TSTP Solution File: RNG008-7 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG008-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:12:02 EDT 2022
% Result : Unsatisfiable 1.74s 1.92s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 6 RR)
% Number of literals : 49 ( 48 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 83 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(b,a) != c,
file('RNG008-7.p',unknown),
[] ).
cnf(4,axiom,
add(additive_identity,A) = A,
file('RNG008-7.p',unknown),
[] ).
cnf(6,axiom,
add(A,additive_identity) = A,
file('RNG008-7.p',unknown),
[] ).
cnf(8,axiom,
add(additive_inverse(A),A) = additive_identity,
file('RNG008-7.p',unknown),
[] ).
cnf(9,axiom,
add(A,additive_inverse(A)) = additive_identity,
file('RNG008-7.p',unknown),
[] ).
cnf(11,axiom,
add(A,add(B,C)) = add(add(A,B),C),
file('RNG008-7.p',unknown),
[] ).
cnf(13,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(14,axiom,
add(A,B) = add(B,A),
file('RNG008-7.p',unknown),
[] ).
cnf(15,axiom,
multiply(A,multiply(B,C)) = multiply(multiply(A,B),C),
file('RNG008-7.p',unknown),
[] ).
cnf(17,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(19,axiom,
multiply(A,add(B,C)) = add(multiply(A,B),multiply(A,C)),
file('RNG008-7.p',unknown),
[] ).
cnf(21,axiom,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
file('RNG008-7.p',unknown),
[] ).
cnf(23,axiom,
multiply(A,A) = A,
file('RNG008-7.p',unknown),
[] ).
cnf(24,axiom,
multiply(a,b) = c,
file('RNG008-7.p',unknown),
[] ).
cnf(30,plain,
add(A,add(additive_inverse(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,9]),4])]),
[iquote('para_into,12.1.1.1,9.1.1,demod,4,flip.1')] ).
cnf(31,plain,
add(additive_inverse(A),add(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,8]),4])]),
[iquote('para_into,12.1.1.1,7.1.1,demod,4,flip.1')] ).
cnf(33,plain,
add(A,add(B,C)) = add(B,add(C,A)),
inference(para_into,[status(thm),theory(equality)],[13,14]),
[iquote('para_into,12.1.1,14.1.1')] ).
cnf(38,plain,
multiply(c,A) = multiply(a,multiply(b,A)),
inference(para_into,[status(thm),theory(equality)],[17,24]),
[iquote('para_into,16.1.1.1,24.1.1')] ).
cnf(42,plain,
multiply(A,multiply(B,multiply(A,B))) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,23])]),
[iquote('para_into,16.1.1,22.1.1,flip.1')] ).
cnf(45,plain,
add(A,add(B,additive_inverse(A))) = B,
inference(para_into,[status(thm),theory(equality)],[30,14]),
[iquote('para_into,29.1.1.2,14.1.1')] ).
cnf(48,plain,
additive_inverse(additive_inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[30,9]),6])]),
[iquote('para_into,29.1.1.2,9.1.1,demod,6,flip.1')] ).
cnf(49,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[30,14]),13]),
[iquote('para_into,29.1.1,14.1.1,demod,13')] ).
cnf(55,plain,
add(A,add(B,add(C,additive_inverse(A)))) = add(B,C),
inference(para_into,[status(thm),theory(equality)],[45,13]),
[iquote('para_into,45.1.1.2,12.1.1')] ).
cnf(69,plain,
add(multiply(A,additive_inverse(B)),multiply(A,B)) = multiply(A,additive_identity),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,8])]),
[iquote('para_into,18.1.1.2,7.1.1,flip.1')] ).
cnf(71,plain,
add(multiply(A,B),multiply(A,additive_identity)) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,6])]),
[iquote('para_into,18.1.1.2,5.1.1,flip.1')] ).
cnf(75,plain,
add(A,add(multiply(B,A),add(multiply(A,B),B))) = add(A,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,23]),21,23,21,23,13])]),
[iquote('para_into,18.1.1,22.1.1,demod,21,23,21,23,13,flip.1')] ).
cnf(77,plain,
add(additive_inverse(add(A,B)),A) = additive_inverse(B),
inference(para_into,[status(thm),theory(equality)],[49,49]),
[iquote('para_into,49.1.1.2,49.1.1')] ).
cnf(81,plain,
add(additive_inverse(A),add(B,add(C,A))) = add(B,C),
inference(para_into,[status(thm),theory(equality)],[49,13]),
[iquote('para_into,49.1.1.2,12.1.1')] ).
cnf(83,plain,
add(additive_inverse(A),add(B,add(A,C))) = add(B,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[49,13]),13])]),
[iquote('para_from,49.1.1,12.1.1.1,demod,13,flip.1')] ).
cnf(87,plain,
multiply(a,multiply(b,c)) = c,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[38,23])]),
[iquote('para_into,37.1.1,22.1.1,flip.1')] ).
cnf(105,plain,
add(multiply(additive_inverse(A),B),multiply(A,B)) = multiply(additive_identity,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[21,8])]),
[iquote('para_into,20.1.1.1,7.1.1,flip.1')] ).
cnf(122,plain,
additive_inverse(add(A,B)) = add(additive_inverse(A),additive_inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[77,49])]),
[iquote('para_into,77.1.1.1.1,49.1.1,flip.1')] ).
cnf(166,plain,
multiply(A,additive_identity) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[71,31]),8])]),
[iquote('para_from,71.1.1,31.1.1.2,demod,8,flip.1')] ).
cnf(169,plain,
add(multiply(A,additive_inverse(B)),multiply(A,B)) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[69]),166]),
[iquote('back_demod,69,demod,166')] ).
cnf(178,plain,
add(A,add(B,add(C,add(D,additive_inverse(A))))) = add(B,add(C,D)),
inference(para_into,[status(thm),theory(equality)],[55,13]),
[iquote('para_into,55.1.1.2.2,12.1.1')] ).
cnf(205,plain,
add(multiply(A,additive_inverse(A)),A) = additive_identity,
inference(para_into,[status(thm),theory(equality)],[169,23]),
[iquote('para_into,169.1.1.2,22.1.1')] ).
cnf(273,plain,
multiply(A,additive_inverse(A)) = additive_inverse(A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[205,49]),6])]),
[iquote('para_from,205.1.1,49.1.1.2,demod,6,flip.1')] ).
cnf(274,plain,
multiply(additive_inverse(A),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[205,45]),6,48])]),
[iquote('para_from,205.1.1,45.1.1.2,demod,6,48,flip.1')] ).
cnf(278,plain,
add(multiply(A,additive_inverse(B)),multiply(B,additive_inverse(A))) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[205,33]),122,19,21,273,21,273,13,178,30])]),
[iquote('para_from,205.1.1,33.1.1,demod,122,19,21,273,21,273,13,178,30,flip.1')] ).
cnf(354,plain,
add(multiply(additive_identity,A),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[75,166]),4,4,4]),
[iquote('para_into,75.1.1.2.1,165.1.1,demod,4,4,4')] ).
cnf(435,plain,
multiply(additive_identity,A) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[354,49]),8])]),
[iquote('para_from,354.1.1,49.1.1.2,demod,8,flip.1')] ).
cnf(440,plain,
add(multiply(additive_inverse(A),B),multiply(A,B)) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[105]),435]),
[iquote('back_demod,105,demod,435')] ).
cnf(500,plain,
add(A,A) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[440,274]),23]),
[iquote('para_into,440.1.1.1,274.1.1,demod,23')] ).
cnf(539,plain,
additive_inverse(A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[500,83]),6,13,500,6]),
[iquote('para_from,499.1.1,83.1.1.2,demod,6,13,500,6')] ).
cnf(540,plain,
add(A,add(B,A)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[500,81]),539,6,13])]),
[iquote('para_from,499.1.1,81.1.1.2,demod,539,6,13,flip.1')] ).
cnf(562,plain,
add(multiply(A,B),multiply(B,A)) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[278]),539,539]),
[iquote('back_demod,278,demod,539,539')] ).
cnf(588,plain,
add(c,multiply(b,a)) = additive_identity,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[562,87]),17,38,42]),
[iquote('para_into,562.1.1.1,87.1.1,demod,17,38,42')] ).
cnf(621,plain,
multiply(b,a) = c,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[588,540]),6]),
[iquote('para_from,588.1.1,540.1.1.2,demod,6')] ).
cnf(623,plain,
$false,
inference(binary,[status(thm)],[621,1]),
[iquote('binary,621.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG008-7 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 02:13:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.74/1.92 ----- Otter 3.3f, August 2004 -----
% 1.74/1.92 The process was started by sandbox2 on n018.cluster.edu,
% 1.74/1.92 Wed Jul 27 02:13:16 2022
% 1.74/1.92 The command was "./otter". The process ID is 28123.
% 1.74/1.92
% 1.74/1.92 set(prolog_style_variables).
% 1.74/1.92 set(auto).
% 1.74/1.92 dependent: set(auto1).
% 1.74/1.92 dependent: set(process_input).
% 1.74/1.92 dependent: clear(print_kept).
% 1.74/1.92 dependent: clear(print_new_demod).
% 1.74/1.92 dependent: clear(print_back_demod).
% 1.74/1.92 dependent: clear(print_back_sub).
% 1.74/1.92 dependent: set(control_memory).
% 1.74/1.92 dependent: assign(max_mem, 12000).
% 1.74/1.92 dependent: assign(pick_given_ratio, 4).
% 1.74/1.92 dependent: assign(stats_level, 1).
% 1.74/1.92 dependent: assign(max_seconds, 10800).
% 1.74/1.92 clear(print_given).
% 1.74/1.92
% 1.74/1.92 list(usable).
% 1.74/1.92 0 [] A=A.
% 1.74/1.92 0 [] add(additive_identity,X)=X.
% 1.74/1.92 0 [] add(X,additive_identity)=X.
% 1.74/1.92 0 [] add(additive_inverse(X),X)=additive_identity.
% 1.74/1.92 0 [] add(X,additive_inverse(X))=additive_identity.
% 1.74/1.92 0 [] add(X,add(Y,Z))=add(add(X,Y),Z).
% 1.74/1.92 0 [] add(X,Y)=add(Y,X).
% 1.74/1.92 0 [] multiply(X,multiply(Y,Z))=multiply(multiply(X,Y),Z).
% 1.74/1.92 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.74/1.92 0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.74/1.92 0 [] multiply(X,X)=X.
% 1.74/1.92 0 [] multiply(a,b)=c.
% 1.74/1.92 0 [] multiply(b,a)!=c.
% 1.74/1.92 end_of_list.
% 1.74/1.92
% 1.74/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.74/1.92
% 1.74/1.92 All clauses are units, and equality is present; the
% 1.74/1.92 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.74/1.92
% 1.74/1.92 dependent: set(knuth_bendix).
% 1.74/1.92 dependent: set(anl_eq).
% 1.74/1.92 dependent: set(para_from).
% 1.74/1.92 dependent: set(para_into).
% 1.74/1.92 dependent: clear(para_from_right).
% 1.74/1.92 dependent: clear(para_into_right).
% 1.74/1.92 dependent: set(para_from_vars).
% 1.74/1.92 dependent: set(eq_units_both_ways).
% 1.74/1.92 dependent: set(dynamic_demod_all).
% 1.74/1.92 dependent: set(dynamic_demod).
% 1.74/1.92 dependent: set(order_eq).
% 1.74/1.92 dependent: set(back_demod).
% 1.74/1.92 dependent: set(lrpo).
% 1.74/1.92
% 1.74/1.92 ------------> process usable:
% 1.74/1.92 ** KEPT (pick-wt=5): 1 [] multiply(b,a)!=c.
% 1.74/1.92
% 1.74/1.92 ------------> process sos:
% 1.74/1.92 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.74/1.92 ** KEPT (pick-wt=5): 3 [] add(additive_identity,A)=A.
% 1.74/1.92 ---> New Demodulator: 4 [new_demod,3] add(additive_identity,A)=A.
% 1.74/1.92 ** KEPT (pick-wt=5): 5 [] add(A,additive_identity)=A.
% 1.74/1.92 ---> New Demodulator: 6 [new_demod,5] add(A,additive_identity)=A.
% 1.74/1.92 ** KEPT (pick-wt=6): 7 [] add(additive_inverse(A),A)=additive_identity.
% 1.74/1.92 ---> New Demodulator: 8 [new_demod,7] add(additive_inverse(A),A)=additive_identity.
% 1.74/1.92 ** KEPT (pick-wt=6): 9 [] add(A,additive_inverse(A))=additive_identity.
% 1.74/1.92 ---> New Demodulator: 10 [new_demod,9] add(A,additive_inverse(A))=additive_identity.
% 1.74/1.92 ** KEPT (pick-wt=11): 12 [copy,11,flip.1] add(add(A,B),C)=add(A,add(B,C)).
% 1.74/1.92 ---> New Demodulator: 13 [new_demod,12] add(add(A,B),C)=add(A,add(B,C)).
% 1.74/1.92 ** KEPT (pick-wt=7): 14 [] add(A,B)=add(B,A).
% 1.74/1.92 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.74/1.92 ---> New Demodulator: 17 [new_demod,16] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.74/1.92 ** KEPT (pick-wt=13): 18 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.74/1.92 ---> New Demodulator: 19 [new_demod,18] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.74/1.92 ** KEPT (pick-wt=13): 20 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.74/1.92 ---> New Demodulator: 21 [new_demod,20] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.74/1.92 ** KEPT (pick-wt=5): 22 [] multiply(A,A)=A.
% 1.74/1.92 ---> New Demodulator: 23 [new_demod,22] multiply(A,A)=A.
% 1.74/1.92 ** KEPT (pick-wt=5): 24 [] multiply(a,b)=c.
% 1.74/1.92 ---> New Demodulator: 25 [new_demod,24] multiply(a,b)=c.
% 1.74/1.92 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.74/1.92 >>>> Starting back demodulation with 4.
% 1.74/1.92 >>>> Starting back demodulation with 6.
% 1.74/1.92 >>>> Starting back demodulation with 8.
% 1.74/1.92 >>>> Starting back demodulation with 10.
% 1.74/1.92 >>>> Starting back demodulation with 13.
% 1.74/1.92 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] add(A,B)=add(B,A).
% 1.74/1.92 >>>> Starting back demodulation with 17.
% 1.74/1.92 >>>> Starting back demodulation with 19.
% 1.74/1.92 >>>> Starting back demodulation with 21.
% 1.74/1.92 >>>> Starting back demodulation with 23.
% 1.74/1.92 >>>> Starting back demodulation with 25.
% 1.74/1.92
% 1.74/1.92 ======= end of input processing =======
% 1.74/1.92
% 1.74/1.92 =========== start of search ===========
% 1.74/1.92
% 1.74/1.92 -------- PROOF --------
% 1.74/1.92
% 1.74/1.92 ----> UNIT CONFLICT at 0.03 sec ----> 623 [binary,621.1,1.1] $F.
% 1.74/1.92
% 1.74/1.92 Length of proof is 36. Level of proof is 11.
% 1.74/1.92
% 1.74/1.92 ---------------- PROOF ----------------
% 1.74/1.92 % SZS status Unsatisfiable
% 1.74/1.92 % SZS output start Refutation
% See solution above
% 1.74/1.92 ------------ end of proof -------------
% 1.74/1.92
% 1.74/1.92
% 1.74/1.92 Search stopped by max_proofs option.
% 1.74/1.92
% 1.74/1.92
% 1.74/1.92 Search stopped by max_proofs option.
% 1.74/1.92
% 1.74/1.92 ============ end of search ============
% 1.74/1.92
% 1.74/1.92 -------------- statistics -------------
% 1.74/1.92 clauses given 65
% 1.74/1.92 clauses generated 1562
% 1.74/1.92 clauses kept 326
% 1.74/1.92 clauses forward subsumed 1510
% 1.74/1.92 clauses back subsumed 0
% 1.74/1.92 Kbytes malloced 2929
% 1.74/1.92
% 1.74/1.92 ----------- times (seconds) -----------
% 1.74/1.92 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.74/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.92
% 1.74/1.92 That finishes the proof of the theorem.
% 1.74/1.92
% 1.74/1.92 Process 28123 finished Wed Jul 27 02:13:17 2022
% 1.74/1.92 Otter interrupted
% 1.74/1.92 PROOF FOUND
%------------------------------------------------------------------------------