TSTP Solution File: KLE063+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE063+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:00:38 EDT 2022
% Result : Theorem 2.19s 2.38s
% Output : Refutation 2.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of clauses : 30 ( 26 unt; 0 nHn; 10 RR)
% Number of literals : 34 ( 24 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE063+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE063+1.p',unknown),
[] ).
cnf(3,axiom,
addition(domain(dollar_c2),domain(dollar_c1)) != domain(dollar_c1),
file('KLE063+1.p',unknown),
[] ).
cnf(5,axiom,
addition(A,B) = addition(B,A),
file('KLE063+1.p',unknown),
[] ).
cnf(6,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE063+1.p',unknown),
[] ).
cnf(7,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(11,axiom,
addition(A,A) = A,
file('KLE063+1.p',unknown),
[] ).
cnf(17,axiom,
multiplication(A,one) = A,
file('KLE063+1.p',unknown),
[] ).
cnf(19,axiom,
multiplication(one,A) = A,
file('KLE063+1.p',unknown),
[] ).
cnf(20,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE063+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE063+1.p',unknown),
[] ).
cnf(30,axiom,
domain(multiplication(A,B)) = domain(multiplication(A,domain(B))),
file('KLE063+1.p',unknown),
[] ).
cnf(32,plain,
domain(multiplication(A,domain(B))) = domain(multiplication(A,B)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[30])]),
[iquote('copy,30,flip.1')] ).
cnf(33,axiom,
addition(domain(A),one) = one,
file('KLE063+1.p',unknown),
[] ).
cnf(37,axiom,
domain(addition(A,B)) = addition(domain(A),domain(B)),
file('KLE063+1.p',unknown),
[] ).
cnf(39,axiom,
addition(dollar_c2,multiplication(domain(dollar_c1),dollar_c2)) = multiplication(domain(dollar_c1),dollar_c2),
file('KLE063+1.p',unknown),
[] ).
cnf(51,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,11])]),
[iquote('para_into,7.1.1.1,11.1.1,flip.1')] ).
cnf(63,plain,
addition(one,domain(A)) = one,
inference(para_into,[status(thm),theory(equality)],[33,5]),
[iquote('para_into,33.1.1,5.1.1')] ).
cnf(91,plain,
addition(multiplication(A,domain(B)),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,33]),17,17])]),
[iquote('para_into,20.1.1.2,33.1.1,demod,17,17,flip.1')] ).
cnf(110,plain,
addition(A,multiplication(domain(B),A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,63]),19,19])]),
[iquote('para_into,22.1.1.1,63.1.1,demod,19,19,flip.1')] ).
cnf(116,plain,
multiplication(domain(dollar_c1),dollar_c2) = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[39]),110])]),
[iquote('back_demod,39,demod,110,flip.1')] ).
cnf(138,plain,
domain(domain(A)) = domain(A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,19]),19]),
[iquote('para_into,31.1.1.1,18.1.1,demod,19')] ).
cnf(163,plain,
( addition(domain(A),domain(B)) = domain(B)
| ~ le_q(A,B) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[37,1])]),
[iquote('para_into,37.1.1.1,1.2.1,flip.1')] ).
cnf(280,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[51,2]),
[iquote('hyper,51,2')] ).
cnf(423,plain,
le_q(multiplication(A,domain(B)),A),
inference(hyper,[status(thm)],[91,2]),
[iquote('hyper,91,2')] ).
cnf(2938,plain,
( le_q(domain(A),domain(B))
| ~ le_q(A,B) ),
inference(para_from,[status(thm),theory(equality)],[163,280]),
[iquote('para_from,163.1.1,280.1.2')] ).
cnf(2969,plain,
le_q(domain(multiplication(A,B)),domain(A)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2938,423]),32]),
[iquote('hyper,2938,423,demod,32')] ).
cnf(2984,plain,
le_q(domain(dollar_c2),domain(dollar_c1)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[2969,116]),138]),
[iquote('para_into,2969.1.1.1,116.1.1,demod,138')] ).
cnf(3004,plain,
addition(domain(dollar_c2),domain(dollar_c1)) = domain(dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2984,163]),138,138,138]),
[iquote('hyper,2984,163,demod,138,138,138')] ).
cnf(3006,plain,
$false,
inference(binary,[status(thm)],[3004,3]),
[iquote('binary,3004.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE063+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n003.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 06:30:26 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.69/1.91 ----- Otter 3.3f, August 2004 -----
% 1.69/1.91 The process was started by sandbox2 on n003.cluster.edu,
% 1.69/1.91 Wed Jul 27 06:30:26 2022
% 1.69/1.91 The command was "./otter". The process ID is 12209.
% 1.69/1.91
% 1.69/1.91 set(prolog_style_variables).
% 1.69/1.91 set(auto).
% 1.69/1.91 dependent: set(auto1).
% 1.69/1.91 dependent: set(process_input).
% 1.69/1.91 dependent: clear(print_kept).
% 1.69/1.91 dependent: clear(print_new_demod).
% 1.69/1.91 dependent: clear(print_back_demod).
% 1.69/1.91 dependent: clear(print_back_sub).
% 1.69/1.91 dependent: set(control_memory).
% 1.69/1.91 dependent: assign(max_mem, 12000).
% 1.69/1.91 dependent: assign(pick_given_ratio, 4).
% 1.69/1.91 dependent: assign(stats_level, 1).
% 1.69/1.91 dependent: assign(max_seconds, 10800).
% 1.69/1.91 clear(print_given).
% 1.69/1.91
% 1.69/1.91 formula_list(usable).
% 1.69/1.91 all A (A=A).
% 1.69/1.91 all A B (addition(A,B)=addition(B,A)).
% 1.69/1.91 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.69/1.91 all A (addition(A,zero)=A).
% 1.69/1.91 all A (addition(A,A)=A).
% 1.69/1.91 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.69/1.91 all A (multiplication(A,one)=A).
% 1.69/1.91 all A (multiplication(one,A)=A).
% 1.69/1.91 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.69/1.91 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.69/1.91 all A (multiplication(A,zero)=zero).
% 1.69/1.91 all A (multiplication(zero,A)=zero).
% 1.69/1.91 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.69/1.91 all X0 (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0)).
% 1.69/1.91 all X0 X1 (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1)))).
% 1.69/1.91 all X0 (addition(domain(X0),one)=one).
% 1.69/1.91 domain(zero)=zero.
% 1.69/1.91 all X0 X1 (domain(addition(X0,X1))=addition(domain(X0),domain(X1))).
% 1.69/1.91 -(all X0 X1 (addition(X0,multiplication(domain(X1),X0))=multiplication(domain(X1),X0)->addition(domain(X0),domain(X1))=domain(X1))).
% 1.69/1.91 end_of_list.
% 1.69/1.91
% 1.69/1.91 -------> usable clausifies to:
% 1.69/1.91
% 1.69/1.91 list(usable).
% 1.69/1.91 0 [] A=A.
% 1.69/1.91 0 [] addition(A,B)=addition(B,A).
% 1.69/1.91 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.69/1.91 0 [] addition(A,zero)=A.
% 1.69/1.91 0 [] addition(A,A)=A.
% 1.69/1.91 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.69/1.91 0 [] multiplication(A,one)=A.
% 1.69/1.91 0 [] multiplication(one,A)=A.
% 1.69/1.91 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.69/1.91 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.69/1.91 0 [] multiplication(A,zero)=zero.
% 1.69/1.91 0 [] multiplication(zero,A)=zero.
% 1.69/1.91 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.69/1.91 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.69/1.91 0 [] addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0).
% 1.69/1.91 0 [] domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))).
% 1.69/1.91 0 [] addition(domain(X0),one)=one.
% 1.69/1.91 0 [] domain(zero)=zero.
% 1.69/1.91 0 [] domain(addition(X0,X1))=addition(domain(X0),domain(X1)).
% 1.69/1.91 0 [] addition($c2,multiplication(domain($c1),$c2))=multiplication(domain($c1),$c2).
% 1.69/1.91 0 [] addition(domain($c2),domain($c1))!=domain($c1).
% 1.69/1.91 end_of_list.
% 1.69/1.91
% 1.69/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.69/1.91
% 1.69/1.91 This is a Horn set with equality. The strategy will be
% 1.69/1.91 Knuth-Bendix and hyper_res, with positive clauses in
% 1.69/1.91 sos and nonpositive clauses in usable.
% 1.69/1.91
% 1.69/1.91 dependent: set(knuth_bendix).
% 1.69/1.91 dependent: set(anl_eq).
% 1.69/1.91 dependent: set(para_from).
% 1.69/1.91 dependent: set(para_into).
% 1.69/1.91 dependent: clear(para_from_right).
% 1.69/1.91 dependent: clear(para_into_right).
% 1.69/1.91 dependent: set(para_from_vars).
% 1.69/1.91 dependent: set(eq_units_both_ways).
% 1.69/1.91 dependent: set(dynamic_demod_all).
% 1.69/1.91 dependent: set(dynamic_demod).
% 1.69/1.91 dependent: set(order_eq).
% 1.69/1.91 dependent: set(back_demod).
% 1.69/1.91 dependent: set(lrpo).
% 1.69/1.91 dependent: set(hyper_res).
% 1.69/1.91 dependent: clear(order_hyper).
% 1.69/1.91
% 1.69/1.91 ------------> process usable:
% 1.69/1.91 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.69/1.91 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.69/1.91 ** KEPT (pick-wt=8): 3 [] addition(domain($c2),domain($c1))!=domain($c1).
% 1.69/1.91
% 1.69/1.91 ------------> process sos:
% 1.69/1.91 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.69/1.91 ** KEPT (pick-wt=7): 5 [] addition(A,B)=addition(B,A).
% 1.69/1.91 ** KEPT (pick-wt=11): 7 [copy,6,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.69/1.91 ---> New Demodulator: 8 [new_demod,7] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.69/1.91 ** KEPT (pick-wt=5): 9 [] addition(A,zero)=A.
% 1.69/1.91 ---> New Demodulator: 10 [new_demod,9] addition(A,zero)=A.
% 2.19/2.38 ** KEPT (pick-wt=5): 11 [] addition(A,A)=A.
% 2.19/2.38 ---> New Demodulator: 12 [new_demod,11] addition(A,A)=A.
% 2.19/2.38 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.19/2.38 ---> New Demodulator: 15 [new_demod,14] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.19/2.38 ** KEPT (pick-wt=5): 16 [] multiplication(A,one)=A.
% 2.19/2.38 ---> New Demodulator: 17 [new_demod,16] multiplication(A,one)=A.
% 2.19/2.38 ** KEPT (pick-wt=5): 18 [] multiplication(one,A)=A.
% 2.19/2.38 ---> New Demodulator: 19 [new_demod,18] multiplication(one,A)=A.
% 2.19/2.38 ** KEPT (pick-wt=13): 20 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.19/2.38 ---> New Demodulator: 21 [new_demod,20] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.19/2.38 ** KEPT (pick-wt=13): 22 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.19/2.38 ---> New Demodulator: 23 [new_demod,22] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.19/2.38 ** KEPT (pick-wt=5): 24 [] multiplication(A,zero)=zero.
% 2.19/2.38 ---> New Demodulator: 25 [new_demod,24] multiplication(A,zero)=zero.
% 2.19/2.38 ** KEPT (pick-wt=5): 26 [] multiplication(zero,A)=zero.
% 2.19/2.38 ---> New Demodulator: 27 [new_demod,26] multiplication(zero,A)=zero.
% 2.19/2.38 ** KEPT (pick-wt=11): 28 [] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 2.19/2.38 ---> New Demodulator: 29 [new_demod,28] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 2.19/2.38 ** KEPT (pick-wt=10): 31 [copy,30,flip.1] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 2.19/2.38 ---> New Demodulator: 32 [new_demod,31] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 2.19/2.38 ** KEPT (pick-wt=6): 33 [] addition(domain(A),one)=one.
% 2.19/2.38 ---> New Demodulator: 34 [new_demod,33] addition(domain(A),one)=one.
% 2.19/2.38 ** KEPT (pick-wt=4): 35 [] domain(zero)=zero.
% 2.19/2.38 ---> New Demodulator: 36 [new_demod,35] domain(zero)=zero.
% 2.19/2.38 ** KEPT (pick-wt=10): 37 [] domain(addition(A,B))=addition(domain(A),domain(B)).
% 2.19/2.38 ---> New Demodulator: 38 [new_demod,37] domain(addition(A,B))=addition(domain(A),domain(B)).
% 2.19/2.38 ** KEPT (pick-wt=11): 39 [] addition($c2,multiplication(domain($c1),$c2))=multiplication(domain($c1),$c2).
% 2.19/2.38 ---> New Demodulator: 40 [new_demod,39] addition($c2,multiplication(domain($c1),$c2))=multiplication(domain($c1),$c2).
% 2.19/2.38 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 2.19/2.38 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] addition(A,B)=addition(B,A).
% 2.19/2.38 >>>> Starting back demodulation with 8.
% 2.19/2.38 >>>> Starting back demodulation with 10.
% 2.19/2.38 >>>> Starting back demodulation with 12.
% 2.19/2.38 >>>> Starting back demodulation with 15.
% 2.19/2.38 >>>> Starting back demodulation with 17.
% 2.19/2.38 >>>> Starting back demodulation with 19.
% 2.19/2.38 >>>> Starting back demodulation with 21.
% 2.19/2.38 >>>> Starting back demodulation with 23.
% 2.19/2.38 >>>> Starting back demodulation with 25.
% 2.19/2.38 >>>> Starting back demodulation with 27.
% 2.19/2.38 >>>> Starting back demodulation with 29.
% 2.19/2.38 >>>> Starting back demodulation with 32.
% 2.19/2.38 >>>> Starting back demodulation with 34.
% 2.19/2.38 >>>> Starting back demodulation with 36.
% 2.19/2.38 >>>> Starting back demodulation with 38.
% 2.19/2.38 >>>> Starting back demodulation with 40.
% 2.19/2.38
% 2.19/2.38 ======= end of input processing =======
% 2.19/2.38
% 2.19/2.38 =========== start of search ===========
% 2.19/2.38
% 2.19/2.38
% 2.19/2.38 Resetting weight limit to 10.
% 2.19/2.38
% 2.19/2.38
% 2.19/2.38 Resetting weight limit to 10.
% 2.19/2.38
% 2.19/2.38 sos_size=2334
% 2.19/2.38
% 2.19/2.38 -------- PROOF --------
% 2.19/2.38
% 2.19/2.38 ----> UNIT CONFLICT at 0.46 sec ----> 3006 [binary,3004.1,3.1] $F.
% 2.19/2.38
% 2.19/2.38 Length of proof is 15. Level of proof is 7.
% 2.19/2.38
% 2.19/2.38 ---------------- PROOF ----------------
% 2.19/2.38 % SZS status Theorem
% 2.19/2.38 % SZS output start Refutation
% See solution above
% 2.19/2.38 ------------ end of proof -------------
% 2.19/2.38
% 2.19/2.38
% 2.19/2.38 Search stopped by max_proofs option.
% 2.19/2.38
% 2.19/2.38
% 2.19/2.38 Search stopped by max_proofs option.
% 2.19/2.38
% 2.19/2.38 ============ end of search ============
% 2.19/2.38
% 2.19/2.38 -------------- statistics -------------
% 2.19/2.38 clauses given 232
% 2.19/2.38 clauses generated 20459
% 2.19/2.38 clauses kept 2913
% 2.19/2.38 clauses forward subsumed 10836
% 2.19/2.38 clauses back subsumed 330
% 2.19/2.38 Kbytes malloced 4882
% 2.19/2.38
% 2.19/2.38 ----------- times (seconds) -----------
% 2.19/2.38 user CPU time 0.46 (0 hr, 0 min, 0 sec)
% 2.19/2.38 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.19/2.38 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.19/2.38
% 2.19/2.38 That finishes the proof of the theorem.
% 2.19/2.38
% 2.19/2.38 Process 12209 finished Wed Jul 27 06:30:28 2022
% 2.19/2.38 Otter interrupted
% 2.19/2.38 PROOF FOUND
%------------------------------------------------------------------------------