%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET885+1 : TPTP v8.1.0. Released v3.2.0.
% 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 13:14:28 EDT 2022
% Result : Theorem 1.58s 1.80s
% Output : Refutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 7 unt; 0 nHn; 8 RR)
% Number of literals : 16 ( 7 equ; 7 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 13 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != singleton(B)
| ~ in(C,A)
| C = B ),
file('SET885+1.p',unknown),
[] ).
cnf(6,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != B ),
file('SET885+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SET885+1.p',unknown),
[] ).
cnf(13,axiom,
dollar_c5 != dollar_c3,
file('SET885+1.p',unknown),
[] ).
cnf(16,axiom,
A = A,
file('SET885+1.p',unknown),
[] ).
cnf(23,axiom,
subset(unordered_pair(dollar_c5,dollar_c4),singleton(dollar_c3)),
file('SET885+1.p',unknown),
[] ).
cnf(26,plain,
in(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[16,6,16]),
[iquote('hyper,16,6,16')] ).
cnf(66,plain,
in(dollar_c5,singleton(dollar_c3)),
inference(hyper,[status(thm)],[23,10,26]),
[iquote('hyper,23,10,26')] ).
cnf(104,plain,
dollar_c5 = dollar_c3,
inference(hyper,[status(thm)],[66,2,16]),
[iquote('hyper,66,2,16')] ).
cnf(106,plain,
$false,
inference(binary,[status(thm)],[104,13]),
[iquote('binary,104.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET885+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n019.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 10:47:07 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.58/1.80 ----- Otter 3.3f, August 2004 -----
% 1.58/1.80 The process was started by sandbox2 on n019.cluster.edu,
% 1.58/1.80 Wed Jul 27 10:47:07 2022
% 1.58/1.80 The command was "./otter". The process ID is 18760.
% 1.58/1.80
% 1.58/1.80 set(prolog_style_variables).
% 1.58/1.80 set(auto).
% 1.58/1.80 dependent: set(auto1).
% 1.58/1.80 dependent: set(process_input).
% 1.58/1.80 dependent: clear(print_kept).
% 1.58/1.80 dependent: clear(print_new_demod).
% 1.58/1.80 dependent: clear(print_back_demod).
% 1.58/1.80 dependent: clear(print_back_sub).
% 1.58/1.80 dependent: set(control_memory).
% 1.58/1.80 dependent: assign(max_mem, 12000).
% 1.58/1.80 dependent: assign(pick_given_ratio, 4).
% 1.58/1.80 dependent: assign(stats_level, 1).
% 1.58/1.80 dependent: assign(max_seconds, 10800).
% 1.58/1.80 clear(print_given).
% 1.58/1.80
% 1.58/1.80 formula_list(usable).
% 1.58/1.80 all A (A=A).
% 1.58/1.80 all A B (in(A,B)-> -in(B,A)).
% 1.58/1.80 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.58/1.80 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.58/1.80 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.58/1.80 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.58/1.80 exists A empty(A).
% 1.58/1.80 exists A (-empty(A)).
% 1.58/1.80 all A B subset(A,A).
% 1.58/1.80 -(all A B C (subset(unordered_pair(A,B),singleton(C))->A=C)).
% 1.58/1.80 end_of_list.
% 1.58/1.80
% 1.58/1.80 -------> usable clausifies to:
% 1.58/1.80
% 1.58/1.80 list(usable).
% 1.58/1.80 0 [] A=A.
% 1.58/1.80 0 [] -in(A,B)| -in(B,A).
% 1.58/1.80 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.58/1.80 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.58/1.80 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.58/1.80 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.58/1.80 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.58/1.80 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.58/1.80 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.58/1.80 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.58/1.80 0 [] C=unordered_pair(A,B)|in($f2(A,B,C),C)|$f2(A,B,C)=A|$f2(A,B,C)=B.
% 1.58/1.80 0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=A.
% 1.58/1.80 0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=B.
% 1.58/1.80 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.58/1.80 0 [] subset(A,B)|in($f3(A,B),A).
% 1.58/1.80 0 [] subset(A,B)| -in($f3(A,B),B).
% 1.58/1.80 0 [] empty($c1).
% 1.58/1.80 0 [] -empty($c2).
% 1.58/1.80 0 [] subset(A,A).
% 1.58/1.80 0 [] subset(unordered_pair($c5,$c4),singleton($c3)).
% 1.58/1.80 0 [] $c5!=$c3.
% 1.58/1.80 end_of_list.
% 1.58/1.80
% 1.58/1.80 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.58/1.80
% 1.58/1.80 This ia a non-Horn set with equality. The strategy will be
% 1.58/1.80 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.58/1.80 deletion, with positive clauses in sos and nonpositive
% 1.58/1.80 clauses in usable.
% 1.58/1.80
% 1.58/1.80 dependent: set(knuth_bendix).
% 1.58/1.80 dependent: set(anl_eq).
% 1.58/1.80 dependent: set(para_from).
% 1.58/1.80 dependent: set(para_into).
% 1.58/1.80 dependent: clear(para_from_right).
% 1.58/1.80 dependent: clear(para_into_right).
% 1.58/1.80 dependent: set(para_from_vars).
% 1.58/1.80 dependent: set(eq_units_both_ways).
% 1.58/1.80 dependent: set(dynamic_demod_all).
% 1.58/1.80 dependent: set(dynamic_demod).
% 1.58/1.80 dependent: set(order_eq).
% 1.58/1.80 dependent: set(back_demod).
% 1.58/1.80 dependent: set(lrpo).
% 1.58/1.80 dependent: set(hyper_res).
% 1.58/1.80 dependent: set(unit_deletion).
% 1.58/1.80 dependent: set(factor).
% 1.58/1.80
% 1.58/1.80 ------------> process usable:
% 1.58/1.80 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.58/1.80 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.58/1.80 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.58/1.80 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.58/1.80 ** KEPT (pick-wt=14): 5 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.58/1.80 ** KEPT (pick-wt=11): 6 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.58/1.80 ** KEPT (pick-wt=11): 7 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.58/1.80 ** KEPT (pick-wt=17): 8 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=B.
% 1.58/1.80 ** KEPT (pick-wt=17): 9 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=C.
% 1.58/1.80 ** KEPT (pick-wt=9): 10 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.58/1.80 ** KEPT (pick-wt=8): 11 [] subset(A,B)| -in($f3(A,B),B).
% 1.58/1.80 ** KEPT (pick-wt=2): 12 [] -empty($c2).
% 1.58/1.80 ** KEPT (pick-wt=3): 13 [] $c5!=$c3.
% 1.58/1.80
% 1.58/1.80 ------------> process sos:
% 1.58/1.80 ** KEPT (pick-wt=3): 16 [] A=A.
% 1.58/1.80 ** KEPT (pick-wt=7): 17 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.58/1.80 ** KEPT (pick-wt=14): 18 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.58/1.80 ** KEPT (pick-wt=23): 19 [] A=unordered_pair(B,C)|in($f2(B,C,A),A)|$f2(B,C,A)=B|$f2(B,C,A)=C.
% 1.58/1.80 ** KEPT (pick-wt=8): 20 [] subset(A,B)|in($f3(A,B),A).
% 1.58/1.80 ** KEPT (pick-wt=2): 21 [] empty($c1).
% 1.58/1.80 ** KEPT (pick-wt=3): 22 [] subset(A,A).
% 1.58/1.80 ** KEPT (pick-wt=6): 23 [] subset(unordered_pair($c5,$c4),singleton($c3)).
% 1.58/1.80 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 1.58/1.80 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.58/1.80
% 1.58/1.80 ======= end of input processing =======
% 1.58/1.80
% 1.58/1.80 =========== start of search ===========
% 1.58/1.80
% 1.58/1.80 -------- PROOF --------
% 1.58/1.80
% 1.58/1.80 ----> UNIT CONFLICT at 0.00 sec ----> 106 [binary,104.1,13.1] $F.
% 1.58/1.80
% 1.58/1.80 Length of proof is 3. Level of proof is 3.
% 1.58/1.80
% 1.58/1.80 ---------------- PROOF ----------------
% 1.58/1.80 % SZS status Theorem
% 1.58/1.80 % SZS output start Refutation
% See solution above
% 1.58/1.80 ------------ end of proof -------------
% 1.58/1.80
% 1.58/1.80
% 1.58/1.80 Search stopped by max_proofs option.
% 1.58/1.80
% 1.58/1.80
% 1.58/1.80 Search stopped by max_proofs option.
% 1.58/1.80
% 1.58/1.80 ============ end of search ============
% 1.58/1.80
% 1.58/1.80 -------------- statistics -------------
% 1.58/1.80 clauses given 9
% 1.58/1.80 clauses generated 111
% 1.58/1.80 clauses kept 104
% 1.58/1.80 clauses forward subsumed 30
% 1.58/1.80 clauses back subsumed 0
% 1.58/1.80 Kbytes malloced 976
% 1.58/1.80
% 1.58/1.80 ----------- times (seconds) -----------
% 1.58/1.80 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.58/1.80 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.58/1.80 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.58/1.80
% 1.58/1.80 That finishes the proof of the theorem.
% 1.58/1.80
% 1.58/1.80 Process 18760 finished Wed Jul 27 10:47:08 2022
% 1.58/1.80 Otter interrupted
% 1.58/1.80 PROOF FOUND
%------------------------------------------------------------------------------