TSTP Solution File: KLE022+4 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE022+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:00:31 EDT 2022
% Result : Theorem 1.77s 1.99s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of clauses : 31 ( 21 unt; 0 nHn; 23 RR)
% Number of literals : 45 ( 22 equ; 18 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE022+4.p',unknown),
[] ).
cnf(3,axiom,
( ~ test(A)
| complement(dollar_f1(A),A) ),
file('KLE022+4.p',unknown),
[] ).
cnf(5,axiom,
( ~ complement(A,B)
| multiplication(B,A) = zero ),
file('KLE022+4.p',unknown),
[] ).
cnf(6,axiom,
( ~ complement(A,B)
| multiplication(A,B) = zero ),
file('KLE022+4.p',unknown),
[] ).
cnf(7,axiom,
( ~ complement(A,B)
| addition(B,A) = one ),
file('KLE022+4.p',unknown),
[] ).
cnf(8,axiom,
( complement(A,B)
| multiplication(B,A) != zero
| multiplication(A,B) != zero
| addition(B,A) != one ),
file('KLE022+4.p',unknown),
[] ).
cnf(9,axiom,
( ~ test(A)
| c(A) != B
| complement(A,B) ),
file('KLE022+4.p',unknown),
[] ).
cnf(10,axiom,
( ~ test(A)
| c(A) = B
| ~ complement(A,B) ),
file('KLE022+4.p',unknown),
[] ).
cnf(13,axiom,
( ~ le_q(dollar_c2,addition(multiplication(dollar_c2,dollar_c1),multiplication(dollar_c2,c(dollar_c1))))
| ~ le_q(addition(multiplication(dollar_c2,dollar_c1),multiplication(dollar_c2,c(dollar_c1))),dollar_c2) ),
file('KLE022+4.p',unknown),
[] ).
cnf(17,axiom,
A = A,
file('KLE022+4.p',unknown),
[] ).
cnf(18,axiom,
addition(A,B) = addition(B,A),
file('KLE022+4.p',unknown),
[] ).
cnf(24,axiom,
addition(A,A) = A,
file('KLE022+4.p',unknown),
[] ).
cnf(30,axiom,
multiplication(A,one) = A,
file('KLE022+4.p',unknown),
[] ).
cnf(33,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE022+4.p',unknown),
[] ).
cnf(42,axiom,
test(dollar_c1),
file('KLE022+4.p',unknown),
[] ).
cnf(50,plain,
complement(dollar_c1,c(dollar_c1)),
inference(hyper,[status(thm)],[42,9,17]),
[iquote('hyper,42,9,17')] ).
cnf(51,plain,
complement(dollar_f1(dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[42,3]),
[iquote('hyper,42,3')] ).
cnf(52,plain,
addition(c(dollar_c1),dollar_c1) = one,
inference(hyper,[status(thm)],[50,7]),
[iquote('hyper,50,7')] ).
cnf(71,plain,
addition(dollar_c1,dollar_f1(dollar_c1)) = one,
inference(hyper,[status(thm)],[51,7]),
[iquote('hyper,51,7')] ).
cnf(73,plain,
multiplication(dollar_f1(dollar_c1),dollar_c1) = zero,
inference(hyper,[status(thm)],[51,6]),
[iquote('hyper,51,6')] ).
cnf(76,plain,
multiplication(dollar_c1,dollar_f1(dollar_c1)) = zero,
inference(hyper,[status(thm)],[51,5]),
[iquote('hyper,51,5')] ).
cnf(79,plain,
( ~ le_q(dollar_c2,addition(multiplication(dollar_c2,dollar_c1),multiplication(dollar_c2,c(dollar_c1))))
| ~ le_q(addition(multiplication(dollar_c2,c(dollar_c1)),multiplication(dollar_c2,dollar_c1)),dollar_c2) ),
inference(para_from,[status(thm),theory(equality)],[18,13]),
[iquote('para_from,18.1.1,13.2.1')] ).
cnf(94,plain,
le_q(A,A),
inference(hyper,[status(thm)],[24,2]),
[iquote('hyper,24,2')] ).
cnf(257,plain,
addition(multiplication(A,c(dollar_c1)),multiplication(A,dollar_c1)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[52,33]),30])]),
[iquote('para_from,52.1.1,33.1.1.2,demod,30,flip.1')] ).
cnf(264,plain,
~ le_q(dollar_c2,addition(multiplication(dollar_c2,dollar_c1),multiplication(dollar_c2,c(dollar_c1)))),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[79]),257]),94]),
[iquote('back_demod,79,demod,257,unit_del,94')] ).
cnf(332,plain,
addition(dollar_f1(dollar_c1),dollar_c1) = one,
inference(para_into,[status(thm),theory(equality)],[71,18]),
[iquote('para_into,71.1.1,18.1.1')] ).
cnf(335,plain,
addition(multiplication(A,dollar_c1),multiplication(A,dollar_f1(dollar_c1))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[71,33]),30])]),
[iquote('para_from,71.1.1,33.1.1.2,demod,30,flip.1')] ).
cnf(349,plain,
complement(dollar_c1,dollar_f1(dollar_c1)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[73,8]),76,332]),17,17,17]),
[iquote('para_from,73.1.1,8.2.1,demod,76,332,unit_del,17,17,17')] ).
cnf(351,plain,
c(dollar_c1) = dollar_f1(dollar_c1),
inference(hyper,[status(thm)],[349,10,42]),
[iquote('hyper,349,10,42')] ).
cnf(377,plain,
~ le_q(dollar_c2,dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[264]),351,335]),
[iquote('back_demod,264,demod,351,335')] ).
cnf(378,plain,
$false,
inference(binary,[status(thm)],[377,94]),
[iquote('binary,377.1,94.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE022+4 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n014.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 06:32:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.77/1.98 ----- Otter 3.3f, August 2004 -----
% 1.77/1.98 The process was started by sandbox2 on n014.cluster.edu,
% 1.77/1.98 Wed Jul 27 06:32:24 2022
% 1.77/1.98 The command was "./otter". The process ID is 2934.
% 1.77/1.98
% 1.77/1.98 set(prolog_style_variables).
% 1.77/1.98 set(auto).
% 1.77/1.98 dependent: set(auto1).
% 1.77/1.98 dependent: set(process_input).
% 1.77/1.98 dependent: clear(print_kept).
% 1.77/1.98 dependent: clear(print_new_demod).
% 1.77/1.98 dependent: clear(print_back_demod).
% 1.77/1.98 dependent: clear(print_back_sub).
% 1.77/1.98 dependent: set(control_memory).
% 1.77/1.98 dependent: assign(max_mem, 12000).
% 1.77/1.98 dependent: assign(pick_given_ratio, 4).
% 1.77/1.98 dependent: assign(stats_level, 1).
% 1.77/1.98 dependent: assign(max_seconds, 10800).
% 1.77/1.98 clear(print_given).
% 1.77/1.98
% 1.77/1.98 formula_list(usable).
% 1.77/1.98 all A (A=A).
% 1.77/1.98 all A B (addition(A,B)=addition(B,A)).
% 1.77/1.98 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.77/1.98 all A (addition(A,zero)=A).
% 1.77/1.98 all A (addition(A,A)=A).
% 1.77/1.98 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.77/1.98 all A (multiplication(A,one)=A).
% 1.77/1.98 all A (multiplication(one,A)=A).
% 1.77/1.98 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.77/1.98 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.77/1.98 all A (multiplication(A,zero)=zero).
% 1.77/1.98 all A (multiplication(zero,A)=zero).
% 1.77/1.98 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.77/1.98 all X0 (test(X0)<-> (exists X1 complement(X1,X0))).
% 1.77/1.98 all X0 X1 (complement(X1,X0)<->multiplication(X0,X1)=zero&multiplication(X1,X0)=zero&addition(X0,X1)=one).
% 1.77/1.98 all X0 X1 (test(X0)-> (c(X0)=X1<->complement(X0,X1))).
% 1.77/1.98 all X0 (-test(X0)->c(X0)=zero).
% 1.77/1.98 all X0 X1 (test(X0)&test(X1)->c(addition(X0,X1))=multiplication(c(X0),c(X1))).
% 1.77/1.98 all X0 X1 (test(X0)&test(X1)->c(multiplication(X0,X1))=addition(c(X0),c(X1))).
% 1.77/1.98 -(all X0 X1 (test(X1)->le_q(X0,addition(multiplication(X0,X1),multiplication(X0,c(X1))))&le_q(addition(multiplication(X0,X1),multiplication(X0,c(X1))),X0))).
% 1.77/1.98 end_of_list.
% 1.77/1.98
% 1.77/1.98 -------> usable clausifies to:
% 1.77/1.98
% 1.77/1.98 list(usable).
% 1.77/1.98 0 [] A=A.
% 1.77/1.98 0 [] addition(A,B)=addition(B,A).
% 1.77/1.98 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.77/1.98 0 [] addition(A,zero)=A.
% 1.77/1.98 0 [] addition(A,A)=A.
% 1.77/1.98 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.77/1.98 0 [] multiplication(A,one)=A.
% 1.77/1.98 0 [] multiplication(one,A)=A.
% 1.77/1.98 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.77/1.98 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.77/1.98 0 [] multiplication(A,zero)=zero.
% 1.77/1.98 0 [] multiplication(zero,A)=zero.
% 1.77/1.98 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.77/1.98 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.77/1.98 0 [] -test(X0)|complement($f1(X0),X0).
% 1.77/1.98 0 [] test(X0)| -complement(X1,X0).
% 1.77/1.98 0 [] -complement(X1,X0)|multiplication(X0,X1)=zero.
% 1.77/1.98 0 [] -complement(X1,X0)|multiplication(X1,X0)=zero.
% 1.77/1.98 0 [] -complement(X1,X0)|addition(X0,X1)=one.
% 1.77/1.98 0 [] complement(X1,X0)|multiplication(X0,X1)!=zero|multiplication(X1,X0)!=zero|addition(X0,X1)!=one.
% 1.77/1.98 0 [] -test(X0)|c(X0)!=X1|complement(X0,X1).
% 1.77/1.98 0 [] -test(X0)|c(X0)=X1| -complement(X0,X1).
% 1.77/1.98 0 [] test(X0)|c(X0)=zero.
% 1.77/1.98 0 [] -test(X0)| -test(X1)|c(addition(X0,X1))=multiplication(c(X0),c(X1)).
% 1.77/1.98 0 [] -test(X0)| -test(X1)|c(multiplication(X0,X1))=addition(c(X0),c(X1)).
% 1.77/1.98 0 [] test($c1).
% 1.77/1.98 0 [] -le_q($c2,addition(multiplication($c2,$c1),multiplication($c2,c($c1))))| -le_q(addition(multiplication($c2,$c1),multiplication($c2,c($c1))),$c2).
% 1.77/1.98 end_of_list.
% 1.77/1.98
% 1.77/1.98 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.77/1.98
% 1.77/1.98 This ia a non-Horn set with equality. The strategy will be
% 1.77/1.98 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.77/1.98 deletion, with positive clauses in sos and nonpositive
% 1.77/1.98 clauses in usable.
% 1.77/1.98
% 1.77/1.98 dependent: set(knuth_bendix).
% 1.77/1.98 dependent: set(anl_eq).
% 1.77/1.98 dependent: set(para_from).
% 1.77/1.98 dependent: set(para_into).
% 1.77/1.98 dependent: clear(para_from_right).
% 1.77/1.98 dependent: clear(para_into_right).
% 1.77/1.98 dependent: set(para_from_vars).
% 1.77/1.98 dependent: set(eq_units_both_ways).
% 1.77/1.98 dependent: set(dynamic_demod_all).
% 1.77/1.98 dependent: set(dynamic_demod).
% 1.77/1.98 dependent: set(order_eq).
% 1.77/1.98 dependent: set(back_demod).
% 1.77/1.98 dependent: set(lrpo).
% 1.77/1.98 dependent: set(hyper_res).
% 1.77/1.98 dependent: set(unit_deletion).
% 1.77/1.98 dependent: set(factor).
% 1.77/1.98
% 1.77/1.98 ------------> process usable:
% 1.77/1.98 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.77/1.99 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.77/1.99 ** KEPT (pick-wt=6): 3 [] -test(A)|complement($f1(A),A).
% 1.77/1.99 ** KEPT (pick-wt=5): 4 [] test(A)| -complement(B,A).
% 1.77/1.99 ** KEPT (pick-wt=8): 5 [] -complement(A,B)|multiplication(B,A)=zero.
% 1.77/1.99 ** KEPT (pick-wt=8): 6 [] -complement(A,B)|multiplication(A,B)=zero.
% 1.77/1.99 ** KEPT (pick-wt=8): 7 [] -complement(A,B)|addition(B,A)=one.
% 1.77/1.99 ** KEPT (pick-wt=18): 8 [] complement(A,B)|multiplication(B,A)!=zero|multiplication(A,B)!=zero|addition(B,A)!=one.
% 1.77/1.99 ** KEPT (pick-wt=9): 9 [] -test(A)|c(A)!=B|complement(A,B).
% 1.77/1.99 ** KEPT (pick-wt=9): 10 [] -test(A)|c(A)=B| -complement(A,B).
% 1.77/1.99 ** KEPT (pick-wt=14): 11 [] -test(A)| -test(B)|c(addition(A,B))=multiplication(c(A),c(B)).
% 1.77/1.99 ** KEPT (pick-wt=14): 12 [] -test(A)| -test(B)|c(multiplication(A,B))=addition(c(A),c(B)).
% 1.77/1.99 ** KEPT (pick-wt=20): 13 [] -le_q($c2,addition(multiplication($c2,$c1),multiplication($c2,c($c1))))| -le_q(addition(multiplication($c2,$c1),multiplication($c2,c($c1))),$c2).
% 1.77/1.99
% 1.77/1.99 ------------> process sos:
% 1.77/1.99 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.77/1.99 ** KEPT (pick-wt=7): 18 [] addition(A,B)=addition(B,A).
% 1.77/1.99 ** KEPT (pick-wt=11): 20 [copy,19,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.77/1.99 ---> New Demodulator: 21 [new_demod,20] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.77/1.99 ** KEPT (pick-wt=5): 22 [] addition(A,zero)=A.
% 1.77/1.99 ---> New Demodulator: 23 [new_demod,22] addition(A,zero)=A.
% 1.77/1.99 ** KEPT (pick-wt=5): 24 [] addition(A,A)=A.
% 1.77/1.99 ---> New Demodulator: 25 [new_demod,24] addition(A,A)=A.
% 1.77/1.99 ** KEPT (pick-wt=11): 27 [copy,26,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.77/1.99 ---> New Demodulator: 28 [new_demod,27] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.77/1.99 ** KEPT (pick-wt=5): 29 [] multiplication(A,one)=A.
% 1.77/1.99 ---> New Demodulator: 30 [new_demod,29] multiplication(A,one)=A.
% 1.77/1.99 ** KEPT (pick-wt=5): 31 [] multiplication(one,A)=A.
% 1.77/1.99 ---> New Demodulator: 32 [new_demod,31] multiplication(one,A)=A.
% 1.77/1.99 ** KEPT (pick-wt=13): 33 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.77/1.99 ---> New Demodulator: 34 [new_demod,33] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.77/1.99 ** KEPT (pick-wt=13): 35 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.77/1.99 ---> New Demodulator: 36 [new_demod,35] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.77/1.99 ** KEPT (pick-wt=5): 37 [] multiplication(A,zero)=zero.
% 1.77/1.99 ---> New Demodulator: 38 [new_demod,37] multiplication(A,zero)=zero.
% 1.77/1.99 ** KEPT (pick-wt=5): 39 [] multiplication(zero,A)=zero.
% 1.77/1.99 ---> New Demodulator: 40 [new_demod,39] multiplication(zero,A)=zero.
% 1.77/1.99 ** KEPT (pick-wt=6): 41 [] test(A)|c(A)=zero.
% 1.77/1.99 ** KEPT (pick-wt=2): 42 [] test($c1).
% 1.77/1.99 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.77/1.99 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] addition(A,B)=addition(B,A).
% 1.77/1.99 >>>> Starting back demodulation with 21.
% 1.77/1.99 >>>> Starting back demodulation with 23.
% 1.77/1.99 >>>> Starting back demodulation with 25.
% 1.77/1.99 >> back demodulating 16 with 25.
% 1.77/1.99 >> back demodulating 15 with 25.
% 1.77/1.99 >> back demodulating 14 with 25.
% 1.77/1.99 >>>> Starting back demodulation with 28.
% 1.77/1.99 >>>> Starting back demodulation with 30.
% 1.77/1.99 >>>> Starting back demodulation with 32.
% 1.77/1.99 >>>> Starting back demodulation with 34.
% 1.77/1.99 >>>> Starting back demodulation with 36.
% 1.77/1.99 >>>> Starting back demodulation with 38.
% 1.77/1.99 >>>> Starting back demodulation with 40.
% 1.77/1.99
% 1.77/1.99 ======= end of input processing =======
% 1.77/1.99
% 1.77/1.99 =========== start of search ===========
% 1.77/1.99
% 1.77/1.99 -------- PROOF --------
% 1.77/1.99
% 1.77/1.99 ----> UNIT CONFLICT at 0.01 sec ----> 378 [binary,377.1,94.1] $F.
% 1.77/1.99
% 1.77/1.99 Length of proof is 15. Level of proof is 6.
% 1.77/1.99
% 1.77/1.99 ---------------- PROOF ----------------
% 1.77/1.99 % SZS status Theorem
% 1.77/1.99 % SZS output start Refutation
% See solution above
% 1.77/1.99 ------------ end of proof -------------
% 1.77/1.99
% 1.77/1.99
% 1.77/1.99 Search stopped by max_proofs option.
% 1.77/1.99
% 1.77/1.99
% 1.77/1.99 Search stopped by max_proofs option.
% 1.77/1.99
% 1.77/1.99 ============ end of search ============
% 1.77/1.99
% 1.77/1.99 -------------- statistics -------------
% 1.77/1.99 clauses given 48
% 1.77/1.99 clauses generated 573
% 1.77/1.99 clauses kept 280
% 1.77/1.99 clauses forward subsumed 390
% 1.77/1.99 clauses back subsumed 2
% 1.77/1.99 Kbytes malloced 1953
% 1.77/1.99
% 1.77/1.99 ----------- times (seconds) -----------
% 1.77/1.99 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.77/1.99 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.99 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.77/1.99
% 1.77/1.99 That finishes the proof of the theorem.
% 1.77/1.99
% 1.77/1.99 Process 2934 finished Wed Jul 27 06:32:26 2022
% 1.77/1.99 Otter interrupted
% 1.77/1.99 PROOF FOUND
%------------------------------------------------------------------------------