%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN013-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:23:19 EDT 2022
% Result : Unsatisfiable 51.03s 51.22s
% Output : Refutation 51.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of clauses : 39 ( 15 unt; 20 nHn; 36 RR)
% Number of literals : 95 ( 41 equ; 30 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
m != n,
file('SYN013-1.p',unknown),
[] ).
cnf(2,plain,
n != m,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(3,axiom,
n != k,
file('SYN013-1.p',unknown),
[] ).
cnf(4,axiom,
k != m,
file('SYN013-1.p',unknown),
[] ).
cnf(5,plain,
m != k,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.1')] ).
cnf(6,axiom,
( A = m
| ~ element(A,m)
| f(A) != m ),
file('SYN013-1.p',unknown),
[] ).
cnf(7,axiom,
( A = m
| ~ element(A,m)
| f(A) != A ),
file('SYN013-1.p',unknown),
[] ).
cnf(8,axiom,
( A = m
| ~ element(A,m)
| element(A,f(A)) ),
file('SYN013-1.p',unknown),
[] ).
cnf(9,axiom,
( A = m
| ~ element(A,m)
| element(f(A),A) ),
file('SYN013-1.p',unknown),
[] ).
cnf(10,axiom,
( A = m
| element(A,m)
| B = m
| B = A
| ~ element(A,B)
| ~ element(B,A) ),
file('SYN013-1.p',unknown),
[] ).
cnf(12,axiom,
( A = n
| element(A,n)
| g(A) != A ),
file('SYN013-1.p',unknown),
[] ).
cnf(13,axiom,
( A = n
| ~ element(A,n)
| B = n
| B = A
| ~ element(A,B)
| ~ element(B,A) ),
file('SYN013-1.p',unknown),
[] ).
cnf(14,axiom,
( A = k
| A != m
| element(A,k) ),
file('SYN013-1.p',unknown),
[] ).
cnf(15,axiom,
( A = k
| A != n
| element(A,k) ),
file('SYN013-1.p',unknown),
[] ).
cnf(16,axiom,
( A = k
| A = m
| A = n
| ~ element(A,k) ),
file('SYN013-1.p',unknown),
[] ).
cnf(22,axiom,
A = A,
file('SYN013-1.p',unknown),
[] ).
cnf(23,axiom,
( A = n
| element(A,n)
| element(A,g(A)) ),
file('SYN013-1.p',unknown),
[] ).
cnf(24,axiom,
( A = n
| element(A,n)
| element(g(A),A) ),
file('SYN013-1.p',unknown),
[] ).
cnf(25,plain,
element(n,k),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[22,15]),3]),
[iquote('hyper,22,15,unit_del,3')] ).
cnf(26,plain,
element(m,k),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[22,14]),5]),
[iquote('hyper,22,14,unit_del,5')] ).
cnf(34,plain,
( element(n,m)
| A = m
| element(A,m)
| k = A
| ~ element(A,k)
| ~ element(k,A) ),
inference(para_into,[status(thm),theory(equality)],[25,10]),
[iquote('para_into,25.1.2,10.3.1')] ).
cnf(40,plain,
( element(n,m)
| ~ element(k,n) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[34]),2,3,25]),
[iquote('factor,34.1.3,unit_del,2,3,25')] ).
cnf(54,plain,
( element(A,m)
| ~ element(k,n)
| A = m
| ~ element(A,n)
| ~ element(n,A) ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[40,10]),2])]),
[iquote('para_into,40.1.1,10.4.1,unit_del,2,factor_simp')] ).
cnf(71,plain,
( element(k,m)
| ~ element(k,n) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[54]),5,25]),
[iquote('factor,54.2.4,unit_del,5,25')] ).
cnf(84,plain,
( element(k,g(k))
| element(k,m) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[23,71]),3]),
[iquote('hyper,23,71,unit_del,3')] ).
cnf(131,plain,
element(k,g(k)),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[84,13,23,26]),3,2,5,3])]),
[iquote('hyper,84,13,23,26,unit_del,3,2,5,3,factor_simp')] ).
cnf(168,plain,
( element(k,m)
| A = m
| element(A,m)
| g(k) = A
| ~ element(A,g(k))
| ~ element(g(k),A) ),
inference(para_into,[status(thm),theory(equality)],[131,10]),
[iquote('para_into,131.1.2,10.3.1')] ).
cnf(174,plain,
( element(k,m)
| g(k) = k
| ~ element(g(k),k) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[168]),5,131]),
[iquote('factor,168.1.3,unit_del,5,131')] ).
cnf(220,plain,
( element(g(k),k)
| element(k,m) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[24,71]),3]),
[iquote('hyper,24,71,unit_del,3')] ).
cnf(287,plain,
element(g(k),k),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[220,13,24,26]),3,2,5,3])]),
[iquote('hyper,220,13,24,26,unit_del,3,2,5,3,factor_simp')] ).
cnf(3142,plain,
( element(k,m)
| g(k) = k ),
inference(hyper,[status(thm)],[174,287]),
[iquote('hyper,174,287')] ).
cnf(3185,plain,
( element(k,n)
| element(k,m) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3142,12]),3,22]),
[iquote('para_from,3142.2.1,12.3.1,unit_del,3,22')] ).
cnf(3219,plain,
element(k,m),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3185,71])]),
[iquote('hyper,3185,71,factor_simp')] ).
cnf(3236,plain,
element(f(k),k),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3219,9]),5]),
[iquote('hyper,3219,9,unit_del,5')] ).
cnf(3237,plain,
element(k,f(k)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3219,8]),5]),
[iquote('hyper,3219,8,unit_del,5')] ).
cnf(3404,plain,
( element(k,n)
| f(k) = k
| f(k) = m ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3237,16]),3236]),
[iquote('para_into,3237.1.2,16.3.1,unit_del,3236')] ).
cnf(5070,plain,
( f(k) = k
| f(k) = m ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3404,13,3219,26]),3,2,5]),
[iquote('hyper,3404,13,3219,26,unit_del,3,2,5')] ).
cnf(5090,plain,
f(k) = m,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[5070,7,3219]),5]),
[iquote('hyper,5070,7,3219,unit_del,5')] ).
cnf(5108,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[5070,6,3219]),5090]),5,5]),
[iquote('hyper,5070,6,3219,demod,5090,unit_del,5,5')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN013-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 11:08:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 51.03/51.22 ----- Otter 3.3f, August 2004 -----
% 51.03/51.22 The process was started by sandbox on n019.cluster.edu,
% 51.03/51.22 Wed Jul 27 11:08:37 2022
% 51.03/51.22 The command was "./otter". The process ID is 25429.
% 51.03/51.22
% 51.03/51.22 set(prolog_style_variables).
% 51.03/51.22 set(auto).
% 51.03/51.22 dependent: set(auto1).
% 51.03/51.22 dependent: set(process_input).
% 51.03/51.22 dependent: clear(print_kept).
% 51.03/51.22 dependent: clear(print_new_demod).
% 51.03/51.22 dependent: clear(print_back_demod).
% 51.03/51.22 dependent: clear(print_back_sub).
% 51.03/51.22 dependent: set(control_memory).
% 51.03/51.22 dependent: assign(max_mem, 12000).
% 51.03/51.22 dependent: assign(pick_given_ratio, 4).
% 51.03/51.22 dependent: assign(stats_level, 1).
% 51.03/51.22 dependent: assign(max_seconds, 10800).
% 51.03/51.22 clear(print_given).
% 51.03/51.22
% 51.03/51.22 list(usable).
% 51.03/51.22 0 [] A=A.
% 51.03/51.22 0 [] m!=n.
% 51.03/51.22 0 [] n!=k.
% 51.03/51.22 0 [] k!=m.
% 51.03/51.22 0 [] Y=m| -element(Y,m)|f(Y)!=m.
% 51.03/51.22 0 [] Y=m| -element(Y,m)|f(Y)!=Y.
% 51.03/51.22 0 [] Y=m| -element(Y,m)|element(Y,f(Y)).
% 51.03/51.22 0 [] Y=m| -element(Y,m)|element(f(Y),Y).
% 51.03/51.22 0 [] Y=m|element(Y,m)|V=m|V=Y| -element(Y,V)| -element(V,Y).
% 51.03/51.22 0 [] Y=n|element(Y,n)|g(Y)!=n.
% 51.03/51.22 0 [] Y=n|element(Y,n)|g(Y)!=Y.
% 51.03/51.22 0 [] Y=n|element(Y,n)|element(Y,g(Y)).
% 51.03/51.22 0 [] Y=n|element(Y,n)|element(g(Y),Y).
% 51.03/51.22 0 [] Y=n| -element(Y,n)|V=n|V=Y| -element(Y,V)| -element(V,Y).
% 51.03/51.22 0 [] Y=k|Y!=m|element(Y,k).
% 51.03/51.22 0 [] Y=k|Y!=n|element(Y,k).
% 51.03/51.22 0 [] Y=k|Y=m|Y=n| -element(Y,k).
% 51.03/51.22 end_of_list.
% 51.03/51.22
% 51.03/51.22 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 51.03/51.22
% 51.03/51.22 This ia a non-Horn set with equality. The strategy will be
% 51.03/51.22 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 51.03/51.22 deletion, with positive clauses in sos and nonpositive
% 51.03/51.22 clauses in usable.
% 51.03/51.22
% 51.03/51.22 dependent: set(knuth_bendix).
% 51.03/51.22 dependent: set(anl_eq).
% 51.03/51.22 dependent: set(para_from).
% 51.03/51.22 dependent: set(para_into).
% 51.03/51.22 dependent: clear(para_from_right).
% 51.03/51.22 dependent: clear(para_into_right).
% 51.03/51.22 dependent: set(para_from_vars).
% 51.03/51.22 dependent: set(eq_units_both_ways).
% 51.03/51.22 dependent: set(dynamic_demod_all).
% 51.03/51.22 dependent: set(dynamic_demod).
% 51.03/51.22 dependent: set(order_eq).
% 51.03/51.22 dependent: set(back_demod).
% 51.03/51.22 dependent: set(lrpo).
% 51.03/51.22 dependent: set(hyper_res).
% 51.03/51.22 dependent: set(unit_deletion).
% 51.03/51.22 dependent: set(factor).
% 51.03/51.22
% 51.03/51.22 ------------> process usable:
% 51.03/51.22 ** KEPT (pick-wt=3): 2 [copy,1,flip.1] n!=m.
% 51.03/51.22 ** KEPT (pick-wt=3): 3 [] n!=k.
% 51.03/51.22 ** KEPT (pick-wt=3): 5 [copy,4,flip.1] m!=k.
% 51.03/51.22 ** KEPT (pick-wt=10): 6 [] A=m| -element(A,m)|f(A)!=m.
% 51.03/51.22 ** KEPT (pick-wt=10): 7 [] A=m| -element(A,m)|f(A)!=A.
% 51.03/51.22 ** KEPT (pick-wt=10): 8 [] A=m| -element(A,m)|element(A,f(A)).
% 51.03/51.22 ** KEPT (pick-wt=10): 9 [] A=m| -element(A,m)|element(f(A),A).
% 51.03/51.22 ** KEPT (pick-wt=18): 10 [] A=m|element(A,m)|B=m|B=A| -element(A,B)| -element(B,A).
% 51.03/51.22 ** KEPT (pick-wt=10): 11 [] A=n|element(A,n)|g(A)!=n.
% 51.03/51.22 ** KEPT (pick-wt=10): 12 [] A=n|element(A,n)|g(A)!=A.
% 51.03/51.22 ** KEPT (pick-wt=18): 13 [] A=n| -element(A,n)|B=n|B=A| -element(A,B)| -element(B,A).
% 51.03/51.22 ** KEPT (pick-wt=9): 14 [] A=k|A!=m|element(A,k).
% 51.03/51.22 ** KEPT (pick-wt=9): 15 [] A=k|A!=n|element(A,k).
% 51.03/51.22 ** KEPT (pick-wt=12): 16 [] A=k|A=m|A=n| -element(A,k).
% 51.03/51.22
% 51.03/51.22 ------------> process sos:
% 51.03/51.22 ** KEPT (pick-wt=3): 22 [] A=A.
% 51.03/51.22 ** KEPT (pick-wt=10): 23 [] A=n|element(A,n)|element(A,g(A)).
% 51.03/51.22 ** KEPT (pick-wt=10): 24 [] A=n|element(A,n)|element(g(A),A).
% 51.03/51.22 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] A=A.
% 51.03/51.22 22 back subsumes 21.
% 51.03/51.22 22 back subsumes 20.
% 51.03/51.22 22 back subsumes 19.
% 51.03/51.22 22 back subsumes 18.
% 51.03/51.22 22 back subsumes 17.
% 51.03/51.22
% 51.03/51.22 ======= end of input processing =======
% 51.03/51.22
% 51.03/51.22 =========== start of search ===========
% 51.03/51.22
% 51.03/51.22
% 51.03/51.22 Resetting weight limit to 12.
% 51.03/51.22
% 51.03/51.22
% 51.03/51.22 Resetting weight limit to 12.
% 51.03/51.22
% 51.03/51.22 sos_size=2049
% 51.03/51.22
% 51.03/51.22 -- HEY sandbox, WE HAVE A PROOF!! --
% 51.03/51.22
% 51.03/51.22 -----> EMPTY CLAUSE at 49.42 sec ----> 5108 [hyper,5070,6,3219,demod,5090,unit_del,5,5] $F.
% 51.03/51.22
% 51.03/51.22 Length of proof is 22. Level of proof is 16.
% 51.03/51.22
% 51.03/51.22 ---------------- PROOF ----------------
% 51.03/51.22 % SZS status Unsatisfiable
% 51.03/51.22 % SZS output start Refutation
% See solution above
% 51.03/51.22 ------------ end of proof -------------
% 51.03/51.22
% 51.03/51.22
% 51.03/51.22 Search stopped by max_proofs option.
% 51.03/51.22
% 51.03/51.22
% 51.03/51.22 Search stopped by max_proofs option.
% 51.03/51.22
% 51.03/51.22 ============ end of search ============
% 51.03/51.22
% 51.03/51.22 -------------- statistics -------------
% 51.03/51.22 clauses given 318
% 51.03/51.22 clauses generated 134818
% 51.03/51.22 clauses kept 5102
% 51.03/51.22 clauses forward subsumed 32398
% 51.03/51.22 clauses back subsumed 3323
% 51.03/51.22 Kbytes malloced 4882
% 51.03/51.22
% 51.03/51.22 ----------- times (seconds) -----------
% 51.03/51.22 user CPU time 49.42 (0 hr, 0 min, 49 sec)
% 51.03/51.22 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 51.03/51.22 wall-clock time 50 (0 hr, 0 min, 50 sec)
% 51.03/51.22
% 51.03/51.22 That finishes the proof of the theorem.
% 51.03/51.22
% 51.03/51.22 Process 25429 finished Wed Jul 27 11:09:27 2022
% 51.03/51.22 Otter interrupted
% 51.03/51.22 PROOF FOUND
%------------------------------------------------------------------------------