TSTP Solution File: KLE035+2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE035+2 : 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 13:00:34 EDT 2022
% Result : Theorem 1.65s 1.81s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 16 unt; 0 nHn; 10 RR)
% Number of literals : 18 ( 9 equ; 4 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE035+2.p',unknown),
[] ).
cnf(13,axiom,
~ le_q(multiplication(multiplication(dollar_c2,addition(dollar_c4,dollar_c3)),c(dollar_c1)),zero),
file('KLE035+2.p',unknown),
[] ).
cnf(18,axiom,
addition(A,B) = addition(B,A),
file('KLE035+2.p',unknown),
[] ).
cnf(23,axiom,
addition(A,zero) = A,
file('KLE035+2.p',unknown),
[] ).
cnf(26,axiom,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('KLE035+2.p',unknown),
[] ).
cnf(28,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[26])]),
[iquote('copy,26,flip.1')] ).
cnf(34,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE035+2.p',unknown),
[] ).
cnf(36,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE035+2.p',unknown),
[] ).
cnf(44,axiom,
le_q(multiplication(multiplication(dollar_c2,dollar_c4),c(dollar_c1)),zero),
file('KLE035+2.p',unknown),
[] ).
cnf(45,plain,
le_q(multiplication(dollar_c2,multiplication(dollar_c4,c(dollar_c1))),zero),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[44]),28]),
[iquote('copy,44,demod,28')] ).
cnf(46,axiom,
le_q(multiplication(multiplication(dollar_c2,dollar_c3),c(dollar_c1)),zero),
file('KLE035+2.p',unknown),
[] ).
cnf(47,plain,
le_q(multiplication(dollar_c2,multiplication(dollar_c3,c(dollar_c1))),zero),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[46]),28]),
[iquote('copy,46,demod,28')] ).
cnf(51,plain,
~ le_q(addition(multiplication(dollar_c2,multiplication(dollar_c4,c(dollar_c1))),multiplication(dollar_c2,multiplication(dollar_c3,c(dollar_c1)))),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),34,36,28,28]),
[iquote('back_demod,13,demod,34,36,28,28')] ).
cnf(164,plain,
addition(zero,A) = A,
inference(para_into,[status(thm),theory(equality)],[23,18]),
[iquote('para_into,22.1.1,18.1.1')] ).
cnf(431,plain,
multiplication(dollar_c2,multiplication(dollar_c4,c(dollar_c1))) = zero,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[45,1]),23]),
[iquote('hyper,45,1,demod,23')] ).
cnf(432,plain,
~ le_q(multiplication(dollar_c2,multiplication(dollar_c3,c(dollar_c1))),zero),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[51]),431,164]),
[iquote('back_demod,51,demod,431,164')] ).
cnf(433,plain,
$false,
inference(binary,[status(thm)],[432,47]),
[iquote('binary,432.1,47.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KLE035+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % 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 06:13:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.60/1.80 ----- Otter 3.3f, August 2004 -----
% 1.60/1.80 The process was started by sandbox on n007.cluster.edu,
% 1.60/1.80 Wed Jul 27 06:13:31 2022
% 1.60/1.80 The command was "./otter". The process ID is 4382.
% 1.60/1.80
% 1.60/1.80 set(prolog_style_variables).
% 1.60/1.80 set(auto).
% 1.60/1.80 dependent: set(auto1).
% 1.60/1.80 dependent: set(process_input).
% 1.60/1.80 dependent: clear(print_kept).
% 1.60/1.80 dependent: clear(print_new_demod).
% 1.60/1.80 dependent: clear(print_back_demod).
% 1.60/1.80 dependent: clear(print_back_sub).
% 1.60/1.80 dependent: set(control_memory).
% 1.60/1.80 dependent: assign(max_mem, 12000).
% 1.60/1.80 dependent: assign(pick_given_ratio, 4).
% 1.60/1.80 dependent: assign(stats_level, 1).
% 1.60/1.80 dependent: assign(max_seconds, 10800).
% 1.60/1.80 clear(print_given).
% 1.60/1.80
% 1.60/1.80 formula_list(usable).
% 1.60/1.80 all A (A=A).
% 1.60/1.80 all A B (addition(A,B)=addition(B,A)).
% 1.60/1.80 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.60/1.80 all A (addition(A,zero)=A).
% 1.60/1.80 all A (addition(A,A)=A).
% 1.60/1.80 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.60/1.80 all A (multiplication(A,one)=A).
% 1.60/1.80 all A (multiplication(one,A)=A).
% 1.60/1.80 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.60/1.80 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.60/1.80 all A (multiplication(A,zero)=zero).
% 1.60/1.80 all A (multiplication(zero,A)=zero).
% 1.60/1.80 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.60/1.80 all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 1.60/1.80 all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 1.60/1.80 all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 1.60/1.80 all X0 (-test(X0)->c(X0)=zero).
% 1.60/1.80 all X0 X1 (test(X0)&test(X1)->c(addition(X0,X1))=multiplication(c(X0),c(X1))).
% 1.60/1.80 all X0 X1 (test(X0)&test(X1)->c(multiplication(X0,X1))=addition(c(X0),c(X1))).
% 1.60/1.80 -(all X0 X1 X2 X3 (test(X3)&test(X2)&le_q(multiplication(multiplication(X2,X0),c(X3)),zero)&le_q(multiplication(multiplication(X2,X1),c(X3)),zero)->le_q(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero))).
% 1.60/1.80 end_of_list.
% 1.60/1.80
% 1.60/1.80 -------> usable clausifies to:
% 1.60/1.80
% 1.60/1.80 list(usable).
% 1.60/1.80 0 [] A=A.
% 1.60/1.80 0 [] addition(A,B)=addition(B,A).
% 1.60/1.80 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.60/1.80 0 [] addition(A,zero)=A.
% 1.60/1.80 0 [] addition(A,A)=A.
% 1.60/1.80 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.60/1.80 0 [] multiplication(A,one)=A.
% 1.60/1.80 0 [] multiplication(one,A)=A.
% 1.60/1.80 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.60/1.80 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.60/1.80 0 [] multiplication(A,zero)=zero.
% 1.60/1.80 0 [] multiplication(zero,A)=zero.
% 1.60/1.80 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.60/1.80 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.60/1.80 0 [] -test(X0)|complement($f1(X0),X0).
% 1.60/1.80 0 [] test(X0)| -complement(X1,X0).
% 1.60/1.80 0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 1.60/1.80 0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 1.60/1.80 0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 1.60/1.80 0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 1.60/1.80 0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 1.60/1.80 0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 1.60/1.80 0 [] test(X0)|c(X0)=zero.
% 1.60/1.80 0 [] -test(X0)| -test(X1)|c(addition(X0,X1))=multiplication(c(X0),c(X1)).
% 1.60/1.80 0 [] -test(X0)| -test(X1)|c(multiplication(X0,X1))=addition(c(X0),c(X1)).
% 1.60/1.80 0 [] test($c1).
% 1.60/1.80 0 [] test($c2).
% 1.60/1.80 0 [] le_q(multiplication(multiplication($c2,$c4),c($c1)),zero).
% 1.60/1.80 0 [] le_q(multiplication(multiplication($c2,$c3),c($c1)),zero).
% 1.60/1.80 0 [] -le_q(multiplication(multiplication($c2,addition($c4,$c3)),c($c1)),zero).
% 1.60/1.80 end_of_list.
% 1.60/1.80
% 1.60/1.80 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.60/1.80
% 1.60/1.80 This ia a non-Horn set with equality. The strategy will be
% 1.60/1.80 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.60/1.80 deletion, with positive clauses in sos and nonpositive
% 1.60/1.80 clauses in usable.
% 1.60/1.80
% 1.60/1.80 dependent: set(knuth_bendix).
% 1.60/1.80 dependent: set(anl_eq).
% 1.60/1.80 dependent: set(para_from).
% 1.60/1.80 dependent: set(para_into).
% 1.60/1.80 dependent: clear(para_from_right).
% 1.60/1.80 dependent: clear(para_into_right).
% 1.60/1.80 dependent: set(para_from_vars).
% 1.60/1.80 dependent: set(eq_units_both_ways).
% 1.60/1.80 dependent: set(dynamic_demod_all).
% 1.60/1.80 dependent: set(dynamic_demod).
% 1.60/1.80 dependent: set(order_eq).
% 1.60/1.80 dependent: set(back_demod).
% 1.60/1.80 dependent: set(lrpo).
% 1.60/1.80 dependent: set(hyper_res).
% 1.65/1.81 dependent: set(unit_deletion).
% 1.65/1.81 dependent: set(factor).
% 1.65/1.81
% 1.65/1.81 ------------> process usable:
% 1.65/1.81 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.65/1.81 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.65/1.81 ** KEPT (pick-wt=6): 3 [] -test(A)|complement($f1(A),A).
% 1.65/1.81 ** KEPT (pick-wt=5): 4 [] test(A)| -complement(B,A).
% 1.65/1.81 ** KEPT (pick-wt=8): 5 [] -complement(A,B)|multiplication(B,A)=zero.
% 1.65/1.81 ** KEPT (pick-wt=8): 6 [] -complement(A,B)|multiplication(A,B)=zero.
% 1.65/1.81 ** KEPT (pick-wt=8): 7 [] -complement(A,B)|addition(B,A)=one.
% 1.65/1.81 ** KEPT (pick-wt=18): 8 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 1.65/1.81 ** KEPT (pick-wt=9): 9 [] -test(A)|c(A)!=B|complement(A,B).
% 1.65/1.81 ** KEPT (pick-wt=9): 10 [] -test(A)|c(A)=B| -complement(A,B).
% 1.65/1.81 ** KEPT (pick-wt=14): 11 [] -test(A)| -test(B)|c(addition(A,B))=multiplication(c(A),c(B)).
% 1.65/1.81 ** KEPT (pick-wt=14): 12 [] -test(A)| -test(B)|c(multiplication(A,B))=addition(c(A),c(B)).
% 1.65/1.81 ** KEPT (pick-wt=10): 13 [] -le_q(multiplication(multiplication($c2,addition($c4,$c3)),c($c1)),zero).
% 1.65/1.81
% 1.65/1.81 ------------> process sos:
% 1.65/1.81 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.65/1.81 ** KEPT (pick-wt=7): 18 [] addition(A,B)=addition(B,A).
% 1.65/1.81 ** KEPT (pick-wt=11): 20 [copy,19,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.65/1.81 ---> New Demodulator: 21 [new_demod,20] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.65/1.81 ** KEPT (pick-wt=5): 22 [] addition(A,zero)=A.
% 1.65/1.81 ---> New Demodulator: 23 [new_demod,22] addition(A,zero)=A.
% 1.65/1.81 ** KEPT (pick-wt=5): 24 [] addition(A,A)=A.
% 1.65/1.81 ---> New Demodulator: 25 [new_demod,24] addition(A,A)=A.
% 1.65/1.81 ** KEPT (pick-wt=11): 27 [copy,26,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.65/1.81 ---> New Demodulator: 28 [new_demod,27] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.65/1.81 ** KEPT (pick-wt=5): 29 [] multiplication(A,one)=A.
% 1.65/1.81 ---> New Demodulator: 30 [new_demod,29] multiplication(A,one)=A.
% 1.65/1.81 ** KEPT (pick-wt=5): 31 [] multiplication(one,A)=A.
% 1.65/1.81 ---> New Demodulator: 32 [new_demod,31] multiplication(one,A)=A.
% 1.65/1.81 ** KEPT (pick-wt=13): 33 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.65/1.81 ---> New Demodulator: 34 [new_demod,33] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.65/1.81 ** KEPT (pick-wt=13): 35 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.65/1.81 ---> New Demodulator: 36 [new_demod,35] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.65/1.81 ** KEPT (pick-wt=5): 37 [] multiplication(A,zero)=zero.
% 1.65/1.81 ---> New Demodulator: 38 [new_demod,37] multiplication(A,zero)=zero.
% 1.65/1.81 ** KEPT (pick-wt=5): 39 [] multiplication(zero,A)=zero.
% 1.65/1.81 ---> New Demodulator: 40 [new_demod,39] multiplication(zero,A)=zero.
% 1.65/1.81 ** KEPT (pick-wt=6): 41 [] test(A)|c(A)=zero.
% 1.65/1.81 ** KEPT (pick-wt=2): 42 [] test($c1).
% 1.65/1.81 ** KEPT (pick-wt=2): 43 [] test($c2).
% 1.65/1.81 ** KEPT (pick-wt=8): 45 [copy,44,demod,28] le_q(multiplication($c2,multiplication($c4,c($c1))),zero).
% 1.65/1.81 ** KEPT (pick-wt=8): 47 [copy,46,demod,28] le_q(multiplication($c2,multiplication($c3,c($c1))),zero).
% 1.65/1.81 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.65/1.81 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] addition(A,B)=addition(B,A).
% 1.65/1.81 >>>> Starting back demodulation with 21.
% 1.65/1.81 >>>> Starting back demodulation with 23.
% 1.65/1.81 >>>> Starting back demodulation with 25.
% 1.65/1.81 >> back demodulating 16 with 25.
% 1.65/1.81 >> back demodulating 15 with 25.
% 1.65/1.81 >> back demodulating 14 with 25.
% 1.65/1.81 >>>> Starting back demodulation with 28.
% 1.65/1.81 >> back demodulating 13 with 28.
% 1.65/1.81 >>>> Starting back demodulation with 30.
% 1.65/1.81 >>>> Starting back demodulation with 32.
% 1.65/1.81 >>>> Starting back demodulation with 34.
% 1.65/1.81 >>>> Starting back demodulation with 36.
% 1.65/1.81 >>>> Starting back demodulation with 38.
% 1.65/1.81 >>>> Starting back demodulation with 40.
% 1.65/1.81
% 1.65/1.81 ======= end of input processing =======
% 1.65/1.81
% 1.65/1.81 =========== start of search ===========
% 1.65/1.81
% 1.65/1.81 -------- PROOF --------
% 1.65/1.81
% 1.65/1.81 ----> UNIT CONFLICT at 0.01 sec ----> 433 [binary,432.1,47.1] $F.
% 1.65/1.81
% 1.65/1.81 Length of proof is 7. Level of proof is 4.
% 1.65/1.81
% 1.65/1.81 ---------------- PROOF ----------------
% 1.65/1.81 % SZS status Theorem
% 1.65/1.81 % SZS output start Refutation
% See solution above
% 1.65/1.81 ------------ end of proof -------------
% 1.65/1.81
% 1.65/1.81
% 1.65/1.81 Search stopped by max_proofs option.
% 1.65/1.81
% 1.65/1.81
% 1.65/1.81 Search stopped by max_proofs option.
% 1.65/1.81
% 1.65/1.81 ============ end of search ============
% 1.65/1.81
% 1.65/1.81 -------------- statistics -------------
% 1.65/1.81 clauses given 41
% 1.65/1.81 clauses generated 478
% 1.65/1.81 clauses kept 292
% 1.65/1.81 clauses forward subsumed 299
% 1.65/1.81 clauses back subsumed 1
% 1.65/1.81 Kbytes malloced 1953
% 1.65/1.81
% 1.65/1.81 ----------- times (seconds) -----------
% 1.65/1.81 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.65/1.81 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.81 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.65/1.81
% 1.65/1.81 That finishes the proof of the theorem.
% 1.65/1.81
% 1.65/1.81 Process 4382 finished Wed Jul 27 06:13:32 2022
% 1.65/1.81 Otter interrupted
% 1.65/1.81 PROOF FOUND
%------------------------------------------------------------------------------