%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG004-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:45:52 EDT 2022
% Result : Unsatisfiable 155.47s 155.61s
% Output : Refutation 155.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of clauses : 24 ( 19 unt; 0 nHn; 11 RR)
% Number of literals : 34 ( 33 equ; 11 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(A,B) != C
| multiply(D,B) != C
| A = D ),
file('ALG004-1.p',unknown),
[] ).
cnf(2,axiom,
( multiply(A,B) != C
| multiply(A,D) != C
| B = D ),
file('ALG004-1.p',unknown),
[] ).
cnf(3,axiom,
multiply(d,d0) != multiply(c,c0),
file('ALG004-1.p',unknown),
[] ).
cnf(4,axiom,
A = A,
file('ALG004-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(multiply(A,B),multiply(C,D)) = multiply(multiply(A,C),multiply(B,D)),
file('ALG004-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(b,b0) = multiply(a,a0),
file('ALG004-1.p',unknown),
[] ).
cnf(8,axiom,
multiply(d,b0) = multiply(c,a0),
file('ALG004-1.p',unknown),
[] ).
cnf(10,axiom,
multiply(b,d0) = multiply(a,c0),
file('ALG004-1.p',unknown),
[] ).
cnf(52,plain,
multiply(multiply(b,A),multiply(d0,B)) = multiply(multiply(a,c0),multiply(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,10])]),
[iquote('para_into,5.1.1.1,10.1.1,flip.1')] ).
cnf(54,plain,
multiply(multiply(d,A),multiply(b0,B)) = multiply(multiply(c,a0),multiply(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,8])]),
[iquote('para_into,5.1.1.1,8.1.1,flip.1')] ).
cnf(58,plain,
multiply(multiply(multiply(A,B),multiply(C,D)),multiply(E,F)) = multiply(multiply(multiply(A,C),E),multiply(multiply(B,D),F)),
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,5.1.1.1,5.1.1')] ).
cnf(69,plain,
multiply(multiply(multiply(A,B),C),multiply(multiply(D,E),F)) = multiply(multiply(multiply(A,D),multiply(B,E)),multiply(C,F)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[58])]),
[iquote('copy,58,flip.1')] ).
cnf(77,plain,
( multiply(multiply(A,B),multiply(C,D)) != E
| multiply(F,multiply(B,D)) != E
| multiply(A,C) = F ),
inference(para_from,[status(thm),theory(equality)],[5,1]),
[iquote('para_from,5.1.1,1.1.1')] ).
cnf(307,plain,
multiply(multiply(a,c0),multiply(b0,A)) = multiply(multiply(a,a0),multiply(d0,A)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[52,6])]),
[iquote('para_into,52.1.1.1,6.1.1,flip.1')] ).
cnf(438,plain,
multiply(multiply(a,b0),multiply(c0,A)) = multiply(multiply(a,a0),multiply(d0,A)),
inference(para_into,[status(thm),theory(equality)],[307,5]),
[iquote('para_into,307.1.1,5.1.1')] ).
cnf(528,plain,
multiply(multiply(A,B),multiply(multiply(a,a0),multiply(d0,C))) = multiply(multiply(A,multiply(a,b0)),multiply(B,multiply(c0,C))),
inference(para_from,[status(thm),theory(equality)],[438,5]),
[iquote('para_from,438.1.1,5.1.1.2')] ).
cnf(1338,plain,
( multiply(multiply(multiply(A,B),multiply(C,D)),E) != F
| multiply(multiply(multiply(A,C),G),multiply(multiply(B,D),H)) != F
| E = multiply(G,H) ),
inference(para_from,[status(thm),theory(equality)],[58,2]),
[iquote('para_from,58.1.1,2.2.1')] ).
cnf(2104,plain,
( multiply(multiply(A,b0),multiply(B,C)) != D
| multiply(multiply(c,a0),multiply(E,C)) != D
| multiply(A,B) = multiply(d,E) ),
inference(para_into,[status(thm),theory(equality)],[77,54]),
[iquote('para_into,77.2.1,54.1.1')] ).
cnf(2505,plain,
multiply(multiply(multiply(A,B),multiply(C,D)),multiply(E,F)) = multiply(multiply(multiply(A,C),multiply(B,D)),multiply(E,F)),
inference(para_into,[status(thm),theory(equality)],[69,5]),
[iquote('para_into,69.1.1,5.1.1')] ).
cnf(3041,plain,
multiply(multiply(A,multiply(a,a0)),multiply(B,multiply(d0,C))) = multiply(multiply(A,multiply(a,b0)),multiply(B,multiply(c0,C))),
inference(para_into,[status(thm),theory(equality)],[528,5]),
[iquote('para_into,528.1.1,5.1.1')] ).
cnf(3044,plain,
multiply(multiply(A,multiply(a,b0)),multiply(B,multiply(c0,C))) = multiply(multiply(A,multiply(a,a0)),multiply(B,multiply(d0,C))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3041])]),
[iquote('copy,3041,flip.1')] ).
cnf(3091,plain,
multiply(multiply(A,b0),multiply(c0,B)) = multiply(multiply(A,a0),multiply(d0,B)),
inference(hyper,[status(thm)],[1338,3044,2505]),
[iquote('hyper,1338,3044,2505')] ).
cnf(3095,plain,
multiply(d,d0) = multiply(c,c0),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[3091,2104,4])]),
[iquote('hyper,3091,2104,4,flip.1')] ).
cnf(3097,plain,
$false,
inference(binary,[status(thm)],[3095,3]),
[iquote('binary,3095.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG004-1 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n026.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 04:05:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 155.47/155.61 ----- Otter 3.3f, August 2004 -----
% 155.47/155.61 The process was started by sandbox2 on n026.cluster.edu,
% 155.47/155.61 Wed Jul 27 04:05:09 2022
% 155.47/155.61 The command was "./otter". The process ID is 26185.
% 155.47/155.61
% 155.47/155.61 set(prolog_style_variables).
% 155.47/155.61 set(auto).
% 155.47/155.61 dependent: set(auto1).
% 155.47/155.61 dependent: set(process_input).
% 155.47/155.61 dependent: clear(print_kept).
% 155.47/155.61 dependent: clear(print_new_demod).
% 155.47/155.61 dependent: clear(print_back_demod).
% 155.47/155.61 dependent: clear(print_back_sub).
% 155.47/155.61 dependent: set(control_memory).
% 155.47/155.61 dependent: assign(max_mem, 12000).
% 155.47/155.61 dependent: assign(pick_given_ratio, 4).
% 155.47/155.61 dependent: assign(stats_level, 1).
% 155.47/155.61 dependent: assign(max_seconds, 10800).
% 155.47/155.61 clear(print_given).
% 155.47/155.61
% 155.47/155.61 list(usable).
% 155.47/155.61 0 [] A=A.
% 155.47/155.61 0 [] multiply(X,Y)!=Z|multiply(U,Y)!=Z|X=U.
% 155.47/155.61 0 [] multiply(X,Y)!=Z|multiply(X,U)!=Z|Y=U.
% 155.47/155.61 0 [] multiply(multiply(X,Y),multiply(Z,U))=multiply(multiply(X,Z),multiply(Y,U)).
% 155.47/155.61 0 [] multiply(b,b0)=multiply(a,a0).
% 155.47/155.61 0 [] multiply(d,b0)=multiply(c,a0).
% 155.47/155.61 0 [] multiply(b,d0)=multiply(a,c0).
% 155.47/155.61 0 [] multiply(d,d0)!=multiply(c,c0).
% 155.47/155.61 end_of_list.
% 155.47/155.61
% 155.47/155.61 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 155.47/155.61
% 155.47/155.61 This is a Horn set with equality. The strategy will be
% 155.47/155.61 Knuth-Bendix and hyper_res, with positive clauses in
% 155.47/155.61 sos and nonpositive clauses in usable.
% 155.47/155.61
% 155.47/155.61 dependent: set(knuth_bendix).
% 155.47/155.61 dependent: set(anl_eq).
% 155.47/155.61 dependent: set(para_from).
% 155.47/155.61 dependent: set(para_into).
% 155.47/155.61 dependent: clear(para_from_right).
% 155.47/155.61 dependent: clear(para_into_right).
% 155.47/155.61 dependent: set(para_from_vars).
% 155.47/155.61 dependent: set(eq_units_both_ways).
% 155.47/155.61 dependent: set(dynamic_demod_all).
% 155.47/155.61 dependent: set(dynamic_demod).
% 155.47/155.61 dependent: set(order_eq).
% 155.47/155.61 dependent: set(back_demod).
% 155.47/155.61 dependent: set(lrpo).
% 155.47/155.61 dependent: set(hyper_res).
% 155.47/155.61 dependent: clear(order_hyper).
% 155.47/155.61
% 155.47/155.61 ------------> process usable:
% 155.47/155.61 ** KEPT (pick-wt=13): 1 [] multiply(A,B)!=C|multiply(D,B)!=C|A=D.
% 155.47/155.61 ** KEPT (pick-wt=13): 2 [] multiply(A,B)!=C|multiply(A,D)!=C|B=D.
% 155.47/155.61 ** KEPT (pick-wt=7): 3 [] multiply(d,d0)!=multiply(c,c0).
% 155.47/155.61
% 155.47/155.61 ------------> process sos:
% 155.47/155.61 ** KEPT (pick-wt=3): 4 [] A=A.
% 155.47/155.61 ** KEPT (pick-wt=15): 5 [] multiply(multiply(A,B),multiply(C,D))=multiply(multiply(A,C),multiply(B,D)).
% 155.47/155.61 ** KEPT (pick-wt=7): 6 [] multiply(b,b0)=multiply(a,a0).
% 155.47/155.61 ---> New Demodulator: 7 [new_demod,6] multiply(b,b0)=multiply(a,a0).
% 155.47/155.61 ** KEPT (pick-wt=7): 8 [] multiply(d,b0)=multiply(c,a0).
% 155.47/155.61 ---> New Demodulator: 9 [new_demod,8] multiply(d,b0)=multiply(c,a0).
% 155.47/155.61 ** KEPT (pick-wt=7): 10 [] multiply(b,d0)=multiply(a,c0).
% 155.47/155.61 ---> New Demodulator: 11 [new_demod,10] multiply(b,d0)=multiply(a,c0).
% 155.47/155.61 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 155.47/155.61 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] multiply(multiply(A,B),multiply(C,D))=multiply(multiply(A,C),multiply(B,D)).
% 155.47/155.61 >>>> Starting back demodulation with 7.
% 155.47/155.61 >>>> Starting back demodulation with 9.
% 155.47/155.61 >>>> Starting back demodulation with 11.
% 155.47/155.61
% 155.47/155.61 ======= end of input processing =======
% 155.47/155.61
% 155.47/155.61 =========== start of search ===========
% 155.47/155.61
% 155.47/155.61
% 155.47/155.61 Resetting weight limit to 23.
% 155.47/155.61
% 155.47/155.61
% 155.47/155.61 Resetting weight limit to 23.
% 155.47/155.61
% 155.47/155.61 sos_size=2280
% 155.47/155.61
% 155.47/155.61 -- HEY sandbox2, WE HAVE A PROOF!! --
% 155.47/155.61
% 155.47/155.61 ----> UNIT CONFLICT at 153.47 sec ----> 3097 [binary,3095.1,3.1] $F.
% 155.47/155.61
% 155.47/155.61 Length of proof is 15. Level of proof is 8.
% 155.47/155.61
% 155.47/155.61 ---------------- PROOF ----------------
% 155.47/155.61 % SZS status Unsatisfiable
% 155.47/155.61 % SZS output start Refutation
% See solution above
% 155.47/155.61 ------------ end of proof -------------
% 155.47/155.61
% 155.47/155.61
% 155.47/155.61 Search stopped by max_proofs option.
% 155.47/155.61
% 155.47/155.61
% 155.47/155.61 Search stopped by max_proofs option.
% 155.47/155.61
% 155.47/155.61 ============ end of search ============
% 155.47/155.61
% 155.47/155.61 -------------- statistics -------------
% 155.47/155.61 clauses given 1998
% 155.47/155.61 clauses generated 14187205
% 155.47/155.61 clauses kept 3056
% 155.47/155.61 clauses forward subsumed 34681
% 155.47/155.61 clauses back subsumed 99
% 155.47/155.61 Kbytes malloced 5859
% 155.47/155.61
% 155.47/155.61 ----------- times (seconds) -----------
% 155.47/155.61 user CPU time 153.47 (0 hr, 2 min, 33 sec)
% 155.47/155.61 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 155.47/155.61 wall-clock time 155 (0 hr, 2 min, 35 sec)
% 155.47/155.61
% 155.47/155.61 That finishes the proof of the theorem.
% 155.47/155.61
% 155.47/155.61 Process 26185 finished Wed Jul 27 04:07:44 2022
% 155.47/155.61 Otter interrupted
% 155.47/155.61 PROOF FOUND
%------------------------------------------------------------------------------