TSTP Solution File: KLE005+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE005+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 13:00:26 EDT 2022
% Result : Theorem 1.70s 1.86s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 10 RR)
% Number of literals : 21 ( 11 equ; 8 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( test(A)
| ~ complement(B,A) ),
file('KLE005+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ complement(A,B)
| multiplication(A,B) = zero ),
file('KLE005+1.p',unknown),
[] ).
cnf(8,axiom,
( complement(A,B)
| multiplication(B,A) != zero
| multiplication(A,B) != zero
| addition(B,A) != one ),
file('KLE005+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ test(A)
| c(A) != B
| complement(A,B) ),
file('KLE005+1.p',unknown),
[] ).
cnf(11,axiom,
c(one) != zero,
file('KLE005+1.p',unknown),
[] ).
cnf(13,axiom,
A = A,
file('KLE005+1.p',unknown),
[] ).
cnf(18,axiom,
addition(A,zero) = A,
file('KLE005+1.p',unknown),
[] ).
cnf(25,axiom,
multiplication(A,one) = A,
file('KLE005+1.p',unknown),
[] ).
cnf(28,axiom,
multiplication(one,A) = A,
file('KLE005+1.p',unknown),
[] ).
cnf(61,plain,
complement(zero,one),
inference(hyper,[status(thm)],[28,8,25,18]),
[iquote('hyper,27,8,25,18')] ).
cnf(62,plain,
test(one),
inference(hyper,[status(thm)],[61,4]),
[iquote('hyper,61,4')] ).
cnf(63,plain,
complement(one,c(one)),
inference(hyper,[status(thm)],[62,9,13]),
[iquote('hyper,62,9,13')] ).
cnf(80,plain,
c(one) = zero,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[63,6]),28]),
[iquote('hyper,63,6,demod,28')] ).
cnf(82,plain,
$false,
inference(binary,[status(thm)],[80,11]),
[iquote('binary,80.1,11.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE005+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n029.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 06:36:14 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.67/1.86 ----- Otter 3.3f, August 2004 -----
% 1.67/1.86 The process was started by sandbox2 on n029.cluster.edu,
% 1.67/1.86 Wed Jul 27 06:36:14 2022
% 1.67/1.86 The command was "./otter". The process ID is 27061.
% 1.67/1.86
% 1.67/1.86 set(prolog_style_variables).
% 1.67/1.86 set(auto).
% 1.67/1.86 dependent: set(auto1).
% 1.67/1.86 dependent: set(process_input).
% 1.67/1.86 dependent: clear(print_kept).
% 1.67/1.86 dependent: clear(print_new_demod).
% 1.67/1.86 dependent: clear(print_back_demod).
% 1.67/1.86 dependent: clear(print_back_sub).
% 1.67/1.86 dependent: set(control_memory).
% 1.67/1.86 dependent: assign(max_mem, 12000).
% 1.67/1.86 dependent: assign(pick_given_ratio, 4).
% 1.67/1.86 dependent: assign(stats_level, 1).
% 1.67/1.86 dependent: assign(max_seconds, 10800).
% 1.67/1.86 clear(print_given).
% 1.67/1.86
% 1.67/1.86 formula_list(usable).
% 1.67/1.86 all A (A=A).
% 1.67/1.86 all A B (addition(A,B)=addition(B,A)).
% 1.67/1.86 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.67/1.86 all A (addition(A,zero)=A).
% 1.67/1.86 all A (addition(A,A)=A).
% 1.67/1.86 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.67/1.86 all A (multiplication(A,one)=A).
% 1.67/1.86 all A (multiplication(one,A)=A).
% 1.67/1.86 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.67/1.86 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.67/1.86 all A (multiplication(A,zero)=zero).
% 1.67/1.86 all A (multiplication(zero,A)=zero).
% 1.67/1.86 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.67/1.86 all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 1.67/1.86 all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 1.67/1.86 all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 1.67/1.86 all X0 (-test(X0)->c(X0)=zero).
% 1.67/1.86 c(one)!=zero.
% 1.67/1.86 end_of_list.
% 1.67/1.86
% 1.67/1.86 -------> usable clausifies to:
% 1.67/1.86
% 1.67/1.86 list(usable).
% 1.67/1.86 0 [] A=A.
% 1.67/1.86 0 [] addition(A,B)=addition(B,A).
% 1.67/1.86 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.67/1.86 0 [] addition(A,zero)=A.
% 1.67/1.86 0 [] addition(A,A)=A.
% 1.67/1.86 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.67/1.86 0 [] multiplication(A,one)=A.
% 1.67/1.86 0 [] multiplication(one,A)=A.
% 1.67/1.86 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.67/1.86 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.67/1.86 0 [] multiplication(A,zero)=zero.
% 1.67/1.86 0 [] multiplication(zero,A)=zero.
% 1.67/1.86 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.67/1.86 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.67/1.86 0 [] -test(X0)|complement($f1(X0),X0).
% 1.67/1.86 0 [] test(X0)| -complement(X1,X0).
% 1.67/1.86 0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 1.67/1.86 0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 1.67/1.86 0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 1.67/1.86 0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 1.67/1.86 0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 1.67/1.86 0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 1.67/1.86 0 [] test(X0)|c(X0)=zero.
% 1.67/1.86 0 [] c(one)!=zero.
% 1.67/1.86 end_of_list.
% 1.67/1.86
% 1.67/1.86 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.67/1.86
% 1.67/1.86 This ia a non-Horn set with equality. The strategy will be
% 1.67/1.86 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.67/1.86 deletion, with positive clauses in sos and nonpositive
% 1.67/1.86 clauses in usable.
% 1.67/1.86
% 1.67/1.86 dependent: set(knuth_bendix).
% 1.67/1.86 dependent: set(anl_eq).
% 1.67/1.86 dependent: set(para_from).
% 1.67/1.86 dependent: set(para_into).
% 1.67/1.86 dependent: clear(para_from_right).
% 1.67/1.86 dependent: clear(para_into_right).
% 1.67/1.86 dependent: set(para_from_vars).
% 1.67/1.86 dependent: set(eq_units_both_ways).
% 1.67/1.86 dependent: set(dynamic_demod_all).
% 1.67/1.86 dependent: set(dynamic_demod).
% 1.67/1.86 dependent: set(order_eq).
% 1.67/1.86 dependent: set(back_demod).
% 1.67/1.86 dependent: set(lrpo).
% 1.67/1.86 dependent: set(hyper_res).
% 1.67/1.86 dependent: set(unit_deletion).
% 1.67/1.86 dependent: set(factor).
% 1.67/1.86
% 1.67/1.86 ------------> process usable:
% 1.67/1.86 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.67/1.86 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.67/1.86 ** KEPT (pick-wt=6): 3 [] -test(A)|complement($f1(A),A).
% 1.67/1.86 ** KEPT (pick-wt=5): 4 [] test(A)| -complement(B,A).
% 1.67/1.86 ** KEPT (pick-wt=8): 5 [] -complement(A,B)|multiplication(B,A)=zero.
% 1.67/1.86 ** KEPT (pick-wt=8): 6 [] -complement(A,B)|multiplication(A,B)=zero.
% 1.67/1.86 ** KEPT (pick-wt=8): 7 [] -complement(A,B)|addition(B,A)=one.
% 1.67/1.86 ** KEPT (pick-wt=18): 8 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 1.67/1.86 ** KEPT (pick-wt=9): 9 [] -test(A)|c(A)!=B|complement(A,B).
% 1.67/1.86 ** KEPT (pick-wt=9): 10 [] -test(A)|c(A)=B| -complement(A,B).
% 1.70/1.86 ** KEPT (pick-wt=4): 11 [] c(one)!=zero.
% 1.70/1.86
% 1.70/1.86 ------------> process sos:
% 1.70/1.86 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.70/1.86 ** KEPT (pick-wt=7): 14 [] addition(A,B)=addition(B,A).
% 1.70/1.86 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.70/1.86 ---> New Demodulator: 17 [new_demod,16] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.70/1.86 ** KEPT (pick-wt=5): 18 [] addition(A,zero)=A.
% 1.70/1.86 ---> New Demodulator: 19 [new_demod,18] addition(A,zero)=A.
% 1.70/1.86 ** KEPT (pick-wt=5): 20 [] addition(A,A)=A.
% 1.70/1.86 ---> New Demodulator: 21 [new_demod,20] addition(A,A)=A.
% 1.70/1.86 ** KEPT (pick-wt=11): 23 [copy,22,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.70/1.86 ---> New Demodulator: 24 [new_demod,23] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.70/1.86 ** KEPT (pick-wt=5): 25 [] multiplication(A,one)=A.
% 1.70/1.86 ---> New Demodulator: 26 [new_demod,25] multiplication(A,one)=A.
% 1.70/1.86 ** KEPT (pick-wt=5): 27 [] multiplication(one,A)=A.
% 1.70/1.86 ---> New Demodulator: 28 [new_demod,27] multiplication(one,A)=A.
% 1.70/1.86 ** KEPT (pick-wt=13): 29 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.70/1.86 ---> New Demodulator: 30 [new_demod,29] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.70/1.86 ** KEPT (pick-wt=13): 31 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.70/1.86 ---> New Demodulator: 32 [new_demod,31] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.70/1.86 ** KEPT (pick-wt=5): 33 [] multiplication(A,zero)=zero.
% 1.70/1.86 ---> New Demodulator: 34 [new_demod,33] multiplication(A,zero)=zero.
% 1.70/1.86 ** KEPT (pick-wt=5): 35 [] multiplication(zero,A)=zero.
% 1.70/1.86 ---> New Demodulator: 36 [new_demod,35] multiplication(zero,A)=zero.
% 1.70/1.86 ** KEPT (pick-wt=6): 37 [] test(A)|c(A)=zero.
% 1.70/1.86 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.70/1.86 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] addition(A,B)=addition(B,A).
% 1.70/1.86 >>>> Starting back demodulation with 17.
% 1.70/1.86 >>>> Starting back demodulation with 19.
% 1.70/1.86 >>>> Starting back demodulation with 21.
% 1.70/1.86 >> back demodulating 12 with 21.
% 1.70/1.86 >>>> Starting back demodulation with 24.
% 1.70/1.86 >>>> Starting back demodulation with 26.
% 1.70/1.86 >>>> Starting back demodulation with 28.
% 1.70/1.86 >>>> Starting back demodulation with 30.
% 1.70/1.86 >>>> Starting back demodulation with 32.
% 1.70/1.86 >>>> Starting back demodulation with 34.
% 1.70/1.86 >>>> Starting back demodulation with 36.
% 1.70/1.86
% 1.70/1.86 ======= end of input processing =======
% 1.70/1.86
% 1.70/1.86 =========== start of search ===========
% 1.70/1.86
% 1.70/1.86 -------- PROOF --------
% 1.70/1.86
% 1.70/1.86 ----> UNIT CONFLICT at 0.00 sec ----> 82 [binary,80.1,11.1] $F.
% 1.70/1.86
% 1.70/1.86 Length of proof is 4. Level of proof is 4.
% 1.70/1.86
% 1.70/1.86 ---------------- PROOF ----------------
% 1.70/1.86 % SZS status Theorem
% 1.70/1.86 % SZS output start Refutation
% See solution above
% 1.70/1.86 ------------ end of proof -------------
% 1.70/1.86
% 1.70/1.86
% 1.70/1.86 Search stopped by max_proofs option.
% 1.70/1.86
% 1.70/1.86
% 1.70/1.86 Search stopped by max_proofs option.
% 1.70/1.86
% 1.70/1.86 ============ end of search ============
% 1.70/1.86
% 1.70/1.86 -------------- statistics -------------
% 1.70/1.86 clauses given 12
% 1.70/1.86 clauses generated 86
% 1.70/1.86 clauses kept 64
% 1.70/1.86 clauses forward subsumed 52
% 1.70/1.86 clauses back subsumed 1
% 1.70/1.86 Kbytes malloced 976
% 1.70/1.86
% 1.70/1.86 ----------- times (seconds) -----------
% 1.70/1.86 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.86 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.86 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.70/1.86
% 1.70/1.86 That finishes the proof of the theorem.
% 1.70/1.86
% 1.70/1.86 Process 27061 finished Wed Jul 27 06:36:16 2022
% 1.70/1.86 Otter interrupted
% 1.70/1.86 PROOF FOUND
%------------------------------------------------------------------------------