1.2,19.1.1')] ).
cnf(231,plain,
inverse(add(inverse(add(inverse(add(inverse(add(A,inverse(add(A,B)))),C)),A)),inverse(add(A,B)))) = A,
inference(para_from,[status(thm),theory(equality)],[140,3]),
[iquote('para_from,139.1.1,3.1.1.1.2')] ).
cnf(238,plain,
inverse(add(A,inverse(add(B,inverse(add(inverse(B),A)))))) = inverse(add(inverse(B),A)),
inference(para_from,[status(thm),theory(equality)],[140,72]),
[iquote('para_from,139.1.1,71.1.1.1.1')] ).
cnf(243,plain,
inverse(add(inverse(add(A,B)),inverse(add(inverse(add(C,A)),B)))) = B,
inference(para_from,[status(thm),theory(equality)],[140,72]),
[iquote('para_from,139.1.1,71.1.1.1.1.1.1')] ).
cnf(265,plain,
inverse(add(A,inverse(add(add(inverse(add(add(A,inverse(A)),A)),inverse(A)),add(inverse(add(add(A,inverse(A)),A)),inverse(A)))))) = add(inverse(add(add(A,inverse(A)),A)),inverse(A)),
inference(para_from,[status(thm),theory(equality)],[216,61]),
[iquote('para_from,215.1.1,61.1.1.1.1')] ).
cnf(279,plain,
inverse(add(A,inverse(add(add(A,inverse(A)),inverse(A))))) = inverse(A),
inference(para_from,[status(thm),theory(equality)],[216,72]),
[iquote('para_from,215.1.1,71.1.1.1.1')] ).
cnf(436,plain,
inverse(add(inverse(A),inverse(A))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[279,41]),238]),
[iquote('para_from,279.1.1,41.1.1.1.2.1.2.1.2,demod,238')] ).
cnf(438,plain,
inverse(add(inverse(add(inverse(A),B)),inverse(add(A,B)))) = B,
inference(para_from,[status(thm),theory(equality)],[279,72]),
[iquote('para_from,279.1.1,71.1.1.1.1.1.1')] ).
cnf(442,plain,
inverse(add(A,A)) = add(inverse(A),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[436,436]),436]),
[iquote('para_into,435.1.1.1.1,435.1.1,demod,436')] ).
cnf(446,plain,
add(inverse(add(add(A,inverse(A)),A)),inverse(A)) = add(inverse(A),inverse(A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[436,216]),216,442])]),
[iquote('para_into,435.1.1.1.1,215.1.1,demod,216,442,flip.1')] ).
cnf(448,plain,
add(inverse(add(A,B)),inverse(add(inverse(A),B))) = add(inverse(B),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[436,140]),140,442])]),
[iquote('para_into,435.1.1.1.1,139.1.1,demod,140,442,flip.1')] ).
cnf(449,plain,
add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,C))) = add(inverse(C),inverse(C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[436,72]),72,442])]),
[iquote('para_into,435.1.1.1.1,71.1.1,demod,72,442,flip.1')] ).
cnf(456,plain,
add(inverse(inverse(A)),inverse(inverse(A))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[436]),442]),
[iquote('back_demod,435,demod,442')] ).
cnf(459,plain,
inverse(add(A,add(A,A))) = add(inverse(A),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[265]),446,446,442,442,456,442,456,446]),
[iquote('back_demod,265,demod,446,446,442,442,456,442,456,446')] ).
cnf(476,plain,
inverse(add(inverse(inverse(A)),A)) = inverse(A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[459,456]),456]),
[iquote('para_into,459.1.1.1.2,455.1.1,demod,456')] ).
cnf(481,plain,
add(inverse(inverse(A)),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[476,456]),476,456])]),
[iquote('para_from,475.1.1,455.1.1.2.1,demod,476,456,flip.1')] ).
cnf(497,plain,
inverse(add(inverse(add(inverse(inverse(inverse(A))),A)),inverse(A))) = A,
inference(para_into,[status(thm),theory(equality)],[438,481]),
[iquote('para_into,437.1.1.1.2.1,481.1.1')] ).
cnf(505,plain,
inverse(add(inverse(add(inverse(A),A)),add(inverse(A),inverse(A)))) = A,
inference(para_into,[status(thm),theory(equality)],[438,442]),
[iquote('para_into,437.1.1.1.2,441.1.1')] ).
cnf(507,plain,
add(inverse(add(inverse(A),B)),inverse(add(A,B))) = add(inverse(B),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[438,456]),438])]),
[iquote('para_from,437.1.1,455.1.1.2.1,demod,438,flip.1')] ).
cnf(517,plain,
inverse(add(inverse(add(inverse(add(A,B)),inverse(inverse(A)))),inverse(A))) = inverse(inverse(A)),
inference(para_from,[status(thm),theory(equality)],[497,13]),
[iquote('para_from,497.1.1,13.1.1.1.1.1.1.1.1')] ).
cnf(522,plain,
inverse(add(inverse(add(inverse(inverse(A)),inverse(A))),A)) = inverse(A),
inference(para_into,[status(thm),theory(equality)],[505,456]),
[iquote('para_into,505.1.1.1.2,455.1.1')] ).
cnf(525,plain,
inverse(add(inverse(add(inverse(add(inverse(A),B)),inverse(A))),A)) = inverse(A),
inference(para_from,[status(thm),theory(equality)],[522,13]),
[iquote('para_from,521.1.1,13.1.1.1.1.1.1.1.1')] ).
cnf(527,plain,
add(inverse(add(inverse(inverse(A)),inverse(A))),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[522,456]),522,456])]),
[iquote('para_from,521.1.1,455.1.1.2.1,demod,522,456,flip.1')] ).
cnf(537,plain,
inverse(add(inverse(add(A,B)),inverse(add(add(inverse(A),inverse(A)),B)))) = B,
inference(para_into,[status(thm),theory(equality)],[243,442]),
[iquote('para_into,243.1.1.1.2.1.1,441.1.1')] ).
cnf(540,plain,
inverse(add(inverse(add(inverse(A),A)),inverse(A))) = A,
inference(para_into,[status(thm),theory(equality)],[243,527]),
[iquote('para_into,243.1.1.1.2.1,527.1.1')] ).
cnf(541,plain,
add(inverse(add(inverse(A),A)),inverse(A)) = add(inverse(A),inverse(A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[540,456]),540])]),
[iquote('para_from,539.1.1,455.1.1.2.1,demod,540,flip.1')] ).
cnf(544,plain,
add(inverse(A),inverse(A)) = inverse(A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[525,541]),442,456,442]),
[iquote('para_into,525.1.1.1.1.1,541.1.1,demod,442,456,442')] ).
cnf(548,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[537]),544,448,544]),
[iquote('back_demod,537,demod,544,448,544')] ).
cnf(559,plain,
add(inverse(add(inverse(A),B)),inverse(add(A,B))) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[507]),544]),
[iquote('back_demod,507,demod,544')] ).
cnf(568,plain,
add(A,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[456]),548,548]),
[iquote('back_demod,455,demod,548,548')] ).
cnf(570,plain,
add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,C))) = inverse(C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[449]),568]),
[iquote('back_demod,449,demod,568')] ).
cnf(575,plain,
inverse(add(inverse(add(inverse(add(A,B)),A)),inverse(A))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[517]),548,548]),
[iquote('back_demod,517,demod,548,548')] ).
cnf(595,plain,
add(inverse(add(inverse(add(A,B)),A)),inverse(A)) = inverse(A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[575,548])]),
[iquote('para_from,575.1.1,547.1.1.1,flip.1')] ).
cnf(601,plain,
add(A,add(B,A)) = add(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[570,595]),548,548,548]),
[iquote('para_from,569.1.1,595.1.1.1.1,demod,548,548,548')] ).
cnf(611,plain,
add(inverse(add(A,B)),inverse(B)) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[601,570]),570]),
[iquote('para_into,601.1.1.2,569.1.1,demod,570')] ).
cnf(615,plain,
add(inverse(add(A,inverse(B))),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[611,548]),548]),
[iquote('para_into,611.1.1.2,547.1.1,demod,548')] ).
cnf(619,plain,
add(A,inverse(add(B,inverse(A)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[611,570]),548,548]),
[iquote('para_from,611.1.1,569.1.1.1.1,demod,548,548')] ).
cnf(623,plain,
add(inverse(A),inverse(add(B,A))) = inverse(A),
inference(para_from,[status(thm),theory(equality)],[615,570]),
[iquote('para_from,615.1.1,569.1.1.1.1')] ).
cnf(633,plain,
add(A,inverse(add(A,inverse(add(B,A))))) = add(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[619,559]),548,548,548,548]),
[iquote('para_from,619.1.1,559.1.1.1.1,demod,548,548,548,548')] ).
cnf(660,plain,
add(add(A,B),A) = add(A,B),
inference(para_from,[status(thm),theory(equality)],[231,619]),
[iquote('para_from,231.1.1,619.1.1.2')] ).
cnf(663,plain,
add(A,inverse(add(inverse(A),B))) = A,
inference(para_from,[status(thm),theory(equality)],[660,619]),
[iquote('para_from,659.1.1,619.1.1.2.1')] ).
cnf(666,plain,
add(A,inverse(add(A,inverse(add(A,B))))) = add(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[660,633]),660]),
[iquote('para_from,659.1.1,633.1.1.2.1.2.1,demod,660')] ).
cnf(668,plain,
add(inverse(A),inverse(add(A,B))) = inverse(A),
inference(para_from,[status(thm),theory(equality)],[660,623]),
[iquote('para_from,659.1.1,623.1.1.2.1')] ).
cnf(675,plain,
inverse(add(A,B)) = inverse(add(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[663,143]),668,548]),
[iquote('para_from,663.1.1,143.1.1.1.2.1.1.1,demod,668,548')] ).
cnf(680,plain,
add(A,B) = add(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[675,633]),666]),
[iquote('para_from,675.1.1,633.1.1.2.1.2,demod,666')] ).
cnf(681,plain,
$false,
inference(binary,[status(thm)],[680,1]),
[iquote('binary,680.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO072-1 : TPTP v8.1.0. Released v2.6.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 02:46:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.98/2.16 ----- Otter 3.3f, August 2004 -----
% 1.98/2.16 The process was started by sandbox2 on n027.cluster.edu,
% 1.98/2.16 Wed Jul 27 02:46:06 2022
% 1.98/2.16 The command was "./otter". The process ID is 21316.
% 1.98/2.16
% 1.98/2.16 set(prolog_style_variables).
% 1.98/2.16 set(auto).
% 1.98/2.16 dependent: set(auto1).
% 1.98/2.16 dependent: set(process_input).
% 1.98/2.16 dependent: clear(print_kept).
% 1.98/2.16 dependent: clear(print_new_demod).
% 1.98/2.16 dependent: clear(print_back_demod).
% 1.98/2.16 dependent: clear(print_back_sub).
% 1.98/2.16 dependent: set(control_memory).
% 1.98/2.16 dependent: assign(max_mem, 12000).
% 1.98/2.16 dependent: assign(pick_given_ratio, 4).
% 1.98/2.16 dependent: assign(stats_level, 1).
% 1.98/2.16 dependent: assign(max_seconds, 10800).
% 1.98/2.16 clear(print_given).
% 1.98/2.16
% 1.98/2.16 list(usable).
% 1.98/2.16 0 [] A=A.
% 1.98/2.16 0 [] inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,D))))))))=C.
% 1.98/2.16 0 [] add(b,a)!=add(a,b).
% 1.98/2.16 end_of_list.
% 1.98/2.16
% 1.98/2.16 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.98/2.16
% 1.98/2.16 All clauses are units, and equality is present; the
% 1.98/2.16 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.98/2.16
% 1.98/2.16 dependent: set(knuth_bendix).
% 1.98/2.16 dependent: set(anl_eq).
% 1.98/2.16 dependent: set(para_from).
% 1.98/2.16 dependent: set(para_into).
% 1.98/2.16 dependent: clear(para_from_right).
% 1.98/2.16 dependent: clear(para_into_right).
% 1.98/2.16 dependent: set(para_from_vars).
% 1.98/2.16 dependent: set(eq_units_both_ways).
% 1.98/2.16 dependent: set(dynamic_demod_all).
% 1.98/2.16 dependent: set(dynamic_demod).
% 1.98/2.16 dependent: set(order_eq).
% 1.98/2.16 dependent: set(back_demod).
% 1.98/2.16 dependent: set(lrpo).
% 1.98/2.16
% 1.98/2.16 ------------> process usable:
% 1.98/2.16 ** KEPT (pick-wt=7): 1 [] add(b,a)!=add(a,b).
% 1.98/2.16
% 1.98/2.16 ------------> process sos:
% 1.98/2.16 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.98/2.16 ** KEPT (pick-wt=22): 3 [] inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,D))))))))=C.
% 1.98/2.16 ---> New Demodulator: 4 [new_demod,3] inverse(add(inverse(add(inverse(add(A,B)),C)),inverse(add(A,inverse(add(inverse(C),inverse(add(C,D))))))))=C.
% 1.98/2.16 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.98/2.16 >>>> Starting back demodulation with 4.
% 1.98/2.16
% 1.98/2.16 ======= end of input processing =======
% 1.98/2.16
% 1.98/2.16 =========== start of search ===========
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Resetting weight limit to 18.
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Resetting weight limit to 18.
% 1.98/2.16
% 1.98/2.16 sos_size=188
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Resetting weight limit to 16.
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Resetting weight limit to 16.
% 1.98/2.16
% 1.98/2.16 sos_size=133
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Resetting weight limit to 13.
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Resetting weight limit to 13.
% 1.98/2.16
% 1.98/2.16 sos_size=56
% 1.98/2.16
% 1.98/2.16 -------- PROOF --------
% 1.98/2.16
% 1.98/2.16 ----> UNIT CONFLICT at 0.37 sec ----> 681 [binary,680.1,1.1] $F.
% 1.98/2.16
% 1.98/2.16 Length of proof is 52. Level of proof is 25.
% 1.98/2.16
% 1.98/2.16 ---------------- PROOF ----------------
% 1.98/2.16 % SZS status Unsatisfiable
% 1.98/2.16 % SZS output start Refutation
% See solution above
% 1.98/2.16 ------------ end of proof -------------
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Search stopped by max_proofs option.
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Search stopped by max_proofs option.
% 1.98/2.16
% 1.98/2.16 ============ end of search ============
% 1.98/2.16
% 1.98/2.16 -------------- statistics -------------
% 1.98/2.16 clauses given 100
% 1.98/2.16 clauses generated 9728
% 1.98/2.16 clauses kept 344
% 1.98/2.16 clauses forward subsumed 2455
% 1.98/2.16 clauses back subsumed 4
% 1.98/2.16 Kbytes malloced 5859
% 1.98/2.16
% 1.98/2.16 ----------- times (seconds) -----------
% 1.98/2.16 user CPU time 0.37 (0 hr, 0 min, 0 sec)
% 1.98/2.16 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.98/2.16 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.16
% 1.98/2.16 That finishes the proof of the theorem.
% 1.98/2.16
% 1.98/2.16 Process 21316 finished Wed Jul 27 02:46:08 2022
% 1.98/2.16 Otter interrupted
% 1.98/2.16 PROOF FOUND
%------------------------------------------------------------------------------