TSTP Solution File: KLE021+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE021+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:00:30 EDT 2022
% Result : Theorem 1.53s 2.14s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 12 unt; 0 nHn; 9 RR)
% Number of literals : 17 ( 11 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(7,axiom,
( ~ complement(A,B)
| addition(B,A) = one ),
file('KLE021+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ test(A)
| c(A) != B
| complement(A,B) ),
file('KLE021+1.p',unknown),
[] ).
cnf(11,axiom,
dollar_c2 != addition(multiplication(dollar_c1,dollar_c2),multiplication(c(dollar_c1),dollar_c2)),
file('KLE021+1.p',unknown),
[] ).
cnf(12,plain,
addition(multiplication(dollar_c1,dollar_c2),multiplication(c(dollar_c1),dollar_c2)) != dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(14,axiom,
A = A,
file('KLE021+1.p',unknown),
[] ).
cnf(15,axiom,
addition(A,B) = addition(B,A),
file('KLE021+1.p',unknown),
[] ).
cnf(29,axiom,
multiplication(one,A) = A,
file('KLE021+1.p',unknown),
[] ).
cnf(32,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE021+1.p',unknown),
[] ).
cnf(39,axiom,
test(dollar_c1),
file('KLE021+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(43,plain,
addition(c(dollar_c1),dollar_c1) = one,
inference(hyper,[status(thm)],[41,7]),
[iquote('hyper,41,7')] ).
cnf(60,plain,
addition(multiplication(c(dollar_c1),dollar_c2),multiplication(dollar_c1,dollar_c2)) != dollar_c2,
inference(para_from,[status(thm),theory(equality)],[15,12]),
[iquote('para_from,15.1.1,12.1.1')] ).
cnf(146,plain,
addition(multiplication(c(dollar_c1),A),multiplication(dollar_c1,A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[43,32]),29])]),
[iquote('para_from,43.1.1,32.1.1.1,demod,29,flip.1')] ).
cnf(148,plain,
$false,
inference(binary,[status(thm)],[146,60]),
[iquote('binary,146.1,60.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE021+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 06:53:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.53/2.13 ----- Otter 3.3f, August 2004 -----
% 1.53/2.13 The process was started by sandbox2 on n023.cluster.edu,
% 1.53/2.13 Wed Jul 27 06:53:03 2022
% 1.53/2.13 The command was "./otter". The process ID is 11962.
% 1.53/2.13
% 1.53/2.13 set(prolog_style_variables).
% 1.53/2.13 set(auto).
% 1.53/2.13 dependent: set(auto1).
% 1.53/2.13 dependent: set(process_input).
% 1.53/2.13 dependent: clear(print_kept).
% 1.53/2.13 dependent: clear(print_new_demod).
% 1.53/2.13 dependent: clear(print_back_demod).
% 1.53/2.13 dependent: clear(print_back_sub).
% 1.53/2.13 dependent: set(control_memory).
% 1.53/2.13 dependent: assign(max_mem, 12000).
% 1.53/2.13 dependent: assign(pick_given_ratio, 4).
% 1.53/2.13 dependent: assign(stats_level, 1).
% 1.53/2.13 dependent: assign(max_seconds, 10800).
% 1.53/2.13 clear(print_given).
% 1.53/2.13
% 1.53/2.13 formula_list(usable).
% 1.53/2.13 all A (A=A).
% 1.53/2.13 all A B (addition(A,B)=addition(B,A)).
% 1.53/2.13 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.53/2.13 all A (addition(A,zero)=A).
% 1.53/2.13 all A (addition(A,A)=A).
% 1.53/2.13 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.53/2.13 all A (multiplication(A,one)=A).
% 1.53/2.13 all A (multiplication(one,A)=A).
% 1.53/2.13 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.53/2.13 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.53/2.13 all A (multiplication(A,zero)=zero).
% 1.53/2.13 all A (multiplication(zero,A)=zero).
% 1.53/2.13 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.53/2.13 all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 1.53/2.13 all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 1.53/2.13 all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 1.53/2.13 all X0 (-test(X0)->c(X0)=zero).
% 1.53/2.13 -(all X0 X1 (test(X1)->X0=addition(multiplication(X1,X0),multiplication(c(X1),X0)))).
% 1.53/2.13 end_of_list.
% 1.53/2.13
% 1.53/2.13 -------> usable clausifies to:
% 1.53/2.13
% 1.53/2.13 list(usable).
% 1.53/2.13 0 [] A=A.
% 1.53/2.13 0 [] addition(A,B)=addition(B,A).
% 1.53/2.13 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.53/2.13 0 [] addition(A,zero)=A.
% 1.53/2.13 0 [] addition(A,A)=A.
% 1.53/2.13 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.53/2.13 0 [] multiplication(A,one)=A.
% 1.53/2.13 0 [] multiplication(one,A)=A.
% 1.53/2.13 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.53/2.13 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.53/2.13 0 [] multiplication(A,zero)=zero.
% 1.53/2.13 0 [] multiplication(zero,A)=zero.
% 1.53/2.13 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.53/2.13 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.53/2.13 0 [] -test(X0)|complement($f1(X0),X0).
% 1.53/2.13 0 [] test(X0)| -complement(X1,X0).
% 1.53/2.13 0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 1.53/2.13 0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 1.53/2.13 0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 1.53/2.13 0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 1.53/2.13 0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 1.53/2.13 0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 1.53/2.13 0 [] test(X0)|c(X0)=zero.
% 1.53/2.13 0 [] test($c1).
% 1.53/2.13 0 [] $c2!=addition(multiplication($c1,$c2),multiplication(c($c1),$c2)).
% 1.53/2.13 end_of_list.
% 1.53/2.13
% 1.53/2.13 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.53/2.13
% 1.53/2.13 This ia a non-Horn set with equality. The strategy will be
% 1.53/2.13 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.53/2.13 deletion, with positive clauses in sos and nonpositive
% 1.53/2.13 clauses in usable.
% 1.53/2.13
% 1.53/2.13 dependent: set(knuth_bendix).
% 1.53/2.13 dependent: set(anl_eq).
% 1.53/2.13 dependent: set(para_from).
% 1.53/2.13 dependent: set(para_into).
% 1.53/2.13 dependent: clear(para_from_right).
% 1.53/2.13 dependent: clear(para_into_right).
% 1.53/2.13 dependent: set(para_from_vars).
% 1.53/2.13 dependent: set(eq_units_both_ways).
% 1.53/2.13 dependent: set(dynamic_demod_all).
% 1.53/2.13 dependent: set(dynamic_demod).
% 1.53/2.13 dependent: set(order_eq).
% 1.53/2.13 dependent: set(back_demod).
% 1.53/2.13 dependent: set(lrpo).
% 1.53/2.13 dependent: set(hyper_res).
% 1.53/2.13 dependent: set(unit_deletion).
% 1.53/2.13 dependent: set(factor).
% 1.53/2.13
% 1.53/2.13 ------------> process usable:
% 1.53/2.13 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.53/2.13 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.53/2.13 ** KEPT (pick-wt=6): 3 [] -test(A)|complement($f1(A),A).
% 1.53/2.13 ** KEPT (pick-wt=5): 4 [] test(A)| -complement(B,A).
% 1.53/2.13 ** KEPT (pick-wt=8): 5 [] -complement(A,B)|multiplication(B,A)=zero.
% 1.53/2.13 ** KEPT (pick-wt=8): 6 [] -complement(A,B)|multiplication(A,B)=zero.
% 1.53/2.13 ** KEPT (pick-wt=8): 7 [] -complement(A,B)|addition(B,A)=one.
% 1.53/2.13 ** KEPT (pick-wt=18): 8 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 1.53/2.14 ** KEPT (pick-wt=9): 9 [] -test(A)|c(A)!=B|complement(A,B).
% 1.53/2.14 ** KEPT (pick-wt=9): 10 [] -test(A)|c(A)=B| -complement(A,B).
% 1.53/2.14 ** KEPT (pick-wt=10): 12 [copy,11,flip.1] addition(multiplication($c1,$c2),multiplication(c($c1),$c2))!=$c2.
% 1.53/2.14
% 1.53/2.14 ------------> process sos:
% 1.53/2.14 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.53/2.14 ** KEPT (pick-wt=7): 15 [] addition(A,B)=addition(B,A).
% 1.53/2.14 ** KEPT (pick-wt=11): 17 [copy,16,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.53/2.14 ---> New Demodulator: 18 [new_demod,17] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.53/2.14 ** KEPT (pick-wt=5): 19 [] addition(A,zero)=A.
% 1.53/2.14 ---> New Demodulator: 20 [new_demod,19] addition(A,zero)=A.
% 1.53/2.14 ** KEPT (pick-wt=5): 21 [] addition(A,A)=A.
% 1.53/2.14 ---> New Demodulator: 22 [new_demod,21] addition(A,A)=A.
% 1.53/2.14 ** KEPT (pick-wt=11): 24 [copy,23,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.53/2.14 ---> New Demodulator: 25 [new_demod,24] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.53/2.14 ** KEPT (pick-wt=5): 26 [] multiplication(A,one)=A.
% 1.53/2.14 ---> New Demodulator: 27 [new_demod,26] multiplication(A,one)=A.
% 1.53/2.14 ** KEPT (pick-wt=5): 28 [] multiplication(one,A)=A.
% 1.53/2.14 ---> New Demodulator: 29 [new_demod,28] multiplication(one,A)=A.
% 1.53/2.14 ** KEPT (pick-wt=13): 30 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.53/2.14 ---> New Demodulator: 31 [new_demod,30] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.53/2.14 ** KEPT (pick-wt=13): 32 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.53/2.14 ---> New Demodulator: 33 [new_demod,32] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.53/2.14 ** KEPT (pick-wt=5): 34 [] multiplication(A,zero)=zero.
% 1.53/2.14 ---> New Demodulator: 35 [new_demod,34] multiplication(A,zero)=zero.
% 1.53/2.14 ** KEPT (pick-wt=5): 36 [] multiplication(zero,A)=zero.
% 1.53/2.14 ---> New Demodulator: 37 [new_demod,36] multiplication(zero,A)=zero.
% 1.53/2.14 ** KEPT (pick-wt=6): 38 [] test(A)|c(A)=zero.
% 1.53/2.14 ** KEPT (pick-wt=2): 39 [] test($c1).
% 1.53/2.14 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.53/2.14 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] addition(A,B)=addition(B,A).
% 1.53/2.14 >>>> Starting back demodulation with 18.
% 1.53/2.14 >>>> Starting back demodulation with 20.
% 1.53/2.14 >>>> Starting back demodulation with 22.
% 1.53/2.14 >> back demodulating 13 with 22.
% 1.53/2.14 >>>> Starting back demodulation with 25.
% 1.53/2.14 >>>> Starting back demodulation with 27.
% 1.53/2.14 >>>> Starting back demodulation with 29.
% 1.53/2.14 >>>> Starting back demodulation with 31.
% 1.53/2.14 >>>> Starting back demodulation with 33.
% 1.53/2.14 >>>> Starting back demodulation with 35.
% 1.53/2.14 >>>> Starting back demodulation with 37.
% 1.53/2.14
% 1.53/2.14 ======= end of input processing =======
% 1.53/2.14
% 1.53/2.14 =========== start of search ===========
% 1.53/2.14
% 1.53/2.14 -------- PROOF --------
% 1.53/2.14
% 1.53/2.14 ----> UNIT CONFLICT at 0.00 sec ----> 148 [binary,146.1,60.1] $F.
% 1.53/2.14
% 1.53/2.14 Length of proof is 5. Level of proof is 3.
% 1.53/2.14
% 1.53/2.14 ---------------- PROOF ----------------
% 1.53/2.14 % SZS status Theorem
% 1.53/2.14 % SZS output start Refutation
% See solution above
% 1.53/2.14 ------------ end of proof -------------
% 1.53/2.14
% 1.53/2.14
% 1.53/2.14 Search stopped by max_proofs option.
% 1.53/2.14
% 1.53/2.14
% 1.53/2.14 Search stopped by max_proofs option.
% 1.53/2.14
% 1.53/2.14 ============ end of search ============
% 1.53/2.14
% 1.53/2.14 -------------- statistics -------------
% 1.53/2.14 clauses given 33
% 1.53/2.14 clauses generated 283
% 1.53/2.14 clauses kept 116
% 1.53/2.14 clauses forward subsumed 201
% 1.53/2.14 clauses back subsumed 1
% 1.53/2.14 Kbytes malloced 1953
% 1.53/2.14
% 1.53/2.14 ----------- times (seconds) -----------
% 1.53/2.14 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.53/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.53/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.53/2.14
% 1.53/2.14 That finishes the proof of the theorem.
% 1.53/2.14
% 1.53/2.14 Process 11962 finished Wed Jul 27 06:53:05 2022
% 1.53/2.14 Otter interrupted
% 1.53/2.14 PROOF FOUND
%------------------------------------------------------------------------------