TSTP Solution File: KLE006+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE006+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 13:00:26 EDT 2022
% Result : Theorem 1.72s 1.93s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 9 RR)
% Number of literals : 14 ( 8 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
( ~ complement(A,B)
| addition(B,A) = one ),
file('KLE006+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ test(A)
| c(A) != B
| complement(A,B) ),
file('KLE006+1.p',unknown),
[] ).
cnf(11,axiom,
one != addition(dollar_c1,c(dollar_c1)),
file('KLE006+1.p',unknown),
[] ).
cnf(12,plain,
addition(dollar_c1,c(dollar_c1)) != one,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(14,axiom,
A = A,
file('KLE006+1.p',unknown),
[] ).
cnf(15,axiom,
addition(A,B) = addition(B,A),
file('KLE006+1.p',unknown),
[] ).
cnf(39,axiom,
test(dollar_c1),
file('KLE006+1.p',unknown),
[] ).
cnf(41,plain,
complement(dollar_c1,c(dollar_c1)),
inference(hyper,[status(thm)],[39,9,14]),
[iquote('hyper,39,9,14')] ).
cnf(44,plain,
addition(c(dollar_c1),dollar_c1) = one,
inference(hyper,[status(thm)],[41,7]),
[iquote('hyper,41,7')] ).
cnf(60,plain,
one != one,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[15,12]),44]),
[iquote('para_from,15.1.1,12.1.1,demod,44')] ).
cnf(61,plain,
$false,
inference(binary,[status(thm)],[60,14]),
[iquote('binary,60.1,14.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE006+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % 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 05:53:18 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.72/1.93 ----- Otter 3.3f, August 2004 -----
% 1.72/1.93 The process was started by sandbox2 on n017.cluster.edu,
% 1.72/1.93 Wed Jul 27 05:53:18 2022
% 1.72/1.93 The command was "./otter". The process ID is 4437.
% 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 formula_list(usable).
% 1.72/1.93 all A (A=A).
% 1.72/1.93 all A B (addition(A,B)=addition(B,A)).
% 1.72/1.93 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.72/1.93 all A (addition(A,zero)=A).
% 1.72/1.93 all A (addition(A,A)=A).
% 1.72/1.93 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.72/1.93 all A (multiplication(A,one)=A).
% 1.72/1.93 all A (multiplication(one,A)=A).
% 1.72/1.93 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.72/1.93 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.72/1.93 all A (multiplication(A,zero)=zero).
% 1.72/1.93 all A (multiplication(zero,A)=zero).
% 1.72/1.93 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.72/1.93 all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 1.72/1.93 all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 1.72/1.93 all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 1.72/1.93 all X0 (-test(X0)->c(X0)=zero).
% 1.72/1.93 -(all X0 (test(X0)->one=addition(X0,c(X0)))).
% 1.72/1.93 end_of_list.
% 1.72/1.93
% 1.72/1.93 -------> usable clausifies to:
% 1.72/1.93
% 1.72/1.93 list(usable).
% 1.72/1.93 0 [] A=A.
% 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 [] -le_q(A,B)|addition(A,B)=B.
% 1.72/1.93 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.72/1.93 0 [] -test(X0)|complement($f1(X0),X0).
% 1.72/1.93 0 [] test(X0)| -complement(X1,X0).
% 1.72/1.93 0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 1.72/1.93 0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 1.72/1.93 0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 1.72/1.93 0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 1.72/1.93 0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 1.72/1.93 0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 1.72/1.93 0 [] test(X0)|c(X0)=zero.
% 1.72/1.93 0 [] test($c1).
% 1.72/1.93 0 [] one!=addition($c1,c($c1)).
% 1.72/1.93 end_of_list.
% 1.72/1.93
% 1.72/1.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.72/1.93
% 1.72/1.93 This ia a non-Horn set with equality. The strategy will be
% 1.72/1.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.72/1.93 deletion, with positive clauses in sos and nonpositive
% 1.72/1.93 clauses in usable.
% 1.72/1.93
% 1.72/1.93 dependent: set(knuth_bendix).
% 1.72/1.93 dependent: set(anl_eq).
% 1.72/1.93 dependent: set(para_from).
% 1.72/1.93 dependent: set(para_into).
% 1.72/1.93 dependent: clear(para_from_right).
% 1.72/1.93 dependent: clear(para_into_right).
% 1.72/1.93 dependent: set(para_from_vars).
% 1.72/1.93 dependent: set(eq_units_both_ways).
% 1.72/1.93 dependent: set(dynamic_demod_all).
% 1.72/1.93 dependent: set(dynamic_demod).
% 1.72/1.93 dependent: set(order_eq).
% 1.72/1.93 dependent: set(back_demod).
% 1.72/1.93 dependent: set(lrpo).
% 1.72/1.93 dependent: set(hyper_res).
% 1.72/1.93 dependent: set(unit_deletion).
% 1.72/1.93 dependent: set(factor).
% 1.72/1.93
% 1.72/1.93 ------------> process usable:
% 1.72/1.93 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.72/1.93 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.72/1.93 ** KEPT (pick-wt=6): 3 [] -test(A)|complement($f1(A),A).
% 1.72/1.93 ** KEPT (pick-wt=5): 4 [] test(A)| -complement(B,A).
% 1.72/1.93 ** KEPT (pick-wt=8): 5 [] -complement(A,B)|multiplication(B,A)=zero.
% 1.72/1.93 ** KEPT (pick-wt=8): 6 [] -complement(A,B)|multiplication(A,B)=zero.
% 1.72/1.93 ** KEPT (pick-wt=8): 7 [] -complement(A,B)|addition(B,A)=one.
% 1.72/1.93 ** KEPT (pick-wt=18): 8 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 1.72/1.93 ** KEPT (pick-wt=9): 9 [] -test(A)|c(A)!=B|complement(A,B).
% 1.72/1.93 ** KEPT (pick-wt=9): 10 [] -test(A)|c(A)=B| -complement(A,B).
% 1.72/1.93 ** KEPT (pick-wt=6): 12 [copy,11,flip.1] addition($c1,c($c1))!=one.
% 1.72/1.93
% 1.72/1.93 ------------> process sos:
% 1.72/1.93 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.72/1.93 ** KEPT (pick-wt=7): 15 [] addition(A,B)=addition(B,A).
% 1.72/1.93 ** KEPT (pick-wt=11): 17 [copy,16,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.72/1.93 ---> New Demodulator: 18 [new_demod,17] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.72/1.93 ** KEPT (pick-wt=5): 19 [] addition(A,zero)=A.
% 1.72/1.93 ---> New Demodulator: 20 [new_demod,19] addition(A,zero)=A.
% 1.72/1.93 ** KEPT (pick-wt=5): 21 [] addition(A,A)=A.
% 1.72/1.93 ---> New Demodulator: 22 [new_demod,21] addition(A,A)=A.
% 1.72/1.93 ** KEPT (pick-wt=11): 24 [copy,23,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.72/1.93 ---> New Demodulator: 25 [new_demod,24] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.72/1.93 ** KEPT (pick-wt=5): 26 [] multiplication(A,one)=A.
% 1.72/1.93 ---> New Demodulator: 27 [new_demod,26] multiplication(A,one)=A.
% 1.72/1.93 ** KEPT (pick-wt=5): 28 [] multiplication(one,A)=A.
% 1.72/1.93 ---> New Demodulator: 29 [new_demod,28] multiplication(one,A)=A.
% 1.72/1.93 ** KEPT (pick-wt=13): 30 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.72/1.93 ---> New Demodulator: 31 [new_demod,30] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.72/1.93 ** KEPT (pick-wt=13): 32 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.72/1.93 ---> New Demodulator: 33 [new_demod,32] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.72/1.93 ** KEPT (pick-wt=5): 34 [] multiplication(A,zero)=zero.
% 1.72/1.93 ---> New Demodulator: 35 [new_demod,34] multiplication(A,zero)=zero.
% 1.72/1.93 ** KEPT (pick-wt=5): 36 [] multiplication(zero,A)=zero.
% 1.72/1.93 ---> New Demodulator: 37 [new_demod,36] multiplication(zero,A)=zero.
% 1.72/1.93 ** KEPT (pick-wt=6): 38 [] test(A)|c(A)=zero.
% 1.72/1.93 ** KEPT (pick-wt=2): 39 [] test($c1).
% 1.72/1.93 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.72/1.93 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] addition(A,B)=addition(B,A).
% 1.72/1.93 >>>> Starting back demodulation with 18.
% 1.72/1.93 >>>> Starting back demodulation with 20.
% 1.72/1.93 >>>> Starting back demodulation with 22.
% 1.72/1.93 >> back demodulating 13 with 22.
% 1.72/1.93 >>>> Starting back demodulation with 25.
% 1.72/1.93 >>>> Starting back demodulation with 27.
% 1.72/1.93 >>>> Starting back demodulation with 29.
% 1.72/1.93 >>>> Starting back demodulation with 31.
% 1.72/1.93 >>>> Starting back demodulation with 33.
% 1.72/1.93 >>>> Starting back demodulation with 35.
% 1.72/1.93 >>>> Starting back demodulation with 37.
% 1.72/1.93
% 1.72/1.93 ======= end of input processing =======
% 1.72/1.93
% 1.72/1.93 =========== start of search ===========
% 1.72/1.93
% 1.72/1.93 -------- PROOF --------
% 1.72/1.93
% 1.72/1.93 ----> UNIT CONFLICT at 0.00 sec ----> 61 [binary,60.1,14.1] $F.
% 1.72/1.93
% 1.72/1.93 Length of proof is 4. Level of proof is 3.
% 1.72/1.93
% 1.72/1.93 ---------------- PROOF ----------------
% 1.72/1.93 % SZS status Theorem
% 1.72/1.93 % SZS output start Refutation
% See solution above
% 1.72/1.93 ------------ end of proof -------------
% 1.72/1.93
% 1.72/1.93
% 1.72/1.93 Search stopped by max_proofs option.
% 1.72/1.93
% 1.72/1.93
% 1.72/1.93 Search stopped by max_proofs option.
% 1.72/1.93
% 1.72/1.93 ============ end of search ============
% 1.72/1.93
% 1.72/1.93 -------------- statistics -------------
% 1.72/1.93 clauses given 6
% 1.72/1.93 clauses generated 21
% 1.72/1.93 clauses kept 41
% 1.72/1.93 clauses forward subsumed 7
% 1.72/1.93 clauses back subsumed 0
% 1.72/1.93 Kbytes malloced 976
% 1.72/1.93
% 1.72/1.93 ----------- times (seconds) -----------
% 1.72/1.93 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.93 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.72/1.93
% 1.72/1.93 That finishes the proof of the theorem.
% 1.72/1.93
% 1.72/1.93 Process 4437 finished Wed Jul 27 05:53:19 2022
% 1.72/1.93 Otter interrupted
% 1.72/1.93 PROOF FOUND
%------------------------------------------------------------------------------