TSTP Solution File: KLE001+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 2.02s 2.18s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 3 RR)
% Number of literals : 6 ( 2 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( le_q(A,B)
| addition(A,B) != B ),
file('KLE001+1.p',unknown),
[] ).
cnf(3,axiom,
~ le_q(addition(dollar_c3,dollar_c1),addition(dollar_c3,dollar_c1)),
file('KLE001+1.p',unknown),
[] ).
cnf(11,axiom,
addition(A,A) = A,
file('KLE001+1.p',unknown),
[] ).
cnf(35,plain,
le_q(A,A),
inference(hyper,[status(thm)],[11,2]),
[iquote('hyper,11,2')] ).
cnf(36,plain,
$false,
inference(binary,[status(thm)],[35,3]),
[iquote('binary,35.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 06:53:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.02/2.18 ----- Otter 3.3f, August 2004 -----
% 2.02/2.18 The process was started by sandbox on n023.cluster.edu,
% 2.02/2.18 Wed Jul 27 06:53:18 2022
% 2.02/2.18 The command was "./otter". The process ID is 13445.
% 2.02/2.18
% 2.02/2.18 set(prolog_style_variables).
% 2.02/2.18 set(auto).
% 2.02/2.18 dependent: set(auto1).
% 2.02/2.18 dependent: set(process_input).
% 2.02/2.18 dependent: clear(print_kept).
% 2.02/2.18 dependent: clear(print_new_demod).
% 2.02/2.18 dependent: clear(print_back_demod).
% 2.02/2.18 dependent: clear(print_back_sub).
% 2.02/2.18 dependent: set(control_memory).
% 2.02/2.18 dependent: assign(max_mem, 12000).
% 2.02/2.18 dependent: assign(pick_given_ratio, 4).
% 2.02/2.18 dependent: assign(stats_level, 1).
% 2.02/2.18 dependent: assign(max_seconds, 10800).
% 2.02/2.18 clear(print_given).
% 2.02/2.18
% 2.02/2.18 formula_list(usable).
% 2.02/2.18 all A (A=A).
% 2.02/2.18 all A B (addition(A,B)=addition(B,A)).
% 2.02/2.18 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 2.02/2.18 all A (addition(A,zero)=A).
% 2.02/2.18 all A (addition(A,A)=A).
% 2.02/2.18 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 2.02/2.18 all A (multiplication(A,one)=A).
% 2.02/2.18 all A (multiplication(one,A)=A).
% 2.02/2.18 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 2.02/2.18 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 2.02/2.18 all A (multiplication(A,zero)=zero).
% 2.02/2.18 all A (multiplication(zero,A)=zero).
% 2.02/2.18 all A B (le_q(A,B)<->addition(A,B)=B).
% 2.02/2.18 -(all X0 X1 X2 (le_q(X0,X1)->le_q(addition(X0,X2),addition(X0,X2)))).
% 2.02/2.18 end_of_list.
% 2.02/2.18
% 2.02/2.18 -------> usable clausifies to:
% 2.02/2.18
% 2.02/2.18 list(usable).
% 2.02/2.18 0 [] A=A.
% 2.02/2.18 0 [] addition(A,B)=addition(B,A).
% 2.02/2.18 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 2.02/2.18 0 [] addition(A,zero)=A.
% 2.02/2.18 0 [] addition(A,A)=A.
% 2.02/2.18 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 2.02/2.18 0 [] multiplication(A,one)=A.
% 2.02/2.18 0 [] multiplication(one,A)=A.
% 2.02/2.18 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.02/2.18 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.02/2.18 0 [] multiplication(A,zero)=zero.
% 2.02/2.18 0 [] multiplication(zero,A)=zero.
% 2.02/2.18 0 [] -le_q(A,B)|addition(A,B)=B.
% 2.02/2.18 0 [] le_q(A,B)|addition(A,B)!=B.
% 2.02/2.18 0 [] le_q($c3,$c2).
% 2.02/2.18 0 [] -le_q(addition($c3,$c1),addition($c3,$c1)).
% 2.02/2.18 end_of_list.
% 2.02/2.18
% 2.02/2.18 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 2.02/2.18
% 2.02/2.18 This is a Horn set with equality. The strategy will be
% 2.02/2.18 Knuth-Bendix and hyper_res, with positive clauses in
% 2.02/2.18 sos and nonpositive clauses in usable.
% 2.02/2.18
% 2.02/2.18 dependent: set(knuth_bendix).
% 2.02/2.18 dependent: set(anl_eq).
% 2.02/2.18 dependent: set(para_from).
% 2.02/2.18 dependent: set(para_into).
% 2.02/2.18 dependent: clear(para_from_right).
% 2.02/2.18 dependent: clear(para_into_right).
% 2.02/2.18 dependent: set(para_from_vars).
% 2.02/2.18 dependent: set(eq_units_both_ways).
% 2.02/2.18 dependent: set(dynamic_demod_all).
% 2.02/2.18 dependent: set(dynamic_demod).
% 2.02/2.18 dependent: set(order_eq).
% 2.02/2.18 dependent: set(back_demod).
% 2.02/2.18 dependent: set(lrpo).
% 2.02/2.18 dependent: set(hyper_res).
% 2.02/2.18 dependent: clear(order_hyper).
% 2.02/2.18
% 2.02/2.18 ------------> process usable:
% 2.02/2.18 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 2.02/2.18 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 2.02/2.18 ** KEPT (pick-wt=7): 3 [] -le_q(addition($c3,$c1),addition($c3,$c1)).
% 2.02/2.18
% 2.02/2.18 ------------> process sos:
% 2.02/2.18 ** KEPT (pick-wt=3): 4 [] A=A.
% 2.02/2.18 ** KEPT (pick-wt=7): 5 [] addition(A,B)=addition(B,A).
% 2.02/2.18 ** KEPT (pick-wt=11): 7 [copy,6,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.02/2.18 ---> New Demodulator: 8 [new_demod,7] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 2.02/2.18 ** KEPT (pick-wt=5): 9 [] addition(A,zero)=A.
% 2.02/2.18 ---> New Demodulator: 10 [new_demod,9] addition(A,zero)=A.
% 2.02/2.18 ** KEPT (pick-wt=5): 11 [] addition(A,A)=A.
% 2.02/2.18 ---> New Demodulator: 12 [new_demod,11] addition(A,A)=A.
% 2.02/2.18 ** KEPT (pick-wt=11): 14 [copy,13,flip.1] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.02/2.18 ---> New Demodulator: 15 [new_demod,14] multiplication(multiplication(A,B),C)=multiplication(A,multiplication(B,C)).
% 2.02/2.18 ** KEPT (pick-wt=5): 16 [] multiplication(A,one)=A.
% 2.02/2.18 ---> New Demodulator: 17 [new_demod,16] multiplication(A,one)=A.
% 2.02/2.18 ** KEPT (pick-wt=5): 18 [] multiplication(one,A)=A.
% 2.02/2.18 ---> New Demodulator: 19 [new_demod,18] multiplication(one,A)=A.
% 2.02/2.18 ** KEPT (pick-wt=13): 20 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.02/2.18 ---> New Demodulator: 21 [new_demod,20] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 2.02/2.18 ** KEPT (pick-wt=13): 22 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.02/2.18 ---> New Demodulator: 23 [new_demod,22] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 2.02/2.18 ** KEPT (pick-wt=5): 24 [] multiplication(A,zero)=zero.
% 2.02/2.18 ---> New Demodulator: 25 [new_demod,24] multiplication(A,zero)=zero.
% 2.02/2.18 ** KEPT (pick-wt=5): 26 [] multiplication(zero,A)=zero.
% 2.02/2.18 ---> New Demodulator: 27 [new_demod,26] multiplication(zero,A)=zero.
% 2.02/2.18 ** KEPT (pick-wt=3): 28 [] le_q($c3,$c2).
% 2.02/2.18 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 2.02/2.18 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] addition(A,B)=addition(B,A).
% 2.02/2.18 >>>> Starting back demodulation with 8.
% 2.02/2.18 >>>> Starting back demodulation with 10.
% 2.02/2.18 >>>> Starting back demodulation with 12.
% 2.02/2.18 >>>> Starting back demodulation with 15.
% 2.02/2.18 >>>> Starting back demodulation with 17.
% 2.02/2.18 >>>> Starting back demodulation with 19.
% 2.02/2.18 >>>> Starting back demodulation with 21.
% 2.02/2.18 >>>> Starting back demodulation with 23.
% 2.02/2.18 >>>> Starting back demodulation with 25.
% 2.02/2.18 >>>> Starting back demodulation with 27.
% 2.02/2.18
% 2.02/2.18 ======= end of input processing =======
% 2.02/2.18
% 2.02/2.18 =========== start of search ===========
% 2.02/2.18
% 2.02/2.18 -------- PROOF --------
% 2.02/2.18
% 2.02/2.18 ----> UNIT CONFLICT at 0.00 sec ----> 36 [binary,35.1,3.1] $F.
% 2.02/2.18
% 2.02/2.18 Length of proof is 1. Level of proof is 1.
% 2.02/2.18
% 2.02/2.18 ---------------- PROOF ----------------
% 2.02/2.18 % SZS status Theorem
% 2.02/2.18 % SZS output start Refutation
% See solution above
% 2.02/2.18 ------------ end of proof -------------
% 2.02/2.18
% 2.02/2.18
% 2.02/2.18 Search stopped by max_proofs option.
% 2.02/2.18
% 2.02/2.18
% 2.02/2.18 Search stopped by max_proofs option.
% 2.02/2.18
% 2.02/2.18 ============ end of search ============
% 2.02/2.18
% 2.02/2.18 -------------- statistics -------------
% 2.02/2.18 clauses given 5
% 2.02/2.18 clauses generated 9
% 2.02/2.18 clauses kept 22
% 2.02/2.18 clauses forward subsumed 5
% 2.02/2.18 clauses back subsumed 0
% 2.02/2.18 Kbytes malloced 976
% 2.02/2.18
% 2.02/2.18 ----------- times (seconds) -----------
% 2.02/2.18 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.18 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.18 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.02/2.18
% 2.02/2.18 That finishes the proof of the theorem.
% 2.02/2.18
% 2.02/2.18 Process 13445 finished Wed Jul 27 06:53:20 2022
% 2.02/2.18 Otter interrupted
% 2.02/2.18 PROOF FOUND
%------------------------------------------------------------------------------