TSTP Solution File: RNG024-7 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG024-7 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 13:12:06 EDT 2022
% Result : Unsatisfiable 1.75s 1.97s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 2 RR)
% Number of literals : 11 ( 10 equ; 1 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 : 20 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
associator(x,y,y) != additive_identity,
file('RNG024-7.p',unknown),
[] ).
cnf(13,axiom,
add(A,additive_inverse(A)) = additive_identity,
file('RNG024-7.p',unknown),
[] ).
cnf(25,axiom,
multiply(multiply(A,B),B) = multiply(A,multiply(B,B)),
file('RNG024-7.p',unknown),
[] ).
cnf(29,axiom,
associator(A,B,C) = add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C)))),
file('RNG024-7.p',unknown),
[] ).
cnf(30,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)],[29])]),
[iquote('copy,29,flip.1')] ).
cnf(37,axiom,
multiply(additive_inverse(A),B) = additive_inverse(multiply(A,B)),
file('RNG024-7.p',unknown),
[] ).
cnf(39,plain,
additive_inverse(multiply(A,B)) = multiply(additive_inverse(A),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[37])]),
[iquote('copy,37,flip.1')] ).
cnf(48,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)],[30]),39]),
[iquote('back_demod,30,demod,39')] ).
cnf(66,plain,
add(multiply(A,B),multiply(additive_inverse(A),B)) = additive_identity,
inference(para_from,[status(thm),theory(equality)],[39,13]),
[iquote('para_from,38.1.1,13.1.1.2')] ).
cnf(374,plain,
associator(A,B,B) = additive_identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[48,25]),66])]),
[iquote('para_into,48.1.1.1,25.1.1,demod,66,flip.1')] ).
cnf(376,plain,
$false,
inference(binary,[status(thm)],[374,1]),
[iquote('binary,374.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG024-7 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n009.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
% 0.13/0.34 % DateTime : Wed Jul 27 02:10:21 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.75/1.96 ----- Otter 3.3f, August 2004 -----
% 1.75/1.96 The process was started by sandbox2 on n009.cluster.edu,
% 1.75/1.96 Wed Jul 27 02:10:21 2022
% 1.75/1.96 The command was "./otter". The process ID is 6344.
% 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 [] add(additive_identity,X)=X.
% 1.75/1.96 0 [] add(X,additive_identity)=X.
% 1.75/1.96 0 [] multiply(additive_identity,X)=additive_identity.
% 1.75/1.96 0 [] multiply(X,additive_identity)=additive_identity.
% 1.75/1.96 0 [] add(additive_inverse(X),X)=additive_identity.
% 1.75/1.96 0 [] add(X,additive_inverse(X))=additive_identity.
% 1.75/1.96 0 [] additive_inverse(additive_inverse(X))=X.
% 1.75/1.96 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.75/1.96 0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.75/1.96 0 [] add(X,Y)=add(Y,X).
% 1.75/1.96 0 [] add(X,add(Y,Z))=add(add(X,Y),Z).
% 1.75/1.96 0 [] multiply(multiply(X,Y),Y)=multiply(X,multiply(Y,Y)).
% 1.75/1.96 0 [] multiply(multiply(X,X),Y)=multiply(X,multiply(X,Y)).
% 1.75/1.96 0 [] associator(X,Y,Z)=add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))).
% 1.75/1.96 0 [] commutator(X,Y)=add(multiply(Y,X),additive_inverse(multiply(X,Y))).
% 1.75/1.96 0 [] multiply(additive_inverse(X),additive_inverse(Y))=multiply(X,Y).
% 1.75/1.96 0 [] multiply(additive_inverse(X),Y)=additive_inverse(multiply(X,Y)).
% 1.75/1.96 0 [] multiply(X,additive_inverse(Y))=additive_inverse(multiply(X,Y)).
% 1.75/1.96 0 [] multiply(X,add(Y,additive_inverse(Z)))=add(multiply(X,Y),additive_inverse(multiply(X,Z))).
% 1.75/1.96 0 [] multiply(add(X,additive_inverse(Y)),Z)=add(multiply(X,Z),additive_inverse(multiply(Y,Z))).
% 1.75/1.96 0 [] multiply(additive_inverse(X),add(Y,Z))=add(additive_inverse(multiply(X,Y)),additive_inverse(multiply(X,Z))).
% 1.75/1.96 0 [] multiply(add(X,Y),additive_inverse(Z))=add(additive_inverse(multiply(X,Z)),additive_inverse(multiply(Y,Z))).
% 1.75/1.96 0 [] associator(x,y,y)!=additive_identity.
% 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=6): 1 [] associator(x,y,y)!=additive_identity.
% 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=5): 3 [] add(additive_identity,A)=A.
% 1.75/1.96 ---> New Demodulator: 4 [new_demod,3] add(additive_identity,A)=A.
% 1.75/1.96 ** KEPT (pick-wt=5): 5 [] add(A,additive_identity)=A.
% 1.75/1.96 ---> New Demodulator: 6 [new_demod,5] add(A,additive_identity)=A.
% 1.75/1.96 ** KEPT (pick-wt=5): 7 [] multiply(additive_identity,A)=additive_identity.
% 1.75/1.96 ---> New Demodulator: 8 [new_demod,7] multiply(additive_identity,A)=additive_identity.
% 1.75/1.96 ** KEPT (pick-wt=5): 9 [] multiply(A,additive_identity)=additive_identity.
% 1.75/1.96 ---> New Demodulator: 10 [new_demod,9] multiply(A,additive_identity)=additive_identity.
% 1.75/1.96 ** KEPT (pick-wt=6): 11 [] add(additive_inverse(A),A)=additive_identity.
% 1.75/1.96 ---> New Demodulator: 12 [new_demod,11] add(additive_inverse(A),A)=additive_identity.
% 1.75/1.96 ** KEPT (pick-wt=6): 13 [] add(A,additive_inverse(A))=additive_identity.
% 1.75/1.96 ---> New Demodulator: 14 [new_demod,13] add(A,additive_inverse(A))=additive_identity.
% 1.75/1.96 ** KEPT (pick-wt=5): 15 [] additive_inverse(additive_inverse(A))=A.
% 1.75/1.96 ---> New Demodulator: 16 [new_demod,15] additive_inverse(additive_inverse(A))=A.
% 1.75/1.96 ** KEPT (pick-wt=13): 17 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.75/1.96 ---> New Demodulator: 18 [new_demod,17] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.75/1.96 ** KEPT (pick-wt=13): 19 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.75/1.96 ---> New Demodulator: 20 [new_demod,19] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.75/1.96 ** KEPT (pick-wt=7): 21 [] add(A,B)=add(B,A).
% 1.75/1.96 ** KEPT (pick-wt=11): 23 [copy,22,flip.1] add(add(A,B),C)=add(A,add(B,C)).
% 1.75/1.96 ---> New Demodulator: 24 [new_demod,23] add(add(A,B),C)=add(A,add(B,C)).
% 1.75/1.96 ** KEPT (pick-wt=11): 25 [] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.75/1.96 ---> New Demodulator: 26 [new_demod,25] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.75/1.96 ** KEPT (pick-wt=11): 27 [] multiply(multiply(A,A),B)=multiply(A,multiply(A,B)).
% 1.75/1.96 ---> New Demodulator: 28 [new_demod,27] multiply(multiply(A,A),B)=multiply(A,multiply(A,B)).
% 1.75/1.96 ** KEPT (pick-wt=17): 30 [copy,29,flip.1] add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C))))=associator(A,B,C).
% 1.75/1.96 ---> New Demodulator: 31 [new_demod,30] add(multiply(multiply(A,B),C),additive_inverse(multiply(A,multiply(B,C))))=associator(A,B,C).
% 1.75/1.96 ** KEPT (pick-wt=12): 33 [copy,32,flip.1] add(multiply(A,B),additive_inverse(multiply(B,A)))=commutator(B,A).
% 1.75/1.96 ---> New Demodulator: 34 [new_demod,33] add(multiply(A,B),additive_inverse(multiply(B,A)))=commutator(B,A).
% 1.75/1.96 ** KEPT (pick-wt=9): 35 [] multiply(additive_inverse(A),additive_inverse(B))=multiply(A,B).
% 1.75/1.96 ---> New Demodulator: 36 [new_demod,35] multiply(additive_inverse(A),additive_inverse(B))=multiply(A,B).
% 1.75/1.96 ** KEPT (pick-wt=9): 38 [copy,37,flip.1] additive_inverse(multiply(A,B))=multiply(additive_inverse(A),B).
% 1.75/1.96 ---> New Demodulator: 39 [new_demod,38] additive_inverse(multiply(A,B))=multiply(additive_inverse(A),B).
% 1.75/1.96 ** KEPT (pick-wt=9): 41 [copy,40,demod,39] multiply(A,additive_inverse(B))=multiply(additive_inverse(A),B).
% 1.75/1.96 ** KEPT (pick-wt=17): 43 [copy,42,demod,18,39] add(multiply(A,B),multiply(A,additive_inverse(C)))=add(multiply(A,B),multiply(additive_inverse(A),C)).
% 1.75/1.96 Following clause subsumed by 2 during input processing: 0 [demod,20,39] add(multiply(A,C),multiply(additive_inverse(B),C))=add(multiply(A,C),multiply(additive_inverse(B),C)).
% 1.75/1.96 Following clause subsumed by 2 during input processing: 0 [demod,18,39,39] add(multiply(additive_inverse(A),B),multiply(additive_inverse(A),C))=add(multiply(additive_inverse(A),B),multiply(additive_inverse(A),C)).
% 1.75/1.96 ** KEPT (pick-wt=19): 45 [copy,44,demod,20,39,39] add(multiply(A,additive_inverse(B)),multiply(C,additive_inverse(B)))=add(multiply(additive_inverse(A),B),multiply(additive_inverse(C),B)).
% 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 >>>> Starting back demodulation with 6.
% 1.75/1.96 >>>> Starting back demodulation with 8.
% 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 >>>> Starting back demodulation with 18.
% 1.75/1.96 >>>> Starting back demodulation with 20.
% 1.75/1.96 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] add(A,B)=add(B,A).
% 1.75/1.96 >>>> Starting back demodulation with 24.
% 1.75/1.96 >>>> Starting back demodulation with 26.
% 1.75/1.96 >>>> Starting back demodulation with 28.
% 1.75/1.96 >>>> Starting back demodulation with 31.
% 1.75/1.96 >>>> Starting back demodulation with 34.
% 1.75/1.96 >>>> Starting back demodulation with 36.
% 1.75/1.96 >>>> Starting back demodulation with 39.
% 1.75/1.96 >> back demodulating 33 with 39.
% 1.75/1.96 >> back demodulating 30 with 39.
% 1.75/1.96 ** KEPT (pick-wt=9): 50 [copy,41,flip.1] multiply(additive_inverse(A),B)=multiply(A,additive_inverse(B)).
% 1.75/1.96 ** KEPT (pick-wt=17): 51 [copy,43,flip.1] add(multiply(A,B),multiply(additive_inverse(A),C))=add(multiply(A,B),multiply(A,additive_inverse(C))).
% 1.75/1.96 ** KEPT (pick-wt=19): 52 [copy,45,flip.1] add(multiply(additive_inverse(A),B),multiply(additive_inverse(C),B))=add(multiply(A,additive_inverse(B)),multiply(C,additive_inverse(B))).
% 1.75/1.96 >>>> Starting back demodulation with 47.
% 1.75/1.96 >>>> Starting back demodulation with 49.
% 1.75/1.96 Following clause subsumed by 41 during input processing: 0 [copy,50,flip.1] multiply(A,additive_inverse(B))=multiply(additive_inverse(A),B).
% 1.75/1.96 Following clause subsumed by 43 during input processing: 0 [copy,51,flip.1] add(multiply(A,B),multiply(A,additive_inverse(C)))=add(multiply(A,B),multiply(additive_inverse(A),C)).
% 1.75/1.97 Following clause subsumed by 45 during input processing: 0 [copy,52,flip.1] add(multiply(A,additive_inverse(B)),multiply(C,additive_inverse(B)))=add(multiply(additive_inverse(A),B),multiply(additive_inverse(C),B)).
% 1.75/1.97
% 1.75/1.97 ======= end of input processing =======
% 1.75/1.97
% 1.75/1.97 =========== start of search ===========
% 1.75/1.97
% 1.75/1.97 -------- PROOF --------
% 1.75/1.97
% 1.75/1.97 ----> UNIT CONFLICT at 0.01 sec ----> 376 [binary,374.1,1.1] $F.
% 1.75/1.97
% 1.75/1.97 Length of proof is 5. Level of proof is 3.
% 1.75/1.97
% 1.75/1.97 ---------------- PROOF ----------------
% 1.75/1.97 % SZS status Unsatisfiable
% 1.75/1.97 % SZS output start Refutation
% See solution above
% 1.75/1.97 ------------ end of proof -------------
% 1.75/1.97
% 1.75/1.97
% 1.75/1.97 Search stopped by max_proofs option.
% 1.75/1.97
% 1.75/1.97
% 1.75/1.97 Search stopped by max_proofs option.
% 1.75/1.97
% 1.75/1.97 ============ end of search ============
% 1.75/1.97
% 1.75/1.97 -------------- statistics -------------
% 1.75/1.97 clauses given 41
% 1.75/1.97 clauses generated 802
% 1.75/1.97 clauses kept 258
% 1.75/1.97 clauses forward subsumed 748
% 1.75/1.97 clauses back subsumed 2
% 1.75/1.97 Kbytes malloced 1953
% 1.75/1.97
% 1.75/1.97 ----------- times (seconds) -----------
% 1.75/1.97 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.75/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.97 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.75/1.97
% 1.75/1.97 That finishes the proof of the theorem.
% 1.75/1.97
% 1.75/1.97 Process 6344 finished Wed Jul 27 02:10:22 2022
% 1.75/1.97 Otter interrupted
% 1.75/1.97 PROOF FOUND
%------------------------------------------------------------------------------