TSTP Solution File: KLE040+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE040+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 13:00:35 EDT 2022
% Result : Theorem 2.95s 3.17s
% Output : Refutation 2.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 20 unt; 0 nHn; 9 RR)
% Number of literals : 41 ( 14 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 56 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE040+2.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE040+2.p',unknown),
[] ).
cnf(4,axiom,
( ~ le_q(addition(multiplication(A,B),C),A)
| le_q(multiplication(C,star(B)),A) ),
file('KLE040+2.p',unknown),
[] ).
cnf(5,axiom,
( ~ le_q(multiplication(star(dollar_c1),star(dollar_c1)),star(dollar_c1))
| ~ le_q(star(dollar_c1),multiplication(star(dollar_c1),star(dollar_c1))) ),
file('KLE040+2.p',unknown),
[] ).
cnf(7,axiom,
addition(A,B) = addition(B,A),
file('KLE040+2.p',unknown),
[] ).
cnf(8,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE040+2.p',unknown),
[] ).
cnf(10,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.1')] ).
cnf(13,axiom,
addition(A,A) = A,
file('KLE040+2.p',unknown),
[] ).
cnf(19,axiom,
multiplication(A,one) = A,
file('KLE040+2.p',unknown),
[] ).
cnf(22,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE040+2.p',unknown),
[] ).
cnf(31,axiom,
le_q(addition(one,multiplication(star(A),A)),star(A)),
file('KLE040+2.p',unknown),
[] ).
cnf(38,plain,
le_q(A,A),
inference(hyper,[status(thm)],[13,2]),
[iquote('hyper,13,2')] ).
cnf(43,plain,
( addition(A,B) = A
| ~ le_q(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,1])]),
[iquote('para_into,7.1.1,1.2.1,flip.1')] ).
cnf(44,plain,
( ~ le_q(addition(A,multiplication(B,C)),B)
| le_q(multiplication(A,star(C)),B) ),
inference(para_from,[status(thm),theory(equality)],[7,4]),
[iquote('para_from,7.1.1,4.1.1')] ).
cnf(57,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,13])]),
[iquote('para_into,9.1.1.1,13.1.1,flip.1')] ).
cnf(113,plain,
( addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,C)
| ~ le_q(B,C) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,1])]),
[iquote('para_into,22.1.1.2,1.2.1,flip.1')] ).
cnf(178,plain,
addition(one,addition(multiplication(star(A),A),star(A))) = star(A),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[31,1]),10]),
[iquote('hyper,31,1,demod,10')] ).
cnf(263,plain,
( ~ le_q(A,B)
| le_q(multiplication(A,star(C)),B)
| ~ le_q(multiplication(B,C),A) ),
inference(para_into,[status(thm),theory(equality)],[44,43]),
[iquote('para_into,44.1.1,43.1.1')] ).
cnf(458,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[57,2]),
[iquote('hyper,57,2')] ).
cnf(474,plain,
le_q(A,addition(B,A)),
inference(para_into,[status(thm),theory(equality)],[458,7]),
[iquote('para_into,458.1.2,7.1.1')] ).
cnf(484,plain,
le_q(A,addition(B,addition(C,A))),
inference(para_into,[status(thm),theory(equality)],[474,10]),
[iquote('para_into,474.1.2,9.1.1')] ).
cnf(495,plain,
( le_q(A,B)
| ~ le_q(addition(C,A),B) ),
inference(para_into,[status(thm),theory(equality)],[484,43]),
[iquote('para_into,484.1.2,43.1.1')] ).
cnf(539,plain,
le_q(multiplication(star(A),A),star(A)),
inference(hyper,[status(thm)],[495,31]),
[iquote('hyper,495,31')] ).
cnf(571,plain,
addition(multiplication(star(A),A),star(A)) = star(A),
inference(hyper,[status(thm)],[539,1]),
[iquote('hyper,539,1')] ).
cnf(572,plain,
addition(one,star(A)) = star(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[178]),571]),
[iquote('back_demod,178,demod,571')] ).
cnf(586,plain,
le_q(one,star(A)),
inference(hyper,[status(thm)],[572,2]),
[iquote('hyper,572,2')] ).
cnf(2374,plain,
( le_q(multiplication(A,B),multiplication(A,C))
| ~ le_q(B,C) ),
inference(para_from,[status(thm),theory(equality)],[113,458]),
[iquote('para_from,113.1.1,458.1.2')] ).
cnf(3409,plain,
le_q(A,multiplication(A,star(B))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2374,586]),19]),
[iquote('hyper,2374,586,demod,19')] ).
cnf(3967,plain,
le_q(multiplication(star(A),star(A)),star(A)),
inference(hyper,[status(thm)],[263,38,539]),
[iquote('hyper,263,38,539')] ).
cnf(3974,plain,
$false,
inference(hyper,[status(thm)],[3967,5,3409]),
[iquote('hyper,3967,5,3409')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE040+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n024.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 06:31:25 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.78/1.99 ----- Otter 3.3f, August 2004 -----
% 1.78/1.99 The process was started by sandbox2 on n024.cluster.edu,
% 1.78/1.99 Wed Jul 27 06:31:25 2022
% 1.78/1.99 The command was "./otter". The process ID is 5458.
% 1.78/1.99
% 1.78/1.99 set(prolog_style_variables).
% 1.78/1.99 set(auto).
% 1.78/1.99 dependent: set(auto1).
% 1.78/1.99 dependent: set(process_input).
% 1.78/1.99 dependent: clear(print_kept).
% 1.78/1.99 dependent: clear(print_new_demod).
% 1.78/1.99 dependent: clear(print_back_demod).
% 1.78/1.99 dependent: clear(print_back_sub).
% 1.78/1.99 dependent: set(control_memory).
% 1.78/1.99 dependent: assign(max_mem, 12000).
% 1.78/1.99 dependent: assign(pick_given_ratio, 4).
% 1.78/1.99 dependent: assign(stats_level, 1).
% 1.78/1.99 dependent: assign(max_seconds, 10800).
% 1.78/1.99 clear(print_given).
% 1.78/1.99
% 1.78/1.99 formula_list(usable).
% 1.78/1.99 all A (A=A).
% 1.78/1.99 all A B (addition(A,B)=addition(B,A)).
% 1.78/1.99 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.78/1.99 all A (addition(A,zero)=A).
% 1.78/1.99 all A (addition(A,A)=A).
% 1.78/1.99 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.78/1.99 all A (multiplication(A,one)=A).
% 1.78/1.99 all A (multiplication(one,A)=A).
% 1.78/1.99 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.78/1.99 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.78/1.99 all A (multiplication(A,zero)=zero).
% 1.78/1.99 all A (multiplication(zero,A)=zero).
% 1.78/1.99 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.78/1.99 all A le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.78/1.99 all A le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.78/1.99 all A B C (le_q(addition(multiplication(A,B),C),B)->le_q(multiplication(star(A),C),B)).
% 1.78/1.99 all A B C (le_q(addition(multiplication(A,B),C),A)->le_q(multiplication(C,star(B)),A)).
% 1.78/1.99 -(all X0 (le_q(multiplication(star(X0),star(X0)),star(X0))&le_q(star(X0),multiplication(star(X0),star(X0))))).
% 1.78/1.99 end_of_list.
% 1.78/1.99
% 1.78/1.99 -------> usable clausifies to:
% 1.78/1.99
% 1.78/1.99 list(usable).
% 1.78/1.99 0 [] A=A.
% 1.78/1.99 0 [] addition(A,B)=addition(B,A).
% 1.78/1.99 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.78/1.99 0 [] addition(A,zero)=A.
% 1.78/1.99 0 [] addition(A,A)=A.
% 1.78/1.99 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.78/1.99 0 [] multiplication(A,one)=A.
% 1.78/1.99 0 [] multiplication(one,A)=A.
% 1.78/1.99 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.78/1.99 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.78/1.99 0 [] multiplication(A,zero)=zero.
% 1.78/1.99 0 [] multiplication(zero,A)=zero.
% 1.78/1.99 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.78/1.99 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.78/1.99 0 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.78/1.99 0 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.78/1.99 0 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.78/1.99 0 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.78/1.99 0 [] -le_q(multiplication(star($c1),star($c1)),star($c1))| -le_q(star($c1),multiplication(star($c1),star($c1))).
% 1.78/1.99 end_of_list.
% 1.78/1.99
% 1.78/1.99 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.78/1.99
% 1.78/1.99 This is a Horn set with equality. The strategy will be
% 1.78/1.99 Knuth-Bendix and hyper_res, with positive clauses in
% 1.78/1.99 sos and nonpositive clauses in usable.
% 1.78/1.99
% 1.78/1.99 dependent: set(knuth_bendix).
% 1.78/1.99 dependent: set(anl_eq).
% 1.78/1.99 dependent: set(para_from).
% 1.78/1.99 dependent: set(para_into).
% 1.78/1.99 dependent: clear(para_from_right).
% 1.78/1.99 dependent: clear(para_into_right).
% 1.78/1.99 dependent: set(para_from_vars).
% 1.78/1.99 dependent: set(eq_units_both_ways).
% 1.78/1.99 dependent: set(dynamic_demod_all).
% 1.78/1.99 dependent: set(dynamic_demod).
% 1.78/1.99 dependent: set(order_eq).
% 1.78/1.99 dependent: set(back_demod).
% 1.78/1.99 dependent: set(lrpo).
% 1.78/1.99 dependent: set(hyper_res).
% 1.78/1.99 dependent: clear(order_hyper).
% 1.78/1.99
% 1.78/1.99 ------------> process usable:
% 1.78/1.99 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.78/1.99 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.78/1.99 ** KEPT (pick-wt=13): 3 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.78/1.99 ** KEPT (pick-wt=13): 4 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.78/1.99 ** KEPT (pick-wt=16): 5 [] -le_q(multiplication(star($c1),star($c1)),star($c1))| -le_q(star($c1),multiplication(star($c1),star($c1))).
% 1.78/1.99
% 1.78/1.99 ------------> process sos:
% 1.78/1.99 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.78/1.99 ** KEPT (pick-wt=7): 7 [] addition(A,B)=addition(B,A).
% 1.78/1.99 ** KEPT (pick-wt=11): 9 [copy,8,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.95/3.17 ---> New Demodulator: 10 [new_demod,9] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.95/3.17 ** KEPT (pick-wt=5): 11 [] addition(A,zero)=A.
% 2.95/3.17 ---> New Demodulator: 12 [new_demod,11] addition(A,zero)=A.
% 2.95/3.17 ** KEPT (pick-wt=5): 13 [] addition(A,A)=A.
% 2.95/3.17 ---> New Demodulator: 14 [new_demod,13] addition(A,A)=A.
% 2.95/3.17 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.95/3.17 ---> New Demodulator: 17 [new_demod,16] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.95/3.17 ** KEPT (pick-wt=5): 18 [] multiplication(A,one)=A.
% 2.95/3.17 ---> New Demodulator: 19 [new_demod,18] multiplication(A,one)=A.
% 2.95/3.17 ** KEPT (pick-wt=5): 20 [] multiplication(one,A)=A.
% 2.95/3.17 ---> New Demodulator: 21 [new_demod,20] multiplication(one,A)=A.
% 2.95/3.17 ** KEPT (pick-wt=13): 22 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.95/3.17 ---> New Demodulator: 23 [new_demod,22] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.95/3.17 ** KEPT (pick-wt=13): 24 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.95/3.17 ---> New Demodulator: 25 [new_demod,24] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.95/3.17 ** KEPT (pick-wt=5): 26 [] multiplication(A,zero)=zero.
% 2.95/3.17 ---> New Demodulator: 27 [new_demod,26] multiplication(A,zero)=zero.
% 2.95/3.17 ** KEPT (pick-wt=5): 28 [] multiplication(zero,A)=zero.
% 2.95/3.17 ---> New Demodulator: 29 [new_demod,28] multiplication(zero,A)=zero.
% 2.95/3.17 ** KEPT (pick-wt=9): 30 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 2.95/3.17 ** KEPT (pick-wt=9): 31 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 2.95/3.17 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 2.95/3.17 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] addition(A,B)=addition(B,A).
% 2.95/3.17 >>>> Starting back demodulation with 10.
% 2.95/3.17 >>>> Starting back demodulation with 12.
% 2.95/3.17 >>>> Starting back demodulation with 14.
% 2.95/3.17 >>>> Starting back demodulation with 17.
% 2.95/3.17 >>>> Starting back demodulation with 19.
% 2.95/3.17 >>>> Starting back demodulation with 21.
% 2.95/3.17 >>>> Starting back demodulation with 23.
% 2.95/3.17 >>>> Starting back demodulation with 25.
% 2.95/3.17 >>>> Starting back demodulation with 27.
% 2.95/3.17 >>>> Starting back demodulation with 29.
% 2.95/3.17
% 2.95/3.17 ======= end of input processing =======
% 2.95/3.17
% 2.95/3.17 =========== start of search ===========
% 2.95/3.17
% 2.95/3.17
% 2.95/3.17 Resetting weight limit to 11.
% 2.95/3.17
% 2.95/3.17
% 2.95/3.17 Resetting weight limit to 11.
% 2.95/3.17
% 2.95/3.17 sos_size=2216
% 2.95/3.17
% 2.95/3.17
% 2.95/3.17 Resetting weight limit to 9.
% 2.95/3.17
% 2.95/3.17
% 2.95/3.17 Resetting weight limit to 9.
% 2.95/3.17
% 2.95/3.17 sos_size=2509
% 2.95/3.17
% 2.95/3.17 -------- PROOF --------
% 2.95/3.17
% 2.95/3.17 -----> EMPTY CLAUSE at 1.16 sec ----> 3974 [hyper,3967,5,3409] $F.
% 2.95/3.17
% 2.95/3.17 Length of proof is 19. Level of proof is 11.
% 2.95/3.17
% 2.95/3.17 ---------------- PROOF ----------------
% 2.95/3.17 % SZS status Theorem
% 2.95/3.17 % SZS output start Refutation
% See solution above
% 2.95/3.17 ------------ end of proof -------------
% 2.95/3.17
% 2.95/3.17
% 2.95/3.17 Search stopped by max_proofs option.
% 2.95/3.17
% 2.95/3.17
% 2.95/3.17 Search stopped by max_proofs option.
% 2.95/3.17
% 2.95/3.17 ============ end of search ============
% 2.95/3.17
% 2.95/3.17 -------------- statistics -------------
% 2.95/3.17 clauses given 447
% 2.95/3.17 clauses generated 58433
% 2.95/3.17 clauses kept 3856
% 2.95/3.17 clauses forward subsumed 19440
% 2.95/3.17 clauses back subsumed 833
% 2.95/3.17 Kbytes malloced 5859
% 2.95/3.17
% 2.95/3.17 ----------- times (seconds) -----------
% 2.95/3.17 user CPU time 1.16 (0 hr, 0 min, 1 sec)
% 2.95/3.17 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.95/3.17 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.95/3.17
% 2.95/3.17 That finishes the proof of the theorem.
% 2.95/3.17
% 2.95/3.17 Process 5458 finished Wed Jul 27 06:31:28 2022
% 2.95/3.17 Otter interrupted
% 2.95/3.17 PROOF FOUND
%------------------------------------------------------------------------------