TSTP Solution File: SET950+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 7.52s 7.73s
% Output : Refutation 7.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 8 unt; 0 nHn; 14 RR)
% Number of literals : 29 ( 10 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != cartesian_product2(B,C)
| ~ in(D,A)
| in(dollar_f2(B,C,A,D),B) ),
file('SET950+1.p',unknown),
[] ).
cnf(3,axiom,
( A != cartesian_product2(B,C)
| ~ in(D,A)
| in(dollar_f1(B,C,A,D),C) ),
file('SET950+1.p',unknown),
[] ).
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('SET950+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(8,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SET950+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(A,dollar_c5)
| ~ in(B,dollar_c4)
| dollar_c3 != ordered_pair(A,B) ),
file('SET950+1.p',unknown),
[] ).
cnf(13,plain,
( ~ in(A,dollar_c5)
| ~ in(B,dollar_c4)
| ordered_pair(A,B) != dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])]),
[iquote('copy,12,flip.3')] ).
cnf(20,axiom,
A = A,
file('SET950+1.p',unknown),
[] ).
cnf(32,axiom,
subset(dollar_c6,cartesian_product2(dollar_c5,dollar_c4)),
file('SET950+1.p',unknown),
[] ).
cnf(33,axiom,
in(dollar_c3,dollar_c6),
file('SET950+1.p',unknown),
[] ).
cnf(50,plain,
in(dollar_c3,cartesian_product2(dollar_c5,dollar_c4)),
inference(hyper,[status(thm)],[32,8,33]),
[iquote('hyper,32,8,33')] ).
cnf(81,plain,
ordered_pair(dollar_f2(dollar_c5,dollar_c4,cartesian_product2(dollar_c5,dollar_c4),dollar_c3),dollar_f1(dollar_c5,dollar_c4,cartesian_product2(dollar_c5,dollar_c4),dollar_c3)) = dollar_c3,
inference(hyper,[status(thm)],[50,5,20]),
[iquote('hyper,50,5,20')] ).
cnf(83,plain,
in(dollar_f1(dollar_c5,dollar_c4,cartesian_product2(dollar_c5,dollar_c4),dollar_c3),dollar_c4),
inference(hyper,[status(thm)],[50,3,20]),
[iquote('hyper,50,3,20')] ).
cnf(84,plain,
in(dollar_f2(dollar_c5,dollar_c4,cartesian_product2(dollar_c5,dollar_c4),dollar_c3),dollar_c5),
inference(hyper,[status(thm)],[50,2,20]),
[iquote('hyper,50,2,20')] ).
cnf(616,plain,
$false,
inference(hyper,[status(thm)],[81,13,84,83]),
[iquote('hyper,81,13,84,83')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET950+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 10:41:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.93/2.12 ----- Otter 3.3f, August 2004 -----
% 1.93/2.12 The process was started by sandbox2 on n025.cluster.edu,
% 1.93/2.12 Wed Jul 27 10:41:00 2022
% 1.93/2.12 The command was "./otter". The process ID is 31453.
% 1.93/2.12
% 1.93/2.12 set(prolog_style_variables).
% 1.93/2.12 set(auto).
% 1.93/2.12 dependent: set(auto1).
% 1.93/2.12 dependent: set(process_input).
% 1.93/2.12 dependent: clear(print_kept).
% 1.93/2.12 dependent: clear(print_new_demod).
% 1.93/2.12 dependent: clear(print_back_demod).
% 1.93/2.12 dependent: clear(print_back_sub).
% 1.93/2.12 dependent: set(control_memory).
% 1.93/2.12 dependent: assign(max_mem, 12000).
% 1.93/2.12 dependent: assign(pick_given_ratio, 4).
% 1.93/2.12 dependent: assign(stats_level, 1).
% 1.93/2.12 dependent: assign(max_seconds, 10800).
% 1.93/2.12 clear(print_given).
% 1.93/2.12
% 1.93/2.12 formula_list(usable).
% 1.93/2.12 all A (A=A).
% 1.93/2.12 all A B (in(A,B)-> -in(B,A)).
% 1.93/2.12 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.93/2.12 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)))))).
% 1.93/2.12 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.93/2.12 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.93/2.12 all A B (-empty(ordered_pair(A,B))).
% 1.93/2.12 exists A empty(A).
% 1.93/2.12 exists A (-empty(A)).
% 1.93/2.12 all A B subset(A,A).
% 1.93/2.12 -(all A B C D (-(subset(A,cartesian_product2(B,C))&in(D,A)& (all E F (-(in(E,B)&in(F,C)&D=ordered_pair(E,F))))))).
% 1.93/2.12 end_of_list.
% 1.93/2.12
% 1.93/2.12 -------> usable clausifies to:
% 1.93/2.12
% 1.93/2.12 list(usable).
% 1.93/2.12 0 [] A=A.
% 1.93/2.12 0 [] -in(A,B)| -in(B,A).
% 1.93/2.12 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.93/2.12 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f2(A,B,C,D),A).
% 1.93/2.12 0 [] C!=cartesian_product2(A,B)| -in(D,C)|in($f1(A,B,C,D),B).
% 1.93/2.12 0 [] C!=cartesian_product2(A,B)| -in(D,C)|D=ordered_pair($f2(A,B,C,D),$f1(A,B,C,D)).
% 1.93/2.12 0 [] C!=cartesian_product2(A,B)|in(D,C)| -in(E,A)| -in(F,B)|D!=ordered_pair(E,F).
% 1.93/2.12 0 [] C=cartesian_product2(A,B)|in($f5(A,B,C),C)|in($f4(A,B,C),A).
% 1.93/2.12 0 [] C=cartesian_product2(A,B)|in($f5(A,B,C),C)|in($f3(A,B,C),B).
% 1.93/2.12 0 [] C=cartesian_product2(A,B)|in($f5(A,B,C),C)|$f5(A,B,C)=ordered_pair($f4(A,B,C),$f3(A,B,C)).
% 1.93/2.12 0 [] C=cartesian_product2(A,B)| -in($f5(A,B,C),C)| -in(X1,A)| -in(X2,B)|$f5(A,B,C)!=ordered_pair(X1,X2).
% 1.93/2.12 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.93/2.12 0 [] subset(A,B)|in($f6(A,B),A).
% 1.93/2.12 0 [] subset(A,B)| -in($f6(A,B),B).
% 1.93/2.12 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.93/2.12 0 [] -empty(ordered_pair(A,B)).
% 1.93/2.12 0 [] empty($c1).
% 1.93/2.12 0 [] -empty($c2).
% 1.93/2.12 0 [] subset(A,A).
% 1.93/2.12 0 [] subset($c6,cartesian_product2($c5,$c4)).
% 1.93/2.12 0 [] in($c3,$c6).
% 1.93/2.12 0 [] -in(E,$c5)| -in(F,$c4)|$c3!=ordered_pair(E,F).
% 1.93/2.12 end_of_list.
% 1.93/2.12
% 1.93/2.12 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.93/2.12
% 1.93/2.12 This ia a non-Horn set with equality. The strategy will be
% 1.93/2.12 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.93/2.12 deletion, with positive clauses in sos and nonpositive
% 1.93/2.12 clauses in usable.
% 1.93/2.12
% 1.93/2.12 dependent: set(knuth_bendix).
% 1.93/2.12 dependent: set(anl_eq).
% 1.93/2.12 dependent: set(para_from).
% 1.93/2.12 dependent: set(para_into).
% 1.93/2.12 dependent: clear(para_from_right).
% 1.93/2.12 dependent: clear(para_into_right).
% 1.93/2.12 dependent: set(para_from_vars).
% 1.93/2.12 dependent: set(eq_units_both_ways).
% 1.93/2.12 dependent: set(dynamic_demod_all).
% 1.93/2.12 dependent: set(dynamic_demod).
% 1.93/2.12 dependent: set(order_eq).
% 1.93/2.12 dependent: set(back_demod).
% 1.93/2.12 dependent: set(lrpo).
% 1.93/2.12 dependent: set(hyper_res).
% 1.93/2.12 dependent: set(unit_deletion).
% 1.93/2.12 dependent: set(factor).
% 1.93/2.12
% 1.93/2.12 ------------> process usable:
% 1.93/2.12 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.93/2.12 ** KEPT (pick-wt=15): 2 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f2(B,C,A,D),B).
% 1.93/2.12 ** KEPT (pick-wt=15): 3 [] A!=cartesian_product2(B,C)| -in(D,A)|in($f1(B,C,A,D),C).
% 1.93/2.12 ** KEPT (pick-wt=21): 5 [copy,4,flip.3] A!=cartesian_product2(B,C)| -in(D,A)|ordered_pair($f2(B,C,A,D),$f1(B,C,A,D))=D.
% 1.93/2.12 ** KEPT (pick-wt=19): 6 [] A!=cartesian_product2(B,C)|in(D,A)| -in(E,B)| -in(F,C)|D!=ordered_pair(E,F).
% 1.93/2.12 ** KEPT (pick-wt=25): 7 [] A=cartesian_product2(B,C)| -in($f5(B,C,A),A)| -in(D,B)| -in(E,C)|$f5(B,C,A)!=ordered_pair(D,E).
% 1.93/2.12 ** KEPT (pick-wt=9): 8 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.93/2.12 ** KEPT (pick-wt=8): 9 [] subset(A,B)| -in($f6(A,B),B).
% 1.93/2.12 ** KEPT (pick-wt=4): 10 [] -empty(ordered_pair(A,B)).
% 1.93/2.12 ** KEPT (pick-wt=2): 11 [] -empty($c2).
% 1.93/2.12 ** KEPT (pick-wt=11): 13 [copy,12,flip.3] -in(A,$c5)| -in(B,$c4)|ordered_pair(A,B)!=$c3.
% 1.93/2.12
% 1.93/2.12 ------------> process sos:
% 1.93/2.12 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.93/2.12 ** KEPT (pick-wt=7): 21 [] unordered_pair(A,B)=unordered_pair(B,A).
% 7.52/7.73 ** KEPT (pick-wt=17): 22 [] A=cartesian_product2(B,C)|in($f5(B,C,A),A)|in($f4(B,C,A),B).
% 7.52/7.73 ** KEPT (pick-wt=17): 23 [] A=cartesian_product2(B,C)|in($f5(B,C,A),A)|in($f3(B,C,A),C).
% 7.52/7.73 ** KEPT (pick-wt=25): 25 [copy,24,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).
% 7.52/7.73 ** KEPT (pick-wt=8): 26 [] subset(A,B)|in($f6(A,B),A).
% 7.52/7.73 ** KEPT (pick-wt=10): 28 [copy,27,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 7.52/7.73 ---> New Demodulator: 29 [new_demod,28] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 7.52/7.73 ** KEPT (pick-wt=2): 30 [] empty($c1).
% 7.52/7.73 ** KEPT (pick-wt=3): 31 [] subset(A,A).
% 7.52/7.73 ** KEPT (pick-wt=5): 32 [] subset($c6,cartesian_product2($c5,$c4)).
% 7.52/7.73 ** KEPT (pick-wt=3): 33 [] in($c3,$c6).
% 7.52/7.73 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 7.52/7.73 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 7.52/7.73 >>>> Starting back demodulation with 29.
% 7.52/7.73
% 7.52/7.73 ======= end of input processing =======
% 7.52/7.73
% 7.52/7.73 =========== start of search ===========
% 7.52/7.73
% 7.52/7.73
% 7.52/7.73 Resetting weight limit to 13.
% 7.52/7.73
% 7.52/7.73
% 7.52/7.73 Resetting weight limit to 13.
% 7.52/7.73
% 7.52/7.73 sos_size=522
% 7.52/7.73
% 7.52/7.73 -------- PROOF --------
% 7.52/7.73
% 7.52/7.73 -----> EMPTY CLAUSE at 5.58 sec ----> 616 [hyper,81,13,84,83] $F.
% 7.52/7.73
% 7.52/7.73 Length of proof is 6. Level of proof is 2.
% 7.52/7.73
% 7.52/7.73 ---------------- PROOF ----------------
% 7.52/7.73 % SZS status Theorem
% 7.52/7.73 % SZS output start Refutation
% See solution above
% 7.52/7.73 ------------ end of proof -------------
% 7.52/7.73
% 7.52/7.73
% 7.52/7.73 Search stopped by max_proofs option.
% 7.52/7.73
% 7.52/7.73
% 7.52/7.73 Search stopped by max_proofs option.
% 7.52/7.73
% 7.52/7.73 ============ end of search ============
% 7.52/7.73
% 7.52/7.73 -------------- statistics -------------
% 7.52/7.73 clauses given 169
% 7.52/7.73 clauses generated 156093
% 7.52/7.73 clauses kept 602
% 7.52/7.73 clauses forward subsumed 691
% 7.52/7.73 clauses back subsumed 0
% 7.52/7.73 Kbytes malloced 5859
% 7.52/7.73
% 7.52/7.73 ----------- times (seconds) -----------
% 7.52/7.73 user CPU time 5.58 (0 hr, 0 min, 5 sec)
% 7.52/7.73 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 7.52/7.73 wall-clock time 8 (0 hr, 0 min, 8 sec)
% 7.52/7.73
% 7.52/7.73 That finishes the proof of the theorem.
% 7.52/7.73
% 7.52/7.73 Process 31453 finished Wed Jul 27 10:41:08 2022
% 7.52/7.73 Otter interrupted
% 7.52/7.73 PROOF FOUND
%------------------------------------------------------------------------------