%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU267+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 13:15:24 EDT 2022
% Result : Theorem 2.04s 2.21s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 4 unt; 0 nHn; 6 RR)
% Number of literals : 20 ( 19 equ; 12 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
( pair_first(ordered_pair(dollar_c4,dollar_c3)) != dollar_c4
| pair_second(ordered_pair(dollar_c4,dollar_c3)) != dollar_c3 ),
file('SEU267+1.p',unknown),
[] ).
cnf(10,axiom,
( A != ordered_pair(B,C)
| D != pair_first(A)
| A != ordered_pair(E,F)
| D = E ),
file('SEU267+1.p',unknown),
[] ).
cnf(11,plain,
( A != ordered_pair(B,C)
| D != pair_first(A)
| D = B ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,factor_simp')] ).
cnf(16,axiom,
( A != ordered_pair(B,C)
| D != pair_second(A)
| A != ordered_pair(E,F)
| D = F ),
file('SEU267+1.p',unknown),
[] ).
cnf(17,plain,
( A != ordered_pair(B,C)
| D != pair_second(A)
| D = C ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[16])]),
[iquote('copy,16,factor_simp')] ).
cnf(24,axiom,
A = A,
file('SEU267+1.p',unknown),
[] ).
cnf(30,plain,
pair_second(ordered_pair(A,B)) = B,
inference(hyper,[status(thm)],[24,17,24]),
[iquote('hyper,24,17,24')] ).
cnf(33,plain,
pair_first(ordered_pair(A,B)) = A,
inference(hyper,[status(thm)],[24,11,24]),
[iquote('hyper,24,11,24')] ).
cnf(35,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[9]),33,30]),24,24]),
[iquote('back_demod,9,demod,33,30,unit_del,24,24')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU267+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Jul 27 07:55:09 EDT 2022
% 0.14/0.35 % CPUTime :
% 2.04/2.21 ----- Otter 3.3f, August 2004 -----
% 2.04/2.21 The process was started by sandbox on n026.cluster.edu,
% 2.04/2.21 Wed Jul 27 07:55:09 2022
% 2.04/2.21 The command was "./otter". The process ID is 20798.
% 2.04/2.21
% 2.04/2.21 set(prolog_style_variables).
% 2.04/2.21 set(auto).
% 2.04/2.21 dependent: set(auto1).
% 2.04/2.21 dependent: set(process_input).
% 2.04/2.21 dependent: clear(print_kept).
% 2.04/2.21 dependent: clear(print_new_demod).
% 2.04/2.21 dependent: clear(print_back_demod).
% 2.04/2.21 dependent: clear(print_back_sub).
% 2.04/2.21 dependent: set(control_memory).
% 2.04/2.21 dependent: assign(max_mem, 12000).
% 2.04/2.21 dependent: assign(pick_given_ratio, 4).
% 2.04/2.21 dependent: assign(stats_level, 1).
% 2.04/2.21 dependent: assign(max_seconds, 10800).
% 2.04/2.21 clear(print_given).
% 2.04/2.21
% 2.04/2.21 formula_list(usable).
% 2.04/2.21 all A (A=A).
% 2.04/2.21 all A exists B element(B,A).
% 2.04/2.21 $T.
% 2.04/2.21 all A B (element(A,B)->empty(B)|in(A,B)).
% 2.04/2.21 all A B (in(A,B)-> -in(B,A)).
% 2.04/2.21 $T.
% 2.04/2.21 empty(empty_set).
% 2.04/2.21 all A B (in(A,B)->element(A,B)).
% 2.04/2.21 exists A empty(A).
% 2.04/2.21 exists A (-empty(A)).
% 2.04/2.21 all A (empty(A)->A=empty_set).
% 2.04/2.21 all A B (-(in(A,B)&empty(B))).
% 2.04/2.21 all A B (-(empty(A)&A!=B&empty(B))).
% 2.04/2.21 $T.
% 2.04/2.21 $T.
% 2.04/2.21 $T.
% 2.04/2.21 all A B (-empty(ordered_pair(A,B))).
% 2.04/2.21 -(all A B (pair_first(ordered_pair(A,B))=A&pair_second(ordered_pair(A,B))=B)).
% 2.04/2.21 all A ((exists B C (A=ordered_pair(B,C)))-> (all B (B=pair_first(A)<-> (all C D (A=ordered_pair(C,D)->B=C))))).
% 2.04/2.21 all A ((exists B C (A=ordered_pair(B,C)))-> (all B (B=pair_second(A)<-> (all C D (A=ordered_pair(C,D)->B=D))))).
% 2.04/2.21 end_of_list.
% 2.04/2.21
% 2.04/2.21 -------> usable clausifies to:
% 2.04/2.21
% 2.04/2.21 list(usable).
% 2.04/2.21 0 [] A=A.
% 2.04/2.21 0 [] element($f1(A),A).
% 2.04/2.21 0 [] $T.
% 2.04/2.21 0 [] -element(A,B)|empty(B)|in(A,B).
% 2.04/2.21 0 [] -in(A,B)| -in(B,A).
% 2.04/2.21 0 [] $T.
% 2.04/2.21 0 [] empty(empty_set).
% 2.04/2.21 0 [] -in(A,B)|element(A,B).
% 2.04/2.21 0 [] empty($c1).
% 2.04/2.21 0 [] -empty($c2).
% 2.04/2.21 0 [] -empty(A)|A=empty_set.
% 2.04/2.21 0 [] -in(A,B)| -empty(B).
% 2.04/2.21 0 [] -empty(A)|A=B| -empty(B).
% 2.04/2.21 0 [] $T.
% 2.04/2.21 0 [] $T.
% 2.04/2.21 0 [] $T.
% 2.04/2.21 0 [] -empty(ordered_pair(A,B)).
% 2.04/2.21 0 [] pair_first(ordered_pair($c4,$c3))!=$c4|pair_second(ordered_pair($c4,$c3))!=$c3.
% 2.04/2.21 0 [] A!=ordered_pair(B,C)|X1!=pair_first(A)|A!=ordered_pair(X2,D)|X1=X2.
% 2.04/2.21 0 [] A!=ordered_pair(B,C)|X1=pair_first(A)|A=ordered_pair($f3(A,X1),$f2(A,X1)).
% 2.04/2.21 0 [] A!=ordered_pair(B,C)|X1=pair_first(A)|X1!=$f3(A,X1).
% 2.04/2.21 0 [] A!=ordered_pair(B,C)|X3!=pair_second(A)|A!=ordered_pair(X4,D)|X3=D.
% 2.04/2.21 0 [] A!=ordered_pair(B,C)|X3=pair_second(A)|A=ordered_pair($f5(A,X3),$f4(A,X3)).
% 2.04/2.21 0 [] A!=ordered_pair(B,C)|X3=pair_second(A)|X3!=$f4(A,X3).
% 2.04/2.21 end_of_list.
% 2.04/2.21
% 2.04/2.21 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.04/2.21
% 2.04/2.21 This ia a non-Horn set with equality. The strategy will be
% 2.04/2.21 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.04/2.21 deletion, with positive clauses in sos and nonpositive
% 2.04/2.21 clauses in usable.
% 2.04/2.21
% 2.04/2.21 dependent: set(knuth_bendix).
% 2.04/2.21 dependent: set(anl_eq).
% 2.04/2.21 dependent: set(para_from).
% 2.04/2.21 dependent: set(para_into).
% 2.04/2.21 dependent: clear(para_from_right).
% 2.04/2.21 dependent: clear(para_into_right).
% 2.04/2.21 dependent: set(para_from_vars).
% 2.04/2.21 dependent: set(eq_units_both_ways).
% 2.04/2.21 dependent: set(dynamic_demod_all).
% 2.04/2.21 dependent: set(dynamic_demod).
% 2.04/2.21 dependent: set(order_eq).
% 2.04/2.21 dependent: set(back_demod).
% 2.04/2.21 dependent: set(lrpo).
% 2.04/2.21 dependent: set(hyper_res).
% 2.04/2.21 dependent: set(unit_deletion).
% 2.04/2.21 dependent: set(factor).
% 2.04/2.21
% 2.04/2.21 ------------> process usable:
% 2.04/2.21 ** KEPT (pick-wt=8): 1 [] -element(A,B)|empty(B)|in(A,B).
% 2.04/2.21 ** KEPT (pick-wt=6): 2 [] -in(A,B)| -in(B,A).
% 2.04/2.21 ** KEPT (pick-wt=6): 3 [] -in(A,B)|element(A,B).
% 2.04/2.21 ** KEPT (pick-wt=2): 4 [] -empty($c2).
% 2.04/2.21 ** KEPT (pick-wt=5): 5 [] -empty(A)|A=empty_set.
% 2.04/2.21 ** KEPT (pick-wt=5): 6 [] -in(A,B)| -empty(B).
% 2.04/2.21 ** KEPT (pick-wt=7): 7 [] -empty(A)|A=B| -empty(B).
% 2.04/2.21 ** KEPT (pick-wt=4): 8 [] -empty(ordered_pair(A,B)).
% 2.04/2.21 ** KEPT (pick-wt=12): 9 [] pair_first(ordered_pair($c4,$c3))!=$c4|pair_second(ordered_pair($c4,$c3))!=$c3.
% 2.04/2.21 ** KEPT (pick-wt=12): 11 [copy,10,factor_simp] A!=ordered_pair(B,C)|D!=pair_first(A)|D=B.
% 2.04/2.21 ** KEPT (pick-wt=18): 13 [copy,12,flip.3] A!=ordered_pair(B,C)|D=pair_first(A)|ordered_pair($f3(A,D),$f2(A,D))=A.
% 2.04/2.21 ** KEPT (pick-wt=14): 15 [copy,14,flip.3] A!=ordered_pair(B,C)|D=pair_first(A)|$f3(A,D)!=D.
% 2.04/2.21 ** KEPT (pick-wt=12): 17 [copy,16,factor_simp] A!=ordered_pair(B,C)|D!=pair_second(A)|D=C.
% 2.04/2.21 ** KEPT (pick-wt=18): 19 [copy,18,flip.3] A!=ordered_pair(B,C)|D=pair_second(A)|ordered_pair($f5(A,D),$f4(A,D))=A.
% 2.04/2.21 ** KEPT (pick-wt=14): 21 [copy,20,flip.3] A!=ordered_pair(B,C)|D=pair_second(A)|$f4(A,D)!=D.
% 2.04/2.21
% 2.04/2.21 ------------> process sos:
% 2.04/2.21 ** KEPT (pick-wt=3): 24 [] A=A.
% 2.04/2.21 ** KEPT (pick-wt=4): 25 [] element($f1(A),A).
% 2.04/2.21 ** KEPT (pick-wt=2): 26 [] empty(empty_set).
% 2.04/2.21 ** KEPT (pick-wt=2): 27 [] empty($c1).
% 2.04/2.21 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] A=A.
% 2.04/2.21 24 back subsumes 23.
% 2.04/2.21
% 2.04/2.21 ======= end of input processing =======
% 2.04/2.21
% 2.04/2.21 =========== start of search ===========
% 2.04/2.21
% 2.04/2.21 -------- PROOF --------
% 2.04/2.21
% 2.04/2.21 -----> EMPTY CLAUSE at 0.00 sec ----> 35 [back_demod,9,demod,33,30,unit_del,24,24] $F.
% 2.04/2.21
% 2.04/2.21 Length of proof is 4. Level of proof is 2.
% 2.04/2.21
% 2.04/2.21 ---------------- PROOF ----------------
% 2.04/2.21 % SZS status Theorem
% 2.04/2.21 % SZS output start Refutation
% See solution above
% 2.04/2.21 ------------ end of proof -------------
% 2.04/2.21
% 2.04/2.21
% 2.04/2.21 Search stopped by max_proofs option.
% 2.04/2.21
% 2.04/2.21
% 2.04/2.21 Search stopped by max_proofs option.
% 2.04/2.21
% 2.04/2.21 ============ end of search ============
% 2.04/2.21
% 2.04/2.21 -------------- statistics -------------
% 2.04/2.21 clauses given 1
% 2.04/2.21 clauses generated 8
% 2.04/2.21 clauses kept 26
% 2.04/2.21 clauses forward subsumed 3
% 2.04/2.21 clauses back subsumed 1
% 2.04/2.21 Kbytes malloced 976
% 2.04/2.21
% 2.04/2.21 ----------- times (seconds) -----------
% 2.04/2.21 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.04/2.21 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.04/2.21 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.04/2.21
% 2.04/2.21 That finishes the proof of the theorem.
% 2.04/2.21
% 2.04/2.21 Process 20798 finished Wed Jul 27 07:55:11 2022
% 2.04/2.21 Otter interrupted
% 2.04/2.21 PROOF FOUND
%------------------------------------------------------------------------------