%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU124+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 13:14:49 EDT 2022
% Result : Theorem 3.05s 3.24s
% Output : Refutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 13 unt; 1 nHn; 11 RR)
% Number of literals : 23 ( 7 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( A != set_union2(B,C)
| in(D,A)
| ~ in(D,C) ),
file('SEU124+1.p',unknown),
[] ).
cnf(8,axiom,
( subset(A,B)
| ~ in(dollar_f2(A,B),B) ),
file('SEU124+1.p',unknown),
[] ).
cnf(14,axiom,
~ subset(dollar_c4,set_union2(dollar_c4,dollar_c3)),
file('SEU124+1.p',unknown),
[] ).
cnf(15,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU124+1.p',unknown),
[] ).
cnf(22,axiom,
set_union2(A,B) = set_union2(B,A),
file('SEU124+1.p',unknown),
[] ).
cnf(24,axiom,
( subset(A,B)
| in(dollar_f2(A,B),A) ),
file('SEU124+1.p',unknown),
[] ).
cnf(25,axiom,
empty(empty_set),
file('SEU124+1.p',unknown),
[] ).
cnf(28,axiom,
empty(dollar_c1),
file('SEU124+1.p',unknown),
[] ).
cnf(30,axiom,
set_union2(A,empty_set) = A,
file('SEU124+1.p',unknown),
[] ).
cnf(41,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[28,15,25]),
[iquote('hyper,28,15,25')] ).
cnf(46,plain,
set_union2(A,dollar_c1) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[30]),41]),
[iquote('back_demod,30,demod,41')] ).
cnf(59,plain,
~ subset(dollar_c4,set_union2(dollar_c3,dollar_c4)),
inference(para_from,[status(thm),theory(equality)],[22,14]),
[iquote('para_from,22.1.1,14.1.2')] ).
cnf(66,plain,
set_union2(dollar_c1,A) = A,
inference(para_into,[status(thm),theory(equality)],[46,22]),
[iquote('para_into,46.1.1,22.1.1')] ).
cnf(374,plain,
in(dollar_f2(dollar_c4,set_union2(dollar_c3,dollar_c4)),dollar_c4),
inference(hyper,[status(thm)],[24,59]),
[iquote('hyper,24,59')] ).
cnf(745,plain,
in(dollar_f2(dollar_c4,set_union2(dollar_c3,dollar_c4)),set_union2(A,dollar_c4)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[374,4,66]),66]),
[iquote('hyper,374,4,65,demod,66')] ).
cnf(3807,plain,
subset(dollar_c4,set_union2(dollar_c3,dollar_c4)),
inference(hyper,[status(thm)],[745,8]),
[iquote('hyper,745,8')] ).
cnf(3808,plain,
$false,
inference(binary,[status(thm)],[3807,59]),
[iquote('binary,3807.1,59.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU124+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n029.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 07:46:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.75/1.94 ----- Otter 3.3f, August 2004 -----
% 1.75/1.94 The process was started by sandbox2 on n029.cluster.edu,
% 1.75/1.94 Wed Jul 27 07:46:59 2022
% 1.75/1.94 The command was "./otter". The process ID is 30107.
% 1.75/1.94
% 1.75/1.94 set(prolog_style_variables).
% 1.75/1.94 set(auto).
% 1.75/1.94 dependent: set(auto1).
% 1.75/1.94 dependent: set(process_input).
% 1.75/1.94 dependent: clear(print_kept).
% 1.75/1.94 dependent: clear(print_new_demod).
% 1.75/1.94 dependent: clear(print_back_demod).
% 1.75/1.94 dependent: clear(print_back_sub).
% 1.75/1.94 dependent: set(control_memory).
% 1.75/1.94 dependent: assign(max_mem, 12000).
% 1.75/1.94 dependent: assign(pick_given_ratio, 4).
% 1.75/1.94 dependent: assign(stats_level, 1).
% 1.75/1.94 dependent: assign(max_seconds, 10800).
% 1.75/1.94 clear(print_given).
% 1.75/1.94
% 1.75/1.94 formula_list(usable).
% 1.75/1.94 all A (A=A).
% 1.75/1.94 all A B (in(A,B)-> -in(B,A)).
% 1.75/1.94 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.75/1.94 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.75/1.94 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.75/1.94 $T.
% 1.75/1.94 $T.
% 1.75/1.94 empty(empty_set).
% 1.75/1.94 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.75/1.94 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.75/1.94 all A B (set_union2(A,A)=A).
% 1.75/1.94 exists A empty(A).
% 1.75/1.94 exists A (-empty(A)).
% 1.75/1.94 all A B subset(A,A).
% 1.75/1.94 all A (set_union2(A,empty_set)=A).
% 1.75/1.94 all A (empty(A)->A=empty_set).
% 1.75/1.94 all A B (-(in(A,B)&empty(B))).
% 1.75/1.94 -(all A B subset(A,set_union2(A,B))).
% 1.75/1.94 all A B (-(empty(A)&A!=B&empty(B))).
% 1.75/1.94 end_of_list.
% 1.75/1.94
% 1.75/1.94 -------> usable clausifies to:
% 1.75/1.94
% 1.75/1.94 list(usable).
% 1.75/1.94 0 [] A=A.
% 1.75/1.94 0 [] -in(A,B)| -in(B,A).
% 1.75/1.94 0 [] set_union2(A,B)=set_union2(B,A).
% 1.75/1.94 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.75/1.94 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.75/1.94 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.75/1.94 0 [] C=set_union2(A,B)|in($f1(A,B,C),C)|in($f1(A,B,C),A)|in($f1(A,B,C),B).
% 1.75/1.94 0 [] C=set_union2(A,B)| -in($f1(A,B,C),C)| -in($f1(A,B,C),A).
% 1.75/1.94 0 [] C=set_union2(A,B)| -in($f1(A,B,C),C)| -in($f1(A,B,C),B).
% 1.75/1.94 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.75/1.94 0 [] subset(A,B)|in($f2(A,B),A).
% 1.75/1.94 0 [] subset(A,B)| -in($f2(A,B),B).
% 1.75/1.94 0 [] $T.
% 1.75/1.94 0 [] $T.
% 1.75/1.94 0 [] empty(empty_set).
% 1.75/1.94 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.75/1.94 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.75/1.94 0 [] set_union2(A,A)=A.
% 1.75/1.94 0 [] empty($c1).
% 1.75/1.94 0 [] -empty($c2).
% 1.75/1.94 0 [] subset(A,A).
% 1.75/1.94 0 [] set_union2(A,empty_set)=A.
% 1.75/1.94 0 [] -empty(A)|A=empty_set.
% 1.75/1.94 0 [] -in(A,B)| -empty(B).
% 1.75/1.94 0 [] -subset($c4,set_union2($c4,$c3)).
% 1.75/1.94 0 [] -empty(A)|A=B| -empty(B).
% 1.75/1.94 end_of_list.
% 1.75/1.94
% 1.75/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.75/1.94
% 1.75/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.75/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.75/1.94 deletion, with positive clauses in sos and nonpositive
% 1.75/1.94 clauses in usable.
% 1.75/1.94
% 1.75/1.94 dependent: set(knuth_bendix).
% 1.75/1.94 dependent: set(anl_eq).
% 1.75/1.94 dependent: set(para_from).
% 1.75/1.94 dependent: set(para_into).
% 1.75/1.94 dependent: clear(para_from_right).
% 1.75/1.94 dependent: clear(para_into_right).
% 1.75/1.94 dependent: set(para_from_vars).
% 1.75/1.94 dependent: set(eq_units_both_ways).
% 1.75/1.94 dependent: set(dynamic_demod_all).
% 1.75/1.94 dependent: set(dynamic_demod).
% 1.75/1.94 dependent: set(order_eq).
% 1.75/1.94 dependent: set(back_demod).
% 1.75/1.94 dependent: set(lrpo).
% 1.75/1.94 dependent: set(hyper_res).
% 1.75/1.94 dependent: set(unit_deletion).
% 1.75/1.94 dependent: set(factor).
% 1.75/1.94
% 1.75/1.94 ------------> process usable:
% 1.75/1.94 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.75/1.94 ** KEPT (pick-wt=14): 2 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.75/1.94 ** KEPT (pick-wt=11): 3 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.75/1.94 ** KEPT (pick-wt=11): 4 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.75/1.94 ** KEPT (pick-wt=17): 5 [] A=set_union2(B,C)| -in($f1(B,C,A),A)| -in($f1(B,C,A),B).
% 1.75/1.94 ** KEPT (pick-wt=17): 6 [] A=set_union2(B,C)| -in($f1(B,C,A),A)| -in($f1(B,C,A),C).
% 1.75/1.94 ** KEPT (pick-wt=9): 7 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.75/1.94 ** KEPT (pick-wt=8): 8 [] subset(A,B)| -in($f2(A,B),B).
% 1.75/1.94 ** KEPT (pick-wt=6): 9 [] empty(A)| -empty(set_union2(A,B)).
% 1.75/1.94 ** KEPT (pick-wt=6): 10 [] empty(A)| -empty(set_union2(B,A)).
% 1.75/1.94 ** KEPT (pick-wt=2): 11 [] -empty($c2).
% 1.75/1.94 ** KEPT (pick-wt=5): 12 [] -empty(A)|A=empty_set.
% 1.75/1.94 ** KEPT (pick-wt=5): 13 [] -in(A,B)| -empty(B).
% 1.75/1.94 ** KEPT (pick-wt=5): 14 [] -subset($c4,set_union2($c4,$c3)).
% 1.75/1.94 ** KEPT (pick-wt=7): 15 [] -empty(A)|A=B| -empty(B).
% 1.75/1.94
% 1.75/1.94 ------------> process sos:
% 1.75/1.94 ** KEPT (pick-wt=3): 21 [] A=A.
% 1.75/1.94 ** KEPT (pick-wt=7): 22 [] set_union2(A,B)=set_union2(B,A).
% 1.75/1.94 ** KEPT (pick-wt=23): 23 [] A=set_union2(B,C)|in($f1(B,C,A),A)|in($f1(B,C,A),B)|in($f1(B,C,A),C).
% 3.05/3.24 ** KEPT (pick-wt=8): 24 [] subset(A,B)|in($f2(A,B),A).
% 3.05/3.24 ** KEPT (pick-wt=2): 25 [] empty(empty_set).
% 3.05/3.24 ** KEPT (pick-wt=5): 26 [] set_union2(A,A)=A.
% 3.05/3.24 ---> New Demodulator: 27 [new_demod,26] set_union2(A,A)=A.
% 3.05/3.24 ** KEPT (pick-wt=2): 28 [] empty($c1).
% 3.05/3.24 ** KEPT (pick-wt=3): 29 [] subset(A,A).
% 3.05/3.24 ** KEPT (pick-wt=5): 30 [] set_union2(A,empty_set)=A.
% 3.05/3.24 ---> New Demodulator: 31 [new_demod,30] set_union2(A,empty_set)=A.
% 3.05/3.24 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] A=A.
% 3.05/3.24 21 back subsumes 20.
% 3.05/3.24 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] set_union2(A,B)=set_union2(B,A).
% 3.05/3.24 >>>> Starting back demodulation with 27.
% 3.05/3.24 >> back demodulating 17 with 27.
% 3.05/3.24 >>>> Starting back demodulation with 31.
% 3.05/3.24
% 3.05/3.24 ======= end of input processing =======
% 3.05/3.24
% 3.05/3.24 =========== start of search ===========
% 3.05/3.24
% 3.05/3.24
% 3.05/3.24 Resetting weight limit to 12.
% 3.05/3.24
% 3.05/3.24
% 3.05/3.24 Resetting weight limit to 12.
% 3.05/3.24
% 3.05/3.24 sos_size=3241
% 3.05/3.24
% 3.05/3.24
% 3.05/3.24 Resetting weight limit to 11.
% 3.05/3.24
% 3.05/3.24
% 3.05/3.24 Resetting weight limit to 11.
% 3.05/3.24
% 3.05/3.24 sos_size=3291
% 3.05/3.24
% 3.05/3.24
% 3.05/3.24 Resetting weight limit to 10.
% 3.05/3.24
% 3.05/3.24
% 3.05/3.24 Resetting weight limit to 10.
% 3.05/3.24
% 3.05/3.24 sos_size=3207
% 3.05/3.24
% 3.05/3.24 -------- PROOF --------
% 3.05/3.24
% 3.05/3.24 ----> UNIT CONFLICT at 1.29 sec ----> 3808 [binary,3807.1,59.1] $F.
% 3.05/3.24
% 3.05/3.24 Length of proof is 7. Level of proof is 5.
% 3.05/3.24
% 3.05/3.24 ---------------- PROOF ----------------
% 3.05/3.24 % SZS status Theorem
% 3.05/3.24 % SZS output start Refutation
% See solution above
% 3.05/3.24 ------------ end of proof -------------
% 3.05/3.24
% 3.05/3.24
% 3.05/3.24 Search stopped by max_proofs option.
% 3.05/3.24
% 3.05/3.24
% 3.05/3.24 Search stopped by max_proofs option.
% 3.05/3.24
% 3.05/3.24 ============ end of search ============
% 3.05/3.24
% 3.05/3.24 -------------- statistics -------------
% 3.05/3.24 clauses given 168
% 3.05/3.24 clauses generated 20192
% 3.05/3.24 clauses kept 3802
% 3.05/3.24 clauses forward subsumed 6328
% 3.05/3.24 clauses back subsumed 419
% 3.05/3.24 Kbytes malloced 4882
% 3.05/3.24
% 3.05/3.24 ----------- times (seconds) -----------
% 3.05/3.24 user CPU time 1.29 (0 hr, 0 min, 1 sec)
% 3.05/3.24 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.05/3.24 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.05/3.24
% 3.05/3.24 That finishes the proof of the theorem.
% 3.05/3.24
% 3.05/3.24 Process 30107 finished Wed Jul 27 07:47:02 2022
% 3.05/3.24 Otter interrupted
% 3.05/3.24 PROOF FOUND
%------------------------------------------------------------------------------