TSTP Solution File: KLE040+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE040+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:00:35 EDT 2022
% Result : Theorem 2.96s 3.15s
% Output : Refutation 2.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 22 unt; 0 nHn; 10 RR)
% Number of literals : 44 ( 17 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 59 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE040+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE040+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ le_q(addition(multiplication(A,B),C),A)
| le_q(multiplication(C,star(B)),A) ),
file('KLE040+1.p',unknown),
[] ).
cnf(5,axiom,
multiplication(star(dollar_c1),star(dollar_c1)) != star(dollar_c1),
file('KLE040+1.p',unknown),
[] ).
cnf(7,axiom,
addition(A,B) = addition(B,A),
file('KLE040+1.p',unknown),
[] ).
cnf(8,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE040+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('KLE040+1.p',unknown),
[] ).
cnf(19,axiom,
multiplication(A,one) = A,
file('KLE040+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE040+1.p',unknown),
[] ).
cnf(31,axiom,
le_q(addition(one,multiplication(star(A),A)),star(A)),
file('KLE040+1.p',unknown),
[] ).
cnf(38,plain,
le_q(A,A),
inference(hyper,[status(thm)],[13,2]),
[iquote('hyper,13,2')] ).
cnf(43,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(44,plain,
( ~ le_q(addition(A,multiplication(B,C)),B)
| le_q(multiplication(A,star(C)),B) ),
inference(para_from,[status(thm),theory(equality)],[7,4]),
[iquote('para_from,7.1.1,4.1.1')] ).
cnf(57,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(102,plain,
( addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,C)
| ~ le_q(B,C) ),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,1])]),
[iquote('para_into,22.1.1.2,1.2.1,flip.1')] ).
cnf(110,plain,
( A = B
| ~ le_q(A,B)
| ~ le_q(B,A) ),
inference(para_into,[status(thm),theory(equality)],[43,1]),
[iquote('para_into,43.1.1,1.2.1')] ).
cnf(189,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(292,plain,
( ~ le_q(A,B)
| le_q(multiplication(A,star(C)),B)
| ~ le_q(multiplication(B,C),A) ),
inference(para_into,[status(thm),theory(equality)],[44,43]),
[iquote('para_into,44.1.1,43.1.1')] ).
cnf(485,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[57,2]),
[iquote('hyper,57,2')] ).
cnf(511,plain,
le_q(A,addition(B,A)),
inference(para_into,[status(thm),theory(equality)],[485,7]),
[iquote('para_into,485.1.2,7.1.1')] ).
cnf(513,plain,
le_q(A,addition(B,addition(C,A))),
inference(para_into,[status(thm),theory(equality)],[511,10]),
[iquote('para_into,511.1.2,9.1.1')] ).
cnf(524,plain,
( le_q(A,B)
| ~ le_q(addition(C,A),B) ),
inference(para_into,[status(thm),theory(equality)],[513,43]),
[iquote('para_into,513.1.2,43.1.1')] ).
cnf(620,plain,
le_q(multiplication(star(A),A),star(A)),
inference(hyper,[status(thm)],[524,31]),
[iquote('hyper,524,31')] ).
cnf(631,plain,
addition(multiplication(star(A),A),star(A)) = star(A),
inference(hyper,[status(thm)],[620,1]),
[iquote('hyper,620,1')] ).
cnf(634,plain,
addition(one,star(A)) = star(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[189]),631]),
[iquote('back_demod,189,demod,631')] ).
cnf(650,plain,
le_q(one,star(A)),
inference(hyper,[status(thm)],[634,2]),
[iquote('hyper,634,2')] ).
cnf(2303,plain,
( le_q(multiplication(A,B),multiplication(A,C))
| ~ le_q(B,C) ),
inference(para_from,[status(thm),theory(equality)],[102,485]),
[iquote('para_from,102.1.1,485.1.2')] ).
cnf(3505,plain,
le_q(A,multiplication(A,star(B))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2303,650]),19]),
[iquote('hyper,2303,650,demod,19')] ).
cnf(4017,plain,
le_q(multiplication(star(A),star(A)),star(A)),
inference(hyper,[status(thm)],[292,38,620]),
[iquote('hyper,292,38,620')] ).
cnf(4022,plain,
multiplication(star(A),star(A)) = star(A),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[4017,110,3505])]),
[iquote('hyper,4017,110,3505,flip.1')] ).
cnf(4024,plain,
$false,
inference(binary,[status(thm)],[4022,5]),
[iquote('binary,4022.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : KLE040+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 06:34:53 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.96/2.12 ----- Otter 3.3f, August 2004 -----
% 1.96/2.12 The process was started by sandbox on n020.cluster.edu,
% 1.96/2.12 Wed Jul 27 06:34:53 2022
% 1.96/2.12 The command was "./otter". The process ID is 27247.
% 1.96/2.12
% 1.96/2.12 set(prolog_style_variables).
% 1.96/2.12 set(auto).
% 1.96/2.12 dependent: set(auto1).
% 1.96/2.12 dependent: set(process_input).
% 1.96/2.12 dependent: clear(print_kept).
% 1.96/2.12 dependent: clear(print_new_demod).
% 1.96/2.12 dependent: clear(print_back_demod).
% 1.96/2.12 dependent: clear(print_back_sub).
% 1.96/2.12 dependent: set(control_memory).
% 1.96/2.12 dependent: assign(max_mem, 12000).
% 1.96/2.12 dependent: assign(pick_given_ratio, 4).
% 1.96/2.12 dependent: assign(stats_level, 1).
% 1.96/2.12 dependent: assign(max_seconds, 10800).
% 1.96/2.12 clear(print_given).
% 1.96/2.12
% 1.96/2.12 formula_list(usable).
% 1.96/2.12 all A (A=A).
% 1.96/2.12 all A B (addition(A,B)=addition(B,A)).
% 1.96/2.12 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.96/2.12 all A (addition(A,zero)=A).
% 1.96/2.12 all A (addition(A,A)=A).
% 1.96/2.12 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.96/2.12 all A (multiplication(A,one)=A).
% 1.96/2.12 all A (multiplication(one,A)=A).
% 1.96/2.12 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.96/2.12 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.96/2.12 all A (multiplication(A,zero)=zero).
% 1.96/2.12 all A (multiplication(zero,A)=zero).
% 1.96/2.12 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.96/2.12 all A le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.96/2.12 all A le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.96/2.12 all A B C (le_q(addition(multiplication(A,B),C),B)->le_q(multiplication(star(A),C),B)).
% 1.96/2.12 all A B C (le_q(addition(multiplication(A,B),C),A)->le_q(multiplication(C,star(B)),A)).
% 1.96/2.12 -(all X0 (multiplication(star(X0),star(X0))=star(X0))).
% 1.96/2.12 end_of_list.
% 1.96/2.12
% 1.96/2.12 -------> usable clausifies to:
% 1.96/2.12
% 1.96/2.12 list(usable).
% 1.96/2.12 0 [] A=A.
% 1.96/2.12 0 [] addition(A,B)=addition(B,A).
% 1.96/2.12 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.96/2.12 0 [] addition(A,zero)=A.
% 1.96/2.12 0 [] addition(A,A)=A.
% 1.96/2.12 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.96/2.12 0 [] multiplication(A,one)=A.
% 1.96/2.12 0 [] multiplication(one,A)=A.
% 1.96/2.12 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.96/2.12 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.96/2.12 0 [] multiplication(A,zero)=zero.
% 1.96/2.12 0 [] multiplication(zero,A)=zero.
% 1.96/2.12 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.96/2.12 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.96/2.12 0 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.96/2.12 0 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.96/2.12 0 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.96/2.12 0 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.96/2.12 0 [] multiplication(star($c1),star($c1))!=star($c1).
% 1.96/2.12 end_of_list.
% 1.96/2.12
% 1.96/2.12 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.96/2.12
% 1.96/2.12 This is a Horn set with equality. The strategy will be
% 1.96/2.12 Knuth-Bendix and hyper_res, with positive clauses in
% 1.96/2.12 sos and nonpositive clauses in usable.
% 1.96/2.12
% 1.96/2.12 dependent: set(knuth_bendix).
% 1.96/2.12 dependent: set(anl_eq).
% 1.96/2.12 dependent: set(para_from).
% 1.96/2.12 dependent: set(para_into).
% 1.96/2.12 dependent: clear(para_from_right).
% 1.96/2.12 dependent: clear(para_into_right).
% 1.96/2.12 dependent: set(para_from_vars).
% 1.96/2.12 dependent: set(eq_units_both_ways).
% 1.96/2.12 dependent: set(dynamic_demod_all).
% 1.96/2.12 dependent: set(dynamic_demod).
% 1.96/2.12 dependent: set(order_eq).
% 1.96/2.12 dependent: set(back_demod).
% 1.96/2.12 dependent: set(lrpo).
% 1.96/2.12 dependent: set(hyper_res).
% 1.96/2.12 dependent: clear(order_hyper).
% 1.96/2.12
% 1.96/2.12 ------------> process usable:
% 1.96/2.12 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.96/2.12 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.96/2.12 ** KEPT (pick-wt=13): 3 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.96/2.12 ** KEPT (pick-wt=13): 4 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.96/2.12 ** KEPT (pick-wt=8): 5 [] multiplication(star($c1),star($c1))!=star($c1).
% 1.96/2.12
% 1.96/2.12 ------------> process sos:
% 1.96/2.12 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.96/2.12 ** KEPT (pick-wt=7): 7 [] addition(A,B)=addition(B,A).
% 1.96/2.12 ** KEPT (pick-wt=11): 9 [copy,8,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.96/2.12 ---> New Demodulator: 10 [new_demod,9] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.96/2.12 ** KEPT (pick-wt=5): 11 [] addition(A,zero)=A.
% 2.96/3.15 ---> New Demodulator: 12 [new_demod,11] addition(A,zero)=A.
% 2.96/3.15 ** KEPT (pick-wt=5): 13 [] addition(A,A)=A.
% 2.96/3.15 ---> New Demodulator: 14 [new_demod,13] addition(A,A)=A.
% 2.96/3.15 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.96/3.15 ---> New Demodulator: 17 [new_demod,16] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.96/3.15 ** KEPT (pick-wt=5): 18 [] multiplication(A,one)=A.
% 2.96/3.15 ---> New Demodulator: 19 [new_demod,18] multiplication(A,one)=A.
% 2.96/3.15 ** KEPT (pick-wt=5): 20 [] multiplication(one,A)=A.
% 2.96/3.15 ---> New Demodulator: 21 [new_demod,20] multiplication(one,A)=A.
% 2.96/3.15 ** KEPT (pick-wt=13): 22 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.96/3.15 ---> New Demodulator: 23 [new_demod,22] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.96/3.15 ** KEPT (pick-wt=13): 24 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.96/3.15 ---> New Demodulator: 25 [new_demod,24] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.96/3.15 ** KEPT (pick-wt=5): 26 [] multiplication(A,zero)=zero.
% 2.96/3.15 ---> New Demodulator: 27 [new_demod,26] multiplication(A,zero)=zero.
% 2.96/3.15 ** KEPT (pick-wt=5): 28 [] multiplication(zero,A)=zero.
% 2.96/3.15 ---> New Demodulator: 29 [new_demod,28] multiplication(zero,A)=zero.
% 2.96/3.15 ** KEPT (pick-wt=9): 30 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 2.96/3.15 ** KEPT (pick-wt=9): 31 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 2.96/3.15 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 2.96/3.15 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] addition(A,B)=addition(B,A).
% 2.96/3.15 >>>> Starting back demodulation with 10.
% 2.96/3.15 >>>> Starting back demodulation with 12.
% 2.96/3.15 >>>> Starting back demodulation with 14.
% 2.96/3.15 >>>> Starting back demodulation with 17.
% 2.96/3.15 >>>> Starting back demodulation with 19.
% 2.96/3.15 >>>> Starting back demodulation with 21.
% 2.96/3.15 >>>> Starting back demodulation with 23.
% 2.96/3.15 >>>> Starting back demodulation with 25.
% 2.96/3.15 >>>> Starting back demodulation with 27.
% 2.96/3.15 >>>> Starting back demodulation with 29.
% 2.96/3.15
% 2.96/3.15 ======= end of input processing =======
% 2.96/3.15
% 2.96/3.15 =========== start of search ===========
% 2.96/3.15
% 2.96/3.15
% 2.96/3.15 Resetting weight limit to 11.
% 2.96/3.15
% 2.96/3.15
% 2.96/3.15 Resetting weight limit to 11.
% 2.96/3.15
% 2.96/3.15 sos_size=2270
% 2.96/3.15
% 2.96/3.15
% 2.96/3.15 Resetting weight limit to 9.
% 2.96/3.15
% 2.96/3.15
% 2.96/3.15 Resetting weight limit to 9.
% 2.96/3.15
% 2.96/3.15 sos_size=2523
% 2.96/3.15
% 2.96/3.15 -------- PROOF --------
% 2.96/3.15
% 2.96/3.15 ----> UNIT CONFLICT at 1.03 sec ----> 4024 [binary,4022.1,5.1] $F.
% 2.96/3.15
% 2.96/3.15 Length of proof is 21. Level of proof is 12.
% 2.96/3.15
% 2.96/3.15 ---------------- PROOF ----------------
% 2.96/3.15 % SZS status Theorem
% 2.96/3.15 % SZS output start Refutation
% See solution above
% 2.96/3.16 ------------ end of proof -------------
% 2.96/3.16
% 2.96/3.16
% 2.96/3.16 Search stopped by max_proofs option.
% 2.96/3.16
% 2.96/3.16
% 2.96/3.16 Search stopped by max_proofs option.
% 2.96/3.16
% 2.96/3.16 ============ end of search ============
% 2.96/3.16
% 2.96/3.16 -------------- statistics -------------
% 2.96/3.16 clauses given 457
% 2.96/3.16 clauses generated 53966
% 2.96/3.16 clauses kept 3899
% 2.96/3.16 clauses forward subsumed 19189
% 2.96/3.16 clauses back subsumed 847
% 2.96/3.16 Kbytes malloced 5859
% 2.96/3.16
% 2.96/3.16 ----------- times (seconds) -----------
% 2.96/3.16 user CPU time 1.03 (0 hr, 0 min, 1 sec)
% 2.96/3.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.96/3.16 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 2.96/3.16
% 2.96/3.16 That finishes the proof of the theorem.
% 2.96/3.16
% 2.96/3.16 Process 27247 finished Wed Jul 27 06:34:56 2022
% 2.96/3.16 Otter interrupted
% 2.96/3.16 PROOF FOUND
%------------------------------------------------------------------------------