TSTP Solution File: BOO024-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO024-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 12:47:37 EDT 2022
% Result : Unsatisfiable 1.75s 1.96s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 5 RR)
% Number of literals : 54 ( 53 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 93 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
add(multiply(a,b),b) != b,
file('BOO024-1.p',unknown),
[] ).
cnf(3,axiom,
multiply(add(A,B),B) = B,
file('BOO024-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,add(B,C)) = add(multiply(B,A),multiply(C,A)),
file('BOO024-1.p',unknown),
[] ).
cnf(6,axiom,
add(A,inverse(A)) = n1,
file('BOO024-1.p',unknown),
[] ).
cnf(8,axiom,
pixley(A,B,C) = add(multiply(A,inverse(B)),add(multiply(A,C),multiply(inverse(B),C))),
file('BOO024-1.p',unknown),
[] ).
cnf(9,plain,
add(multiply(A,inverse(B)),add(multiply(A,C),multiply(inverse(B),C))) = pixley(A,B,C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.1')] ).
cnf(12,axiom,
pixley(A,A,B) = B,
file('BOO024-1.p',unknown),
[] ).
cnf(16,axiom,
pixley(A,B,A) = A,
file('BOO024-1.p',unknown),
[] ).
cnf(17,plain,
add(multiply(A,B),multiply(C,B)) = multiply(B,add(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(19,plain,
multiply(n1,inverse(A)) = inverse(A),
inference(para_into,[status(thm),theory(equality)],[3,6]),
[iquote('para_into,3.1.1.1,6.1.1')] ).
cnf(20,plain,
multiply(A,n1) = add(multiply(B,A),multiply(inverse(B),A)),
inference(para_into,[status(thm),theory(equality)],[5,6]),
[iquote('para_into,5.1.1.2,6.1.1')] ).
cnf(21,plain,
add(multiply(A,add(B,add(A,C))),multiply(C,add(B,add(A,C)))) = add(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,3])]),
[iquote('para_into,5.1.1,3.1.1,flip.1')] ).
cnf(23,plain,
add(multiply(A,B),multiply(inverse(A),B)) = multiply(B,n1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[20])]),
[iquote('copy,20,flip.1')] ).
cnf(24,plain,
add(multiply(A,B),multiply(inverse(A),B)) = add(multiply(C,B),multiply(inverse(C),B)),
inference(para_into,[status(thm),theory(equality)],[20,20]),
[iquote('para_into,20.1.1,20.1.1')] ).
cnf(25,plain,
add(multiply(A,add(B,n1)),multiply(inverse(A),add(B,n1))) = n1,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,3])]),
[iquote('para_into,20.1.1,3.1.1,flip.1')] ).
cnf(59,plain,
add(multiply(A,inverse(A)),multiply(B,n1)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,23]),12]),
[iquote('para_into,9.1.1.2,23.1.1,demod,12')] ).
cnf(66,plain,
add(inverse(n1),multiply(A,n1)) = A,
inference(para_into,[status(thm),theory(equality)],[59,19]),
[iquote('para_into,59.1.1.1,18.1.1')] ).
cnf(75,plain,
add(inverse(n1),add(multiply(A,B),multiply(inverse(A),B))) = B,
inference(para_into,[status(thm),theory(equality)],[66,20]),
[iquote('para_into,65.1.1.2,20.1.1')] ).
cnf(77,plain,
add(inverse(n1),n1) = add(A,n1),
inference(para_into,[status(thm),theory(equality)],[66,3]),
[iquote('para_into,65.1.1.2,3.1.1')] ).
cnf(79,plain,
multiply(A,B) = add(multiply(inverse(n1),A),multiply(multiply(B,n1),A)),
inference(para_from,[status(thm),theory(equality)],[66,5]),
[iquote('para_from,65.1.1,5.1.1.2')] ).
cnf(81,plain,
add(A,n1) = add(B,n1),
inference(para_into,[status(thm),theory(equality)],[77,77]),
[iquote('para_into,77.1.1,77.1.1')] ).
cnf(82,plain,
multiply(A,add(B,n1)) = add(multiply(C,A),multiply(n1,A)),
inference(para_from,[status(thm),theory(equality)],[81,5]),
[iquote('para_from,81.1.1,5.1.1.2')] ).
cnf(83,plain,
add(multiply(A,B),multiply(n1,B)) = multiply(B,add(C,n1)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[82])]),
[iquote('copy,82,flip.1')] ).
cnf(87,plain,
add(A,multiply(B,A)) = multiply(A,add(add(C,A),B)),
inference(para_into,[status(thm),theory(equality)],[17,3]),
[iquote('para_into,17.1.1.1,3.1.1')] ).
cnf(91,plain,
add(multiply(A,B),B) = multiply(B,add(A,add(C,B))),
inference(para_into,[status(thm),theory(equality)],[17,3]),
[iquote('para_into,17.1.1.2,3.1.1')] ).
cnf(95,plain,
multiply(A,add(add(B,A),C)) = add(A,multiply(C,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[87])]),
[iquote('copy,87,flip.1')] ).
cnf(99,plain,
multiply(A,add(B,add(C,A))) = add(multiply(B,A),A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[91])]),
[iquote('copy,91,flip.1')] ).
cnf(103,plain,
multiply(multiply(A,add(B,C)),multiply(C,A)) = multiply(C,A),
inference(para_from,[status(thm),theory(equality)],[17,3]),
[iquote('para_from,17.1.1,3.1.1.1')] ).
cnf(261,plain,
multiply(inverse(A),add(B,n1)) = add(inverse(A),inverse(A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[83,19]),19])]),
[iquote('para_into,83.1.1.1,18.1.1,demod,19,flip.1')] ).
cnf(269,plain,
add(multiply(A,inverse(B)),inverse(B)) = add(inverse(B),inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[83,19]),261]),
[iquote('para_into,83.1.1.2,18.1.1,demod,261')] ).
cnf(283,plain,
add(multiply(A,add(B,n1)),add(inverse(A),inverse(A))) = n1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),261]),
[iquote('back_demod,25,demod,261')] ).
cnf(380,plain,
add(add(inverse(A),inverse(A)),add(inverse(inverse(A)),inverse(inverse(A)))) = n1,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[261,24]),261,261,283]),
[iquote('para_from,260.1.1,24.1.1.1,demod,261,261,283')] ).
cnf(416,plain,
multiply(A,add(add(B,A),add(C,A))) = add(A,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[87,3])]),
[iquote('para_into,87.1.1.2,3.1.1,flip.1')] ).
cnf(467,plain,
multiply(b,add(a,add(A,b))) != b,
inference(para_from,[status(thm),theory(equality)],[91,1]),
[iquote('para_from,91.1.1,1.1.1')] ).
cnf(558,plain,
multiply(inverse(A),n1) = add(inverse(A),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[283,99]),269]),
[iquote('para_from,282.1.1,99.1.1.2,demod,269')] ).
cnf(567,plain,
add(inverse(n1),add(inverse(A),inverse(A))) = inverse(A),
inference(para_from,[status(thm),theory(equality)],[558,66]),
[iquote('para_from,557.1.1,65.1.1.2')] ).
cnf(569,plain,
add(inverse(n1),n1) = n1,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[558,75]),558,380]),
[iquote('para_from,557.1.1,75.1.1.2.1,demod,558,380')] ).
cnf(592,plain,
add(A,n1) = n1,
inference(para_into,[status(thm),theory(equality)],[569,81]),
[iquote('para_into,569.1.1,81.1.1')] ).
cnf(597,plain,
multiply(multiply(A,n1),multiply(n1,A)) = multiply(n1,A),
inference(para_from,[status(thm),theory(equality)],[592,103]),
[iquote('para_from,591.1.1,103.1.1.1.2')] ).
cnf(616,plain,
multiply(inverse(A),inverse(A)) = add(inverse(A),inverse(A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[567,99]),269]),
[iquote('para_from,567.1.1,99.1.1.2,demod,269')] ).
cnf(624,plain,
add(add(A,A),add(A,A)) = add(A,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[416,21]),416]),
[iquote('para_from,415.1.1,21.1.1.1,demod,416')] ).
cnf(625,plain,
multiply(A,add(A,A)) = add(A,A),
inference(para_from,[status(thm),theory(equality)],[624,416]),
[iquote('para_from,623.1.1,415.1.1.2')] ).
cnf(629,plain,
add(multiply(A,A),multiply(A,A)) = add(A,A),
inference(para_into,[status(thm),theory(equality)],[625,5]),
[iquote('para_into,625.1.1,5.1.1')] ).
cnf(636,plain,
add(inverse(A),inverse(A)) = inverse(A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[629,9]),616,624,16]),
[iquote('para_from,629.1.1,9.1.1.2,demod,616,624,16')] ).
cnf(650,plain,
multiply(inverse(A),n1) = inverse(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[558]),636]),
[iquote('back_demod,557,demod,636')] ).
cnf(658,plain,
add(inverse(A),multiply(B,n1)) = multiply(n1,add(inverse(A),B)),
inference(para_from,[status(thm),theory(equality)],[650,17]),
[iquote('para_from,649.1.1,17.1.1.1')] ).
cnf(704,plain,
multiply(n1,add(inverse(n1),A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[658,66])]),
[iquote('para_into,658.1.1,65.1.1,flip.1')] ).
cnf(717,plain,
multiply(add(inverse(n1),A),n1) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[704,79]),650,66]),
[iquote('para_into,703.1.1,79.1.1,demod,650,66')] ).
cnf(740,plain,
multiply(A,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[704,597]),717,704]),
[iquote('para_from,703.1.1,597.1.1.2,demod,717,704')] ).
cnf(745,plain,
add(add(inverse(n1),A),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[704,87]),592,717]),
[iquote('para_from,703.1.1,87.1.1.2,demod,592,717')] ).
cnf(811,plain,
multiply(b,add(a,b)) != b,
inference(para_from,[status(thm),theory(equality)],[745,467]),
[iquote('para_from,745.1.1,467.1.1.2.2')] ).
cnf(813,plain,
add(A,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[745,95]),740,740])]),
[iquote('para_from,745.1.1,95.1.1.2,demod,740,740,flip.1')] ).
cnf(818,plain,
multiply(A,add(B,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[813,21]),813,813])]),
[iquote('para_into,812.1.1,21.1.1,demod,813,813,flip.1')] ).
cnf(820,plain,
$false,
inference(binary,[status(thm)],[818,811]),
[iquote('binary,818.1,811.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : BOO024-1 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 01:55:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.75/1.96 ----- Otter 3.3f, August 2004 -----
% 1.75/1.96 The process was started by sandbox2 on n017.cluster.edu,
% 1.75/1.96 Wed Jul 27 01:55:33 2022
% 1.75/1.96 The command was "./otter". The process ID is 2637.
% 1.75/1.96
% 1.75/1.96 set(prolog_style_variables).
% 1.75/1.96 set(auto).
% 1.75/1.96 dependent: set(auto1).
% 1.75/1.96 dependent: set(process_input).
% 1.75/1.96 dependent: clear(print_kept).
% 1.75/1.96 dependent: clear(print_new_demod).
% 1.75/1.96 dependent: clear(print_back_demod).
% 1.75/1.96 dependent: clear(print_back_sub).
% 1.75/1.96 dependent: set(control_memory).
% 1.75/1.96 dependent: assign(max_mem, 12000).
% 1.75/1.96 dependent: assign(pick_given_ratio, 4).
% 1.75/1.96 dependent: assign(stats_level, 1).
% 1.75/1.96 dependent: assign(max_seconds, 10800).
% 1.75/1.96 clear(print_given).
% 1.75/1.96
% 1.75/1.96 list(usable).
% 1.75/1.96 0 [] A=A.
% 1.75/1.96 0 [] multiply(add(X,Y),Y)=Y.
% 1.75/1.96 0 [] multiply(X,add(Y,Z))=add(multiply(Y,X),multiply(Z,X)).
% 1.75/1.96 0 [] add(X,inverse(X))=n1.
% 1.75/1.96 0 [] pixley(X,Y,Z)=add(multiply(X,inverse(Y)),add(multiply(X,Z),multiply(inverse(Y),Z))).
% 1.75/1.96 0 [] pixley(X,X,Y)=Y.
% 1.75/1.96 0 [] pixley(X,Y,Y)=X.
% 1.75/1.96 0 [] pixley(X,Y,X)=X.
% 1.75/1.96 0 [] add(multiply(a,b),b)!=b.
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.75/1.96
% 1.75/1.96 All clauses are units, and equality is present; the
% 1.75/1.96 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.75/1.96
% 1.75/1.96 dependent: set(knuth_bendix).
% 1.75/1.96 dependent: set(anl_eq).
% 1.75/1.96 dependent: set(para_from).
% 1.75/1.96 dependent: set(para_into).
% 1.75/1.96 dependent: clear(para_from_right).
% 1.75/1.96 dependent: clear(para_into_right).
% 1.75/1.96 dependent: set(para_from_vars).
% 1.75/1.96 dependent: set(eq_units_both_ways).
% 1.75/1.96 dependent: set(dynamic_demod_all).
% 1.75/1.96 dependent: set(dynamic_demod).
% 1.75/1.96 dependent: set(order_eq).
% 1.75/1.96 dependent: set(back_demod).
% 1.75/1.96 dependent: set(lrpo).
% 1.75/1.96
% 1.75/1.96 ------------> process usable:
% 1.75/1.96 ** KEPT (pick-wt=7): 1 [] add(multiply(a,b),b)!=b.
% 1.75/1.96
% 1.75/1.96 ------------> process sos:
% 1.75/1.96 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.75/1.96 ** KEPT (pick-wt=7): 3 [] multiply(add(A,B),B)=B.
% 1.75/1.96 ---> New Demodulator: 4 [new_demod,3] multiply(add(A,B),B)=B.
% 1.75/1.96 ** KEPT (pick-wt=13): 5 [] multiply(A,add(B,C))=add(multiply(B,A),multiply(C,A)).
% 1.75/1.96 ** KEPT (pick-wt=6): 6 [] add(A,inverse(A))=n1.
% 1.75/1.96 ---> New Demodulator: 7 [new_demod,6] add(A,inverse(A))=n1.
% 1.75/1.96 ** KEPT (pick-wt=18): 9 [copy,8,flip.1] add(multiply(A,inverse(B)),add(multiply(A,C),multiply(inverse(B),C)))=pixley(A,B,C).
% 1.75/1.96 ---> New Demodulator: 10 [new_demod,9] add(multiply(A,inverse(B)),add(multiply(A,C),multiply(inverse(B),C)))=pixley(A,B,C).
% 1.75/1.96 ** KEPT (pick-wt=6): 11 [] pixley(A,A,B)=B.
% 1.75/1.96 ---> New Demodulator: 12 [new_demod,11] pixley(A,A,B)=B.
% 1.75/1.96 ** KEPT (pick-wt=6): 13 [] pixley(A,B,B)=A.
% 1.75/1.96 ---> New Demodulator: 14 [new_demod,13] pixley(A,B,B)=A.
% 1.75/1.96 ** KEPT (pick-wt=6): 15 [] pixley(A,B,A)=A.
% 1.75/1.96 ---> New Demodulator: 16 [new_demod,15] pixley(A,B,A)=A.
% 1.75/1.96 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.75/1.96 >>>> Starting back demodulation with 4.
% 1.75/1.96 ** KEPT (pick-wt=13): 17 [copy,5,flip.1] add(multiply(A,B),multiply(C,B))=multiply(B,add(A,C)).
% 1.75/1.96 >>>> Starting back demodulation with 7.
% 1.75/1.96 >>>> Starting back demodulation with 10.
% 1.75/1.96 >>>> Starting back demodulation with 12.
% 1.75/1.96 >>>> Starting back demodulation with 14.
% 1.75/1.96 >>>> Starting back demodulation with 16.
% 1.75/1.96 Following clause subsumed by 5 during input processing: 0 [copy,17,flip.1] multiply(A,add(B,C))=add(multiply(B,A),multiply(C,A)).
% 1.75/1.96
% 1.75/1.96 ======= end of input processing =======
% 1.75/1.96
% 1.75/1.96 =========== start of search ===========
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Resetting weight limit to 14.
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Resetting weight limit to 14.
% 1.75/1.96
% 1.75/1.96 sos_size=301
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Resetting weight limit to 13.
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Resetting weight limit to 13.
% 1.75/1.96
% 1.75/1.96 sos_size=144
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Resetting weight limit to 11.
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Resetting weight limit to 11.
% 1.75/1.96
% 1.75/1.96 sos_size=146
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Resetting weight limit to 9.
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Resetting weight limit to 9.
% 1.75/1.96
% 1.75/1.96 sos_size=162
% 1.75/1.96
% 1.75/1.96 -------- PROOF --------
% 1.75/1.96
% 1.75/1.96 ----> UNIT CONFLICT at 0.09 sec ----> 820 [binary,818.1,811.1] $F.
% 1.75/1.96
% 1.75/1.96 Length of proof is 46. Level of proof is 21.
% 1.75/1.96
% 1.75/1.96 ---------------- PROOF ----------------
% 1.75/1.96 % SZS status Unsatisfiable
% 1.75/1.96 % SZS output start Refutation
% See solution above
% 1.75/1.96 ------------ end of proof -------------
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Search stopped by max_proofs option.
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Search stopped by max_proofs option.
% 1.75/1.96
% 1.75/1.96 ============ end of search ============
% 1.75/1.96
% 1.75/1.96 -------------- statistics -------------
% 1.75/1.96 clauses given 140
% 1.75/1.96 clauses generated 4962
% 1.75/1.96 clauses kept 553
% 1.75/1.96 clauses forward subsumed 1988
% 1.75/1.96 clauses back subsumed 13
% 1.75/1.96 Kbytes malloced 5859
% 1.75/1.96
% 1.75/1.96 ----------- times (seconds) -----------
% 1.75/1.96 user CPU time 0.09 (0 hr, 0 min, 0 sec)
% 1.75/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.96 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.75/1.96
% 1.75/1.96 That finishes the proof of the theorem.
% 1.75/1.96
% 1.75/1.96 Process 2637 finished Wed Jul 27 01:55:34 2022
% 1.75/1.96 Otter interrupted
% 1.75/1.96 PROOF FOUND
%------------------------------------------------------------------------------