TSTP Solution File: SET910+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET910+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:14:30 EDT 2022
% Result : Theorem 1.93s 2.10s
% Output : Refutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 5 RR)
% Number of literals : 6 ( 2 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
~ in(dollar_c3,dollar_c4),
file('SET910+1.p',unknown),
[] ).
cnf(4,axiom,
( set_intersection2(A,singleton(B)) != singleton(B)
| in(B,A) ),
file('SET910+1.p',unknown),
[] ).
cnf(10,axiom,
set_intersection2(dollar_c4,singleton(dollar_c3)) = singleton(dollar_c3),
file('SET910+1.p',unknown),
[] ).
cnf(14,plain,
in(dollar_c3,dollar_c4),
inference(hyper,[status(thm)],[10,4]),
[iquote('hyper,10,4')] ).
cnf(15,plain,
$false,
inference(binary,[status(thm)],[14,3]),
[iquote('binary,14.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET910+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 10:59:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.93/2.10 ----- Otter 3.3f, August 2004 -----
% 1.93/2.10 The process was started by sandbox on n015.cluster.edu,
% 1.93/2.10 Wed Jul 27 10:59:57 2022
% 1.93/2.10 The command was "./otter". The process ID is 32256.
% 1.93/2.10
% 1.93/2.10 set(prolog_style_variables).
% 1.93/2.10 set(auto).
% 1.93/2.10 dependent: set(auto1).
% 1.93/2.10 dependent: set(process_input).
% 1.93/2.10 dependent: clear(print_kept).
% 1.93/2.10 dependent: clear(print_new_demod).
% 1.93/2.10 dependent: clear(print_back_demod).
% 1.93/2.10 dependent: clear(print_back_sub).
% 1.93/2.10 dependent: set(control_memory).
% 1.93/2.10 dependent: assign(max_mem, 12000).
% 1.93/2.10 dependent: assign(pick_given_ratio, 4).
% 1.93/2.10 dependent: assign(stats_level, 1).
% 1.93/2.10 dependent: assign(max_seconds, 10800).
% 1.93/2.10 clear(print_given).
% 1.93/2.10
% 1.93/2.10 formula_list(usable).
% 1.93/2.10 all A (A=A).
% 1.93/2.10 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.93/2.10 all A B (set_intersection2(A,A)=A).
% 1.93/2.10 all A B (in(A,B)-> -in(B,A)).
% 1.93/2.10 exists A empty(A).
% 1.93/2.10 exists A (-empty(A)).
% 1.93/2.10 -(all A B (set_intersection2(A,singleton(B))=singleton(B)->in(B,A))).
% 1.93/2.10 all A B (set_intersection2(A,singleton(B))=singleton(B)->in(B,A)).
% 1.93/2.10 end_of_list.
% 1.93/2.10
% 1.93/2.10 -------> usable clausifies to:
% 1.93/2.10
% 1.93/2.10 list(usable).
% 1.93/2.10 0 [] A=A.
% 1.93/2.10 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.93/2.10 0 [] set_intersection2(A,A)=A.
% 1.93/2.10 0 [] -in(A,B)| -in(B,A).
% 1.93/2.10 0 [] empty($c1).
% 1.93/2.10 0 [] -empty($c2).
% 1.93/2.10 0 [] set_intersection2($c4,singleton($c3))=singleton($c3).
% 1.93/2.10 0 [] -in($c3,$c4).
% 1.93/2.10 0 [] set_intersection2(A,singleton(B))!=singleton(B)|in(B,A).
% 1.93/2.10 end_of_list.
% 1.93/2.10
% 1.93/2.10 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.93/2.10
% 1.93/2.10 This is a Horn set with equality. The strategy will be
% 1.93/2.10 Knuth-Bendix and hyper_res, with positive clauses in
% 1.93/2.10 sos and nonpositive clauses in usable.
% 1.93/2.10
% 1.93/2.10 dependent: set(knuth_bendix).
% 1.93/2.10 dependent: set(anl_eq).
% 1.93/2.10 dependent: set(para_from).
% 1.93/2.10 dependent: set(para_into).
% 1.93/2.10 dependent: clear(para_from_right).
% 1.93/2.10 dependent: clear(para_into_right).
% 1.93/2.10 dependent: set(para_from_vars).
% 1.93/2.10 dependent: set(eq_units_both_ways).
% 1.93/2.10 dependent: set(dynamic_demod_all).
% 1.93/2.10 dependent: set(dynamic_demod).
% 1.93/2.10 dependent: set(order_eq).
% 1.93/2.10 dependent: set(back_demod).
% 1.93/2.10 dependent: set(lrpo).
% 1.93/2.10 dependent: set(hyper_res).
% 1.93/2.10 dependent: clear(order_hyper).
% 1.93/2.10
% 1.93/2.10 ------------> process usable:
% 1.93/2.10 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.93/2.10 ** KEPT (pick-wt=2): 2 [] -empty($c2).
% 1.93/2.10 ** KEPT (pick-wt=3): 3 [] -in($c3,$c4).
% 1.93/2.10 ** KEPT (pick-wt=10): 4 [] set_intersection2(A,singleton(B))!=singleton(B)|in(B,A).
% 1.93/2.10
% 1.93/2.10 ------------> process sos:
% 1.93/2.10 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.93/2.10 ** KEPT (pick-wt=7): 6 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.93/2.10 ** KEPT (pick-wt=5): 7 [] set_intersection2(A,A)=A.
% 1.93/2.10 ---> New Demodulator: 8 [new_demod,7] set_intersection2(A,A)=A.
% 1.93/2.10 ** KEPT (pick-wt=2): 9 [] empty($c1).
% 1.93/2.10 ** KEPT (pick-wt=7): 10 [] set_intersection2($c4,singleton($c3))=singleton($c3).
% 1.93/2.10 ---> New Demodulator: 11 [new_demod,10] set_intersection2($c4,singleton($c3))=singleton($c3).
% 1.93/2.10 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.93/2.10 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.93/2.10 >>>> Starting back demodulation with 8.
% 1.93/2.10 >>>> Starting back demodulation with 11.
% 1.93/2.10
% 1.93/2.10 ======= end of input processing =======
% 1.93/2.10
% 1.93/2.10 =========== start of search ===========
% 1.93/2.10
% 1.93/2.10 -------- PROOF --------
% 1.93/2.10
% 1.93/2.10 ----> UNIT CONFLICT at 0.00 sec ----> 15 [binary,14.1,3.1] $F.
% 1.93/2.10
% 1.93/2.10 Length of proof is 1. Level of proof is 1.
% 1.93/2.10
% 1.93/2.10 ---------------- PROOF ----------------
% 1.93/2.10 % SZS status Theorem
% 1.93/2.10 % SZS output start Refutation
% See solution above
% 1.93/2.10 ------------ end of proof -------------
% 1.93/2.10
% 1.93/2.10
% 1.93/2.10 Search stopped by max_proofs option.
% 1.93/2.10
% 1.93/2.10
% 1.93/2.10 Search stopped by max_proofs option.
% 1.93/2.10
% 1.93/2.10 ============ end of search ============
% 1.93/2.10
% 1.93/2.10 -------------- statistics -------------
% 1.93/2.10 clauses given 6
% 1.93/2.10 clauses generated 10
% 1.93/2.10 clauses kept 12
% 1.93/2.10 clauses forward subsumed 9
% 1.93/2.10 clauses back subsumed 0
% 1.93/2.10 Kbytes malloced 976
% 1.93/2.10
% 1.93/2.10 ----------- times (seconds) -----------
% 1.93/2.10 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.10 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.93/2.10
% 1.93/2.10 That finishes the proof of the theorem.
% 1.93/2.10
% 1.93/2.10 Process 32256 finished Wed Jul 27 10:59:58 2022
% 1.93/2.10 Otter interrupted
% 1.93/2.10 PROOF FOUND
%------------------------------------------------------------------------------