TSTP Solution File: BOO010-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO010-2 : TPTP v8.1.0. Released v1.0.0.
% 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 12:47:33 EDT 2022
% Result : Unsatisfiable 1.66s 1.89s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 11
% Syntax : Number of clauses : 23 ( 23 unt; 0 nHn; 4 RR)
% Number of literals : 23 ( 22 equ; 3 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
add(a,multiply(a,b)) != a,
file('BOO010-2.p',unknown),
[] ).
cnf(3,axiom,
add(A,B) = add(B,A),
file('BOO010-2.p',unknown),
[] ).
cnf(4,axiom,
multiply(A,B) = multiply(B,A),
file('BOO010-2.p',unknown),
[] ).
cnf(5,axiom,
add(multiply(A,B),C) = multiply(add(A,C),add(B,C)),
file('BOO010-2.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('BOO010-2.p',unknown),
[] ).
cnf(14,axiom,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
file('BOO010-2.p',unknown),
[] ).
cnf(17,axiom,
add(inverse(A),A) = multiplicative_identity,
file('BOO010-2.p',unknown),
[] ).
cnf(22,axiom,
multiply(inverse(A),A) = additive_identity,
file('BOO010-2.p',unknown),
[] ).
cnf(26,axiom,
multiply(multiplicative_identity,A) = A,
file('BOO010-2.p',unknown),
[] ).
cnf(28,axiom,
add(A,additive_identity) = A,
file('BOO010-2.p',unknown),
[] ).
cnf(30,axiom,
add(additive_identity,A) = A,
file('BOO010-2.p',unknown),
[] ).
cnf(33,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(35,plain,
add(multiply(a,b),a) != a,
inference(para_from,[status(thm),theory(equality)],[3,1]),
[iquote('para_from,3.1.1,1.1.1')] ).
cnf(41,plain,
add(multiply(b,a),a) != a,
inference(para_into,[status(thm),theory(equality)],[35,4]),
[iquote('para_into,35.1.1.1,4.1.1')] ).
cnf(42,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(46,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(59,plain,
multiply(A,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[46,22]),30]),
[iquote('para_into,46.1.1.1,21.1.1,demod,30')] ).
cnf(70,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)],[33]),59]),
[iquote('back_demod,33,demod,59')] ).
cnf(126,plain,
multiply(additive_identity,A) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[42,22]),28,22]),
[iquote('para_into,42.1.1.2,21.1.1,demod,28,22')] ).
cnf(129,plain,
multiply(A,additive_identity) = additive_identity,
inference(para_into,[status(thm),theory(equality)],[126,4]),
[iquote('para_into,126.1.1,4.1.1')] ).
cnf(434,plain,
add(multiply(A,B),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[70,129]),129,28,30,129,30]),
[iquote('para_into,70.1.1.1.1,128.1.1,demod,129,28,30,129,30')] ).
cnf(436,plain,
$false,
inference(binary,[status(thm)],[434,41]),
[iquote('binary,434.1,41.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : BOO010-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % 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 02:24:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.87 ----- Otter 3.3f, August 2004 -----
% 1.66/1.87 The process was started by sandbox2 on n010.cluster.edu,
% 1.66/1.87 Wed Jul 27 02:24:55 2022
% 1.66/1.87 The command was "./otter". The process ID is 17708.
% 1.66/1.87
% 1.66/1.87 set(prolog_style_variables).
% 1.66/1.87 set(auto).
% 1.66/1.87 dependent: set(auto1).
% 1.66/1.87 dependent: set(process_input).
% 1.66/1.87 dependent: clear(print_kept).
% 1.66/1.87 dependent: clear(print_new_demod).
% 1.66/1.87 dependent: clear(print_back_demod).
% 1.66/1.87 dependent: clear(print_back_sub).
% 1.66/1.87 dependent: set(control_memory).
% 1.66/1.87 dependent: assign(max_mem, 12000).
% 1.66/1.87 dependent: assign(pick_given_ratio, 4).
% 1.66/1.87 dependent: assign(stats_level, 1).
% 1.66/1.87 dependent: assign(max_seconds, 10800).
% 1.66/1.87 clear(print_given).
% 1.66/1.87
% 1.66/1.87 list(usable).
% 1.66/1.87 0 [] A=A.
% 1.66/1.87 0 [] add(X,Y)=add(Y,X).
% 1.66/1.87 0 [] multiply(X,Y)=multiply(Y,X).
% 1.66/1.87 0 [] add(multiply(X,Y),Z)=multiply(add(X,Z),add(Y,Z)).
% 1.66/1.87 0 [] add(X,multiply(Y,Z))=multiply(add(X,Y),add(X,Z)).
% 1.66/1.87 0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.66/1.87 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.66/1.87 0 [] add(X,inverse(X))=multiplicative_identity.
% 1.66/1.87 0 [] add(inverse(X),X)=multiplicative_identity.
% 1.66/1.87 0 [] multiply(X,inverse(X))=additive_identity.
% 1.66/1.87 0 [] multiply(inverse(X),X)=additive_identity.
% 1.66/1.87 0 [] multiply(X,multiplicative_identity)=X.
% 1.66/1.87 0 [] multiply(multiplicative_identity,X)=X.
% 1.66/1.87 0 [] add(X,additive_identity)=X.
% 1.66/1.87 0 [] add(additive_identity,X)=X.
% 1.66/1.87 0 [] add(a,multiply(a,b))!=a.
% 1.66/1.87 end_of_list.
% 1.66/1.87
% 1.66/1.87 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.66/1.87
% 1.66/1.87 All clauses are units, and equality is present; the
% 1.66/1.87 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.66/1.87
% 1.66/1.87 dependent: set(knuth_bendix).
% 1.66/1.87 dependent: set(anl_eq).
% 1.66/1.87 dependent: set(para_from).
% 1.66/1.87 dependent: set(para_into).
% 1.66/1.87 dependent: clear(para_from_right).
% 1.66/1.87 dependent: clear(para_into_right).
% 1.66/1.87 dependent: set(para_from_vars).
% 1.66/1.87 dependent: set(eq_units_both_ways).
% 1.66/1.87 dependent: set(dynamic_demod_all).
% 1.66/1.87 dependent: set(dynamic_demod).
% 1.66/1.87 dependent: set(order_eq).
% 1.66/1.87 dependent: set(back_demod).
% 1.66/1.87 dependent: set(lrpo).
% 1.66/1.87
% 1.66/1.87 ------------> process usable:
% 1.66/1.87 ** KEPT (pick-wt=7): 1 [] add(a,multiply(a,b))!=a.
% 1.66/1.87
% 1.66/1.87 ------------> process sos:
% 1.66/1.87 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.66/1.87 ** KEPT (pick-wt=7): 3 [] add(A,B)=add(B,A).
% 1.66/1.87 ** KEPT (pick-wt=7): 4 [] multiply(A,B)=multiply(B,A).
% 1.66/1.87 ** KEPT (pick-wt=13): 6 [copy,5,flip.1] multiply(add(A,B),add(C,B))=add(multiply(A,C),B).
% 1.66/1.87 ---> New Demodulator: 7 [new_demod,6] multiply(add(A,B),add(C,B))=add(multiply(A,C),B).
% 1.66/1.87 ** KEPT (pick-wt=13): 9 [copy,8,flip.1] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.66/1.87 ---> New Demodulator: 10 [new_demod,9] multiply(add(A,B),add(A,C))=add(A,multiply(B,C)).
% 1.66/1.87 ** KEPT (pick-wt=13): 11 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.66/1.87 ---> New Demodulator: 12 [new_demod,11] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.66/1.87 ** KEPT (pick-wt=13): 13 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.66/1.87 ---> New Demodulator: 14 [new_demod,13] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.66/1.87 ** KEPT (pick-wt=6): 15 [] add(A,inverse(A))=multiplicative_identity.
% 1.66/1.87 ---> New Demodulator: 16 [new_demod,15] add(A,inverse(A))=multiplicative_identity.
% 1.66/1.87 ** KEPT (pick-wt=6): 17 [] add(inverse(A),A)=multiplicative_identity.
% 1.66/1.87 ---> New Demodulator: 18 [new_demod,17] add(inverse(A),A)=multiplicative_identity.
% 1.66/1.87 ** KEPT (pick-wt=6): 19 [] multiply(A,inverse(A))=additive_identity.
% 1.66/1.87 ---> New Demodulator: 20 [new_demod,19] multiply(A,inverse(A))=additive_identity.
% 1.66/1.87 ** KEPT (pick-wt=6): 21 [] multiply(inverse(A),A)=additive_identity.
% 1.66/1.87 ---> New Demodulator: 22 [new_demod,21] multiply(inverse(A),A)=additive_identity.
% 1.66/1.87 ** KEPT (pick-wt=5): 23 [] multiply(A,multiplicative_identity)=A.
% 1.66/1.87 ---> New Demodulator: 24 [new_demod,23] multiply(A,multiplicative_identity)=A.
% 1.66/1.87 ** KEPT (pick-wt=5): 25 [] multiply(multiplicative_identity,A)=A.
% 1.66/1.87 ---> New Demodulator: 26 [new_demod,25] multiply(multiplicative_identity,A)=A.
% 1.66/1.87 ** KEPT (pick-wt=5): 27 [] add(A,additive_identity)=A.
% 1.66/1.87 ---> New Demodulator: 28 [new_demod,27] add(A,additive_identity)=A.
% 1.66/1.87 ** KEPT (pick-wt=5): 29 [] add(additive_identity,A)=A.
% 1.66/1.87 ---> New Demodulator: 30 [new_demod,29] add(additive_identity,A)=A.
% 1.66/1.87 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.66/1.89 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] add(A,B)=add(B,A).
% 1.66/1.89 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] multiply(A,B)=multiply(B,A).
% 1.66/1.89 >>>> Starting back demodulation with 7.
% 1.66/1.89 >>>> Starting back demodulation with 10.
% 1.66/1.89 >>>> Starting back demodulation with 12.
% 1.66/1.89 >> back demodulating 9 with 12.
% 1.66/1.89 >> back demodulating 6 with 12.
% 1.66/1.89 >>>> Starting back demodulation with 14.
% 1.66/1.89 >>>> Starting back demodulation with 16.
% 1.66/1.89 >>>> Starting back demodulation with 18.
% 1.66/1.89 >>>> Starting back demodulation with 20.
% 1.66/1.89 >>>> Starting back demodulation with 22.
% 1.66/1.89 >>>> Starting back demodulation with 24.
% 1.66/1.89 >>>> Starting back demodulation with 26.
% 1.66/1.89 >>>> Starting back demodulation with 28.
% 1.66/1.89 >>>> Starting back demodulation with 30.
% 1.66/1.89 >>>> Starting back demodulation with 32.
% 1.66/1.89 >>>> Starting back demodulation with 34.
% 1.66/1.89
% 1.66/1.89 ======= end of input processing =======
% 1.66/1.89
% 1.66/1.89 =========== start of search ===========
% 1.66/1.89
% 1.66/1.89 -------- PROOF --------
% 1.66/1.89
% 1.66/1.89 ----> UNIT CONFLICT at 0.02 sec ----> 436 [binary,434.1,41.1] $F.
% 1.66/1.89
% 1.66/1.89 Length of proof is 11. Level of proof is 4.
% 1.66/1.89
% 1.66/1.89 ---------------- PROOF ----------------
% 1.66/1.89 % SZS status Unsatisfiable
% 1.66/1.89 % SZS output start Refutation
% See solution above
% 1.66/1.89 ------------ end of proof -------------
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89 ============ end of search ============
% 1.66/1.89
% 1.66/1.89 -------------- statistics -------------
% 1.66/1.89 clauses given 51
% 1.66/1.89 clauses generated 921
% 1.66/1.89 clauses kept 252
% 1.66/1.89 clauses forward subsumed 788
% 1.66/1.89 clauses back subsumed 0
% 1.66/1.89 Kbytes malloced 2929
% 1.66/1.89
% 1.66/1.89 ----------- times (seconds) -----------
% 1.66/1.89 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.66/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.66/1.89
% 1.66/1.89 That finishes the proof of the theorem.
% 1.66/1.89
% 1.66/1.89 Process 17708 finished Wed Jul 27 02:24:56 2022
% 1.66/1.89 Otter interrupted
% 1.66/1.89 PROOF FOUND
%------------------------------------------------------------------------------