TSTP Solution File: BOO029-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO029-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 12:47:38 EDT 2022
% Result : Unsatisfiable 1.64s 1.88s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 3 RR)
% Number of literals : 34 ( 33 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 : 72 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
add(b,inverse(b)) != add(a,inverse(a)),
file('BOO029-1.p',unknown),
[] ).
cnf(3,axiom,
add(A,multiply(B,multiply(A,C))) = A,
file('BOO029-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(add(A,B),add(A,inverse(B))) = A,
file('BOO029-1.p',unknown),
[] ).
cnf(9,axiom,
multiply(A,add(B,add(A,C))) = A,
file('BOO029-1.p',unknown),
[] ).
cnf(13,axiom,
add(multiply(A,B),multiply(A,inverse(B))) = A,
file('BOO029-1.p',unknown),
[] ).
cnf(15,axiom,
add(A,B) = add(B,A),
file('BOO029-1.p',unknown),
[] ).
cnf(16,axiom,
multiply(A,B) = multiply(B,A),
file('BOO029-1.p',unknown),
[] ).
cnf(18,axiom,
add(add(A,B),C) = add(A,add(B,C)),
file('BOO029-1.p',unknown),
[] ).
cnf(19,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('BOO029-1.p',unknown),
[] ).
cnf(26,plain,
add(A,multiply(B,multiply(C,A))) = A,
inference(para_into,[status(thm),theory(equality)],[3,16]),
[iquote('para_into,3.1.1.2.2,16.1.1')] ).
cnf(40,plain,
add(A,multiply(B,A)) = A,
inference(para_from,[status(thm),theory(equality)],[9,3]),
[iquote('para_from,9.1.1,3.1.1.2.2')] ).
cnf(46,plain,
multiply(add(A,B),add(inverse(B),A)) = A,
inference(para_into,[status(thm),theory(equality)],[7,15]),
[iquote('para_into,7.1.1.2,15.1.1')] ).
cnf(50,plain,
add(A,add(B,multiply(C,A))) = add(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[7,3]),18]),
[iquote('para_from,7.1.1,3.1.1.2.2,demod,18')] ).
cnf(60,plain,
add(A,multiply(A,B)) = A,
inference(para_into,[status(thm),theory(equality)],[40,16]),
[iquote('para_into,40.1.1.2,16.1.1')] ).
cnf(78,plain,
add(multiply(A,B),multiply(B,inverse(A))) = B,
inference(para_into,[status(thm),theory(equality)],[13,16]),
[iquote('para_into,13.1.1.1,16.1.1')] ).
cnf(84,plain,
add(multiply(A,B),multiply(inverse(B),A)) = A,
inference(para_into,[status(thm),theory(equality)],[13,16]),
[iquote('para_into,13.1.1.2,16.1.1')] ).
cnf(86,plain,
add(multiply(A,inverse(B)),multiply(A,B)) = A,
inference(para_into,[status(thm),theory(equality)],[13,15]),
[iquote('para_into,13.1.1,15.1.1')] ).
cnf(104,plain,
add(multiply(A,B),A) = A,
inference(para_into,[status(thm),theory(equality)],[60,15]),
[iquote('para_into,60.1.1,15.1.1')] ).
cnf(159,plain,
add(multiply(A,multiply(B,C)),C) = C,
inference(para_into,[status(thm),theory(equality)],[26,15]),
[iquote('para_into,26.1.1,15.1.1')] ).
cnf(290,plain,
multiply(A,add(inverse(A),multiply(A,B))) = multiply(A,B),
inference(para_into,[status(thm),theory(equality)],[46,104]),
[iquote('para_into,46.1.1.1,104.1.1')] ).
cnf(314,plain,
add(multiply(A,multiply(B,multiply(C,D))),D) = D,
inference(para_into,[status(thm),theory(equality)],[159,19]),
[iquote('para_into,159.1.1.1.2,19.1.1')] ).
cnf(406,plain,
add(multiply(inverse(A),B),multiply(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[84,15]),
[iquote('para_into,84.1.1,15.1.1')] ).
cnf(426,plain,
add(inverse(A),multiply(A,B)) = add(inverse(A),B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[50,78])]),
[iquote('para_into,50.1.1.2,78.1.1,flip.1')] ).
cnf(434,plain,
multiply(A,add(inverse(A),B)) = multiply(A,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[290]),426]),
[iquote('back_demod,290,demod,426')] ).
cnf(482,plain,
add(A,multiply(B,inverse(A))) = add(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[86,50])]),
[iquote('para_from,86.1.1,50.1.1.2,flip.1')] ).
cnf(700,plain,
add(A,multiply(inverse(A),B)) = add(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[406,50])]),
[iquote('para_from,406.1.1,50.1.1.2,flip.1')] ).
cnf(718,plain,
multiply(A,multiply(inverse(A),B)) = multiply(A,inverse(A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[434,60])]),
[iquote('para_into,434.1.1.2,60.1.1,flip.1')] ).
cnf(1035,plain,
add(multiply(A,inverse(A)),B) = B,
inference(para_from,[status(thm),theory(equality)],[718,314]),
[iquote('para_from,718.1.1,314.1.1.1')] ).
cnf(1044,plain,
multiply(inverse(multiply(A,inverse(A))),B) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1035,700]),1035])]),
[iquote('para_into,1034.1.1,700.1.1,demod,1035,flip.1')] ).
cnf(1047,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1035,482]),1035])]),
[iquote('para_into,1034.1.1,482.1.1,demod,1035,flip.1')] ).
cnf(1096,plain,
add(A,inverse(A)) = inverse(multiply(B,inverse(B))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1044,78]),1047]),
[iquote('para_from,1044.1.1,78.1.1.2,demod,1047')] ).
cnf(1098,plain,
inverse(multiply(A,inverse(A))) = add(B,inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1096])]),
[iquote('copy,1096,flip.1')] ).
cnf(1138,plain,
inverse(multiply(A,inverse(A))) != add(a,inverse(a)),
inference(para_from,[status(thm),theory(equality)],[1096,1]),
[iquote('para_from,1096.1.1,1.1.1')] ).
cnf(1139,plain,
$false,
inference(binary,[status(thm)],[1138,1098]),
[iquote('binary,1138.1,1098.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO029-1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 02:37:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.60/1.81 ----- Otter 3.3f, August 2004 -----
% 1.60/1.81 The process was started by sandbox on n018.cluster.edu,
% 1.60/1.81 Wed Jul 27 02:37:31 2022
% 1.60/1.81 The command was "./otter". The process ID is 31263.
% 1.60/1.81
% 1.60/1.81 set(prolog_style_variables).
% 1.60/1.81 set(auto).
% 1.60/1.81 dependent: set(auto1).
% 1.60/1.81 dependent: set(process_input).
% 1.60/1.81 dependent: clear(print_kept).
% 1.60/1.81 dependent: clear(print_new_demod).
% 1.60/1.81 dependent: clear(print_back_demod).
% 1.60/1.81 dependent: clear(print_back_sub).
% 1.60/1.81 dependent: set(control_memory).
% 1.60/1.81 dependent: assign(max_mem, 12000).
% 1.60/1.81 dependent: assign(pick_given_ratio, 4).
% 1.60/1.81 dependent: assign(stats_level, 1).
% 1.60/1.81 dependent: assign(max_seconds, 10800).
% 1.60/1.81 clear(print_given).
% 1.60/1.81
% 1.60/1.81 list(usable).
% 1.60/1.81 0 [] A=A.
% 1.60/1.81 0 [] add(X,multiply(Y,multiply(X,Z)))=X.
% 1.60/1.81 0 [] add(add(multiply(X,Y),multiply(Y,Z)),Y)=Y.
% 1.60/1.81 0 [] multiply(add(X,Y),add(X,inverse(Y)))=X.
% 1.60/1.81 0 [] multiply(X,add(Y,add(X,Z)))=X.
% 1.60/1.81 0 [] multiply(multiply(add(X,Y),add(Y,Z)),Y)=Y.
% 1.60/1.81 0 [] add(multiply(X,Y),multiply(X,inverse(Y)))=X.
% 1.60/1.81 0 [] add(X,Y)=add(Y,X).
% 1.60/1.81 0 [] multiply(X,Y)=multiply(Y,X).
% 1.60/1.81 0 [] add(add(X,Y),Z)=add(X,add(Y,Z)).
% 1.60/1.81 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.60/1.82 0 [] add(b,inverse(b))!=add(a,inverse(a)).
% 1.60/1.82 end_of_list.
% 1.60/1.82
% 1.60/1.82 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.60/1.82
% 1.60/1.82 All clauses are units, and equality is present; the
% 1.60/1.82 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.60/1.82
% 1.60/1.82 dependent: set(knuth_bendix).
% 1.60/1.82 dependent: set(anl_eq).
% 1.60/1.82 dependent: set(para_from).
% 1.60/1.82 dependent: set(para_into).
% 1.60/1.82 dependent: clear(para_from_right).
% 1.60/1.82 dependent: clear(para_into_right).
% 1.60/1.82 dependent: set(para_from_vars).
% 1.60/1.82 dependent: set(eq_units_both_ways).
% 1.60/1.82 dependent: set(dynamic_demod_all).
% 1.60/1.82 dependent: set(dynamic_demod).
% 1.60/1.82 dependent: set(order_eq).
% 1.60/1.82 dependent: set(back_demod).
% 1.60/1.82 dependent: set(lrpo).
% 1.60/1.82
% 1.60/1.82 ------------> process usable:
% 1.60/1.82 ** KEPT (pick-wt=9): 1 [] add(b,inverse(b))!=add(a,inverse(a)).
% 1.60/1.82
% 1.60/1.82 ------------> process sos:
% 1.60/1.82 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.60/1.82 ** KEPT (pick-wt=9): 3 [] add(A,multiply(B,multiply(A,C)))=A.
% 1.60/1.82 ---> New Demodulator: 4 [new_demod,3] add(A,multiply(B,multiply(A,C)))=A.
% 1.60/1.82 ** KEPT (pick-wt=11): 5 [] add(add(multiply(A,B),multiply(B,C)),B)=B.
% 1.60/1.82 ---> New Demodulator: 6 [new_demod,5] add(add(multiply(A,B),multiply(B,C)),B)=B.
% 1.60/1.82 ** KEPT (pick-wt=10): 7 [] multiply(add(A,B),add(A,inverse(B)))=A.
% 1.60/1.82 ---> New Demodulator: 8 [new_demod,7] multiply(add(A,B),add(A,inverse(B)))=A.
% 1.60/1.82 ** KEPT (pick-wt=9): 9 [] multiply(A,add(B,add(A,C)))=A.
% 1.60/1.82 ---> New Demodulator: 10 [new_demod,9] multiply(A,add(B,add(A,C)))=A.
% 1.60/1.82 ** KEPT (pick-wt=11): 11 [] multiply(multiply(add(A,B),add(B,C)),B)=B.
% 1.60/1.82 ---> New Demodulator: 12 [new_demod,11] multiply(multiply(add(A,B),add(B,C)),B)=B.
% 1.60/1.82 ** KEPT (pick-wt=10): 13 [] add(multiply(A,B),multiply(A,inverse(B)))=A.
% 1.60/1.82 ---> New Demodulator: 14 [new_demod,13] add(multiply(A,B),multiply(A,inverse(B)))=A.
% 1.60/1.82 ** KEPT (pick-wt=7): 15 [] add(A,B)=add(B,A).
% 1.60/1.82 ** KEPT (pick-wt=7): 16 [] multiply(A,B)=multiply(B,A).
% 1.60/1.82 ** KEPT (pick-wt=11): 17 [] add(add(A,B),C)=add(A,add(B,C)).
% 1.60/1.82 ---> New Demodulator: 18 [new_demod,17] add(add(A,B),C)=add(A,add(B,C)).
% 1.60/1.82 ** KEPT (pick-wt=11): 19 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.60/1.82 ---> New Demodulator: 20 [new_demod,19] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.60/1.82 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.60/1.82 >>>> Starting back demodulation with 4.
% 1.60/1.82 >>>> Starting back demodulation with 6.
% 1.60/1.82 >>>> Starting back demodulation with 8.
% 1.60/1.82 >>>> Starting back demodulation with 10.
% 1.60/1.82 >>>> Starting back demodulation with 12.
% 1.60/1.82 >>>> Starting back demodulation with 14.
% 1.60/1.82 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] add(A,B)=add(B,A).
% 1.60/1.82 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] multiply(A,B)=multiply(B,A).
% 1.60/1.82 >>>> Starting back demodulation with 18.
% 1.60/1.82 >> back demodulating 5 with 18.
% 1.60/1.82 >>>> Starting back demodulation with 20.
% 1.60/1.82 >> back demodulating 11 with 20.
% 1.60/1.82 >>>> Starting back demodulation with 22.
% 1.60/1.82 >>>> Starting back demodulation with 24.
% 1.60/1.82
% 1.60/1.82 ======= end of input processing =======
% 1.60/1.82
% 1.60/1.82 =========== start of search ===========
% 1.60/1.82
% 1.60/1.82
% 1.60/1.82 Resetting weight limit to 11.
% 1.60/1.82
% 1.60/1.82
% 1.60/1.82 Resetting weight limit to 11.
% 1.60/1.82
% 1.60/1.82 sos_size=371
% 1.64/1.88
% 1.64/1.88 -------- PROOF --------
% 1.64/1.88
% 1.64/1.88 ----> UNIT CONFLICT at 0.10 sec ----> 1139 [binary,1138.1,1098.1] $F.
% 1.64/1.88
% 1.64/1.88 Length of proof is 24. Level of proof is 10.
% 1.64/1.88
% 1.64/1.88 ---------------- PROOF ----------------
% 1.64/1.88 % SZS status Unsatisfiable
% 1.64/1.88 % SZS output start Refutation
% See solution above
% 1.64/1.89 ------------ end of proof -------------
% 1.64/1.89
% 1.64/1.89
% 1.64/1.89 Search stopped by max_proofs option.
% 1.64/1.89
% 1.64/1.89
% 1.64/1.89 Search stopped by max_proofs option.
% 1.64/1.89
% 1.64/1.89 ============ end of search ============
% 1.64/1.89
% 1.64/1.89 -------------- statistics -------------
% 1.64/1.89 clauses given 124
% 1.64/1.89 clauses generated 11099
% 1.64/1.89 clauses kept 599
% 1.64/1.89 clauses forward subsumed 8008
% 1.64/1.89 clauses back subsumed 0
% 1.64/1.89 Kbytes malloced 4882
% 1.64/1.89
% 1.64/1.89 ----------- times (seconds) -----------
% 1.64/1.89 user CPU time 0.10 (0 hr, 0 min, 0 sec)
% 1.64/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.64/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.64/1.89
% 1.64/1.89 That finishes the proof of the theorem.
% 1.64/1.89
% 1.64/1.89 Process 31263 finished Wed Jul 27 02:37:32 2022
% 1.64/1.89 Otter interrupted
% 1.64/1.89 PROOF FOUND
%------------------------------------------------------------------------------