TSTP Solution File: SET959+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET959+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 13:14:36 EDT 2022
% Result : Theorem 2.32s 2.53s
% Output : Refutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of clauses : 21 ( 7 unt; 5 nHn; 18 RR)
% Number of literals : 39 ( 14 equ; 12 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 : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( ~ in(A,dollar_c4)
| A = ordered_pair(dollar_f2(A),dollar_f1(A)) ),
file('SET959+1.p',unknown),
[] ).
cnf(5,plain,
( ~ in(A,dollar_c4)
| ordered_pair(dollar_f2(A),dollar_f1(A)) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.2')] ).
cnf(6,axiom,
( ~ in(A,dollar_c3)
| A = ordered_pair(dollar_f4(A),dollar_f3(A)) ),
file('SET959+1.p',unknown),
[] ).
cnf(7,plain,
( ~ in(A,dollar_c3)
| ordered_pair(dollar_f4(A),dollar_f3(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('SET959+1.p',unknown),
[] ).
cnf(9,axiom,
( in(ordered_pair(A,B),dollar_c4)
| ~ in(ordered_pair(A,B),dollar_c3) ),
file('SET959+1.p',unknown),
[] ).
cnf(10,axiom,
dollar_c4 != dollar_c3,
file('SET959+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ in(dollar_f5(A,B),A)
| ~ in(dollar_f5(A,B),B)
| A = B ),
file('SET959+1.p',unknown),
[] ).
cnf(14,axiom,
A = A,
file('SET959+1.p',unknown),
[] ).
cnf(20,axiom,
( in(dollar_f5(A,B),A)
| in(dollar_f5(A,B),B)
| A = B ),
file('SET959+1.p',unknown),
[] ).
cnf(44,plain,
( in(dollar_f5(A,dollar_c3),A)
| A = dollar_c3
| ordered_pair(dollar_f4(dollar_f5(A,dollar_c3)),dollar_f3(dollar_f5(A,dollar_c3))) = dollar_f5(A,dollar_c3) ),
inference(hyper,[status(thm)],[20,7]),
[iquote('hyper,20,7')] ).
cnf(68,plain,
( A != dollar_c3
| in(dollar_f5(dollar_c4,A),dollar_c4)
| in(dollar_f5(dollar_c4,A),A) ),
inference(para_from,[status(thm),theory(equality)],[20,10]),
[iquote('para_from,20.3.1,10.1.1')] ).
cnf(290,plain,
( in(dollar_f5(dollar_c4,dollar_c3),dollar_c4)
| in(dollar_f5(dollar_c4,dollar_c3),dollar_c3) ),
inference(hyper,[status(thm)],[68,14]),
[iquote('hyper,68,14')] ).
cnf(306,plain,
( in(dollar_f5(dollar_c4,dollar_c3),dollar_c3)
| ordered_pair(dollar_f2(dollar_f5(dollar_c4,dollar_c3)),dollar_f1(dollar_f5(dollar_c4,dollar_c3))) = dollar_f5(dollar_c4,dollar_c3) ),
inference(hyper,[status(thm)],[290,5]),
[iquote('hyper,290,5')] ).
cnf(1505,plain,
( ~ in(ordered_pair(dollar_f2(dollar_f5(dollar_c4,dollar_c3)),dollar_f1(dollar_f5(dollar_c4,dollar_c3))),dollar_c4)
| in(dollar_f5(dollar_c4,dollar_c3),dollar_c3) ),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[306,8])]),
[iquote('para_from,306.2.1,8.2.1,factor_simp')] ).
cnf(1506,plain,
( ~ in(dollar_f5(dollar_c4,dollar_c3),dollar_c4)
| in(dollar_f5(dollar_c4,dollar_c3),dollar_c3) ),
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[1505,306])]),
[iquote('para_into,1505.1.1,306.2.1,factor_simp')] ).
cnf(1508,plain,
in(dollar_f5(dollar_c4,dollar_c3),dollar_c3),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[1506,290])]),
[iquote('hyper,1506,290,factor_simp')] ).
cnf(1513,plain,
ordered_pair(dollar_f4(dollar_f5(dollar_c4,dollar_c3)),dollar_f3(dollar_f5(dollar_c4,dollar_c3))) = dollar_f5(dollar_c4,dollar_c3),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[1508,11,44]),10,10]),
[iquote('hyper,1508,11,44,unit_del,10,10')] ).
cnf(1556,plain,
in(dollar_f5(dollar_c4,dollar_c3),dollar_c4),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1513,9]),1513]),1508]),
[iquote('para_from,1512.1.1,9.2.1,demod,1513,unit_del,1508')] ).
cnf(1566,plain,
dollar_c4 = dollar_c3,
inference(hyper,[status(thm)],[1556,11,1508]),
[iquote('hyper,1556,11,1508')] ).
cnf(1568,plain,
$false,
inference(binary,[status(thm)],[1566,10]),
[iquote('binary,1566.1,10.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET959+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.00/0.12 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:07:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.32/2.53 ----- Otter 3.3f, August 2004 -----
% 2.32/2.53 The process was started by sandbox on n017.cluster.edu,
% 2.32/2.53 Wed Jul 27 10:07:18 2022
% 2.32/2.53 The command was "./otter". The process ID is 10501.
% 2.32/2.53
% 2.32/2.53 set(prolog_style_variables).
% 2.32/2.53 set(auto).
% 2.32/2.53 dependent: set(auto1).
% 2.32/2.53 dependent: set(process_input).
% 2.32/2.53 dependent: clear(print_kept).
% 2.32/2.53 dependent: clear(print_new_demod).
% 2.32/2.53 dependent: clear(print_back_demod).
% 2.32/2.53 dependent: clear(print_back_sub).
% 2.32/2.53 dependent: set(control_memory).
% 2.32/2.53 dependent: assign(max_mem, 12000).
% 2.32/2.53 dependent: assign(pick_given_ratio, 4).
% 2.32/2.53 dependent: assign(stats_level, 1).
% 2.32/2.53 dependent: assign(max_seconds, 10800).
% 2.32/2.53 clear(print_given).
% 2.32/2.53
% 2.32/2.53 formula_list(usable).
% 2.32/2.53 all A (A=A).
% 2.32/2.53 all A B (in(A,B)-> -in(B,A)).
% 2.32/2.53 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 2.32/2.53 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 2.32/2.53 all A B (-empty(ordered_pair(A,B))).
% 2.32/2.53 exists A empty(A).
% 2.32/2.53 exists A (-empty(A)).
% 2.32/2.53 -(all A B ((all C (-(in(C,A)& (all D E (C!=ordered_pair(D,E))))))& (all C (-(in(C,B)& (all D E (C!=ordered_pair(D,E))))))& (all C D (in(ordered_pair(C,D),A)<->in(ordered_pair(C,D),B)))->A=B)).
% 2.32/2.53 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 2.32/2.53 end_of_list.
% 2.32/2.53
% 2.32/2.53 -------> usable clausifies to:
% 2.32/2.53
% 2.32/2.53 list(usable).
% 2.32/2.53 0 [] A=A.
% 2.32/2.53 0 [] -in(A,B)| -in(B,A).
% 2.32/2.53 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.32/2.53 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 2.32/2.53 0 [] -empty(ordered_pair(A,B)).
% 2.32/2.53 0 [] empty($c1).
% 2.32/2.53 0 [] -empty($c2).
% 2.32/2.53 0 [] -in(C,$c4)|C=ordered_pair($f2(C),$f1(C)).
% 2.32/2.53 0 [] -in(X1,$c3)|X1=ordered_pair($f4(X1),$f3(X1)).
% 2.32/2.53 0 [] -in(ordered_pair(X2,D),$c4)|in(ordered_pair(X2,D),$c3).
% 2.32/2.53 0 [] in(ordered_pair(X2,D),$c4)| -in(ordered_pair(X2,D),$c3).
% 2.32/2.53 0 [] $c4!=$c3.
% 2.32/2.53 0 [] in($f5(A,B),A)|in($f5(A,B),B)|A=B.
% 2.32/2.53 0 [] -in($f5(A,B),A)| -in($f5(A,B),B)|A=B.
% 2.32/2.53 end_of_list.
% 2.32/2.53
% 2.32/2.53 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.32/2.53
% 2.32/2.53 This ia a non-Horn set with equality. The strategy will be
% 2.32/2.53 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.32/2.53 deletion, with positive clauses in sos and nonpositive
% 2.32/2.53 clauses in usable.
% 2.32/2.53
% 2.32/2.53 dependent: set(knuth_bendix).
% 2.32/2.53 dependent: set(anl_eq).
% 2.32/2.53 dependent: set(para_from).
% 2.32/2.53 dependent: set(para_into).
% 2.32/2.53 dependent: clear(para_from_right).
% 2.32/2.53 dependent: clear(para_into_right).
% 2.32/2.53 dependent: set(para_from_vars).
% 2.32/2.53 dependent: set(eq_units_both_ways).
% 2.32/2.53 dependent: set(dynamic_demod_all).
% 2.32/2.53 dependent: set(dynamic_demod).
% 2.32/2.53 dependent: set(order_eq).
% 2.32/2.53 dependent: set(back_demod).
% 2.32/2.53 dependent: set(lrpo).
% 2.32/2.53 dependent: set(hyper_res).
% 2.32/2.53 dependent: set(unit_deletion).
% 2.32/2.53 dependent: set(factor).
% 2.32/2.53
% 2.32/2.53 ------------> process usable:
% 2.32/2.53 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.32/2.53 ** KEPT (pick-wt=4): 2 [] -empty(ordered_pair(A,B)).
% 2.32/2.53 ** KEPT (pick-wt=2): 3 [] -empty($c2).
% 2.32/2.53 ** KEPT (pick-wt=10): 5 [copy,4,flip.2] -in(A,$c4)|ordered_pair($f2(A),$f1(A))=A.
% 2.32/2.53 ** KEPT (pick-wt=10): 7 [copy,6,flip.2] -in(A,$c3)|ordered_pair($f4(A),$f3(A))=A.
% 2.32/2.53 ** KEPT (pick-wt=10): 8 [] -in(ordered_pair(A,B),$c4)|in(ordered_pair(A,B),$c3).
% 2.32/2.53 ** KEPT (pick-wt=10): 9 [] in(ordered_pair(A,B),$c4)| -in(ordered_pair(A,B),$c3).
% 2.32/2.53 ** KEPT (pick-wt=3): 10 [] $c4!=$c3.
% 2.32/2.53 ** KEPT (pick-wt=13): 11 [] -in($f5(A,B),A)| -in($f5(A,B),B)|A=B.
% 2.32/2.53
% 2.32/2.53 ------------> process sos:
% 2.32/2.53 ** KEPT (pick-wt=3): 14 [] A=A.
% 2.32/2.53 ** KEPT (pick-wt=7): 15 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.32/2.53 ** KEPT (pick-wt=10): 17 [copy,16,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.32/2.53 ---> New Demodulator: 18 [new_demod,17] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.32/2.53 ** KEPT (pick-wt=2): 19 [] empty($c1).
% 2.32/2.53 ** KEPT (pick-wt=13): 20 [] in($f5(A,B),A)|in($f5(A,B),B)|A=B.
% 2.32/2.53 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 2.32/2.53 14 back subsumes 13.
% 2.32/2.53 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 2.32/2.53 >>>> Starting back demodulation with 18.
% 2.32/2.53
% 2.32/2.53 ======= end of input processing =======
% 2.32/2.53
% 2.32/2.53 =========== start of search ===========
% 2.32/2.53
% 2.32/2.53
% 2.32/2.53 Resetting weight limit to 20.
% 2.32/2.53
% 2.32/2.53
% 2.32/2.53 Resetting weight limit to 20.
% 2.32/2.53
% 2.32/2.53 sos_size=1227
% 2.32/2.53
% 2.32/2.53
% 2.32/2.53 Resetting weight limit to 19.
% 2.32/2.53
% 2.32/2.53
% 2.32/2.53 Resetting weight limit to 19.
% 2.32/2.53
% 2.32/2.53 sos_size=1303
% 2.32/2.53
% 2.32/2.53 -------- PROOF --------
% 2.32/2.53
% 2.32/2.53 ----> UNIT CONFLICT at 0.58 sec ----> 1568 [binary,1566.1,10.1] $F.
% 2.32/2.53
% 2.32/2.53 Length of proof is 12. Level of proof is 9.
% 2.32/2.53
% 2.32/2.53 ---------------- PROOF ----------------
% 2.32/2.53 % SZS status Theorem
% 2.32/2.53 % SZS output start Refutation
% See solution above
% 2.32/2.53 ------------ end of proof -------------
% 2.32/2.53
% 2.32/2.53
% 2.32/2.53 Search stopped by max_proofs option.
% 2.32/2.53
% 2.32/2.53
% 2.32/2.53 Search stopped by max_proofs option.
% 2.32/2.53
% 2.32/2.53 ============ end of search ============
% 2.32/2.53
% 2.32/2.53 -------------- statistics -------------
% 2.32/2.53 clauses given 104
% 2.32/2.53 clauses generated 14964
% 2.32/2.53 clauses kept 1537
% 2.32/2.53 clauses forward subsumed 2224
% 2.32/2.53 clauses back subsumed 261
% 2.32/2.53 Kbytes malloced 4882
% 2.32/2.53
% 2.32/2.53 ----------- times (seconds) -----------
% 2.32/2.53 user CPU time 0.58 (0 hr, 0 min, 0 sec)
% 2.32/2.53 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.32/2.53 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.32/2.53
% 2.32/2.53 That finishes the proof of the theorem.
% 2.32/2.53
% 2.32/2.53 Process 10501 finished Wed Jul 27 10:07:20 2022
% 2.32/2.53 Otter interrupted
% 2.32/2.53 PROOF FOUND
%------------------------------------------------------------------------------