%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU152+1 : TPTP v8.1.0. Released v3.3.0.
% 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 13:14:56 EDT 2022
% Result : Theorem 1.78s 1.93s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 9 ( 3 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
set_union2(singleton(dollar_c2),dollar_c1) != dollar_c1,
file('SEU152+1.p',unknown),
[] ).
cnf(4,axiom,
( subset(singleton(A),B)
| ~ in(A,B) ),
file('SEU152+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ subset(A,B)
| set_union2(A,B) = B ),
file('SEU152+1.p',unknown),
[] ).
cnf(10,axiom,
in(dollar_c2,dollar_c1),
file('SEU152+1.p',unknown),
[] ).
cnf(12,plain,
subset(singleton(dollar_c2),dollar_c1),
inference(hyper,[status(thm)],[10,4]),
[iquote('hyper,10,4')] ).
cnf(14,plain,
set_union2(singleton(dollar_c2),dollar_c1) = dollar_c1,
inference(hyper,[status(thm)],[12,5]),
[iquote('hyper,12,5')] ).
cnf(16,plain,
$false,
inference(binary,[status(thm)],[14,2]),
[iquote('binary,14.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU152+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 07:59:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.78/1.93 ----- Otter 3.3f, August 2004 -----
% 1.78/1.93 The process was started by sandbox on n019.cluster.edu,
% 1.78/1.93 Wed Jul 27 07:59:22 2022
% 1.78/1.93 The command was "./otter". The process ID is 2984.
% 1.78/1.93
% 1.78/1.93 set(prolog_style_variables).
% 1.78/1.93 set(auto).
% 1.78/1.93 dependent: set(auto1).
% 1.78/1.93 dependent: set(process_input).
% 1.78/1.93 dependent: clear(print_kept).
% 1.78/1.93 dependent: clear(print_new_demod).
% 1.78/1.93 dependent: clear(print_back_demod).
% 1.78/1.93 dependent: clear(print_back_sub).
% 1.78/1.93 dependent: set(control_memory).
% 1.78/1.93 dependent: assign(max_mem, 12000).
% 1.78/1.93 dependent: assign(pick_given_ratio, 4).
% 1.78/1.93 dependent: assign(stats_level, 1).
% 1.78/1.93 dependent: assign(max_seconds, 10800).
% 1.78/1.93 clear(print_given).
% 1.78/1.93
% 1.78/1.93 formula_list(usable).
% 1.78/1.93 all A (A=A).
% 1.78/1.93 all A B (in(A,B)-> -in(B,A)).
% 1.78/1.93 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.78/1.93 $T.
% 1.78/1.93 $T.
% 1.78/1.93 all A B (set_union2(A,A)=A).
% 1.78/1.93 -(all A B (in(A,B)->set_union2(singleton(A),B)=B)).
% 1.78/1.93 all A B (subset(singleton(A),B)<->in(A,B)).
% 1.78/1.93 all A B subset(A,A).
% 1.78/1.93 all A B (subset(A,B)->set_union2(A,B)=B).
% 1.78/1.93 end_of_list.
% 1.78/1.93
% 1.78/1.93 -------> usable clausifies to:
% 1.78/1.93
% 1.78/1.93 list(usable).
% 1.78/1.93 0 [] A=A.
% 1.78/1.93 0 [] -in(A,B)| -in(B,A).
% 1.78/1.93 0 [] set_union2(A,B)=set_union2(B,A).
% 1.78/1.93 0 [] $T.
% 1.78/1.93 0 [] $T.
% 1.78/1.93 0 [] set_union2(A,A)=A.
% 1.78/1.93 0 [] in($c2,$c1).
% 1.78/1.93 0 [] set_union2(singleton($c2),$c1)!=$c1.
% 1.78/1.93 0 [] -subset(singleton(A),B)|in(A,B).
% 1.78/1.93 0 [] subset(singleton(A),B)| -in(A,B).
% 1.78/1.93 0 [] subset(A,A).
% 1.78/1.93 0 [] -subset(A,B)|set_union2(A,B)=B.
% 1.78/1.93 end_of_list.
% 1.78/1.93
% 1.78/1.93 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.78/1.93
% 1.78/1.93 This is a Horn set with equality. The strategy will be
% 1.78/1.93 Knuth-Bendix and hyper_res, with positive clauses in
% 1.78/1.93 sos and nonpositive clauses in usable.
% 1.78/1.93
% 1.78/1.93 dependent: set(knuth_bendix).
% 1.78/1.93 dependent: set(anl_eq).
% 1.78/1.93 dependent: set(para_from).
% 1.78/1.93 dependent: set(para_into).
% 1.78/1.93 dependent: clear(para_from_right).
% 1.78/1.93 dependent: clear(para_into_right).
% 1.78/1.93 dependent: set(para_from_vars).
% 1.78/1.93 dependent: set(eq_units_both_ways).
% 1.78/1.93 dependent: set(dynamic_demod_all).
% 1.78/1.93 dependent: set(dynamic_demod).
% 1.78/1.93 dependent: set(order_eq).
% 1.78/1.93 dependent: set(back_demod).
% 1.78/1.93 dependent: set(lrpo).
% 1.78/1.93 dependent: set(hyper_res).
% 1.78/1.93 dependent: clear(order_hyper).
% 1.78/1.93
% 1.78/1.93 ------------> process usable:
% 1.78/1.93 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.78/1.93 ** KEPT (pick-wt=6): 2 [] set_union2(singleton($c2),$c1)!=$c1.
% 1.78/1.93 ** KEPT (pick-wt=7): 3 [] -subset(singleton(A),B)|in(A,B).
% 1.78/1.93 ** KEPT (pick-wt=7): 4 [] subset(singleton(A),B)| -in(A,B).
% 1.78/1.93 ** KEPT (pick-wt=8): 5 [] -subset(A,B)|set_union2(A,B)=B.
% 1.78/1.93
% 1.78/1.93 ------------> process sos:
% 1.78/1.93 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.78/1.93 ** KEPT (pick-wt=7): 7 [] set_union2(A,B)=set_union2(B,A).
% 1.78/1.93 ** KEPT (pick-wt=5): 8 [] set_union2(A,A)=A.
% 1.78/1.93 ---> New Demodulator: 9 [new_demod,8] set_union2(A,A)=A.
% 1.78/1.93 ** KEPT (pick-wt=3): 10 [] in($c2,$c1).
% 1.78/1.93 ** KEPT (pick-wt=3): 11 [] subset(A,A).
% 1.78/1.93 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.78/1.93 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.78/1.93 >>>> Starting back demodulation with 9.
% 1.78/1.93
% 1.78/1.93 ======= end of input processing =======
% 1.78/1.93
% 1.78/1.93 =========== start of search ===========
% 1.78/1.93
% 1.78/1.93 -------- PROOF --------
% 1.78/1.93
% 1.78/1.93 ----> UNIT CONFLICT at 0.00 sec ----> 16 [binary,14.1,2.1] $F.
% 1.78/1.93
% 1.78/1.93 Length of proof is 2. Level of proof is 2.
% 1.78/1.93
% 1.78/1.93 ---------------- PROOF ----------------
% 1.78/1.93 % SZS status Theorem
% 1.78/1.93 % SZS output start Refutation
% See solution above
% 1.78/1.93 ------------ end of proof -------------
% 1.78/1.93
% 1.78/1.93
% 1.78/1.93 Search stopped by max_proofs option.
% 1.78/1.93
% 1.78/1.93
% 1.78/1.93 Search stopped by max_proofs option.
% 1.78/1.93
% 1.78/1.93 ============ end of search ============
% 1.78/1.93
% 1.78/1.93 -------------- statistics -------------
% 1.78/1.93 clauses given 4
% 1.78/1.93 clauses generated 4
% 1.78/1.93 clauses kept 13
% 1.78/1.93 clauses forward subsumed 3
% 1.78/1.93 clauses back subsumed 0
% 1.78/1.93 Kbytes malloced 976
% 1.78/1.93
% 1.78/1.93 ----------- times (seconds) -----------
% 1.78/1.93 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.78/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.78/1.93 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.78/1.93
% 1.78/1.93 That finishes the proof of the theorem.
% 1.78/1.93
% 1.78/1.93 Process 2984 finished Wed Jul 27 07:59:23 2022
% 1.78/1.93 Otter interrupted
% 1.78/1.93 PROOF FOUND
%------------------------------------------------------------------------------