%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO069-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 12:47:41 EDT 2022
% Result : Unsatisfiable 1.78s 1.94s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of clauses : 19 ( 19 unt; 0 nHn; 2 RR)
% Number of literals : 19 ( 18 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 74 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b,inverse(b)) != a,
file('BOO069-1.p',unknown),
[] ).
cnf(3,axiom,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,G))),multiply(D,multiply(G,F,E),C)) = B,
file('BOO069-1.p',unknown),
[] ).
cnf(5,plain,
multiply(multiply(A,B,C),inverse(multiply(multiply(D,E,F),G,multiply(D,E,H))),multiply(E,multiply(H,G,F),D)) = multiply(B,multiply(C,inverse(multiply(A,B,I)),I),A),
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.1,3.1.1')] ).
cnf(10,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,multiply(E,multiply(F,G,H),I)),inverse(multiply(multiply(I,E,H),G,multiply(I,E,F))),multiply(C,D,multiply(J,inverse(J),K)))),multiply(D,K,C)) = B,
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.3.2,3.1.1')] ).
cnf(24,plain,
multiply(inverse(A),multiply(B,inverse(multiply(A,inverse(A),C)),C),A) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,3])]),
[iquote('para_into,5.1.1,3.1.1,flip.1')] ).
cnf(55,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),multiply(F,inverse(multiply(E,inverse(E),G)),G),multiply(C,D,inverse(E)))),multiply(D,F,C)) = B,
inference(para_from,[status(thm),theory(equality)],[24,3]),
[iquote('para_from,23.1.1,3.1.1.3.2')] ).
cnf(201,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),multiply(D,inverse(D),E))),multiply(inverse(C),E,C)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,55]),24]),
[iquote('para_into,10.1.1.2.1,55.1.1,demod,24')] ).
cnf(205,plain,
multiply(inverse(A),B,A) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[201,201]),201])]),
[iquote('para_into,200.1.1.1,200.1.1,demod,201,flip.1')] ).
cnf(221,plain,
multiply(multiply(A,inverse(A),B),inverse(multiply(C,inverse(C),inverse(inverse(D)))),D) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[201,201]),205]),
[iquote('para_into,200.1.1.2.1,200.1.1,demod,205')] ).
cnf(237,plain,
multiply(A,inverse(multiply(B,inverse(B),C)),C) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[24]),205]),
[iquote('back_demod,23,demod,205')] ).
cnf(264,plain,
multiply(inverse(inverse(A)),inverse(multiply(multiply(B,C,D),E,multiply(B,C,F))),multiply(C,multiply(F,E,D),B)) = A,
inference(para_from,[status(thm),theory(equality)],[205,3]),
[iquote('para_from,204.1.1,3.1.1.1')] ).
cnf(271,plain,
multiply(A,inverse(inverse(inverse(B))),B) = A,
inference(para_into,[status(thm),theory(equality)],[237,205]),
[iquote('para_into,237.1.1.2.1,204.1.1')] ).
cnf(273,plain,
inverse(multiply(A,inverse(A),B)) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[237,205]),
[iquote('para_into,237.1.1,204.1.1')] ).
cnf(275,plain,
multiply(A,inverse(B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[237]),273]),
[iquote('back_demod,237,demod,273')] ).
cnf(278,plain,
multiply(A,inverse(A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[221]),273,271]),
[iquote('back_demod,221,demod,273,271')] ).
cnf(305,plain,
multiply(A,inverse(multiply(multiply(B,C,D),E,multiply(B,C,F))),multiply(C,multiply(F,E,D),B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),278]),
[iquote('back_demod,3,demod,278')] ).
cnf(309,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[264]),305]),
[iquote('back_demod,264,demod,305')] ).
cnf(320,plain,
multiply(A,B,inverse(B)) = A,
inference(para_into,[status(thm),theory(equality)],[275,309]),
[iquote('para_into,275.1.1.2,309.1.1')] ).
cnf(322,plain,
$false,
inference(binary,[status(thm)],[320,1]),
[iquote('binary,320.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : BOO069-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 02:30:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.78/1.94 ----- Otter 3.3f, August 2004 -----
% 1.78/1.94 The process was started by sandbox2 on n012.cluster.edu,
% 1.78/1.94 Wed Jul 27 02:30:51 2022
% 1.78/1.94 The command was "./otter". The process ID is 28079.
% 1.78/1.94
% 1.78/1.94 set(prolog_style_variables).
% 1.78/1.94 set(auto).
% 1.78/1.94 dependent: set(auto1).
% 1.78/1.94 dependent: set(process_input).
% 1.78/1.94 dependent: clear(print_kept).
% 1.78/1.94 dependent: clear(print_new_demod).
% 1.78/1.94 dependent: clear(print_back_demod).
% 1.78/1.94 dependent: clear(print_back_sub).
% 1.78/1.94 dependent: set(control_memory).
% 1.78/1.94 dependent: assign(max_mem, 12000).
% 1.78/1.94 dependent: assign(pick_given_ratio, 4).
% 1.78/1.94 dependent: assign(stats_level, 1).
% 1.78/1.94 dependent: assign(max_seconds, 10800).
% 1.78/1.94 clear(print_given).
% 1.78/1.94
% 1.78/1.94 list(usable).
% 1.78/1.94 0 [] A=A.
% 1.78/1.94 0 [] multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,G))),multiply(D,multiply(G,F,E),C))=B.
% 1.78/1.94 0 [] multiply(a,b,inverse(b))!=a.
% 1.78/1.94 end_of_list.
% 1.78/1.94
% 1.78/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.78/1.94
% 1.78/1.94 All clauses are units, and equality is present; the
% 1.78/1.94 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.78/1.94
% 1.78/1.94 dependent: set(knuth_bendix).
% 1.78/1.94 dependent: set(anl_eq).
% 1.78/1.94 dependent: set(para_from).
% 1.78/1.94 dependent: set(para_into).
% 1.78/1.94 dependent: clear(para_from_right).
% 1.78/1.94 dependent: clear(para_into_right).
% 1.78/1.94 dependent: set(para_from_vars).
% 1.78/1.94 dependent: set(eq_units_both_ways).
% 1.78/1.94 dependent: set(dynamic_demod_all).
% 1.78/1.94 dependent: set(dynamic_demod).
% 1.78/1.94 dependent: set(order_eq).
% 1.78/1.94 dependent: set(back_demod).
% 1.78/1.94 dependent: set(lrpo).
% 1.78/1.94
% 1.78/1.94 ------------> process usable:
% 1.78/1.94 ** KEPT (pick-wt=7): 1 [] multiply(a,b,inverse(b))!=a.
% 1.78/1.94
% 1.78/1.94 ------------> process sos:
% 1.78/1.94 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.78/1.94 ** KEPT (pick-wt=26): 3 [] multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,G))),multiply(D,multiply(G,F,E),C))=B.
% 1.78/1.94 ---> New Demodulator: 4 [new_demod,3] multiply(multiply(A,inverse(A),B),inverse(multiply(multiply(C,D,E),F,multiply(C,D,G))),multiply(D,multiply(G,F,E),C))=B.
% 1.78/1.94 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.78/1.94 >>>> Starting back demodulation with 4.
% 1.78/1.94
% 1.78/1.94 ======= end of input processing =======
% 1.78/1.94
% 1.78/1.94 =========== start of search ===========
% 1.78/1.94
% 1.78/1.94
% 1.78/1.94 Resetting weight limit to 38.
% 1.78/1.94
% 1.78/1.94
% 1.78/1.94 Resetting weight limit to 38.
% 1.78/1.94
% 1.78/1.94 sos_size=117
% 1.78/1.94
% 1.78/1.94 -------- PROOF --------
% 1.78/1.94
% 1.78/1.94 ----> UNIT CONFLICT at 0.04 sec ----> 322 [binary,320.1,1.1] $F.
% 1.78/1.94
% 1.78/1.94 Length of proof is 16. Level of proof is 11.
% 1.78/1.94
% 1.78/1.94 ---------------- PROOF ----------------
% 1.78/1.94 % SZS status Unsatisfiable
% 1.78/1.94 % SZS output start Refutation
% See solution above
% 1.78/1.94 ------------ end of proof -------------
% 1.78/1.94
% 1.78/1.94
% 1.78/1.94 Search stopped by max_proofs option.
% 1.78/1.94
% 1.78/1.94
% 1.78/1.94 Search stopped by max_proofs option.
% 1.78/1.94
% 1.78/1.94 ============ end of search ============
% 1.78/1.94
% 1.78/1.94 -------------- statistics -------------
% 1.78/1.94 clauses given 22
% 1.78/1.94 clauses generated 1203
% 1.78/1.94 clauses kept 207
% 1.78/1.94 clauses forward subsumed 343
% 1.78/1.94 clauses back subsumed 4
% 1.78/1.94 Kbytes malloced 7812
% 1.78/1.94
% 1.78/1.94 ----------- times (seconds) -----------
% 1.78/1.94 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.78/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.78/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.78/1.94
% 1.78/1.94 That finishes the proof of the theorem.
% 1.78/1.94
% 1.78/1.94 Process 28079 finished Wed Jul 27 02:30:52 2022
% 1.78/1.94 Otter interrupted
% 1.78/1.94 PROOF FOUND
%------------------------------------------------------------------------------