TSTP Solution File: BOO017-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO017-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 12:47:36 EDT 2022
% Result : Unsatisfiable 1.98s 2.14s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 7 RR)
% Number of literals : 27 ( 26 equ; 4 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 37 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(x,z) != x,
file('BOO017-2.p',unknown),
[] ).
cnf(3,axiom,
add(A,B) = add(B,A),
file('BOO017-2.p',unknown),
[] ).
cnf(4,axiom,
multiply(A,B) = multiply(B,A),
file('BOO017-2.p',unknown),
[] ).
cnf(5,axiom,
add(multiply(A,B),C) = multiply(add(A,C),add(B,C)),
file('BOO017-2.p',unknown),
[] ).
cnf(6,plain,
multiply(add(A,B),add(C,B)) = add(multiply(A,C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(12,axiom,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
file('BOO017-2.p',unknown),
[] ).
cnf(14,axiom,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
file('BOO017-2.p',unknown),
[] ).
cnf(17,axiom,
add(inverse(A),A) = multiplicative_identity,
file('BOO017-2.p',unknown),
[] ).
cnf(22,axiom,
multiply(inverse(A),A) = additive_identity,
file('BOO017-2.p',unknown),
[] ).
cnf(26,axiom,
multiply(multiplicative_identity,A) = A,
file('BOO017-2.p',unknown),
[] ).
cnf(28,axiom,
add(A,additive_identity) = A,
file('BOO017-2.p',unknown),
[] ).
cnf(30,axiom,
add(additive_identity,A) = A,
file('BOO017-2.p',unknown),
[] ).
cnf(31,axiom,
add(x,y) = z,
file('BOO017-2.p',unknown),
[] ).
cnf(35,plain,
add(add(multiply(A,B),multiply(C,B)),add(multiply(A,C),multiply(C,C))) = add(multiply(A,B),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[6]),14,12,12]),
[iquote('back_demod,6,demod,14,12,12')] ).
cnf(37,plain,
add(y,x) = z,
inference(para_into,[status(thm),theory(equality)],[31,3]),
[iquote('para_into,31.1.1,3.1.1')] ).
cnf(41,plain,
multiply(z,x) != x,
inference(para_from,[status(thm),theory(equality)],[4,1]),
[iquote('para_from,4.1.1,1.1.1')] ).
cnf(45,plain,
multiply(z,A) = add(multiply(y,A),multiply(x,A)),
inference(para_into,[status(thm),theory(equality)],[12,37]),
[iquote('para_into,11.1.1.1,37.1.1')] ).
cnf(46,plain,
add(multiply(additive_identity,A),multiply(B,A)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,30])]),
[iquote('para_into,11.1.1.1,29.1.1,flip.1')] ).
cnf(50,plain,
add(multiply(inverse(A),B),multiply(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,17]),26])]),
[iquote('para_into,11.1.1.1,17.1.1,demod,26,flip.1')] ).
cnf(57,plain,
add(multiply(y,x),multiply(x,x)) != x,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[41]),45]),
[iquote('back_demod,41,demod,45')] ).
cnf(81,plain,
multiply(A,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[50,22]),30]),
[iquote('para_into,50.1.1.1,21.1.1,demod,30')] ).
cnf(97,plain,
add(multiply(y,x),x) != x,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[57]),81]),
[iquote('back_demod,57,demod,81')] ).
cnf(98,plain,
add(add(multiply(A,B),multiply(C,B)),add(multiply(A,C),C)) = add(multiply(A,B),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[35]),81]),
[iquote('back_demod,35,demod,81')] ).
cnf(140,plain,
multiply(additive_identity,A) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[46,22]),28,22]),
[iquote('para_into,46.1.1.2,21.1.1,demod,28,22')] ).
cnf(143,plain,
multiply(A,additive_identity) = additive_identity,
inference(para_into,[status(thm),theory(equality)],[140,4]),
[iquote('para_into,140.1.1,4.1.1')] ).
cnf(894,plain,
add(multiply(A,B),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[98,143]),143,28,30,143,30]),
[iquote('para_into,98.1.1.1.1,142.1.1,demod,143,28,30,143,30')] ).
cnf(896,plain,
$false,
inference(binary,[status(thm)],[894,97]),
[iquote('binary,894.1,97.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : BOO017-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 02:53:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.91/2.10 ----- Otter 3.3f, August 2004 -----
% 1.91/2.10 The process was started by sandbox on n023.cluster.edu,
% 1.91/2.10 Wed Jul 27 02:53:03 2022
% 1.91/2.10 The command was "./otter". The process ID is 7544.
% 1.91/2.10
% 1.91/2.10 set(prolog_style_variables).
% 1.91/2.10 set(auto).
% 1.91/2.10 dependent: set(auto1).
% 1.91/2.10 dependent: set(process_input).
% 1.91/2.10 dependent: clear(print_kept).
% 1.91/2.10 dependent: clear(print_new_demod).
% 1.91/2.10 dependent: clear(print_back_demod).
% 1.91/2.10 dependent: clear(print_back_sub).
% 1.91/2.10 dependent: set(control_memory).
% 1.91/2.10 dependent: assign(max_mem, 12000).
% 1.91/2.10 dependent: assign(pick_given_ratio, 4).
% 1.91/2.10 dependent: assign(stats_level, 1).
% 1.91/2.10 dependent: assign(max_seconds, 10800).
% 1.91/2.10 clear(print_given).
% 1.91/2.10
% 1.91/2.10 list(usable).
% 1.91/2.10 0 [] A=A.
% 1.91/2.10 0 [] add(X,Y)=add(Y,X).
% 1.91/2.10 0 [] multiply(X,Y)=multiply(Y,X).
% 1.91/2.10 0 [] add(multiply(X,Y),Z)=multiply(add(X,Z),add(Y,Z)).
% 1.91/2.10 0 [] add(X,multiply(Y,Z))=multiply(add(X,Y),add(X,Z)).
% 1.91/2.10 0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.91/2.10 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.91/2.10 0 [] add(X,inverse(X))=multiplicative_identity.
% 1.91/2.10 0 [] add(inverse(X),X)=multiplicative_identity.
% 1.91/2.10 0 [] multiply(X,inverse(X))=additive_identity.
% 1.91/2.10 0 [] multiply(inverse(X),X)=additive_identity.
% 1.91/2.10 0 [] multiply(X,multiplicative_identity)=X.
% 1.91/2.10 0 [] multiply(multiplicative_identity,X)=X.
% 1.91/2.10 0 [] add(X,additive_identity)=X.
% 1.91/2.10 0 [] add(additive_identity,X)=X.
% 1.91/2.10 0 [] add(x,y)=z.
% 1.91/2.10 0 [] multiply(x,z)!=x.
% 1.91/2.10 end_of_list.
% 1.91/2.10
% 1.91/2.10 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.91/2.10
% 1.91/2.10 All clauses are units, and equality is present; the
% 1.91/2.10 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.91/2.10
% 1.91/2.10 dependent: set(knuth_bendix).
% 1.91/2.10 dependent: set(anl_eq).
% 1.91/2.10 dependent: set(para_from).
% 1.91/2.10 dependent: set(para_into).
% 1.91/2.10 dependent: clear(para_from_right).
% 1.91/2.10 dependent: clear(para_into_right).
% 1.91/2.10 dependent: set(para_from_vars).
% 1.91/2.10 dependent: set(eq_units_both_ways).
% 1.91/2.10 dependent: set(dynamic_demod_all).
% 1.91/2.10 dependent: set(dynamic_demod).
% 1.91/2.10 dependent: set(order_eq).
% 1.91/2.10 dependent: set(back_demod).
% 1.91/2.10 dependent: set(lrpo).
% 1.91/2.10
% 1.91/2.10 ------------> process usable:
% 1.91/2.10 ** KEPT (pick-wt=5): 1 [] multiply(x,z)!=x.
% 1.91/2.10
% 1.91/2.10 ------------> process sos:
% 1.91/2.10 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.91/2.10 ** KEPT (pick-wt=7): 3 [] add(A,B)=add(B,A).
% 1.91/2.10 ** KEPT (pick-wt=7): 4 [] multiply(A,B)=multiply(B,A).
% 1.91/2.10 ** KEPT (pick-wt=13): 6 [copy,5,flip.1] multiply(add(A,B),add(C,B))=add(multiply(A,C),B).
% 1.91/2.10 ---> New Demodulator: 7 [new_demod,6] multiply(add(A,B),add(C,B))=add(multiply(A,C),B).
% 1.91/2.10 ** KEPT (pick-wt=13): 9 [copy,8,flip.1] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.91/2.10 ---> New Demodulator: 10 [new_demod,9] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.91/2.10 ** KEPT (pick-wt=13): 11 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.91/2.10 ---> New Demodulator: 12 [new_demod,11] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.91/2.10 ** KEPT (pick-wt=13): 13 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.91/2.10 ---> New Demodulator: 14 [new_demod,13] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.91/2.10 ** KEPT (pick-wt=6): 15 [] add(A,inverse(A))=multiplicative_identity.
% 1.91/2.10 ---> New Demodulator: 16 [new_demod,15] add(A,inverse(A))=multiplicative_identity.
% 1.91/2.10 ** KEPT (pick-wt=6): 17 [] add(inverse(A),A)=multiplicative_identity.
% 1.91/2.10 ---> New Demodulator: 18 [new_demod,17] add(inverse(A),A)=multiplicative_identity.
% 1.91/2.10 ** KEPT (pick-wt=6): 19 [] multiply(A,inverse(A))=additive_identity.
% 1.91/2.10 ---> New Demodulator: 20 [new_demod,19] multiply(A,inverse(A))=additive_identity.
% 1.91/2.10 ** KEPT (pick-wt=6): 21 [] multiply(inverse(A),A)=additive_identity.
% 1.91/2.10 ---> New Demodulator: 22 [new_demod,21] multiply(inverse(A),A)=additive_identity.
% 1.91/2.10 ** KEPT (pick-wt=5): 23 [] multiply(A,multiplicative_identity)=A.
% 1.91/2.10 ---> New Demodulator: 24 [new_demod,23] multiply(A,multiplicative_identity)=A.
% 1.91/2.10 ** KEPT (pick-wt=5): 25 [] multiply(multiplicative_identity,A)=A.
% 1.91/2.10 ---> New Demodulator: 26 [new_demod,25] multiply(multiplicative_identity,A)=A.
% 1.91/2.10 ** KEPT (pick-wt=5): 27 [] add(A,additive_identity)=A.
% 1.91/2.10 ---> New Demodulator: 28 [new_demod,27] add(A,additive_identity)=A.
% 1.91/2.10 ** KEPT (pick-wt=5): 29 [] add(additive_identity,A)=A.
% 1.91/2.10 ---> New Demodulator: 30 [new_demod,29] add(additive_identity,A)=A.
% 1.91/2.10 ** KEPT (pick-wt=5): 31 [] add(x,y)=z.
% 1.91/2.10 ---> New Demodulator: 32 [new_demod,31] add(x,y)=z.
% 1.98/2.14 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.98/2.14 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] add(A,B)=add(B,A).
% 1.98/2.14 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] multiply(A,B)=multiply(B,A).
% 1.98/2.14 >>>> Starting back demodulation with 7.
% 1.98/2.14 >>>> Starting back demodulation with 10.
% 1.98/2.14 >>>> Starting back demodulation with 12.
% 1.98/2.14 >> back demodulating 9 with 12.
% 1.98/2.14 >> back demodulating 6 with 12.
% 1.98/2.14 >>>> Starting back demodulation with 14.
% 1.98/2.14 >>>> Starting back demodulation with 16.
% 1.98/2.14 >>>> Starting back demodulation with 18.
% 1.98/2.14 >>>> Starting back demodulation with 20.
% 1.98/2.14 >>>> Starting back demodulation with 22.
% 1.98/2.14 >>>> Starting back demodulation with 24.
% 1.98/2.14 >>>> Starting back demodulation with 26.
% 1.98/2.14 >>>> Starting back demodulation with 28.
% 1.98/2.14 >>>> Starting back demodulation with 30.
% 1.98/2.14 >>>> Starting back demodulation with 32.
% 1.98/2.14 >>>> Starting back demodulation with 34.
% 1.98/2.14 >>>> Starting back demodulation with 36.
% 1.98/2.14
% 1.98/2.14 ======= end of input processing =======
% 1.98/2.14
% 1.98/2.14 =========== start of search ===========
% 1.98/2.14
% 1.98/2.14
% 1.98/2.14 Resetting weight limit to 14.
% 1.98/2.14
% 1.98/2.14
% 1.98/2.14 Resetting weight limit to 14.
% 1.98/2.14
% 1.98/2.14 sos_size=399
% 1.98/2.14
% 1.98/2.14 -------- PROOF --------
% 1.98/2.14
% 1.98/2.14 ----> UNIT CONFLICT at 0.04 sec ----> 896 [binary,894.1,97.1] $F.
% 1.98/2.14
% 1.98/2.14 Length of proof is 14. Level of proof is 4.
% 1.98/2.14
% 1.98/2.14 ---------------- PROOF ----------------
% 1.98/2.14 % SZS status Unsatisfiable
% 1.98/2.14 % SZS output start Refutation
% See solution above
% 1.98/2.14 ------------ end of proof -------------
% 1.98/2.14
% 1.98/2.14
% 1.98/2.14 Search stopped by max_proofs option.
% 1.98/2.14
% 1.98/2.14
% 1.98/2.14 Search stopped by max_proofs option.
% 1.98/2.14
% 1.98/2.14 ============ end of search ============
% 1.98/2.14
% 1.98/2.14 -------------- statistics -------------
% 1.98/2.14 clauses given 81
% 1.98/2.14 clauses generated 1841
% 1.98/2.14 clauses kept 543
% 1.98/2.14 clauses forward subsumed 1523
% 1.98/2.14 clauses back subsumed 30
% 1.98/2.14 Kbytes malloced 4882
% 1.98/2.14
% 1.98/2.14 ----------- times (seconds) -----------
% 1.98/2.14 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.98/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.14
% 1.98/2.14 That finishes the proof of the theorem.
% 1.98/2.14
% 1.98/2.14 Process 7544 finished Wed Jul 27 02:53:05 2022
% 1.98/2.14 Otter interrupted
% 1.98/2.14 PROOF FOUND
%------------------------------------------------------------------------------