%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LDA003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:05:48 EDT 2022
% Result : Unsatisfiable 1.72s 1.95s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 10 RR)
% Number of literals : 14 ( 10 equ; 1 neg)
% Maximal clause size : 1 ( 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; 4 con; 0-2 aty)
% Number of variables : 9 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
~ left(n3,u),
file('LDA003-1.p',unknown),
[] ).
cnf(4,axiom,
f(A,f(B,C)) = f(f(A,B),f(A,C)),
file('LDA003-1.p',unknown),
[] ).
cnf(5,plain,
f(f(A,B),f(A,C)) = f(A,f(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(7,axiom,
left(A,f(A,B)),
file('LDA003-1.p',unknown),
[] ).
cnf(8,axiom,
n2 = f(n1,n1),
file('LDA003-1.p',unknown),
[] ).
cnf(10,plain,
f(n1,n1) = n2,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.1')] ).
cnf(11,axiom,
n3 = f(n2,n1),
file('LDA003-1.p',unknown),
[] ).
cnf(12,plain,
f(n2,n1) = n3,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(14,axiom,
u = f(n2,n2),
file('LDA003-1.p',unknown),
[] ).
cnf(16,plain,
f(n2,n2) = u,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[14])]),
[iquote('copy,14,flip.1')] ).
cnf(27,plain,
f(f(n2,A),n3) = f(n2,f(A,n1)),
inference(para_into,[status(thm),theory(equality)],[5,12]),
[iquote('para_into,5.1.1.2,12.1.1')] ).
cnf(121,plain,
f(n3,n3) = u,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[27,12]),10,16]),
[iquote('para_into,27.1.1.1,12.1.1,demod,10,16')] ).
cnf(130,plain,
left(n3,u),
inference(para_from,[status(thm),theory(equality)],[121,7]),
[iquote('para_from,121.1.1,7.1.2')] ).
cnf(131,plain,
$false,
inference(binary,[status(thm)],[130,2]),
[iquote('binary,130.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LDA003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 02:20:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.95 ----- Otter 3.3f, August 2004 -----
% 1.72/1.95 The process was started by sandbox on n027.cluster.edu,
% 1.72/1.95 Wed Jul 27 02:20:06 2022
% 1.72/1.95 The command was "./otter". The process ID is 18375.
% 1.72/1.95
% 1.72/1.95 set(prolog_style_variables).
% 1.72/1.95 set(auto).
% 1.72/1.95 dependent: set(auto1).
% 1.72/1.95 dependent: set(process_input).
% 1.72/1.95 dependent: clear(print_kept).
% 1.72/1.95 dependent: clear(print_new_demod).
% 1.72/1.95 dependent: clear(print_back_demod).
% 1.72/1.95 dependent: clear(print_back_sub).
% 1.72/1.95 dependent: set(control_memory).
% 1.72/1.95 dependent: assign(max_mem, 12000).
% 1.72/1.95 dependent: assign(pick_given_ratio, 4).
% 1.72/1.95 dependent: assign(stats_level, 1).
% 1.72/1.95 dependent: assign(max_seconds, 10800).
% 1.72/1.95 clear(print_given).
% 1.72/1.95
% 1.72/1.95 list(usable).
% 1.72/1.95 0 [] A=A.
% 1.72/1.95 0 [] f(X,f(Y,Z))=f(f(X,Y),f(X,Z)).
% 1.72/1.95 0 [] left(X,f(X,Y)).
% 1.72/1.95 0 [] -left(X,Y)| -left(Y,Z)|left(X,Z).
% 1.72/1.95 0 [] n2=f(n1,n1).
% 1.72/1.95 0 [] n3=f(n2,n1).
% 1.72/1.95 0 [] u=f(n2,n2).
% 1.72/1.95 0 [] -left(n3,u).
% 1.72/1.95 end_of_list.
% 1.72/1.95
% 1.72/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 1.72/1.95
% 1.72/1.95 This is a Horn set with equality. The strategy will be
% 1.72/1.95 Knuth-Bendix and hyper_res, with positive clauses in
% 1.72/1.95 sos and nonpositive clauses in usable.
% 1.72/1.95
% 1.72/1.95 dependent: set(knuth_bendix).
% 1.72/1.95 dependent: set(anl_eq).
% 1.72/1.95 dependent: set(para_from).
% 1.72/1.95 dependent: set(para_into).
% 1.72/1.95 dependent: clear(para_from_right).
% 1.72/1.95 dependent: clear(para_into_right).
% 1.72/1.95 dependent: set(para_from_vars).
% 1.72/1.95 dependent: set(eq_units_both_ways).
% 1.72/1.95 dependent: set(dynamic_demod_all).
% 1.72/1.95 dependent: set(dynamic_demod).
% 1.72/1.95 dependent: set(order_eq).
% 1.72/1.95 dependent: set(back_demod).
% 1.72/1.95 dependent: set(lrpo).
% 1.72/1.95 dependent: set(hyper_res).
% 1.72/1.95 dependent: clear(order_hyper).
% 1.72/1.95
% 1.72/1.95 ------------> process usable:
% 1.72/1.95 ** KEPT (pick-wt=9): 1 [] -left(A,B)| -left(B,C)|left(A,C).
% 1.72/1.95 ** KEPT (pick-wt=3): 2 [] -left(n3,u).
% 1.72/1.95
% 1.72/1.95 ------------> process sos:
% 1.72/1.95 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.72/1.95 ** KEPT (pick-wt=13): 5 [copy,4,flip.1] f(f(A,B),f(A,C))=f(A,f(B,C)).
% 1.72/1.95 ---> New Demodulator: 6 [new_demod,5] f(f(A,B),f(A,C))=f(A,f(B,C)).
% 1.72/1.95 ** KEPT (pick-wt=5): 7 [] left(A,f(A,B)).
% 1.72/1.95 ** KEPT (pick-wt=5): 9 [copy,8,flip.1] f(n1,n1)=n2.
% 1.72/1.95 ---> New Demodulator: 10 [new_demod,9] f(n1,n1)=n2.
% 1.72/1.95 ** KEPT (pick-wt=5): 12 [copy,11,flip.1] f(n2,n1)=n3.
% 1.72/1.95 ---> New Demodulator: 13 [new_demod,12] f(n2,n1)=n3.
% 1.72/1.95 ** KEPT (pick-wt=5): 15 [copy,14,flip.1] f(n2,n2)=u.
% 1.72/1.95 ---> New Demodulator: 16 [new_demod,15] f(n2,n2)=u.
% 1.72/1.95 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.72/1.95 >>>> Starting back demodulation with 6.
% 1.72/1.95 >>>> Starting back demodulation with 10.
% 1.72/1.95 >>>> Starting back demodulation with 13.
% 1.72/1.95 >>>> Starting back demodulation with 16.
% 1.72/1.95
% 1.72/1.95 ======= end of input processing =======
% 1.72/1.95
% 1.72/1.95 =========== start of search ===========
% 1.72/1.95
% 1.72/1.95 -------- PROOF --------
% 1.72/1.95
% 1.72/1.95 ----> UNIT CONFLICT at 0.00 sec ----> 131 [binary,130.1,2.1] $F.
% 1.72/1.95
% 1.72/1.95 Length of proof is 7. Level of proof is 4.
% 1.72/1.95
% 1.72/1.95 ---------------- PROOF ----------------
% 1.72/1.95 % SZS status Unsatisfiable
% 1.72/1.95 % SZS output start Refutation
% See solution above
% 1.72/1.95 ------------ end of proof -------------
% 1.72/1.95
% 1.72/1.95
% 1.72/1.95 Search stopped by max_proofs option.
% 1.72/1.95
% 1.72/1.95
% 1.72/1.95 Search stopped by max_proofs option.
% 1.72/1.95
% 1.72/1.95 ============ end of search ============
% 1.72/1.95
% 1.72/1.95 -------------- statistics -------------
% 1.72/1.95 clauses given 27
% 1.72/1.95 clauses generated 153
% 1.72/1.95 clauses kept 84
% 1.72/1.95 clauses forward subsumed 82
% 1.72/1.95 clauses back subsumed 0
% 1.72/1.95 Kbytes malloced 976
% 1.72/1.95
% 1.72/1.95 ----------- times (seconds) -----------
% 1.72/1.95 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.95 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.72/1.95
% 1.72/1.95 That finishes the proof of the theorem.
% 1.72/1.95
% 1.72/1.95 Process 18375 finished Wed Jul 27 02:20:08 2022
% 1.72/1.95 Otter interrupted
% 1.72/1.95 PROOF FOUND
%------------------------------------------------------------------------------