TSTP Solution File: NUM533+2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM533+2 : TPTP v8.1.0. Released v4.0.0.
% 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 13:08:44 EDT 2022
% Result : Theorem 1.80s 1.98s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 7 ( 5 unt; 0 nHn; 7 RR)
% Number of literals : 9 ( 0 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 2 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(14,axiom,
( ~ aElementOf0(A,xA)
| aElementOf0(A,xB) ),
file('NUM533+2.p',unknown),
[] ).
cnf(15,axiom,
( ~ aElementOf0(A,xB)
| aElementOf0(A,xC) ),
file('NUM533+2.p',unknown),
[] ).
cnf(16,axiom,
~ aElementOf0(dollar_c1,xC),
file('NUM533+2.p',unknown),
[] ).
cnf(26,axiom,
aElementOf0(dollar_c1,xA),
file('NUM533+2.p',unknown),
[] ).
cnf(54,plain,
aElementOf0(dollar_c1,xB),
inference(hyper,[status(thm)],[26,14]),
[iquote('hyper,26,14')] ).
cnf(79,plain,
aElementOf0(dollar_c1,xC),
inference(hyper,[status(thm)],[54,15]),
[iquote('hyper,54,15')] ).
cnf(80,plain,
$false,
inference(binary,[status(thm)],[79,16]),
[iquote('binary,79.1,16.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM533+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n010.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 09:35:09 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.80/1.98 ----- Otter 3.3f, August 2004 -----
% 1.80/1.98 The process was started by sandbox on n010.cluster.edu,
% 1.80/1.98 Wed Jul 27 09:35:10 2022
% 1.80/1.98 The command was "./otter". The process ID is 14447.
% 1.80/1.98
% 1.80/1.98 set(prolog_style_variables).
% 1.80/1.98 set(auto).
% 1.80/1.98 dependent: set(auto1).
% 1.80/1.98 dependent: set(process_input).
% 1.80/1.98 dependent: clear(print_kept).
% 1.80/1.98 dependent: clear(print_new_demod).
% 1.80/1.98 dependent: clear(print_back_demod).
% 1.80/1.98 dependent: clear(print_back_sub).
% 1.80/1.98 dependent: set(control_memory).
% 1.80/1.98 dependent: assign(max_mem, 12000).
% 1.80/1.98 dependent: assign(pick_given_ratio, 4).
% 1.80/1.98 dependent: assign(stats_level, 1).
% 1.80/1.98 dependent: assign(max_seconds, 10800).
% 1.80/1.98 clear(print_given).
% 1.80/1.98
% 1.80/1.98 formula_list(usable).
% 1.80/1.98 all A (A=A).
% 1.80/1.98 all W0 (aSet0(W0)->$T).
% 1.80/1.98 all W0 (aElement0(W0)->$T).
% 1.80/1.98 all W0 (aSet0(W0)-> (all W1 (aElementOf0(W1,W0)->aElement0(W1)))).
% 1.80/1.98 all W0 (aSet0(W0)-> (isFinite0(W0)->$T)).
% 1.80/1.98 all W0 (W0=slcrc0<->aSet0(W0)& -(exists W1 aElementOf0(W1,W0))).
% 1.80/1.98 isFinite0(slcrc0).
% 1.80/1.98 all W0 (aSet0(W0)-> (isCountable0(W0)->$T)).
% 1.80/1.98 all W0 (aSet0(W0)&isCountable0(W0)-> -isFinite0(W0)).
% 1.80/1.98 all W0 (aSet0(W0)&isCountable0(W0)->W0!=slcrc0).
% 1.80/1.98 all W0 (aSet0(W0)-> (all W1 (aSubsetOf0(W1,W0)<->aSet0(W1)& (all W2 (aElementOf0(W2,W1)->aElementOf0(W2,W0)))))).
% 1.80/1.98 all W0 (aSet0(W0)&isFinite0(W0)-> (all W1 (aSubsetOf0(W1,W0)->isFinite0(W1)))).
% 1.80/1.98 all W0 (aSet0(W0)->aSubsetOf0(W0,W0)).
% 1.80/1.98 all W0 W1 (aSet0(W0)&aSet0(W1)-> (aSubsetOf0(W0,W1)&aSubsetOf0(W1,W0)->W0=W1)).
% 1.80/1.98 aSet0(xA).
% 1.80/1.98 aSet0(xB).
% 1.80/1.98 aSet0(xC).
% 1.80/1.98 -((all W0 (aElementOf0(W0,xA)->aElementOf0(W0,xB)))&aSubsetOf0(xA,xB)& (all W0 (aElementOf0(W0,xB)->aElementOf0(W0,xC)))&aSubsetOf0(xB,xC)-> (all W0 (aElementOf0(W0,xA)->aElementOf0(W0,xC)))|aSubsetOf0(xA,xC)).
% 1.80/1.98 end_of_list.
% 1.80/1.98
% 1.80/1.98 -------> usable clausifies to:
% 1.80/1.98
% 1.80/1.98 list(usable).
% 1.80/1.98 0 [] A=A.
% 1.80/1.98 0 [] -aSet0(W0)|$T.
% 1.80/1.98 0 [] -aElement0(W0)|$T.
% 1.80/1.98 0 [] -aSet0(W0)| -aElementOf0(W1,W0)|aElement0(W1).
% 1.80/1.98 0 [] -aSet0(W0)| -isFinite0(W0)|$T.
% 1.80/1.98 0 [] W0!=slcrc0|aSet0(W0).
% 1.80/1.98 0 [] W0!=slcrc0| -aElementOf0(W1,W0).
% 1.80/1.98 0 [] W0=slcrc0| -aSet0(W0)|aElementOf0($f1(W0),W0).
% 1.80/1.98 0 [] isFinite0(slcrc0).
% 1.80/1.98 0 [] -aSet0(W0)| -isCountable0(W0)|$T.
% 1.80/1.98 0 [] -aSet0(W0)| -isCountable0(W0)| -isFinite0(W0).
% 1.80/1.98 0 [] -aSet0(W0)| -isCountable0(W0)|W0!=slcrc0.
% 1.80/1.98 0 [] -aSet0(W0)| -aSubsetOf0(W1,W0)|aSet0(W1).
% 1.80/1.98 0 [] -aSet0(W0)| -aSubsetOf0(W1,W0)| -aElementOf0(W2,W1)|aElementOf0(W2,W0).
% 1.80/1.98 0 [] -aSet0(W0)|aSubsetOf0(W1,W0)| -aSet0(W1)|aElementOf0($f2(W0,W1),W1).
% 1.80/1.98 0 [] -aSet0(W0)|aSubsetOf0(W1,W0)| -aSet0(W1)| -aElementOf0($f2(W0,W1),W0).
% 1.80/1.98 0 [] -aSet0(W0)| -isFinite0(W0)| -aSubsetOf0(W1,W0)|isFinite0(W1).
% 1.80/1.98 0 [] -aSet0(W0)|aSubsetOf0(W0,W0).
% 1.80/1.98 0 [] -aSet0(W0)| -aSet0(W1)| -aSubsetOf0(W0,W1)| -aSubsetOf0(W1,W0)|W0=W1.
% 1.80/1.98 0 [] aSet0(xA).
% 1.80/1.98 0 [] aSet0(xB).
% 1.80/1.98 0 [] aSet0(xC).
% 1.80/1.98 0 [] -aElementOf0(W0,xA)|aElementOf0(W0,xB).
% 1.80/1.98 0 [] aSubsetOf0(xA,xB).
% 1.80/1.98 0 [] -aElementOf0(X1,xB)|aElementOf0(X1,xC).
% 1.80/1.98 0 [] aSubsetOf0(xB,xC).
% 1.80/1.98 0 [] aElementOf0($c1,xA).
% 1.80/1.98 0 [] -aElementOf0($c1,xC).
% 1.80/1.98 0 [] -aSubsetOf0(xA,xC).
% 1.80/1.98 end_of_list.
% 1.80/1.98
% 1.80/1.98 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.80/1.98
% 1.80/1.98 This ia a non-Horn set with equality. The strategy will be
% 1.80/1.98 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.80/1.98 deletion, with positive clauses in sos and nonpositive
% 1.80/1.98 clauses in usable.
% 1.80/1.98
% 1.80/1.98 dependent: set(knuth_bendix).
% 1.80/1.98 dependent: set(anl_eq).
% 1.80/1.98 dependent: set(para_from).
% 1.80/1.98 dependent: set(para_into).
% 1.80/1.98 dependent: clear(para_from_right).
% 1.80/1.98 dependent: clear(para_into_right).
% 1.80/1.98 dependent: set(para_from_vars).
% 1.80/1.98 dependent: set(eq_units_both_ways).
% 1.80/1.98 dependent: set(dynamic_demod_all).
% 1.80/1.98 dependent: set(dynamic_demod).
% 1.80/1.98 dependent: set(order_eq).
% 1.80/1.98 dependent: set(back_demod).
% 1.80/1.98 dependent: set(lrpo).
% 1.80/1.98 dependent: set(hyper_res).
% 1.80/1.98 dependent: set(unit_deletion).
% 1.80/1.98 dependent: set(factor).
% 1.80/1.98
% 1.80/1.98 ------------> process usable:
% 1.80/1.98 ** KEPT (pick-wt=7): 1 [] -aSet0(A)| -aElementOf0(B,A)|aElement0(B).
% 1.80/1.98 ** KEPT (pick-wt=5): 2 [] A!=slcrc0|aSet0(A).
% 1.80/1.98 ** KEPT (pick-wt=6): 3 [] A!=slcrc0| -aElementOf0(B,A).
% 1.80/1.98 ** KEPT (pick-wt=9): 4 [] A=slcrc0| -aSet0(A)|aElementOf0($f1(A),A).
% 1.80/1.98 ** KEPT (pick-wt=6): 5 [] -aSet0(A)| -isCountable0(A)| -isFinite0(A).
% 1.80/1.98 ** KEPT (pick-wt=7): 6 [] -aSet0(A)| -isCountable0(A)|A!=slcrc0.
% 1.80/1.98 ** KEPT (pick-wt=7): 7 [] -aSet0(A)| -aSubsetOf0(B,A)|aSet0(B).
% 1.80/1.98 ** KEPT (pick-wt=11): 8 [] -aSet0(A)| -aSubsetOf0(B,A)| -aElementOf0(C,B)|aElementOf0(C,A).
% 1.80/1.98 ** KEPT (pick-wt=12): 9 [] -aSet0(A)|aSubsetOf0(B,A)| -aSet0(B)|aElementOf0($f2(A,B),B).
% 1.80/1.98 ** KEPT (pick-wt=12): 10 [] -aSet0(A)|aSubsetOf0(B,A)| -aSet0(B)| -aElementOf0($f2(A,B),A).
% 1.80/1.98 ** KEPT (pick-wt=9): 11 [] -aSet0(A)| -isFinite0(A)| -aSubsetOf0(B,A)|isFinite0(B).
% 1.80/1.98 ** KEPT (pick-wt=5): 12 [] -aSet0(A)|aSubsetOf0(A,A).
% 1.80/1.98 ** KEPT (pick-wt=13): 13 [] -aSet0(A)| -aSet0(B)| -aSubsetOf0(A,B)| -aSubsetOf0(B,A)|A=B.
% 1.80/1.98 ** KEPT (pick-wt=6): 14 [] -aElementOf0(A,xA)|aElementOf0(A,xB).
% 1.80/1.98 ** KEPT (pick-wt=6): 15 [] -aElementOf0(A,xB)|aElementOf0(A,xC).
% 1.80/1.98 ** KEPT (pick-wt=3): 16 [] -aElementOf0($c1,xC).
% 1.80/1.98 ** KEPT (pick-wt=3): 17 [] -aSubsetOf0(xA,xC).
% 1.80/1.98
% 1.80/1.98 ------------> process sos:
% 1.80/1.98 ** KEPT (pick-wt=3): 19 [] A=A.
% 1.80/1.98 ** KEPT (pick-wt=2): 20 [] isFinite0(slcrc0).
% 1.80/1.98 ** KEPT (pick-wt=2): 21 [] aSet0(xA).
% 1.80/1.98 ** KEPT (pick-wt=2): 22 [] aSet0(xB).
% 1.80/1.98 ** KEPT (pick-wt=2): 23 [] aSet0(xC).
% 1.80/1.98 ** KEPT (pick-wt=3): 24 [] aSubsetOf0(xA,xB).
% 1.80/1.98 ** KEPT (pick-wt=3): 25 [] aSubsetOf0(xB,xC).
% 1.80/1.98 ** KEPT (pick-wt=3): 26 [] aElementOf0($c1,xA).
% 1.80/1.98 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] A=A.
% 1.80/1.98 19 back subsumes 18.
% 1.80/1.98
% 1.80/1.98 ======= end of input processing =======
% 1.80/1.98
% 1.80/1.98 =========== start of search ===========
% 1.80/1.98
% 1.80/1.98 -------- PROOF --------
% 1.80/1.98
% 1.80/1.98 ----> UNIT CONFLICT at 0.00 sec ----> 80 [binary,79.1,16.1] $F.
% 1.80/1.98
% 1.80/1.98 Length of proof is 2. Level of proof is 2.
% 1.80/1.98
% 1.80/1.98 ---------------- PROOF ----------------
% 1.80/1.98 % SZS status Theorem
% 1.80/1.98 % SZS output start Refutation
% See solution above
% 1.80/1.98 ------------ end of proof -------------
% 1.80/1.98
% 1.80/1.98
% 1.80/1.98 Search stopped by max_proofs option.
% 1.80/1.98
% 1.80/1.98
% 1.80/1.98 Search stopped by max_proofs option.
% 1.80/1.98
% 1.80/1.98 ============ end of search ============
% 1.80/1.98
% 1.80/1.98 -------------- statistics -------------
% 1.80/1.98 clauses given 17
% 1.80/1.98 clauses generated 153
% 1.80/1.98 clauses kept 79
% 1.80/1.98 clauses forward subsumed 88
% 1.80/1.98 clauses back subsumed 1
% 1.80/1.98 Kbytes malloced 976
% 1.80/1.98
% 1.80/1.98 ----------- times (seconds) -----------
% 1.80/1.98 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/1.98 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.80/1.98
% 1.80/1.98 That finishes the proof of the theorem.
% 1.80/1.98
% 1.80/1.98 Process 14447 finished Wed Jul 27 09:35:11 2022
% 1.80/1.98 Otter interrupted
% 1.80/1.98 PROOF FOUND
%------------------------------------------------------------------------------