%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO002-2 : TPTP v8.1.0. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 12:47:30 EDT 2022
% Result : Unsatisfiable 1.95s 2.19s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 2 RR)
% Number of literals : 29 ( 28 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 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 : 99 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,inverse(a),b) != b,
file('BOO002-2.p',unknown),
[] ).
cnf(4,axiom,
multiply(multiply(A,B,C),D,multiply(A,B,E)) = multiply(A,B,multiply(C,D,E)),
file('BOO002-2.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B,B) = B,
file('BOO002-2.p',unknown),
[] ).
cnf(8,axiom,
multiply(A,A,B) = A,
file('BOO002-2.p',unknown),
[] ).
cnf(10,axiom,
multiply(inverse(A),A,B) = B,
file('BOO002-2.p',unknown),
[] ).
cnf(12,axiom,
multiply(A,B,A) = A,
file('BOO002-2.p',unknown),
[] ).
cnf(13,plain,
multiply(A,B,multiply(A,C,D)) = multiply(A,C,multiply(A,B,D)),
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,3.1.1.1,11.1.1')] ).
cnf(14,plain,
multiply(A,B,multiply(C,A,D)) = multiply(C,A,multiply(A,B,D)),
inference(para_into,[status(thm),theory(equality)],[4,6]),
[iquote('para_into,3.1.1.1,5.1.1')] ).
cnf(15,plain,
multiply(multiply(A,B,multiply(C,D,E)),F,multiply(multiply(A,B,C),D,G)) = multiply(multiply(A,B,C),D,multiply(multiply(A,B,E),F,G)),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.1,3.1.1')] ).
cnf(17,plain,
multiply(multiply(A,B,C),D,A) = multiply(A,B,multiply(C,D,A)),
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,3.1.1.3,11.1.1')] ).
cnf(20,plain,
multiply(multiply(A,B,C),D,B) = multiply(A,B,multiply(C,D,B)),
inference(para_into,[status(thm),theory(equality)],[4,6]),
[iquote('para_into,3.1.1.3,5.1.1')] ).
cnf(24,plain,
multiply(A,B,multiply(C,multiply(A,B,C),D)) = multiply(A,B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,8])]),
[iquote('para_into,3.1.1,7.1.1,flip.1')] ).
cnf(29,plain,
multiply(A,B,multiply(A,C,B)) = multiply(A,C,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,6])]),
[iquote('para_into,13.1.1.3,5.1.1,flip.1')] ).
cnf(51,plain,
multiply(A,B,multiply(B,C,A)) = multiply(B,C,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,12])]),
[iquote('para_into,14.1.1.3,11.1.1,flip.1')] ).
cnf(122,plain,
multiply(multiply(A,B,multiply(C,D,E)),F,D) = multiply(multiply(A,B,C),D,multiply(multiply(A,B,E),F,D)),
inference(para_into,[status(thm),theory(equality)],[15,6]),
[iquote('para_into,15.1.1.3,5.1.1')] ).
cnf(183,plain,
multiply(A,B,multiply(A,B,C)) = multiply(A,B,C),
inference(para_into,[status(thm),theory(equality)],[24,6]),
[iquote('para_into,23.1.1.3,5.1.1')] ).
cnf(187,plain,
multiply(A,multiply(B,C,A),multiply(D,B,multiply(B,C,A))) = multiply(B,C,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[24,51]),20,24]),
[iquote('para_from,23.1.1,51.1.1.3,demod,20,24')] ).
cnf(221,plain,
multiply(A,B,multiply(C,D,multiply(A,B,E))) = multiply(A,B,multiply(C,D,E)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[183,4]),4])]),
[iquote('para_from,183.1.1,3.1.1.3,demod,4,flip.1')] ).
cnf(899,plain,
multiply(A,multiply(B,C,A),B) = multiply(B,C,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[187,13]),8,12]),
[iquote('para_into,187.1.1.3,13.1.1,demod,8,12')] ).
cnf(1007,plain,
multiply(multiply(A,B,C),D,C) = multiply(C,multiply(A,B,C),multiply(A,D,C)),
inference(para_from,[status(thm),theory(equality)],[899,17]),
[iquote('para_from,898.1.1,17.1.1.1')] ).
cnf(1409,plain,
multiply(A,multiply(B,C,A),multiply(B,C,D)) = multiply(B,C,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[221,24]),6])]),
[iquote('para_into,221.1.1.3,23.1.1,demod,6,flip.1')] ).
cnf(1514,plain,
multiply(A,multiply(B,C,A),multiply(B,D,C)) = multiply(B,C,A),
inference(para_into,[status(thm),theory(equality)],[1409,29]),
[iquote('para_into,1409.1.1.3,29.1.1')] ).
cnf(1532,plain,
multiply(A,multiply(B,C,A),C) = multiply(B,C,A),
inference(para_into,[status(thm),theory(equality)],[1409,6]),
[iquote('para_into,1409.1.1.3,5.1.1')] ).
cnf(2453,plain,
multiply(multiply(A,B,C),multiply(A,C,D),D) = multiply(A,C,D),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1514,899]),1514]),
[iquote('para_from,1513.1.1,898.1.1.2,demod,1514')] ).
cnf(2763,plain,
multiply(multiply(A,B,C),D,multiply(C,D,A)) = multiply(C,D,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2453,1532]),122,12,1532,1532]),
[iquote('para_into,2453.1.1.2,1531.1.1,demod,122,12,1532,1532')] ).
cnf(2797,plain,
multiply(multiply(A,B,C),D,multiply(B,D,C)) = multiply(B,D,C),
inference(para_into,[status(thm),theory(equality)],[2763,1532]),
[iquote('para_into,2763.1.1.1,1531.1.1')] ).
cnf(2805,plain,
multiply(A,multiply(B,inverse(C),A),multiply(B,C,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2797,10]),1007,10]),
[iquote('para_into,2797.1.1.3,9.1.1,demod,1007,10')] ).
cnf(2821,plain,
multiply(A,inverse(A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2805,8]),899]),
[iquote('para_into,2805.1.1.3,7.1.1,demod,899')] ).
cnf(2823,plain,
$false,
inference(binary,[status(thm)],[2821,1]),
[iquote('binary,2821.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : BOO002-2 : TPTP v8.1.0. Released v1.1.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 02:31:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.19 ----- Otter 3.3f, August 2004 -----
% 1.95/2.19 The process was started by sandbox2 on n005.cluster.edu,
% 1.95/2.19 Wed Jul 27 02:31:50 2022
% 1.95/2.19 The command was "./otter". The process ID is 8584.
% 1.95/2.19
% 1.95/2.19 set(prolog_style_variables).
% 1.95/2.19 set(auto).
% 1.95/2.19 dependent: set(auto1).
% 1.95/2.19 dependent: set(process_input).
% 1.95/2.19 dependent: clear(print_kept).
% 1.95/2.19 dependent: clear(print_new_demod).
% 1.95/2.19 dependent: clear(print_back_demod).
% 1.95/2.19 dependent: clear(print_back_sub).
% 1.95/2.19 dependent: set(control_memory).
% 1.95/2.19 dependent: assign(max_mem, 12000).
% 1.95/2.19 dependent: assign(pick_given_ratio, 4).
% 1.95/2.19 dependent: assign(stats_level, 1).
% 1.95/2.19 dependent: assign(max_seconds, 10800).
% 1.95/2.19 clear(print_given).
% 1.95/2.19
% 1.95/2.19 list(usable).
% 1.95/2.19 0 [] A=A.
% 1.95/2.19 0 [] multiply(multiply(V,W,X),Y,multiply(V,W,Z))=multiply(V,W,multiply(X,Y,Z)).
% 1.95/2.19 0 [] multiply(Y,X,X)=X.
% 1.95/2.19 0 [] multiply(X,X,Y)=X.
% 1.95/2.19 0 [] multiply(inverse(Y),Y,X)=X.
% 1.95/2.19 0 [] multiply(X,Y,X)=X.
% 1.95/2.19 0 [] multiply(a,inverse(a),b)!=b.
% 1.95/2.19 end_of_list.
% 1.95/2.19
% 1.95/2.19 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.95/2.19
% 1.95/2.19 All clauses are units, and equality is present; the
% 1.95/2.19 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.95/2.19
% 1.95/2.19 dependent: set(knuth_bendix).
% 1.95/2.19 dependent: set(anl_eq).
% 1.95/2.19 dependent: set(para_from).
% 1.95/2.19 dependent: set(para_into).
% 1.95/2.19 dependent: clear(para_from_right).
% 1.95/2.19 dependent: clear(para_into_right).
% 1.95/2.19 dependent: set(para_from_vars).
% 1.95/2.19 dependent: set(eq_units_both_ways).
% 1.95/2.19 dependent: set(dynamic_demod_all).
% 1.95/2.19 dependent: set(dynamic_demod).
% 1.95/2.19 dependent: set(order_eq).
% 1.95/2.19 dependent: set(back_demod).
% 1.95/2.19 dependent: set(lrpo).
% 1.95/2.19
% 1.95/2.19 ------------> process usable:
% 1.95/2.19 ** KEPT (pick-wt=7): 1 [] multiply(a,inverse(a),b)!=b.
% 1.95/2.19
% 1.95/2.19 ------------> process sos:
% 1.95/2.19 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.95/2.19 ** KEPT (pick-wt=18): 3 [] multiply(multiply(A,B,C),D,multiply(A,B,E))=multiply(A,B,multiply(C,D,E)).
% 1.95/2.19 ---> New Demodulator: 4 [new_demod,3] multiply(multiply(A,B,C),D,multiply(A,B,E))=multiply(A,B,multiply(C,D,E)).
% 1.95/2.19 ** KEPT (pick-wt=6): 5 [] multiply(A,B,B)=B.
% 1.95/2.19 ---> New Demodulator: 6 [new_demod,5] multiply(A,B,B)=B.
% 1.95/2.19 ** KEPT (pick-wt=6): 7 [] multiply(A,A,B)=A.
% 1.95/2.19 ---> New Demodulator: 8 [new_demod,7] multiply(A,A,B)=A.
% 1.95/2.19 ** KEPT (pick-wt=7): 9 [] multiply(inverse(A),A,B)=B.
% 1.95/2.19 ---> New Demodulator: 10 [new_demod,9] multiply(inverse(A),A,B)=B.
% 1.95/2.19 ** KEPT (pick-wt=6): 11 [] multiply(A,B,A)=A.
% 1.95/2.19 ---> New Demodulator: 12 [new_demod,11] multiply(A,B,A)=A.
% 1.95/2.19 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.95/2.19 >>>> Starting back demodulation with 4.
% 1.95/2.19 >>>> Starting back demodulation with 6.
% 1.95/2.19 >>>> Starting back demodulation with 8.
% 1.95/2.19 >>>> Starting back demodulation with 10.
% 1.95/2.19 >>>> Starting back demodulation with 12.
% 1.95/2.19
% 1.95/2.19 ======= end of input processing =======
% 1.95/2.19
% 1.95/2.19 =========== start of search ===========
% 1.95/2.19
% 1.95/2.19
% 1.95/2.19 Resetting weight limit to 18.
% 1.95/2.19
% 1.95/2.19
% 1.95/2.19 Resetting weight limit to 18.
% 1.95/2.19
% 1.95/2.19 sos_size=1147
% 1.95/2.19
% 1.95/2.19 -------- PROOF --------
% 1.95/2.19
% 1.95/2.19 ----> UNIT CONFLICT at 0.30 sec ----> 2823 [binary,2821.1,1.1] $F.
% 1.95/2.19
% 1.95/2.19 Length of proof is 22. Level of proof is 10.
% 1.95/2.19
% 1.95/2.19 ---------------- PROOF ----------------
% 1.95/2.19 % SZS status Unsatisfiable
% 1.95/2.19 % SZS output start Refutation
% See solution above
% 1.95/2.19 ------------ end of proof -------------
% 1.95/2.19
% 1.95/2.19
% 1.95/2.19 Search stopped by max_proofs option.
% 1.95/2.19
% 1.95/2.19
% 1.95/2.19 Search stopped by max_proofs option.
% 1.95/2.19
% 1.95/2.19 ============ end of search ============
% 1.95/2.19
% 1.95/2.19 -------------- statistics -------------
% 1.95/2.19 clauses given 63
% 1.95/2.19 clauses generated 7859
% 1.95/2.19 clauses kept 1616
% 1.95/2.19 clauses forward subsumed 4907
% 1.95/2.19 clauses back subsumed 30
% 1.95/2.19 Kbytes malloced 4882
% 1.95/2.19
% 1.95/2.19 ----------- times (seconds) -----------
% 1.95/2.19 user CPU time 0.30 (0 hr, 0 min, 0 sec)
% 1.95/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.95/2.19
% 1.95/2.19 That finishes the proof of the theorem.
% 1.95/2.19
% 1.95/2.19 Process 8584 finished Wed Jul 27 02:31:52 2022
% 1.95/2.19 Otter interrupted
% 1.95/2.19 PROOF FOUND
%------------------------------------------------------------------------------