TSTP Solution File: KLE026+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE026+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 13:00:32 EDT 2022
% Result : Theorem 2.22s 2.44s
% Output : Refutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 22 ( 19 unt; 0 nHn; 11 RR)
% Number of literals : 25 ( 14 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE026+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ test(A)
| complement(dollar_f1(A),A) ),
file('KLE026+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ complement(A,B)
| addition(B,A) = one ),
file('KLE026+1.p',unknown),
[] ).
cnf(11,axiom,
~ le_q(multiplication(dollar_c2,dollar_c3),multiplication(dollar_c3,dollar_c1)),
file('KLE026+1.p',unknown),
[] ).
cnf(15,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE026+1.p',unknown),
[] ).
cnf(16,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(20,axiom,
addition(A,A) = A,
file('KLE026+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('KLE026+1.p',unknown),
[] ).
cnf(24,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[22])]),
[iquote('copy,22,flip.1')] ).
cnf(28,axiom,
multiplication(one,A) = A,
file('KLE026+1.p',unknown),
[] ).
cnf(31,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE026+1.p',unknown),
[] ).
cnf(38,axiom,
test(dollar_c2),
file('KLE026+1.p',unknown),
[] ).
cnf(40,axiom,
multiplication(dollar_c2,dollar_c3) = multiplication(multiplication(dollar_c2,dollar_c3),dollar_c1),
file('KLE026+1.p',unknown),
[] ).
cnf(41,plain,
multiplication(dollar_c2,multiplication(dollar_c3,dollar_c1)) = multiplication(dollar_c2,dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[40]),24])]),
[iquote('copy,40,demod,24,flip.1')] ).
cnf(45,plain,
complement(dollar_f1(dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[38,3]),
[iquote('hyper,38,3')] ).
cnf(61,plain,
addition(dollar_c2,dollar_f1(dollar_c2)) = one,
inference(hyper,[status(thm)],[45,7]),
[iquote('hyper,45,7')] ).
cnf(105,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[20,16])]),
[iquote('para_from,20.1.1,16.1.1.1,flip.1')] ).
cnf(205,plain,
addition(multiplication(dollar_c2,A),multiplication(dollar_f1(dollar_c2),A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[61,31]),28])]),
[iquote('para_from,61.1.1,31.1.1.1,demod,28,flip.1')] ).
cnf(1317,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[105,2]),
[iquote('hyper,105,2')] ).
cnf(2898,plain,
le_q(multiplication(dollar_c2,A),A),
inference(para_from,[status(thm),theory(equality)],[205,1317]),
[iquote('para_from,205.1.1,1317.1.2')] ).
cnf(2899,plain,
le_q(multiplication(dollar_c2,dollar_c3),multiplication(dollar_c3,dollar_c1)),
inference(para_into,[status(thm),theory(equality)],[2898,41]),
[iquote('para_into,2898.1.1,41.1.1')] ).
cnf(2900,plain,
$false,
inference(binary,[status(thm)],[2899,11]),
[iquote('binary,2899.1,11.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE026+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:55:33 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.71/1.94 ----- Otter 3.3f, August 2004 -----
% 1.71/1.94 The process was started by sandbox on n017.cluster.edu,
% 1.71/1.94 Wed Jul 27 05:55:33 2022
% 1.71/1.94 The command was "./otter". The process ID is 7165.
% 1.71/1.94
% 1.71/1.94 set(prolog_style_variables).
% 1.71/1.94 set(auto).
% 1.71/1.94 dependent: set(auto1).
% 1.71/1.94 dependent: set(process_input).
% 1.71/1.94 dependent: clear(print_kept).
% 1.71/1.94 dependent: clear(print_new_demod).
% 1.71/1.94 dependent: clear(print_back_demod).
% 1.71/1.94 dependent: clear(print_back_sub).
% 1.71/1.94 dependent: set(control_memory).
% 1.71/1.94 dependent: assign(max_mem, 12000).
% 1.71/1.94 dependent: assign(pick_given_ratio, 4).
% 1.71/1.94 dependent: assign(stats_level, 1).
% 1.71/1.94 dependent: assign(max_seconds, 10800).
% 1.71/1.94 clear(print_given).
% 1.71/1.94
% 1.71/1.94 formula_list(usable).
% 1.71/1.94 all A (A=A).
% 1.71/1.94 all A B (addition(A,B)=addition(B,A)).
% 1.71/1.94 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.71/1.94 all A (addition(A,zero)=A).
% 1.71/1.94 all A (addition(A,A)=A).
% 1.71/1.94 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.71/1.94 all A (multiplication(A,one)=A).
% 1.71/1.94 all A (multiplication(one,A)=A).
% 1.71/1.94 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.71/1.94 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.71/1.94 all A (multiplication(A,zero)=zero).
% 1.71/1.94 all A (multiplication(zero,A)=zero).
% 1.71/1.94 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.71/1.94 all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 1.71/1.94 all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 1.71/1.94 all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 1.71/1.94 all X0 (-test(X0)->c(X0)=zero).
% 1.71/1.94 -(all X0 X1 X2 (test(X1)&test(X2)-> (multiplication(X1,X0)=multiplication(multiplication(X1,X0),X2)->le_q(multiplication(X1,X0),multiplication(X0,X2))))).
% 1.71/1.94 end_of_list.
% 1.71/1.94
% 1.71/1.94 -------> usable clausifies to:
% 1.71/1.94
% 1.71/1.94 list(usable).
% 1.71/1.94 0 [] A=A.
% 1.71/1.94 0 [] addition(A,B)=addition(B,A).
% 1.71/1.94 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.71/1.94 0 [] addition(A,zero)=A.
% 1.71/1.94 0 [] addition(A,A)=A.
% 1.71/1.94 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.71/1.94 0 [] multiplication(A,one)=A.
% 1.71/1.94 0 [] multiplication(one,A)=A.
% 1.71/1.94 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.71/1.94 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.71/1.94 0 [] multiplication(A,zero)=zero.
% 1.71/1.94 0 [] multiplication(zero,A)=zero.
% 1.71/1.94 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.71/1.94 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.71/1.94 0 [] -test(X0)|complement($f1(X0),X0).
% 1.71/1.94 0 [] test(X0)| -complement(X1,X0).
% 1.71/1.94 0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 1.71/1.94 0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 1.71/1.94 0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 1.71/1.94 0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 1.71/1.94 0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 1.71/1.94 0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 1.71/1.94 0 [] test(X0)|c(X0)=zero.
% 1.71/1.94 0 [] test($c2).
% 1.71/1.94 0 [] test($c1).
% 1.71/1.94 0 [] multiplication($c2,$c3)=multiplication(multiplication($c2,$c3),$c1).
% 1.71/1.94 0 [] -le_q(multiplication($c2,$c3),multiplication($c3,$c1)).
% 1.71/1.94 end_of_list.
% 1.71/1.94
% 1.71/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.71/1.94
% 1.71/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.71/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.94 deletion, with positive clauses in sos and nonpositive
% 1.71/1.94 clauses in usable.
% 1.71/1.94
% 1.71/1.94 dependent: set(knuth_bendix).
% 1.71/1.94 dependent: set(anl_eq).
% 1.71/1.94 dependent: set(para_from).
% 1.71/1.94 dependent: set(para_into).
% 1.71/1.94 dependent: clear(para_from_right).
% 1.71/1.94 dependent: clear(para_into_right).
% 1.71/1.94 dependent: set(para_from_vars).
% 1.71/1.94 dependent: set(eq_units_both_ways).
% 1.71/1.94 dependent: set(dynamic_demod_all).
% 1.71/1.94 dependent: set(dynamic_demod).
% 1.71/1.94 dependent: set(order_eq).
% 1.71/1.94 dependent: set(back_demod).
% 1.71/1.94 dependent: set(lrpo).
% 1.71/1.94 dependent: set(hyper_res).
% 1.71/1.94 dependent: set(unit_deletion).
% 1.71/1.94 dependent: set(factor).
% 1.71/1.94
% 1.71/1.94 ------------> process usable:
% 1.71/1.94 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.71/1.94 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.71/1.94 ** KEPT (pick-wt=6): 3 [] -test(A)|complement($f1(A),A).
% 1.71/1.94 ** KEPT (pick-wt=5): 4 [] test(A)| -complement(B,A).
% 1.71/1.94 ** KEPT (pick-wt=8): 5 [] -complement(A,B)|multiplication(B,A)=zero.
% 1.71/1.94 ** KEPT (pick-wt=8): 6 [] -complement(A,B)|multiplication(A,B)=zero.
% 2.22/2.44 ** KEPT (pick-wt=8): 7 [] -complement(A,B)|addition(B,A)=one.
% 2.22/2.44 ** KEPT (pick-wt=18): 8 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 2.22/2.44 ** KEPT (pick-wt=9): 9 [] -test(A)|c(A)!=B|complement(A,B).
% 2.22/2.44 ** KEPT (pick-wt=9): 10 [] -test(A)|c(A)=B| -complement(A,B).
% 2.22/2.44 ** KEPT (pick-wt=7): 11 [] -le_q(multiplication($c2,$c3),multiplication($c3,$c1)).
% 2.22/2.44
% 2.22/2.44 ------------> process sos:
% 2.22/2.44 ** KEPT (pick-wt=3): 13 [] A=A.
% 2.22/2.44 ** KEPT (pick-wt=7): 14 [] addition(A,B)=addition(B,A).
% 2.22/2.44 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.22/2.44 ---> New Demodulator: 17 [new_demod,16] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.22/2.44 ** KEPT (pick-wt=5): 18 [] addition(A,zero)=A.
% 2.22/2.44 ---> New Demodulator: 19 [new_demod,18] addition(A,zero)=A.
% 2.22/2.44 ** KEPT (pick-wt=5): 20 [] addition(A,A)=A.
% 2.22/2.44 ---> New Demodulator: 21 [new_demod,20] addition(A,A)=A.
% 2.22/2.44 ** KEPT (pick-wt=11): 23 [copy,22,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.22/2.44 ---> New Demodulator: 24 [new_demod,23] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.22/2.44 ** KEPT (pick-wt=5): 25 [] multiplication(A,one)=A.
% 2.22/2.44 ---> New Demodulator: 26 [new_demod,25] multiplication(A,one)=A.
% 2.22/2.44 ** KEPT (pick-wt=5): 27 [] multiplication(one,A)=A.
% 2.22/2.44 ---> New Demodulator: 28 [new_demod,27] multiplication(one,A)=A.
% 2.22/2.44 ** KEPT (pick-wt=13): 29 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.22/2.44 ---> New Demodulator: 30 [new_demod,29] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.22/2.44 ** KEPT (pick-wt=13): 31 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.22/2.44 ---> New Demodulator: 32 [new_demod,31] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.22/2.44 ** KEPT (pick-wt=5): 33 [] multiplication(A,zero)=zero.
% 2.22/2.44 ---> New Demodulator: 34 [new_demod,33] multiplication(A,zero)=zero.
% 2.22/2.44 ** KEPT (pick-wt=5): 35 [] multiplication(zero,A)=zero.
% 2.22/2.44 ---> New Demodulator: 36 [new_demod,35] multiplication(zero,A)=zero.
% 2.22/2.44 ** KEPT (pick-wt=6): 37 [] test(A)|c(A)=zero.
% 2.22/2.44 ** KEPT (pick-wt=2): 38 [] test($c2).
% 2.22/2.44 ** KEPT (pick-wt=2): 39 [] test($c1).
% 2.22/2.44 ** KEPT (pick-wt=9): 41 [copy,40,demod,24,flip.1] multiplication($c2,multiplication($c3,$c1))=multiplication($c2,$c3).
% 2.22/2.44 ---> New Demodulator: 42 [new_demod,41] multiplication($c2,multiplication($c3,$c1))=multiplication($c2,$c3).
% 2.22/2.44 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 2.22/2.44 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] addition(A,B)=addition(B,A).
% 2.22/2.44 >>>> Starting back demodulation with 17.
% 2.22/2.44 >>>> Starting back demodulation with 19.
% 2.22/2.44 >>>> Starting back demodulation with 21.
% 2.22/2.44 >> back demodulating 12 with 21.
% 2.22/2.44 >>>> Starting back demodulation with 24.
% 2.22/2.44 >>>> Starting back demodulation with 26.
% 2.22/2.44 >>>> Starting back demodulation with 28.
% 2.22/2.44 >>>> Starting back demodulation with 30.
% 2.22/2.44 >>>> Starting back demodulation with 32.
% 2.22/2.44 >>>> Starting back demodulation with 34.
% 2.22/2.44 >>>> Starting back demodulation with 36.
% 2.22/2.44 >>>> Starting back demodulation with 42.
% 2.22/2.44
% 2.22/2.44 ======= end of input processing =======
% 2.22/2.44
% 2.22/2.44 =========== start of search ===========
% 2.22/2.44
% 2.22/2.44
% 2.22/2.44 Resetting weight limit to 7.
% 2.22/2.44
% 2.22/2.44
% 2.22/2.44 Resetting weight limit to 7.
% 2.22/2.44
% 2.22/2.44 sos_size=2203
% 2.22/2.44
% 2.22/2.44 -------- PROOF --------
% 2.22/2.44
% 2.22/2.44 ----> UNIT CONFLICT at 0.51 sec ----> 2900 [binary,2899.1,11.1] $F.
% 2.22/2.44
% 2.22/2.44 Length of proof is 10. Level of proof is 5.
% 2.22/2.44
% 2.22/2.44 ---------------- PROOF ----------------
% 2.22/2.44 % SZS status Theorem
% 2.22/2.44 % SZS output start Refutation
% See solution above
% 2.22/2.44 ------------ end of proof -------------
% 2.22/2.44
% 2.22/2.44
% 2.22/2.44 Search stopped by max_proofs option.
% 2.22/2.44
% 2.22/2.44
% 2.22/2.44 Search stopped by max_proofs option.
% 2.22/2.44
% 2.22/2.44 ============ end of search ============
% 2.22/2.44
% 2.22/2.44 -------------- statistics -------------
% 2.22/2.44 clauses given 287
% 2.22/2.44 clauses generated 10785
% 2.22/2.44 clauses kept 2762
% 2.22/2.44 clauses forward subsumed 5348
% 2.22/2.44 clauses back subsumed 564
% 2.22/2.44 Kbytes malloced 4882
% 2.22/2.44
% 2.22/2.44 ----------- times (seconds) -----------
% 2.22/2.44 user CPU time 0.51 (0 hr, 0 min, 0 sec)
% 2.22/2.44 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.22/2.44 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.22/2.44
% 2.22/2.44 That finishes the proof of the theorem.
% 2.22/2.44
% 2.22/2.44 Process 7165 finished Wed Jul 27 05:55:35 2022
% 2.22/2.44 Otter interrupted
% 2.22/2.45 PROOF FOUND
%------------------------------------------------------------------------------