TSTP Solution File: KLE002+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:00:26 EDT 2022
% Result : Theorem 1.83s 2.03s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 9 unt; 0 nHn; 8 RR)
% Number of literals : 15 ( 8 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ le_q(A,B)
| addition(A,B) = B ),
file('KLE002+1.p',unknown),
[] ).
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE002+1.p',unknown),
[] ).
cnf(3,axiom,
~ le_q(multiplication(dollar_c3,dollar_c1),multiplication(dollar_c2,dollar_c1)),
file('KLE002+1.p',unknown),
[] ).
cnf(5,axiom,
addition(A,B) = addition(B,A),
file('KLE002+1.p',unknown),
[] ).
cnf(22,axiom,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('KLE002+1.p',unknown),
[] ).
cnf(28,axiom,
le_q(dollar_c3,dollar_c2),
file('KLE002+1.p',unknown),
[] ).
cnf(29,plain,
addition(dollar_c3,dollar_c2) = dollar_c2,
inference(hyper,[status(thm)],[28,1]),
[iquote('hyper,28,1')] ).
cnf(39,plain,
( le_q(A,B)
| addition(B,A) != B ),
inference(para_from,[status(thm),theory(equality)],[5,2]),
[iquote('para_from,5.1.1,2.2.1')] ).
cnf(50,plain,
addition(dollar_c2,dollar_c3) = dollar_c2,
inference(para_into,[status(thm),theory(equality)],[29,5]),
[iquote('para_into,29.1.1,5.1.1')] ).
cnf(94,plain,
addition(multiplication(dollar_c2,A),multiplication(dollar_c3,A)) = multiplication(dollar_c2,A),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,50])]),
[iquote('para_into,22.1.1.1,50.1.1,flip.1')] ).
cnf(1740,plain,
le_q(multiplication(dollar_c3,A),multiplication(dollar_c2,A)),
inference(hyper,[status(thm)],[94,39]),
[iquote('hyper,94,39')] ).
cnf(1741,plain,
$false,
inference(binary,[status(thm)],[1740,3]),
[iquote('binary,1740.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE002+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n018.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 06:34:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.59/1.79 ----- Otter 3.3f, August 2004 -----
% 1.59/1.79 The process was started by sandbox on n018.cluster.edu,
% 1.59/1.79 Wed Jul 27 06:34:46 2022
% 1.59/1.79 The command was "./otter". The process ID is 9634.
% 1.59/1.79
% 1.59/1.79 set(prolog_style_variables).
% 1.59/1.79 set(auto).
% 1.59/1.79 dependent: set(auto1).
% 1.59/1.79 dependent: set(process_input).
% 1.59/1.79 dependent: clear(print_kept).
% 1.59/1.79 dependent: clear(print_new_demod).
% 1.59/1.79 dependent: clear(print_back_demod).
% 1.59/1.79 dependent: clear(print_back_sub).
% 1.59/1.79 dependent: set(control_memory).
% 1.59/1.79 dependent: assign(max_mem, 12000).
% 1.59/1.79 dependent: assign(pick_given_ratio, 4).
% 1.59/1.79 dependent: assign(stats_level, 1).
% 1.59/1.79 dependent: assign(max_seconds, 10800).
% 1.59/1.79 clear(print_given).
% 1.59/1.79
% 1.59/1.79 formula_list(usable).
% 1.59/1.79 all A (A=A).
% 1.59/1.79 all A B (addition(A,B)=addition(B,A)).
% 1.59/1.79 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.59/1.79 all A (addition(A,zero)=A).
% 1.59/1.79 all A (addition(A,A)=A).
% 1.59/1.79 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.59/1.79 all A (multiplication(A,one)=A).
% 1.59/1.79 all A (multiplication(one,A)=A).
% 1.59/1.79 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.59/1.79 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.59/1.79 all A (multiplication(A,zero)=zero).
% 1.59/1.79 all A (multiplication(zero,A)=zero).
% 1.59/1.79 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.59/1.79 -(all X0 X1 X2 (le_q(X0,X1)->le_q(multiplication(X0,X2),multiplication(X1,X2)))).
% 1.59/1.79 end_of_list.
% 1.59/1.79
% 1.59/1.79 -------> usable clausifies to:
% 1.59/1.79
% 1.59/1.79 list(usable).
% 1.59/1.79 0 [] A=A.
% 1.59/1.79 0 [] addition(A,B)=addition(B,A).
% 1.59/1.79 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.59/1.79 0 [] addition(A,zero)=A.
% 1.59/1.79 0 [] addition(A,A)=A.
% 1.59/1.79 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.59/1.79 0 [] multiplication(A,one)=A.
% 1.59/1.79 0 [] multiplication(one,A)=A.
% 1.59/1.79 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.59/1.79 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.59/1.79 0 [] multiplication(A,zero)=zero.
% 1.59/1.79 0 [] multiplication(zero,A)=zero.
% 1.59/1.79 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.59/1.79 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.59/1.79 0 [] le_q($c3,$c2).
% 1.59/1.79 0 [] -le_q(multiplication($c3,$c1),multiplication($c2,$c1)).
% 1.59/1.79 end_of_list.
% 1.59/1.79
% 1.59/1.79 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.59/1.79
% 1.59/1.79 This is a Horn set with equality. The strategy will be
% 1.59/1.79 Knuth-Bendix and hyper_res, with positive clauses in
% 1.59/1.79 sos and nonpositive clauses in usable.
% 1.59/1.79
% 1.59/1.79 dependent: set(knuth_bendix).
% 1.59/1.79 dependent: set(anl_eq).
% 1.59/1.79 dependent: set(para_from).
% 1.59/1.79 dependent: set(para_into).
% 1.59/1.79 dependent: clear(para_from_right).
% 1.59/1.79 dependent: clear(para_into_right).
% 1.59/1.79 dependent: set(para_from_vars).
% 1.59/1.79 dependent: set(eq_units_both_ways).
% 1.59/1.79 dependent: set(dynamic_demod_all).
% 1.59/1.79 dependent: set(dynamic_demod).
% 1.59/1.79 dependent: set(order_eq).
% 1.59/1.79 dependent: set(back_demod).
% 1.59/1.79 dependent: set(lrpo).
% 1.59/1.79 dependent: set(hyper_res).
% 1.59/1.79 dependent: clear(order_hyper).
% 1.59/1.79
% 1.59/1.79 ------------> process usable:
% 1.59/1.79 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.59/1.79 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.59/1.79 ** KEPT (pick-wt=7): 3 [] -le_q(multiplication($c3,$c1),multiplication($c2,$c1)).
% 1.59/1.79
% 1.59/1.79 ------------> process sos:
% 1.59/1.80 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.59/1.80 ** KEPT (pick-wt=7): 5 [] addition(A,B)=addition(B,A).
% 1.59/1.80 ** KEPT (pick-wt=11): 7 [copy,6,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.59/1.80 ---> New Demodulator: 8 [new_demod,7] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.59/1.80 ** KEPT (pick-wt=5): 9 [] addition(A,zero)=A.
% 1.59/1.80 ---> New Demodulator: 10 [new_demod,9] addition(A,zero)=A.
% 1.59/1.80 ** KEPT (pick-wt=5): 11 [] addition(A,A)=A.
% 1.59/1.80 ---> New Demodulator: 12 [new_demod,11] addition(A,A)=A.
% 1.59/1.80 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.59/1.80 ---> New Demodulator: 15 [new_demod,14] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 1.59/1.80 ** KEPT (pick-wt=5): 16 [] multiplication(A,one)=A.
% 1.59/1.80 ---> New Demodulator: 17 [new_demod,16] multiplication(A,one)=A.
% 1.59/1.80 ** KEPT (pick-wt=5): 18 [] multiplication(one,A)=A.
% 1.59/1.80 ---> New Demodulator: 19 [new_demod,18] multiplication(one,A)=A.
% 1.59/1.80 ** KEPT (pick-wt=13): 20 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.83/2.03 ---> New Demodulator: 21 [new_demod,20] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.83/2.03 ** KEPT (pick-wt=13): 22 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.83/2.03 ---> New Demodulator: 23 [new_demod,22] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.83/2.03 ** KEPT (pick-wt=5): 24 [] multiplication(A,zero)=zero.
% 1.83/2.03 ---> New Demodulator: 25 [new_demod,24] multiplication(A,zero)=zero.
% 1.83/2.03 ** KEPT (pick-wt=5): 26 [] multiplication(zero,A)=zero.
% 1.83/2.03 ---> New Demodulator: 27 [new_demod,26] multiplication(zero,A)=zero.
% 1.83/2.03 ** KEPT (pick-wt=3): 28 [] le_q($c3,$c2).
% 1.83/2.03 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.83/2.03 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] addition(A,B)=addition(B,A).
% 1.83/2.03 >>>> Starting back demodulation with 8.
% 1.83/2.03 >>>> Starting back demodulation with 10.
% 1.83/2.03 >>>> Starting back demodulation with 12.
% 1.83/2.03 >>>> Starting back demodulation with 15.
% 1.83/2.03 >>>> Starting back demodulation with 17.
% 1.83/2.03 >>>> Starting back demodulation with 19.
% 1.83/2.03 >>>> Starting back demodulation with 21.
% 1.83/2.03 >>>> Starting back demodulation with 23.
% 1.83/2.03 >>>> Starting back demodulation with 25.
% 1.83/2.03 >>>> Starting back demodulation with 27.
% 1.83/2.03
% 1.83/2.03 ======= end of input processing =======
% 1.83/2.03
% 1.83/2.03 =========== start of search ===========
% 1.83/2.03
% 1.83/2.03 -------- PROOF --------
% 1.83/2.03
% 1.83/2.03 ----> UNIT CONFLICT at 0.23 sec ----> 1741 [binary,1740.1,3.1] $F.
% 1.83/2.03
% 1.83/2.03 Length of proof is 5. Level of proof is 4.
% 1.83/2.03
% 1.83/2.03 ---------------- PROOF ----------------
% 1.83/2.03 % SZS status Theorem
% 1.83/2.03 % SZS output start Refutation
% See solution above
% 1.83/2.03 ------------ end of proof -------------
% 1.83/2.03
% 1.83/2.03
% 1.83/2.03 Search stopped by max_proofs option.
% 1.83/2.03
% 1.83/2.03
% 1.83/2.03 Search stopped by max_proofs option.
% 1.83/2.03
% 1.83/2.03 ============ end of search ============
% 1.83/2.03
% 1.83/2.03 -------------- statistics -------------
% 1.83/2.03 clauses given 156
% 1.83/2.03 clauses generated 7248
% 1.83/2.03 clauses kept 1680
% 1.83/2.03 clauses forward subsumed 5490
% 1.83/2.03 clauses back subsumed 206
% 1.83/2.03 Kbytes malloced 2929
% 1.83/2.03
% 1.83/2.03 ----------- times (seconds) -----------
% 1.83/2.03 user CPU time 0.23 (0 hr, 0 min, 0 sec)
% 1.83/2.03 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.83/2.03 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.83/2.03
% 1.83/2.03 That finishes the proof of the theorem.
% 1.83/2.03
% 1.83/2.03 Process 9634 finished Wed Jul 27 06:34:48 2022
% 1.83/2.03 Otter interrupted
% 1.83/2.03 PROOF FOUND
%------------------------------------------------------------------------------