%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : RNG011-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 13:12:04 EDT 2022
% Result : Unsatisfiable 1.77s 1.99s
% Output : Refutation 1.77s
% 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 : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 2 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(associator(a,a,b),a),associator(a,a,b)) != additive_identity,
file('RNG011-5.p',unknown),
[] ).
cnf(45,axiom,
multiply(multiply(associator(A,A,B),A),associator(A,A,B)) = additive_identity,
file('RNG011-5.p',unknown),
[] ).
cnf(47,plain,
$false,
inference(binary,[status(thm)],[45,1]),
[iquote('binary,45.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : RNG011-5 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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 02:01:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.77/1.99 ----- Otter 3.3f, August 2004 -----
% 1.77/1.99 The process was started by sandbox2 on n007.cluster.edu,
% 1.77/1.99 Wed Jul 27 02:01:01 2022
% 1.77/1.99 The command was "./otter". The process ID is 12781.
% 1.77/1.99
% 1.77/1.99 set(prolog_style_variables).
% 1.77/1.99 set(auto).
% 1.77/1.99 dependent: set(auto1).
% 1.77/1.99 dependent: set(process_input).
% 1.77/1.99 dependent: clear(print_kept).
% 1.77/1.99 dependent: clear(print_new_demod).
% 1.77/1.99 dependent: clear(print_back_demod).
% 1.77/1.99 dependent: clear(print_back_sub).
% 1.77/1.99 dependent: set(control_memory).
% 1.77/1.99 dependent: assign(max_mem, 12000).
% 1.77/1.99 dependent: assign(pick_given_ratio, 4).
% 1.77/1.99 dependent: assign(stats_level, 1).
% 1.77/1.99 dependent: assign(max_seconds, 10800).
% 1.77/1.99 clear(print_given).
% 1.77/1.99
% 1.77/1.99 list(usable).
% 1.77/1.99 0 [] A=A.
% 1.77/1.99 0 [] add(X,Y)=add(Y,X).
% 1.77/1.99 0 [] add(add(X,Y),Z)=add(X,add(Y,Z)).
% 1.77/1.99 0 [] add(X,additive_identity)=X.
% 1.77/1.99 0 [] add(additive_identity,X)=X.
% 1.77/1.99 0 [] add(X,additive_inverse(X))=additive_identity.
% 1.77/1.99 0 [] add(additive_inverse(X),X)=additive_identity.
% 1.77/1.99 0 [] additive_inverse(additive_identity)=additive_identity.
% 1.77/1.99 0 [] add(X,add(additive_inverse(X),Y))=Y.
% 1.77/1.99 0 [] additive_inverse(add(X,Y))=add(additive_inverse(X),additive_inverse(Y)).
% 1.77/1.99 0 [] additive_inverse(additive_inverse(X))=X.
% 1.77/1.99 0 [] multiply(X,additive_identity)=additive_identity.
% 1.77/1.99 0 [] multiply(additive_identity,X)=additive_identity.
% 1.77/1.99 0 [] multiply(additive_inverse(X),additive_inverse(Y))=multiply(X,Y).
% 1.77/1.99 0 [] multiply(X,additive_inverse(Y))=additive_inverse(multiply(X,Y)).
% 1.77/1.99 0 [] multiply(additive_inverse(X),Y)=additive_inverse(multiply(X,Y)).
% 1.77/1.99 0 [] multiply(X,add(Y,Z))=add(multiply(X,Y),multiply(X,Z)).
% 1.77/1.99 0 [] multiply(add(X,Y),Z)=add(multiply(X,Z),multiply(Y,Z)).
% 1.77/1.99 0 [] multiply(multiply(X,Y),Y)=multiply(X,multiply(Y,Y)).
% 1.77/1.99 0 [] associator(X,Y,Z)=add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))).
% 1.77/1.99 0 [] commutator(X,Y)=add(multiply(Y,X),additive_inverse(multiply(X,Y))).
% 1.77/1.99 0 [] multiply(multiply(associator(X,X,Y),X),associator(X,X,Y))=additive_identity.
% 1.77/1.99 0 [] multiply(multiply(associator(a,a,b),a),associator(a,a,b))!=additive_identity.
% 1.77/1.99 end_of_list.
% 1.77/1.99
% 1.77/1.99 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.77/1.99
% 1.77/1.99 All clauses are units, and equality is present; the
% 1.77/1.99 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.77/1.99
% 1.77/1.99 dependent: set(knuth_bendix).
% 1.77/1.99 dependent: set(anl_eq).
% 1.77/1.99 dependent: set(para_from).
% 1.77/1.99 dependent: set(para_into).
% 1.77/1.99 dependent: clear(para_from_right).
% 1.77/1.99 dependent: clear(para_into_right).
% 1.77/1.99 dependent: set(para_from_vars).
% 1.77/1.99 dependent: set(eq_units_both_ways).
% 1.77/1.99 dependent: set(dynamic_demod_all).
% 1.77/1.99 dependent: set(dynamic_demod).
% 1.77/1.99 dependent: set(order_eq).
% 1.77/1.99 dependent: set(back_demod).
% 1.77/1.99 dependent: set(lrpo).
% 1.77/1.99
% 1.77/1.99 ------------> process usable:
% 1.77/1.99 ** KEPT (pick-wt=13): 1 [] multiply(multiply(associator(a,a,b),a),associator(a,a,b))!=additive_identity.
% 1.77/1.99
% 1.77/1.99 ------------> process sos:
% 1.77/1.99 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.77/1.99 ** KEPT (pick-wt=7): 3 [] add(A,B)=add(B,A).
% 1.77/1.99 ** KEPT (pick-wt=11): 4 [] add(add(A,B),C)=add(A,add(B,C)).
% 1.77/1.99 ---> New Demodulator: 5 [new_demod,4] add(add(A,B),C)=add(A,add(B,C)).
% 1.77/1.99 ** KEPT (pick-wt=5): 6 [] add(A,additive_identity)=A.
% 1.77/1.99 ---> New Demodulator: 7 [new_demod,6] add(A,additive_identity)=A.
% 1.77/1.99 ** KEPT (pick-wt=5): 8 [] add(additive_identity,A)=A.
% 1.77/1.99 ---> New Demodulator: 9 [new_demod,8] add(additive_identity,A)=A.
% 1.77/1.99 ** KEPT (pick-wt=6): 10 [] add(A,additive_inverse(A))=additive_identity.
% 1.77/1.99 ---> New Demodulator: 11 [new_demod,10] add(A,additive_inverse(A))=additive_identity.
% 1.77/1.99 ** KEPT (pick-wt=6): 12 [] add(additive_inverse(A),A)=additive_identity.
% 1.77/1.99 ---> New Demodulator: 13 [new_demod,12] add(additive_inverse(A),A)=additive_identity.
% 1.77/1.99 ** KEPT (pick-wt=4): 14 [] additive_inverse(additive_identity)=additive_identity.
% 1.77/1.99 ---> New Demodulator: 15 [new_demod,14] additive_inverse(additive_identity)=additive_identity.
% 1.77/1.99 ** KEPT (pick-wt=8): 16 [] add(A,add(additive_inverse(A),B))=B.
% 1.77/1.99 ---> New Demodulator: 17 [new_demod,16] add(A,add(additive_inverse(A),B))=B.
% 1.77/1.99 ** KEPT (pick-wt=10): 18 [] additive_inverse(add(A,B))=add(additive_inverse(A),additive_inverse(B)).
% 1.77/1.99 ---> New Demodulator: 19 [new_demod,18] additive_inverse(add(A,B))=add(additive_inverse(A),additive_inverse(B)).
% 1.77/1.99 ** KEPT (pick-wt=5): 20 [] additive_inverse(additive_inverse(A))=A.
% 1.77/1.99 -------- PROOF --------
% 1.77/1.99
% 1.77/1.99 ---> New Demodulator: 21 [new_demod,20] additive_inverse(additive_inverse(A))=A.
% 1.77/1.99 ** KEPT (pick-wt=5): 22 [] multiply(A,additive_identity)=additive_identity.
% 1.77/1.99 ---> New Demodulator: 23 [new_demod,22] multiply(A,additive_identity)=additive_identity.
% 1.77/1.99 ** KEPT (pick-wt=5): 24 [] multiply(additive_identity,A)=additive_identity.
% 1.77/1.99 ---> New Demodulator: 25 [new_demod,24] multiply(additive_identity,A)=additive_identity.
% 1.77/1.99 ** KEPT (pick-wt=9): 26 [] multiply(additive_inverse(A),additive_inverse(B))=multiply(A,B).
% 1.77/1.99 ---> New Demodulator: 27 [new_demod,26] multiply(additive_inverse(A),additive_inverse(B))=multiply(A,B).
% 1.77/1.99 ** KEPT (pick-wt=9): 29 [copy,28,flip.1] additive_inverse(multiply(A,B))=multiply(A,additive_inverse(B)).
% 1.77/1.99 ---> New Demodulator: 30 [new_demod,29] additive_inverse(multiply(A,B))=multiply(A,additive_inverse(B)).
% 1.77/1.99 ** KEPT (pick-wt=9): 32 [copy,31,demod,30] multiply(additive_inverse(A),B)=multiply(A,additive_inverse(B)).
% 1.77/1.99 ** KEPT (pick-wt=13): 33 [] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.77/1.99 ---> New Demodulator: 34 [new_demod,33] multiply(A,add(B,C))=add(multiply(A,B),multiply(A,C)).
% 1.77/1.99 ** KEPT (pick-wt=13): 35 [] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.77/1.99 ---> New Demodulator: 36 [new_demod,35] multiply(add(A,B),C)=add(multiply(A,C),multiply(B,C)).
% 1.77/1.99 ** KEPT (pick-wt=11): 37 [] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.77/1.99 ---> New Demodulator: 38 [new_demod,37] multiply(multiply(A,B),B)=multiply(A,multiply(B,B)).
% 1.77/1.99 ** KEPT (pick-wt=17): 40 [copy,39,demod,30,30,flip.1] add(multiply(multiply(A,B),C),multiply(A,multiply(B,additive_inverse(C))))=associator(A,B,C).
% 1.77/1.99 ---> New Demodulator: 41 [new_demod,40] add(multiply(multiply(A,B),C),multiply(A,multiply(B,additive_inverse(C))))=associator(A,B,C).
% 1.77/1.99 ** KEPT (pick-wt=12): 43 [copy,42,demod,30,flip.1] add(multiply(A,B),multiply(B,additive_inverse(A)))=commutator(B,A).
% 1.77/1.99 ---> New Demodulator: 44 [new_demod,43] add(multiply(A,B),multiply(B,additive_inverse(A)))=commutator(B,A).
% 1.77/1.99 ** KEPT (pick-wt=13): 45 [] multiply(multiply(associator(A,A,B),A),associator(A,A,B))=additive_identity.
% 1.77/1.99 ---> New Demodulator: 46 [new_demod,45] multiply(multiply(associator(A,A,B),A),associator(A,A,B))=additive_identity.
% 1.77/1.99
% 1.77/1.99 ----> UNIT CONFLICT at 0.00 sec ----> 47 [binary,45.1,1.1] $F.
% 1.77/1.99
% 1.77/1.99 Length of proof is 0. Level of proof is 0.
% 1.77/1.99
% 1.77/1.99 ---------------- PROOF ----------------
% 1.77/1.99 % SZS status Unsatisfiable
% 1.77/1.99 % SZS output start Refutation
% See solution above
% 1.77/1.99 ------------ end of proof -------------
% 1.77/1.99
% 1.77/1.99
% 1.77/1.99 Search stopped by max_proofs option.
% 1.77/1.99
% 1.77/1.99
% 1.77/1.99 Search stopped by max_proofs option.
% 1.77/1.99
% 1.77/1.99 ============ end of search ============
% 1.77/1.99
% 1.77/1.99 -------------- statistics -------------
% 1.77/1.99 clauses given 0
% 1.77/1.99 clauses generated 0
% 1.77/1.99 clauses kept 23
% 1.77/1.99 clauses forward subsumed 0
% 1.77/1.99 clauses back subsumed 0
% 1.77/1.99 Kbytes malloced 976
% 1.77/1.99
% 1.77/1.99 ----------- times (seconds) -----------
% 1.77/1.99 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.99 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.99 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.77/1.99
% 1.77/1.99 That finishes the proof of the theorem.
% 1.77/1.99
% 1.77/1.99 Process 12781 finished Wed Jul 27 02:01:02 2022
% 1.77/1.99 Otter interrupted
% 1.77/1.99 PROOF FOUND
%------------------------------------------------------------------------------