TSTP Solution File: KLE071+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE071+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 13:00:40 EDT 2022
% Result : Theorem 1.97s 2.14s
% Output : Refutation 1.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 27 ( 27 unt; 0 nHn; 6 RR)
% Number of literals : 27 ( 26 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
addition(domain(dollar_c3),multiplication(domain(dollar_c2),domain(dollar_c1))) != multiplication(addition(domain(dollar_c3),domain(dollar_c2)),addition(domain(dollar_c3),domain(dollar_c1))),
file('KLE071+1.p',unknown),
[] ).
cnf(4,plain,
multiplication(addition(domain(dollar_c3),domain(dollar_c2)),addition(domain(dollar_c3),domain(dollar_c1))) != addition(domain(dollar_c3),multiplication(domain(dollar_c2),domain(dollar_c1))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(5,axiom,
A = A,
file('KLE071+1.p',unknown),
[] ).
cnf(6,axiom,
addition(A,B) = addition(B,A),
file('KLE071+1.p',unknown),
[] ).
cnf(7,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE071+1.p',unknown),
[] ).
cnf(9,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(18,axiom,
multiplication(A,one) = A,
file('KLE071+1.p',unknown),
[] ).
cnf(20,axiom,
multiplication(one,A) = A,
file('KLE071+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE071+1.p',unknown),
[] ).
cnf(24,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE071+1.p',unknown),
[] ).
cnf(29,axiom,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
file('KLE071+1.p',unknown),
[] ).
cnf(31,axiom,
domain(multiplication(A,B)) = domain(multiplication(A,domain(B))),
file('KLE071+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)],[31])]),
[iquote('copy,31,flip.1')] ).
cnf(34,axiom,
addition(domain(A),one) = one,
file('KLE071+1.p',unknown),
[] ).
cnf(40,plain,
addition(multiplication(domain(dollar_c3),domain(dollar_c3)),addition(multiplication(domain(dollar_c2),domain(dollar_c3)),addition(multiplication(domain(dollar_c3),domain(dollar_c1)),multiplication(domain(dollar_c2),domain(dollar_c1))))) != addition(domain(dollar_c3),multiplication(domain(dollar_c2),domain(dollar_c1))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),22,24,24,9]),
[iquote('back_demod,4,demod,22,24,24,9')] ).
cnf(52,plain,
addition(A,addition(B,C)) = addition(B,addition(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,6]),9]),
[iquote('para_into,8.1.1.1,6.1.1,demod,9')] ).
cnf(62,plain,
addition(one,domain(A)) = one,
inference(para_into,[status(thm),theory(equality)],[34,6]),
[iquote('para_into,34.1.1,6.1.1')] ).
cnf(86,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)],[22,34]),18,18])]),
[iquote('para_into,21.1.1.2,34.1.1,demod,18,18,flip.1')] ).
cnf(103,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)],[24,62]),20,20])]),
[iquote('para_into,23.1.1.1,62.1.1,demod,20,20,flip.1')] ).
cnf(109,plain,
multiplication(domain(A),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[29]),103])]),
[iquote('back_demod,29,demod,103,flip.1')] ).
cnf(126,plain,
domain(domain(A)) = domain(A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,20]),20]),
[iquote('para_into,32.1.1.1,19.1.1,demod,20')] ).
cnf(131,plain,
multiplication(domain(A),domain(A)) = domain(A),
inference(para_from,[status(thm),theory(equality)],[126,109]),
[iquote('para_from,126.1.1,109.1.1.1')] ).
cnf(132,plain,
addition(domain(dollar_c3),addition(multiplication(domain(dollar_c2),domain(dollar_c3)),addition(multiplication(domain(dollar_c3),domain(dollar_c1)),multiplication(domain(dollar_c2),domain(dollar_c1))))) != addition(domain(dollar_c3),multiplication(domain(dollar_c2),domain(dollar_c1))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[40]),131]),
[iquote('back_demod,40,demod,131')] ).
cnf(313,plain,
addition(A,addition(multiplication(A,domain(B)),C)) = addition(A,C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[86,52]),24,9,86]),
[iquote('para_into,85.1.1,52.1.1,demod,24,9,86')] ).
cnf(432,plain,
addition(A,addition(multiplication(domain(B),A),C)) = addition(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[103,9])]),
[iquote('para_from,102.1.1,8.1.1.1,flip.1')] ).
cnf(434,plain,
addition(domain(dollar_c3),multiplication(domain(dollar_c2),domain(dollar_c1))) != addition(domain(dollar_c3),multiplication(domain(dollar_c2),domain(dollar_c1))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[132]),432,313]),
[iquote('back_demod,132,demod,432,313')] ).
cnf(435,plain,
$false,
inference(binary,[status(thm)],[434,5]),
[iquote('binary,434.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KLE071+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % 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 06:27:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.93/2.12 ----- Otter 3.3f, August 2004 -----
% 1.93/2.12 The process was started by sandbox on n013.cluster.edu,
% 1.93/2.12 Wed Jul 27 06:27:15 2022
% 1.93/2.12 The command was "./otter". The process ID is 28861.
% 1.93/2.12
% 1.93/2.12 set(prolog_style_variables).
% 1.93/2.12 set(auto).
% 1.93/2.12 dependent: set(auto1).
% 1.93/2.12 dependent: set(process_input).
% 1.93/2.12 dependent: clear(print_kept).
% 1.93/2.12 dependent: clear(print_new_demod).
% 1.93/2.12 dependent: clear(print_back_demod).
% 1.93/2.12 dependent: clear(print_back_sub).
% 1.93/2.12 dependent: set(control_memory).
% 1.93/2.12 dependent: assign(max_mem, 12000).
% 1.93/2.12 dependent: assign(pick_given_ratio, 4).
% 1.93/2.12 dependent: assign(stats_level, 1).
% 1.93/2.12 dependent: assign(max_seconds, 10800).
% 1.93/2.12 clear(print_given).
% 1.93/2.12
% 1.93/2.12 formula_list(usable).
% 1.93/2.12 all A (A=A).
% 1.93/2.12 all A B (addition(A,B)=addition(B,A)).
% 1.93/2.12 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.93/2.12 all A (addition(A,zero)=A).
% 1.93/2.12 all A (addition(A,A)=A).
% 1.93/2.12 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.93/2.12 all A (multiplication(A,one)=A).
% 1.93/2.12 all A (multiplication(one,A)=A).
% 1.93/2.12 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.93/2.12 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.93/2.12 all A (multiplication(A,zero)=zero).
% 1.93/2.12 all A (multiplication(zero,A)=zero).
% 1.93/2.12 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.93/2.12 all X0 (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0)).
% 1.93/2.12 all X0 X1 (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1)))).
% 1.93/2.12 all X0 (addition(domain(X0),one)=one).
% 1.93/2.12 domain(zero)=zero.
% 1.93/2.12 all X0 X1 (domain(addition(X0,X1))=addition(domain(X0),domain(X1))).
% 1.93/2.12 -(all X0 X1 X2 (addition(domain(X0),multiplication(domain(X1),domain(X2)))=multiplication(addition(domain(X0),domain(X1)),addition(domain(X0),domain(X2))))).
% 1.93/2.12 end_of_list.
% 1.93/2.12
% 1.93/2.12 -------> usable clausifies to:
% 1.93/2.12
% 1.93/2.12 list(usable).
% 1.93/2.12 0 [] A=A.
% 1.93/2.12 0 [] addition(A,B)=addition(B,A).
% 1.93/2.12 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.93/2.12 0 [] addition(A,zero)=A.
% 1.93/2.12 0 [] addition(A,A)=A.
% 1.93/2.12 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.93/2.12 0 [] multiplication(A,one)=A.
% 1.93/2.12 0 [] multiplication(one,A)=A.
% 1.93/2.12 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.93/2.12 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.93/2.12 0 [] multiplication(A,zero)=zero.
% 1.93/2.12 0 [] multiplication(zero,A)=zero.
% 1.93/2.12 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.93/2.12 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.93/2.12 0 [] addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0).
% 1.93/2.12 0 [] domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))).
% 1.93/2.12 0 [] addition(domain(X0),one)=one.
% 1.93/2.12 0 [] domain(zero)=zero.
% 1.93/2.12 0 [] domain(addition(X0,X1))=addition(domain(X0),domain(X1)).
% 1.93/2.12 0 [] addition(domain($c3),multiplication(domain($c2),domain($c1)))!=multiplication(addition(domain($c3),domain($c2)),addition(domain($c3),domain($c1))).
% 1.93/2.12 end_of_list.
% 1.93/2.12
% 1.93/2.12 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.93/2.12
% 1.93/2.12 This is a Horn set with equality. The strategy will be
% 1.93/2.12 Knuth-Bendix and hyper_res, with positive clauses in
% 1.93/2.12 sos and nonpositive clauses in usable.
% 1.93/2.12
% 1.93/2.12 dependent: set(knuth_bendix).
% 1.93/2.12 dependent: set(anl_eq).
% 1.93/2.12 dependent: set(para_from).
% 1.93/2.12 dependent: set(para_into).
% 1.93/2.12 dependent: clear(para_from_right).
% 1.93/2.12 dependent: clear(para_into_right).
% 1.93/2.12 dependent: set(para_from_vars).
% 1.93/2.12 dependent: set(eq_units_both_ways).
% 1.93/2.12 dependent: set(dynamic_demod_all).
% 1.93/2.12 dependent: set(dynamic_demod).
% 1.93/2.12 dependent: set(order_eq).
% 1.93/2.12 dependent: set(back_demod).
% 1.93/2.12 dependent: set(lrpo).
% 1.93/2.12 dependent: set(hyper_res).
% 1.93/2.12 dependent: clear(order_hyper).
% 1.93/2.12
% 1.93/2.12 ------------> process usable:
% 1.93/2.12 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.93/2.12 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.93/2.12 ** KEPT (pick-wt=20): 4 [copy,3,flip.1] multiplication(addition(domain($c3),domain($c2)),addition(domain($c3),domain($c1)))!=addition(domain($c3),multiplication(domain($c2),domain($c1))).
% 1.93/2.12
% 1.93/2.12 ------------> process sos:
% 1.93/2.12 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.93/2.12 ** KEPT (pick-wt=7): 6 [] addition(A,B)=addition(B,A).
% 1.93/2.12 ** KEPT (pick-wt=11): 8 [copy,7,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.93/2.12 ---> New Demodulator: 9 [new_demod,8] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.97/2.14 ** KEPT (pick-wt=5): 10 [] addition(A,zero)=A.
% 1.97/2.14 ---> New Demodulator: 11 [new_demod,10] addition(A,zero)=A.
% 1.97/2.14 ** KEPT (pick-wt=5): 12 [] addition(A,A)=A.
% 1.97/2.14 ---> New Demodulator: 13 [new_demod,12] addition(A,A)=A.
% 1.97/2.14 ** KEPT (pick-wt=11): 15 [copy,14,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.97/2.14 ---> New Demodulator: 16 [new_demod,15] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.97/2.14 ** KEPT (pick-wt=5): 17 [] multiplication(A,one)=A.
% 1.97/2.14 ---> New Demodulator: 18 [new_demod,17] multiplication(A,one)=A.
% 1.97/2.14 ** KEPT (pick-wt=5): 19 [] multiplication(one,A)=A.
% 1.97/2.14 ---> New Demodulator: 20 [new_demod,19] multiplication(one,A)=A.
% 1.97/2.14 ** KEPT (pick-wt=13): 21 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.97/2.14 ---> New Demodulator: 22 [new_demod,21] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.97/2.14 ** KEPT (pick-wt=13): 23 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.97/2.14 ---> New Demodulator: 24 [new_demod,23] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.97/2.14 ** KEPT (pick-wt=5): 25 [] multiplication(A,zero)=zero.
% 1.97/2.14 ---> New Demodulator: 26 [new_demod,25] multiplication(A,zero)=zero.
% 1.97/2.14 ** KEPT (pick-wt=5): 27 [] multiplication(zero,A)=zero.
% 1.97/2.14 ---> New Demodulator: 28 [new_demod,27] multiplication(zero,A)=zero.
% 1.97/2.14 ** KEPT (pick-wt=11): 29 [] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 1.97/2.14 ---> New Demodulator: 30 [new_demod,29] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 1.97/2.14 ** KEPT (pick-wt=10): 32 [copy,31,flip.1] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 1.97/2.14 ---> New Demodulator: 33 [new_demod,32] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 1.97/2.14 ** KEPT (pick-wt=6): 34 [] addition(domain(A),one)=one.
% 1.97/2.14 ---> New Demodulator: 35 [new_demod,34] addition(domain(A),one)=one.
% 1.97/2.14 ** KEPT (pick-wt=4): 36 [] domain(zero)=zero.
% 1.97/2.14 ---> New Demodulator: 37 [new_demod,36] domain(zero)=zero.
% 1.97/2.14 ** KEPT (pick-wt=10): 38 [] domain(addition(A,B))=addition(domain(A),domain(B)).
% 1.97/2.14 ---> New Demodulator: 39 [new_demod,38] domain(addition(A,B))=addition(domain(A),domain(B)).
% 1.97/2.14 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.97/2.14 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] addition(A,B)=addition(B,A).
% 1.97/2.14 >>>> Starting back demodulation with 9.
% 1.97/2.14 >>>> Starting back demodulation with 11.
% 1.97/2.14 >>>> Starting back demodulation with 13.
% 1.97/2.14 >>>> Starting back demodulation with 16.
% 1.97/2.14 >>>> Starting back demodulation with 18.
% 1.97/2.14 >>>> Starting back demodulation with 20.
% 1.97/2.14 >>>> Starting back demodulation with 22.
% 1.97/2.14 >> back demodulating 4 with 22.
% 1.97/2.14 >>>> Starting back demodulation with 24.
% 1.97/2.14 >>>> Starting back demodulation with 26.
% 1.97/2.14 >>>> Starting back demodulation with 28.
% 1.97/2.14 >>>> Starting back demodulation with 30.
% 1.97/2.14 >>>> Starting back demodulation with 33.
% 1.97/2.14 >>>> Starting back demodulation with 35.
% 1.97/2.14 >>>> Starting back demodulation with 37.
% 1.97/2.14 >>>> Starting back demodulation with 39.
% 1.97/2.14
% 1.97/2.14 ======= end of input processing =======
% 1.97/2.14
% 1.97/2.14 =========== start of search ===========
% 1.97/2.14
% 1.97/2.14 -------- PROOF --------
% 1.97/2.14
% 1.97/2.14 ----> UNIT CONFLICT at 0.02 sec ----> 435 [binary,434.1,5.1] $F.
% 1.97/2.14
% 1.97/2.14 Length of proof is 15. Level of proof is 6.
% 1.97/2.14
% 1.97/2.14 ---------------- PROOF ----------------
% 1.97/2.14 % SZS status Theorem
% 1.97/2.14 % SZS output start Refutation
% See solution above
% 1.97/2.14 ------------ end of proof -------------
% 1.97/2.14
% 1.97/2.14
% 1.97/2.14 Search stopped by max_proofs option.
% 1.97/2.14
% 1.97/2.14
% 1.97/2.14 Search stopped by max_proofs option.
% 1.97/2.14
% 1.97/2.14 ============ end of search ============
% 1.97/2.14
% 1.97/2.14 -------------- statistics -------------
% 1.97/2.14 clauses given 62
% 1.97/2.14 clauses generated 1486
% 1.97/2.14 clauses kept 371
% 1.97/2.14 clauses forward subsumed 1159
% 1.97/2.14 clauses back subsumed 19
% 1.97/2.14 Kbytes malloced 1953
% 1.97/2.14
% 1.97/2.14 ----------- times (seconds) -----------
% 1.97/2.14 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.97/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.97/2.14 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.97/2.14
% 1.97/2.14 That finishes the proof of the theorem.
% 1.97/2.14
% 1.97/2.14 Process 28861 finished Wed Jul 27 06:27:16 2022
% 1.97/2.14 Otter interrupted
% 1.97/2.14 PROOF FOUND
%------------------------------------------------------------------------------