TSTP Solution File: BOO004-4 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO004-4 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 12:47:31 EDT 2022
% Result : Unsatisfiable 1.63s 1.82s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 2 RR)
% Number of literals : 23 ( 22 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
add(a,a) != a,
file('BOO004-4.p',unknown),
[] ).
cnf(3,axiom,
add(A,B) = add(B,A),
file('BOO004-4.p',unknown),
[] ).
cnf(4,axiom,
multiply(A,B) = multiply(B,A),
file('BOO004-4.p',unknown),
[] ).
cnf(5,axiom,
add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)),
file('BOO004-4.p',unknown),
[] ).
cnf(6,plain,
multiply(add(A,B),add(A,C)) = add(A,multiply(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(9,axiom,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
file('BOO004-4.p',unknown),
[] ).
cnf(11,axiom,
add(A,additive_identity) = A,
file('BOO004-4.p',unknown),
[] ).
cnf(13,axiom,
multiply(A,multiplicative_identity) = A,
file('BOO004-4.p',unknown),
[] ).
cnf(14,axiom,
add(A,inverse(A)) = multiplicative_identity,
file('BOO004-4.p',unknown),
[] ).
cnf(17,axiom,
multiply(A,inverse(A)) = additive_identity,
file('BOO004-4.p',unknown),
[] ).
cnf(18,plain,
add(multiply(add(A,B),A),multiply(add(A,B),C)) = add(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[6]),9]),
[iquote('back_demod,6,demod,9')] ).
cnf(20,plain,
add(inverse(A),A) = multiplicative_identity,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,14])]),
[iquote('para_into,3.1.1,14.1.1,flip.1')] ).
cnf(23,plain,
add(additive_identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3,11])]),
[iquote('para_into,3.1.1,10.1.1,flip.1')] ).
cnf(30,plain,
add(multiply(A,additive_identity),multiply(A,B)) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,23])]),
[iquote('para_into,8.1.1.2,22.1.1,flip.1')] ).
cnf(32,plain,
add(multiply(A,inverse(B)),multiply(A,B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,20]),13])]),
[iquote('para_into,8.1.1.2,20.1.1,demod,13,flip.1')] ).
cnf(51,plain,
multiply(A,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,17]),23]),
[iquote('para_into,32.1.1.1,16.1.1,demod,23')] ).
cnf(69,plain,
add(A,multiply(A,B)) = add(A,multiply(additive_identity,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[18,11]),51,11]),
[iquote('para_into,18.1.1.1.1,10.1.1,demod,51,11')] ).
cnf(92,plain,
add(A,multiply(additive_identity,B)) = add(A,multiply(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[69])]),
[iquote('copy,69,flip.1')] ).
cnf(116,plain,
multiply(A,additive_identity) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[30,17]),11,17]),
[iquote('para_into,30.1.1.2,16.1.1,demod,11,17')] ).
cnf(119,plain,
multiply(additive_identity,A) = additive_identity,
inference(para_into,[status(thm),theory(equality)],[116,4]),
[iquote('para_into,116.1.1,4.1.1')] ).
cnf(120,plain,
add(A,multiply(A,B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[92]),119,11])]),
[iquote('back_demod,92,demod,119,11,flip.1')] ).
cnf(144,plain,
add(A,A) = A,
inference(para_into,[status(thm),theory(equality)],[120,51]),
[iquote('para_into,120.1.1.2,50.1.1')] ).
cnf(146,plain,
$false,
inference(binary,[status(thm)],[144,1]),
[iquote('binary,144.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : BOO004-4 : TPTP v8.1.0. Released v1.1.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Jul 27 02:27:38 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.63/1.82 ----- Otter 3.3f, August 2004 -----
% 1.63/1.82 The process was started by sandbox on n021.cluster.edu,
% 1.63/1.82 Wed Jul 27 02:27:38 2022
% 1.63/1.82 The command was "./otter". The process ID is 15922.
% 1.63/1.82
% 1.63/1.82 set(prolog_style_variables).
% 1.63/1.82 set(auto).
% 1.63/1.82 dependent: set(auto1).
% 1.63/1.82 dependent: set(process_input).
% 1.63/1.82 dependent: clear(print_kept).
% 1.63/1.82 dependent: clear(print_new_demod).
% 1.63/1.82 dependent: clear(print_back_demod).
% 1.63/1.82 dependent: clear(print_back_sub).
% 1.63/1.82 dependent: set(control_memory).
% 1.63/1.82 dependent: assign(max_mem, 12000).
% 1.63/1.82 dependent: assign(pick_given_ratio, 4).
% 1.63/1.82 dependent: assign(stats_level, 1).
% 1.63/1.82 dependent: assign(max_seconds, 10800).
% 1.63/1.82 clear(print_given).
% 1.63/1.82
% 1.63/1.82 list(usable).
% 1.63/1.82 0 [] A=A.
% 1.63/1.82 0 [] add(X,Y)=add(Y,X).
% 1.63/1.82 0 [] multiply(X,Y)=multiply(Y,X).
% 1.63/1.82 0 [] add(X,multiply(Y,Z))=multiply(add(X,Y),add(X,Z)).
% 1.63/1.82 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.63/1.82 0 [] add(X,additive_identity)=X.
% 1.63/1.82 0 [] multiply(X,multiplicative_identity)=X.
% 1.63/1.82 0 [] add(X,inverse(X))=multiplicative_identity.
% 1.63/1.82 0 [] multiply(X,inverse(X))=additive_identity.
% 1.63/1.82 0 [] add(a,a)!=a.
% 1.63/1.82 end_of_list.
% 1.63/1.82
% 1.63/1.82 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.63/1.82
% 1.63/1.82 All clauses are units, and equality is present; the
% 1.63/1.82 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.63/1.82
% 1.63/1.82 dependent: set(knuth_bendix).
% 1.63/1.82 dependent: set(anl_eq).
% 1.63/1.82 dependent: set(para_from).
% 1.63/1.82 dependent: set(para_into).
% 1.63/1.82 dependent: clear(para_from_right).
% 1.63/1.82 dependent: clear(para_into_right).
% 1.63/1.82 dependent: set(para_from_vars).
% 1.63/1.82 dependent: set(eq_units_both_ways).
% 1.63/1.82 dependent: set(dynamic_demod_all).
% 1.63/1.82 dependent: set(dynamic_demod).
% 1.63/1.82 dependent: set(order_eq).
% 1.63/1.82 dependent: set(back_demod).
% 1.63/1.82 dependent: set(lrpo).
% 1.63/1.82
% 1.63/1.82 ------------> process usable:
% 1.63/1.82 ** KEPT (pick-wt=5): 1 [] add(a,a)!=a.
% 1.63/1.82
% 1.63/1.82 ------------> process sos:
% 1.63/1.82 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.63/1.82 ** KEPT (pick-wt=7): 3 [] add(A,B)=add(B,A).
% 1.63/1.82 ** KEPT (pick-wt=7): 4 [] multiply(A,B)=multiply(B,A).
% 1.63/1.82 ** KEPT (pick-wt=13): 6 [copy,5,flip.1] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.63/1.82 ---> New Demodulator: 7 [new_demod,6] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.63/1.82 ** KEPT (pick-wt=13): 8 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.63/1.82 ---> New Demodulator: 9 [new_demod,8] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.63/1.82 ** KEPT (pick-wt=5): 10 [] add(A,additive_identity)=A.
% 1.63/1.82 ---> New Demodulator: 11 [new_demod,10] add(A,additive_identity)=A.
% 1.63/1.82 ** KEPT (pick-wt=5): 12 [] multiply(A,multiplicative_identity)=A.
% 1.63/1.82 ---> New Demodulator: 13 [new_demod,12] multiply(A,multiplicative_identity)=A.
% 1.63/1.82 ** KEPT (pick-wt=6): 14 [] add(A,inverse(A))=multiplicative_identity.
% 1.63/1.82 ---> New Demodulator: 15 [new_demod,14] add(A,inverse(A))=multiplicative_identity.
% 1.63/1.82 ** KEPT (pick-wt=6): 16 [] multiply(A,inverse(A))=additive_identity.
% 1.63/1.82 ---> New Demodulator: 17 [new_demod,16] multiply(A,inverse(A))=additive_identity.
% 1.63/1.82 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.63/1.82 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] add(A,B)=add(B,A).
% 1.63/1.82 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] multiply(A,B)=multiply(B,A).
% 1.63/1.82 >>>> Starting back demodulation with 7.
% 1.63/1.82 >>>> Starting back demodulation with 9.
% 1.63/1.82 >> back demodulating 6 with 9.
% 1.63/1.82 >>>> Starting back demodulation with 11.
% 1.63/1.82 >>>> Starting back demodulation with 13.
% 1.63/1.82 >>>> Starting back demodulation with 15.
% 1.63/1.82 >>>> Starting back demodulation with 17.
% 1.63/1.82 >>>> Starting back demodulation with 19.
% 1.63/1.82
% 1.63/1.82 ======= end of input processing =======
% 1.63/1.82
% 1.63/1.82 =========== start of search ===========
% 1.63/1.82
% 1.63/1.82 -------- PROOF --------
% 1.63/1.82
% 1.63/1.82 ----> UNIT CONFLICT at 0.00 sec ----> 146 [binary,144.1,1.1] $F.
% 1.63/1.82
% 1.63/1.82 Length of proof is 13. Level of proof is 7.
% 1.63/1.82
% 1.63/1.82 ---------------- PROOF ----------------
% 1.63/1.82 % SZS status Unsatisfiable
% 1.63/1.82 % SZS output start Refutation
% See solution above
% 1.63/1.82 ------------ end of proof -------------
% 1.63/1.82
% 1.63/1.82
% 1.63/1.82 Search stopped by max_proofs option.
% 1.63/1.82
% 1.63/1.82
% 1.63/1.82 Search stopped by max_proofs option.
% 1.63/1.82
% 1.63/1.82 ============ end of search ============
% 1.63/1.82
% 1.63/1.82 -------------- statistics -------------
% 1.63/1.82 clauses given 25
% 1.63/1.82 clauses generated 222
% 1.63/1.82 clauses kept 79
% 1.63/1.82 clauses forward subsumed 195
% 1.63/1.82 clauses back subsumed 0
% 1.63/1.82 Kbytes malloced 1953
% 1.63/1.82
% 1.63/1.82 ----------- times (seconds) -----------
% 1.63/1.82 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.63/1.82 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.63/1.82 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.63/1.82
% 1.63/1.82 That finishes the proof of the theorem.
% 1.63/1.82
% 1.63/1.82 Process 15922 finished Wed Jul 27 02:27:39 2022
% 1.63/1.82 Otter interrupted
% 1.63/1.82 PROOF FOUND
%------------------------------------------------------------------------------