TSTP Solution File: BOO013-2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 1.58s 1.81s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 12 RR)
% Number of literals : 19 ( 18 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
b != c,
file('BOO013-2.p',unknown),
[] ).
cnf(2,plain,
c != 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('BOO013-2.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = multiply(B,A),
file('BOO013-2.p',unknown),
[] ).
cnf(12,axiom,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
file('BOO013-2.p',unknown),
[] ).
cnf(27,axiom,
multiply(multiplicative_identity,A) = A,
file('BOO013-2.p',unknown),
[] ).
cnf(29,axiom,
add(A,additive_identity) = A,
file('BOO013-2.p',unknown),
[] ).
cnf(32,axiom,
add(a,b) = multiplicative_identity,
file('BOO013-2.p',unknown),
[] ).
cnf(34,axiom,
add(a,c) = multiplicative_identity,
file('BOO013-2.p',unknown),
[] ).
cnf(36,axiom,
multiply(a,b) = additive_identity,
file('BOO013-2.p',unknown),
[] ).
cnf(39,axiom,
multiply(a,c) = additive_identity,
file('BOO013-2.p',unknown),
[] ).
cnf(44,plain,
add(b,a) = multiplicative_identity,
inference(para_into,[status(thm),theory(equality)],[32,4]),
[iquote('para_into,32.1.1,4.1.1')] ).
cnf(46,plain,
add(c,a) = multiplicative_identity,
inference(para_into,[status(thm),theory(equality)],[34,4]),
[iquote('para_into,34.1.1,4.1.1')] ).
cnf(52,plain,
add(multiply(c,A),multiply(a,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,46]),27])]),
[iquote('para_into,12.1.1.1,46.1.1,demod,27,flip.1')] ).
cnf(54,plain,
add(multiply(b,A),multiply(a,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,44]),27])]),
[iquote('para_into,12.1.1.1,44.1.1,demod,27,flip.1')] ).
cnf(106,plain,
multiply(c,b) = b,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[52,36]),29]),
[iquote('para_into,52.1.1.2,36.1.1,demod,29')] ).
cnf(198,plain,
multiply(b,c) = b,
inference(para_into,[status(thm),theory(equality)],[106,5]),
[iquote('para_into,106.1.1,5.1.1')] ).
cnf(364,plain,
c = b,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[54,198]),39,29])]),
[iquote('para_into,54.1.1.1,198.1.1,demod,39,29,flip.1')] ).
cnf(366,plain,
$false,
inference(binary,[status(thm)],[364,2]),
[iquote('binary,364.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO013-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n010.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 02:24:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.58/1.80 ----- Otter 3.3f, August 2004 -----
% 1.58/1.80 The process was started by sandbox on n010.cluster.edu,
% 1.58/1.80 Wed Jul 27 02:24:25 2022
% 1.58/1.80 The command was "./otter". The process ID is 14803.
% 1.58/1.80
% 1.58/1.80 set(prolog_style_variables).
% 1.58/1.80 set(auto).
% 1.58/1.80 dependent: set(auto1).
% 1.58/1.80 dependent: set(process_input).
% 1.58/1.80 dependent: clear(print_kept).
% 1.58/1.80 dependent: clear(print_new_demod).
% 1.58/1.80 dependent: clear(print_back_demod).
% 1.58/1.80 dependent: clear(print_back_sub).
% 1.58/1.80 dependent: set(control_memory).
% 1.58/1.80 dependent: assign(max_mem, 12000).
% 1.58/1.80 dependent: assign(pick_given_ratio, 4).
% 1.58/1.80 dependent: assign(stats_level, 1).
% 1.58/1.80 dependent: assign(max_seconds, 10800).
% 1.58/1.80 clear(print_given).
% 1.58/1.80
% 1.58/1.80 list(usable).
% 1.58/1.80 0 [] A=A.
% 1.58/1.80 0 [] add(X,Y)=add(Y,X).
% 1.58/1.80 0 [] multiply(X,Y)=multiply(Y,X).
% 1.58/1.80 0 [] add(multiply(X,Y),Z)=multiply(add(X,Z),add(Y,Z)).
% 1.58/1.80 0 [] add(X,multiply(Y,Z))=multiply(add(X,Y),add(X,Z)).
% 1.58/1.80 0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.58/1.80 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.58/1.80 0 [] add(X,inverse(X))=multiplicative_identity.
% 1.58/1.80 0 [] add(inverse(X),X)=multiplicative_identity.
% 1.58/1.80 0 [] multiply(X,inverse(X))=additive_identity.
% 1.58/1.80 0 [] multiply(inverse(X),X)=additive_identity.
% 1.58/1.80 0 [] multiply(X,multiplicative_identity)=X.
% 1.58/1.80 0 [] multiply(multiplicative_identity,X)=X.
% 1.58/1.80 0 [] add(X,additive_identity)=X.
% 1.58/1.80 0 [] add(additive_identity,X)=X.
% 1.58/1.80 0 [] add(a,b)=multiplicative_identity.
% 1.58/1.80 0 [] add(a,c)=multiplicative_identity.
% 1.58/1.80 0 [] multiply(a,b)=additive_identity.
% 1.58/1.80 0 [] multiply(a,c)=additive_identity.
% 1.58/1.80 0 [] b!=c.
% 1.58/1.80 end_of_list.
% 1.58/1.80
% 1.58/1.80 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.58/1.80
% 1.58/1.80 All clauses are units, and equality is present; the
% 1.58/1.80 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.58/1.80
% 1.58/1.80 dependent: set(knuth_bendix).
% 1.58/1.80 dependent: set(anl_eq).
% 1.58/1.80 dependent: set(para_from).
% 1.58/1.80 dependent: set(para_into).
% 1.58/1.80 dependent: clear(para_from_right).
% 1.58/1.80 dependent: clear(para_into_right).
% 1.58/1.80 dependent: set(para_from_vars).
% 1.58/1.80 dependent: set(eq_units_both_ways).
% 1.58/1.80 dependent: set(dynamic_demod_all).
% 1.58/1.80 dependent: set(dynamic_demod).
% 1.58/1.80 dependent: set(order_eq).
% 1.58/1.80 dependent: set(back_demod).
% 1.58/1.80 dependent: set(lrpo).
% 1.58/1.80
% 1.58/1.80 ------------> process usable:
% 1.58/1.80 ** KEPT (pick-wt=3): 2 [copy,1,flip.1] c!=b.
% 1.58/1.80
% 1.58/1.80 ------------> process sos:
% 1.58/1.80 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.58/1.80 ** KEPT (pick-wt=7): 4 [] add(A,B)=add(B,A).
% 1.58/1.80 ** KEPT (pick-wt=7): 5 [] multiply(A,B)=multiply(B,A).
% 1.58/1.80 ** KEPT (pick-wt=13): 7 [copy,6,flip.1] multiply(add(A,B),add(C,B))=add(multiply(A,C),B).
% 1.58/1.80 ---> New Demodulator: 8 [new_demod,7] multiply(add(A,B),add(C,B))=add(multiply(A,C),B).
% 1.58/1.80 ** KEPT (pick-wt=13): 10 [copy,9,flip.1] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.58/1.80 ---> New Demodulator: 11 [new_demod,10] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.58/1.80 ** KEPT (pick-wt=13): 12 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.58/1.80 ---> New Demodulator: 13 [new_demod,12] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.58/1.80 ** KEPT (pick-wt=13): 14 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.58/1.80 ---> New Demodulator: 15 [new_demod,14] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.58/1.80 ** KEPT (pick-wt=6): 16 [] add(A,inverse(A))=multiplicative_identity.
% 1.58/1.80 ---> New Demodulator: 17 [new_demod,16] add(A,inverse(A))=multiplicative_identity.
% 1.58/1.80 ** KEPT (pick-wt=6): 18 [] add(inverse(A),A)=multiplicative_identity.
% 1.58/1.80 ---> New Demodulator: 19 [new_demod,18] add(inverse(A),A)=multiplicative_identity.
% 1.58/1.80 ** KEPT (pick-wt=6): 20 [] multiply(A,inverse(A))=additive_identity.
% 1.58/1.80 ---> New Demodulator: 21 [new_demod,20] multiply(A,inverse(A))=additive_identity.
% 1.58/1.80 ** KEPT (pick-wt=6): 22 [] multiply(inverse(A),A)=additive_identity.
% 1.58/1.80 ---> New Demodulator: 23 [new_demod,22] multiply(inverse(A),A)=additive_identity.
% 1.58/1.80 ** KEPT (pick-wt=5): 24 [] multiply(A,multiplicative_identity)=A.
% 1.58/1.80 ---> New Demodulator: 25 [new_demod,24] multiply(A,multiplicative_identity)=A.
% 1.58/1.80 ** KEPT (pick-wt=5): 26 [] multiply(multiplicative_identity,A)=A.
% 1.58/1.80 ---> New Demodulator: 27 [new_demod,26] multiply(multiplicative_identity,A)=A.
% 1.58/1.80 ** KEPT (pick-wt=5): 28 [] add(A,additive_identity)=A.
% 1.58/1.80 ---> New Demodulator: 29 [new_demod,28] add(A,additive_identity)=A.
% 1.58/1.80 ** KEPT (pick-wt=5): 30 [] add(additive_identity,A)=A.
% 1.58/1.81 ---> New Demodulator: 31 [new_demod,30] add(additive_identity,A)=A.
% 1.58/1.81 ** KEPT (pick-wt=5): 32 [] add(a,b)=multiplicative_identity.
% 1.58/1.81 ---> New Demodulator: 33 [new_demod,32] add(a,b)=multiplicative_identity.
% 1.58/1.81 ** KEPT (pick-wt=5): 34 [] add(a,c)=multiplicative_identity.
% 1.58/1.81 ---> New Demodulator: 35 [new_demod,34] add(a,c)=multiplicative_identity.
% 1.58/1.81 ** KEPT (pick-wt=5): 36 [] multiply(a,b)=additive_identity.
% 1.58/1.81 ---> New Demodulator: 37 [new_demod,36] multiply(a,b)=additive_identity.
% 1.58/1.81 ** KEPT (pick-wt=5): 38 [] multiply(a,c)=additive_identity.
% 1.58/1.81 ---> New Demodulator: 39 [new_demod,38] multiply(a,c)=additive_identity.
% 1.58/1.81 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.58/1.81 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] add(A,B)=add(B,A).
% 1.58/1.81 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] multiply(A,B)=multiply(B,A).
% 1.58/1.81 >>>> Starting back demodulation with 8.
% 1.58/1.81 >>>> Starting back demodulation with 11.
% 1.58/1.81 >>>> Starting back demodulation with 13.
% 1.58/1.81 >> back demodulating 10 with 13.
% 1.58/1.81 >> back demodulating 7 with 13.
% 1.58/1.81 >>>> Starting back demodulation with 15.
% 1.58/1.81 >>>> Starting back demodulation with 17.
% 1.58/1.81 >>>> Starting back demodulation with 19.
% 1.58/1.81 >>>> Starting back demodulation with 21.
% 1.58/1.81 >>>> Starting back demodulation with 23.
% 1.58/1.81 >>>> Starting back demodulation with 25.
% 1.58/1.81 >>>> Starting back demodulation with 27.
% 1.58/1.81 >>>> Starting back demodulation with 29.
% 1.58/1.81 >>>> Starting back demodulation with 31.
% 1.58/1.81 >>>> Starting back demodulation with 33.
% 1.58/1.81 >>>> Starting back demodulation with 35.
% 1.58/1.81 >>>> Starting back demodulation with 37.
% 1.58/1.81 >>>> Starting back demodulation with 39.
% 1.58/1.81 >>>> Starting back demodulation with 41.
% 1.58/1.81 >>>> Starting back demodulation with 43.
% 1.58/1.81
% 1.58/1.81 ======= end of input processing =======
% 1.58/1.81
% 1.58/1.81 =========== start of search ===========
% 1.58/1.81
% 1.58/1.81 -------- PROOF --------
% 1.58/1.81
% 1.58/1.81 ----> UNIT CONFLICT at 0.01 sec ----> 366 [binary,364.1,2.1] $F.
% 1.58/1.81
% 1.58/1.81 Length of proof is 8. Level of proof is 5.
% 1.58/1.81
% 1.58/1.81 ---------------- PROOF ----------------
% 1.58/1.81 % SZS status Unsatisfiable
% 1.58/1.81 % SZS output start Refutation
% See solution above
% 1.58/1.81 ------------ end of proof -------------
% 1.58/1.81
% 1.58/1.81
% 1.58/1.81 Search stopped by max_proofs option.
% 1.58/1.81
% 1.58/1.81
% 1.58/1.81 Search stopped by max_proofs option.
% 1.58/1.81
% 1.58/1.81 ============ end of search ============
% 1.58/1.81
% 1.58/1.81 -------------- statistics -------------
% 1.58/1.81 clauses given 35
% 1.58/1.81 clauses generated 333
% 1.58/1.81 clauses kept 192
% 1.58/1.81 clauses forward subsumed 186
% 1.58/1.81 clauses back subsumed 0
% 1.58/1.81 Kbytes malloced 1953
% 1.58/1.81
% 1.58/1.81 ----------- times (seconds) -----------
% 1.58/1.81 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.58/1.81 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.58/1.81 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.58/1.81
% 1.58/1.81 That finishes the proof of the theorem.
% 1.58/1.81
% 1.58/1.81 Process 14803 finished Wed Jul 27 02:24:26 2022
% 1.58/1.81 Otter interrupted
% 1.58/1.81 PROOF FOUND
%------------------------------------------------------------------------------