TSTP Solution File: KLE093+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE093+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 13:00:43 EDT 2022
% Result : Theorem 1.79s 1.98s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 30 ( 26 unt; 0 nHn; 7 RR)
% Number of literals : 34 ( 23 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE093+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE093+1.p',unknown),
[] ).
cnf(5,axiom,
domain(star(dollar_c1)) != one,
file('KLE093+1.p',unknown),
[] ).
cnf(7,axiom,
addition(A,B) = addition(B,A),
file('KLE093+1.p',unknown),
[] ).
cnf(8,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE093+1.p',unknown),
[] ).
cnf(10,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.1')] ).
cnf(13,axiom,
addition(A,A) = A,
file('KLE093+1.p',unknown),
[] ).
cnf(18,axiom,
multiplication(A,one) = A,
file('KLE093+1.p',unknown),
[] ).
cnf(21,axiom,
multiplication(one,A) = A,
file('KLE093+1.p',unknown),
[] ).
cnf(24,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE093+1.p',unknown),
[] ).
cnf(31,axiom,
le_q(addition(one,multiplication(star(A),A)),star(A)),
file('KLE093+1.p',unknown),
[] ).
cnf(32,axiom,
addition(A,multiplication(domain(A),A)) = multiplication(domain(A),A),
file('KLE093+1.p',unknown),
[] ).
cnf(37,axiom,
addition(domain(A),one) = one,
file('KLE093+1.p',unknown),
[] ).
cnf(41,axiom,
domain(addition(A,B)) = addition(domain(A),domain(B)),
file('KLE093+1.p',unknown),
[] ).
cnf(54,plain,
( addition(A,B) = A
| ~ le_q(B,A) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[7,1])]),
[iquote('para_into,7.1.1,1.2.1,flip.1')] ).
cnf(66,plain,
addition(A,addition(A,B)) = addition(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,13])]),
[iquote('para_into,9.1.1.1,13.1.1,flip.1')] ).
cnf(81,plain,
addition(one,domain(A)) = one,
inference(para_into,[status(thm),theory(equality)],[37,7]),
[iquote('para_into,37.1.1,7.1.1')] ).
cnf(134,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)],[24,81]),21,21])]),
[iquote('para_into,24.1.1.1,80.1.1,demod,21,21,flip.1')] ).
cnf(140,plain,
multiplication(domain(A),A) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[32]),134])]),
[iquote('back_demod,32,demod,134,flip.1')] ).
cnf(150,plain,
domain(one) = one,
inference(para_into,[status(thm),theory(equality)],[140,18]),
[iquote('para_into,140.1.1,18.1.1')] ).
cnf(196,plain,
addition(one,addition(multiplication(star(A),A),star(A))) = star(A),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[31,1]),10]),
[iquote('hyper,31,1,demod,10')] ).
cnf(795,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[66,2]),
[iquote('hyper,66,2')] ).
cnf(813,plain,
le_q(A,addition(B,A)),
inference(para_into,[status(thm),theory(equality)],[795,7]),
[iquote('para_into,795.1.2,7.1.1')] ).
cnf(816,plain,
le_q(A,addition(B,addition(C,A))),
inference(para_into,[status(thm),theory(equality)],[813,10]),
[iquote('para_into,813.1.2,9.1.1')] ).
cnf(829,plain,
( le_q(A,B)
| ~ le_q(addition(C,A),B) ),
inference(para_into,[status(thm),theory(equality)],[816,54]),
[iquote('para_into,816.1.2,54.1.1')] ).
cnf(1265,plain,
le_q(multiplication(star(A),A),star(A)),
inference(hyper,[status(thm)],[829,31]),
[iquote('hyper,829,31')] ).
cnf(1279,plain,
addition(multiplication(star(A),A),star(A)) = star(A),
inference(hyper,[status(thm)],[1265,1]),
[iquote('hyper,1265,1')] ).
cnf(1282,plain,
addition(one,star(A)) = star(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[196]),1279]),
[iquote('back_demod,196,demod,1279')] ).
cnf(1344,plain,
domain(star(A)) = one,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1282,41]),150,81]),
[iquote('para_from,1282.1.1,41.1.1.1,demod,150,81')] ).
cnf(1346,plain,
$false,
inference(binary,[status(thm)],[1344,5]),
[iquote('binary,1344.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE093+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n024.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 06:33:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.88 ----- Otter 3.3f, August 2004 -----
% 1.66/1.88 The process was started by sandbox2 on n024.cluster.edu,
% 1.66/1.88 Wed Jul 27 06:33:40 2022
% 1.66/1.88 The command was "./otter". The process ID is 9946.
% 1.66/1.88
% 1.66/1.88 set(prolog_style_variables).
% 1.66/1.88 set(auto).
% 1.66/1.88 dependent: set(auto1).
% 1.66/1.88 dependent: set(process_input).
% 1.66/1.88 dependent: clear(print_kept).
% 1.66/1.88 dependent: clear(print_new_demod).
% 1.66/1.88 dependent: clear(print_back_demod).
% 1.66/1.88 dependent: clear(print_back_sub).
% 1.66/1.88 dependent: set(control_memory).
% 1.66/1.88 dependent: assign(max_mem, 12000).
% 1.66/1.88 dependent: assign(pick_given_ratio, 4).
% 1.66/1.88 dependent: assign(stats_level, 1).
% 1.66/1.88 dependent: assign(max_seconds, 10800).
% 1.66/1.88 clear(print_given).
% 1.66/1.88
% 1.66/1.88 formula_list(usable).
% 1.66/1.88 all A (A=A).
% 1.66/1.88 all A B (addition(A,B)=addition(B,A)).
% 1.66/1.88 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.66/1.88 all A (addition(A,zero)=A).
% 1.66/1.88 all A (addition(A,A)=A).
% 1.66/1.88 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.66/1.88 all A (multiplication(A,one)=A).
% 1.66/1.88 all A (multiplication(one,A)=A).
% 1.66/1.88 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.66/1.88 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.66/1.88 all A (multiplication(A,zero)=zero).
% 1.66/1.88 all A (multiplication(zero,A)=zero).
% 1.66/1.88 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.66/1.88 all A le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.66/1.88 all A le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.66/1.88 all A B C (le_q(addition(multiplication(A,B),C),B)->le_q(multiplication(star(A),C),B)).
% 1.66/1.88 all A B C (le_q(addition(multiplication(A,B),C),A)->le_q(multiplication(C,star(B)),A)).
% 1.66/1.88 all X0 (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0)).
% 1.66/1.88 all X0 X1 (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1)))).
% 1.66/1.88 all X0 (addition(domain(X0),one)=one).
% 1.66/1.88 domain(zero)=zero.
% 1.66/1.88 all X0 X1 (domain(addition(X0,X1))=addition(domain(X0),domain(X1))).
% 1.66/1.88 -(all X0 (domain(star(X0))=one)).
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 -------> usable clausifies to:
% 1.66/1.88
% 1.66/1.88 list(usable).
% 1.66/1.88 0 [] A=A.
% 1.66/1.88 0 [] addition(A,B)=addition(B,A).
% 1.66/1.88 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.66/1.88 0 [] addition(A,zero)=A.
% 1.66/1.88 0 [] addition(A,A)=A.
% 1.66/1.88 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.66/1.88 0 [] multiplication(A,one)=A.
% 1.66/1.88 0 [] multiplication(one,A)=A.
% 1.66/1.88 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.66/1.88 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.66/1.88 0 [] multiplication(A,zero)=zero.
% 1.66/1.88 0 [] multiplication(zero,A)=zero.
% 1.66/1.88 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.66/1.88 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.66/1.88 0 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.66/1.88 0 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.66/1.88 0 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.66/1.88 0 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.66/1.88 0 [] addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0).
% 1.66/1.88 0 [] domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))).
% 1.66/1.88 0 [] addition(domain(X0),one)=one.
% 1.66/1.88 0 [] domain(zero)=zero.
% 1.66/1.88 0 [] domain(addition(X0,X1))=addition(domain(X0),domain(X1)).
% 1.66/1.88 0 [] domain(star($c1))!=one.
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.66/1.88
% 1.66/1.88 This is a Horn set with equality. The strategy will be
% 1.66/1.88 Knuth-Bendix and hyper_res, with positive clauses in
% 1.66/1.88 sos and nonpositive clauses in usable.
% 1.66/1.88
% 1.66/1.88 dependent: set(knuth_bendix).
% 1.66/1.88 dependent: set(anl_eq).
% 1.66/1.88 dependent: set(para_from).
% 1.66/1.88 dependent: set(para_into).
% 1.66/1.88 dependent: clear(para_from_right).
% 1.66/1.88 dependent: clear(para_into_right).
% 1.66/1.88 dependent: set(para_from_vars).
% 1.66/1.88 dependent: set(eq_units_both_ways).
% 1.66/1.88 dependent: set(dynamic_demod_all).
% 1.66/1.88 dependent: set(dynamic_demod).
% 1.66/1.88 dependent: set(order_eq).
% 1.66/1.88 dependent: set(back_demod).
% 1.66/1.88 dependent: set(lrpo).
% 1.66/1.88 dependent: set(hyper_res).
% 1.66/1.88 dependent: clear(order_hyper).
% 1.66/1.88
% 1.66/1.88 ------------> process usable:
% 1.66/1.88 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.66/1.88 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.66/1.88 ** KEPT (pick-wt=13): 3 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.79/1.98 ** KEPT (pick-wt=13): 4 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.79/1.98 ** KEPT (pick-wt=5): 5 [] domain(star($c1))!=one.
% 1.79/1.98
% 1.79/1.98 ------------> process sos:
% 1.79/1.98 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.79/1.98 ** KEPT (pick-wt=7): 7 [] addition(A,B)=addition(B,A).
% 1.79/1.98 ** KEPT (pick-wt=11): 9 [copy,8,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.79/1.98 ---> New Demodulator: 10 [new_demod,9] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.79/1.98 ** KEPT (pick-wt=5): 11 [] addition(A,zero)=A.
% 1.79/1.98 ---> New Demodulator: 12 [new_demod,11] addition(A,zero)=A.
% 1.79/1.98 ** KEPT (pick-wt=5): 13 [] addition(A,A)=A.
% 1.79/1.98 ---> New Demodulator: 14 [new_demod,13] addition(A,A)=A.
% 1.79/1.98 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.79/1.98 ---> New Demodulator: 17 [new_demod,16] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.79/1.98 ** KEPT (pick-wt=5): 18 [] multiplication(A,one)=A.
% 1.79/1.98 ---> New Demodulator: 19 [new_demod,18] multiplication(A,one)=A.
% 1.79/1.98 ** KEPT (pick-wt=5): 20 [] multiplication(one,A)=A.
% 1.79/1.98 ---> New Demodulator: 21 [new_demod,20] multiplication(one,A)=A.
% 1.79/1.98 ** KEPT (pick-wt=13): 22 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.79/1.98 ---> New Demodulator: 23 [new_demod,22] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.79/1.98 ** KEPT (pick-wt=13): 24 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.79/1.98 ---> New Demodulator: 25 [new_demod,24] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.79/1.98 ** KEPT (pick-wt=5): 26 [] multiplication(A,zero)=zero.
% 1.79/1.98 ---> New Demodulator: 27 [new_demod,26] multiplication(A,zero)=zero.
% 1.79/1.98 ** KEPT (pick-wt=5): 28 [] multiplication(zero,A)=zero.
% 1.79/1.98 ---> New Demodulator: 29 [new_demod,28] multiplication(zero,A)=zero.
% 1.79/1.98 ** KEPT (pick-wt=9): 30 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.79/1.98 ** KEPT (pick-wt=9): 31 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.79/1.98 ** KEPT (pick-wt=11): 32 [] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 1.79/1.98 ---> New Demodulator: 33 [new_demod,32] addition(A,multiplication(domain(A),A))=multiplication(domain(A),A).
% 1.79/1.98 ** KEPT (pick-wt=10): 35 [copy,34,flip.1] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 1.79/1.98 ---> New Demodulator: 36 [new_demod,35] domain(multiplication(A,domain(B)))=domain(multiplication(A,B)).
% 1.79/1.98 ** KEPT (pick-wt=6): 37 [] addition(domain(A),one)=one.
% 1.79/1.98 ---> New Demodulator: 38 [new_demod,37] addition(domain(A),one)=one.
% 1.79/1.98 ** KEPT (pick-wt=4): 39 [] domain(zero)=zero.
% 1.79/1.98 ---> New Demodulator: 40 [new_demod,39] domain(zero)=zero.
% 1.79/1.98 ** KEPT (pick-wt=10): 41 [] domain(addition(A,B))=addition(domain(A),domain(B)).
% 1.79/1.98 ---> New Demodulator: 42 [new_demod,41] domain(addition(A,B))=addition(domain(A),domain(B)).
% 1.79/1.98 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.79/1.98 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] addition(A,B)=addition(B,A).
% 1.79/1.98 >>>> Starting back demodulation with 10.
% 1.79/1.98 >>>> Starting back demodulation with 12.
% 1.79/1.98 >>>> Starting back demodulation with 14.
% 1.79/1.98 >>>> Starting back demodulation with 17.
% 1.79/1.98 >>>> Starting back demodulation with 19.
% 1.79/1.98 >>>> Starting back demodulation with 21.
% 1.79/1.98 >>>> Starting back demodulation with 23.
% 1.79/1.98 >>>> Starting back demodulation with 25.
% 1.79/1.98 >>>> Starting back demodulation with 27.
% 1.79/1.98 >>>> Starting back demodulation with 29.
% 1.79/1.98 >>>> Starting back demodulation with 33.
% 1.79/1.98 >>>> Starting back demodulation with 36.
% 1.79/1.98 >>>> Starting back demodulation with 38.
% 1.79/1.98 >>>> Starting back demodulation with 40.
% 1.79/1.98 >>>> Starting back demodulation with 42.
% 1.79/1.98
% 1.79/1.98 ======= end of input processing =======
% 1.79/1.98
% 1.79/1.98 =========== start of search ===========
% 1.79/1.98
% 1.79/1.98 -------- PROOF --------
% 1.79/1.98
% 1.79/1.98 ----> UNIT CONFLICT at 0.10 sec ----> 1346 [binary,1344.1,5.1] $F.
% 1.79/1.98
% 1.79/1.98 Length of proof is 16. Level of proof is 10.
% 1.79/1.98
% 1.79/1.98 ---------------- PROOF ----------------
% 1.79/1.98 % SZS status Theorem
% 1.79/1.98 % SZS output start Refutation
% See solution above
% 1.79/1.98 ------------ end of proof -------------
% 1.79/1.98
% 1.79/1.98
% 1.79/1.98 Search stopped by max_proofs option.
% 1.79/1.98
% 1.79/1.98
% 1.79/1.98 Search stopped by max_proofs option.
% 1.79/1.98
% 1.79/1.98 ============ end of search ============
% 1.79/1.98
% 1.79/1.98 -------------- statistics -------------
% 1.79/1.98 clauses given 154
% 1.79/1.98 clauses generated 5260
% 1.79/1.98 clauses kept 1198
% 1.79/1.98 clauses forward subsumed 4192
% 1.79/1.98 clauses back subsumed 223
% 1.79/1.98 Kbytes malloced 3906
% 1.79/1.98
% 1.79/1.98 ----------- times (seconds) -----------
% 1.79/1.98 user CPU time 0.10 (0 hr, 0 min, 0 sec)
% 1.79/1.98 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.79/1.98 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.79/1.98
% 1.79/1.98 That finishes the proof of the theorem.
% 1.79/1.98
% 1.79/1.98 Process 9946 finished Wed Jul 27 06:33:41 2022
% 1.79/1.98 Otter interrupted
% 1.79/1.98 PROOF FOUND
%------------------------------------------------------------------------------