TSTP Solution File: KLE169-10 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE169-10 : TPTP v8.1.0. Released v7.5.0.
% 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 : Unsatisfiable 1.80s 2.04s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 29 ( 29 unt; 0 nHn; 6 RR)
% Number of literals : 29 ( 28 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 50 ( 11 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
le_q(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) != true,
file('KLE169-10.p',unknown),
[] ).
cnf(4,axiom,
ife_q3(A,A,B,C) = B,
file('KLE169-10.p',unknown),
[] ).
cnf(6,axiom,
ife_q2(A,A,B,C) = B,
file('KLE169-10.p',unknown),
[] ).
cnf(9,axiom,
addition(A,B) = addition(B,A),
file('KLE169-10.p',unknown),
[] ).
cnf(10,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE169-10.p',unknown),
[] ).
cnf(12,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(15,axiom,
addition(A,A) = A,
file('KLE169-10.p',unknown),
[] ).
cnf(23,axiom,
multiplication(one,A) = A,
file('KLE169-10.p',unknown),
[] ).
cnf(25,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE169-10.p',unknown),
[] ).
cnf(26,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE169-10.p',unknown),
[] ).
cnf(32,axiom,
ife_q2(le_q(A,B),true,addition(A,B),B) = B,
file('KLE169-10.p',unknown),
[] ).
cnf(34,axiom,
ife_q3(addition(A,B),B,le_q(A,B),true) = true,
file('KLE169-10.p',unknown),
[] ).
cnf(36,axiom,
le_q(addition(one,multiplication(A,star(A))),star(A)) = true,
file('KLE169-10.p',unknown),
[] ).
cnf(44,axiom,
sigma = addition(a,b),
file('KLE169-10.p',unknown),
[] ).
cnf(45,plain,
addition(a,b) = sigma,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[44])]),
[iquote('copy,44,flip.1')] ).
cnf(47,plain,
addition(b,a) = sigma,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,45])]),
[iquote('para_into,9.1.1,45.1.1,flip.1')] ).
cnf(55,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,15])]),
[iquote('para_into,11.1.1.1,15.1.1,flip.1')] ).
cnf(57,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,9]),12]),
[iquote('para_into,11.1.1.1,9.1.1,demod,12')] ).
cnf(120,plain,
multiplication(sigma,A) = addition(multiplication(b,A),multiplication(a,A)),
inference(para_into,[status(thm),theory(equality)],[26,47]),
[iquote('para_into,26.1.1.1,47.1.1')] ).
cnf(124,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))))) != true,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),120,25,25]),
[iquote('back_demod,1,demod,120,25,25')] ).
cnf(188,plain,
le_q(A,addition(A,B)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,55]),4]),
[iquote('para_into,34.1.1.1,55.1.1,demod,4')] ).
cnf(216,plain,
addition(one,addition(multiplication(A,star(A)),star(A))) = star(A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[36,32]),12,6]),
[iquote('para_from,36.1.1,32.1.1.1,demod,12,6')] ).
cnf(415,plain,
le_q(A,addition(B,addition(A,C))) = true,
inference(para_from,[status(thm),theory(equality)],[57,188]),
[iquote('para_from,57.1.1,188.1.1.2')] ).
cnf(931,plain,
le_q(one,addition(A,star(B))) = true,
inference(para_from,[status(thm),theory(equality)],[216,415]),
[iquote('para_from,216.1.1,415.1.1.2.2')] ).
cnf(937,plain,
addition(multiplication(A,star(A)),star(A)) = star(A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[216,32]),931,6])]),
[iquote('para_from,216.1.1,32.1.1.3,demod,931,6,flip.1')] ).
cnf(938,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)],[216,26]),23,937])]),
[iquote('para_from,216.1.1,26.1.1.1,demod,23,937,flip.1')] ).
cnf(1054,plain,
le_q(A,addition(B,multiplication(star(C),A))) = true,
inference(para_from,[status(thm),theory(equality)],[938,415]),
[iquote('para_from,938.1.1,415.1.1.2.2')] ).
cnf(1076,plain,
le_q(A,addition(multiplication(star(B),A),C)) = true,
inference(para_into,[status(thm),theory(equality)],[1054,9]),
[iquote('para_into,1054.1.1.2,9.1.1')] ).
cnf(1078,plain,
$false,
inference(binary,[status(thm)],[1076,124]),
[iquote('binary,1076.1,124.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE169-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n005.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 06:26:35 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.72/1.93 ----- Otter 3.3f, August 2004 -----
% 1.72/1.93 The process was started by sandbox on n005.cluster.edu,
% 1.72/1.93 Wed Jul 27 06:26:35 2022
% 1.72/1.93 The command was "./otter". The process ID is 2051.
% 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 list(usable).
% 1.72/1.93 0 [] A=A.
% 1.72/1.93 0 [] ife_q3(A,A,B,C)=B.
% 1.72/1.93 0 [] ife_q2(A,A,B,C)=B.
% 1.72/1.93 0 [] ife_q(A,A,B,C)=B.
% 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 [] ife_q2(le_q(A,B),true,addition(A,B),B)=B.
% 1.72/1.93 0 [] ife_q3(addition(A,B),B,le_q(A,B),true)=true.
% 1.72/1.93 0 [] le_q(addition(one,multiplication(A,star(A))),star(A))=true.
% 1.72/1.93 0 [] le_q(addition(one,multiplication(star(A),A)),star(A))=true.
% 1.72/1.93 0 [] ife_q(le_q(addition(multiplication(A,B),C),B),true,le_q(multiplication(star(A),C),B),true)=true.
% 1.72/1.93 0 [] ife_q(le_q(addition(multiplication(A,B),C),A),true,le_q(multiplication(C,star(B)),A),true)=true.
% 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))))!=true.
% 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=1.
% 1.72/1.93
% 1.72/1.93 All clauses are units, and equality is present; the
% 1.72/1.93 strategy will be Knuth-Bendix with positive clauses in sos.
% 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
% 1.72/1.93 ------------> process usable:
% 1.72/1.93 ** KEPT (pick-wt=16): 1 [] le_q(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a))))!=true.
% 1.72/1.93
% 1.72/1.93 ------------> process sos:
% 1.72/1.93 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.72/1.93 ** KEPT (pick-wt=7): 3 [] ife_q3(A,A,B,C)=B.
% 1.72/1.93 ---> New Demodulator: 4 [new_demod,3] ife_q3(A,A,B,C)=B.
% 1.72/1.93 ** KEPT (pick-wt=7): 5 [] ife_q2(A,A,B,C)=B.
% 1.72/1.93 ---> New Demodulator: 6 [new_demod,5] ife_q2(A,A,B,C)=B.
% 1.72/1.93 ** KEPT (pick-wt=7): 7 [] ife_q(A,A,B,C)=B.
% 1.72/1.93 ---> New Demodulator: 8 [new_demod,7] ife_q(A,A,B,C)=B.
% 1.72/1.93 ** KEPT (pick-wt=7): 9 [] addition(A,B)=addition(B,A).
% 1.72/1.93 ** KEPT (pick-wt=11): 11 [copy,10,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.72/1.93 ---> New Demodulator: 12 [new_demod,11] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.72/1.93 ** KEPT (pick-wt=5): 13 [] addition(A,zero)=A.
% 1.72/1.93 ---> New Demodulator: 14 [new_demod,13] addition(A,zero)=A.
% 1.72/1.93 ** KEPT (pick-wt=5): 15 [] addition(A,A)=A.
% 1.72/1.93 ---> New Demodulator: 16 [new_demod,15] addition(A,A)=A.
% 1.72/1.93 ** KEPT (pick-wt=11): 18 [copy,17,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.72/1.93 ---> New Demodulator: 19 [new_demod,18] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.72/1.93 ** KEPT (pick-wt=5): 20 [] multiplication(A,one)=A.
% 1.72/1.93 ---> New Demodulator: 21 [new_demod,20] multiplication(A,one)=A.
% 1.72/1.93 ** KEPT (pick-wt=5): 22 [] multiplication(one,A)=A.
% 1.72/1.93 ---> New Demodulator: 23 [new_demod,22] multiplication(one,A)=A.
% 1.72/1.93 ** KEPT (pick-wt=13): 24 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.72/1.93 ---> New Demodulator: 25 [new_demod,24] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.80/2.04 ** KEPT (pick-wt=13): 26 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.80/2.04 ---> New Demodulator: 27 [new_demod,26] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.80/2.04 ** KEPT (pick-wt=5): 28 [] multiplication(A,zero)=zero.
% 1.80/2.04 ---> New Demodulator: 29 [new_demod,28] multiplication(A,zero)=zero.
% 1.80/2.04 ** KEPT (pick-wt=5): 30 [] multiplication(zero,A)=zero.
% 1.80/2.04 ---> New Demodulator: 31 [new_demod,30] multiplication(zero,A)=zero.
% 1.80/2.04 ** KEPT (pick-wt=11): 32 [] ife_q2(le_q(A,B),true,addition(A,B),B)=B.
% 1.80/2.04 ---> New Demodulator: 33 [new_demod,32] ife_q2(le_q(A,B),true,addition(A,B),B)=B.
% 1.80/2.04 ** KEPT (pick-wt=11): 34 [] ife_q3(addition(A,B),B,le_q(A,B),true)=true.
% 1.80/2.04 ---> New Demodulator: 35 [new_demod,34] ife_q3(addition(A,B),B,le_q(A,B),true)=true.
% 1.80/2.04 ** KEPT (pick-wt=11): 36 [] le_q(addition(one,multiplication(A,star(A))),star(A))=true.
% 1.80/2.04 ---> New Demodulator: 37 [new_demod,36] le_q(addition(one,multiplication(A,star(A))),star(A))=true.
% 1.80/2.04 ** KEPT (pick-wt=11): 38 [] le_q(addition(one,multiplication(star(A),A)),star(A))=true.
% 1.80/2.04 ---> New Demodulator: 39 [new_demod,38] le_q(addition(one,multiplication(star(A),A)),star(A))=true.
% 1.80/2.04 ** KEPT (pick-wt=18): 40 [] ife_q(le_q(addition(multiplication(A,B),C),B),true,le_q(multiplication(star(A),C),B),true)=true.
% 1.80/2.04 ---> New Demodulator: 41 [new_demod,40] ife_q(le_q(addition(multiplication(A,B),C),B),true,le_q(multiplication(star(A),C),B),true)=true.
% 1.80/2.04 ** KEPT (pick-wt=18): 42 [] ife_q(le_q(addition(multiplication(A,B),C),A),true,le_q(multiplication(C,star(B)),A),true)=true.
% 1.80/2.04 ---> New Demodulator: 43 [new_demod,42] ife_q(le_q(addition(multiplication(A,B),C),A),true,le_q(multiplication(C,star(B)),A),true)=true.
% 1.80/2.04 ** KEPT (pick-wt=5): 45 [copy,44,flip.1] addition(a,b)=sigma.
% 1.80/2.04 ---> New Demodulator: 46 [new_demod,45] addition(a,b)=sigma.
% 1.80/2.04 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.80/2.04 >>>> Starting back demodulation with 4.
% 1.80/2.04 >>>> Starting back demodulation with 6.
% 1.80/2.04 >>>> Starting back demodulation with 8.
% 1.80/2.04 Following clause subsumed by 9 during input processing: 0 [copy,9,flip.1] addition(A,B)=addition(B,A).
% 1.80/2.04 >>>> Starting back demodulation with 12.
% 1.80/2.04 >>>> Starting back demodulation with 14.
% 1.80/2.04 >>>> Starting back demodulation with 16.
% 1.80/2.04 >>>> Starting back demodulation with 19.
% 1.80/2.04 >>>> Starting back demodulation with 21.
% 1.80/2.04 >>>> Starting back demodulation with 23.
% 1.80/2.04 >>>> Starting back demodulation with 25.
% 1.80/2.04 >>>> Starting back demodulation with 27.
% 1.80/2.04 >>>> Starting back demodulation with 29.
% 1.80/2.04 >>>> Starting back demodulation with 31.
% 1.80/2.04 >>>> Starting back demodulation with 33.
% 1.80/2.04 >>>> Starting back demodulation with 35.
% 1.80/2.04 >>>> Starting back demodulation with 37.
% 1.80/2.04 >>>> Starting back demodulation with 39.
% 1.80/2.04 >>>> Starting back demodulation with 41.
% 1.80/2.04 >>>> Starting back demodulation with 43.
% 1.80/2.04 >>>> Starting back demodulation with 46.
% 1.80/2.04
% 1.80/2.04 ======= end of input processing =======
% 1.80/2.04
% 1.80/2.04 =========== start of search ===========
% 1.80/2.04
% 1.80/2.04
% 1.80/2.04 Resetting weight limit to 11.
% 1.80/2.04
% 1.80/2.04
% 1.80/2.04 Resetting weight limit to 11.
% 1.80/2.04
% 1.80/2.04 sos_size=244
% 1.80/2.04
% 1.80/2.04 -------- PROOF --------
% 1.80/2.04
% 1.80/2.04 ----> UNIT CONFLICT at 0.12 sec ----> 1078 [binary,1076.1,124.1] $F.
% 1.80/2.04
% 1.80/2.04 Length of proof is 15. Level of proof is 9.
% 1.80/2.04
% 1.80/2.04 ---------------- PROOF ----------------
% 1.80/2.04 % SZS status Unsatisfiable
% 1.80/2.04 % SZS output start Refutation
% See solution above
% 1.80/2.04 ------------ end of proof -------------
% 1.80/2.04
% 1.80/2.04
% 1.80/2.04 Search stopped by max_proofs option.
% 1.80/2.04
% 1.80/2.04
% 1.80/2.04 Search stopped by max_proofs option.
% 1.80/2.04
% 1.80/2.04 ============ end of search ============
% 1.80/2.04
% 1.80/2.04 -------------- statistics -------------
% 1.80/2.04 clauses given 268
% 1.80/2.04 clauses generated 11265
% 1.80/2.04 clauses kept 590
% 1.80/2.04 clauses forward subsumed 7053
% 1.80/2.04 clauses back subsumed 22
% 1.80/2.04 Kbytes malloced 5859
% 1.80/2.04
% 1.80/2.04 ----------- times (seconds) -----------
% 1.80/2.04 user CPU time 0.12 (0 hr, 0 min, 0 sec)
% 1.80/2.04 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/2.04 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.80/2.04
% 1.80/2.04 That finishes the proof of the theorem.
% 1.80/2.04
% 1.80/2.04 Process 2051 finished Wed Jul 27 06:26:37 2022
% 1.80/2.04 Otter interrupted
% 1.80/2.04 PROOF FOUND
%------------------------------------------------------------------------------