TSTP Solution File: KLE089+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE089+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:00:42 EDT 2022
% Result : Theorem 2.04s 2.27s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 11 unt; 0 nHn; 6 RR)
% Number of literals : 11 ( 10 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
multiplication(domain(dollar_c2),dollar_c1) != zero,
file('KLE089+1.p',unknown),
[] ).
cnf(10,axiom,
addition(A,zero) = A,
file('KLE089+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE089+1.p',unknown),
[] ).
cnf(29,axiom,
multiplication(antidomain(A),A) = zero,
file('KLE089+1.p',unknown),
[] ).
cnf(35,axiom,
domain(A) = antidomain(antidomain(A)),
file('KLE089+1.p',unknown),
[] ).
cnf(44,axiom,
addition(domain(dollar_c2),antidomain(dollar_c1)) = antidomain(dollar_c1),
file('KLE089+1.p',unknown),
[] ).
cnf(45,plain,
addition(antidomain(antidomain(dollar_c2)),antidomain(dollar_c1)) = antidomain(dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[44]),35]),
[iquote('copy,44,demod,35')] ).
cnf(47,plain,
multiplication(antidomain(antidomain(dollar_c2)),dollar_c1) != zero,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),35]),
[iquote('back_demod,3,demod,35')] ).
cnf(258,plain,
addition(multiplication(antidomain(antidomain(dollar_c2)),A),multiplication(antidomain(dollar_c1),A)) = multiplication(antidomain(dollar_c1),A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[45,22])]),
[iquote('para_from,45.1.1,22.1.1.1,flip.1')] ).
cnf(1124,plain,
multiplication(antidomain(antidomain(dollar_c2)),dollar_c1) = zero,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[258,29]),10,29]),
[iquote('para_into,258.1.1.2,28.1.1,demod,10,29')] ).
cnf(1126,plain,
$false,
inference(binary,[status(thm)],[1124,47]),
[iquote('binary,1124.1,47.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE089+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 06:27:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.80/1.98 ----- Otter 3.3f, August 2004 -----
% 1.80/1.98 The process was started by sandbox on n012.cluster.edu,
% 1.80/1.98 Wed Jul 27 06:27:05 2022
% 1.80/1.98 The command was "./otter". The process ID is 11623.
% 1.80/1.98
% 1.80/1.98 set(prolog_style_variables).
% 1.80/1.98 set(auto).
% 1.80/1.98 dependent: set(auto1).
% 1.80/1.98 dependent: set(process_input).
% 1.80/1.98 dependent: clear(print_kept).
% 1.80/1.98 dependent: clear(print_new_demod).
% 1.80/1.98 dependent: clear(print_back_demod).
% 1.80/1.98 dependent: clear(print_back_sub).
% 1.80/1.98 dependent: set(control_memory).
% 1.80/1.98 dependent: assign(max_mem, 12000).
% 1.80/1.98 dependent: assign(pick_given_ratio, 4).
% 1.80/1.98 dependent: assign(stats_level, 1).
% 1.80/1.98 dependent: assign(max_seconds, 10800).
% 1.80/1.98 clear(print_given).
% 1.80/1.98
% 1.80/1.98 formula_list(usable).
% 1.80/1.98 all A (A=A).
% 1.80/1.98 all A B (addition(A,B)=addition(B,A)).
% 1.80/1.98 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.80/1.98 all A (addition(A,zero)=A).
% 1.80/1.98 all A (addition(A,A)=A).
% 1.80/1.98 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.80/1.98 all A (multiplication(A,one)=A).
% 1.80/1.98 all A (multiplication(one,A)=A).
% 1.80/1.98 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.80/1.98 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.80/1.98 all A (multiplication(A,zero)=zero).
% 1.80/1.98 all A (multiplication(zero,A)=zero).
% 1.80/1.98 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.80/1.98 all X0 (multiplication(antidomain(X0),X0)=zero).
% 1.80/1.98 all X0 X1 (addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))=antidomain(multiplication(X0,antidomain(antidomain(X1))))).
% 1.80/1.98 all X0 (addition(antidomain(antidomain(X0)),antidomain(X0))=one).
% 1.80/1.98 all X0 (domain(X0)=antidomain(antidomain(X0))).
% 1.80/1.98 all X0 (multiplication(X0,coantidomain(X0))=zero).
% 1.80/1.98 all X0 X1 (addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)))=coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))).
% 1.80/1.98 all X0 (addition(coantidomain(coantidomain(X0)),coantidomain(X0))=one).
% 1.80/1.98 all X0 (codomain(X0)=coantidomain(coantidomain(X0))).
% 1.80/1.98 -(all X0 X1 (addition(domain(X0),antidomain(X1))=antidomain(X1)->multiplication(domain(X0),X1)=zero)).
% 1.80/1.98 end_of_list.
% 1.80/1.98
% 1.80/1.98 -------> usable clausifies to:
% 1.80/1.98
% 1.80/1.98 list(usable).
% 1.80/1.98 0 [] A=A.
% 1.80/1.98 0 [] addition(A,B)=addition(B,A).
% 1.80/1.98 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.80/1.98 0 [] addition(A,zero)=A.
% 1.80/1.98 0 [] addition(A,A)=A.
% 1.80/1.98 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.80/1.98 0 [] multiplication(A,one)=A.
% 1.80/1.98 0 [] multiplication(one,A)=A.
% 1.80/1.98 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.80/1.98 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.80/1.98 0 [] multiplication(A,zero)=zero.
% 1.80/1.98 0 [] multiplication(zero,A)=zero.
% 1.80/1.98 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.80/1.98 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.80/1.98 0 [] multiplication(antidomain(X0),X0)=zero.
% 1.80/1.98 0 [] addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))=antidomain(multiplication(X0,antidomain(antidomain(X1)))).
% 1.80/1.98 0 [] addition(antidomain(antidomain(X0)),antidomain(X0))=one.
% 1.80/1.98 0 [] domain(X0)=antidomain(antidomain(X0)).
% 1.80/1.98 0 [] multiplication(X0,coantidomain(X0))=zero.
% 1.80/1.98 0 [] addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)))=coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)).
% 1.80/1.98 0 [] addition(coantidomain(coantidomain(X0)),coantidomain(X0))=one.
% 1.80/1.98 0 [] codomain(X0)=coantidomain(coantidomain(X0)).
% 1.80/1.98 0 [] addition(domain($c2),antidomain($c1))=antidomain($c1).
% 1.80/1.98 0 [] multiplication(domain($c2),$c1)!=zero.
% 1.80/1.98 end_of_list.
% 1.80/1.98
% 1.80/1.98 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.80/1.98
% 1.80/1.98 This is a Horn set with equality. The strategy will be
% 1.80/1.98 Knuth-Bendix and hyper_res, with positive clauses in
% 1.80/1.98 sos and nonpositive clauses in usable.
% 1.80/1.98
% 1.80/1.98 dependent: set(knuth_bendix).
% 1.80/1.98 dependent: set(anl_eq).
% 1.80/1.98 dependent: set(para_from).
% 1.80/1.98 dependent: set(para_into).
% 1.80/1.98 dependent: clear(para_from_right).
% 1.80/1.98 dependent: clear(para_into_right).
% 1.80/1.98 dependent: set(para_from_vars).
% 1.80/1.98 dependent: set(eq_units_both_ways).
% 1.80/1.98 dependent: set(dynamic_demod_all).
% 1.80/1.98 dependent: set(dynamic_demod).
% 1.80/1.98 dependent: set(order_eq).
% 1.80/1.98 dependent: set(back_demod).
% 1.80/1.98 dependent: set(lrpo).
% 1.80/1.98 dependent: set(hyper_res).
% 1.80/1.98 dependent: clear(order_hyper).
% 1.80/1.98
% 1.80/1.98 ------------> process usable:
% 1.80/1.98 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.80/1.98 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.80/1.98 ** KEPT (pick-wt=6): 3 [] multiplication(domain($c2),$c1)!=zero.
% 1.80/1.98
% 1.80/1.98 ------------> process sos:
% 1.80/1.98 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.80/1.98 ** KEPT (pick-wt=7): 5 [] addition(A,B)=addition(B,A).
% 1.80/1.98 ** KEPT (pick-wt=11): 7 [copy,6,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.80/1.98 ---> New Demodulator: 8 [new_demod,7] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.80/1.98 ** KEPT (pick-wt=5): 9 [] addition(A,zero)=A.
% 1.80/1.98 ---> New Demodulator: 10 [new_demod,9] addition(A,zero)=A.
% 1.80/1.98 ** KEPT (pick-wt=5): 11 [] addition(A,A)=A.
% 1.80/1.98 ---> New Demodulator: 12 [new_demod,11] addition(A,A)=A.
% 1.80/1.98 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.80/1.98 ---> New Demodulator: 15 [new_demod,14] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.80/1.98 ** KEPT (pick-wt=5): 16 [] multiplication(A,one)=A.
% 1.80/1.98 ---> New Demodulator: 17 [new_demod,16] multiplication(A,one)=A.
% 1.80/1.98 ** KEPT (pick-wt=5): 18 [] multiplication(one,A)=A.
% 1.80/1.98 ---> New Demodulator: 19 [new_demod,18] multiplication(one,A)=A.
% 1.80/1.98 ** KEPT (pick-wt=13): 20 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.80/1.98 ---> New Demodulator: 21 [new_demod,20] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.80/1.98 ** KEPT (pick-wt=13): 22 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.80/1.98 ---> New Demodulator: 23 [new_demod,22] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.80/1.98 ** KEPT (pick-wt=5): 24 [] multiplication(A,zero)=zero.
% 1.80/1.98 ---> New Demodulator: 25 [new_demod,24] multiplication(A,zero)=zero.
% 1.80/1.98 ** KEPT (pick-wt=5): 26 [] multiplication(zero,A)=zero.
% 1.80/1.98 ---> New Demodulator: 27 [new_demod,26] multiplication(zero,A)=zero.
% 1.80/1.98 ** KEPT (pick-wt=6): 28 [] multiplication(antidomain(A),A)=zero.
% 1.80/1.98 ---> New Demodulator: 29 [new_demod,28] multiplication(antidomain(A),A)=zero.
% 1.80/1.98 ** KEPT (pick-wt=18): 30 [] addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B)))))=antidomain(multiplication(A,antidomain(antidomain(B)))).
% 1.80/1.98 ---> New Demodulator: 31 [new_demod,30] addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B)))))=antidomain(multiplication(A,antidomain(antidomain(B)))).
% 1.80/1.98 ** KEPT (pick-wt=8): 32 [] addition(antidomain(antidomain(A)),antidomain(A))=one.
% 1.80/1.98 ---> New Demodulator: 33 [new_demod,32] addition(antidomain(antidomain(A)),antidomain(A))=one.
% 1.80/1.98 ** KEPT (pick-wt=6): 34 [] domain(A)=antidomain(antidomain(A)).
% 1.80/1.98 ---> New Demodulator: 35 [new_demod,34] domain(A)=antidomain(antidomain(A)).
% 1.80/1.98 ** KEPT (pick-wt=6): 36 [] multiplication(A,coantidomain(A))=zero.
% 1.80/1.98 ---> New Demodulator: 37 [new_demod,36] multiplication(A,coantidomain(A))=zero.
% 1.80/1.98 ** KEPT (pick-wt=18): 38 [] addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B)))=coantidomain(multiplication(coantidomain(coantidomain(A)),B)).
% 1.80/1.98 ---> New Demodulator: 39 [new_demod,38] addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B)))=coantidomain(multiplication(coantidomain(coantidomain(A)),B)).
% 1.80/1.98 ** KEPT (pick-wt=8): 40 [] addition(coantidomain(coantidomain(A)),coantidomain(A))=one.
% 1.80/1.98 ---> New Demodulator: 41 [new_demod,40] addition(coantidomain(coantidomain(A)),coantidomain(A))=one.
% 1.80/1.98 ** KEPT (pick-wt=6): 42 [] codomain(A)=coantidomain(coantidomain(A)).
% 1.80/1.98 ---> New Demodulator: 43 [new_demod,42] codomain(A)=coantidomain(coantidomain(A)).
% 1.80/1.98 ** KEPT (pick-wt=9): 45 [copy,44,demod,35] addition(antidomain(antidomain($c2)),antidomain($c1))=antidomain($c1).
% 1.80/1.98 ---> New Demodulator: 46 [new_demod,45] addition(antidomain(antidomain($c2)),antidomain($c1))=antidomain($c1).
% 1.80/1.98 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.80/1.98 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] addition(A,B)=addition(B,A).
% 2.04/2.27 >>>> Starting back demodulation with 8.
% 2.04/2.27 >>>> Starting back demodulation with 10.
% 2.04/2.27 >>>> Starting back demodulation with 12.
% 2.04/2.27 >>>> Starting back demodulation with 15.
% 2.04/2.27 >>>> Starting back demodulation with 17.
% 2.04/2.27 >>>> Starting back demodulation with 19.
% 2.04/2.27 >>>> Starting back demodulation with 21.
% 2.04/2.27 >>>> Starting back demodulation with 23.
% 2.04/2.27 >>>> Starting back demodulation with 25.
% 2.04/2.27 >>>> Starting back demodulation with 27.
% 2.04/2.27 >>>> Starting back demodulation with 29.
% 2.04/2.27 >>>> Starting back demodulation with 31.
% 2.04/2.27 >>>> Starting back demodulation with 33.
% 2.04/2.27 >>>> Starting back demodulation with 35.
% 2.04/2.27 >> back demodulating 3 with 35.
% 2.04/2.27 >>>> Starting back demodulation with 37.
% 2.04/2.27 >>>> Starting back demodulation with 39.
% 2.04/2.27 >>>> Starting back demodulation with 41.
% 2.04/2.27 >>>> Starting back demodulation with 43.
% 2.04/2.27 >>>> Starting back demodulation with 46.
% 2.04/2.27
% 2.04/2.27 ======= end of input processing =======
% 2.04/2.27
% 2.04/2.27 =========== start of search ===========
% 2.04/2.27
% 2.04/2.27
% 2.04/2.27 Resetting weight limit to 9.
% 2.04/2.27
% 2.04/2.27
% 2.04/2.27 Resetting weight limit to 9.
% 2.04/2.27
% 2.04/2.27 sos_size=530
% 2.04/2.27
% 2.04/2.27
% 2.04/2.27 Resetting weight limit to 8.
% 2.04/2.27
% 2.04/2.27
% 2.04/2.27 Resetting weight limit to 8.
% 2.04/2.27
% 2.04/2.27 sos_size=559
% 2.04/2.27
% 2.04/2.27 -------- PROOF --------
% 2.04/2.27
% 2.04/2.27 ----> UNIT CONFLICT at 0.29 sec ----> 1126 [binary,1124.1,47.1] $F.
% 2.04/2.27
% 2.04/2.27 Length of proof is 4. Level of proof is 3.
% 2.04/2.27
% 2.04/2.27 ---------------- PROOF ----------------
% 2.04/2.27 % SZS status Theorem
% 2.04/2.27 % SZS output start Refutation
% See solution above
% 2.04/2.27 ------------ end of proof -------------
% 2.04/2.27
% 2.04/2.27
% 2.04/2.27 Search stopped by max_proofs option.
% 2.04/2.27
% 2.04/2.27
% 2.04/2.27 Search stopped by max_proofs option.
% 2.04/2.27
% 2.04/2.27 ============ end of search ============
% 2.04/2.27
% 2.04/2.27 -------------- statistics -------------
% 2.04/2.27 clauses given 386
% 2.04/2.27 clauses generated 50719
% 2.04/2.27 clauses kept 937
% 2.04/2.27 clauses forward subsumed 11231
% 2.04/2.27 clauses back subsumed 64
% 2.04/2.27 Kbytes malloced 5859
% 2.04/2.27
% 2.04/2.27 ----------- times (seconds) -----------
% 2.04/2.27 user CPU time 0.29 (0 hr, 0 min, 0 sec)
% 2.04/2.27 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.04/2.27 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.04/2.27
% 2.04/2.27 That finishes the proof of the theorem.
% 2.04/2.27
% 2.04/2.27 Process 11623 finished Wed Jul 27 06:27:07 2022
% 2.04/2.27 Otter interrupted
% 2.04/2.27 PROOF FOUND
%------------------------------------------------------------------------------