TSTP Solution File: KLE048+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE048+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:00:36 EDT 2022
% Result : Theorem 2.33s 2.54s
% Output : Refutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of clauses : 28 ( 21 unt; 0 nHn; 16 RR)
% Number of literals : 35 ( 19 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE048+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE048+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ le_q(addition(multiplication(A,B),C),B)
| le_q(multiplication(star(A),C),B) ),
file('KLE048+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ test(A)
| complement(dollar_f1(A),A) ),
file('KLE048+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ complement(A,B)
| addition(B,A) = one ),
file('KLE048+1.p',unknown),
[] ).
cnf(13,axiom,
star(dollar_c1) != one,
file('KLE048+1.p',unknown),
[] ).
cnf(16,axiom,
addition(A,B) = addition(B,A),
file('KLE048+1.p',unknown),
[] ).
cnf(17,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE048+1.p',unknown),
[] ).
cnf(19,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[17])]),
[iquote('copy,17,flip.1')] ).
cnf(22,axiom,
addition(A,A) = A,
file('KLE048+1.p',unknown),
[] ).
cnf(28,axiom,
multiplication(A,one) = A,
file('KLE048+1.p',unknown),
[] ).
cnf(30,axiom,
multiplication(one,A) = A,
file('KLE048+1.p',unknown),
[] ).
cnf(33,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE048+1.p',unknown),
[] ).
cnf(39,axiom,
le_q(addition(one,multiplication(A,star(A))),star(A)),
file('KLE048+1.p',unknown),
[] ).
cnf(42,axiom,
test(dollar_c1),
file('KLE048+1.p',unknown),
[] ).
cnf(45,plain,
complement(dollar_f1(dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[42,5]),
[iquote('hyper,42,5')] ).
cnf(56,plain,
addition(dollar_c1,dollar_f1(dollar_c1)) = one,
inference(hyper,[status(thm)],[45,9]),
[iquote('hyper,45,9')] ).
cnf(62,plain,
( addition(A,B) = A
| ~ le_q(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,1])]),
[iquote('para_into,16.1.1,1.2.1,flip.1')] ).
cnf(78,plain,
le_q(A,A),
inference(hyper,[status(thm)],[22,2]),
[iquote('hyper,22,2')] ).
cnf(83,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,22])]),
[iquote('para_into,18.1.1.1,22.1.1,flip.1')] ).
cnf(104,plain,
( ~ le_q(addition(A,B),one)
| le_q(multiplication(star(A),B),one) ),
inference(para_from,[status(thm),theory(equality)],[28,3]),
[iquote('para_from,27.1.1,3.1.1.1')] ).
cnf(165,plain,
addition(one,addition(multiplication(A,star(A)),star(A))) = star(A),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[39,1]),19]),
[iquote('hyper,39,1,demod,19')] ).
cnf(977,plain,
addition(dollar_c1,one) = one,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[83,56]),56]),
[iquote('para_into,83.1.1.2,55.1.1,demod,56')] ).
cnf(1072,plain,
addition(multiplication(dollar_c1,A),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[977,33]),30,30])]),
[iquote('para_from,977.1.1,33.1.1.1,demod,30,30,flip.1')] ).
cnf(1944,plain,
le_q(star(dollar_c1),one),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[104,977]),28]),78]),
[iquote('para_into,104.1.1,977.1.1,demod,28,unit_del,78')] ).
cnf(1977,plain,
addition(one,star(dollar_c1)) = one,
inference(hyper,[status(thm)],[1944,62]),
[iquote('hyper,1944,62')] ).
cnf(3004,plain,
star(dollar_c1) = one,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[165,1072]),1977])]),
[iquote('para_into,165.1.1.2,1072.1.1,demod,1977,flip.1')] ).
cnf(3006,plain,
$false,
inference(binary,[status(thm)],[3004,13]),
[iquote('binary,3004.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE048+1 : TPTP v8.1.0. Released v4.0.0.
% 0.13/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 06:34:16 EDT 2022
% 0.19/0.35 % CPUTime :
% 1.77/1.97 ----- Otter 3.3f, August 2004 -----
% 1.77/1.97 The process was started by sandbox on n018.cluster.edu,
% 1.77/1.97 Wed Jul 27 06:34:16 2022
% 1.77/1.97 The command was "./otter". The process ID is 6056.
% 1.77/1.97
% 1.77/1.97 set(prolog_style_variables).
% 1.77/1.97 set(auto).
% 1.77/1.97 dependent: set(auto1).
% 1.77/1.97 dependent: set(process_input).
% 1.77/1.97 dependent: clear(print_kept).
% 1.77/1.97 dependent: clear(print_new_demod).
% 1.77/1.97 dependent: clear(print_back_demod).
% 1.77/1.97 dependent: clear(print_back_sub).
% 1.77/1.97 dependent: set(control_memory).
% 1.77/1.97 dependent: assign(max_mem, 12000).
% 1.77/1.97 dependent: assign(pick_given_ratio, 4).
% 1.77/1.97 dependent: assign(stats_level, 1).
% 1.77/1.97 dependent: assign(max_seconds, 10800).
% 1.77/1.97 clear(print_given).
% 1.77/1.97
% 1.77/1.97 formula_list(usable).
% 1.77/1.97 all A (A=A).
% 1.77/1.97 all A B (addition(A,B)=addition(B,A)).
% 1.77/1.97 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.77/1.97 all A (addition(A,zero)=A).
% 1.77/1.97 all A (addition(A,A)=A).
% 1.77/1.97 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.77/1.97 all A (multiplication(A,one)=A).
% 1.77/1.97 all A (multiplication(one,A)=A).
% 1.77/1.97 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.77/1.97 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.77/1.97 all A (multiplication(A,zero)=zero).
% 1.77/1.97 all A (multiplication(zero,A)=zero).
% 1.77/1.97 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.77/1.97 all A le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.77/1.97 all A le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.77/1.97 all A B C (le_q(addition(multiplication(A,B),C),B)->le_q(multiplication(star(A),C),B)).
% 1.77/1.97 all A B C (le_q(addition(multiplication(A,B),C),A)->le_q(multiplication(C,star(B)),A)).
% 1.77/1.97 all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 1.77/1.97 all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 1.77/1.97 all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 1.77/1.97 all X0 (-test(X0)->c(X0)=zero).
% 1.77/1.97 -(all X0 (test(X0)->star(X0)=one)).
% 1.77/1.97 end_of_list.
% 1.77/1.97
% 1.77/1.97 -------> usable clausifies to:
% 1.77/1.97
% 1.77/1.97 list(usable).
% 1.77/1.97 0 [] A=A.
% 1.77/1.97 0 [] addition(A,B)=addition(B,A).
% 1.77/1.97 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.77/1.97 0 [] addition(A,zero)=A.
% 1.77/1.97 0 [] addition(A,A)=A.
% 1.77/1.97 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.77/1.97 0 [] multiplication(A,one)=A.
% 1.77/1.97 0 [] multiplication(one,A)=A.
% 1.77/1.97 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.77/1.97 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.77/1.97 0 [] multiplication(A,zero)=zero.
% 1.77/1.97 0 [] multiplication(zero,A)=zero.
% 1.77/1.97 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.77/1.97 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.77/1.97 0 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.77/1.97 0 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.77/1.97 0 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.77/1.97 0 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.77/1.97 0 [] -test(X0)|complement($f1(X0),X0).
% 1.77/1.97 0 [] test(X0)| -complement(X1,X0).
% 1.77/1.97 0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 1.77/1.97 0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 1.77/1.97 0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 1.77/1.97 0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 1.77/1.97 0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 1.77/1.97 0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 1.77/1.97 0 [] test(X0)|c(X0)=zero.
% 1.77/1.97 0 [] test($c1).
% 1.77/1.97 0 [] star($c1)!=one.
% 1.77/1.97 end_of_list.
% 1.77/1.97
% 1.77/1.97 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.77/1.97
% 1.77/1.97 This ia a non-Horn set with equality. The strategy will be
% 1.77/1.97 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.77/1.97 deletion, with positive clauses in sos and nonpositive
% 1.77/1.97 clauses in usable.
% 1.77/1.97
% 1.77/1.97 dependent: set(knuth_bendix).
% 1.77/1.97 dependent: set(anl_eq).
% 1.77/1.97 dependent: set(para_from).
% 1.77/1.97 dependent: set(para_into).
% 1.77/1.97 dependent: clear(para_from_right).
% 1.77/1.97 dependent: clear(para_into_right).
% 1.77/1.97 dependent: set(para_from_vars).
% 1.77/1.97 dependent: set(eq_units_both_ways).
% 1.77/1.97 dependent: set(dynamic_demod_all).
% 1.77/1.97 dependent: set(dynamic_demod).
% 1.77/1.97 dependent: set(order_eq).
% 1.77/1.97 dependent: set(back_demod).
% 1.77/1.97 dependent: set(lrpo).
% 1.77/1.97 dependent: set(hyper_res).
% 1.77/1.97 dependent: set(unit_deletion).
% 1.77/1.97 dependent: set(factor).
% 1.77/1.97
% 1.77/1.97 ------------> process usable:
% 2.33/2.54 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 2.33/2.54 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 2.33/2.54 ** KEPT (pick-wt=13): 3 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 2.33/2.54 ** KEPT (pick-wt=13): 4 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 2.33/2.54 ** KEPT (pick-wt=6): 5 [] -test(A)|complement($f1(A),A).
% 2.33/2.54 ** KEPT (pick-wt=5): 6 [] test(A)| -complement(B,A).
% 2.33/2.54 ** KEPT (pick-wt=8): 7 [] -complement(A,B)|multiplication(B,A)=zero.
% 2.33/2.54 ** KEPT (pick-wt=8): 8 [] -complement(A,B)|multiplication(A,B)=zero.
% 2.33/2.54 ** KEPT (pick-wt=8): 9 [] -complement(A,B)|addition(B,A)=one.
% 2.33/2.54 ** KEPT (pick-wt=18): 10 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 2.33/2.54 ** KEPT (pick-wt=9): 11 [] -test(A)|c(A)!=B|complement(A,B).
% 2.33/2.54 ** KEPT (pick-wt=9): 12 [] -test(A)|c(A)=B| -complement(A,B).
% 2.33/2.54 ** KEPT (pick-wt=4): 13 [] star($c1)!=one.
% 2.33/2.54
% 2.33/2.54 ------------> process sos:
% 2.33/2.54 ** KEPT (pick-wt=3): 15 [] A=A.
% 2.33/2.54 ** KEPT (pick-wt=7): 16 [] addition(A,B)=addition(B,A).
% 2.33/2.54 ** KEPT (pick-wt=11): 18 [copy,17,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.33/2.54 ---> New Demodulator: 19 [new_demod,18] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.33/2.54 ** KEPT (pick-wt=5): 20 [] addition(A,zero)=A.
% 2.33/2.54 ---> New Demodulator: 21 [new_demod,20] addition(A,zero)=A.
% 2.33/2.54 ** KEPT (pick-wt=5): 22 [] addition(A,A)=A.
% 2.33/2.54 ---> New Demodulator: 23 [new_demod,22] addition(A,A)=A.
% 2.33/2.54 ** KEPT (pick-wt=11): 25 [copy,24,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.33/2.54 ---> New Demodulator: 26 [new_demod,25] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.33/2.54 ** KEPT (pick-wt=5): 27 [] multiplication(A,one)=A.
% 2.33/2.54 ---> New Demodulator: 28 [new_demod,27] multiplication(A,one)=A.
% 2.33/2.54 ** KEPT (pick-wt=5): 29 [] multiplication(one,A)=A.
% 2.33/2.54 ---> New Demodulator: 30 [new_demod,29] multiplication(one,A)=A.
% 2.33/2.54 ** KEPT (pick-wt=13): 31 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.33/2.54 ---> New Demodulator: 32 [new_demod,31] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.33/2.54 ** KEPT (pick-wt=13): 33 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.33/2.54 ---> New Demodulator: 34 [new_demod,33] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.33/2.54 ** KEPT (pick-wt=5): 35 [] multiplication(A,zero)=zero.
% 2.33/2.54 ---> New Demodulator: 36 [new_demod,35] multiplication(A,zero)=zero.
% 2.33/2.54 ** KEPT (pick-wt=5): 37 [] multiplication(zero,A)=zero.
% 2.33/2.54 ---> New Demodulator: 38 [new_demod,37] multiplication(zero,A)=zero.
% 2.33/2.54 ** KEPT (pick-wt=9): 39 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 2.33/2.54 ** KEPT (pick-wt=9): 40 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 2.33/2.54 ** KEPT (pick-wt=6): 41 [] test(A)|c(A)=zero.
% 2.33/2.54 ** KEPT (pick-wt=2): 42 [] test($c1).
% 2.33/2.54 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 2.33/2.54 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] addition(A,B)=addition(B,A).
% 2.33/2.54 >>>> Starting back demodulation with 19.
% 2.33/2.54 >>>> Starting back demodulation with 21.
% 2.33/2.54 >>>> Starting back demodulation with 23.
% 2.33/2.54 >> back demodulating 14 with 23.
% 2.33/2.54 >>>> Starting back demodulation with 26.
% 2.33/2.54 >>>> Starting back demodulation with 28.
% 2.33/2.54 >>>> Starting back demodulation with 30.
% 2.33/2.54 >>>> Starting back demodulation with 32.
% 2.33/2.54 >>>> Starting back demodulation with 34.
% 2.33/2.54 >>>> Starting back demodulation with 36.
% 2.33/2.54 >>>> Starting back demodulation with 38.
% 2.33/2.54
% 2.33/2.54 ======= end of input processing =======
% 2.33/2.54
% 2.33/2.54 =========== start of search ===========
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Resetting weight limit to 8.
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Resetting weight limit to 8.
% 2.33/2.54
% 2.33/2.54 sos_size=1868
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Resetting weight limit to 7.
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Resetting weight limit to 7.
% 2.33/2.54
% 2.33/2.54 sos_size=1914
% 2.33/2.54
% 2.33/2.54 -------- PROOF --------
% 2.33/2.54
% 2.33/2.54 ----> UNIT CONFLICT at 0.55 sec ----> 3006 [binary,3004.1,13.1] $F.
% 2.33/2.54
% 2.33/2.54 Length of proof is 13. Level of proof is 6.
% 2.33/2.54
% 2.33/2.54 ---------------- PROOF ----------------
% 2.33/2.54 % SZS status Theorem
% 2.33/2.54 % SZS output start Refutation
% See solution above
% 2.33/2.54 ------------ end of proof -------------
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Search stopped by max_proofs option.
% 2.33/2.54
% 2.33/2.54
% 2.33/2.54 Search stopped by max_proofs option.
% 2.33/2.54
% 2.33/2.54 ============ end of search ============
% 2.33/2.54
% 2.33/2.54 -------------- statistics -------------
% 2.33/2.54 clauses given 326
% 2.33/2.54 clauses generated 15575
% 2.33/2.54 clauses kept 2882
% 2.33/2.54 clauses forward subsumed 7186
% 2.33/2.54 clauses back subsumed 577
% 2.33/2.54 Kbytes malloced 4882
% 2.33/2.54
% 2.33/2.54 ----------- times (seconds) -----------
% 2.33/2.54 user CPU time 0.55 (0 hr, 0 min, 0 sec)
% 2.33/2.54 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.33/2.54 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.33/2.54
% 2.33/2.54 That finishes the proof of the theorem.
% 2.33/2.54
% 2.33/2.54 Process 6056 finished Wed Jul 27 06:34:18 2022
% 2.33/2.54 Otter interrupted
% 2.33/2.54 PROOF FOUND
%------------------------------------------------------------------------------