TSTP Solution File: SET949+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 1.84s 2.05s
% Output : Refutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 6 RR)
% Number of literals : 11 ( 7 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 11 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( A != cartesian_product2(B,C)
| ~ in(D,A)
| D = ordered_pair(dollar_f2(B,C,A,D),dollar_f1(B,C,A,D)) ),
file('SET949+1.p',unknown),
[] ).
cnf(5,plain,
( A != cartesian_product2(B,C)
| ~ in(D,A)
| ordered_pair(dollar_f2(B,C,A,D),dollar_f1(B,C,A,D)) = D ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.3')] ).
cnf(10,axiom,
ordered_pair(A,B) != dollar_c5,
file('SET949+1.p',unknown),
[] ).
cnf(17,axiom,
A = A,
file('SET949+1.p',unknown),
[] ).
cnf(27,axiom,
in(dollar_c5,cartesian_product2(dollar_c4,dollar_c3)),
file('SET949+1.p',unknown),
[] ).
cnf(34,plain,
ordered_pair(dollar_f2(dollar_c4,dollar_c3,cartesian_product2(dollar_c4,dollar_c3),dollar_c5),dollar_f1(dollar_c4,dollar_c3,cartesian_product2(dollar_c4,dollar_c3),dollar_c5)) = dollar_c5,
inference(hyper,[status(thm)],[27,5,17]),
[iquote('hyper,27,5,17')] ).
cnf(36,plain,
$false,
inference(binary,[status(thm)],[34,10]),
[iquote('binary,34.1,10.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET949+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 10:42:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.84/2.05 ----- Otter 3.3f, August 2004 -----
% 1.84/2.05 The process was started by sandbox on n020.cluster.edu,
% 1.84/2.05 Wed Jul 27 10:42:53 2022
% 1.84/2.05 The command was "./otter". The process ID is 15097.
% 1.84/2.05
% 1.84/2.05 set(prolog_style_variables).
% 1.84/2.05 set(auto).
% 1.84/2.05 dependent: set(auto1).
% 1.84/2.05 dependent: set(process_input).
% 1.84/2.05 dependent: clear(print_kept).
% 1.84/2.05 dependent: clear(print_new_demod).
% 1.84/2.05 dependent: clear(print_back_demod).
% 1.84/2.05 dependent: clear(print_back_sub).
% 1.84/2.05 dependent: set(control_memory).
% 1.84/2.05 dependent: assign(max_mem, 12000).
% 1.84/2.05 dependent: assign(pick_given_ratio, 4).
% 1.84/2.05 dependent: assign(stats_level, 1).
% 1.84/2.05 dependent: assign(max_seconds, 10800).
% 1.84/2.05 clear(print_given).
% 1.84/2.05
% 1.84/2.05 formula_list(usable).
% 1.84/2.05 all A (A=A).
% 1.84/2.05 all A B (in(A,B)-> -in(B,A)).
% 1.84/2.05 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.84/2.05 all A B C (C=cartesian_product2(A,B)<-> (all D (in(D,C)<-> (exists E F (in(E,A)&in(F,B)&D=ordered_pair(E,F)))))).
% 1.84/2.05 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.84/2.05 all A B (-empty(ordered_pair(A,B))).
% 1.84/2.05 exists A empty(A).
% 1.84/2.05 exists A (-empty(A)).
% 1.84/2.05 -(all A B C (-(in(A,cartesian_product2(B,C))& (all D E (ordered_pair(D,E)!=A))))).
% 1.84/2.05 end_of_list.
% 1.84/2.05
% 1.84/2.05 -------> usable clausifies to:
% 1.84/2.05
% 1.84/2.05 list(usable).
% 1.84/2.05 0 [] A=A.
% 1.84/2.05 0 [] -in(A,B)| -in(B,A).
% 1.84/2.05 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.84/2.05 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f2(A,B,C,D),A).
% 1.84/2.05 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f1(A,B,C,D),B).
% 1.84/2.05 0 [] C!=cartesian_product2(A,B)| -in(D,C)|D=ordered_pair($f2(A,B,C,D),$f1(A,B,C,D)).
% 1.84/2.05 0 [] C!=cartesian_product2(A,B)|in(D,C)| -in(E,A)| -in(F,B)|D!=ordered_pair(E,F).
% 1.84/2.05 0 [] C=cartesian_product2(A,B)|in($f5(A,B,C),C)|in($f4(A,B,C),A).
% 1.84/2.05 0 [] C=cartesian_product2(A,B)|in($f5(A,B,C),C)|in($f3(A,B,C),B).
% 1.84/2.05 0 [] C=cartesian_product2(A,B)|in($f5(A,B,C),C)|$f5(A,B,C)=ordered_pair($f4(A,B,C),$f3(A,B,C)).
% 1.84/2.05 0 [] C=cartesian_product2(A,B)| -in($f5(A,B,C),C)| -in(X1,A)| -in(X2,B)|$f5(A,B,C)!=ordered_pair(X1,X2).
% 1.84/2.05 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.84/2.05 0 [] -empty(ordered_pair(A,B)).
% 1.84/2.05 0 [] empty($c1).
% 1.84/2.05 0 [] -empty($c2).
% 1.84/2.05 0 [] in($c5,cartesian_product2($c4,$c3)).
% 1.84/2.05 0 [] ordered_pair(D,E)!=$c5.
% 1.84/2.05 end_of_list.
% 1.84/2.05
% 1.84/2.05 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.84/2.05
% 1.84/2.05 This ia a non-Horn set with equality. The strategy will be
% 1.84/2.05 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.84/2.05 deletion, with positive clauses in sos and nonpositive
% 1.84/2.05 clauses in usable.
% 1.84/2.05
% 1.84/2.05 dependent: set(knuth_bendix).
% 1.84/2.05 dependent: set(anl_eq).
% 1.84/2.05 dependent: set(para_from).
% 1.84/2.05 dependent: set(para_into).
% 1.84/2.05 dependent: clear(para_from_right).
% 1.84/2.05 dependent: clear(para_into_right).
% 1.84/2.05 dependent: set(para_from_vars).
% 1.84/2.05 dependent: set(eq_units_both_ways).
% 1.84/2.05 dependent: set(dynamic_demod_all).
% 1.84/2.05 dependent: set(dynamic_demod).
% 1.84/2.05 dependent: set(order_eq).
% 1.84/2.05 dependent: set(back_demod).
% 1.84/2.05 dependent: set(lrpo).
% 1.84/2.05 dependent: set(hyper_res).
% 1.84/2.05 dependent: set(unit_deletion).
% 1.84/2.05 dependent: set(factor).
% 1.84/2.05
% 1.84/2.05 ------------> process usable:
% 1.84/2.05 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.84/2.05 ** KEPT (pick-wt=15): 2 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f2(B,C,A,D),B).
% 1.84/2.05 ** KEPT (pick-wt=15): 3 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f1(B,C,A,D),C).
% 1.84/2.05 ** KEPT (pick-wt=21): 5 [copy,4,flip.3] A!=cartesian_product2(B,C)| -in(D,A)|ordered_pair($f2(B,C,A,D),$f1(B,C,A,D))=D.
% 1.84/2.05 ** KEPT (pick-wt=19): 6 [] A!=cartesian_product2(B,C)|in(D,A)| -in(E,B)| -in(F,C)|D!=ordered_pair(E,F).
% 1.84/2.05 ** KEPT (pick-wt=25): 7 [] A=cartesian_product2(B,C)| -in($f5(B,C,A),A)| -in(D,B)| -in(E,C)|$f5(B,C,A)!=ordered_pair(D,E).
% 1.84/2.05 ** KEPT (pick-wt=4): 8 [] -empty(ordered_pair(A,B)).
% 1.84/2.05 ** KEPT (pick-wt=2): 9 [] -empty($c2).
% 1.84/2.05 ** KEPT (pick-wt=5): 10 [] ordered_pair(A,B)!=$c5.
% 1.84/2.05
% 1.84/2.05 ------------> process sos:
% 1.84/2.05 ** KEPT (pick-wt=3): 17 [] A=A.
% 1.84/2.05 ** KEPT (pick-wt=7): 18 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.84/2.05 ** KEPT (pick-wt=17): 19 [] A=cartesian_product2(B,C)|in($f5(B,C,A),A)|in($f4(B,C,A),B).
% 1.84/2.05 ** KEPT (pick-wt=17): 20 [] A=cartesian_product2(B,C)|in($f5(B,C,A),A)|in($f3(B,C,A),C).
% 1.84/2.05 ** KEPT (pick-wt=25): 22 [copy,21,flip.3] A=cartesian_product2(B,C)|in($f5(B,C,A),A)|ordered_pair($f4(B,C,A),$f3(B,C,A))=$f5(B,C,A).
% 1.84/2.05 ** KEPT (pick-wt=10): 24 [copy,23,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.84/2.05 ---> New Demodulator: 25 [new_demod,24] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.84/2.05 ** KEPT (pick-wt=2): 26 [] empty($c1).
% 1.84/2.05 ** KEPT (pick-wt=5): 27 [] in($c5,cartesian_product2($c4,$c3)).
% 1.84/2.05 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] A=A.
% 1.84/2.05 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.84/2.05 >>>> Starting back demodulation with 25.
% 1.84/2.05
% 1.84/2.05 ======= end of input processing =======
% 1.84/2.05
% 1.84/2.05 =========== start of search ===========
% 1.84/2.05
% 1.84/2.05 -------- PROOF --------
% 1.84/2.05
% 1.84/2.05 ----> UNIT CONFLICT at 0.00 sec ----> 36 [binary,34.1,10.1] $F.
% 1.84/2.05
% 1.84/2.05 Length of proof is 2. Level of proof is 2.
% 1.84/2.05
% 1.84/2.05 ---------------- PROOF ----------------
% 1.84/2.05 % SZS status Theorem
% 1.84/2.05 % SZS output start Refutation
% See solution above
% 1.84/2.05 ------------ end of proof -------------
% 1.84/2.05
% 1.84/2.05
% 1.84/2.05 Search stopped by max_proofs option.
% 1.84/2.05
% 1.84/2.05
% 1.84/2.05 Search stopped by max_proofs option.
% 1.84/2.05
% 1.84/2.05 ============ end of search ============
% 1.84/2.05
% 1.84/2.05 -------------- statistics -------------
% 1.84/2.05 clauses given 3
% 1.84/2.05 clauses generated 20
% 1.84/2.05 clauses kept 30
% 1.84/2.05 clauses forward subsumed 9
% 1.84/2.05 clauses back subsumed 0
% 1.84/2.05 Kbytes malloced 976
% 1.84/2.05
% 1.84/2.05 ----------- times (seconds) -----------
% 1.84/2.05 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.84/2.05 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.84/2.05 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.84/2.05
% 1.84/2.05 That finishes the proof of the theorem.
% 1.84/2.05
% 1.84/2.05 Process 15097 finished Wed Jul 27 10:42:55 2022
% 1.84/2.05 Otter interrupted
% 1.84/2.05 PROOF FOUND
%------------------------------------------------------------------------------