%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE141+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:00:49 EDT 2022
% Result : Theorem 1.85s 2.06s
% Output : Refutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of clauses : 14 ( 10 unt; 0 nHn; 5 RR)
% Number of literals : 18 ( 7 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 23 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( ~ le_q(A,addition(multiplication(B,A),C))
| le_q(A,multiplication(strong_iteration(B),C)) ),
file('KLE141+2.p',unknown),
[] ).
cnf(5,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE141+2.p',unknown),
[] ).
cnf(6,axiom,
( ~ le_q(multiplication(strong_iteration(one),dollar_c1),strong_iteration(one))
| ~ le_q(strong_iteration(one),multiplication(strong_iteration(one),dollar_c1)) ),
file('KLE141+2.p',unknown),
[] ).
cnf(9,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE141+2.p',unknown),
[] ).
cnf(10,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(14,axiom,
addition(A,A) = A,
file('KLE141+2.p',unknown),
[] ).
cnf(19,axiom,
multiplication(A,one) = A,
file('KLE141+2.p',unknown),
[] ).
cnf(21,axiom,
multiplication(one,A) = A,
file('KLE141+2.p',unknown),
[] ).
cnf(62,plain,
( ~ le_q(A,addition(A,B))
| le_q(A,multiplication(strong_iteration(one),B)) ),
inference(para_from,[status(thm),theory(equality)],[21,3]),
[iquote('para_from,21.1.1,3.1.2.1')] ).
cnf(70,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,14])]),
[iquote('para_into,10.1.1.1,14.1.1,flip.1')] ).
cnf(521,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[70,5]),
[iquote('hyper,70,5')] ).
cnf(864,plain,
le_q(A,multiplication(strong_iteration(one),B)),
inference(hyper,[status(thm)],[62,521]),
[iquote('hyper,62,521')] ).
cnf(870,plain,
le_q(A,strong_iteration(one)),
inference(para_into,[status(thm),theory(equality)],[864,19]),
[iquote('para_into,864.1.2,19.1.1')] ).
cnf(873,plain,
$false,
inference(hyper,[status(thm)],[870,6,864]),
[iquote('hyper,870,6,864')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE141+2 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 06:35:31 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.85/2.03 ----- Otter 3.3f, August 2004 -----
% 1.85/2.03 The process was started by sandbox on n018.cluster.edu,
% 1.85/2.03 Wed Jul 27 06:35:31 2022
% 1.85/2.03 The command was "./otter". The process ID is 15023.
% 1.85/2.03
% 1.85/2.03 set(prolog_style_variables).
% 1.85/2.03 set(auto).
% 1.85/2.03 dependent: set(auto1).
% 1.85/2.03 dependent: set(process_input).
% 1.85/2.03 dependent: clear(print_kept).
% 1.85/2.03 dependent: clear(print_new_demod).
% 1.85/2.03 dependent: clear(print_back_demod).
% 1.85/2.03 dependent: clear(print_back_sub).
% 1.85/2.03 dependent: set(control_memory).
% 1.85/2.03 dependent: assign(max_mem, 12000).
% 1.85/2.03 dependent: assign(pick_given_ratio, 4).
% 1.85/2.03 dependent: assign(stats_level, 1).
% 1.85/2.03 dependent: assign(max_seconds, 10800).
% 1.85/2.03 clear(print_given).
% 1.85/2.03
% 1.85/2.03 formula_list(usable).
% 1.85/2.03 all A (A=A).
% 1.85/2.03 all A B (addition(A,B)=addition(B,A)).
% 1.85/2.03 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.85/2.03 all A (addition(A,zero)=A).
% 1.85/2.03 all A (addition(A,A)=A).
% 1.85/2.03 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.85/2.03 all A (multiplication(A,one)=A).
% 1.85/2.03 all A (multiplication(one,A)=A).
% 1.85/2.03 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.85/2.03 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.85/2.03 all A (multiplication(zero,A)=zero).
% 1.85/2.03 all A (addition(one,multiplication(A,star(A)))=star(A)).
% 1.85/2.03 all A (addition(one,multiplication(star(A),A))=star(A)).
% 1.85/2.03 all A B C (le_q(addition(multiplication(A,C),B),C)->le_q(multiplication(star(A),B),C)).
% 1.85/2.03 all A B C (le_q(addition(multiplication(C,A),B),C)->le_q(multiplication(B,star(A)),C)).
% 1.85/2.03 all A (strong_iteration(A)=addition(multiplication(A,strong_iteration(A)),one)).
% 1.85/2.03 all A B C (le_q(C,addition(multiplication(A,C),B))->le_q(C,multiplication(strong_iteration(A),B))).
% 1.85/2.03 all A (strong_iteration(A)=addition(star(A),multiplication(strong_iteration(A),zero))).
% 1.85/2.03 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.85/2.03 -(all X0 (le_q(multiplication(strong_iteration(one),X0),strong_iteration(one))&le_q(strong_iteration(one),multiplication(strong_iteration(one),X0)))).
% 1.85/2.03 end_of_list.
% 1.85/2.03
% 1.85/2.03 -------> usable clausifies to:
% 1.85/2.03
% 1.85/2.03 list(usable).
% 1.85/2.03 0 [] A=A.
% 1.85/2.03 0 [] addition(A,B)=addition(B,A).
% 1.85/2.03 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.85/2.03 0 [] addition(A,zero)=A.
% 1.85/2.03 0 [] addition(A,A)=A.
% 1.85/2.03 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.85/2.03 0 [] multiplication(A,one)=A.
% 1.85/2.03 0 [] multiplication(one,A)=A.
% 1.85/2.03 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.85/2.03 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.85/2.03 0 [] multiplication(zero,A)=zero.
% 1.85/2.03 0 [] addition(one,multiplication(A,star(A)))=star(A).
% 1.85/2.03 0 [] addition(one,multiplication(star(A),A))=star(A).
% 1.85/2.03 0 [] -le_q(addition(multiplication(A,C),B),C)|le_q(multiplication(star(A),B),C).
% 1.85/2.03 0 [] -le_q(addition(multiplication(C,A),B),C)|le_q(multiplication(B,star(A)),C).
% 1.85/2.03 0 [] strong_iteration(A)=addition(multiplication(A,strong_iteration(A)),one).
% 1.85/2.03 0 [] -le_q(C,addition(multiplication(A,C),B))|le_q(C,multiplication(strong_iteration(A),B)).
% 1.85/2.03 0 [] strong_iteration(A)=addition(star(A),multiplication(strong_iteration(A),zero)).
% 1.85/2.03 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.85/2.03 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.85/2.03 0 [] -le_q(multiplication(strong_iteration(one),$c1),strong_iteration(one))| -le_q(strong_iteration(one),multiplication(strong_iteration(one),$c1)).
% 1.85/2.03 end_of_list.
% 1.85/2.03
% 1.85/2.03 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.85/2.03
% 1.85/2.03 This is a Horn set with equality. The strategy will be
% 1.85/2.03 Knuth-Bendix and hyper_res, with positive clauses in
% 1.85/2.03 sos and nonpositive clauses in usable.
% 1.85/2.03
% 1.85/2.03 dependent: set(knuth_bendix).
% 1.85/2.03 dependent: set(anl_eq).
% 1.85/2.03 dependent: set(para_from).
% 1.85/2.03 dependent: set(para_into).
% 1.85/2.03 dependent: clear(para_from_right).
% 1.85/2.03 dependent: clear(para_into_right).
% 1.85/2.03 dependent: set(para_from_vars).
% 1.85/2.03 dependent: set(eq_units_both_ways).
% 1.85/2.03 dependent: set(dynamic_demod_all).
% 1.85/2.03 dependent: set(dynamic_demod).
% 1.85/2.03 dependent: set(order_eq).
% 1.85/2.03 dependent: set(back_demod).
% 1.85/2.03 dependent: set(lrpo).
% 1.85/2.03 dependent: set(hyper_res).
% 1.85/2.03 dependent: clear(order_hyper).
% 1.85/2.03
% 1.85/2.03 ------------> process usable:
% 1.85/2.03 ** KEPT (pick-wt=13): 1 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.85/2.06 ** KEPT (pick-wt=13): 2 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.85/2.06 ** KEPT (pick-wt=13): 3 [] -le_q(A,addition(multiplication(B,A),C))|le_q(A,multiplication(strong_iteration(B),C)).
% 1.85/2.06 ** KEPT (pick-wt=8): 4 [] -le_q(A,B)|addition(A,B)=B.
% 1.85/2.06 ** KEPT (pick-wt=8): 5 [] le_q(A,B)|addition(A,B)!=B.
% 1.85/2.06 ** KEPT (pick-wt=14): 6 [] -le_q(multiplication(strong_iteration(one),$c1),strong_iteration(one))| -le_q(strong_iteration(one),multiplication(strong_iteration(one),$c1)).
% 1.85/2.06
% 1.85/2.06 ------------> process sos:
% 1.85/2.06 ** KEPT (pick-wt=3): 7 [] A=A.
% 1.85/2.06 ** KEPT (pick-wt=7): 8 [] addition(A,B)=addition(B,A).
% 1.85/2.06 ** KEPT (pick-wt=11): 10 [copy,9,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.85/2.06 ---> New Demodulator: 11 [new_demod,10] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.85/2.06 ** KEPT (pick-wt=5): 12 [] addition(A,zero)=A.
% 1.85/2.06 ---> New Demodulator: 13 [new_demod,12] addition(A,zero)=A.
% 1.85/2.06 ** KEPT (pick-wt=5): 14 [] addition(A,A)=A.
% 1.85/2.06 ---> New Demodulator: 15 [new_demod,14] addition(A,A)=A.
% 1.85/2.06 ** KEPT (pick-wt=11): 17 [copy,16,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.85/2.06 ---> New Demodulator: 18 [new_demod,17] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.85/2.06 ** KEPT (pick-wt=5): 19 [] multiplication(A,one)=A.
% 1.85/2.06 ---> New Demodulator: 20 [new_demod,19] multiplication(A,one)=A.
% 1.85/2.06 ** KEPT (pick-wt=5): 21 [] multiplication(one,A)=A.
% 1.85/2.06 ---> New Demodulator: 22 [new_demod,21] multiplication(one,A)=A.
% 1.85/2.06 ** KEPT (pick-wt=13): 23 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.85/2.06 ---> New Demodulator: 24 [new_demod,23] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.85/2.06 ** KEPT (pick-wt=13): 25 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.85/2.06 ---> New Demodulator: 26 [new_demod,25] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.85/2.06 ** KEPT (pick-wt=5): 27 [] multiplication(zero,A)=zero.
% 1.85/2.06 ---> New Demodulator: 28 [new_demod,27] multiplication(zero,A)=zero.
% 1.85/2.06 ** KEPT (pick-wt=9): 29 [] addition(one,multiplication(A,star(A)))=star(A).
% 1.85/2.06 ---> New Demodulator: 30 [new_demod,29] addition(one,multiplication(A,star(A)))=star(A).
% 1.85/2.06 ** KEPT (pick-wt=9): 31 [] addition(one,multiplication(star(A),A))=star(A).
% 1.85/2.06 ---> New Demodulator: 32 [new_demod,31] addition(one,multiplication(star(A),A))=star(A).
% 1.85/2.06 ** KEPT (pick-wt=9): 34 [copy,33,flip.1] addition(multiplication(A,strong_iteration(A)),one)=strong_iteration(A).
% 1.85/2.06 ---> New Demodulator: 35 [new_demod,34] addition(multiplication(A,strong_iteration(A)),one)=strong_iteration(A).
% 1.85/2.06 ** KEPT (pick-wt=10): 37 [copy,36,flip.1] addition(star(A),multiplication(strong_iteration(A),zero))=strong_iteration(A).
% 1.85/2.06 ---> New Demodulator: 38 [new_demod,37] addition(star(A),multiplication(strong_iteration(A),zero))=strong_iteration(A).
% 1.85/2.06 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.85/2.06 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] addition(A,B)=addition(B,A).
% 1.85/2.06 >>>> Starting back demodulation with 11.
% 1.85/2.06 >>>> Starting back demodulation with 13.
% 1.85/2.06 >>>> Starting back demodulation with 15.
% 1.85/2.06 >>>> Starting back demodulation with 18.
% 1.85/2.06 >>>> Starting back demodulation with 20.
% 1.85/2.06 >>>> Starting back demodulation with 22.
% 1.85/2.06 >>>> Starting back demodulation with 24.
% 1.85/2.06 >>>> Starting back demodulation with 26.
% 1.85/2.06 >>>> Starting back demodulation with 28.
% 1.85/2.06 >>>> Starting back demodulation with 30.
% 1.85/2.06 >>>> Starting back demodulation with 32.
% 1.85/2.06 >>>> Starting back demodulation with 35.
% 1.85/2.06 >>>> Starting back demodulation with 38.
% 1.85/2.06
% 1.85/2.06 ======= end of input processing =======
% 1.85/2.06
% 1.85/2.06 =========== start of search ===========
% 1.85/2.06
% 1.85/2.06 -------- PROOF --------
% 1.85/2.06
% 1.85/2.06 -----> EMPTY CLAUSE at 0.03 sec ----> 873 [hyper,870,6,864] $F.
% 1.85/2.06
% 1.85/2.06 Length of proof is 6. Level of proof is 5.
% 1.85/2.06
% 1.85/2.06 ---------------- PROOF ----------------
% 1.85/2.06 % SZS status Theorem
% 1.85/2.06 % SZS output start Refutation
% See solution above
% 1.85/2.06 ------------ end of proof -------------
% 1.85/2.06
% 1.85/2.06
% 1.85/2.06 Search stopped by max_proofs option.
% 1.85/2.06
% 1.85/2.06
% 1.85/2.06 Search stopped by max_proofs option.
% 1.85/2.06
% 1.85/2.06 ============ end of search ============
% 1.85/2.06
% 1.85/2.06 -------------- statistics -------------
% 1.85/2.06 clauses given 113
% 1.85/2.06 clauses generated 3126
% 1.85/2.06 clauses kept 761
% 1.85/2.06 clauses forward subsumed 2343
% 1.85/2.06 clauses back subsumed 175
% 1.85/2.06 Kbytes malloced 2929
% 1.85/2.06
% 1.85/2.06 ----------- times (seconds) -----------
% 1.85/2.06 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.85/2.06 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.85/2.06 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.85/2.06
% 1.85/2.06 That finishes the proof of the theorem.
% 1.85/2.06
% 1.85/2.06 Process 15023 finished Wed Jul 27 06:35:33 2022
% 1.85/2.06 Otter interrupted
% 1.85/2.06 PROOF FOUND
%------------------------------------------------------------------------------