TSTP Solution File: ALG210+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ALG210+2 : TPTP v8.1.0. Released v3.1.0.
% 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 12:46:18 EDT 2022
% Result : Theorem 1.71s 1.93s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 46 ( 40 unt; 0 nHn; 30 RR)
% Number of literals : 53 ( 42 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ element(A)
| times(A,dollar_f1(A)) = A ),
file('ALG210+2.p',unknown),
[] ).
cnf(2,axiom,
( ~ element(A)
| times(A,A) = dollar_f1(A) ),
file('ALG210+2.p',unknown),
[] ).
cnf(3,plain,
( ~ element(A)
| dollar_f1(A) = times(A,A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[2])]),
[iquote('copy,2,flip.2')] ).
cnf(4,axiom,
( element(A)
| times(A,B) != A
| times(A,A) != B ),
file('ALG210+2.p',unknown),
[] ).
cnf(5,axiom,
~ element(dollar_c1),
file('ALG210+2.p',unknown),
[] ).
cnf(6,axiom,
A = A,
file('ALG210+2.p',unknown),
[] ).
cnf(7,axiom,
times(times(A,B),C) = times(B,times(C,A)),
file('ALG210+2.p',unknown),
[] ).
cnf(8,axiom,
element(dollar_c3),
file('ALG210+2.p',unknown),
[] ).
cnf(9,axiom,
element(dollar_c2),
file('ALG210+2.p',unknown),
[] ).
cnf(10,axiom,
dollar_c1 = times(dollar_c3,dollar_c2),
file('ALG210+2.p',unknown),
[] ).
cnf(12,plain,
times(dollar_c3,dollar_c2) = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(13,plain,
times(A,times(B,C)) = times(times(C,A),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(15,plain,
dollar_f1(dollar_c3) = times(dollar_c3,dollar_c3),
inference(hyper,[status(thm)],[8,3]),
[iquote('hyper,8,3')] ).
cnf(16,plain,
times(dollar_c3,times(dollar_c3,dollar_c3)) = dollar_c3,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[8,1]),15]),
[iquote('hyper,8,1,demod,15')] ).
cnf(19,plain,
dollar_f1(dollar_c2) = times(dollar_c2,dollar_c2),
inference(hyper,[status(thm)],[9,3]),
[iquote('hyper,9,3')] ).
cnf(20,plain,
times(dollar_c2,times(dollar_c2,dollar_c2)) = dollar_c2,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[9,1]),19]),
[iquote('hyper,9,1,demod,19')] ).
cnf(23,plain,
times(dollar_c2,times(A,dollar_c3)) = times(dollar_c1,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,12])]),
[iquote('para_into,7.1.1.1,11.1.1,flip.1')] ).
cnf(24,plain,
times(times(A,times(B,C)),D) = times(B,times(D,times(C,A))),
inference(para_into,[status(thm),theory(equality)],[7,7]),
[iquote('para_into,7.1.1.1,7.1.1')] ).
cnf(25,plain,
( times(dollar_f1(A),times(B,A)) = times(A,B)
| ~ element(A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,1])]),
[iquote('para_into,7.1.1.1,1.2.1,flip.1')] ).
cnf(27,plain,
times(A,times(B,times(C,D))) = times(times(D,times(A,C)),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[24])]),
[iquote('copy,24,flip.1')] ).
cnf(31,plain,
times(times(dollar_c3,dollar_c3),times(A,dollar_c3)) = times(dollar_c3,A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[16,7])]),
[iquote('para_from,16.1.1,7.1.1.1,flip.1')] ).
cnf(45,plain,
times(times(dollar_c2,A),dollar_c3) = times(A,dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,12])]),
[iquote('para_into,13.1.1.2,11.1.1,flip.1')] ).
cnf(51,plain,
times(times(dollar_c3,dollar_c3),dollar_c3) = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,16])]),
[iquote('para_into,13.1.1,16.1.1,flip.1')] ).
cnf(67,plain,
times(dollar_c1,times(dollar_c3,dollar_c3)) = times(dollar_c2,dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[51,23])]),
[iquote('para_from,51.1.1,22.1.1.2,flip.1')] ).
cnf(69,plain,
times(times(dollar_c3,A),times(dollar_c3,dollar_c3)) = times(A,dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[51,13])]),
[iquote('para_from,51.1.1,13.1.1.2,flip.1')] ).
cnf(124,plain,
times(times(dollar_c3,dollar_c1),dollar_c3) = times(dollar_c2,dollar_c3),
inference(para_into,[status(thm),theory(equality)],[67,13]),
[iquote('para_into,66.1.1,13.1.1')] ).
cnf(130,plain,
times(times(dollar_c3,dollar_c3),times(A,dollar_c1)) = times(times(dollar_c2,dollar_c3),A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[67,7])]),
[iquote('para_from,66.1.1,7.1.1.1,flip.1')] ).
cnf(135,plain,
times(dollar_c1,times(dollar_c3,dollar_c1)) = times(dollar_c1,dollar_c2),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[124,23]),23])]),
[iquote('para_from,124.1.1,22.1.1.2,demod,23,flip.1')] ).
cnf(142,plain,
times(times(dollar_c1,dollar_c1),dollar_c3) = times(dollar_c1,dollar_c2),
inference(para_into,[status(thm),theory(equality)],[135,13]),
[iquote('para_into,135.1.1,13.1.1')] ).
cnf(155,plain,
( times(dollar_c3,times(dollar_c3,dollar_c1)) = dollar_c1
| ~ element(dollar_c3) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,124]),15,31,12])]),
[iquote('para_into,25.1.1.2,124.1.1,demod,15,31,12,flip.1')] ).
cnf(174,plain,
times(dollar_c2,times(dollar_c1,dollar_c2)) = times(dollar_c1,times(dollar_c1,dollar_c1)),
inference(para_from,[status(thm),theory(equality)],[142,23]),
[iquote('para_from,142.1.1,22.1.1.2')] ).
cnf(180,plain,
times(dollar_c3,times(dollar_c3,dollar_c1)) = dollar_c1,
inference(hyper,[status(thm)],[155,8]),
[iquote('hyper,155,8')] ).
cnf(183,plain,
times(times(dollar_c1,dollar_c3),dollar_c3) = dollar_c1,
inference(para_into,[status(thm),theory(equality)],[180,13]),
[iquote('para_into,180.1.1,13.1.1')] ).
cnf(196,plain,
times(dollar_c2,dollar_c1) = times(dollar_c1,times(dollar_c1,dollar_c3)),
inference(para_from,[status(thm),theory(equality)],[183,23]),
[iquote('para_from,183.1.1,22.1.1.2')] ).
cnf(243,plain,
times(times(dollar_c1,A),dollar_c2) = times(A,times(dollar_c1,times(dollar_c1,dollar_c3))),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[196,13])]),
[iquote('para_from,195.1.1,13.1.1.2,flip.1')] ).
cnf(251,plain,
times(times(dollar_c2,dollar_c3),A) = times(dollar_c3,times(dollar_c2,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[31,45]),130]),
[iquote('para_into,30.1.1.2,45.1.1,demod,130')] ).
cnf(293,plain,
times(times(A,B),dollar_c3) = times(A,times(dollar_c3,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,31]),69])]),
[iquote('para_into,27.1.1.2,30.1.1,demod,69,flip.1')] ).
cnf(328,plain,
times(dollar_c2,dollar_c3) = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[183]),293,67]),
[iquote('back_demod,183,demod,293,67')] ).
cnf(346,plain,
times(dollar_c3,times(dollar_c2,A)) = times(dollar_c1,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[251]),328])]),
[iquote('back_demod,251,demod,328,flip.1')] ).
cnf(390,plain,
times(dollar_c1,times(dollar_c1,dollar_c3)) = times(dollar_c1,dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[328,23]),196]),
[iquote('para_from,327.1.1,22.1.1.2,demod,196')] ).
cnf(402,plain,
times(times(dollar_c1,A),dollar_c2) = times(A,times(dollar_c1,dollar_c2)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[243]),390]),
[iquote('back_demod,243,demod,390')] ).
cnf(406,plain,
times(dollar_c2,dollar_c1) = times(dollar_c1,dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[196]),390]),
[iquote('back_demod,195,demod,390')] ).
cnf(510,plain,
times(dollar_c1,times(dollar_c2,dollar_c2)) = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[346,20]),12])]),
[iquote('para_into,346.1.1.2,20.1.1,demod,12,flip.1')] ).
cnf(590,plain,
times(dollar_c1,times(dollar_c1,dollar_c1)) = dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[510,13]),406,402,174]),
[iquote('para_into,510.1.1,13.1.1,demod,406,402,174')] ).
cnf(612,plain,
element(dollar_c1),
inference(hyper,[status(thm)],[590,4,6]),
[iquote('hyper,590,4,6')] ).
cnf(613,plain,
$false,
inference(binary,[status(thm)],[612,5]),
[iquote('binary,612.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ALG210+2 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.11/0.32 % Computer : n012.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Wed Jul 27 03:51:35 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.71/1.93 ----- Otter 3.3f, August 2004 -----
% 1.71/1.93 The process was started by sandbox2 on n012.cluster.edu,
% 1.71/1.93 Wed Jul 27 03:51:35 2022
% 1.71/1.93 The command was "./otter". The process ID is 12176.
% 1.71/1.93
% 1.71/1.93 set(prolog_style_variables).
% 1.71/1.93 set(auto).
% 1.71/1.93 dependent: set(auto1).
% 1.71/1.93 dependent: set(process_input).
% 1.71/1.93 dependent: clear(print_kept).
% 1.71/1.93 dependent: clear(print_new_demod).
% 1.71/1.93 dependent: clear(print_back_demod).
% 1.71/1.93 dependent: clear(print_back_sub).
% 1.71/1.93 dependent: set(control_memory).
% 1.71/1.93 dependent: assign(max_mem, 12000).
% 1.71/1.93 dependent: assign(pick_given_ratio, 4).
% 1.71/1.93 dependent: assign(stats_level, 1).
% 1.71/1.93 dependent: assign(max_seconds, 10800).
% 1.71/1.93 clear(print_given).
% 1.71/1.93
% 1.71/1.93 formula_list(usable).
% 1.71/1.93 all A (A=A).
% 1.71/1.93 all A B C (times(times(A,B),C)=times(B,times(C,A))).
% 1.71/1.93 all B (element(B)<-> (exists C (times(B,C)=B×(B,B)=C))).
% 1.71/1.93 -(all A B C (element(A)&element(B)&C=times(A,B)->element(C))).
% 1.71/1.93 end_of_list.
% 1.71/1.93
% 1.71/1.93 -------> usable clausifies to:
% 1.71/1.93
% 1.71/1.93 list(usable).
% 1.71/1.93 0 [] A=A.
% 1.71/1.93 0 [] times(times(A,B),C)=times(B,times(C,A)).
% 1.71/1.93 0 [] -element(B)|times(B,$f1(B))=B.
% 1.71/1.93 0 [] -element(B)|times(B,B)=$f1(B).
% 1.71/1.93 0 [] element(B)|times(B,C)!=B|times(B,B)!=C.
% 1.71/1.93 0 [] element($c3).
% 1.71/1.93 0 [] element($c2).
% 1.71/1.93 0 [] $c1=times($c3,$c2).
% 1.71/1.93 0 [] -element($c1).
% 1.71/1.93 end_of_list.
% 1.71/1.93
% 1.71/1.93 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.71/1.93
% 1.71/1.93 This is a Horn set with equality. The strategy will be
% 1.71/1.93 Knuth-Bendix and hyper_res, with positive clauses in
% 1.71/1.93 sos and nonpositive clauses in usable.
% 1.71/1.93
% 1.71/1.93 dependent: set(knuth_bendix).
% 1.71/1.93 dependent: set(anl_eq).
% 1.71/1.93 dependent: set(para_from).
% 1.71/1.93 dependent: set(para_into).
% 1.71/1.93 dependent: clear(para_from_right).
% 1.71/1.93 dependent: clear(para_into_right).
% 1.71/1.93 dependent: set(para_from_vars).
% 1.71/1.93 dependent: set(eq_units_both_ways).
% 1.71/1.93 dependent: set(dynamic_demod_all).
% 1.71/1.93 dependent: set(dynamic_demod).
% 1.71/1.93 dependent: set(order_eq).
% 1.71/1.93 dependent: set(back_demod).
% 1.71/1.93 dependent: set(lrpo).
% 1.71/1.93 dependent: set(hyper_res).
% 1.71/1.93 dependent: clear(order_hyper).
% 1.71/1.93
% 1.71/1.93 ------------> process usable:
% 1.71/1.93 ** KEPT (pick-wt=8): 1 [] -element(A)|times(A,$f1(A))=A.
% 1.71/1.93 ** KEPT (pick-wt=8): 3 [copy,2,flip.2] -element(A)|$f1(A)=times(A,A).
% 1.71/1.93 ** KEPT (pick-wt=12): 4 [] element(A)|times(A,B)!=A|times(A,A)!=B.
% 1.71/1.93 ** KEPT (pick-wt=2): 5 [] -element($c1).
% 1.71/1.93
% 1.71/1.93 ------------> process sos:
% 1.71/1.93 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.71/1.93 ** KEPT (pick-wt=11): 7 [] times(times(A,B),C)=times(B,times(C,A)).
% 1.71/1.93 ** KEPT (pick-wt=2): 8 [] element($c3).
% 1.71/1.93 ** KEPT (pick-wt=2): 9 [] element($c2).
% 1.71/1.93 ** KEPT (pick-wt=5): 11 [copy,10,flip.1] times($c3,$c2)=$c1.
% 1.71/1.93 ---> New Demodulator: 12 [new_demod,11] times($c3,$c2)=$c1.
% 1.71/1.93 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.71/1.93 ** KEPT (pick-wt=11): 13 [copy,7,flip.1] times(A,times(B,C))=times(times(C,A),B).
% 1.71/1.93 >>>> Starting back demodulation with 12.
% 1.71/1.93 Following clause subsumed by 7 during input processing: 0 [copy,13,flip.1] times(times(A,B),C)=times(B,times(C,A)).
% 1.71/1.93
% 1.71/1.93 ======= end of input processing =======
% 1.71/1.93
% 1.71/1.93 =========== start of search ===========
% 1.71/1.93
% 1.71/1.93 -------- PROOF --------
% 1.71/1.93
% 1.71/1.93 ----> UNIT CONFLICT at 0.03 sec ----> 613 [binary,612.1,5.1] $F.
% 1.71/1.93
% 1.71/1.93 Length of proof is 36. Level of proof is 14.
% 1.71/1.93
% 1.71/1.93 ---------------- PROOF ----------------
% 1.71/1.93 % SZS status Theorem
% 1.71/1.93 % SZS output start Refutation
% See solution above
% 1.71/1.93 ------------ end of proof -------------
% 1.71/1.93
% 1.71/1.93
% 1.71/1.93 Search stopped by max_proofs option.
% 1.71/1.93
% 1.71/1.93
% 1.71/1.93 Search stopped by max_proofs option.
% 1.71/1.93
% 1.71/1.93 ============ end of search ============
% 1.71/1.93
% 1.71/1.93 -------------- statistics -------------
% 1.71/1.93 clauses given 43
% 1.71/1.93 clauses generated 701
% 1.71/1.93 clauses kept 518
% 1.71/1.93 clauses forward subsumed 505
% 1.71/1.93 clauses back subsumed 1
% 1.71/1.93 Kbytes malloced 2929
% 1.71/1.93
% 1.71/1.93 ----------- times (seconds) -----------
% 1.71/1.93 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.71/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.93 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.71/1.93
% 1.71/1.93 That finishes the proof of the theorem.
% 1.71/1.93
% 1.71/1.93 Process 12176 finished Wed Jul 27 03:51:37 2022
% 1.71/1.93 Otter interrupted
% 1.71/1.93 PROOF FOUND
%------------------------------------------------------------------------------