%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE170+1.002 : TPTP v8.1.0. Released v5.2.0.
% 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 13:00:54 EDT 2022
% Result : Theorem 2.53s 2.70s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 24 unt; 0 nHn; 7 RR)
% Number of literals : 41 ( 14 equ; 10 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 : 57 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE170+1.002.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE170+1.002.p',unknown),
[] ).
cnf(5,axiom,
~ le_q(multiplication(a,a),star(a)),
file('KLE170+1.002.p',unknown),
[] ).
cnf(7,axiom,
addition(A,B) = addition(B,A),
file('KLE170+1.002.p',unknown),
[] ).
cnf(8,axiom,
addition(A,addition(B,C)) = addition(addition(A,B),C),
file('KLE170+1.002.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('KLE170+1.002.p',unknown),
[] ).
cnf(19,axiom,
multiplication(A,one) = A,
file('KLE170+1.002.p',unknown),
[] ).
cnf(22,axiom,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('KLE170+1.002.p',unknown),
[] ).
cnf(30,axiom,
le_q(addition(one,multiplication(A,star(A))),star(A)),
file('KLE170+1.002.p',unknown),
[] ).
cnf(31,axiom,
le_q(addition(one,multiplication(star(A),A)),star(A)),
file('KLE170+1.002.p',unknown),
[] ).
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(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(103,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(190,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(467,plain,
le_q(A,addition(A,B)),
inference(hyper,[status(thm)],[57,2]),
[iquote('hyper,57,2')] ).
cnf(483,plain,
le_q(A,addition(B,A)),
inference(para_into,[status(thm),theory(equality)],[467,7]),
[iquote('para_into,467.1.2,7.1.1')] ).
cnf(485,plain,
le_q(A,addition(B,addition(C,A))),
inference(para_into,[status(thm),theory(equality)],[483,10]),
[iquote('para_into,483.1.2,9.1.1')] ).
cnf(501,plain,
( le_q(A,addition(B,C))
| ~ le_q(A,C) ),
inference(para_into,[status(thm),theory(equality)],[485,43]),
[iquote('para_into,485.1.2.2,43.1.1')] ).
cnf(505,plain,
( le_q(A,B)
| ~ le_q(addition(C,A),B) ),
inference(para_into,[status(thm),theory(equality)],[485,43]),
[iquote('para_into,485.1.2,43.1.1')] ).
cnf(535,plain,
( le_q(A,B)
| ~ le_q(A,C)
| ~ le_q(C,B) ),
inference(para_into,[status(thm),theory(equality)],[501,43]),
[iquote('para_into,501.1.2,43.1.1')] ).
cnf(564,plain,
le_q(multiplication(star(A),A),star(A)),
inference(hyper,[status(thm)],[505,31]),
[iquote('hyper,505,31')] ).
cnf(565,plain,
le_q(multiplication(A,star(A)),star(A)),
inference(hyper,[status(thm)],[505,30]),
[iquote('hyper,505,30')] ).
cnf(573,plain,
addition(multiplication(star(A),A),star(A)) = star(A),
inference(hyper,[status(thm)],[564,1]),
[iquote('hyper,564,1')] ).
cnf(574,plain,
addition(one,star(A)) = star(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[190]),573]),
[iquote('back_demod,190,demod,573')] ).
cnf(628,plain,
le_q(one,star(A)),
inference(hyper,[status(thm)],[574,2]),
[iquote('hyper,574,2')] ).
cnf(2218,plain,
( le_q(multiplication(A,B),multiplication(A,C))
| ~ le_q(B,C) ),
inference(para_from,[status(thm),theory(equality)],[103,467]),
[iquote('para_from,103.1.1,467.1.2')] ).
cnf(3374,plain,
le_q(A,multiplication(A,star(B))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2218,628]),19]),
[iquote('hyper,2218,628,demod,19')] ).
cnf(3399,plain,
le_q(A,star(A)),
inference(hyper,[status(thm)],[3374,535,565]),
[iquote('hyper,3374,535,565')] ).
cnf(3405,plain,
le_q(multiplication(A,B),multiplication(A,star(B))),
inference(hyper,[status(thm)],[3399,2218]),
[iquote('hyper,3399,2218')] ).
cnf(3859,plain,
le_q(multiplication(A,A),star(A)),
inference(hyper,[status(thm)],[3405,535,565]),
[iquote('hyper,3405,535,565')] ).
cnf(3860,plain,
$false,
inference(binary,[status(thm)],[3859,5]),
[iquote('binary,3859.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE170+1.002 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n009.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 06:29:06 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.63/1.82 ----- Otter 3.3f, August 2004 -----
% 1.63/1.82 The process was started by sandbox on n009.cluster.edu,
% 1.63/1.82 Wed Jul 27 06:29:06 2022
% 1.63/1.82 The command was "./otter". The process ID is 24202.
% 1.63/1.82
% 1.63/1.82 set(prolog_style_variables).
% 1.63/1.82 set(auto).
% 1.63/1.82 dependent: set(auto1).
% 1.63/1.82 dependent: set(process_input).
% 1.63/1.82 dependent: clear(print_kept).
% 1.63/1.82 dependent: clear(print_new_demod).
% 1.63/1.82 dependent: clear(print_back_demod).
% 1.63/1.82 dependent: clear(print_back_sub).
% 1.63/1.82 dependent: set(control_memory).
% 1.63/1.82 dependent: assign(max_mem, 12000).
% 1.63/1.82 dependent: assign(pick_given_ratio, 4).
% 1.63/1.82 dependent: assign(stats_level, 1).
% 1.63/1.82 dependent: assign(max_seconds, 10800).
% 1.63/1.82 clear(print_given).
% 1.63/1.82
% 1.63/1.82 formula_list(usable).
% 1.63/1.82 all A (A=A).
% 1.63/1.82 all A B (addition(A,B)=addition(B,A)).
% 1.63/1.82 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.63/1.82 all A (addition(A,zero)=A).
% 1.63/1.82 all A (addition(A,A)=A).
% 1.63/1.82 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.63/1.82 all A (multiplication(A,one)=A).
% 1.63/1.82 all A (multiplication(one,A)=A).
% 1.63/1.82 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.63/1.82 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.63/1.82 all A (multiplication(A,zero)=zero).
% 1.63/1.82 all A (multiplication(zero,A)=zero).
% 1.63/1.82 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.63/1.82 all A le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.63/1.82 all A le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.63/1.82 all A B C (le_q(addition(multiplication(A,B),C),B)->le_q(multiplication(star(A),C),B)).
% 1.63/1.82 all A B C (le_q(addition(multiplication(A,B),C),A)->le_q(multiplication(C,star(B)),A)).
% 1.63/1.82 -le_q(multiplication(a,a),star(a)).
% 1.63/1.82 end_of_list.
% 1.63/1.82
% 1.63/1.82 -------> usable clausifies to:
% 1.63/1.82
% 1.63/1.82 list(usable).
% 1.63/1.82 0 [] A=A.
% 1.63/1.82 0 [] addition(A,B)=addition(B,A).
% 1.63/1.82 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.63/1.82 0 [] addition(A,zero)=A.
% 1.63/1.82 0 [] addition(A,A)=A.
% 1.63/1.82 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.63/1.82 0 [] multiplication(A,one)=A.
% 1.63/1.82 0 [] multiplication(one,A)=A.
% 1.63/1.82 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.63/1.82 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.63/1.82 0 [] multiplication(A,zero)=zero.
% 1.63/1.82 0 [] multiplication(zero,A)=zero.
% 1.63/1.82 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.63/1.82 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.63/1.82 0 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 1.63/1.82 0 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 1.63/1.82 0 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.63/1.82 0 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.63/1.82 0 [] -le_q(multiplication(a,a),star(a)).
% 1.63/1.82 end_of_list.
% 1.63/1.82
% 1.63/1.82 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.63/1.82
% 1.63/1.82 This is a Horn set with equality. The strategy will be
% 1.63/1.82 Knuth-Bendix and hyper_res, with positive clauses in
% 1.63/1.82 sos and nonpositive clauses in usable.
% 1.63/1.82
% 1.63/1.82 dependent: set(knuth_bendix).
% 1.63/1.82 dependent: set(anl_eq).
% 1.63/1.82 dependent: set(para_from).
% 1.63/1.82 dependent: set(para_into).
% 1.63/1.82 dependent: clear(para_from_right).
% 1.63/1.82 dependent: clear(para_into_right).
% 1.63/1.82 dependent: set(para_from_vars).
% 1.63/1.82 dependent: set(eq_units_both_ways).
% 1.63/1.82 dependent: set(dynamic_demod_all).
% 1.63/1.82 dependent: set(dynamic_demod).
% 1.63/1.82 dependent: set(order_eq).
% 1.63/1.82 dependent: set(back_demod).
% 1.63/1.82 dependent: set(lrpo).
% 1.63/1.82 dependent: set(hyper_res).
% 1.63/1.82 dependent: clear(order_hyper).
% 1.63/1.82
% 1.63/1.82 ------------> process usable:
% 1.63/1.82 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.63/1.82 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.63/1.82 ** KEPT (pick-wt=13): 3 [] -le_q(addition(multiplication(A,B),C),B)|le_q(multiplication(star(A),C),B).
% 1.63/1.82 ** KEPT (pick-wt=13): 4 [] -le_q(addition(multiplication(A,B),C),A)|le_q(multiplication(C,star(B)),A).
% 1.63/1.82 ** KEPT (pick-wt=6): 5 [] -le_q(multiplication(a,a),star(a)).
% 1.63/1.82
% 1.63/1.82 ------------> process sos:
% 1.63/1.82 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.63/1.82 ** KEPT (pick-wt=7): 7 [] addition(A,B)=addition(B,A).
% 1.63/1.82 ** KEPT (pick-wt=11): 9 [copy,8,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.63/1.82 ---> New Demodulator: 10 [new_demod,9] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.63/1.82 ** KEPT (pick-wt=5): 11 [] addition(A,zero)=A.
% 1.63/1.82 ---> New Demodulator: 12 [new_demod,11] addition(A,zero)=A.
% 2.53/2.70 ** KEPT (pick-wt=5): 13 [] addition(A,A)=A.
% 2.53/2.70 ---> New Demodulator: 14 [new_demod,13] addition(A,A)=A.
% 2.53/2.70 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.53/2.70 ---> New Demodulator: 17 [new_demod,16] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.53/2.70 ** KEPT (pick-wt=5): 18 [] multiplication(A,one)=A.
% 2.53/2.70 ---> New Demodulator: 19 [new_demod,18] multiplication(A,one)=A.
% 2.53/2.70 ** KEPT (pick-wt=5): 20 [] multiplication(one,A)=A.
% 2.53/2.70 ---> New Demodulator: 21 [new_demod,20] multiplication(one,A)=A.
% 2.53/2.70 ** KEPT (pick-wt=13): 22 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.53/2.70 ---> New Demodulator: 23 [new_demod,22] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.53/2.70 ** KEPT (pick-wt=13): 24 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.53/2.70 ---> New Demodulator: 25 [new_demod,24] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.53/2.70 ** KEPT (pick-wt=5): 26 [] multiplication(A,zero)=zero.
% 2.53/2.70 ---> New Demodulator: 27 [new_demod,26] multiplication(A,zero)=zero.
% 2.53/2.70 ** KEPT (pick-wt=5): 28 [] multiplication(zero,A)=zero.
% 2.53/2.70 ---> New Demodulator: 29 [new_demod,28] multiplication(zero,A)=zero.
% 2.53/2.70 ** KEPT (pick-wt=9): 30 [] le_q(addition(one,multiplication(A,star(A))),star(A)).
% 2.53/2.70 ** KEPT (pick-wt=9): 31 [] le_q(addition(one,multiplication(star(A),A)),star(A)).
% 2.53/2.70 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 2.53/2.70 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] addition(A,B)=addition(B,A).
% 2.53/2.70 >>>> Starting back demodulation with 10.
% 2.53/2.70 >>>> Starting back demodulation with 12.
% 2.53/2.70 >>>> Starting back demodulation with 14.
% 2.53/2.70 >>>> Starting back demodulation with 17.
% 2.53/2.70 >>>> Starting back demodulation with 19.
% 2.53/2.70 >>>> Starting back demodulation with 21.
% 2.53/2.70 >>>> Starting back demodulation with 23.
% 2.53/2.70 >>>> Starting back demodulation with 25.
% 2.53/2.70 >>>> Starting back demodulation with 27.
% 2.53/2.70 >>>> Starting back demodulation with 29.
% 2.53/2.70
% 2.53/2.70 ======= end of input processing =======
% 2.53/2.70
% 2.53/2.70 =========== start of search ===========
% 2.53/2.70
% 2.53/2.70
% 2.53/2.70 Resetting weight limit to 11.
% 2.53/2.70
% 2.53/2.70
% 2.53/2.70 Resetting weight limit to 11.
% 2.53/2.70
% 2.53/2.70 sos_size=2168
% 2.53/2.70
% 2.53/2.70
% 2.53/2.70 Resetting weight limit to 10.
% 2.53/2.70
% 2.53/2.70
% 2.53/2.70 Resetting weight limit to 10.
% 2.53/2.70
% 2.53/2.70 sos_size=2299
% 2.53/2.70
% 2.53/2.70
% 2.53/2.70 Resetting weight limit to 9.
% 2.53/2.70
% 2.53/2.70
% 2.53/2.70 Resetting weight limit to 9.
% 2.53/2.70
% 2.53/2.70 sos_size=2480
% 2.53/2.70
% 2.53/2.70 -------- PROOF --------
% 2.53/2.70
% 2.53/2.70 ----> UNIT CONFLICT at 0.88 sec ----> 3860 [binary,3859.1,5.1] $F.
% 2.53/2.70
% 2.53/2.70 Length of proof is 21. Level of proof is 14.
% 2.53/2.70
% 2.53/2.70 ---------------- PROOF ----------------
% 2.53/2.70 % SZS status Theorem
% 2.53/2.70 % SZS output start Refutation
% See solution above
% 2.53/2.70 ------------ end of proof -------------
% 2.53/2.70
% 2.53/2.70
% 2.53/2.70 Search stopped by max_proofs option.
% 2.53/2.70
% 2.53/2.70
% 2.53/2.70 Search stopped by max_proofs option.
% 2.53/2.70
% 2.53/2.70 ============ end of search ============
% 2.53/2.70
% 2.53/2.70 -------------- statistics -------------
% 2.53/2.70 clauses given 369
% 2.53/2.70 clauses generated 31217
% 2.53/2.70 clauses kept 3754
% 2.53/2.70 clauses forward subsumed 13442
% 2.53/2.70 clauses back subsumed 817
% 2.53/2.70 Kbytes malloced 5859
% 2.53/2.70
% 2.53/2.70 ----------- times (seconds) -----------
% 2.53/2.70 user CPU time 0.88 (0 hr, 0 min, 0 sec)
% 2.53/2.70 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.53/2.70 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.53/2.70
% 2.53/2.70 That finishes the proof of the theorem.
% 2.53/2.70
% 2.53/2.70 Process 24202 finished Wed Jul 27 06:29:08 2022
% 2.53/2.70 Otter interrupted
% 2.53/2.70 PROOF FOUND
%------------------------------------------------------------------------------