TSTP Solution File: KLE169+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE169+1 : TPTP v8.1.0. Released v5.2.0.
% 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 13:00:54 EDT 2022
% Result : Theorem 4.74s 4.94s
% Output : Refutation 4.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 31 ( 22 unt; 0 nHn; 13 RR)
% Number of literals : 41 ( 20 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE169+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE169+1.p',unknown),
[] ).
cnf(5,axiom,
~ le_q(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
file('KLE169+1.p',unknown),
[] ).
cnf(7,axiom,
addition(A,B) = addition(B,A),
file('KLE169+1.p',unknown),
[] ).
cnf(8,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE169+1.p',unknown),
[] ).
cnf(9,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('KLE169+1.p',unknown),
[] ).
cnf(21,axiom,
multiplication(one,A) = A,
file('KLE169+1.p',unknown),
[] ).
cnf(23,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE169+1.p',unknown),
[] ).
cnf(24,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE169+1.p',unknown),
[] ).
cnf(31,axiom,
le_q(addition(one,multiplication(star(A),A)),star(A)),
file('KLE169+1.p',unknown),
[] ).
cnf(32,axiom,
sigma = addition(a,b),
file('KLE169+1.p',unknown),
[] ).
cnf(33,plain,
addition(a,b) = sigma,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[32])]),
[iquote('copy,32,flip.1')] ).
cnf(46,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(49,plain,
( le_q(A,B)
| addition(B,A) != B ),
inference(para_from,[status(thm),theory(equality)],[7,2]),
[iquote('para_from,7.1.1,2.2.1')] ).
cnf(60,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,13])]),
[iquote('para_into,9.1.1.1,13.1.1,flip.1')] ).
cnf(63,plain,
( addition(A,addition(B,C)) = addition(B,C)
| ~ le_q(A,B) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,1])]),
[iquote('para_into,9.1.1.1,1.2.1,flip.1')] ).
cnf(67,plain,
( addition(A,addition(B,C)) = C
| ~ le_q(addition(A,B),C) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,1])]),
[iquote('para_into,9.1.1,1.2.1,flip.1')] ).
cnf(70,plain,
addition(b,a) = sigma,
inference(para_into,[status(thm),theory(equality)],[33,7]),
[iquote('para_into,33.1.1,7.1.1')] ).
cnf(136,plain,
multiplication(sigma,A) = addition(multiplication(b,A),multiplication(a,A)),
inference(para_into,[status(thm),theory(equality)],[24,70]),
[iquote('para_into,24.1.1.1,70.1.1')] ).
cnf(150,plain,
~ le_q(multiplication(a,multiplication(b,a)),addition(multiplication(star(sigma),multiplication(a,multiplication(b,a))),multiplication(star(sigma),multiplication(a,multiplication(a,a))))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[5]),136,23,23]),
[iquote('back_demod,5,demod,136,23,23')] ).
cnf(526,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[60,2]),
[iquote('hyper,60,2')] ).
cnf(666,plain,
( le_q(A,addition(B,C))
| ~ le_q(A,B) ),
inference(para_from,[status(thm),theory(equality)],[63,526]),
[iquote('para_from,63.1.1,526.1.2')] ).
cnf(822,plain,
( le_q(A,B)
| ~ le_q(addition(A,C),B) ),
inference(para_from,[status(thm),theory(equality)],[67,526]),
[iquote('para_from,67.1.1,526.1.2')] ).
cnf(1320,plain,
( le_q(A,B)
| ~ le_q(A,C)
| ~ le_q(C,B) ),
inference(para_into,[status(thm),theory(equality)],[666,1]),
[iquote('para_into,666.1.2,1.2.1')] ).
cnf(1632,plain,
le_q(one,star(A)),
inference(hyper,[status(thm)],[822,31]),
[iquote('hyper,822,31')] ).
cnf(1643,plain,
addition(star(A),one) = star(A),
inference(hyper,[status(thm)],[1632,46]),
[iquote('hyper,1632,46')] ).
cnf(1741,plain,
addition(multiplication(star(A),B),B) = multiplication(star(A),B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1643,24]),21])]),
[iquote('para_from,1643.1.1,24.1.1.1,demod,21,flip.1')] ).
cnf(3550,plain,
le_q(A,multiplication(star(B),A)),
inference(hyper,[status(thm)],[1741,49]),
[iquote('hyper,1741,49')] ).
cnf(3563,plain,
le_q(A,addition(multiplication(star(B),A),C)),
inference(hyper,[status(thm)],[3550,1320,526]),
[iquote('hyper,3550,1320,526')] ).
cnf(3564,plain,
$false,
inference(binary,[status(thm)],[3563,150]),
[iquote('binary,3563.1,150.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE169+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.12 % 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 06:30:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.93 ----- Otter 3.3f, August 2004 -----
% 1.72/1.93 The process was started by sandbox2 on n005.cluster.edu,
% 1.72/1.93 Wed Jul 27 06:30:05 2022
% 1.72/1.93 The command was "./otter". The process ID is 7510.
% 1.72/1.93
% 1.72/1.93 set(prolog_style_variables).
% 1.72/1.93 set(auto).
% 1.72/1.93 dependent: set(auto1).
% 1.72/1.93 dependent: set(process_input).
% 1.72/1.93 dependent: clear(print_kept).
% 1.72/1.93 dependent: clear(print_new_demod).
% 1.72/1.93 dependent: clear(print_back_demod).
% 1.72/1.93 dependent: clear(print_back_sub).
% 1.72/1.93 dependent: set(control_memory).
% 1.72/1.93 dependent: assign(max_mem, 12000).
% 1.72/1.93 dependent: assign(pick_given_ratio, 4).
% 1.72/1.93 dependent: assign(stats_level, 1).
% 1.72/1.93 dependent: assign(max_seconds, 10800).
% 1.72/1.93 clear(print_given).
% 1.72/1.93
% 1.72/1.93 formula_list(usable).
% 1.72/1.93 all A (A=A).
% 1.72/1.93 all A B (addition(A,B)=addition(B,A)).
% 1.72/1.93 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.72/1.93 all A (addition(A,zero)=A).
% 1.72/1.93 all A (addition(A,A)=A).
% 1.72/1.93 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.72/1.93 all A (multiplication(A,one)=A).
% 1.72/1.93 all A (multiplication(one,A)=A).
% 1.72/1.93 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.72/1.93 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.72/1.93 all A (multiplication(A,zero)=zero).
% 1.72/1.93 all A (multiplication(zero,A)=zero).
% 1.72/1.93 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.72/1.93 all A le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.72/1.93 all A le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.72/1.93 all A B C (le_q(addition(multiplication(A,B),C),B)->le_q(multiplication(star(A),C),B)).
% 1.72/1.93 all A B C (le_q(addition(multiplication(A,B),C),A)->le_q(multiplication(C,star(B)),A)).
% 1.72/1.93 sigma=addition(a,b).
% 1.72/1.93 -le_q(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))).
% 1.72/1.93 end_of_list.
% 1.72/1.93
% 1.72/1.93 -------> usable clausifies to:
% 1.72/1.93
% 1.72/1.93 list(usable).
% 1.72/1.93 0 [] A=A.
% 1.72/1.93 0 [] addition(A,B)=addition(B,A).
% 1.72/1.93 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.72/1.93 0 [] addition(A,zero)=A.
% 1.72/1.93 0 [] addition(A,A)=A.
% 1.72/1.93 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.72/1.93 0 [] multiplication(A,one)=A.
% 1.72/1.93 0 [] multiplication(one,A)=A.
% 1.72/1.93 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.72/1.93 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.72/1.93 0 [] multiplication(A,zero)=zero.
% 1.72/1.93 0 [] multiplication(zero,A)=zero.
% 1.72/1.93 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.72/1.93 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.72/1.93 0 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.72/1.93 0 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.72/1.93 0 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.72/1.93 0 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.72/1.93 0 [] sigma=addition(a,b).
% 1.72/1.93 0 [] -le_q(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))).
% 1.72/1.93 end_of_list.
% 1.72/1.93
% 1.72/1.93 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.72/1.93
% 1.72/1.93 This is a Horn set with equality. The strategy will be
% 1.72/1.93 Knuth-Bendix and hyper_res, with positive clauses in
% 1.72/1.93 sos and nonpositive clauses in usable.
% 1.72/1.93
% 1.72/1.93 dependent: set(knuth_bendix).
% 1.72/1.93 dependent: set(anl_eq).
% 1.72/1.93 dependent: set(para_from).
% 1.72/1.93 dependent: set(para_into).
% 1.72/1.93 dependent: clear(para_from_right).
% 1.72/1.93 dependent: clear(para_into_right).
% 1.72/1.93 dependent: set(para_from_vars).
% 1.72/1.93 dependent: set(eq_units_both_ways).
% 1.72/1.93 dependent: set(dynamic_demod_all).
% 1.72/1.93 dependent: set(dynamic_demod).
% 1.72/1.93 dependent: set(order_eq).
% 1.72/1.93 dependent: set(back_demod).
% 1.72/1.93 dependent: set(lrpo).
% 1.72/1.93 dependent: set(hyper_res).
% 1.72/1.93 dependent: clear(order_hyper).
% 1.72/1.93
% 1.72/1.93 ------------> process usable:
% 1.72/1.93 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.72/1.93 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.72/1.93 ** KEPT (pick-wt=13): 3 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.72/1.93 ** KEPT (pick-wt=13): 4 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.72/1.93 ** KEPT (pick-wt=14): 5 [] -le_q(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))).
% 1.72/1.93
% 1.72/1.93 ------------> process sos:
% 1.72/1.93 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.72/1.93 ** KEPT (pick-wt=7): 7 [] addition(A,B)=addition(B,A).
% 4.74/4.94 ** KEPT (pick-wt=11): 9 [copy,8,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 4.74/4.94 ---> New Demodulator: 10 [new_demod,9] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 4.74/4.94 ** KEPT (pick-wt=5): 11 [] addition(A,zero)=A.
% 4.74/4.94 ---> New Demodulator: 12 [new_demod,11] addition(A,zero)=A.
% 4.74/4.94 ** KEPT (pick-wt=5): 13 [] addition(A,A)=A.
% 4.74/4.94 ---> New Demodulator: 14 [new_demod,13] addition(A,A)=A.
% 4.74/4.94 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 4.74/4.94 ---> New Demodulator: 17 [new_demod,16] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 4.74/4.94 ** KEPT (pick-wt=5): 18 [] multiplication(A,one)=A.
% 4.74/4.94 ---> New Demodulator: 19 [new_demod,18] multiplication(A,one)=A.
% 4.74/4.94 ** KEPT (pick-wt=5): 20 [] multiplication(one,A)=A.
% 4.74/4.94 ---> New Demodulator: 21 [new_demod,20] multiplication(one,A)=A.
% 4.74/4.94 ** KEPT (pick-wt=13): 22 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 4.74/4.94 ---> New Demodulator: 23 [new_demod,22] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 4.74/4.94 ** KEPT (pick-wt=13): 24 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 4.74/4.94 ---> New Demodulator: 25 [new_demod,24] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 4.74/4.94 ** KEPT (pick-wt=5): 26 [] multiplication(A,zero)=zero.
% 4.74/4.94 ---> New Demodulator: 27 [new_demod,26] multiplication(A,zero)=zero.
% 4.74/4.94 ** KEPT (pick-wt=5): 28 [] multiplication(zero,A)=zero.
% 4.74/4.94 ---> New Demodulator: 29 [new_demod,28] multiplication(zero,A)=zero.
% 4.74/4.94 ** KEPT (pick-wt=9): 30 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 4.74/4.94 ** KEPT (pick-wt=9): 31 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 4.74/4.94 ** KEPT (pick-wt=5): 33 [copy,32,flip.1] addition(a,b)=sigma.
% 4.74/4.94 ---> New Demodulator: 34 [new_demod,33] addition(a,b)=sigma.
% 4.74/4.94 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 4.74/4.94 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] addition(A,B)=addition(B,A).
% 4.74/4.94 >>>> Starting back demodulation with 10.
% 4.74/4.94 >>>> Starting back demodulation with 12.
% 4.74/4.94 >>>> Starting back demodulation with 14.
% 4.74/4.94 >>>> Starting back demodulation with 17.
% 4.74/4.94 >>>> Starting back demodulation with 19.
% 4.74/4.94 >>>> Starting back demodulation with 21.
% 4.74/4.94 >>>> Starting back demodulation with 23.
% 4.74/4.94 >>>> Starting back demodulation with 25.
% 4.74/4.94 >>>> Starting back demodulation with 27.
% 4.74/4.94 >>>> Starting back demodulation with 29.
% 4.74/4.94 >>>> Starting back demodulation with 34.
% 4.74/4.94
% 4.74/4.94 ======= end of input processing =======
% 4.74/4.94
% 4.74/4.94 =========== start of search ===========
% 4.74/4.94
% 4.74/4.94
% 4.74/4.94 Resetting weight limit to 9.
% 4.74/4.94
% 4.74/4.94
% 4.74/4.94 Resetting weight limit to 9.
% 4.74/4.94
% 4.74/4.94 sos_size=1684
% 4.74/4.94
% 4.74/4.94
% 4.74/4.94 Resetting weight limit to 8.
% 4.74/4.94
% 4.74/4.94
% 4.74/4.94 Resetting weight limit to 8.
% 4.74/4.94
% 4.74/4.94 sos_size=1400
% 4.74/4.94
% 4.74/4.94 -------- PROOF --------
% 4.74/4.94
% 4.74/4.94 ----> UNIT CONFLICT at 2.97 sec ----> 3564 [binary,3563.1,150.1] $F.
% 4.74/4.94
% 4.74/4.94 Length of proof is 19. Level of proof is 9.
% 4.74/4.94
% 4.74/4.94 ---------------- PROOF ----------------
% 4.74/4.94 % SZS status Theorem
% 4.74/4.94 % SZS output start Refutation
% See solution above
% 4.74/4.94 ------------ end of proof -------------
% 4.74/4.94
% 4.74/4.94
% 4.74/4.94 Search stopped by max_proofs option.
% 4.74/4.94
% 4.74/4.94
% 4.74/4.94 Search stopped by max_proofs option.
% 4.74/4.94
% 4.74/4.94 ============ end of search ============
% 4.74/4.94
% 4.74/4.94 -------------- statistics -------------
% 4.74/4.94 clauses given 1223
% 4.74/4.94 clauses generated 555650
% 4.74/4.94 clauses kept 3459
% 4.74/4.94 clauses forward subsumed 49168
% 4.74/4.94 clauses back subsumed 1021
% 4.74/4.94 Kbytes malloced 5859
% 4.74/4.94
% 4.74/4.94 ----------- times (seconds) -----------
% 4.74/4.94 user CPU time 2.97 (0 hr, 0 min, 2 sec)
% 4.74/4.94 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 4.74/4.94 wall-clock time 5 (0 hr, 0 min, 5 sec)
% 4.74/4.94
% 4.74/4.94 That finishes the proof of the theorem.
% 4.74/4.94
% 4.74/4.94 Process 7510 finished Wed Jul 27 06:30:10 2022
% 4.74/4.94 Otter interrupted
% 4.74/4.94 PROOF FOUND
%------------------------------------------------------------------------------