%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : BOO002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 2.18s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 25 ( 25 unt; 0 nHn; 2 RR)
% Number of literals : 25 ( 24 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 : 81 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,inverse(a),b) != b,
file('BOO002-1.p',unknown),
[] ).
cnf(4,axiom,
multiply(multiply(A,B,C),D,multiply(A,B,E)) = multiply(A,B,multiply(C,D,E)),
file('BOO002-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B,B) = B,
file('BOO002-1.p',unknown),
[] ).
cnf(8,axiom,
multiply(A,A,B) = A,
file('BOO002-1.p',unknown),
[] ).
cnf(10,axiom,
multiply(inverse(A),A,B) = B,
file('BOO002-1.p',unknown),
[] ).
cnf(12,plain,
multiply(A,B,A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,8]),8,8]),
[iquote('para_into,3.1.1.1,7.1.1,demod,8,8')] ).
cnf(16,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(21,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(25,plain,
multiply(multiply(A,B,C),D,A) = multiply(A,B,multiply(C,D,A)),
inference(para_from,[status(thm),theory(equality)],[12,4]),
[iquote('para_from,11.1.1,3.1.1.3')] ).
cnf(52,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)],[16,12])]),
[iquote('para_into,16.1.1.1,11.1.1,flip.1')] ).
cnf(55,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)],[16,4]),
[iquote('para_into,16.1.1.1,3.1.1')] ).
cnf(148,plain,
multiply(A,B,multiply(A,B,C)) = multiply(A,B,C),
inference(para_into,[status(thm),theory(equality)],[21,6]),
[iquote('para_into,20.1.1.3,5.1.1')] ).
cnf(152,plain,
multiply(A,multiply(B,multiply(A,C,B),D),multiply(A,C,B)) = multiply(A,C,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[21,52]),21]),
[iquote('para_from,20.1.1,52.1.1.3,demod,21')] ).
cnf(180,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)],[148,4]),4])]),
[iquote('para_from,148.1.1,3.1.1.3,demod,4,flip.1')] ).
cnf(742,plain,
multiply(A,multiply(B,C,A),B) = multiply(B,C,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[152,21]),6])]),
[iquote('para_from,152.1.1,20.1.1.3,demod,6,flip.1')] ).
cnf(815,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)],[742,25]),
[iquote('para_from,741.1.1,25.1.1.1')] ).
cnf(1123,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)],[180,21]),6])]),
[iquote('para_into,180.1.1.3,20.1.1,demod,6,flip.1')] ).
cnf(1208,plain,
multiply(A,multiply(B,C,A),multiply(B,D,C)) = multiply(B,C,A),
inference(para_into,[status(thm),theory(equality)],[1123,52]),
[iquote('para_into,1123.1.1.3,52.1.1')] ).
cnf(1234,plain,
multiply(A,multiply(B,C,A),C) = multiply(B,C,A),
inference(para_into,[status(thm),theory(equality)],[1123,6]),
[iquote('para_into,1123.1.1.3,5.1.1')] ).
cnf(2025,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)],[1208,742]),1208]),
[iquote('para_from,1207.1.1,741.1.1.2,demod,1208')] ).
cnf(2644,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)],[2025,1234]),55,12,1234,1234]),
[iquote('para_into,2025.1.1.2,1233.1.1,demod,55,12,1234,1234')] ).
cnf(2674,plain,
multiply(multiply(A,B,C),D,multiply(B,D,C)) = multiply(B,D,C),
inference(para_into,[status(thm),theory(equality)],[2644,1234]),
[iquote('para_into,2644.1.1.1,1233.1.1')] ).
cnf(2682,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)],[2674,10]),815,10]),
[iquote('para_into,2674.1.1.3,9.1.1,demod,815,10')] ).
cnf(2698,plain,
multiply(A,inverse(A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2682,8]),742]),
[iquote('para_into,2682.1.1.3,7.1.1,demod,742')] ).
cnf(2700,plain,
$false,
inference(binary,[status(thm)],[2698,1]),
[iquote('binary,2698.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : BOO002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 02:35:07 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.95/2.18 ----- Otter 3.3f, August 2004 -----
% 1.95/2.18 The process was started by sandbox2 on n019.cluster.edu,
% 1.95/2.18 Wed Jul 27 02:35:07 2022
% 1.95/2.18 The command was "./otter". The process ID is 17666.
% 1.95/2.18
% 1.95/2.18 set(prolog_style_variables).
% 1.95/2.18 set(auto).
% 1.95/2.18 dependent: set(auto1).
% 1.95/2.18 dependent: set(process_input).
% 1.95/2.18 dependent: clear(print_kept).
% 1.95/2.18 dependent: clear(print_new_demod).
% 1.95/2.18 dependent: clear(print_back_demod).
% 1.95/2.18 dependent: clear(print_back_sub).
% 1.95/2.18 dependent: set(control_memory).
% 1.95/2.18 dependent: assign(max_mem, 12000).
% 1.95/2.18 dependent: assign(pick_given_ratio, 4).
% 1.95/2.18 dependent: assign(stats_level, 1).
% 1.95/2.18 dependent: assign(max_seconds, 10800).
% 1.95/2.18 clear(print_given).
% 1.95/2.18
% 1.95/2.18 list(usable).
% 1.95/2.18 0 [] A=A.
% 1.95/2.18 0 [] multiply(multiply(V,W,X),Y,multiply(V,W,Z))=multiply(V,W,multiply(X,Y,Z)).
% 1.95/2.18 0 [] multiply(Y,X,X)=X.
% 1.95/2.18 0 [] multiply(X,X,Y)=X.
% 1.95/2.18 0 [] multiply(inverse(Y),Y,X)=X.
% 1.95/2.18 0 [] multiply(a,inverse(a),b)!=b.
% 1.95/2.18 end_of_list.
% 1.95/2.18
% 1.95/2.18 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.95/2.18
% 1.95/2.18 All clauses are units, and equality is present; the
% 1.95/2.18 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.95/2.18
% 1.95/2.18 dependent: set(knuth_bendix).
% 1.95/2.18 dependent: set(anl_eq).
% 1.95/2.18 dependent: set(para_from).
% 1.95/2.18 dependent: set(para_into).
% 1.95/2.18 dependent: clear(para_from_right).
% 1.95/2.18 dependent: clear(para_into_right).
% 1.95/2.18 dependent: set(para_from_vars).
% 1.95/2.18 dependent: set(eq_units_both_ways).
% 1.95/2.18 dependent: set(dynamic_demod_all).
% 1.95/2.18 dependent: set(dynamic_demod).
% 1.95/2.18 dependent: set(order_eq).
% 1.95/2.18 dependent: set(back_demod).
% 1.95/2.18 dependent: set(lrpo).
% 1.95/2.18
% 1.95/2.18 ------------> process usable:
% 1.95/2.18 ** KEPT (pick-wt=7): 1 [] multiply(a,inverse(a),b)!=b.
% 1.95/2.18
% 1.95/2.18 ------------> process sos:
% 1.95/2.18 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.95/2.18 ** KEPT (pick-wt=18): 3 [] multiply(multiply(A,B,C),D,multiply(A,B,E))=multiply(A,B,multiply(C,D,E)).
% 1.95/2.18 ---> New Demodulator: 4 [new_demod,3] multiply(multiply(A,B,C),D,multiply(A,B,E))=multiply(A,B,multiply(C,D,E)).
% 1.95/2.18 ** KEPT (pick-wt=6): 5 [] multiply(A,B,B)=B.
% 1.95/2.18 ---> New Demodulator: 6 [new_demod,5] multiply(A,B,B)=B.
% 1.95/2.18 ** KEPT (pick-wt=6): 7 [] multiply(A,A,B)=A.
% 1.95/2.18 ---> New Demodulator: 8 [new_demod,7] multiply(A,A,B)=A.
% 1.95/2.18 ** KEPT (pick-wt=7): 9 [] multiply(inverse(A),A,B)=B.
% 1.95/2.18 ---> New Demodulator: 10 [new_demod,9] multiply(inverse(A),A,B)=B.
% 1.95/2.18 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.95/2.18 >>>> Starting back demodulation with 4.
% 1.95/2.18 >>>> Starting back demodulation with 6.
% 1.95/2.18 >>>> Starting back demodulation with 8.
% 1.95/2.18 >>>> Starting back demodulation with 10.
% 1.95/2.18
% 1.95/2.18 ======= end of input processing =======
% 1.95/2.18
% 1.95/2.18 =========== start of search ===========
% 1.95/2.18
% 1.95/2.18
% 1.95/2.18 Resetting weight limit to 18.
% 1.95/2.18
% 1.95/2.18
% 1.95/2.18 Resetting weight limit to 18.
% 1.95/2.18
% 1.95/2.18 sos_size=1210
% 1.95/2.18
% 1.95/2.18 -------- PROOF --------
% 1.95/2.18
% 1.95/2.18 ----> UNIT CONFLICT at 0.29 sec ----> 2700 [binary,2698.1,1.1] $F.
% 1.95/2.18
% 1.95/2.18 Length of proof is 19. Level of proof is 10.
% 1.95/2.18
% 1.95/2.18 ---------------- PROOF ----------------
% 1.95/2.18 % SZS status Unsatisfiable
% 1.95/2.18 % 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 58
% 1.95/2.19 clauses generated 6879
% 1.95/2.19 clauses kept 1632
% 1.95/2.19 clauses forward subsumed 4260
% 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 0.29 (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 17666 finished Wed Jul 27 02:35:09 2022
% 1.95/2.19 Otter interrupted
% 1.95/2.19 PROOF FOUND
%------------------------------------------------------------------------------