%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO005-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 1.67s 1.89s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 3 RR)
% Number of literals : 25 ( 24 equ; 2 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 : 37 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
add(a,multiplicative_identity) != multiplicative_identity,
file('BOO005-4.p',unknown),
[] ).
cnf(3,axiom,
add(A,B) = add(B,A),
file('BOO005-4.p',unknown),
[] ).
cnf(4,axiom,
multiply(A,B) = multiply(B,A),
file('BOO005-4.p',unknown),
[] ).
cnf(5,axiom,
add(A,multiply(B,C)) = multiply(add(A,B),add(A,C)),
file('BOO005-4.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('BOO005-4.p',unknown),
[] ).
cnf(11,axiom,
add(A,additive_identity) = A,
file('BOO005-4.p',unknown),
[] ).
cnf(13,axiom,
multiply(A,multiplicative_identity) = A,
file('BOO005-4.p',unknown),
[] ).
cnf(14,axiom,
add(A,inverse(A)) = multiplicative_identity,
file('BOO005-4.p',unknown),
[] ).
cnf(17,axiom,
multiply(A,inverse(A)) = additive_identity,
file('BOO005-4.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(24,plain,
add(multiplicative_identity,a) != multiplicative_identity,
inference(para_from,[status(thm),theory(equality)],[3,1]),
[iquote('para_from,3.1.1,1.1.1')] ).
cnf(29,plain,
multiply(multiplicative_identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,13])]),
[iquote('para_into,4.1.1,12.1.1,flip.1')] ).
cnf(33,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(35,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,
add(multiply(A,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]),11]),
[iquote('para_into,18.1.1.1.1,10.1.1,demod,11')] ).
cnf(82,plain,
multiply(A,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,17]),23]),
[iquote('para_into,35.1.1.1,16.1.1,demod,23')] ).
cnf(96,plain,
add(A,multiply(A,B)) = add(A,multiply(additive_identity,B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[51]),82]),
[iquote('back_demod,51,demod,82')] ).
cnf(119,plain,
multiply(A,additive_identity) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,17]),11,17]),
[iquote('para_into,33.1.1.2,16.1.1,demod,11,17')] ).
cnf(122,plain,
multiply(additive_identity,A) = additive_identity,
inference(para_into,[status(thm),theory(equality)],[119,4]),
[iquote('para_into,119.1.1,4.1.1')] ).
cnf(123,plain,
add(A,multiply(A,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[96]),122,11]),
[iquote('back_demod,96,demod,122,11')] ).
cnf(159,plain,
add(multiplicative_identity,A) = multiplicative_identity,
inference(para_into,[status(thm),theory(equality)],[123,29]),
[iquote('para_into,123.1.1.2,29.1.1')] ).
cnf(161,plain,
$false,
inference(binary,[status(thm)],[159,24]),
[iquote('binary,159.1,24.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : BOO005-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 02:38:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.67/1.89 ----- Otter 3.3f, August 2004 -----
% 1.67/1.89 The process was started by sandbox on n014.cluster.edu,
% 1.67/1.89 Wed Jul 27 02:38:09 2022
% 1.67/1.89 The command was "./otter". The process ID is 12777.
% 1.67/1.89
% 1.67/1.89 set(prolog_style_variables).
% 1.67/1.89 set(auto).
% 1.67/1.89 dependent: set(auto1).
% 1.67/1.89 dependent: set(process_input).
% 1.67/1.89 dependent: clear(print_kept).
% 1.67/1.89 dependent: clear(print_new_demod).
% 1.67/1.89 dependent: clear(print_back_demod).
% 1.67/1.89 dependent: clear(print_back_sub).
% 1.67/1.89 dependent: set(control_memory).
% 1.67/1.89 dependent: assign(max_mem, 12000).
% 1.67/1.89 dependent: assign(pick_given_ratio, 4).
% 1.67/1.89 dependent: assign(stats_level, 1).
% 1.67/1.89 dependent: assign(max_seconds, 10800).
% 1.67/1.89 clear(print_given).
% 1.67/1.89
% 1.67/1.89 list(usable).
% 1.67/1.89 0 [] A=A.
% 1.67/1.89 0 [] add(X,Y)=add(Y,X).
% 1.67/1.89 0 [] multiply(X,Y)=multiply(Y,X).
% 1.67/1.89 0 [] add(X,multiply(Y,Z))=multiply(add(X,Y),add(X,Z)).
% 1.67/1.89 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.67/1.89 0 [] add(X,additive_identity)=X.
% 1.67/1.89 0 [] multiply(X,multiplicative_identity)=X.
% 1.67/1.89 0 [] add(X,inverse(X))=multiplicative_identity.
% 1.67/1.89 0 [] multiply(X,inverse(X))=additive_identity.
% 1.67/1.89 0 [] add(a,multiplicative_identity)!=multiplicative_identity.
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.67/1.89
% 1.67/1.89 All clauses are units, and equality is present; the
% 1.67/1.89 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.67/1.89
% 1.67/1.89 dependent: set(knuth_bendix).
% 1.67/1.89 dependent: set(anl_eq).
% 1.67/1.89 dependent: set(para_from).
% 1.67/1.89 dependent: set(para_into).
% 1.67/1.89 dependent: clear(para_from_right).
% 1.67/1.89 dependent: clear(para_into_right).
% 1.67/1.89 dependent: set(para_from_vars).
% 1.67/1.89 dependent: set(eq_units_both_ways).
% 1.67/1.89 dependent: set(dynamic_demod_all).
% 1.67/1.89 dependent: set(dynamic_demod).
% 1.67/1.89 dependent: set(order_eq).
% 1.67/1.89 dependent: set(back_demod).
% 1.67/1.89 dependent: set(lrpo).
% 1.67/1.89
% 1.67/1.89 ------------> process usable:
% 1.67/1.89 ** KEPT (pick-wt=5): 1 [] add(a,multiplicative_identity)!=multiplicative_identity.
% 1.67/1.89
% 1.67/1.89 ------------> process sos:
% 1.67/1.89 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.67/1.89 ** KEPT (pick-wt=7): 3 [] add(A,B)=add(B,A).
% 1.67/1.89 ** KEPT (pick-wt=7): 4 [] multiply(A,B)=multiply(B,A).
% 1.67/1.89 ** KEPT (pick-wt=13): 6 [copy,5,flip.1] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.67/1.89 ---> New Demodulator: 7 [new_demod,6] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.67/1.89 ** KEPT (pick-wt=13): 8 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.67/1.89 ---> New Demodulator: 9 [new_demod,8] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.67/1.89 ** KEPT (pick-wt=5): 10 [] add(A,additive_identity)=A.
% 1.67/1.89 ---> New Demodulator: 11 [new_demod,10] add(A,additive_identity)=A.
% 1.67/1.89 ** KEPT (pick-wt=5): 12 [] multiply(A,multiplicative_identity)=A.
% 1.67/1.89 ---> New Demodulator: 13 [new_demod,12] multiply(A,multiplicative_identity)=A.
% 1.67/1.89 ** KEPT (pick-wt=6): 14 [] add(A,inverse(A))=multiplicative_identity.
% 1.67/1.89 ---> New Demodulator: 15 [new_demod,14] add(A,inverse(A))=multiplicative_identity.
% 1.67/1.89 ** KEPT (pick-wt=6): 16 [] multiply(A,inverse(A))=additive_identity.
% 1.67/1.89 ---> New Demodulator: 17 [new_demod,16] multiply(A,inverse(A))=additive_identity.
% 1.67/1.89 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.67/1.89 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] add(A,B)=add(B,A).
% 1.67/1.89 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] multiply(A,B)=multiply(B,A).
% 1.67/1.89 >>>> Starting back demodulation with 7.
% 1.67/1.89 >>>> Starting back demodulation with 9.
% 1.67/1.89 >> back demodulating 6 with 9.
% 1.67/1.89 >>>> Starting back demodulation with 11.
% 1.67/1.89 >>>> Starting back demodulation with 13.
% 1.67/1.89 >>>> Starting back demodulation with 15.
% 1.67/1.89 >>>> Starting back demodulation with 17.
% 1.67/1.89 >>>> Starting back demodulation with 19.
% 1.67/1.89
% 1.67/1.89 ======= end of input processing =======
% 1.67/1.89
% 1.67/1.89 =========== start of search ===========
% 1.67/1.89
% 1.67/1.89 -------- PROOF --------
% 1.67/1.89
% 1.67/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 161 [binary,159.1,24.1] $F.
% 1.67/1.89
% 1.67/1.89 Length of proof is 15. Level of proof is 6.
% 1.67/1.89
% 1.67/1.89 ---------------- PROOF ----------------
% 1.67/1.89 % SZS status Unsatisfiable
% 1.67/1.89 % SZS output start Refutation
% See solution above
% 1.67/1.89 ------------ end of proof -------------
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89 ============ end of search ============
% 1.67/1.89
% 1.67/1.89 -------------- statistics -------------
% 1.67/1.89 clauses given 27
% 1.67/1.89 clauses generated 248
% 1.67/1.89 clauses kept 88
% 1.67/1.89 clauses forward subsumed 217
% 1.67/1.89 clauses back subsumed 0
% 1.67/1.89 Kbytes malloced 1953
% 1.67/1.89
% 1.67/1.89 ----------- times (seconds) -----------
% 1.67/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.67/1.89
% 1.67/1.89 That finishes the proof of the theorem.
% 1.67/1.89
% 1.67/1.89 Process 12777 finished Wed Jul 27 02:38:11 2022
% 1.67/1.89 Otter interrupted
% 1.67/1.89 PROOF FOUND
%------------------------------------------------------------------------------