TSTP Solution File: KLE138+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 13:00:48 EDT 2022
% Result : Theorem 1.64s 1.83s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 9 unt; 0 nHn; 3 RR)
% Number of literals : 9 ( 8 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 7 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(6,axiom,
strong_iteration(zero) != one,
file('KLE138+1.p',unknown),
[] ).
cnf(8,axiom,
addition(A,B) = addition(B,A),
file('KLE138+1.p',unknown),
[] ).
cnf(12,axiom,
addition(A,zero) = A,
file('KLE138+1.p',unknown),
[] ).
cnf(27,axiom,
multiplication(zero,A) = zero,
file('KLE138+1.p',unknown),
[] ).
cnf(33,axiom,
strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('KLE138+1.p',unknown),
[] ).
cnf(34,plain,
addition(multiplication(A,strong_iteration(A)),one) = strong_iteration(A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[33])]),
[iquote('copy,33,flip.1')] ).
cnf(51,plain,
addition(zero,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[8,12])]),
[iquote('para_into,8.1.1,12.1.1,flip.1')] ).
cnf(245,plain,
strong_iteration(zero) = one,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,27]),51])]),
[iquote('para_into,34.1.1.1,27.1.1,demod,51,flip.1')] ).
cnf(247,plain,
$false,
inference(binary,[status(thm)],[245,6]),
[iquote('binary,245.1,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE138+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n016.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 06:52:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.64/1.82 ----- Otter 3.3f, August 2004 -----
% 1.64/1.82 The process was started by sandbox on n016.cluster.edu,
% 1.64/1.82 Wed Jul 27 06:52:52 2022
% 1.64/1.82 The command was "./otter". The process ID is 11402.
% 1.64/1.82
% 1.64/1.82 set(prolog_style_variables).
% 1.64/1.82 set(auto).
% 1.64/1.82 dependent: set(auto1).
% 1.64/1.82 dependent: set(process_input).
% 1.64/1.82 dependent: clear(print_kept).
% 1.64/1.82 dependent: clear(print_new_demod).
% 1.64/1.82 dependent: clear(print_back_demod).
% 1.64/1.82 dependent: clear(print_back_sub).
% 1.64/1.82 dependent: set(control_memory).
% 1.64/1.82 dependent: assign(max_mem, 12000).
% 1.64/1.82 dependent: assign(pick_given_ratio, 4).
% 1.64/1.82 dependent: assign(stats_level, 1).
% 1.64/1.82 dependent: assign(max_seconds, 10800).
% 1.64/1.82 clear(print_given).
% 1.64/1.82
% 1.64/1.82 formula_list(usable).
% 1.64/1.82 all A (A=A).
% 1.64/1.82 all A B (addition(A,B)=addition(B,A)).
% 1.64/1.82 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.64/1.82 all A (addition(A,zero)=A).
% 1.64/1.82 all A (addition(A,A)=A).
% 1.64/1.82 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.64/1.82 all A (multiplication(A,one)=A).
% 1.64/1.82 all A (multiplication(one,A)=A).
% 1.64/1.82 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.64/1.82 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.64/1.82 all A (multiplication(zero,A)=zero).
% 1.64/1.82 all A (addition(one,multiplication(A,star(A)))=star(A)).
% 1.64/1.82 all A (addition(one,multiplication(star(A),A))=star(A)).
% 1.64/1.82 all A B C (le_q(addition(multiplication(A,C),B),C)->le_q(multiplication(star(A),B),C)).
% 1.64/1.82 all A B C (le_q(addition(multiplication(C,A),B),C)->le_q(multiplication(B,star(A)),C)).
% 1.64/1.82 all A (strong_iteration(A)=addition(multiplication(A,strong_iteration(A)),one)).
% 1.64/1.82 all A B C (le_q(C,addition(multiplication(A,C),B))->le_q(C,multiplication(strong_iteration(A),B))).
% 1.64/1.82 all A (strong_iteration(A)=addition(star(A),multiplication(strong_iteration(A),zero))).
% 1.64/1.82 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.64/1.82 strong_iteration(zero)!=one.
% 1.64/1.82 end_of_list.
% 1.64/1.82
% 1.64/1.82 -------> usable clausifies to:
% 1.64/1.82
% 1.64/1.82 list(usable).
% 1.64/1.82 0 [] A=A.
% 1.64/1.82 0 [] addition(A,B)=addition(B,A).
% 1.64/1.82 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.64/1.82 0 [] addition(A,zero)=A.
% 1.64/1.82 0 [] addition(A,A)=A.
% 1.64/1.82 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.64/1.82 0 [] multiplication(A,one)=A.
% 1.64/1.82 0 [] multiplication(one,A)=A.
% 1.64/1.82 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.64/1.82 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.64/1.82 0 [] multiplication(zero,A)=zero.
% 1.64/1.82 0 [] addition(one,multiplication(A,star(A)))=star(A).
% 1.64/1.82 0 [] addition(one,multiplication(star(A),A))=star(A).
% 1.64/1.82 0 [] -le_q(addition(multiplication(A,C),B),C)|le_q(multiplication(star(A),B),C).
% 1.64/1.82 0 [] -le_q(addition(multiplication(C,A),B),C)|le_q(multiplication(B,star(A)),C).
% 1.64/1.82 0 [] strong_iteration(A)=addition(multiplication(A,strong_iteration(A)),one).
% 1.64/1.82 0 [] -le_q(C,addition(multiplication(A,C),B))|le_q(C,multiplication(strong_iteration(A),B)).
% 1.64/1.82 0 [] strong_iteration(A)=addition(star(A),multiplication(strong_iteration(A),zero)).
% 1.64/1.82 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.64/1.82 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.64/1.82 0 [] strong_iteration(zero)!=one.
% 1.64/1.82 end_of_list.
% 1.64/1.82
% 1.64/1.82 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.64/1.82
% 1.64/1.82 This is a Horn set with equality. The strategy will be
% 1.64/1.82 Knuth-Bendix and hyper_res, with positive clauses in
% 1.64/1.82 sos and nonpositive clauses in usable.
% 1.64/1.82
% 1.64/1.82 dependent: set(knuth_bendix).
% 1.64/1.82 dependent: set(anl_eq).
% 1.64/1.82 dependent: set(para_from).
% 1.64/1.82 dependent: set(para_into).
% 1.64/1.82 dependent: clear(para_from_right).
% 1.64/1.82 dependent: clear(para_into_right).
% 1.64/1.82 dependent: set(para_from_vars).
% 1.64/1.82 dependent: set(eq_units_both_ways).
% 1.64/1.82 dependent: set(dynamic_demod_all).
% 1.64/1.82 dependent: set(dynamic_demod).
% 1.64/1.82 dependent: set(order_eq).
% 1.64/1.82 dependent: set(back_demod).
% 1.64/1.82 dependent: set(lrpo).
% 1.64/1.82 dependent: set(hyper_res).
% 1.64/1.82 dependent: clear(order_hyper).
% 1.64/1.82
% 1.64/1.82 ------------> process usable:
% 1.64/1.82 ** KEPT (pick-wt=13): 1 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.64/1.82 ** KEPT (pick-wt=13): 2 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.64/1.82 ** KEPT (pick-wt=13): 3 [] -le_q(A,addition(multiplication(B,A),C))|le_q(A,multiplication(strong_iteration(B),C)).
% 1.64/1.82 ** KEPT (pick-wt=8): 4 [] -le_q(A,B)|addition(A,B)=B.
% 1.64/1.83 ** KEPT (pick-wt=8): 5 [] le_q(A,B)|addition(A,B)!=B.
% 1.64/1.83 ** KEPT (pick-wt=4): 6 [] strong_iteration(zero)!=one.
% 1.64/1.83
% 1.64/1.83 ------------> process sos:
% 1.64/1.83 ** KEPT (pick-wt=3): 7 [] A=A.
% 1.64/1.83 ** KEPT (pick-wt=7): 8 [] addition(A,B)=addition(B,A).
% 1.64/1.83 ** KEPT (pick-wt=11): 10 [copy,9,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.64/1.83 ---> New Demodulator: 11 [new_demod,10] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.64/1.83 ** KEPT (pick-wt=5): 12 [] addition(A,zero)=A.
% 1.64/1.83 ---> New Demodulator: 13 [new_demod,12] addition(A,zero)=A.
% 1.64/1.83 ** KEPT (pick-wt=5): 14 [] addition(A,A)=A.
% 1.64/1.83 ---> New Demodulator: 15 [new_demod,14] addition(A,A)=A.
% 1.64/1.83 ** KEPT (pick-wt=11): 17 [copy,16,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.64/1.83 ---> New Demodulator: 18 [new_demod,17] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.64/1.83 ** KEPT (pick-wt=5): 19 [] multiplication(A,one)=A.
% 1.64/1.83 ---> New Demodulator: 20 [new_demod,19] multiplication(A,one)=A.
% 1.64/1.83 ** KEPT (pick-wt=5): 21 [] multiplication(one,A)=A.
% 1.64/1.83 ---> New Demodulator: 22 [new_demod,21] multiplication(one,A)=A.
% 1.64/1.83 ** KEPT (pick-wt=13): 23 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.64/1.83 ---> New Demodulator: 24 [new_demod,23] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.64/1.83 ** KEPT (pick-wt=13): 25 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.64/1.83 ---> New Demodulator: 26 [new_demod,25] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.64/1.83 ** KEPT (pick-wt=5): 27 [] multiplication(zero,A)=zero.
% 1.64/1.83 ---> New Demodulator: 28 [new_demod,27] multiplication(zero,A)=zero.
% 1.64/1.83 ** KEPT (pick-wt=9): 29 [] addition(one,multiplication(A,star(A)))=star(A).
% 1.64/1.83 ---> New Demodulator: 30 [new_demod,29] addition(one,multiplication(A,star(A)))=star(A).
% 1.64/1.83 ** KEPT (pick-wt=9): 31 [] addition(one,multiplication(star(A),A))=star(A).
% 1.64/1.83 ---> New Demodulator: 32 [new_demod,31] addition(one,multiplication(star(A),A))=star(A).
% 1.64/1.83 ** KEPT (pick-wt=9): 34 [copy,33,flip.1] addition(multiplication(A,strong_iteration(A)),one)=strong_iteration(A).
% 1.64/1.83 ---> New Demodulator: 35 [new_demod,34] addition(multiplication(A,strong_iteration(A)),one)=strong_iteration(A).
% 1.64/1.83 ** KEPT (pick-wt=10): 37 [copy,36,flip.1] addition(star(A),multiplication(strong_iteration(A),zero))=strong_iteration(A).
% 1.64/1.83 ---> New Demodulator: 38 [new_demod,37] addition(star(A),multiplication(strong_iteration(A),zero))=strong_iteration(A).
% 1.64/1.83 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.64/1.83 Following clause subsumed by 8 during input processing: 0 [copy,8,flip.1] addition(A,B)=addition(B,A).
% 1.64/1.83 >>>> Starting back demodulation with 11.
% 1.64/1.83 >>>> Starting back demodulation with 13.
% 1.64/1.83 >>>> Starting back demodulation with 15.
% 1.64/1.83 >>>> Starting back demodulation with 18.
% 1.64/1.83 >>>> Starting back demodulation with 20.
% 1.64/1.83 >>>> Starting back demodulation with 22.
% 1.64/1.83 >>>> Starting back demodulation with 24.
% 1.64/1.83 >>>> Starting back demodulation with 26.
% 1.64/1.83 >>>> Starting back demodulation with 28.
% 1.64/1.83 >>>> Starting back demodulation with 30.
% 1.64/1.83 >>>> Starting back demodulation with 32.
% 1.64/1.83 >>>> Starting back demodulation with 35.
% 1.64/1.83 >>>> Starting back demodulation with 38.
% 1.64/1.83
% 1.64/1.83 ======= end of input processing =======
% 1.64/1.83
% 1.64/1.83 =========== start of search ===========
% 1.64/1.83
% 1.64/1.83 -------- PROOF --------
% 1.64/1.83
% 1.64/1.83 ----> UNIT CONFLICT at 0.01 sec ----> 247 [binary,245.1,6.1] $F.
% 1.64/1.83
% 1.64/1.83 Length of proof is 3. Level of proof is 2.
% 1.64/1.83
% 1.64/1.83 ---------------- PROOF ----------------
% 1.64/1.83 % SZS status Theorem
% 1.64/1.83 % SZS output start Refutation
% See solution above
% 1.64/1.83 ------------ end of proof -------------
% 1.64/1.83
% 1.64/1.83
% 1.64/1.83 Search stopped by max_proofs option.
% 1.64/1.83
% 1.64/1.83
% 1.64/1.83 Search stopped by max_proofs option.
% 1.64/1.83
% 1.64/1.83 ============ end of search ============
% 1.64/1.83
% 1.64/1.83 -------------- statistics -------------
% 1.64/1.83 clauses given 41
% 1.64/1.83 clauses generated 623
% 1.64/1.83 clauses kept 203
% 1.64/1.83 clauses forward subsumed 439
% 1.64/1.83 clauses back subsumed 7
% 1.64/1.83 Kbytes malloced 1953
% 1.64/1.83
% 1.64/1.83 ----------- times (seconds) -----------
% 1.64/1.83 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.64/1.83 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.64/1.83 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.64/1.83
% 1.64/1.83 That finishes the proof of the theorem.
% 1.64/1.83
% 1.64/1.83 Process 11402 finished Wed Jul 27 06:52:53 2022
% 1.64/1.83 Otter interrupted
% 1.64/1.83 PROOF FOUND
%------------------------------------------------------------------------------