TSTP Solution File: RNG021-7 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG021-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 13:12:05 EDT 2022
% Result : Unsatisfiable 1.72s 1.94s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% 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 : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 57 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
associator(add(u,v),x,y) != add(associator(u,x,y),associator(v,x,y)),
file('RNG021-7.p',unknown),
[] ).
cnf(2,plain,
add(associator(u,x,y),associator(v,x,y)) != associator(add(u,v),x,y),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(5,axiom,
add(additive_identity,A) = A,
file('RNG021-7.p',unknown),
[] ).
cnf(14,axiom,
add(A,additive_inverse(A)) = additive_identity,
file('RNG021-7.p',unknown),
[] ).
cnf(17,axiom,
additive_inverse(additive_inverse(A)) = A,
file('RNG021-7.p',unknown),
[] ).
cnf(21,axiom,
multiply(add(A,B),C) = add(multiply(A,C),multiply(B,C)),
file('RNG021-7.p',unknown),
[] ).
cnf(22,axiom,
add(A,B) = add(B,A),
file('RNG021-7.p',unknown),
[] ).
cnf(23,axiom,
add(A,add(B,C)) = add(add(A,B),C),
file('RNG021-7.p',unknown),
[] ).
cnf(25,plain,
add(add(A,B),C) = add(A,add(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[23])]),
[iquote('copy,23,flip.1')] ).
cnf(30,axiom,
associator(A,B,C) = add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),
file('RNG021-7.p',unknown),
[] ).
cnf(31,plain,
add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))) = associator(A,B,C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[30])]),
[iquote('copy,30,flip.1')] ).
cnf(38,axiom,
multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)),
file('RNG021-7.p',unknown),
[] ).
cnf(40,plain,
additive_inverse(multiply(A,B)) = multiply(additive_inverse(A),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[38])]),
[iquote('copy,38,flip.1')] ).
cnf(49,plain,
add(multiply(multiply(A,B),C),multiply(additive_inverse(A),multiply(B,C))) = associator(A,B,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[31]),40]),
[iquote('back_demod,31,demod,40')] ).
cnf(123,plain,
add(A,add(B,C)) = add(B,add(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,22]),25]),
[iquote('para_into,24.1.1.1,22.1.1,demod,25')] ).
cnf(124,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)],[25,14]),5])]),
[iquote('para_into,24.1.1.1,14.1.1,demod,5,flip.1')] ).
cnf(136,plain,
add(additive_inverse(A),add(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[124,22]),25]),
[iquote('para_into,124.1.1,22.1.1,demod,25')] ).
cnf(152,plain,
add(additive_inverse(add(A,B)),A) = additive_inverse(B),
inference(para_into,[status(thm),theory(equality)],[136,136]),
[iquote('para_into,136.1.1.2,136.1.1')] ).
cnf(181,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)],[152,136])]),
[iquote('para_into,152.1.1.1.1,136.1.1,flip.1')] ).
cnf(364,plain,
add(multiply(multiply(A,B),C),add(multiply(multiply(D,B),C),add(multiply(additive_inverse(A),multiply(B,C)),multiply(additive_inverse(D),multiply(B,C))))) = associator(add(A,D),B,C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,21]),21,181,21,25]),
[iquote('para_into,49.1.1.1.1,20.1.1,demod,21,181,21,25')] ).
cnf(410,plain,
multiply(multiply(A,B),C) = add(multiply(A,multiply(B,C)),associator(A,B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[49,136]),40,17])]),
[iquote('para_from,49.1.1,136.1.1.2,demod,40,17,flip.1')] ).
cnf(412,plain,
add(multiply(A,multiply(B,C)),add(associator(A,B,C),add(multiply(additive_inverse(A),multiply(B,C)),D))) = add(associator(A,B,C),D),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[49,25]),410,25])]),
[iquote('para_from,49.1.1,24.1.1.1,demod,410,25,flip.1')] ).
cnf(418,plain,
add(multiply(A,multiply(B,C)),add(associator(A,B,C),add(D,multiply(additive_inverse(A),multiply(B,C))))) = add(D,associator(A,B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[49,123]),410,25])]),
[iquote('para_from,49.1.1,123.1.1.2,demod,410,25,flip.1')] ).
cnf(436,plain,
add(associator(A,B,C),associator(D,B,C)) = associator(add(A,D),B,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[364]),410,410,25,418,25,412]),
[iquote('back_demod,364,demod,410,410,25,418,25,412')] ).
cnf(438,plain,
$false,
inference(binary,[status(thm)],[436,2]),
[iquote('binary,436.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : RNG021-7 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n004.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 02:10:36 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.72/1.93 ----- Otter 3.3f, August 2004 -----
% 1.72/1.93 The process was started by sandbox on n004.cluster.edu,
% 1.72/1.93 Wed Jul 27 02:10:36 2022
% 1.72/1.93 The command was "./otter". The process ID is 17613.
% 1.72/1.93
% 1.72/1.93 set(prolog_style_variables).
% 1.72/1.93 set(auto).
% 1.72/1.93 dependent: set(auto1).
% 1.72/1.93 dependent: set(process_input).
% 1.72/1.93 dependent: clear(print_kept).
% 1.72/1.93 dependent: clear(print_new_demod).
% 1.72/1.93 dependent: clear(print_back_demod).
% 1.72/1.93 dependent: clear(print_back_sub).
% 1.72/1.93 dependent: set(control_memory).
% 1.72/1.93 dependent: assign(max_mem, 12000).
% 1.72/1.93 dependent: assign(pick_given_ratio, 4).
% 1.72/1.93 dependent: assign(stats_level, 1).
% 1.72/1.93 dependent: assign(max_seconds, 10800).
% 1.72/1.93 clear(print_given).
% 1.72/1.93
% 1.72/1.93 list(usable).
% 1.72/1.93 0 [] A=A.
% 1.72/1.93 0 [] add(additive_identity,X)=X.
% 1.72/1.93 0 [] add(X,additive_identity)=X.
% 1.72/1.93 0 [] multiply(additive_identity,X)=additive_identity.
% 1.72/1.93 0 [] multiply(X,additive_identity)=additive_identity.
% 1.72/1.93 0 [] add(additive_inverse(X),X)=additive_identity.
% 1.72/1.93 0 [] add(X,additive_inverse(X))=additive_identity.
% 1.72/1.93 0 [] additive_inverse(additive_inverse(X))=X.
% 1.72/1.93 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.72/1.93 0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.72/1.93 0 [] add(X,Y)=add(Y,X).
% 1.72/1.93 0 [] add(X,add(Y,Z))=add(add(X,Y),Z).
% 1.72/1.93 0 [] multiply(multiply(X,Y),Y)=multiply(X,multiply(Y,Y)).
% 1.72/1.93 0 [] multiply(multiply(X,X),Y)=multiply(X,multiply(X,Y)).
% 1.72/1.93 0 [] associator(X,Y,Z)=add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))).
% 1.72/1.93 0 [] commutator(X,Y)=add(multiply(Y,X),additive_inverse(multiply(X,Y))).
% 1.72/1.93 0 [] multiply(additive_inverse(X),additive_inverse(Y))=multiply(X,Y).
% 1.72/1.93 0 [] multiply(additive_inverse(X),Y)=additive_inverse(multiply(X,Y)).
% 1.72/1.93 0 [] multiply(X,additive_inverse(Y))=additive_inverse(multiply(X,Y)).
% 1.72/1.93 0 [] multiply(X,add(Y,additive_inverse(Z)))=add(multiply(X,Y),additive_inverse(multiply(X,Z))).
% 1.72/1.93 0 [] multiply(add(X,additive_inverse(Y)),Z)=add(multiply(X,Z),additive_inverse(multiply(Y,Z))).
% 1.72/1.93 0 [] multiply(additive_inverse(X),add(Y,Z))=add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))).
% 1.72/1.93 0 [] multiply(add(X,Y),additive_inverse(Z))=add(additive_inverse(multiply(X,Z)),additive_inverse(multiply(Y,Z))).
% 1.72/1.93 0 [] associator(add(u,v),x,y)!=add(associator(u,x,y),associator(v,x,y)).
% 1.72/1.93 end_of_list.
% 1.72/1.93
% 1.72/1.93 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.72/1.93
% 1.72/1.93 All clauses are units, and equality is present; the
% 1.72/1.93 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.72/1.93
% 1.72/1.93 dependent: set(knuth_bendix).
% 1.72/1.93 dependent: set(anl_eq).
% 1.72/1.93 dependent: set(para_from).
% 1.72/1.93 dependent: set(para_into).
% 1.72/1.93 dependent: clear(para_from_right).
% 1.72/1.93 dependent: clear(para_into_right).
% 1.72/1.93 dependent: set(para_from_vars).
% 1.72/1.93 dependent: set(eq_units_both_ways).
% 1.72/1.93 dependent: set(dynamic_demod_all).
% 1.72/1.93 dependent: set(dynamic_demod).
% 1.72/1.93 dependent: set(order_eq).
% 1.72/1.93 dependent: set(back_demod).
% 1.72/1.93 dependent: set(lrpo).
% 1.72/1.93
% 1.72/1.93 ------------> process usable:
% 1.72/1.93 ** KEPT (pick-wt=16): 2 [copy,1,flip.1] add(associator(u,x,y),associator(v,x,y))!=associator(add(u,v),x,y).
% 1.72/1.93
% 1.72/1.93 ------------> process sos:
% 1.72/1.93 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.72/1.93 ** KEPT (pick-wt=5): 4 [] add(additive_identity,A)=A.
% 1.72/1.93 ---> New Demodulator: 5 [new_demod,4] add(additive_identity,A)=A.
% 1.72/1.93 ** KEPT (pick-wt=5): 6 [] add(A,additive_identity)=A.
% 1.72/1.93 ---> New Demodulator: 7 [new_demod,6] add(A,additive_identity)=A.
% 1.72/1.93 ** KEPT (pick-wt=5): 8 [] multiply(additive_identity,A)=additive_identity.
% 1.72/1.93 ---> New Demodulator: 9 [new_demod,8] multiply(additive_identity,A)=additive_identity.
% 1.72/1.93 ** KEPT (pick-wt=5): 10 [] multiply(A,additive_identity)=additive_identity.
% 1.72/1.93 ---> New Demodulator: 11 [new_demod,10] multiply(A,additive_identity)=additive_identity.
% 1.72/1.93 ** KEPT (pick-wt=6): 12 [] add(additive_inverse(A),A)=additive_identity.
% 1.72/1.93 ---> New Demodulator: 13 [new_demod,12] add(additive_inverse(A),A)=additive_identity.
% 1.72/1.93 ** KEPT (pick-wt=6): 14 [] add(A,additive_inverse(A))=additive_identity.
% 1.72/1.93 ---> New Demodulator: 15 [new_demod,14] add(A,additive_inverse(A))=additive_identity.
% 1.72/1.93 ** KEPT (pick-wt=5): 16 [] additive_inverse(additive_inverse(A))=A.
% 1.72/1.93 ---> New Demodulator: 17 [new_demod,16] additive_inverse(additive_inverse(A))=A.
% 1.72/1.93 ** KEPT (pick-wt=13): 18 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.72/1.93 ---> New Demodulator: 19 [new_demod,18] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.72/1.93 ** KEPT (pick-wt=13): 20 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.72/1.93 ---> New Demodulator: 21 [new_demod,20] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.72/1.93 ** KEPT (pick-wt=7): 22 [] add(A,B)=add(B,A).
% 1.72/1.93 ** KEPT (pick-wt=11): 24 [copy,23,flip.1] add(add(A,B),C)=add(A,add(B,C)).
% 1.72/1.93 ---> New Demodulator: 25 [new_demod,24] add(add(A,B),C)=add(A,add(B,C)).
% 1.72/1.93 ** KEPT (pick-wt=11): 26 [] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.72/1.93 ---> New Demodulator: 27 [new_demod,26] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.72/1.93 ** KEPT (pick-wt=11): 28 [] multiply(multiply(A,A),B)=multiply(A,multiply(A,B)).
% 1.72/1.93 ---> New Demodulator: 29 [new_demod,28] multiply(multiply(A,A),B)=multiply(A,multiply(A,B)).
% 1.72/1.93 ** KEPT (pick-wt=17): 31 [copy,30,flip.1] add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C))))=associator(A,B,C).
% 1.72/1.93 ---> New Demodulator: 32 [new_demod,31] add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C))))=associator(A,B,C).
% 1.72/1.93 ** KEPT (pick-wt=12): 34 [copy,33,flip.1] add(multiply(A,B),additive_inverse(multiply(B,A)))=commutator(B,A).
% 1.72/1.93 ---> New Demodulator: 35 [new_demod,34] add(multiply(A,B),additive_inverse(multiply(B,A)))=commutator(B,A).
% 1.72/1.93 ** KEPT (pick-wt=9): 36 [] multiply(additive_inverse(A),additive_inverse(B))=multiply(A,B).
% 1.72/1.93 ---> New Demodulator: 37 [new_demod,36] multiply(additive_inverse(A),additive_inverse(B))=multiply(A,B).
% 1.72/1.93 ** KEPT (pick-wt=9): 39 [copy,38,flip.1] additive_inverse(multiply(A,B))=multiply(additive_inverse(A),B).
% 1.72/1.93 ---> New Demodulator: 40 [new_demod,39] additive_inverse(multiply(A,B))=multiply(additive_inverse(A),B).
% 1.72/1.93 ** KEPT (pick-wt=9): 42 [copy,41,demod,40] multiply(A,additive_inverse(B))=multiply(additive_inverse(A),B).
% 1.72/1.93 ** KEPT (pick-wt=17): 44 [copy,43,demod,19,40] add(multiply(A,B),multiply(A,additive_inverse(C)))=add(multiply(A,B),multiply(additive_inverse(A),C)).
% 1.72/1.93 Following clause subsumed by 3 during input processing: 0 [demod,21,40] add(multiply(A,C),multiply(additive_inverse(B),C))=add(multiply(A,C),multiply(additive_inverse(B),C)).
% 1.72/1.93 Following clause subsumed by 3 during input processing: 0 [demod,19,40,40] add(multiply(additive_inverse(A),B),multiply(additive_inverse(A),C))=add(multiply(additive_inverse(A),B),multiply(additive_inverse(A),C)).
% 1.72/1.93 ** KEPT (pick-wt=19): 46 [copy,45,demod,21,40,40] add(multiply(A,additive_inverse(B)),multiply(C,additive_inverse(B)))=add(multiply(additive_inverse(A),B),multiply(additive_inverse(C),B)).
% 1.72/1.93 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.72/1.93 >>>> Starting back demodulation with 5.
% 1.72/1.93 >>>> Starting back demodulation with 7.
% 1.72/1.93 >>>> Starting back demodulation with 9.
% 1.72/1.93 >>>> Starting back demodulation with 11.
% 1.72/1.93 >>>> Starting back demodulation with 13.
% 1.72/1.93 >>>> Starting back demodulation with 15.
% 1.72/1.93 >>>> Starting back demodulation with 17.
% 1.72/1.93 >>>> Starting back demodulation with 19.
% 1.72/1.93 >>>> Starting back demodulation with 21.
% 1.72/1.93 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] add(A,B)=add(B,A).
% 1.72/1.93 >>>> Starting back demodulation with 25.
% 1.72/1.93 >>>> Starting back demodulation with 27.
% 1.72/1.93 >>>> Starting back demodulation with 29.
% 1.72/1.93 >>>> Starting back demodulation with 32.
% 1.72/1.93 >>>> Starting back demodulation with 35.
% 1.72/1.93 >>>> Starting back demodulation with 37.
% 1.72/1.93 >>>> Starting back demodulation with 40.
% 1.72/1.93 >> back demodulating 34 with 40.
% 1.72/1.93 >> back demodulating 31 with 40.
% 1.72/1.93 ** KEPT (pick-wt=9): 51 [copy,42,flip.1] multiply(additive_inverse(A),B)=multiply(A,additive_inverse(B)).
% 1.72/1.93 ** KEPT (pick-wt=17): 52 [copy,44,flip.1] add(multiply(A,B),multiply(additive_inverse(A),C))=add(multiply(A,B),multiply(A,additive_inverse(C))).
% 1.72/1.93 ** KEPT (pick-wt=19): 53 [copy,46,flip.1] add(multiply(additive_inverse(A),B),multiply(additive_inverse(C),B))=add(multiply(A,additive_inverse(B)),multiply(C,additive_inverse(B))).
% 1.72/1.93 >>>> Starting back demodulation with 48.
% 1.72/1.93 >>>> Starting back demodulation with 50.
% 1.72/1.93 Following clause subsumed by 42 during input processing: 0 [copy,51,flip.1] multiply(A,additive_inverse(B))=multiply(additive_inverse(A),B).
% 1.72/1.94 Following clause subsumed by 44 during input processing: 0 [copy,52,flip.1] add(multiply(A,B),multiply(A,additive_inverse(C)))=add(multiply(A,B),multiply(additive_inverse(A),C)).
% 1.72/1.94 Following clause subsumed by 46 during input processing: 0 [copy,53,flip.1] add(multiply(A,additive_inverse(B)),multiply(C,additive_inverse(B)))=add(multiply(additive_inverse(A),B),multiply(additive_inverse(C),B)).
% 1.72/1.94
% 1.72/1.94 ======= end of input processing =======
% 1.72/1.94
% 1.72/1.94 =========== start of search ===========
% 1.72/1.94
% 1.72/1.94 -------- PROOF --------
% 1.72/1.94
% 1.72/1.94 ----> UNIT CONFLICT at 0.02 sec ----> 438 [binary,436.1,2.1] $F.
% 1.72/1.94
% 1.72/1.94 Length of proof is 15. Level of proof is 7.
% 1.72/1.94
% 1.72/1.94 ---------------- PROOF ----------------
% 1.72/1.94 % SZS status Unsatisfiable
% 1.72/1.94 % SZS output start Refutation
% See solution above
% 1.72/1.94 ------------ end of proof -------------
% 1.72/1.94
% 1.72/1.94
% 1.72/1.94 Search stopped by max_proofs option.
% 1.72/1.94
% 1.72/1.94
% 1.72/1.94 Search stopped by max_proofs option.
% 1.72/1.94
% 1.72/1.94 ============ end of search ============
% 1.72/1.94
% 1.72/1.94 -------------- statistics -------------
% 1.72/1.94 clauses given 41
% 1.72/1.94 clauses generated 836
% 1.72/1.94 clauses kept 291
% 1.72/1.94 clauses forward subsumed 772
% 1.72/1.94 clauses back subsumed 2
% 1.72/1.94 Kbytes malloced 2929
% 1.72/1.94
% 1.72/1.94 ----------- times (seconds) -----------
% 1.72/1.94 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.72/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.72/1.94
% 1.72/1.94 That finishes the proof of the theorem.
% 1.72/1.94
% 1.72/1.94 Process 17613 finished Wed Jul 27 02:10:37 2022
% 1.72/1.94 Otter interrupted
% 1.72/1.94 PROOF FOUND
%------------------------------------------------------------------------------