TSTP Solution File: KLE051+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : KLE051+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:00:37 EDT 2022
% Result : Theorem 1.76s 1.95s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 2
% Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 2 RR)
% Number of literals : 3 ( 2 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 1 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
addition(dollar_c1,dollar_c1) != dollar_c1,
file('KLE051+1.p',unknown),
[] ).
cnf(11,axiom,
addition(A,A) = A,
file('KLE051+1.p',unknown),
[] ).
cnf(13,plain,
$false,
inference(binary,[status(thm)],[11,3]),
[iquote('binary,11.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : KLE051+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n008.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 06:34:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.76/1.95
% 1.76/1.95 -------- PROOF --------
% 1.76/1.95 ----- Otter 3.3f, August 2004 -----
% 1.76/1.95 The process was started by sandbox on n008.cluster.edu,
% 1.76/1.95 Wed Jul 27 06:34:08 2022
% 1.76/1.95 The command was "./otter". The process ID is 13727.
% 1.76/1.95
% 1.76/1.95 set(prolog_style_variables).
% 1.76/1.95 set(auto).
% 1.76/1.95 dependent: set(auto1).
% 1.76/1.95 dependent: set(process_input).
% 1.76/1.95 dependent: clear(print_kept).
% 1.76/1.95 dependent: clear(print_new_demod).
% 1.76/1.95 dependent: clear(print_back_demod).
% 1.76/1.95 dependent: clear(print_back_sub).
% 1.76/1.95 dependent: set(control_memory).
% 1.76/1.95 dependent: assign(max_mem, 12000).
% 1.76/1.95 dependent: assign(pick_given_ratio, 4).
% 1.76/1.95 dependent: assign(stats_level, 1).
% 1.76/1.95 dependent: assign(max_seconds, 10800).
% 1.76/1.95 clear(print_given).
% 1.76/1.95
% 1.76/1.95 formula_list(usable).
% 1.76/1.95 all A (A=A).
% 1.76/1.95 all A B (addition(A,B)=addition(B,A)).
% 1.76/1.95 all C B A (addition(A,addition(B,C))=addition(addition(A,B),C)).
% 1.76/1.95 all A (addition(A,zero)=A).
% 1.76/1.95 all A (addition(A,A)=A).
% 1.76/1.95 all A B C (multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C)).
% 1.76/1.95 all A (multiplication(A,one)=A).
% 1.76/1.95 all A (multiplication(one,A)=A).
% 1.76/1.95 all A B C (multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C))).
% 1.76/1.95 all A B C (multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C))).
% 1.76/1.95 all A (multiplication(A,zero)=zero).
% 1.76/1.95 all A (multiplication(zero,A)=zero).
% 1.76/1.95 all A B (le_q(A,B)<->addition(A,B)=B).
% 1.76/1.95 all X0 (addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0)).
% 1.76/1.95 all X0 X1 (domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1)))).
% 1.76/1.95 all X0 (addition(domain(X0),one)=one).
% 1.76/1.95 domain(zero)=zero.
% 1.76/1.95 all X0 X1 (domain(addition(X0,X1))=addition(domain(X0),domain(X1))).
% 1.76/1.95 -(all X0 (addition(X0,X0)=X0)).
% 1.76/1.95 end_of_list.
% 1.76/1.95
% 1.76/1.95 -------> usable clausifies to:
% 1.76/1.95
% 1.76/1.95 list(usable).
% 1.76/1.95 0 [] A=A.
% 1.76/1.95 0 [] addition(A,B)=addition(B,A).
% 1.76/1.95 0 [] addition(A,addition(B,C))=addition(addition(A,B),C).
% 1.76/1.95 0 [] addition(A,zero)=A.
% 1.76/1.95 0 [] addition(A,A)=A.
% 1.76/1.95 0 [] multiplication(A,multiplication(B,C))=multiplication(multiplication(A,B),C).
% 1.76/1.95 0 [] multiplication(A,one)=A.
% 1.76/1.95 0 [] multiplication(one,A)=A.
% 1.76/1.95 0 [] multiplication(A,addition(B,C))=addition(multiplication(A,B),multiplication(A,C)).
% 1.76/1.95 0 [] multiplication(addition(A,B),C)=addition(multiplication(A,C),multiplication(B,C)).
% 1.76/1.95 0 [] multiplication(A,zero)=zero.
% 1.76/1.95 0 [] multiplication(zero,A)=zero.
% 1.76/1.95 0 [] -le_q(A,B)|addition(A,B)=B.
% 1.76/1.95 0 [] le_q(A,B)|addition(A,B)!=B.
% 1.76/1.95 0 [] addition(X0,multiplication(domain(X0),X0))=multiplication(domain(X0),X0).
% 1.76/1.95 0 [] domain(multiplication(X0,X1))=domain(multiplication(X0,domain(X1))).
% 1.76/1.95 0 [] addition(domain(X0),one)=one.
% 1.76/1.95 0 [] domain(zero)=zero.
% 1.76/1.95 0 [] domain(addition(X0,X1))=addition(domain(X0),domain(X1)).
% 1.76/1.95 0 [] addition($c1,$c1)!=$c1.
% 1.76/1.95 end_of_list.
% 1.76/1.95
% 1.76/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.76/1.95
% 1.76/1.95 This is a Horn set with equality. The strategy will be
% 1.76/1.95 Knuth-Bendix and hyper_res, with positive clauses in
% 1.76/1.95 sos and nonpositive clauses in usable.
% 1.76/1.95
% 1.76/1.95 dependent: set(knuth_bendix).
% 1.76/1.95 dependent: set(anl_eq).
% 1.76/1.95 dependent: set(para_from).
% 1.76/1.95 dependent: set(para_into).
% 1.76/1.95 dependent: clear(para_from_right).
% 1.76/1.95 dependent: clear(para_into_right).
% 1.76/1.95 dependent: set(para_from_vars).
% 1.76/1.95 dependent: set(eq_units_both_ways).
% 1.76/1.95 dependent: set(dynamic_demod_all).
% 1.76/1.95 dependent: set(dynamic_demod).
% 1.76/1.95 dependent: set(order_eq).
% 1.76/1.95 dependent: set(back_demod).
% 1.76/1.95 dependent: set(lrpo).
% 1.76/1.95 dependent: set(hyper_res).
% 1.76/1.95 dependent: clear(order_hyper).
% 1.76/1.95
% 1.76/1.95 ------------> process usable:
% 1.76/1.95 ** KEPT (pick-wt=8): 1 [] -le_q(A,B)|addition(A,B)=B.
% 1.76/1.95 ** KEPT (pick-wt=8): 2 [] le_q(A,B)|addition(A,B)!=B.
% 1.76/1.95 ** KEPT (pick-wt=5): 3 [] addition($c1,$c1)!=$c1.
% 1.76/1.95
% 1.76/1.95 ------------> process sos:
% 1.76/1.95 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.76/1.95 ** KEPT (pick-wt=7): 5 [] addition(A,B)=addition(B,A).
% 1.76/1.95 ** KEPT (pick-wt=11): 7 [copy,6,flip.1] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.76/1.95 ---> New Demodulator: 8 [new_demod,7] addition(addition(A,B),C)=addition(A,addition(B,C)).
% 1.76/1.95 ** KEPT (pick-wt=5): 9 [] addition(A,zero)=A.
% 1.76/1.95 ---> New Demodulator: 10 [new_demod,9] addition(A,zero)=A.
% 1.76/1.95 ** KEPT (pick-wt=5): 11 [] addition(A,A)=A.
% 1.76/1.95 ---> New Demodulator: 12 [new_demod,11] addition(A,A)=A.
% 1.76/1.95
% 1.76/1.95 ----> UNIT CONFLICT at 0.00 sec ----> 13 [binary,11.1,3.1] $F.
% 1.76/1.95
% 1.76/1.95 Length of proof is 0. Level of proof is 0.
% 1.76/1.95
% 1.76/1.95 ---------------- PROOF ----------------
% 1.76/1.95 % SZS status Theorem
% 1.76/1.95 % SZS output start Refutation
% See solution above
% 1.76/1.95 ------------ end of proof -------------
% 1.76/1.95
% 1.76/1.95
% 1.76/1.95 Search stopped by max_proofs option.
% 1.76/1.95
% 1.76/1.95
% 1.76/1.95 Search stopped by max_proofs option.
% 1.76/1.95
% 1.76/1.95 ============ end of search ============
% 1.76/1.95
% 1.76/1.95 -------------- statistics -------------
% 1.76/1.95 clauses given 0
% 1.76/1.95 clauses generated 0
% 1.76/1.95 clauses kept 8
% 1.76/1.95 clauses forward subsumed 0
% 1.76/1.95 clauses back subsumed 0
% 1.76/1.95 Kbytes malloced 976
% 1.76/1.95
% 1.76/1.95 ----------- times (seconds) -----------
% 1.76/1.95 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.95 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.76/1.95
% 1.76/1.95 That finishes the proof of the theorem.
% 1.76/1.95
% 1.76/1.95 Process 13727 finished Wed Jul 27 06:34:10 2022
% 1.76/1.95 Otter interrupted
% 1.76/1.95 PROOF FOUND
%------------------------------------------------------------------------------