TSTP Solution File: SEU161+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU161+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:14:59 EDT 2022
% Result : Theorem 1.67s 1.88s
% Output : Refutation 1.67s
% 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 ( 3 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(2,axiom,
set_union2(singleton(dollar_c2),dollar_c1) != dollar_c1,
file('SEU161+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ in(A,B)
| set_union2(singleton(A),B) = B ),
file('SEU161+1.p',unknown),
[] ).
cnf(8,axiom,
in(dollar_c2,dollar_c1),
file('SEU161+1.p',unknown),
[] ).
cnf(9,plain,
set_union2(singleton(dollar_c2),dollar_c1) = dollar_c1,
inference(hyper,[status(thm)],[8,3]),
[iquote('hyper,8,3')] ).
cnf(11,plain,
$false,
inference(binary,[status(thm)],[9,2]),
[iquote('binary,9.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU161+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 07:43:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.88 ----- Otter 3.3f, August 2004 -----
% 1.67/1.88 The process was started by sandbox2 on n012.cluster.edu,
% 1.67/1.88 Wed Jul 27 07:43:35 2022
% 1.67/1.88 The command was "./otter". The process ID is 32589.
% 1.67/1.88
% 1.67/1.88 set(prolog_style_variables).
% 1.67/1.88 set(auto).
% 1.67/1.88 dependent: set(auto1).
% 1.67/1.88 dependent: set(process_input).
% 1.67/1.88 dependent: clear(print_kept).
% 1.67/1.88 dependent: clear(print_new_demod).
% 1.67/1.88 dependent: clear(print_back_demod).
% 1.67/1.88 dependent: clear(print_back_sub).
% 1.67/1.88 dependent: set(control_memory).
% 1.67/1.88 dependent: assign(max_mem, 12000).
% 1.67/1.88 dependent: assign(pick_given_ratio, 4).
% 1.67/1.88 dependent: assign(stats_level, 1).
% 1.67/1.88 dependent: assign(max_seconds, 10800).
% 1.67/1.88 clear(print_given).
% 1.67/1.88
% 1.67/1.88 formula_list(usable).
% 1.67/1.88 all A (A=A).
% 1.67/1.88 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.67/1.88 all A B (set_union2(A,A)=A).
% 1.67/1.88 all A B (in(A,B)-> -in(B,A)).
% 1.67/1.88 $T.
% 1.67/1.88 $T.
% 1.67/1.88 -(all A B (in(A,B)->set_union2(singleton(A),B)=B)).
% 1.67/1.88 all A B (in(A,B)->set_union2(singleton(A),B)=B).
% 1.67/1.88 end_of_list.
% 1.67/1.88
% 1.67/1.88 -------> usable clausifies to:
% 1.67/1.88
% 1.67/1.88 list(usable).
% 1.67/1.88 0 [] A=A.
% 1.67/1.88 0 [] set_union2(A,B)=set_union2(B,A).
% 1.67/1.88 0 [] set_union2(A,A)=A.
% 1.67/1.88 0 [] -in(A,B)| -in(B,A).
% 1.67/1.88 0 [] $T.
% 1.67/1.88 0 [] $T.
% 1.67/1.88 0 [] in($c2,$c1).
% 1.67/1.88 0 [] set_union2(singleton($c2),$c1)!=$c1.
% 1.67/1.88 0 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 1.67/1.88 end_of_list.
% 1.67/1.88
% 1.67/1.88 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.67/1.88
% 1.67/1.88 This is a Horn set with equality. The strategy will be
% 1.67/1.88 Knuth-Bendix and hyper_res, with positive clauses in
% 1.67/1.88 sos and nonpositive clauses in usable.
% 1.67/1.88
% 1.67/1.88 dependent: set(knuth_bendix).
% 1.67/1.88 dependent: set(anl_eq).
% 1.67/1.88 dependent: set(para_from).
% 1.67/1.88 dependent: set(para_into).
% 1.67/1.88 dependent: clear(para_from_right).
% 1.67/1.88 dependent: clear(para_into_right).
% 1.67/1.88 dependent: set(para_from_vars).
% 1.67/1.88 dependent: set(eq_units_both_ways).
% 1.67/1.88 dependent: set(dynamic_demod_all).
% 1.67/1.88 dependent: set(dynamic_demod).
% 1.67/1.88 dependent: set(order_eq).
% 1.67/1.88 dependent: set(back_demod).
% 1.67/1.88 dependent: set(lrpo).
% 1.67/1.88 dependent: set(hyper_res).
% 1.67/1.88 dependent: clear(order_hyper).
% 1.67/1.88
% 1.67/1.88 ------------> process usable:
% 1.67/1.88 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.67/1.88 ** KEPT (pick-wt=6): 2 [] set_union2(singleton($c2),$c1)!=$c1.
% 1.67/1.88 ** KEPT (pick-wt=9): 3 [] -in(A,B)|set_union2(singleton(A),B)=B.
% 1.67/1.88
% 1.67/1.88 ------------> process sos:
% 1.67/1.88 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.67/1.88 ** KEPT (pick-wt=7): 5 [] set_union2(A,B)=set_union2(B,A).
% 1.67/1.88 ** KEPT (pick-wt=5): 6 [] set_union2(A,A)=A.
% 1.67/1.88 ---> New Demodulator: 7 [new_demod,6] set_union2(A,A)=A.
% 1.67/1.88 ** KEPT (pick-wt=3): 8 [] in($c2,$c1).
% 1.67/1.88 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.67/1.88 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.67/1.88 >>>> Starting back demodulation with 7.
% 1.67/1.88
% 1.67/1.88 ======= end of input processing =======
% 1.67/1.88
% 1.67/1.88 =========== start of search ===========
% 1.67/1.88
% 1.67/1.88 -------- PROOF --------
% 1.67/1.88
% 1.67/1.88 ----> UNIT CONFLICT at 0.00 sec ----> 11 [binary,9.1,2.1] $F.
% 1.67/1.88
% 1.67/1.88 Length of proof is 1. Level of proof is 1.
% 1.67/1.88
% 1.67/1.88 ---------------- PROOF ----------------
% 1.67/1.88 % SZS status Theorem
% 1.67/1.88 % SZS output start Refutation
% See solution above
% 1.67/1.88 ------------ end of proof -------------
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88 ============ end of search ============
% 1.67/1.88
% 1.67/1.88 -------------- statistics -------------
% 1.67/1.88 clauses given 2
% 1.67/1.88 clauses generated 1
% 1.67/1.88 clauses kept 8
% 1.67/1.88 clauses forward subsumed 2
% 1.67/1.88 clauses back subsumed 0
% 1.67/1.88 Kbytes malloced 976
% 1.67/1.88
% 1.67/1.88 ----------- times (seconds) -----------
% 1.67/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.88 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.67/1.88
% 1.67/1.88 That finishes the proof of the theorem.
% 1.67/1.88
% 1.67/1.88 Process 32589 finished Wed Jul 27 07:43:37 2022
% 1.67/1.88 Otter interrupted
% 1.67/1.88 PROOF FOUND
%------------------------------------------------------------------------------