%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET958+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:14:35 EDT 2022
% Result : Theorem 1.67s 1.89s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of clauses : 11 ( 6 unt; 1 nHn; 10 RR)
% Number of literals : 16 ( 3 equ; 5 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( subset(A,B)
| ~ in(dollar_f1(A,B),B) ),
file('SET958+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ in(A,dollar_c4)
| A = ordered_pair(dollar_f3(A),dollar_f2(A)) ),
file('SET958+1.p',unknown),
[] ).
cnf(7,plain,
( ~ in(A,dollar_c4)
| ordered_pair(dollar_f3(A),dollar_f2(A)) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.2')] ).
cnf(8,axiom,
( ~ in(ordered_pair(A,B),dollar_c4)
| in(ordered_pair(A,B),dollar_c3) ),
file('SET958+1.p',unknown),
[] ).
cnf(9,axiom,
~ subset(dollar_c4,dollar_c3),
file('SET958+1.p',unknown),
[] ).
cnf(13,axiom,
( subset(A,B)
| in(dollar_f1(A,B),A) ),
file('SET958+1.p',unknown),
[] ).
cnf(19,plain,
in(dollar_f1(dollar_c4,dollar_c3),dollar_c4),
inference(hyper,[status(thm)],[13,9]),
[iquote('hyper,13,9')] ).
cnf(27,plain,
ordered_pair(dollar_f3(dollar_f1(dollar_c4,dollar_c3)),dollar_f2(dollar_f1(dollar_c4,dollar_c3))) = dollar_f1(dollar_c4,dollar_c3),
inference(hyper,[status(thm)],[19,7]),
[iquote('hyper,19,7')] ).
cnf(72,plain,
in(dollar_f1(dollar_c4,dollar_c3),dollar_c3),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[27,8]),27]),19]),
[iquote('para_from,26.1.1,8.2.1,demod,27,unit_del,19')] ).
cnf(74,plain,
subset(dollar_c4,dollar_c3),
inference(hyper,[status(thm)],[72,3]),
[iquote('hyper,72,3')] ).
cnf(75,plain,
$false,
inference(binary,[status(thm)],[74,9]),
[iquote('binary,74.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET958+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 11:07:22 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.89 ----- Otter 3.3f, August 2004 -----
% 1.67/1.89 The process was started by sandbox2 on n027.cluster.edu,
% 1.67/1.89 Wed Jul 27 11:07:22 2022
% 1.67/1.89 The command was "./otter". The process ID is 15187.
% 1.67/1.89
% 1.67/1.89 set(prolog_style_variables).
% 1.67/1.89 set(auto).
% 1.67/1.89 dependent: set(auto1).
% 1.67/1.89 dependent: set(process_input).
% 1.67/1.89 dependent: clear(print_kept).
% 1.67/1.89 dependent: clear(print_new_demod).
% 1.67/1.89 dependent: clear(print_back_demod).
% 1.67/1.89 dependent: clear(print_back_sub).
% 1.67/1.89 dependent: set(control_memory).
% 1.67/1.89 dependent: assign(max_mem, 12000).
% 1.67/1.89 dependent: assign(pick_given_ratio, 4).
% 1.67/1.89 dependent: assign(stats_level, 1).
% 1.67/1.89 dependent: assign(max_seconds, 10800).
% 1.67/1.89 clear(print_given).
% 1.67/1.89
% 1.67/1.89 formula_list(usable).
% 1.67/1.89 all A (A=A).
% 1.67/1.89 all A B (in(A,B)-> -in(B,A)).
% 1.67/1.89 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.67/1.89 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.67/1.89 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.67/1.89 all A B (-empty(ordered_pair(A,B))).
% 1.67/1.89 exists A empty(A).
% 1.67/1.89 exists A (-empty(A)).
% 1.67/1.89 all A B subset(A,A).
% 1.67/1.89 -(all A B ((all C (-(in(C,A)& (all D E (C!=ordered_pair(D,E))))))& (all C D (in(ordered_pair(C,D),A)->in(ordered_pair(C,D),B)))->subset(A,B))).
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 -------> usable clausifies to:
% 1.67/1.89
% 1.67/1.89 list(usable).
% 1.67/1.89 0 [] A=A.
% 1.67/1.89 0 [] -in(A,B)| -in(B,A).
% 1.67/1.89 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.67/1.89 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.67/1.89 0 [] subset(A,B)|in($f1(A,B),A).
% 1.67/1.89 0 [] subset(A,B)| -in($f1(A,B),B).
% 1.67/1.89 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.67/1.89 0 [] -empty(ordered_pair(A,B)).
% 1.67/1.89 0 [] empty($c1).
% 1.67/1.89 0 [] -empty($c2).
% 1.67/1.89 0 [] subset(A,A).
% 1.67/1.89 0 [] -in(C,$c4)|C=ordered_pair($f3(C),$f2(C)).
% 1.67/1.89 0 [] -in(ordered_pair(X1,D),$c4)|in(ordered_pair(X1,D),$c3).
% 1.67/1.89 0 [] -subset($c4,$c3).
% 1.67/1.89 end_of_list.
% 1.67/1.89
% 1.67/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.67/1.89
% 1.67/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.67/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.67/1.89 deletion, with positive clauses in sos and nonpositive
% 1.67/1.89 clauses in usable.
% 1.67/1.89
% 1.67/1.89 dependent: set(knuth_bendix).
% 1.67/1.89 dependent: set(anl_eq).
% 1.67/1.89 dependent: set(para_from).
% 1.67/1.89 dependent: set(para_into).
% 1.67/1.89 dependent: clear(para_from_right).
% 1.67/1.89 dependent: clear(para_into_right).
% 1.67/1.89 dependent: set(para_from_vars).
% 1.67/1.89 dependent: set(eq_units_both_ways).
% 1.67/1.89 dependent: set(dynamic_demod_all).
% 1.67/1.89 dependent: set(dynamic_demod).
% 1.67/1.89 dependent: set(order_eq).
% 1.67/1.89 dependent: set(back_demod).
% 1.67/1.89 dependent: set(lrpo).
% 1.67/1.89 dependent: set(hyper_res).
% 1.67/1.89 dependent: set(unit_deletion).
% 1.67/1.89 dependent: set(factor).
% 1.67/1.89
% 1.67/1.89 ------------> process usable:
% 1.67/1.89 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.67/1.89 ** KEPT (pick-wt=9): 2 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.67/1.89 ** KEPT (pick-wt=8): 3 [] subset(A,B)| -in($f1(A,B),B).
% 1.67/1.89 ** KEPT (pick-wt=4): 4 [] -empty(ordered_pair(A,B)).
% 1.67/1.89 ** KEPT (pick-wt=2): 5 [] -empty($c2).
% 1.67/1.89 ** KEPT (pick-wt=10): 7 [copy,6,flip.2] -in(A,$c4)|ordered_pair($f3(A),$f2(A))=A.
% 1.67/1.89 ** KEPT (pick-wt=10): 8 [] -in(ordered_pair(A,B),$c4)|in(ordered_pair(A,B),$c3).
% 1.67/1.89 ** KEPT (pick-wt=3): 9 [] -subset($c4,$c3).
% 1.67/1.89
% 1.67/1.89 ------------> process sos:
% 1.67/1.89 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.67/1.89 ** KEPT (pick-wt=7): 12 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.67/1.89 ** KEPT (pick-wt=8): 13 [] subset(A,B)|in($f1(A,B),A).
% 1.67/1.89 ** KEPT (pick-wt=10): 15 [copy,14,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.67/1.89 ---> New Demodulator: 16 [new_demod,15] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.67/1.89 ** KEPT (pick-wt=2): 17 [] empty($c1).
% 1.67/1.89 ** KEPT (pick-wt=3): 18 [] subset(A,A).
% 1.67/1.89 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.67/1.89 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.67/1.89 >>>> Starting back demodulation with 16.
% 1.67/1.89
% 1.67/1.89 ======= end of input processing =======
% 1.67/1.89
% 1.67/1.89 =========== start of search ===========
% 1.67/1.89
% 1.67/1.89 -------- PROOF --------
% 1.67/1.89
% 1.67/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 75 [binary,74.1,9.1] $F.
% 1.67/1.89
% 1.67/1.89 Length of proof is 5. Level of proof is 4.
% 1.67/1.89
% 1.67/1.89 ---------------- PROOF ----------------
% 1.67/1.89 % SZS status Theorem
% 1.67/1.89 % SZS output start Refutation
% See solution above
% 1.67/1.89 ------------ end of proof -------------
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89
% 1.67/1.89 Search stopped by max_proofs option.
% 1.67/1.89
% 1.67/1.89 ============ end of search ============
% 1.67/1.89
% 1.67/1.89 -------------- statistics -------------
% 1.67/1.89 clauses given 18
% 1.67/1.89 clauses generated 116
% 1.67/1.89 clauses kept 55
% 1.67/1.89 clauses forward subsumed 86
% 1.67/1.89 clauses back subsumed 0
% 1.67/1.89 Kbytes malloced 1953
% 1.67/1.89
% 1.67/1.89 ----------- times (seconds) -----------
% 1.67/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.89
% 1.67/1.89 That finishes the proof of the theorem.
% 1.67/1.89
% 1.67/1.89 Process 15187 finished Wed Jul 27 11:07:23 2022
% 1.67/1.89 Otter interrupted
% 1.67/1.89 PROOF FOUND
%------------------------------------------------------------------------------