TSTP Solution File: SET788+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET788+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 13:14:15 EDT 2022
% Result : Theorem 1.66s 1.88s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 26 ( 7 unt; 15 nHn; 25 RR)
% Number of literals : 56 ( 0 equ; 8 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ e_qualish(A,B)
| ~ a_member_of(C,A)
| a_member_of(C,B) ),
file('SET788+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ e_qualish(A,B)
| a_member_of(C,A)
| ~ a_member_of(C,B) ),
file('SET788+1.p',unknown),
[] ).
cnf(3,axiom,
( e_qualish(A,B)
| ~ a_member_of(dollar_f1(A,B),A)
| ~ a_member_of(dollar_f1(A,B),B) ),
file('SET788+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ e_qualish(dollar_c2,dollar_c1)
| ~ e_qualish(dollar_c1,dollar_c2) ),
file('SET788+1.p',unknown),
[] ).
cnf(6,axiom,
( e_qualish(A,B)
| a_member_of(dollar_f1(A,B),A)
| a_member_of(dollar_f1(A,B),B) ),
file('SET788+1.p',unknown),
[] ).
cnf(7,axiom,
( e_qualish(dollar_c2,dollar_c1)
| e_qualish(dollar_c1,dollar_c2) ),
file('SET788+1.p',unknown),
[] ).
cnf(9,plain,
( a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c1)
| a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c2)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c2)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c1) ),
inference(hyper,[status(thm)],[6,4,6]),
[iquote('hyper,6,4,6')] ).
cnf(11,plain,
( a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c2)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c2)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[9,2,6])])])]),
[iquote('hyper,9,2,6,factor_simp,factor_simp,factor_simp')] ).
cnf(14,plain,
( a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c1)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c2)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[9,1,6])])])]),
[iquote('hyper,9,1,6,factor_simp,factor_simp,factor_simp')] ).
cnf(22,plain,
( a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c2)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c1)
| e_qualish(dollar_c2,dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[11,2,7])]),
[iquote('hyper,11,2,7,factor_simp')] ).
cnf(26,plain,
( a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c2)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c2)
| e_qualish(dollar_c1,dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[11,2,7])]),
[iquote('hyper,11,2,7,factor_simp')] ).
cnf(30,plain,
( a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c2)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c1)
| e_qualish(dollar_c1,dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[14,3,11])])]),
[iquote('hyper,14,3,11,factor_simp,factor_simp')] ).
cnf(41,plain,
( a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c2)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[22,1,11])])])]),
[iquote('hyper,22,1,11,factor_simp,factor_simp,factor_simp')] ).
cnf(46,plain,
( a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c2)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[26,1,41])])]),
[iquote('hyper,26,1,41,factor_simp,factor_simp')] ).
cnf(49,plain,
( a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c2)
| e_qualish(dollar_c2,dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[46,3,41])]),
[iquote('hyper,46,3,41,factor_simp')] ).
cnf(52,plain,
( a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c2)
| a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[30,4,6])])]),
[iquote('hyper,30,4,6,factor_simp,factor_simp')] ).
cnf(53,plain,
( a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c2)
| a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[49,4,6])]),
[iquote('hyper,49,4,6,factor_simp')] ).
cnf(54,plain,
( a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c1)
| e_qualish(dollar_c2,dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[52,2,7])]),
[iquote('hyper,52,2,7,factor_simp')] ).
cnf(58,plain,
( a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c2)
| e_qualish(dollar_c1,dollar_c2) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[52,2,7])]),
[iquote('hyper,52,2,7,factor_simp')] ).
cnf(62,plain,
a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c1),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[54,1,52])])]),
[iquote('hyper,54,1,52,factor_simp,factor_simp')] ).
cnf(78,plain,
a_member_of(dollar_f1(dollar_c2,dollar_c1),dollar_c2),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[58,1,62])]),
[iquote('hyper,58,1,62,factor_simp')] ).
cnf(79,plain,
e_qualish(dollar_c2,dollar_c1),
inference(hyper,[status(thm)],[78,3,62]),
[iquote('hyper,78,3,62')] ).
cnf(83,plain,
a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c1),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[53,1,79])]),
[iquote('hyper,53,1,79,factor_simp')] ).
cnf(84,plain,
a_member_of(dollar_f1(dollar_c1,dollar_c2),dollar_c2),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[53,2,79])]),
[iquote('hyper,53,2,79,factor_simp')] ).
cnf(94,plain,
e_qualish(dollar_c1,dollar_c2),
inference(hyper,[status(thm)],[84,3,83]),
[iquote('hyper,84,3,83')] ).
cnf(97,plain,
$false,
inference(hyper,[status(thm)],[94,4,79]),
[iquote('hyper,94,4,79')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET788+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:45:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.88 ----- Otter 3.3f, August 2004 -----
% 1.66/1.88 The process was started by sandbox on n010.cluster.edu,
% 1.66/1.88 Wed Jul 27 10:45:39 2022
% 1.66/1.88 The command was "./otter". The process ID is 4845.
% 1.66/1.88
% 1.66/1.88 set(prolog_style_variables).
% 1.66/1.88 set(auto).
% 1.66/1.88 dependent: set(auto1).
% 1.66/1.88 dependent: set(process_input).
% 1.66/1.88 dependent: clear(print_kept).
% 1.66/1.88 dependent: clear(print_new_demod).
% 1.66/1.88 dependent: clear(print_back_demod).
% 1.66/1.88 dependent: clear(print_back_sub).
% 1.66/1.88 dependent: set(control_memory).
% 1.66/1.88 dependent: assign(max_mem, 12000).
% 1.66/1.88 dependent: assign(pick_given_ratio, 4).
% 1.66/1.88 dependent: assign(stats_level, 1).
% 1.66/1.88 dependent: assign(max_seconds, 10800).
% 1.66/1.88 clear(print_given).
% 1.66/1.88
% 1.66/1.88 formula_list(usable).
% 1.66/1.88 -((all X Y (e_qualish(X,Y)<-> (all Z (a_member_of(Z,X)<->a_member_of(Z,Y)))))-> (all X Y (e_qualish(X,Y)<->e_qualish(Y,X)))).
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 -------> usable clausifies to:
% 1.66/1.88
% 1.66/1.88 list(usable).
% 1.66/1.88 0 [] -e_qualish(X,Y)| -a_member_of(Z,X)|a_member_of(Z,Y).
% 1.66/1.88 0 [] -e_qualish(X,Y)|a_member_of(Z,X)| -a_member_of(Z,Y).
% 1.66/1.88 0 [] e_qualish(X,Y)|a_member_of($f1(X,Y),X)|a_member_of($f1(X,Y),Y).
% 1.66/1.88 0 [] e_qualish(X,Y)| -a_member_of($f1(X,Y),X)| -a_member_of($f1(X,Y),Y).
% 1.66/1.88 0 [] e_qualish($c2,$c1)|e_qualish($c1,$c2).
% 1.66/1.88 0 [] -e_qualish($c2,$c1)| -e_qualish($c1,$c2).
% 1.66/1.88 end_of_list.
% 1.66/1.88
% 1.66/1.88 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.66/1.88
% 1.66/1.88 This is a non-Horn set without equality. The strategy will
% 1.66/1.88 be ordered hyper_res, unit deletion, and factoring, with
% 1.66/1.88 satellites in sos and with nuclei in usable.
% 1.66/1.88
% 1.66/1.88 dependent: set(hyper_res).
% 1.66/1.88 dependent: set(factor).
% 1.66/1.88 dependent: set(unit_deletion).
% 1.66/1.88
% 1.66/1.88 ------------> process usable:
% 1.66/1.88 ** KEPT (pick-wt=9): 1 [] -e_qualish(A,B)| -a_member_of(C,A)|a_member_of(C,B).
% 1.66/1.88 ** KEPT (pick-wt=9): 2 [] -e_qualish(A,B)|a_member_of(C,A)| -a_member_of(C,B).
% 1.66/1.88 ** KEPT (pick-wt=13): 3 [] e_qualish(A,B)| -a_member_of($f1(A,B),A)| -a_member_of($f1(A,B),B).
% 1.66/1.88 ** KEPT (pick-wt=6): 4 [] -e_qualish($c2,$c1)| -e_qualish($c1,$c2).
% 1.66/1.88
% 1.66/1.88 ------------> process sos:
% 1.66/1.88 ** KEPT (pick-wt=13): 6 [] e_qualish(A,B)|a_member_of($f1(A,B),A)|a_member_of($f1(A,B),B).
% 1.66/1.88 ** KEPT (pick-wt=6): 7 [] e_qualish($c2,$c1)|e_qualish($c1,$c2).
% 1.66/1.88
% 1.66/1.88 ======= end of input processing =======
% 1.66/1.88
% 1.66/1.88 =========== start of search ===========
% 1.66/1.88
% 1.66/1.88 -------- PROOF --------
% 1.66/1.88
% 1.66/1.88 -----> EMPTY CLAUSE at 0.01 sec ----> 97 [hyper,94,4,79] $F.
% 1.66/1.88
% 1.66/1.88 Length of proof is 19. Level of proof is 10.
% 1.66/1.88
% 1.66/1.88 ---------------- PROOF ----------------
% 1.66/1.88 % SZS status Theorem
% 1.66/1.88 % SZS output start Refutation
% See solution above
% 1.66/1.88 ------------ end of proof -------------
% 1.66/1.88
% 1.66/1.88
% 1.66/1.88 Search stopped by max_proofs option.
% 1.66/1.88
% 1.66/1.88
% 1.66/1.88 Search stopped by max_proofs option.
% 1.66/1.88
% 1.66/1.88 ============ end of search ============
% 1.66/1.88
% 1.66/1.88 -------------- statistics -------------
% 1.66/1.88 clauses given 24
% 1.66/1.88 clauses generated 535
% 1.66/1.88 clauses kept 96
% 1.66/1.88 clauses forward subsumed 444
% 1.66/1.88 clauses back subsumed 68
% 1.66/1.88 Kbytes malloced 976
% 1.66/1.88
% 1.66/1.88 ----------- times (seconds) -----------
% 1.66/1.88 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.66/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.88 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.66/1.88
% 1.66/1.88 That finishes the proof of the theorem.
% 1.66/1.88
% 1.66/1.88 Process 4845 finished Wed Jul 27 10:45:41 2022
% 1.66/1.88 Otter interrupted
% 1.66/1.88 PROOF FOUND
%------------------------------------------------------------------------------