TSTP Solution File: SET906+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 13:14:30 EDT 2022
% Result : Theorem 1.54s 1.76s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 11 ( 8 unt; 0 nHn; 7 RR)
% Number of literals : 17 ( 5 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 18 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != B ),
file('SET906+1.p',unknown),
[] ).
cnf(8,axiom,
( A != set_union2(B,C)
| in(D,A)
| ~ in(D,B) ),
file('SET906+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SET906+1.p',unknown),
[] ).
cnf(17,axiom,
~ in(dollar_c5,dollar_c3),
file('SET906+1.p',unknown),
[] ).
cnf(23,axiom,
A = A,
file('SET906+1.p',unknown),
[] ).
cnf(30,axiom,
set_union2(A,A) = A,
file('SET906+1.p',unknown),
[] ).
cnf(33,axiom,
subset(set_union2(unordered_pair(dollar_c5,dollar_c4),dollar_c3),dollar_c3),
file('SET906+1.p',unknown),
[] ).
cnf(40,plain,
in(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[23,3,23]),
[iquote('hyper,23,3,23')] ).
cnf(78,plain,
in(A,set_union2(unordered_pair(A,B),C)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[40,8,30]),30]),
[iquote('hyper,40,8,29,demod,30')] ).
cnf(785,plain,
in(dollar_c5,dollar_c3),
inference(hyper,[status(thm)],[78,12,33]),
[iquote('hyper,78,12,33')] ).
cnf(786,plain,
$false,
inference(binary,[status(thm)],[785,17]),
[iquote('binary,785.1,17.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET906+1 : TPTP v8.1.0. Released v3.2.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 10:55:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.24/1.66 ----- Otter 3.3f, August 2004 -----
% 1.24/1.66 The process was started by sandbox2 on n028.cluster.edu,
% 1.24/1.66 Wed Jul 27 10:55:19 2022
% 1.24/1.66 The command was "./otter". The process ID is 15358.
% 1.24/1.66
% 1.24/1.66 set(prolog_style_variables).
% 1.24/1.66 set(auto).
% 1.24/1.66 dependent: set(auto1).
% 1.24/1.66 dependent: set(process_input).
% 1.24/1.66 dependent: clear(print_kept).
% 1.24/1.66 dependent: clear(print_new_demod).
% 1.24/1.66 dependent: clear(print_back_demod).
% 1.24/1.66 dependent: clear(print_back_sub).
% 1.24/1.66 dependent: set(control_memory).
% 1.24/1.66 dependent: assign(max_mem, 12000).
% 1.24/1.66 dependent: assign(pick_given_ratio, 4).
% 1.24/1.66 dependent: assign(stats_level, 1).
% 1.24/1.66 dependent: assign(max_seconds, 10800).
% 1.24/1.66 clear(print_given).
% 1.24/1.66
% 1.24/1.66 formula_list(usable).
% 1.24/1.66 all A (A=A).
% 1.24/1.66 all A B (in(A,B)-> -in(B,A)).
% 1.24/1.66 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.24/1.66 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.24/1.66 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.24/1.66 all A B C (C=set_union2(A,B)<-> (all D (in(D,C)<->in(D,A)|in(D,B)))).
% 1.24/1.66 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.24/1.66 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.24/1.66 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.24/1.66 all A B (set_union2(A,A)=A).
% 1.24/1.66 exists A empty(A).
% 1.24/1.66 exists A (-empty(A)).
% 1.24/1.66 all A B subset(A,A).
% 1.24/1.66 -(all A B C (subset(set_union2(unordered_pair(A,B),C),C)->in(A,C))).
% 1.24/1.66 end_of_list.
% 1.24/1.66
% 1.24/1.66 -------> usable clausifies to:
% 1.24/1.66
% 1.24/1.66 list(usable).
% 1.24/1.66 0 [] A=A.
% 1.24/1.66 0 [] -in(A,B)| -in(B,A).
% 1.24/1.66 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.24/1.66 0 [] set_union2(A,B)=set_union2(B,A).
% 1.24/1.66 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.24/1.66 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.24/1.66 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.24/1.66 0 [] C=unordered_pair(A,B)|in($f1(A,B,C),C)|$f1(A,B,C)=A|$f1(A,B,C)=B.
% 1.24/1.66 0 [] C=unordered_pair(A,B)| -in($f1(A,B,C),C)|$f1(A,B,C)!=A.
% 1.24/1.66 0 [] C=unordered_pair(A,B)| -in($f1(A,B,C),C)|$f1(A,B,C)!=B.
% 1.24/1.66 0 [] C!=set_union2(A,B)| -in(D,C)|in(D,A)|in(D,B).
% 1.24/1.66 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,A).
% 1.24/1.66 0 [] C!=set_union2(A,B)|in(D,C)| -in(D,B).
% 1.24/1.66 0 [] C=set_union2(A,B)|in($f2(A,B,C),C)|in($f2(A,B,C),A)|in($f2(A,B,C),B).
% 1.24/1.66 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),A).
% 1.24/1.66 0 [] C=set_union2(A,B)| -in($f2(A,B,C),C)| -in($f2(A,B,C),B).
% 1.24/1.66 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.24/1.66 0 [] subset(A,B)|in($f3(A,B),A).
% 1.24/1.66 0 [] subset(A,B)| -in($f3(A,B),B).
% 1.24/1.66 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.24/1.66 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.24/1.66 0 [] set_union2(A,A)=A.
% 1.24/1.66 0 [] empty($c1).
% 1.24/1.66 0 [] -empty($c2).
% 1.24/1.66 0 [] subset(A,A).
% 1.24/1.66 0 [] subset(set_union2(unordered_pair($c5,$c4),$c3),$c3).
% 1.24/1.66 0 [] -in($c5,$c3).
% 1.24/1.66 end_of_list.
% 1.24/1.66
% 1.24/1.66 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.24/1.66
% 1.24/1.66 This ia a non-Horn set with equality. The strategy will be
% 1.24/1.66 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.24/1.66 deletion, with positive clauses in sos and nonpositive
% 1.24/1.66 clauses in usable.
% 1.24/1.66
% 1.24/1.66 dependent: set(knuth_bendix).
% 1.24/1.66 dependent: set(anl_eq).
% 1.24/1.66 dependent: set(para_from).
% 1.24/1.66 dependent: set(para_into).
% 1.24/1.66 dependent: clear(para_from_right).
% 1.24/1.66 dependent: clear(para_into_right).
% 1.24/1.66 dependent: set(para_from_vars).
% 1.24/1.66 dependent: set(eq_units_both_ways).
% 1.24/1.66 dependent: set(dynamic_demod_all).
% 1.24/1.66 dependent: set(dynamic_demod).
% 1.24/1.66 dependent: set(order_eq).
% 1.24/1.66 dependent: set(back_demod).
% 1.24/1.66 dependent: set(lrpo).
% 1.24/1.66 dependent: set(hyper_res).
% 1.24/1.66 dependent: set(unit_deletion).
% 1.24/1.66 dependent: set(factor).
% 1.24/1.66
% 1.24/1.66 ------------> process usable:
% 1.24/1.66 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.24/1.66 ** KEPT (pick-wt=14): 2 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.24/1.66 ** KEPT (pick-wt=11): 3 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.24/1.66 ** KEPT (pick-wt=11): 4 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.24/1.66 ** KEPT (pick-wt=17): 5 [] A=unordered_pair(B,C)| -in($f1(B,C,A),A)|$f1(B,C,A)!=B.
% 1.24/1.66 ** KEPT (pick-wt=17): 6 [] A=unordered_pair(B,C)| -in($f1(B,C,A),A)|$f1(B,C,A)!=C.
% 1.24/1.66 ** KEPT (pick-wt=14): 7 [] A!=set_union2(B,C)| -in(D,A)|in(D,B)|in(D,C).
% 1.24/1.66 ** KEPT (pick-wt=11): 8 [] A!=set_union2(B,C)|in(D,A)| -in(D,B).
% 1.24/1.66 ** KEPT (pick-wt=11): 9 [] A!=set_union2(B,C)|in(D,A)| -in(D,C).
% 1.24/1.66 ** KEPT (pick-wt=17): 10 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),B).
% 1.24/1.66 ** KEPT (pick-wt=17): 11 [] A=set_union2(B,C)| -in($f2(B,C,A),A)| -in($f2(B,C,A),C).
% 1.24/1.66 ** KEPT (pick-wt=9): 12 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.24/1.66 ** KEPT (pick-wt=8): 13 [] subset(A,B)| -in($f3(A,B),B).
% 1.54/1.76 ** KEPT (pick-wt=6): 14 [] empty(A)| -empty(set_union2(A,B)).
% 1.54/1.76 ** KEPT (pick-wt=6): 15 [] empty(A)| -empty(set_union2(B,A)).
% 1.54/1.76 ** KEPT (pick-wt=2): 16 [] -empty($c2).
% 1.54/1.76 ** KEPT (pick-wt=3): 17 [] -in($c5,$c3).
% 1.54/1.76
% 1.54/1.76 ------------> process sos:
% 1.54/1.76 ** KEPT (pick-wt=3): 23 [] A=A.
% 1.54/1.76 ** KEPT (pick-wt=7): 24 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.54/1.76 ** KEPT (pick-wt=7): 25 [] set_union2(A,B)=set_union2(B,A).
% 1.54/1.76 ** KEPT (pick-wt=23): 26 [] A=unordered_pair(B,C)|in($f1(B,C,A),A)|$f1(B,C,A)=B|$f1(B,C,A)=C.
% 1.54/1.76 ** KEPT (pick-wt=23): 27 [] A=set_union2(B,C)|in($f2(B,C,A),A)|in($f2(B,C,A),B)|in($f2(B,C,A),C).
% 1.54/1.76 ** KEPT (pick-wt=8): 28 [] subset(A,B)|in($f3(A,B),A).
% 1.54/1.76 ** KEPT (pick-wt=5): 29 [] set_union2(A,A)=A.
% 1.54/1.76 ---> New Demodulator: 30 [new_demod,29] set_union2(A,A)=A.
% 1.54/1.76 ** KEPT (pick-wt=2): 31 [] empty($c1).
% 1.54/1.76 ** KEPT (pick-wt=3): 32 [] subset(A,A).
% 1.54/1.76 ** KEPT (pick-wt=7): 33 [] subset(set_union2(unordered_pair($c5,$c4),$c3),$c3).
% 1.54/1.76 Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] A=A.
% 1.54/1.76 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.54/1.76 Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.54/1.76 >>>> Starting back demodulation with 30.
% 1.54/1.76 >> back demodulating 20 with 30.
% 1.54/1.76
% 1.54/1.76 ======= end of input processing =======
% 1.54/1.76
% 1.54/1.76 =========== start of search ===========
% 1.54/1.76
% 1.54/1.76 -------- PROOF --------
% 1.54/1.76
% 1.54/1.76 ----> UNIT CONFLICT at 0.10 sec ----> 786 [binary,785.1,17.1] $F.
% 1.54/1.76
% 1.54/1.76 Length of proof is 3. Level of proof is 3.
% 1.54/1.76
% 1.54/1.76 ---------------- PROOF ----------------
% 1.54/1.76 % SZS status Theorem
% 1.54/1.76 % SZS output start Refutation
% See solution above
% 1.54/1.76 ------------ end of proof -------------
% 1.54/1.76
% 1.54/1.76
% 1.54/1.76 Search stopped by max_proofs option.
% 1.54/1.76
% 1.54/1.76
% 1.54/1.76 Search stopped by max_proofs option.
% 1.54/1.76
% 1.54/1.76 ============ end of search ============
% 1.54/1.76
% 1.54/1.76 -------------- statistics -------------
% 1.54/1.76 clauses given 18
% 1.54/1.76 clauses generated 1368
% 1.54/1.76 clauses kept 784
% 1.54/1.76 clauses forward subsumed 607
% 1.54/1.76 clauses back subsumed 2
% 1.54/1.76 Kbytes malloced 2929
% 1.54/1.76
% 1.54/1.76 ----------- times (seconds) -----------
% 1.54/1.76 user CPU time 0.10 (0 hr, 0 min, 0 sec)
% 1.54/1.76 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.54/1.76 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.54/1.76
% 1.54/1.76 That finishes the proof of the theorem.
% 1.54/1.76
% 1.54/1.76 Process 15358 finished Wed Jul 27 10:55:20 2022
% 1.54/1.76 Otter interrupted
% 1.54/1.76 PROOF FOUND
%------------------------------------------------------------------------------