TSTP Solution File: KLE041+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE041+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 2.56s 2.80s
% Output : Refutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of clauses : 46 ( 34 unt; 0 nHn; 18 RR)
% Number of literals : 60 ( 22 equ; 15 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE041+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE041+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ le_q(addition(multiplication(A,B),C),B)
| le_q(multiplication(star(A),C),B) ),
file('KLE041+1.p',unknown),
[] ).
cnf(5,axiom,
~ le_q(star(dollar_c2),star(dollar_c1)),
file('KLE041+1.p',unknown),
[] ).
cnf(7,axiom,
addition(A,B) = addition(B,A),
file('KLE041+1.p',unknown),
[] ).
cnf(8,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE041+1.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('KLE041+1.p',unknown),
[] ).
cnf(19,axiom,
multiplication(A,one) = A,
file('KLE041+1.p',unknown),
[] ).
cnf(21,axiom,
multiplication(one,A) = A,
file('KLE041+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE041+1.p',unknown),
[] ).
cnf(24,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE041+1.p',unknown),
[] ).
cnf(30,axiom,
le_q(addition(one,multiplication(A,star(A))),star(A)),
file('KLE041+1.p',unknown),
[] ).
cnf(31,axiom,
le_q(addition(one,multiplication(star(A),A)),star(A)),
file('KLE041+1.p',unknown),
[] ).
cnf(32,axiom,
le_q(dollar_c2,dollar_c1),
file('KLE041+1.p',unknown),
[] ).
cnf(33,plain,
addition(dollar_c2,dollar_c1) = dollar_c1,
inference(hyper,[status(thm)],[32,1]),
[iquote('hyper,32,1')] ).
cnf(41,plain,
le_q(A,A),
inference(hyper,[status(thm)],[13,2]),
[iquote('hyper,13,2')] ).
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(48,plain,
( ~ le_q(addition(A,multiplication(B,C)),C)
| le_q(multiplication(star(B),A),C) ),
inference(para_from,[status(thm),theory(equality)],[7,3]),
[iquote('para_from,7.1.1,3.1.1')] ).
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(58,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(70,plain,
addition(dollar_c1,dollar_c2) = dollar_c1,
inference(para_into,[status(thm),theory(equality)],[33,7]),
[iquote('para_into,33.1.1,7.1.1')] ).
cnf(112,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(122,plain,
addition(multiplication(dollar_c1,A),multiplication(dollar_c2,A)) = multiplication(dollar_c1,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[24,70])]),
[iquote('para_into,24.1.1.1,70.1.1,flip.1')] ).
cnf(166,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(300,plain,
( ~ le_q(A,B)
| le_q(multiplication(star(C),A),B)
| ~ le_q(multiplication(C,B),A) ),
inference(para_into,[status(thm),theory(equality)],[48,46]),
[iquote('para_into,48.1.1,46.1.1')] ).
cnf(509,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[58,2]),
[iquote('hyper,58,2')] ).
cnf(527,plain,
le_q(A,addition(B,A)),
inference(para_into,[status(thm),theory(equality)],[509,7]),
[iquote('para_into,509.1.2,7.1.1')] ).
cnf(529,plain,
le_q(A,addition(B,addition(C,A))),
inference(para_into,[status(thm),theory(equality)],[527,10]),
[iquote('para_into,527.1.2,9.1.1')] ).
cnf(537,plain,
( le_q(A,addition(B,C))
| ~ le_q(A,C) ),
inference(para_into,[status(thm),theory(equality)],[529,46]),
[iquote('para_into,529.1.2.2,46.1.1')] ).
cnf(541,plain,
( le_q(A,B)
| ~ le_q(addition(C,A),B) ),
inference(para_into,[status(thm),theory(equality)],[529,46]),
[iquote('para_into,529.1.2,46.1.1')] ).
cnf(731,plain,
( le_q(A,B)
| ~ le_q(A,C)
| ~ le_q(C,B) ),
inference(para_into,[status(thm),theory(equality)],[537,46]),
[iquote('para_into,537.1.2,46.1.1')] ).
cnf(768,plain,
le_q(multiplication(star(A),A),star(A)),
inference(hyper,[status(thm)],[541,31]),
[iquote('hyper,541,31')] ).
cnf(769,plain,
le_q(multiplication(A,star(A)),star(A)),
inference(hyper,[status(thm)],[541,30]),
[iquote('hyper,541,30')] ).
cnf(782,plain,
addition(multiplication(star(A),A),star(A)) = star(A),
inference(hyper,[status(thm)],[768,1]),
[iquote('hyper,768,1')] ).
cnf(785,plain,
addition(one,star(A)) = star(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[166]),782]),
[iquote('back_demod,166,demod,782')] ).
cnf(801,plain,
le_q(one,star(A)),
inference(hyper,[status(thm)],[785,2]),
[iquote('hyper,785,2')] ).
cnf(819,plain,
addition(A,multiplication(star(B),A)) = multiplication(star(B),A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[785,24]),21])]),
[iquote('para_from,785.1.1,24.1.1.1,demod,21,flip.1')] ).
cnf(2543,plain,
( le_q(multiplication(A,B),multiplication(A,C))
| ~ le_q(B,C) ),
inference(para_from,[status(thm),theory(equality)],[112,509]),
[iquote('para_from,112.1.1,509.1.2')] ).
cnf(2963,plain,
le_q(multiplication(dollar_c2,A),multiplication(dollar_c1,A)),
inference(hyper,[status(thm)],[122,49]),
[iquote('hyper,122,49')] ).
cnf(3080,plain,
le_q(multiplication(dollar_c2,star(dollar_c1)),star(dollar_c1)),
inference(hyper,[status(thm)],[731,2963,769]),
[iquote('hyper,731,2963,769')] ).
cnf(3492,plain,
le_q(multiplication(star(dollar_c2),star(dollar_c1)),star(dollar_c1)),
inference(hyper,[status(thm)],[300,41,3080]),
[iquote('hyper,300,41,3080')] ).
cnf(3498,plain,
multiplication(star(dollar_c2),star(dollar_c1)) = star(dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[3492,46]),819]),
[iquote('hyper,3492,46,demod,819')] ).
cnf(3557,plain,
le_q(A,multiplication(A,star(B))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2543,801]),19]),
[iquote('hyper,2543,801,demod,19')] ).
cnf(3596,plain,
le_q(star(dollar_c2),star(dollar_c1)),
inference(para_into,[status(thm),theory(equality)],[3557,3498]),
[iquote('para_into,3557.1.2,3498.1.1')] ).
cnf(3597,plain,
$false,
inference(binary,[status(thm)],[3596,5]),
[iquote('binary,3596.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE041+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n007.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 06:16:46 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.90 ----- Otter 3.3f, August 2004 -----
% 1.67/1.90 The process was started by sandbox2 on n007.cluster.edu,
% 1.67/1.90 Wed Jul 27 06:16:46 2022
% 1.67/1.90 The command was "./otter". The process ID is 6218.
% 1.67/1.90
% 1.67/1.90 set(prolog_style_variables).
% 1.67/1.90 set(auto).
% 1.67/1.90 dependent: set(auto1).
% 1.67/1.90 dependent: set(process_input).
% 1.67/1.90 dependent: clear(print_kept).
% 1.67/1.90 dependent: clear(print_new_demod).
% 1.67/1.90 dependent: clear(print_back_demod).
% 1.67/1.90 dependent: clear(print_back_sub).
% 1.67/1.90 dependent: set(control_memory).
% 1.67/1.90 dependent: assign(max_mem, 12000).
% 1.67/1.90 dependent: assign(pick_given_ratio, 4).
% 1.67/1.90 dependent: assign(stats_level, 1).
% 1.67/1.90 dependent: assign(max_seconds, 10800).
% 1.67/1.90 clear(print_given).
% 1.67/1.90
% 1.67/1.90 formula_list(usable).
% 1.67/1.90 all A (A=A).
% 1.67/1.90 all A B (addition(A,B)=addition(B,A)).
% 1.67/1.90 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.67/1.90 all A (addition(A,zero)=A).
% 1.67/1.90 all A (addition(A,A)=A).
% 1.67/1.90 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.67/1.90 all A (multiplication(A,one)=A).
% 1.67/1.90 all A (multiplication(one,A)=A).
% 1.67/1.90 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.67/1.90 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.67/1.90 all A (multiplication(A,zero)=zero).
% 1.67/1.90 all A (multiplication(zero,A)=zero).
% 1.67/1.90 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.67/1.90 all A le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.67/1.90 all A le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.67/1.90 all A B C (le_q(addition(multiplication(A,B),C),B)->le_q(multiplication(star(A),C),B)).
% 1.67/1.90 all A B C (le_q(addition(multiplication(A,B),C),A)->le_q(multiplication(C,star(B)),A)).
% 1.67/1.90 -(all X0 X1 (le_q(X0,X1)->le_q(star(X0),star(X1)))).
% 1.67/1.90 end_of_list.
% 1.67/1.90
% 1.67/1.90 -------> usable clausifies to:
% 1.67/1.90
% 1.67/1.90 list(usable).
% 1.67/1.90 0 [] A=A.
% 1.67/1.90 0 [] addition(A,B)=addition(B,A).
% 1.67/1.90 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.67/1.90 0 [] addition(A,zero)=A.
% 1.67/1.90 0 [] addition(A,A)=A.
% 1.67/1.90 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.67/1.90 0 [] multiplication(A,one)=A.
% 1.67/1.90 0 [] multiplication(one,A)=A.
% 1.67/1.90 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.67/1.90 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.67/1.90 0 [] multiplication(A,zero)=zero.
% 1.67/1.90 0 [] multiplication(zero,A)=zero.
% 1.67/1.90 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.67/1.90 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.67/1.90 0 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.67/1.90 0 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.67/1.90 0 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.67/1.90 0 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.67/1.90 0 [] le_q($c2,$c1).
% 1.67/1.90 0 [] -le_q(star($c2),star($c1)).
% 1.67/1.90 end_of_list.
% 1.67/1.90
% 1.67/1.90 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.67/1.90
% 1.67/1.90 This is a Horn set with equality. The strategy will be
% 1.67/1.90 Knuth-Bendix and hyper_res, with positive clauses in
% 1.67/1.90 sos and nonpositive clauses in usable.
% 1.67/1.90
% 1.67/1.90 dependent: set(knuth_bendix).
% 1.67/1.90 dependent: set(anl_eq).
% 1.67/1.90 dependent: set(para_from).
% 1.67/1.90 dependent: set(para_into).
% 1.67/1.90 dependent: clear(para_from_right).
% 1.67/1.90 dependent: clear(para_into_right).
% 1.67/1.90 dependent: set(para_from_vars).
% 1.67/1.90 dependent: set(eq_units_both_ways).
% 1.67/1.90 dependent: set(dynamic_demod_all).
% 1.67/1.90 dependent: set(dynamic_demod).
% 1.67/1.90 dependent: set(order_eq).
% 1.67/1.90 dependent: set(back_demod).
% 1.67/1.90 dependent: set(lrpo).
% 1.67/1.90 dependent: set(hyper_res).
% 1.67/1.90 dependent: clear(order_hyper).
% 1.67/1.90
% 1.67/1.90 ------------> process usable:
% 1.67/1.90 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.67/1.90 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.67/1.90 ** KEPT (pick-wt=13): 3 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.67/1.90 ** KEPT (pick-wt=13): 4 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.67/1.90 ** KEPT (pick-wt=5): 5 [] -le_q(star($c2),star($c1)).
% 1.67/1.90
% 1.67/1.90 ------------> process sos:
% 1.67/1.90 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.67/1.90 ** KEPT (pick-wt=7): 7 [] addition(A,B)=addition(B,A).
% 1.67/1.90 ** KEPT (pick-wt=11): 9 [copy,8,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.67/1.90 ---> New Demodulator: 10 [new_demod,9] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.67/1.90 ** KEPT (pick-wt=5): 11 [] addition(A,zero)=A.
% 2.56/2.80 ---> New Demodulator: 12 [new_demod,11] addition(A,zero)=A.
% 2.56/2.80 ** KEPT (pick-wt=5): 13 [] addition(A,A)=A.
% 2.56/2.80 ---> New Demodulator: 14 [new_demod,13] addition(A,A)=A.
% 2.56/2.80 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.56/2.80 ---> New Demodulator: 17 [new_demod,16] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.56/2.80 ** KEPT (pick-wt=5): 18 [] multiplication(A,one)=A.
% 2.56/2.80 ---> New Demodulator: 19 [new_demod,18] multiplication(A,one)=A.
% 2.56/2.80 ** KEPT (pick-wt=5): 20 [] multiplication(one,A)=A.
% 2.56/2.80 ---> New Demodulator: 21 [new_demod,20] multiplication(one,A)=A.
% 2.56/2.80 ** KEPT (pick-wt=13): 22 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.56/2.80 ---> New Demodulator: 23 [new_demod,22] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.56/2.80 ** KEPT (pick-wt=13): 24 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.56/2.80 ---> New Demodulator: 25 [new_demod,24] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.56/2.80 ** KEPT (pick-wt=5): 26 [] multiplication(A,zero)=zero.
% 2.56/2.80 ---> New Demodulator: 27 [new_demod,26] multiplication(A,zero)=zero.
% 2.56/2.80 ** KEPT (pick-wt=5): 28 [] multiplication(zero,A)=zero.
% 2.56/2.80 ---> New Demodulator: 29 [new_demod,28] multiplication(zero,A)=zero.
% 2.56/2.80 ** KEPT (pick-wt=9): 30 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 2.56/2.80 ** KEPT (pick-wt=9): 31 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 2.56/2.80 ** KEPT (pick-wt=3): 32 [] le_q($c2,$c1).
% 2.56/2.80 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 2.56/2.80 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] addition(A,B)=addition(B,A).
% 2.56/2.80 >>>> Starting back demodulation with 10.
% 2.56/2.80 >>>> Starting back demodulation with 12.
% 2.56/2.80 >>>> Starting back demodulation with 14.
% 2.56/2.80 >>>> Starting back demodulation with 17.
% 2.56/2.80 >>>> Starting back demodulation with 19.
% 2.56/2.80 >>>> Starting back demodulation with 21.
% 2.56/2.80 >>>> Starting back demodulation with 23.
% 2.56/2.80 >>>> Starting back demodulation with 25.
% 2.56/2.80 >>>> Starting back demodulation with 27.
% 2.56/2.80 >>>> Starting back demodulation with 29.
% 2.56/2.80
% 2.56/2.80 ======= end of input processing =======
% 2.56/2.80
% 2.56/2.80 =========== start of search ===========
% 2.56/2.80
% 2.56/2.80
% 2.56/2.80 Resetting weight limit to 10.
% 2.56/2.80
% 2.56/2.80
% 2.56/2.80 Resetting weight limit to 10.
% 2.56/2.80
% 2.56/2.80 sos_size=2108
% 2.56/2.80
% 2.56/2.80 -------- PROOF --------
% 2.56/2.80
% 2.56/2.80 ----> UNIT CONFLICT at 0.89 sec ----> 3597 [binary,3596.1,5.1] $F.
% 2.56/2.80
% 2.56/2.80 Length of proof is 31. Level of proof is 12.
% 2.56/2.80
% 2.56/2.80 ---------------- PROOF ----------------
% 2.56/2.80 % SZS status Theorem
% 2.56/2.80 % SZS output start Refutation
% See solution above
% 2.56/2.80 ------------ end of proof -------------
% 2.56/2.80
% 2.56/2.80
% 2.56/2.80 Search stopped by max_proofs option.
% 2.56/2.80
% 2.56/2.80
% 2.56/2.80 Search stopped by max_proofs option.
% 2.56/2.80
% 2.56/2.80 ============ end of search ============
% 2.56/2.80
% 2.56/2.80 -------------- statistics -------------
% 2.56/2.80 clauses given 624
% 2.56/2.80 clauses generated 68502
% 2.56/2.80 clauses kept 3475
% 2.56/2.80 clauses forward subsumed 18267
% 2.56/2.80 clauses back subsumed 782
% 2.56/2.80 Kbytes malloced 5859
% 2.56/2.80
% 2.56/2.80 ----------- times (seconds) -----------
% 2.56/2.80 user CPU time 0.89 (0 hr, 0 min, 0 sec)
% 2.56/2.80 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.56/2.80 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.56/2.80
% 2.56/2.80 That finishes the proof of the theorem.
% 2.56/2.80
% 2.56/2.80 Process 6218 finished Wed Jul 27 06:16:48 2022
% 2.56/2.80 Otter interrupted
% 2.56/2.80 PROOF FOUND
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