TSTP Solution File: BOO013-4 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% 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 12:47:34 EDT 2022
% Result : Unsatisfiable 1.73s 1.93s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 10 RR)
% Number of literals : 21 ( 20 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
b != inverse(a),
file('BOO013-4.p',unknown),
[] ).
cnf(2,plain,
inverse(a) != b,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
add(A,B) = add(B,A),
file('BOO013-4.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = multiply(B,A),
file('BOO013-4.p',unknown),
[] ).
cnf(9,axiom,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
file('BOO013-4.p',unknown),
[] ).
cnf(12,axiom,
add(A,additive_identity) = A,
file('BOO013-4.p',unknown),
[] ).
cnf(14,axiom,
multiply(A,multiplicative_identity) = A,
file('BOO013-4.p',unknown),
[] ).
cnf(15,axiom,
add(A,inverse(A)) = multiplicative_identity,
file('BOO013-4.p',unknown),
[] ).
cnf(17,axiom,
multiply(A,inverse(A)) = additive_identity,
file('BOO013-4.p',unknown),
[] ).
cnf(19,axiom,
add(a,b) = multiplicative_identity,
file('BOO013-4.p',unknown),
[] ).
cnf(21,axiom,
multiply(a,b) = additive_identity,
file('BOO013-4.p',unknown),
[] ).
cnf(25,plain,
add(b,a) = multiplicative_identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,19])]),
[iquote('para_into,4.1.1,19.1.1,flip.1')] ).
cnf(28,plain,
add(additive_identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,12])]),
[iquote('para_into,4.1.1,11.1.1,flip.1')] ).
cnf(33,plain,
multiply(b,a) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,21])]),
[iquote('para_into,5.1.1,21.1.1,flip.1')] ).
cnf(39,plain,
multiply(inverse(A),A) = additive_identity,
inference(para_into,[status(thm),theory(equality)],[17,5]),
[iquote('para_into,17.1.1,5.1.1')] ).
cnf(43,plain,
add(multiply(A,b),multiply(A,a)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,25]),14])]),
[iquote('para_into,9.1.1.2,25.1.1,demod,14,flip.1')] ).
cnf(47,plain,
add(multiply(A,B),multiply(A,inverse(B))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,15]),14])]),
[iquote('para_into,9.1.1.2,15.1.1,demod,14,flip.1')] ).
cnf(63,plain,
multiply(inverse(a),b) = inverse(a),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[43,39]),12]),
[iquote('para_into,43.1.1.2,39.1.1,demod,12')] ).
cnf(112,plain,
multiply(b,inverse(a)) = inverse(a),
inference(para_into,[status(thm),theory(equality)],[63,5]),
[iquote('para_into,63.1.1,5.1.1')] ).
cnf(199,plain,
inverse(a) = b,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[47,33]),112,28]),
[iquote('para_into,47.1.1.1,33.1.1,demod,112,28')] ).
cnf(201,plain,
$false,
inference(binary,[status(thm)],[199,2]),
[iquote('binary,199.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : BOO013-4 : TPTP v8.1.0. Released v1.1.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 02:45:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.73/1.93 ----- Otter 3.3f, August 2004 -----
% 1.73/1.93 The process was started by sandbox on n027.cluster.edu,
% 1.73/1.93 Wed Jul 27 02:45:51 2022
% 1.73/1.93 The command was "./otter". The process ID is 19383.
% 1.73/1.93
% 1.73/1.93 set(prolog_style_variables).
% 1.73/1.93 set(auto).
% 1.73/1.93 dependent: set(auto1).
% 1.73/1.93 dependent: set(process_input).
% 1.73/1.93 dependent: clear(print_kept).
% 1.73/1.93 dependent: clear(print_new_demod).
% 1.73/1.93 dependent: clear(print_back_demod).
% 1.73/1.93 dependent: clear(print_back_sub).
% 1.73/1.93 dependent: set(control_memory).
% 1.73/1.93 dependent: assign(max_mem, 12000).
% 1.73/1.93 dependent: assign(pick_given_ratio, 4).
% 1.73/1.93 dependent: assign(stats_level, 1).
% 1.73/1.93 dependent: assign(max_seconds, 10800).
% 1.73/1.93 clear(print_given).
% 1.73/1.93
% 1.73/1.93 list(usable).
% 1.73/1.93 0 [] A=A.
% 1.73/1.93 0 [] add(X,Y)=add(Y,X).
% 1.73/1.93 0 [] multiply(X,Y)=multiply(Y,X).
% 1.73/1.93 0 [] add(X,multiply(Y,Z))=multiply(add(X,Y),add(X,Z)).
% 1.73/1.93 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.73/1.93 0 [] add(X,additive_identity)=X.
% 1.73/1.93 0 [] multiply(X,multiplicative_identity)=X.
% 1.73/1.93 0 [] add(X,inverse(X))=multiplicative_identity.
% 1.73/1.93 0 [] multiply(X,inverse(X))=additive_identity.
% 1.73/1.93 0 [] add(a,b)=multiplicative_identity.
% 1.73/1.93 0 [] multiply(a,b)=additive_identity.
% 1.73/1.93 0 [] b!=inverse(a).
% 1.73/1.93 end_of_list.
% 1.73/1.93
% 1.73/1.93 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.73/1.93
% 1.73/1.93 All clauses are units, and equality is present; the
% 1.73/1.93 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.73/1.93
% 1.73/1.93 dependent: set(knuth_bendix).
% 1.73/1.93 dependent: set(anl_eq).
% 1.73/1.93 dependent: set(para_from).
% 1.73/1.93 dependent: set(para_into).
% 1.73/1.93 dependent: clear(para_from_right).
% 1.73/1.93 dependent: clear(para_into_right).
% 1.73/1.93 dependent: set(para_from_vars).
% 1.73/1.93 dependent: set(eq_units_both_ways).
% 1.73/1.93 dependent: set(dynamic_demod_all).
% 1.73/1.93 dependent: set(dynamic_demod).
% 1.73/1.93 dependent: set(order_eq).
% 1.73/1.93 dependent: set(back_demod).
% 1.73/1.93 dependent: set(lrpo).
% 1.73/1.93
% 1.73/1.93 ------------> process usable:
% 1.73/1.93 ** KEPT (pick-wt=4): 2 [copy,1,flip.1] inverse(a)!=b.
% 1.73/1.93
% 1.73/1.93 ------------> process sos:
% 1.73/1.93 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.73/1.93 ** KEPT (pick-wt=7): 4 [] add(A,B)=add(B,A).
% 1.73/1.93 ** KEPT (pick-wt=7): 5 [] multiply(A,B)=multiply(B,A).
% 1.73/1.93 ** KEPT (pick-wt=13): 7 [copy,6,flip.1] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.73/1.93 ---> New Demodulator: 8 [new_demod,7] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.73/1.93 ** KEPT (pick-wt=13): 9 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.73/1.93 ---> New Demodulator: 10 [new_demod,9] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.73/1.93 ** KEPT (pick-wt=5): 11 [] add(A,additive_identity)=A.
% 1.73/1.93 ---> New Demodulator: 12 [new_demod,11] add(A,additive_identity)=A.
% 1.73/1.93 ** KEPT (pick-wt=5): 13 [] multiply(A,multiplicative_identity)=A.
% 1.73/1.93 ---> New Demodulator: 14 [new_demod,13] multiply(A,multiplicative_identity)=A.
% 1.73/1.93 ** KEPT (pick-wt=6): 15 [] add(A,inverse(A))=multiplicative_identity.
% 1.73/1.93 ---> New Demodulator: 16 [new_demod,15] add(A,inverse(A))=multiplicative_identity.
% 1.73/1.93 ** KEPT (pick-wt=6): 17 [] multiply(A,inverse(A))=additive_identity.
% 1.73/1.93 ---> New Demodulator: 18 [new_demod,17] multiply(A,inverse(A))=additive_identity.
% 1.73/1.93 ** KEPT (pick-wt=5): 19 [] add(a,b)=multiplicative_identity.
% 1.73/1.93 ---> New Demodulator: 20 [new_demod,19] add(a,b)=multiplicative_identity.
% 1.73/1.93 ** KEPT (pick-wt=5): 21 [] multiply(a,b)=additive_identity.
% 1.73/1.93 ---> New Demodulator: 22 [new_demod,21] multiply(a,b)=additive_identity.
% 1.73/1.93 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.73/1.93 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] add(A,B)=add(B,A).
% 1.73/1.93 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] multiply(A,B)=multiply(B,A).
% 1.73/1.93 >>>> Starting back demodulation with 8.
% 1.73/1.93 >>>> Starting back demodulation with 10.
% 1.73/1.93 >> back demodulating 7 with 10.
% 1.73/1.93 >>>> Starting back demodulation with 12.
% 1.73/1.93 >>>> Starting back demodulation with 14.
% 1.73/1.93 >>>> Starting back demodulation with 16.
% 1.73/1.93 >>>> Starting back demodulation with 18.
% 1.73/1.93 >>>> Starting back demodulation with 20.
% 1.73/1.93 >>>> Starting back demodulation with 22.
% 1.73/1.93 >>>> Starting back demodulation with 24.
% 1.73/1.93
% 1.73/1.93 ======= end of input processing =======
% 1.73/1.93
% 1.73/1.93 =========== start of search ===========
% 1.73/1.93
% 1.73/1.93 -------- PROOF --------
% 1.73/1.93
% 1.73/1.93 ----> UNIT CONFLICT at 0.00 sec ----> 201 [binary,199.1,2.1] $F.
% 1.73/1.93
% 1.73/1.93 Length of proof is 10. Level of proof is 5.
% 1.73/1.93
% 1.73/1.93 ---------------- PROOF ----------------
% 1.73/1.93 % SZS status Unsatisfiable
% 1.73/1.93 % SZS output start Refutation
% See solution above
% 1.73/1.93 ------------ end of proof -------------
% 1.73/1.93
% 1.73/1.93
% 1.73/1.93 Search stopped by max_proofs option.
% 1.73/1.93
% 1.73/1.93
% 1.73/1.93 Search stopped by max_proofs option.
% 1.73/1.93
% 1.73/1.93 ============ end of search ============
% 1.73/1.93
% 1.73/1.93 -------------- statistics -------------
% 1.73/1.93 clauses given 36
% 1.73/1.93 clauses generated 328
% 1.73/1.93 clauses kept 105
% 1.73/1.93 clauses forward subsumed 278
% 1.73/1.93 clauses back subsumed 0
% 1.73/1.93 Kbytes malloced 1953
% 1.73/1.93
% 1.73/1.93 ----------- times (seconds) -----------
% 1.73/1.93 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.93 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.73/1.93
% 1.73/1.93 That finishes the proof of the theorem.
% 1.73/1.93
% 1.73/1.93 Process 19383 finished Wed Jul 27 02:45:53 2022
% 1.73/1.93 Otter interrupted
% 1.73/1.93 PROOF FOUND
%------------------------------------------------------------------------------