TSTP Solution File: KLE167+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE167+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 2.92s 2.74s
% Output : Refutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 23 ( 19 unt; 0 nHn; 6 RR)
% Number of literals : 27 ( 17 equ; 6 neg)
% Maximal clause size : 2 ( 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 : 33 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE167+1.p',unknown),
[] ).
cnf(6,axiom,
( multiplication(dollar_c2,dollar_c1) = zero
| ~ le_q(dollar_c2,multiplication(dollar_c2,star(dollar_c1))) ),
file('KLE167+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ le_q(multiplication(dollar_c2,star(dollar_c1)),dollar_c2)
| ~ le_q(dollar_c2,multiplication(dollar_c2,star(dollar_c1))) ),
file('KLE167+1.p',unknown),
[] ).
cnf(10,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE167+1.p',unknown),
[] ).
cnf(11,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(14,axiom,
addition(A,zero) = A,
file('KLE167+1.p',unknown),
[] ).
cnf(15,axiom,
addition(A,A) = A,
file('KLE167+1.p',unknown),
[] ).
cnf(17,axiom,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('KLE167+1.p',unknown),
[] ).
cnf(18,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[17])]),
[iquote('copy,17,flip.1')] ).
cnf(21,axiom,
multiplication(A,one) = A,
file('KLE167+1.p',unknown),
[] ).
cnf(24,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE167+1.p',unknown),
[] ).
cnf(29,axiom,
multiplication(zero,A) = zero,
file('KLE167+1.p',unknown),
[] ).
cnf(30,axiom,
addition(one,multiplication(A,star(A))) = star(A),
file('KLE167+1.p',unknown),
[] ).
cnf(47,plain,
le_q(A,A),
inference(hyper,[status(thm)],[15,5]),
[iquote('hyper,15,5')] ).
cnf(71,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,15])]),
[iquote('para_into,11.1.1.1,15.1.1,flip.1')] ).
cnf(117,plain,
( multiplication(dollar_c2,multiplication(dollar_c1,A)) = zero
| ~ le_q(dollar_c2,multiplication(dollar_c2,star(dollar_c1))) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[18,6]),29])]),
[iquote('para_into,18.1.1.1,6.1.1,demod,29,flip.1')] ).
cnf(204,plain,
addition(A,multiplication(A,multiplication(B,star(B)))) = multiplication(A,star(B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[30,24]),21])]),
[iquote('para_from,30.1.1,24.1.1.2,demod,21,flip.1')] ).
cnf(531,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[71,5]),
[iquote('hyper,71,5')] ).
cnf(3334,plain,
le_q(A,multiplication(A,star(B))),
inference(para_from,[status(thm),theory(equality)],[204,531]),
[iquote('para_from,204.1.1,531.1.2')] ).
cnf(3342,plain,
multiplication(dollar_c2,multiplication(dollar_c1,A)) = zero,
inference(hyper,[status(thm)],[3334,117]),
[iquote('hyper,3334,117')] ).
cnf(3408,plain,
multiplication(dollar_c2,star(dollar_c1)) = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[3342,204]),14])]),
[iquote('para_from,3342.1.1,204.1.1.2,demod,14,flip.1')] ).
cnf(3415,plain,
~ le_q(dollar_c2,dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[7]),3408,3408]),
[iquote('back_demod,7,demod,3408,3408')] ).
cnf(3416,plain,
$false,
inference(binary,[status(thm)],[3415,47]),
[iquote('binary,3415.1,47.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE167+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.14 % Command : otter-tptp-script %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.35 % CPULimit : 300
% 0.20/0.35 % WCLimit : 300
% 0.20/0.35 % DateTime : Wed Jul 27 06:35:38 EDT 2022
% 0.20/0.35 % CPUTime :
% 2.16/2.00 ----- Otter 3.3f, August 2004 -----
% 2.16/2.00 The process was started by sandbox on n008.cluster.edu,
% 2.16/2.00 Wed Jul 27 06:35:38 2022
% 2.16/2.00 The command was "./otter". The process ID is 21502.
% 2.16/2.00
% 2.16/2.00 set(prolog_style_variables).
% 2.16/2.00 set(auto).
% 2.16/2.00 dependent: set(auto1).
% 2.16/2.00 dependent: set(process_input).
% 2.16/2.00 dependent: clear(print_kept).
% 2.16/2.00 dependent: clear(print_new_demod).
% 2.16/2.00 dependent: clear(print_back_demod).
% 2.16/2.00 dependent: clear(print_back_sub).
% 2.16/2.00 dependent: set(control_memory).
% 2.16/2.00 dependent: assign(max_mem, 12000).
% 2.16/2.00 dependent: assign(pick_given_ratio, 4).
% 2.16/2.00 dependent: assign(stats_level, 1).
% 2.16/2.00 dependent: assign(max_seconds, 10800).
% 2.16/2.00 clear(print_given).
% 2.16/2.00
% 2.16/2.00 formula_list(usable).
% 2.16/2.00 all A (A=A).
% 2.16/2.00 all A B (addition(A,B)=addition(B,A)).
% 2.16/2.00 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 2.16/2.00 all A (addition(A,zero)=A).
% 2.16/2.00 all A (addition(A,A)=A).
% 2.16/2.00 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 2.16/2.00 all A (multiplication(A,one)=A).
% 2.16/2.00 all A (multiplication(one,A)=A).
% 2.16/2.00 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 2.16/2.00 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 2.16/2.00 all A (multiplication(zero,A)=zero).
% 2.16/2.00 all A (addition(one,multiplication(A,star(A)))=star(A)).
% 2.16/2.00 all A (addition(one,multiplication(star(A),A))=star(A)).
% 2.16/2.00 all A B C (le_q(addition(multiplication(A,C),B),C)->le_q(multiplication(star(A),B),C)).
% 2.16/2.00 all A B C (le_q(addition(multiplication(C,A),B),C)->le_q(multiplication(B,star(A)),C)).
% 2.16/2.00 all A (strong_iteration(A)=addition(multiplication(A,strong_iteration(A)),one)).
% 2.16/2.00 all A B C (le_q(C,addition(multiplication(A,C),B))->le_q(C,multiplication(strong_iteration(A),B))).
% 2.16/2.00 all A (strong_iteration(A)=addition(star(A),multiplication(strong_iteration(A),zero))).
% 2.16/2.00 all A B (le_q(A,B)<->addition(A,B)=B).
% 2.16/2.00 -(all X0 X1 ((multiplication(X0,X1)=zero->le_q(multiplication(X0,star(X1)),X0))&le_q(X0,multiplication(X0,star(X1))))).
% 2.16/2.00 end_of_list.
% 2.16/2.00
% 2.16/2.00 -------> usable clausifies to:
% 2.16/2.00
% 2.16/2.00 list(usable).
% 2.16/2.00 0 [] A=A.
% 2.16/2.00 0 [] addition(A,B)=addition(B,A).
% 2.16/2.00 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 2.16/2.00 0 [] addition(A,zero)=A.
% 2.16/2.00 0 [] addition(A,A)=A.
% 2.16/2.00 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 2.16/2.00 0 [] multiplication(A,one)=A.
% 2.16/2.00 0 [] multiplication(one,A)=A.
% 2.16/2.00 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.16/2.00 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.16/2.00 0 [] multiplication(zero,A)=zero.
% 2.16/2.00 0 [] addition(one,multiplication(A,star(A)))=star(A).
% 2.16/2.00 0 [] addition(one,multiplication(star(A),A))=star(A).
% 2.16/2.00 0 [] -le_q(addition(multiplication(A,C),B),C)|le_q(multiplication(star(A),B),C).
% 2.16/2.00 0 [] -le_q(addition(multiplication(C,A),B),C)|le_q(multiplication(B,star(A)),C).
% 2.16/2.00 0 [] strong_iteration(A)=addition(multiplication(A,strong_iteration(A)),one).
% 2.16/2.00 0 [] -le_q(C,addition(multiplication(A,C),B))|le_q(C,multiplication(strong_iteration(A),B)).
% 2.16/2.00 0 [] strong_iteration(A)=addition(star(A),multiplication(strong_iteration(A),zero)).
% 2.16/2.00 0 [] -le_q(A,B)|addition(A,B)=B.
% 2.16/2.00 0 [] le_q(A,B)|addition(A,B)!=B.
% 2.16/2.00 0 [] multiplication($c2,$c1)=zero| -le_q($c2,multiplication($c2,star($c1))).
% 2.16/2.00 0 [] -le_q(multiplication($c2,star($c1)),$c2)| -le_q($c2,multiplication($c2,star($c1))).
% 2.16/2.00 end_of_list.
% 2.16/2.00
% 2.16/2.00 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 2.16/2.00
% 2.16/2.00 This is a Horn set with equality. The strategy will be
% 2.16/2.00 Knuth-Bendix and hyper_res, with positive clauses in
% 2.16/2.00 sos and nonpositive clauses in usable.
% 2.16/2.00
% 2.16/2.00 dependent: set(knuth_bendix).
% 2.16/2.00 dependent: set(anl_eq).
% 2.16/2.00 dependent: set(para_from).
% 2.16/2.00 dependent: set(para_into).
% 2.16/2.00 dependent: clear(para_from_right).
% 2.16/2.00 dependent: clear(para_into_right).
% 2.16/2.00 dependent: set(para_from_vars).
% 2.16/2.00 dependent: set(eq_units_both_ways).
% 2.16/2.00 dependent: set(dynamic_demod_all).
% 2.16/2.00 dependent: set(dynamic_demod).
% 2.16/2.00 dependent: set(order_eq).
% 2.16/2.00 dependent: set(back_demod).
% 2.16/2.00 dependent: set(lrpo).
% 2.16/2.00 dependent: set(hyper_res).
% 2.16/2.00 dependent: clear(order_hyper).
% 2.16/2.00
% 2.16/2.00 ------------> process usable:
% 2.16/2.00 ** KEPT (pick-wt=13): 1 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 2.92/2.74 ** KEPT (pick-wt=13): 2 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 2.92/2.74 ** KEPT (pick-wt=13): 3 [] -le_q(A,addition(multiplication(B,A),C))|le_q(A,multiplication(strong_iteration(B),C)).
% 2.92/2.74 ** KEPT (pick-wt=8): 4 [] -le_q(A,B)|addition(A,B)=B.
% 2.92/2.74 ** KEPT (pick-wt=8): 5 [] le_q(A,B)|addition(A,B)!=B.
% 2.92/2.74 ** KEPT (pick-wt=11): 6 [] multiplication($c2,$c1)=zero| -le_q($c2,multiplication($c2,star($c1))).
% 2.92/2.74 ** KEPT (pick-wt=12): 7 [] -le_q(multiplication($c2,star($c1)),$c2)| -le_q($c2,multiplication($c2,star($c1))).
% 2.92/2.74
% 2.92/2.74 ------------> process sos:
% 2.92/2.74 ** KEPT (pick-wt=3): 8 [] A=A.
% 2.92/2.74 ** KEPT (pick-wt=7): 9 [] addition(A,B)=addition(B,A).
% 2.92/2.74 ** KEPT (pick-wt=11): 11 [copy,10,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.92/2.74 ---> New Demodulator: 12 [new_demod,11] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.92/2.74 ** KEPT (pick-wt=5): 13 [] addition(A,zero)=A.
% 2.92/2.74 ---> New Demodulator: 14 [new_demod,13] addition(A,zero)=A.
% 2.92/2.74 ** KEPT (pick-wt=5): 15 [] addition(A,A)=A.
% 2.92/2.74 ---> New Demodulator: 16 [new_demod,15] addition(A,A)=A.
% 2.92/2.74 ** KEPT (pick-wt=11): 18 [copy,17,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.92/2.74 ---> New Demodulator: 19 [new_demod,18] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.92/2.74 ** KEPT (pick-wt=5): 20 [] multiplication(A,one)=A.
% 2.92/2.74 ---> New Demodulator: 21 [new_demod,20] multiplication(A,one)=A.
% 2.92/2.74 ** KEPT (pick-wt=5): 22 [] multiplication(one,A)=A.
% 2.92/2.74 ---> New Demodulator: 23 [new_demod,22] multiplication(one,A)=A.
% 2.92/2.74 ** KEPT (pick-wt=13): 24 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.92/2.74 ---> New Demodulator: 25 [new_demod,24] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.92/2.74 ** KEPT (pick-wt=13): 26 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.92/2.74 ---> New Demodulator: 27 [new_demod,26] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.92/2.74 ** KEPT (pick-wt=5): 28 [] multiplication(zero,A)=zero.
% 2.92/2.74 ---> New Demodulator: 29 [new_demod,28] multiplication(zero,A)=zero.
% 2.92/2.74 ** KEPT (pick-wt=9): 30 [] addition(one,multiplication(A,star(A)))=star(A).
% 2.92/2.74 ---> New Demodulator: 31 [new_demod,30] addition(one,multiplication(A,star(A)))=star(A).
% 2.92/2.74 ** KEPT (pick-wt=9): 32 [] addition(one,multiplication(star(A),A))=star(A).
% 2.92/2.74 ---> New Demodulator: 33 [new_demod,32] addition(one,multiplication(star(A),A))=star(A).
% 2.92/2.74 ** KEPT (pick-wt=9): 35 [copy,34,flip.1] addition(multiplication(A,strong_iteration(A)),one)=strong_iteration(A).
% 2.92/2.74 ---> New Demodulator: 36 [new_demod,35] addition(multiplication(A,strong_iteration(A)),one)=strong_iteration(A).
% 2.92/2.74 ** KEPT (pick-wt=10): 38 [copy,37,flip.1] addition(star(A),multiplication(strong_iteration(A),zero))=strong_iteration(A).
% 2.92/2.74 ---> New Demodulator: 39 [new_demod,38] addition(star(A),multiplication(strong_iteration(A),zero))=strong_iteration(A).
% 2.92/2.74 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] A=A.
% 2.92/2.74 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] addition(A,B)=addition(B,A).
% 2.92/2.74 >>>> Starting back demodulation with 12.
% 2.92/2.74 >>>> Starting back demodulation with 14.
% 2.92/2.74 >>>> Starting back demodulation with 16.
% 2.92/2.74 >>>> Starting back demodulation with 19.
% 2.92/2.74 >>>> Starting back demodulation with 21.
% 2.92/2.74 >>>> Starting back demodulation with 23.
% 2.92/2.74 >>>> Starting back demodulation with 25.
% 2.92/2.74 >>>> Starting back demodulation with 27.
% 2.92/2.74 >>>> Starting back demodulation with 29.
% 2.92/2.74 >>>> Starting back demodulation with 31.
% 2.92/2.74 >>>> Starting back demodulation with 33.
% 2.92/2.74 >>>> Starting back demodulation with 36.
% 2.92/2.74 >>>> Starting back demodulation with 39.
% 2.92/2.74
% 2.92/2.74 ======= end of input processing =======
% 2.92/2.74
% 2.92/2.74 =========== start of search ===========
% 2.92/2.74
% 2.92/2.74
% 2.92/2.74 Resetting weight limit to 9.
% 2.92/2.74
% 2.92/2.74
% 2.92/2.74 Resetting weight limit to 9.
% 2.92/2.74
% 2.92/2.74 sos_size=1695
% 2.92/2.74
% 2.92/2.74
% 2.92/2.74 Resetting weight limit to 8.
% 2.92/2.74
% 2.92/2.74
% 2.92/2.74 Resetting weight limit to 8.
% 2.92/2.74
% 2.92/2.74 sos_size=1889
% 2.92/2.74
% 2.92/2.74 -------- PROOF --------
% 2.92/2.74
% 2.92/2.74 ----> UNIT CONFLICT at 0.73 sec ----> 3416 [binary,3415.1,47.1] $F.
% 2.92/2.74
% 2.92/2.74 Length of proof is 11. Level of proof is 7.
% 2.92/2.74
% 2.92/2.74 ---------------- PROOF ----------------
% 2.92/2.74 % SZS status Theorem
% 2.92/2.74 % SZS output start Refutation
% See solution above
% 2.92/2.74 ------------ end of proof -------------
% 2.92/2.74
% 2.92/2.74
% 2.92/2.74 Search stopped by max_proofs option.
% 2.92/2.74
% 2.92/2.74
% 2.92/2.74 Search stopped by max_proofs option.
% 2.92/2.74
% 2.92/2.74 ============ end of search ============
% 2.92/2.74
% 2.92/2.74 -------------- statistics -------------
% 2.92/2.74 clauses given 582
% 2.92/2.74 clauses generated 79490
% 2.92/2.74 clauses kept 3201
% 2.92/2.74 clauses forward subsumed 27136
% 2.92/2.74 clauses back subsumed 677
% 2.92/2.74 Kbytes malloced 6835
% 2.92/2.74
% 2.92/2.74 ----------- times (seconds) -----------
% 2.92/2.74 user CPU time 0.73 (0 hr, 0 min, 0 sec)
% 2.92/2.74 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.92/2.74 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.92/2.74
% 2.92/2.74 That finishes the proof of the theorem.
% 2.92/2.74
% 2.92/2.74 Process 21502 finished Wed Jul 27 06:35:41 2022
% 2.92/2.74 Otter interrupted
% 2.92/2.74 PROOF FOUND
%------------------------------------------------------------------------------