%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU145+1 : TPTP v8.1.0. Released v3.3.0.
% 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 13:14:54 EDT 2022
% Result : Theorem 6.70s 6.93s
% Output : Refutation 6.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 23 ( 12 unt; 4 nHn; 16 RR)
% Number of literals : 41 ( 10 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ in(A,B)
| ~ in(B,A) ),
file('SEU145+1.p',unknown),
[] ).
cnf(2,axiom,
( A != singleton(B)
| ~ in(C,A)
| C = B ),
file('SEU145+1.p',unknown),
[] ).
cnf(3,axiom,
( A != singleton(B)
| in(C,A)
| C != B ),
file('SEU145+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SEU145+1.p',unknown),
[] ).
cnf(6,axiom,
( subset(A,B)
| ~ in(dollar_f2(A,B),B) ),
file('SEU145+1.p',unknown),
[] ).
cnf(9,axiom,
( A != set_difference(B,C)
| in(D,A)
| ~ in(D,B)
| in(D,C) ),
file('SEU145+1.p',unknown),
[] ).
cnf(12,axiom,
~ in(dollar_c1,dollar_c3),
file('SEU145+1.p',unknown),
[] ).
cnf(13,axiom,
~ subset(dollar_c3,set_difference(dollar_c2,singleton(dollar_c1))),
file('SEU145+1.p',unknown),
[] ).
cnf(14,plain,
~ in(A,A),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.1.2')] ).
cnf(18,axiom,
A = A,
file('SEU145+1.p',unknown),
[] ).
cnf(20,axiom,
( subset(A,B)
| in(dollar_f2(A,B),A) ),
file('SEU145+1.p',unknown),
[] ).
cnf(22,axiom,
subset(dollar_c3,dollar_c2),
file('SEU145+1.p',unknown),
[] ).
cnf(25,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[18,3,18]),
[iquote('hyper,18,3,18')] ).
cnf(42,plain,
in(dollar_f2(dollar_c3,set_difference(dollar_c2,singleton(dollar_c1))),dollar_c3),
inference(hyper,[status(thm)],[20,13]),
[iquote('hyper,20,13')] ).
cnf(43,plain,
( in(dollar_f2(singleton(A),B),singleton(A))
| in(A,B) ),
inference(hyper,[status(thm)],[20,5,25]),
[iquote('hyper,20,5,25')] ).
cnf(92,plain,
in(dollar_f2(dollar_c3,set_difference(dollar_c2,singleton(dollar_c1))),dollar_c2),
inference(hyper,[status(thm)],[42,5,22]),
[iquote('hyper,42,5,22')] ).
cnf(137,plain,
( in(dollar_f2(dollar_c3,set_difference(dollar_c2,singleton(dollar_c1))),set_difference(dollar_c2,A))
| in(dollar_f2(dollar_c3,set_difference(dollar_c2,singleton(dollar_c1))),A) ),
inference(hyper,[status(thm)],[92,9,18]),
[iquote('hyper,92,9,18')] ).
cnf(918,plain,
in(dollar_f2(singleton(A),A),singleton(A)),
inference(hyper,[status(thm)],[43,14]),
[iquote('hyper,43,14')] ).
cnf(1007,plain,
dollar_f2(singleton(A),A) = A,
inference(hyper,[status(thm)],[918,2,18]),
[iquote('hyper,918,2,18')] ).
cnf(1019,plain,
( A = B
| C != singleton(A)
| ~ in(B,C) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1007,2]),1007]),
[iquote('para_into,1006.1.1,2.3.1,demod,1007')] ).
cnf(1438,plain,
( ~ in(A,dollar_c3)
| B != singleton(dollar_c1)
| ~ in(A,B) ),
inference(para_from,[status(thm),theory(equality)],[1019,12]),
[iquote('para_from,1019.1.1,12.1.1')] ).
cnf(1871,plain,
in(dollar_f2(dollar_c3,set_difference(dollar_c2,singleton(dollar_c1))),singleton(dollar_c1)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[137,6]),13]),
[iquote('hyper,137,6,unit_del,13')] ).
cnf(1879,plain,
$false,
inference(hyper,[status(thm)],[1871,1438,42,18]),
[iquote('hyper,1871,1438,42,18')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU145+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % 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 07:54:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.61/1.90 ----- Otter 3.3f, August 2004 -----
% 1.61/1.90 The process was started by sandbox2 on n027.cluster.edu,
% 1.61/1.90 Wed Jul 27 07:54:06 2022
% 1.61/1.90 The command was "./otter". The process ID is 25238.
% 1.61/1.90
% 1.61/1.90 set(prolog_style_variables).
% 1.61/1.90 set(auto).
% 1.61/1.90 dependent: set(auto1).
% 1.61/1.90 dependent: set(process_input).
% 1.61/1.90 dependent: clear(print_kept).
% 1.61/1.90 dependent: clear(print_new_demod).
% 1.61/1.90 dependent: clear(print_back_demod).
% 1.61/1.90 dependent: clear(print_back_sub).
% 1.61/1.90 dependent: set(control_memory).
% 1.61/1.90 dependent: assign(max_mem, 12000).
% 1.61/1.90 dependent: assign(pick_given_ratio, 4).
% 1.61/1.90 dependent: assign(stats_level, 1).
% 1.61/1.90 dependent: assign(max_seconds, 10800).
% 1.61/1.90 clear(print_given).
% 1.61/1.90
% 1.61/1.90 formula_list(usable).
% 1.61/1.90 all A (A=A).
% 1.61/1.90 all A B (in(A,B)-> -in(B,A)).
% 1.61/1.90 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.61/1.90 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.61/1.90 all A B C (C=set_difference(A,B)<-> (all D (in(D,C)<->in(D,A)& -in(D,B)))).
% 1.61/1.90 $T.
% 1.61/1.90 $T.
% 1.61/1.90 -(all A B C (subset(A,B)->in(C,A)|subset(A,set_difference(B,singleton(C))))).
% 1.61/1.90 all A B subset(A,A).
% 1.61/1.90 end_of_list.
% 1.61/1.90
% 1.61/1.90 -------> usable clausifies to:
% 1.61/1.90
% 1.61/1.90 list(usable).
% 1.61/1.90 0 [] A=A.
% 1.61/1.90 0 [] -in(A,B)| -in(B,A).
% 1.61/1.90 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.61/1.90 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.61/1.90 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.61/1.90 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.61/1.90 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.61/1.90 0 [] subset(A,B)|in($f2(A,B),A).
% 1.61/1.90 0 [] subset(A,B)| -in($f2(A,B),B).
% 1.61/1.90 0 [] C!=set_difference(A,B)| -in(D,C)|in(D,A).
% 1.61/1.90 0 [] C!=set_difference(A,B)| -in(D,C)| -in(D,B).
% 1.61/1.90 0 [] C!=set_difference(A,B)|in(D,C)| -in(D,A)|in(D,B).
% 1.61/1.90 0 [] C=set_difference(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),A).
% 1.61/1.90 0 [] C=set_difference(A,B)|in($f3(A,B,C),C)| -in($f3(A,B,C),B).
% 1.61/1.90 0 [] C=set_difference(A,B)| -in($f3(A,B,C),C)| -in($f3(A,B,C),A)|in($f3(A,B,C),B).
% 1.61/1.90 0 [] $T.
% 1.61/1.90 0 [] $T.
% 1.61/1.90 0 [] subset($c3,$c2).
% 1.61/1.90 0 [] -in($c1,$c3).
% 1.61/1.90 0 [] -subset($c3,set_difference($c2,singleton($c1))).
% 1.61/1.90 0 [] subset(A,A).
% 1.61/1.90 end_of_list.
% 1.61/1.90
% 1.61/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.61/1.90
% 1.61/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.61/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.61/1.90 deletion, with positive clauses in sos and nonpositive
% 1.61/1.90 clauses in usable.
% 1.61/1.90
% 1.61/1.90 dependent: set(knuth_bendix).
% 1.61/1.90 dependent: set(anl_eq).
% 1.61/1.90 dependent: set(para_from).
% 1.61/1.90 dependent: set(para_into).
% 1.61/1.90 dependent: clear(para_from_right).
% 1.61/1.90 dependent: clear(para_into_right).
% 1.61/1.90 dependent: set(para_from_vars).
% 1.61/1.90 dependent: set(eq_units_both_ways).
% 1.61/1.90 dependent: set(dynamic_demod_all).
% 1.61/1.90 dependent: set(dynamic_demod).
% 1.61/1.90 dependent: set(order_eq).
% 1.61/1.90 dependent: set(back_demod).
% 1.61/1.90 dependent: set(lrpo).
% 1.61/1.90 dependent: set(hyper_res).
% 1.61/1.90 dependent: set(unit_deletion).
% 1.61/1.90 dependent: set(factor).
% 1.61/1.90
% 1.61/1.90 ------------> process usable:
% 1.61/1.90 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.61/1.90 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.61/1.90 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.61/1.90 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.61/1.90 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.61/1.90 ** KEPT (pick-wt=8): 6 [] subset(A,B)| -in($f2(A,B),B).
% 1.61/1.90 ** KEPT (pick-wt=11): 7 [] A!=set_difference(B,C)| -in(D,A)|in(D,B).
% 1.61/1.90 ** KEPT (pick-wt=11): 8 [] A!=set_difference(B,C)| -in(D,A)| -in(D,C).
% 1.61/1.90 ** KEPT (pick-wt=14): 9 [] A!=set_difference(B,C)|in(D,A)| -in(D,B)|in(D,C).
% 1.61/1.90 ** KEPT (pick-wt=17): 10 [] A=set_difference(B,C)|in($f3(B,C,A),A)| -in($f3(B,C,A),C).
% 1.61/1.90 ** KEPT (pick-wt=23): 11 [] A=set_difference(B,C)| -in($f3(B,C,A),A)| -in($f3(B,C,A),B)|in($f3(B,C,A),C).
% 1.61/1.90 ** KEPT (pick-wt=3): 12 [] -in($c1,$c3).
% 1.61/1.90 ** KEPT (pick-wt=6): 13 [] -subset($c3,set_difference($c2,singleton($c1))).
% 1.61/1.90
% 1.61/1.90 ------------> process sos:
% 1.61/1.90 ** KEPT (pick-wt=3): 18 [] A=A.
% 1.61/1.90 ** KEPT (pick-wt=14): 19 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.61/1.90 ** KEPT (pick-wt=8): 20 [] subset(A,B)|in($f2(A,B),A).
% 1.61/1.90 ** KEPT (pick-wt=17): 21 [] A=set_difference(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),B).
% 1.61/1.90 ** KEPT (pick-wt=3): 22 [] subset($c3,$c2).
% 1.61/1.90 ** KEPT (pick-wt=3): 23 [] subset(A,A).
% 1.61/1.90 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 1.61/1.90
% 1.61/1.90 ======= end of input processing =======
% 1.61/1.90
% 1.61/1.90 =========== start of search ===========
% 1.61/1.90
% 1.61/1.90
% 1.61/1.90 Resetting weight limit to 13.
% 1.61/1.90
% 1.61/1.90
% 1.61/1.90 Resetting weight limit to 13.
% 6.70/6.93
% 6.70/6.93 sos_size=1069
% 6.70/6.93
% 6.70/6.93
% 6.70/6.93 Resetting weight limit to 11.
% 6.70/6.93
% 6.70/6.93
% 6.70/6.93 Resetting weight limit to 11.
% 6.70/6.93
% 6.70/6.93 sos_size=1155
% 6.70/6.93
% 6.70/6.93
% 6.70/6.93 Resetting weight limit to 10.
% 6.70/6.93
% 6.70/6.93
% 6.70/6.93 Resetting weight limit to 10.
% 6.70/6.93
% 6.70/6.93 sos_size=1219
% 6.70/6.93
% 6.70/6.93 -------- PROOF --------
% 6.70/6.93
% 6.70/6.93 -----> EMPTY CLAUSE at 5.10 sec ----> 1879 [hyper,1871,1438,42,18] $F.
% 6.70/6.93
% 6.70/6.93 Length of proof is 11. Level of proof is 6.
% 6.70/6.93
% 6.70/6.93 ---------------- PROOF ----------------
% 6.70/6.93 % SZS status Theorem
% 6.70/6.93 % SZS output start Refutation
% See solution above
% 6.70/6.93 ------------ end of proof -------------
% 6.70/6.93
% 6.70/6.93
% 6.70/6.93 Search stopped by max_proofs option.
% 6.70/6.93
% 6.70/6.93
% 6.70/6.93 Search stopped by max_proofs option.
% 6.70/6.93
% 6.70/6.93 ============ end of search ============
% 6.70/6.93
% 6.70/6.93 -------------- statistics -------------
% 6.70/6.93 clauses given 537
% 6.70/6.93 clauses generated 370766
% 6.70/6.93 clauses kept 1767
% 6.70/6.93 clauses forward subsumed 11591
% 6.70/6.93 clauses back subsumed 34
% 6.70/6.93 Kbytes malloced 7812
% 6.70/6.93
% 6.70/6.93 ----------- times (seconds) -----------
% 6.70/6.93 user CPU time 5.10 (0 hr, 0 min, 5 sec)
% 6.70/6.93 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 6.70/6.93 wall-clock time 7 (0 hr, 0 min, 7 sec)
% 6.70/6.93
% 6.70/6.93 That finishes the proof of the theorem.
% 6.70/6.93
% 6.70/6.93 Process 25238 finished Wed Jul 27 07:54:13 2022
% 6.70/6.93 Otter interrupted
% 6.70/6.93 PROOF FOUND
%------------------------------------------------------------------------------