TSTP Solution File: KLE069+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE069+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 13:00:39 EDT 2022
% Result : Theorem 1.65s 1.83s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 4 RR)
% Number of literals : 20 ( 19 equ; 3 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
multiplication(domain(dollar_c2),addition(domain(dollar_c2),domain(dollar_c1))) != domain(dollar_c2),
file('KLE069+1.p',unknown),
[] ).
cnf(4,axiom,
A = A,
file('KLE069+1.p',unknown),
[] ).
cnf(5,axiom,
addition(A,B) = addition(B,A),
file('KLE069+1.p',unknown),
[] ).
cnf(17,axiom,
multiplication(A,one) = A,
file('KLE069+1.p',unknown),
[] ).
cnf(19,axiom,
multiplication(one,A) = A,
file('KLE069+1.p',unknown),
[] ).
cnf(21,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE069+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE069+1.p',unknown),
[] ).
cnf(28,axiom,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
file('KLE069+1.p',unknown),
[] ).
cnf(30,axiom,
domain(multiplication(A,B)) = domain(multiplication(A,domain(B))),
file('KLE069+1.p',unknown),
[] ).
cnf(31,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('KLE069+1.p',unknown),
[] ).
cnf(39,plain,
addition(multiplication(domain(dollar_c2),domain(dollar_c2)),multiplication(domain(dollar_c2),domain(dollar_c1))) != domain(dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),21]),
[iquote('back_demod,3,demod,21')] ).
cnf(61,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(89,plain,
addition(A,multiplication(A,domain(B))) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[61,21]),17,17])]),
[iquote('para_from,61.1.1,20.1.1.2,demod,17,17,flip.1')] ).
cnf(102,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)],[22,61]),19,19])]),
[iquote('para_into,22.1.1.1,61.1.1,demod,19,19,flip.1')] ).
cnf(108,plain,
multiplication(domain(A),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[28]),102])]),
[iquote('back_demod,28,demod,102,flip.1')] ).
cnf(125,plain,
domain(domain(A)) = domain(A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[31,19]),19]),
[iquote('para_into,31.1.1.1,18.1.1,demod,19')] ).
cnf(130,plain,
multiplication(domain(A),domain(A)) = domain(A),
inference(para_from,[status(thm),theory(equality)],[125,108]),
[iquote('para_from,125.1.1,108.1.1.1')] ).
cnf(131,plain,
domain(dollar_c2) != domain(dollar_c2),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[39]),130,89]),
[iquote('back_demod,39,demod,130,89')] ).
cnf(132,plain,
$false,
inference(binary,[status(thm)],[131,4]),
[iquote('binary,131.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE069+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 06:26:21 EDT 2022
% 0.12/0.35 % CPUTime :
% 1.65/1.83 ----- Otter 3.3f, August 2004 -----
% 1.65/1.83 The process was started by sandbox2 on n009.cluster.edu,
% 1.65/1.83 Wed Jul 27 06:26:21 2022
% 1.65/1.83 The command was "./otter". The process ID is 18792.
% 1.65/1.83
% 1.65/1.83 set(prolog_style_variables).
% 1.65/1.83 set(auto).
% 1.65/1.83 dependent: set(auto1).
% 1.65/1.83 dependent: set(process_input).
% 1.65/1.83 dependent: clear(print_kept).
% 1.65/1.83 dependent: clear(print_new_demod).
% 1.65/1.83 dependent: clear(print_back_demod).
% 1.65/1.83 dependent: clear(print_back_sub).
% 1.65/1.83 dependent: set(control_memory).
% 1.65/1.83 dependent: assign(max_mem, 12000).
% 1.65/1.83 dependent: assign(pick_given_ratio, 4).
% 1.65/1.83 dependent: assign(stats_level, 1).
% 1.65/1.83 dependent: assign(max_seconds, 10800).
% 1.65/1.83 clear(print_given).
% 1.65/1.83
% 1.65/1.83 formula_list(usable).
% 1.65/1.83 all A (A=A).
% 1.65/1.83 all A B (addition(A,B)=addition(B,A)).
% 1.65/1.83 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.65/1.83 all A (addition(A,zero)=A).
% 1.65/1.83 all A (addition(A,A)=A).
% 1.65/1.83 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.65/1.83 all A (multiplication(A,one)=A).
% 1.65/1.83 all A (multiplication(one,A)=A).
% 1.65/1.83 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.65/1.83 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.65/1.83 all A (multiplication(A,zero)=zero).
% 1.65/1.83 all A (multiplication(zero,A)=zero).
% 1.65/1.83 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.65/1.83 all X0 (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0)).
% 1.65/1.83 all X0 X1 (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1)))).
% 1.65/1.83 all X0 (addition(domain(X0),one)=one).
% 1.65/1.83 domain(zero)=zero.
% 1.65/1.83 all X0 X1 (domain(addition(X0,X1))=addition(domain(X0),domain(X1))).
% 1.65/1.83 -(all X0 X1 (multiplication(domain(X0),addition(domain(X0),domain(X1)))=domain(X0))).
% 1.65/1.83 end_of_list.
% 1.65/1.83
% 1.65/1.83 -------> usable clausifies to:
% 1.65/1.83
% 1.65/1.83 list(usable).
% 1.65/1.83 0 [] A=A.
% 1.65/1.83 0 [] addition(A,B)=addition(B,A).
% 1.65/1.83 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.65/1.83 0 [] addition(A,zero)=A.
% 1.65/1.83 0 [] addition(A,A)=A.
% 1.65/1.83 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.65/1.83 0 [] multiplication(A,one)=A.
% 1.65/1.83 0 [] multiplication(one,A)=A.
% 1.65/1.83 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.65/1.83 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.65/1.83 0 [] multiplication(A,zero)=zero.
% 1.65/1.83 0 [] multiplication(zero,A)=zero.
% 1.65/1.83 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.65/1.83 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.65/1.83 0 [] addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0).
% 1.65/1.83 0 [] domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))).
% 1.65/1.83 0 [] addition(domain(X0),one)=one.
% 1.65/1.83 0 [] domain(zero)=zero.
% 1.65/1.83 0 [] domain(addition(X0,X1))=addition(domain(X0),domain(X1)).
% 1.65/1.83 0 [] multiplication(domain($c2),addition(domain($c2),domain($c1)))!=domain($c2).
% 1.65/1.83 end_of_list.
% 1.65/1.83
% 1.65/1.83 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.65/1.83
% 1.65/1.83 This is a Horn set with equality. The strategy will be
% 1.65/1.83 Knuth-Bendix and hyper_res, with positive clauses in
% 1.65/1.83 sos and nonpositive clauses in usable.
% 1.65/1.83
% 1.65/1.83 dependent: set(knuth_bendix).
% 1.65/1.83 dependent: set(anl_eq).
% 1.65/1.83 dependent: set(para_from).
% 1.65/1.83 dependent: set(para_into).
% 1.65/1.83 dependent: clear(para_from_right).
% 1.65/1.83 dependent: clear(para_into_right).
% 1.65/1.83 dependent: set(para_from_vars).
% 1.65/1.83 dependent: set(eq_units_both_ways).
% 1.65/1.83 dependent: set(dynamic_demod_all).
% 1.65/1.83 dependent: set(dynamic_demod).
% 1.65/1.83 dependent: set(order_eq).
% 1.65/1.83 dependent: set(back_demod).
% 1.65/1.83 dependent: set(lrpo).
% 1.65/1.83 dependent: set(hyper_res).
% 1.65/1.83 dependent: clear(order_hyper).
% 1.65/1.83
% 1.65/1.83 ------------> process usable:
% 1.65/1.83 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.65/1.83 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.65/1.83 ** KEPT (pick-wt=11): 3 [] multiplication(domain($c2),addition(domain($c2),domain($c1)))!=domain($c2).
% 1.65/1.83
% 1.65/1.83 ------------> process sos:
% 1.65/1.83 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.65/1.83 ** KEPT (pick-wt=7): 5 [] addition(A,B)=addition(B,A).
% 1.65/1.83 ** KEPT (pick-wt=11): 7 [copy,6,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.65/1.83 ---> New Demodulator: 8 [new_demod,7] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.65/1.83 ** KEPT (pick-wt=5): 9 [] addition(A,zero)=A.
% 1.65/1.83 ---> New Demodulator: 10 [new_demod,9] addition(A,zero)=A.
% 1.65/1.83 ** KEPT (pick-wt=5): 11 [] addition(A,A)=A.
% 1.65/1.83 ---> New Demodulator: 12 [new_demod,11] addition(A,A)=A.
% 1.65/1.83 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.65/1.83 ---> New Demodulator: 15 [new_demod,14] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.65/1.83 ** KEPT (pick-wt=5): 16 [] multiplication(A,one)=A.
% 1.65/1.83 ---> New Demodulator: 17 [new_demod,16] multiplication(A,one)=A.
% 1.65/1.83 ** KEPT (pick-wt=5): 18 [] multiplication(one,A)=A.
% 1.65/1.83 ---> New Demodulator: 19 [new_demod,18] multiplication(one,A)=A.
% 1.65/1.83 ** KEPT (pick-wt=13): 20 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.65/1.83 ---> New Demodulator: 21 [new_demod,20] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.65/1.83 ** KEPT (pick-wt=13): 22 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.65/1.83 ---> New Demodulator: 23 [new_demod,22] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.65/1.83 ** KEPT (pick-wt=5): 24 [] multiplication(A,zero)=zero.
% 1.65/1.83 ---> New Demodulator: 25 [new_demod,24] multiplication(A,zero)=zero.
% 1.65/1.83 ** KEPT (pick-wt=5): 26 [] multiplication(zero,A)=zero.
% 1.65/1.83 ---> New Demodulator: 27 [new_demod,26] multiplication(zero,A)=zero.
% 1.65/1.83 ** KEPT (pick-wt=11): 28 [] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 1.65/1.83 ---> New Demodulator: 29 [new_demod,28] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 1.65/1.83 ** KEPT (pick-wt=10): 31 [copy,30,flip.1] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 1.65/1.83 ---> New Demodulator: 32 [new_demod,31] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 1.65/1.83 ** KEPT (pick-wt=6): 33 [] addition(domain(A),one)=one.
% 1.65/1.83 ---> New Demodulator: 34 [new_demod,33] addition(domain(A),one)=one.
% 1.65/1.83 ** KEPT (pick-wt=4): 35 [] domain(zero)=zero.
% 1.65/1.83 ---> New Demodulator: 36 [new_demod,35] domain(zero)=zero.
% 1.65/1.83 ** KEPT (pick-wt=10): 37 [] domain(addition(A,B))=addition(domain(A),domain(B)).
% 1.65/1.83 ---> New Demodulator: 38 [new_demod,37] domain(addition(A,B))=addition(domain(A),domain(B)).
% 1.65/1.83 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.65/1.83 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] addition(A,B)=addition(B,A).
% 1.65/1.83 >>>> Starting back demodulation with 8.
% 1.65/1.83 >>>> Starting back demodulation with 10.
% 1.65/1.83 >>>> Starting back demodulation with 12.
% 1.65/1.83 >>>> Starting back demodulation with 15.
% 1.65/1.83 >>>> Starting back demodulation with 17.
% 1.65/1.83 >>>> Starting back demodulation with 19.
% 1.65/1.83 >>>> Starting back demodulation with 21.
% 1.65/1.83 >> back demodulating 3 with 21.
% 1.65/1.83 >>>> Starting back demodulation with 23.
% 1.65/1.83 >>>> Starting back demodulation with 25.
% 1.65/1.83 >>>> Starting back demodulation with 27.
% 1.65/1.83 >>>> Starting back demodulation with 29.
% 1.65/1.83 >>>> Starting back demodulation with 32.
% 1.65/1.83 >>>> Starting back demodulation with 34.
% 1.65/1.83 >>>> Starting back demodulation with 36.
% 1.65/1.83 >>>> Starting back demodulation with 38.
% 1.65/1.83
% 1.65/1.83 ======= end of input processing =======
% 1.65/1.83
% 1.65/1.83 =========== start of search ===========
% 1.65/1.83
% 1.65/1.83 -------- PROOF --------
% 1.65/1.83
% 1.65/1.83 ----> UNIT CONFLICT at 0.01 sec ----> 132 [binary,131.1,4.1] $F.
% 1.65/1.83
% 1.65/1.83 Length of proof is 9. Level of proof is 5.
% 1.65/1.83
% 1.65/1.83 ---------------- PROOF ----------------
% 1.65/1.83 % SZS status Theorem
% 1.65/1.83 % SZS output start Refutation
% See solution above
% 1.65/1.83 ------------ end of proof -------------
% 1.65/1.83
% 1.65/1.83
% 1.65/1.83 Search stopped by max_proofs option.
% 1.65/1.83
% 1.65/1.83
% 1.65/1.83 Search stopped by max_proofs option.
% 1.65/1.83
% 1.65/1.83 ============ end of search ============
% 1.65/1.83
% 1.65/1.83 -------------- statistics -------------
% 1.65/1.83 clauses given 32
% 1.65/1.83 clauses generated 354
% 1.65/1.83 clauses kept 95
% 1.65/1.83 clauses forward subsumed 290
% 1.65/1.83 clauses back subsumed 8
% 1.65/1.83 Kbytes malloced 1953
% 1.65/1.83
% 1.65/1.83 ----------- times (seconds) -----------
% 1.65/1.83 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.65/1.83 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.65/1.83 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.65/1.83
% 1.65/1.83 That finishes the proof of the theorem.
% 1.65/1.83
% 1.65/1.83 Process 18792 finished Wed Jul 27 06:26:22 2022
% 1.65/1.83 Otter interrupted
% 1.65/1.83 PROOF FOUND
%------------------------------------------------------------------------------