TSTP Solution File: KLE083+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE083+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:00:41 EDT 2022
% Result : Theorem 2.08s 2.29s
% Output : Refutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 4 RR)
% Number of literals : 12 ( 11 equ; 3 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 : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
dollar_c1 != multiplication(domain(dollar_c1),dollar_c1),
file('KLE083+1.p',unknown),
[] ).
cnf(4,plain,
multiplication(domain(dollar_c1),dollar_c1) != dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(11,axiom,
addition(A,zero) = A,
file('KLE083+1.p',unknown),
[] ).
cnf(20,axiom,
multiplication(one,A) = A,
file('KLE083+1.p',unknown),
[] ).
cnf(23,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE083+1.p',unknown),
[] ).
cnf(29,axiom,
multiplication(antidomain(A),A) = zero,
file('KLE083+1.p',unknown),
[] ).
cnf(33,axiom,
addition(antidomain(antidomain(A)),antidomain(A)) = one,
file('KLE083+1.p',unknown),
[] ).
cnf(36,axiom,
domain(A) = antidomain(antidomain(A)),
file('KLE083+1.p',unknown),
[] ).
cnf(45,plain,
multiplication(antidomain(antidomain(dollar_c1)),dollar_c1) != dollar_c1,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),36]),
[iquote('back_demod,4,demod,36')] ).
cnf(175,plain,
addition(multiplication(antidomain(antidomain(A)),B),multiplication(antidomain(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[33,23]),20])]),
[iquote('para_from,33.1.1,23.1.1.1,demod,20,flip.1')] ).
cnf(976,plain,
multiplication(antidomain(antidomain(A)),A) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[175,29]),11]),
[iquote('para_into,175.1.1.2,29.1.1,demod,11')] ).
cnf(978,plain,
$false,
inference(binary,[status(thm)],[976,45]),
[iquote('binary,976.1,45.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE083+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n013.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 06:28:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.93/2.11 ----- Otter 3.3f, August 2004 -----
% 1.93/2.11 The process was started by sandbox2 on n013.cluster.edu,
% 1.93/2.11 Wed Jul 27 06:28:45 2022
% 1.93/2.11 The command was "./otter". The process ID is 945.
% 1.93/2.11
% 1.93/2.11 set(prolog_style_variables).
% 1.93/2.11 set(auto).
% 1.93/2.11 dependent: set(auto1).
% 1.93/2.11 dependent: set(process_input).
% 1.93/2.11 dependent: clear(print_kept).
% 1.93/2.11 dependent: clear(print_new_demod).
% 1.93/2.11 dependent: clear(print_back_demod).
% 1.93/2.11 dependent: clear(print_back_sub).
% 1.93/2.11 dependent: set(control_memory).
% 1.93/2.11 dependent: assign(max_mem, 12000).
% 1.93/2.11 dependent: assign(pick_given_ratio, 4).
% 1.93/2.11 dependent: assign(stats_level, 1).
% 1.93/2.11 dependent: assign(max_seconds, 10800).
% 1.93/2.11 clear(print_given).
% 1.93/2.11
% 1.93/2.11 formula_list(usable).
% 1.93/2.11 all A (A=A).
% 1.93/2.11 all A B (addition(A,B)=addition(B,A)).
% 1.93/2.11 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.93/2.11 all A (addition(A,zero)=A).
% 1.93/2.11 all A (addition(A,A)=A).
% 1.93/2.11 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.93/2.11 all A (multiplication(A,one)=A).
% 1.93/2.11 all A (multiplication(one,A)=A).
% 1.93/2.11 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.93/2.11 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.93/2.11 all A (multiplication(A,zero)=zero).
% 1.93/2.11 all A (multiplication(zero,A)=zero).
% 1.93/2.11 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.93/2.11 all X0 (multiplication(antidomain(X0),X0)=zero).
% 1.93/2.11 all X0 X1 (addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))=antidomain(multiplication(X0,antidomain(antidomain(X1))))).
% 1.93/2.11 all X0 (addition(antidomain(antidomain(X0)),antidomain(X0))=one).
% 1.93/2.11 all X0 (domain(X0)=antidomain(antidomain(X0))).
% 1.93/2.11 all X0 (multiplication(X0,coantidomain(X0))=zero).
% 1.93/2.11 all X0 X1 (addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)))=coantidomain(multiplication(coantidomain(coantidomain(X0)),X1))).
% 1.93/2.11 all X0 (addition(coantidomain(coantidomain(X0)),coantidomain(X0))=one).
% 1.93/2.11 all X0 (codomain(X0)=coantidomain(coantidomain(X0))).
% 1.93/2.11 -(all X0 (X0=multiplication(domain(X0),X0))).
% 1.93/2.11 end_of_list.
% 1.93/2.11
% 1.93/2.11 -------> usable clausifies to:
% 1.93/2.11
% 1.93/2.11 list(usable).
% 1.93/2.11 0 [] A=A.
% 1.93/2.11 0 [] addition(A,B)=addition(B,A).
% 1.93/2.11 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.93/2.11 0 [] addition(A,zero)=A.
% 1.93/2.11 0 [] addition(A,A)=A.
% 1.93/2.11 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.93/2.11 0 [] multiplication(A,one)=A.
% 1.93/2.11 0 [] multiplication(one,A)=A.
% 1.93/2.11 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.93/2.11 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.93/2.11 0 [] multiplication(A,zero)=zero.
% 1.93/2.11 0 [] multiplication(zero,A)=zero.
% 1.93/2.11 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.93/2.11 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.93/2.11 0 [] multiplication(antidomain(X0),X0)=zero.
% 1.93/2.11 0 [] addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,antidomain(antidomain(X1)))))=antidomain(multiplication(X0,antidomain(antidomain(X1)))).
% 1.93/2.11 0 [] addition(antidomain(antidomain(X0)),antidomain(X0))=one.
% 1.93/2.11 0 [] domain(X0)=antidomain(antidomain(X0)).
% 1.93/2.11 0 [] multiplication(X0,coantidomain(X0))=zero.
% 1.93/2.11 0 [] addition(coantidomain(multiplication(X0,X1)),coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)))=coantidomain(multiplication(coantidomain(coantidomain(X0)),X1)).
% 1.93/2.11 0 [] addition(coantidomain(coantidomain(X0)),coantidomain(X0))=one.
% 1.93/2.11 0 [] codomain(X0)=coantidomain(coantidomain(X0)).
% 1.93/2.11 0 [] $c1!=multiplication(domain($c1),$c1).
% 1.93/2.11 end_of_list.
% 1.93/2.11
% 1.93/2.11 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.93/2.11
% 1.93/2.11 This is a Horn set with equality. The strategy will be
% 1.93/2.11 Knuth-Bendix and hyper_res, with positive clauses in
% 1.93/2.11 sos and nonpositive clauses in usable.
% 1.93/2.11
% 1.93/2.11 dependent: set(knuth_bendix).
% 1.93/2.11 dependent: set(anl_eq).
% 1.93/2.11 dependent: set(para_from).
% 1.93/2.11 dependent: set(para_into).
% 1.93/2.11 dependent: clear(para_from_right).
% 1.93/2.11 dependent: clear(para_into_right).
% 1.93/2.11 dependent: set(para_from_vars).
% 1.93/2.11 dependent: set(eq_units_both_ways).
% 1.93/2.11 dependent: set(dynamic_demod_all).
% 1.93/2.11 dependent: set(dynamic_demod).
% 1.93/2.11 dependent: set(order_eq).
% 1.93/2.11 dependent: set(back_demod).
% 1.93/2.11 dependent: set(lrpo).
% 1.93/2.11 dependent: set(hyper_res).
% 1.93/2.11 dependent: clear(order_hyper).
% 1.93/2.11
% 1.93/2.11 ------------> process usable:
% 1.93/2.11 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.93/2.11 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.93/2.11 ** KEPT (pick-wt=6): 4 [copy,3,flip.1] multiplication(domain($c1),$c1)!=$c1.
% 1.93/2.11
% 1.93/2.11 ------------> process sos:
% 1.93/2.11 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.93/2.11 ** KEPT (pick-wt=7): 6 [] addition(A,B)=addition(B,A).
% 1.93/2.11 ** KEPT (pick-wt=11): 8 [copy,7,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.93/2.11 ---> New Demodulator: 9 [new_demod,8] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.93/2.11 ** KEPT (pick-wt=5): 10 [] addition(A,zero)=A.
% 1.93/2.11 ---> New Demodulator: 11 [new_demod,10] addition(A,zero)=A.
% 1.93/2.11 ** KEPT (pick-wt=5): 12 [] addition(A,A)=A.
% 1.93/2.11 ---> New Demodulator: 13 [new_demod,12] addition(A,A)=A.
% 1.93/2.11 ** KEPT (pick-wt=11): 15 [copy,14,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.93/2.11 ---> New Demodulator: 16 [new_demod,15] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.93/2.11 ** KEPT (pick-wt=5): 17 [] multiplication(A,one)=A.
% 1.93/2.11 ---> New Demodulator: 18 [new_demod,17] multiplication(A,one)=A.
% 1.93/2.11 ** KEPT (pick-wt=5): 19 [] multiplication(one,A)=A.
% 1.93/2.11 ---> New Demodulator: 20 [new_demod,19] multiplication(one,A)=A.
% 1.93/2.11 ** KEPT (pick-wt=13): 21 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.93/2.11 ---> New Demodulator: 22 [new_demod,21] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.93/2.11 ** KEPT (pick-wt=13): 23 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.93/2.11 ---> New Demodulator: 24 [new_demod,23] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.93/2.11 ** KEPT (pick-wt=5): 25 [] multiplication(A,zero)=zero.
% 1.93/2.11 ---> New Demodulator: 26 [new_demod,25] multiplication(A,zero)=zero.
% 1.93/2.11 ** KEPT (pick-wt=5): 27 [] multiplication(zero,A)=zero.
% 1.93/2.11 ---> New Demodulator: 28 [new_demod,27] multiplication(zero,A)=zero.
% 1.93/2.11 ** KEPT (pick-wt=6): 29 [] multiplication(antidomain(A),A)=zero.
% 1.93/2.11 ---> New Demodulator: 30 [new_demod,29] multiplication(antidomain(A),A)=zero.
% 1.93/2.11 ** KEPT (pick-wt=18): 31 [] addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B)))))=antidomain(multiplication(A,antidomain(antidomain(B)))).
% 1.93/2.11 ---> New Demodulator: 32 [new_demod,31] addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B)))))=antidomain(multiplication(A,antidomain(antidomain(B)))).
% 1.93/2.11 ** KEPT (pick-wt=8): 33 [] addition(antidomain(antidomain(A)),antidomain(A))=one.
% 1.93/2.11 ---> New Demodulator: 34 [new_demod,33] addition(antidomain(antidomain(A)),antidomain(A))=one.
% 1.93/2.11 ** KEPT (pick-wt=6): 35 [] domain(A)=antidomain(antidomain(A)).
% 1.93/2.11 ---> New Demodulator: 36 [new_demod,35] domain(A)=antidomain(antidomain(A)).
% 1.93/2.11 ** KEPT (pick-wt=6): 37 [] multiplication(A,coantidomain(A))=zero.
% 1.93/2.11 ---> New Demodulator: 38 [new_demod,37] multiplication(A,coantidomain(A))=zero.
% 1.93/2.11 ** KEPT (pick-wt=18): 39 [] addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B)))=coantidomain(multiplication(coantidomain(coantidomain(A)),B)).
% 1.93/2.11 ---> New Demodulator: 40 [new_demod,39] addition(coantidomain(multiplication(A,B)),coantidomain(multiplication(coantidomain(coantidomain(A)),B)))=coantidomain(multiplication(coantidomain(coantidomain(A)),B)).
% 1.93/2.11 ** KEPT (pick-wt=8): 41 [] addition(coantidomain(coantidomain(A)),coantidomain(A))=one.
% 1.93/2.11 ---> New Demodulator: 42 [new_demod,41] addition(coantidomain(coantidomain(A)),coantidomain(A))=one.
% 1.93/2.11 ** KEPT (pick-wt=6): 43 [] codomain(A)=coantidomain(coantidomain(A)).
% 1.93/2.11 ---> New Demodulator: 44 [new_demod,43] codomain(A)=coantidomain(coantidomain(A)).
% 1.93/2.11 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.93/2.11 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] addition(A,B)=addition(B,A).
% 1.93/2.11 >>>> Starting back demodulation with 9.
% 1.93/2.11 >>>> Starting back demodulation with 11.
% 1.93/2.11 >>>> Starting back demodulation with 13.
% 1.93/2.11 >>>> Starting back demodulation with 16.
% 1.93/2.11 >>>> Starting back demodulation with 18.
% 1.93/2.11 >>>> Starting back demodulation with 20.
% 1.93/2.11 >>>> Starting back demodulation with 22.
% 2.08/2.29 >>>> Starting back demodulation with 24.
% 2.08/2.29 >>>> Starting back demodulation with 26.
% 2.08/2.29 >>>> Starting back demodulation with 28.
% 2.08/2.29 >>>> Starting back demodulation with 30.
% 2.08/2.29 >>>> Starting back demodulation with 32.
% 2.08/2.29 >>>> Starting back demodulation with 34.
% 2.08/2.29 >>>> Starting back demodulation with 36.
% 2.08/2.29 >> back demodulating 4 with 36.
% 2.08/2.29 >>>> Starting back demodulation with 38.
% 2.08/2.29 >>>> Starting back demodulation with 40.
% 2.08/2.29 >>>> Starting back demodulation with 42.
% 2.08/2.29 >>>> Starting back demodulation with 44.
% 2.08/2.29
% 2.08/2.29 ======= end of input processing =======
% 2.08/2.29
% 2.08/2.29 =========== start of search ===========
% 2.08/2.29
% 2.08/2.29
% 2.08/2.29 Resetting weight limit to 8.
% 2.08/2.29
% 2.08/2.29
% 2.08/2.29 Resetting weight limit to 8.
% 2.08/2.29
% 2.08/2.29 sos_size=496
% 2.08/2.29
% 2.08/2.29 -------- PROOF --------
% 2.08/2.29
% 2.08/2.29 ----> UNIT CONFLICT at 0.17 sec ----> 978 [binary,976.1,45.1] $F.
% 2.08/2.29
% 2.08/2.29 Length of proof is 4. Level of proof is 2.
% 2.08/2.29
% 2.08/2.29 ---------------- PROOF ----------------
% 2.08/2.29 % SZS status Theorem
% 2.08/2.29 % SZS output start Refutation
% See solution above
% 2.08/2.29 ------------ end of proof -------------
% 2.08/2.29
% 2.08/2.29
% 2.08/2.29 Search stopped by max_proofs option.
% 2.08/2.29
% 2.08/2.29
% 2.08/2.29 Search stopped by max_proofs option.
% 2.08/2.29
% 2.08/2.29 ============ end of search ============
% 2.08/2.29
% 2.08/2.29 -------------- statistics -------------
% 2.08/2.29 clauses given 251
% 2.08/2.29 clauses generated 24282
% 2.08/2.29 clauses kept 792
% 2.08/2.29 clauses forward subsumed 7236
% 2.08/2.29 clauses back subsumed 44
% 2.08/2.29 Kbytes malloced 5859
% 2.08/2.29
% 2.08/2.29 ----------- times (seconds) -----------
% 2.08/2.29 user CPU time 0.17 (0 hr, 0 min, 0 sec)
% 2.08/2.29 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.08/2.29 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.08/2.29
% 2.08/2.29 That finishes the proof of the theorem.
% 2.08/2.29
% 2.08/2.29 Process 945 finished Wed Jul 27 06:28:47 2022
% 2.08/2.29 Otter interrupted
% 2.08/2.29 PROOF FOUND
%------------------------------------------------------------------------------