TSTP Solution File: RNG010-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG010-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 13:12:03 EDT 2022
% Result : Unsatisfiable 1.74s 1.96s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 2
% Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 2 RR)
% Number of literals : 3 ( 2 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
multiply(multiply(A,B),A) != multiply(A,multiply(B,A)),
file('RNG010-2.p',unknown),
[] ).
cnf(27,axiom,
multiply(multiply(A,B),B) = multiply(A,multiply(B,B)),
file('RNG010-2.p',unknown),
[] ).
cnf(29,plain,
$false,
inference(binary,[status(thm)],[27,3]),
[iquote('binary,27.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : RNG010-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 01:31:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.74/1.96 ----- Otter 3.3f, August 2004 -----
% 1.74/1.96 The process was started by sandbox on n017.cluster.edu,
% 1.74/1.96 Wed Jul 27 01:31:48 2022
% 1.74/1.96 The command was "./otter". The process ID is 7371.
% 1.74/1.96
% 1.74/1.96 set(prolog_style_variables).
% 1.74/1.96 set(auto).
% 1.74/1.96 dependent: set(auto1).
% 1.74/1.96 dependent: set(process_input).
% 1.74/1.96 dependent: clear(print_kept).
% 1.74/1.96 dependent: clear(print_new_demod).
% 1.74/1.96 dependent: clear(print_back_demod).
% 1.74/1.96 dependent: clear(print_back_sub).
% 1.74/1.96 dependent: set(control_memory).
% 1.74/1.96 dependent: assign(max_mem, 12000).
% 1.74/1.96 dependent: assign(pick_given_ratio, 4).
% 1.74/1.96 dependent: assign(stats_level, 1).
% 1.74/1.96 dependent: assign(max_seconds, 10800).
% 1.74/1.96 clear(print_given).
% 1.74/1.96
% 1.74/1.96 list(usable).
% 1.74/1.96 0 [] A=A.
% 1.74/1.96 0 [] add(additive_identity,X)=X.
% 1.74/1.96 0 [] multiply(additive_identity,X)=additive_identity.
% 1.74/1.96 0 [] multiply(X,additive_identity)=additive_identity.
% 1.74/1.96 0 [] add(additive_inverse(X),X)=additive_identity.
% 1.74/1.96 0 [] additive_inverse(add(X,Y))=add(additive_inverse(X),additive_inverse(Y)).
% 1.74/1.96 0 [] additive_inverse(additive_inverse(X))=X.
% 1.74/1.96 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.74/1.96 0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.74/1.96 0 [] multiply(multiply(X,Y),Y)=multiply(X,multiply(Y,Y)).
% 1.74/1.96 0 [] multiply(multiply(X,X),Y)=multiply(X,multiply(X,Y)).
% 1.74/1.96 0 [] multiply(additive_inverse(X),Y)=additive_inverse(multiply(X,Y)).
% 1.74/1.96 0 [] multiply(X,additive_inverse(Y))=additive_inverse(multiply(X,Y)).
% 1.74/1.96 0 [] additive_inverse(additive_identity)=additive_identity.
% 1.74/1.96 0 [] add(X,Y)=add(Y,X).
% 1.74/1.96 0 [] add(X,add(Y,Z))=add(add(X,Y),Z).
% 1.74/1.96 0 [] add(X,Z)!=add(Y,Z)|X=Y.
% 1.74/1.96 0 [] add(Z,X)!=add(Z,Y)|X=Y.
% 1.74/1.96 0 [] associator(X,Y,Z)=add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))).
% 1.74/1.96 0 [] multiply(multiply(Y,X),Y)!=multiply(Y,multiply(X,Y)).
% 1.74/1.96 0 [] associator(Y,X,Z)!=additive_inverse(associator(X,Y,Z)).
% 1.74/1.96 0 [] associator(Z,Y,X)!=additive_inverse(associator(X,Y,Z)).
% 1.74/1.96 0 [] multiply(Z,multiply(X,multiply(Y,X)))=multiply(multiply(multiply(Z,X),Y),X).
% 1.74/1.96 0 [] multiply(multiply(X,multiply(Y,X)),Z)=multiply(X,multiply(Y,multiply(X,Z))).
% 1.74/1.96 0 [] associator(multiply(cx,cx),cy,cz)!=add(multiply(associator(cx,cy,cz),cx),multiply(cx,associator(cx,cy,cz))).
% 1.74/1.96 end_of_list.
% 1.74/1.96
% 1.74/1.96 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.74/1.96
% 1.74/1.96 This is a Horn set with equality. The strategy will be
% 1.74/1.96 Knuth-Bendix and hyper_res, with positive clauses in
% 1.74/1.96 sos and nonpositive clauses in usable.
% 1.74/1.96
% 1.74/1.96 dependent: set(knuth_bendix).
% 1.74/1.96 dependent: set(anl_eq).
% 1.74/1.96 dependent: set(para_from).
% 1.74/1.96 dependent: set(para_into).
% 1.74/1.96 dependent: clear(para_from_right).
% 1.74/1.96 dependent: clear(para_into_right).
% 1.74/1.96 dependent: set(para_from_vars).
% 1.74/1.96 dependent: set(eq_units_both_ways).
% 1.74/1.96 dependent: set(dynamic_demod_all).
% 1.74/1.96 dependent: set(dynamic_demod).
% 1.74/1.96 dependent: set(order_eq).
% 1.74/1.96 dependent: set(back_demod).
% 1.74/1.96 dependent: set(lrpo).
% 1.74/1.96 dependent: set(hyper_res).
% 1.74/1.96 dependent: clear(order_hyper).
% 1.74/1.96
% 1.74/1.96 ------------> process usable:
% 1.74/1.96 ** KEPT (pick-wt=10): 1 [] add(A,B)!=add(C,B)|A=C.
% 1.74/1.96 ** KEPT (pick-wt=10): 2 [] add(A,B)!=add(A,C)|B=C.
% 1.74/1.96 ** KEPT (pick-wt=11): 3 [] multiply(multiply(A,B),A)!=multiply(A,multiply(B,A)).
% 1.74/1.96 ** KEPT (pick-wt=10): 5 [copy,4,flip.1] additive_inverse(associator(A,B,C))!=associator(B,A,C).
% 1.74/1.96 ** KEPT (pick-wt=10): 7 [copy,6,flip.1] additive_inverse(associator(A,B,C))!=associator(C,B,A).
% 1.74/1.96 ** KEPT (pick-wt=20): 9 [copy,8,flip.1] add(multiply(associator(cx,cy,cz),cx),multiply(cx,associator(cx,cy,cz)))!=associator(multiply(cx,cx),cy,cz).
% 1.74/1.96
% 1.74/1.96 ------------> process sos:
% 1.74/1.96 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.74/1.96 ** KEPT (pick-wt=5): 11 [] add(additive_identity,A)=A.
% 1.74/1.96 ---> New Demodulator: 12 [new_demod,11] add(additive_identity,A)=A.
% 1.74/1.96 ** KEPT (pick-wt=5): 13 [] multiply(additive_identity,A)=additive_identity.
% 1.74/1.96 ---> New Demodulator: 14 [new_demod,13] multiply(additive_identity,A)=additive_identity.
% 1.74/1.96 ** KEPT (pick-wt=5): 15 [] multiply(A,additive_identity)=additive_identity.
% 1.74/1.96 ---> New Demodulator: 16 [new_demod,15] multiply(A,additive_identity)=additive_identity.
% 1.74/1.96 ** KEPT (pick-wt=6): 17 [] add(additive_inverse(A),A)=additive_identity.
% 1.74/1.96 ---> New Demodulator: 18 [new_demod,17] add(additive_inverse(A),A)=additive_identity.
% 1.74/1.96 ** KEPT (pick-wt=10): 19 [] additive_inverse(add(A,B))=add(add
% 1.74/1.96 -------- PROOF --------
% 1.74/1.96 itive_inverse(A),additive_inverse(B)).
% 1.74/1.96 ---> New Demodulator: 20 [new_demod,19] additive_inverse(add(A,B))=add(additive_inverse(A),additive_inverse(B)).
% 1.74/1.96 ** KEPT (pick-wt=5): 21 [] additive_inverse(additive_inverse(A))=A.
% 1.74/1.96 ---> New Demodulator: 22 [new_demod,21] additive_inverse(additive_inverse(A))=A.
% 1.74/1.96 ** KEPT (pick-wt=13): 23 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.74/1.96 ---> New Demodulator: 24 [new_demod,23] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.74/1.96 ** KEPT (pick-wt=13): 25 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.74/1.96 ---> New Demodulator: 26 [new_demod,25] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.74/1.96 ** KEPT (pick-wt=11): 27 [] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.74/1.96 ---> New Demodulator: 28 [new_demod,27] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.74/1.96
% 1.74/1.96 ----> UNIT CONFLICT at 0.00 sec ----> 29 [binary,27.1,3.1] $F.
% 1.74/1.96
% 1.74/1.96 Length of proof is 0. Level of proof is 0.
% 1.74/1.96
% 1.74/1.96 ---------------- PROOF ----------------
% 1.74/1.96 % SZS status Unsatisfiable
% 1.74/1.96 % SZS output start Refutation
% See solution above
% 1.74/1.96 ------------ end of proof -------------
% 1.74/1.96
% 1.74/1.96
% 1.74/1.96 Search stopped by max_proofs option.
% 1.74/1.96
% 1.74/1.96
% 1.74/1.96 Search stopped by max_proofs option.
% 1.74/1.96
% 1.74/1.96 ============ end of search ============
% 1.74/1.96
% 1.74/1.96 -------------- statistics -------------
% 1.74/1.96 clauses given 0
% 1.74/1.96 clauses generated 0
% 1.74/1.96 clauses kept 16
% 1.74/1.96 clauses forward subsumed 0
% 1.74/1.96 clauses back subsumed 0
% 1.74/1.96 Kbytes malloced 976
% 1.74/1.96
% 1.74/1.96 ----------- times (seconds) -----------
% 1.74/1.96 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.96 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.96
% 1.74/1.96 That finishes the proof of the theorem.
% 1.74/1.96
% 1.74/1.96 Process 7371 finished Wed Jul 27 01:31:49 2022
% 1.74/1.96 Otter interrupted
% 1.74/1.96 PROOF FOUND
%------------------------------------------------------------------------------