%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET876+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 13:14:27 EDT 2022
% Result : Theorem 1.96s 2.12s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 5 unt; 2 nHn; 5 RR)
% Number of literals : 12 ( 6 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != singleton(B)
| ~ in(C,A)
| C = B ),
file('SET876+1.p',unknown),
[] ).
cnf(7,axiom,
dollar_c4 != dollar_c3,
file('SET876+1.p',unknown),
[] ).
cnf(8,axiom,
~ disjoint(singleton(dollar_c4),singleton(dollar_c3)),
file('SET876+1.p',unknown),
[] ).
cnf(10,axiom,
A = A,
file('SET876+1.p',unknown),
[] ).
cnf(12,axiom,
( in(A,B)
| disjoint(singleton(A),B) ),
file('SET876+1.p',unknown),
[] ).
cnf(20,plain,
( disjoint(singleton(A),singleton(B))
| A = B ),
inference(hyper,[status(thm)],[12,2,10]),
[iquote('hyper,12,2,10')] ).
cnf(65,plain,
dollar_c4 = dollar_c3,
inference(hyper,[status(thm)],[20,8]),
[iquote('hyper,20,8')] ).
cnf(67,plain,
$false,
inference(binary,[status(thm)],[65,7]),
[iquote('binary,65.1,7.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET876+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n011.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 10:50:55 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.96/2.12 ----- Otter 3.3f, August 2004 -----
% 1.96/2.12 The process was started by sandbox2 on n011.cluster.edu,
% 1.96/2.12 Wed Jul 27 10:50:55 2022
% 1.96/2.12 The command was "./otter". The process ID is 6780.
% 1.96/2.12
% 1.96/2.12 set(prolog_style_variables).
% 1.96/2.12 set(auto).
% 1.96/2.12 dependent: set(auto1).
% 1.96/2.12 dependent: set(process_input).
% 1.96/2.12 dependent: clear(print_kept).
% 1.96/2.12 dependent: clear(print_new_demod).
% 1.96/2.12 dependent: clear(print_back_demod).
% 1.96/2.12 dependent: clear(print_back_sub).
% 1.96/2.12 dependent: set(control_memory).
% 1.96/2.12 dependent: assign(max_mem, 12000).
% 1.96/2.12 dependent: assign(pick_given_ratio, 4).
% 1.96/2.12 dependent: assign(stats_level, 1).
% 1.96/2.12 dependent: assign(max_seconds, 10800).
% 1.96/2.12 clear(print_given).
% 1.96/2.12
% 1.96/2.12 formula_list(usable).
% 1.96/2.12 all A (A=A).
% 1.96/2.12 all A B (in(A,B)-> -in(B,A)).
% 1.96/2.12 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.96/2.12 all A B (-in(A,B)->disjoint(singleton(A),B)).
% 1.96/2.12 exists A empty(A).
% 1.96/2.12 exists A (-empty(A)).
% 1.96/2.12 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.96/2.12 -(all A B (A!=B->disjoint(singleton(A),singleton(B)))).
% 1.96/2.12 end_of_list.
% 1.96/2.12
% 1.96/2.12 -------> usable clausifies to:
% 1.96/2.12
% 1.96/2.12 list(usable).
% 1.96/2.12 0 [] A=A.
% 1.96/2.12 0 [] -in(A,B)| -in(B,A).
% 1.96/2.12 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.96/2.12 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.96/2.12 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.96/2.12 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.96/2.12 0 [] in(A,B)|disjoint(singleton(A),B).
% 1.96/2.12 0 [] empty($c1).
% 1.96/2.12 0 [] -empty($c2).
% 1.96/2.12 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.96/2.12 0 [] $c4!=$c3.
% 1.96/2.12 0 [] -disjoint(singleton($c4),singleton($c3)).
% 1.96/2.12 end_of_list.
% 1.96/2.12
% 1.96/2.12 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.96/2.12
% 1.96/2.12 This ia a non-Horn set with equality. The strategy will be
% 1.96/2.12 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.96/2.12 deletion, with positive clauses in sos and nonpositive
% 1.96/2.12 clauses in usable.
% 1.96/2.12
% 1.96/2.12 dependent: set(knuth_bendix).
% 1.96/2.12 dependent: set(anl_eq).
% 1.96/2.12 dependent: set(para_from).
% 1.96/2.12 dependent: set(para_into).
% 1.96/2.12 dependent: clear(para_from_right).
% 1.96/2.12 dependent: clear(para_into_right).
% 1.96/2.12 dependent: set(para_from_vars).
% 1.96/2.12 dependent: set(eq_units_both_ways).
% 1.96/2.12 dependent: set(dynamic_demod_all).
% 1.96/2.12 dependent: set(dynamic_demod).
% 1.96/2.12 dependent: set(order_eq).
% 1.96/2.12 dependent: set(back_demod).
% 1.96/2.12 dependent: set(lrpo).
% 1.96/2.12 dependent: set(hyper_res).
% 1.96/2.12 dependent: set(unit_deletion).
% 1.96/2.12 dependent: set(factor).
% 1.96/2.12
% 1.96/2.12 ------------> process usable:
% 1.96/2.12 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.96/2.12 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.96/2.12 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.96/2.12 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.96/2.12 ** KEPT (pick-wt=2): 5 [] -empty($c2).
% 1.96/2.12 ** KEPT (pick-wt=6): 6 [] -disjoint(A,B)|disjoint(B,A).
% 1.96/2.12 ** KEPT (pick-wt=3): 7 [] $c4!=$c3.
% 1.96/2.12 ** KEPT (pick-wt=5): 8 [] -disjoint(singleton($c4),singleton($c3)).
% 1.96/2.12
% 1.96/2.12 ------------> process sos:
% 1.96/2.12 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.96/2.12 ** KEPT (pick-wt=14): 11 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.96/2.12 ** KEPT (pick-wt=7): 12 [] in(A,B)|disjoint(singleton(A),B).
% 1.96/2.12 ** KEPT (pick-wt=2): 13 [] empty($c1).
% 1.96/2.12 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.96/2.12
% 1.96/2.12 ======= end of input processing =======
% 1.96/2.12
% 1.96/2.12 =========== start of search ===========
% 1.96/2.12
% 1.96/2.12 -------- PROOF --------
% 1.96/2.12
% 1.96/2.12 ----> UNIT CONFLICT at 0.00 sec ----> 67 [binary,65.1,7.1] $F.
% 1.96/2.12
% 1.96/2.12 Length of proof is 2. Level of proof is 2.
% 1.96/2.12
% 1.96/2.12 ---------------- PROOF ----------------
% 1.96/2.12 % SZS status Theorem
% 1.96/2.12 % SZS output start Refutation
% See solution above
% 1.96/2.12 ------------ end of proof -------------
% 1.96/2.12
% 1.96/2.12
% 1.96/2.12 Search stopped by max_proofs option.
% 1.96/2.12
% 1.96/2.12
% 1.96/2.12 Search stopped by max_proofs option.
% 1.96/2.12
% 1.96/2.12 ============ end of search ============
% 1.96/2.12
% 1.96/2.12 -------------- statistics -------------
% 1.96/2.12 clauses given 10
% 1.96/2.12 clauses generated 69
% 1.96/2.12 clauses kept 65
% 1.96/2.12 clauses forward subsumed 16
% 1.96/2.12 clauses back subsumed 0
% 1.96/2.12 Kbytes malloced 976
% 1.96/2.12
% 1.96/2.12 ----------- times (seconds) -----------
% 1.96/2.12 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.96/2.12
% 1.96/2.12 That finishes the proof of the theorem.
% 1.96/2.12
% 1.96/2.12 Process 6780 finished Wed Jul 27 10:50:57 2022
% 1.96/2.12 Otter interrupted
% 1.96/2.12 PROOF FOUND
%------------------------------------------------------------------------------