TSTP Solution File: NUM533+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM533+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 1.98s 2.16s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of clauses : 14 ( 11 unt; 1 nHn; 14 RR)
% Number of literals : 23 ( 0 equ; 9 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(8,axiom,
( ~ aSet0(A)
| ~ aSubsetOf0(B,A)
| ~ aElementOf0(C,B)
| aElementOf0(C,A) ),
file('NUM533+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ aSet0(A)
| aSubsetOf0(B,A)
| ~ aSet0(B)
| aElementOf0(dollar_f2(A,B),B) ),
file('NUM533+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ aSet0(A)
| aSubsetOf0(B,A)
| ~ aSet0(B)
| ~ aElementOf0(dollar_f2(A,B),A) ),
file('NUM533+1.p',unknown),
[] ).
cnf(14,axiom,
~ aSubsetOf0(xA,xC),
file('NUM533+1.p',unknown),
[] ).
cnf(18,axiom,
aSet0(xA),
file('NUM533+1.p',unknown),
[] ).
cnf(19,axiom,
aSet0(xB),
file('NUM533+1.p',unknown),
[] ).
cnf(20,axiom,
aSet0(xC),
file('NUM533+1.p',unknown),
[] ).
cnf(21,axiom,
aSubsetOf0(xA,xB),
file('NUM533+1.p',unknown),
[] ).
cnf(22,axiom,
aSubsetOf0(xB,xC),
file('NUM533+1.p',unknown),
[] ).
cnf(33,plain,
aElementOf0(dollar_f2(xC,xA),xA),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[20,9,18]),14]),
[iquote('hyper,20,9,18,unit_del,14')] ).
cnf(58,plain,
aElementOf0(dollar_f2(xC,xA),xB),
inference(hyper,[status(thm)],[33,8,19,21]),
[iquote('hyper,33,8,19,21')] ).
cnf(82,plain,
aElementOf0(dollar_f2(xC,xA),xC),
inference(hyper,[status(thm)],[58,8,20,22]),
[iquote('hyper,58,8,20,22')] ).
cnf(91,plain,
aSubsetOf0(xA,xC),
inference(hyper,[status(thm)],[82,10,20,18]),
[iquote('hyper,82,10,20,18')] ).
cnf(92,plain,
$false,
inference(binary,[status(thm)],[91,14]),
[iquote('binary,91.1,14.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : NUM533+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 09:43:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.16 ----- Otter 3.3f, August 2004 -----
% 1.98/2.16 The process was started by sandbox2 on n013.cluster.edu,
% 1.98/2.16 Wed Jul 27 09:43:15 2022
% 1.98/2.16 The command was "./otter". The process ID is 12205.
% 1.98/2.16
% 1.98/2.16 set(prolog_style_variables).
% 1.98/2.16 set(auto).
% 1.98/2.16 dependent: set(auto1).
% 1.98/2.16 dependent: set(process_input).
% 1.98/2.16 dependent: clear(print_kept).
% 1.98/2.16 dependent: clear(print_new_demod).
% 1.98/2.16 dependent: clear(print_back_demod).
% 1.98/2.16 dependent: clear(print_back_sub).
% 1.98/2.16 dependent: set(control_memory).
% 1.98/2.16 dependent: assign(max_mem, 12000).
% 1.98/2.16 dependent: assign(pick_given_ratio, 4).
% 1.98/2.16 dependent: assign(stats_level, 1).
% 1.98/2.16 dependent: assign(max_seconds, 10800).
% 1.98/2.16 clear(print_given).
% 1.98/2.16
% 1.98/2.16 formula_list(usable).
% 1.98/2.16 all A (A=A).
% 1.98/2.16 all W0 (aSet0(W0)->$T).
% 1.98/2.16 all W0 (aElement0(W0)->$T).
% 1.98/2.16 all W0 (aSet0(W0)-> (all W1 (aElementOf0(W1,W0)->aElement0(W1)))).
% 1.98/2.16 all W0 (aSet0(W0)-> (isFinite0(W0)->$T)).
% 1.98/2.16 all W0 (W0=slcrc0<->aSet0(W0)& -(exists W1 aElementOf0(W1,W0))).
% 1.98/2.16 isFinite0(slcrc0).
% 1.98/2.16 all W0 (aSet0(W0)-> (isCountable0(W0)->$T)).
% 1.98/2.16 all W0 (aSet0(W0)&isCountable0(W0)-> -isFinite0(W0)).
% 1.98/2.16 all W0 (aSet0(W0)&isCountable0(W0)->W0!=slcrc0).
% 1.98/2.16 all W0 (aSet0(W0)-> (all W1 (aSubsetOf0(W1,W0)<->aSet0(W1)& (all W2 (aElementOf0(W2,W1)->aElementOf0(W2,W0)))))).
% 1.98/2.16 all W0 (aSet0(W0)&isFinite0(W0)-> (all W1 (aSubsetOf0(W1,W0)->isFinite0(W1)))).
% 1.98/2.16 all W0 (aSet0(W0)->aSubsetOf0(W0,W0)).
% 1.98/2.16 all W0 W1 (aSet0(W0)&aSet0(W1)-> (aSubsetOf0(W0,W1)&aSubsetOf0(W1,W0)->W0=W1)).
% 1.98/2.16 aSet0(xA).
% 1.98/2.16 aSet0(xB).
% 1.98/2.16 aSet0(xC).
% 1.98/2.16 -(aSubsetOf0(xA,xB)&aSubsetOf0(xB,xC)->aSubsetOf0(xA,xC)).
% 1.98/2.16 end_of_list.
% 1.98/2.16
% 1.98/2.16 -------> usable clausifies to:
% 1.98/2.16
% 1.98/2.16 list(usable).
% 1.98/2.16 0 [] A=A.
% 1.98/2.16 0 [] -aSet0(W0)|$T.
% 1.98/2.16 0 [] -aElement0(W0)|$T.
% 1.98/2.16 0 [] -aSet0(W0)| -aElementOf0(W1,W0)|aElement0(W1).
% 1.98/2.16 0 [] -aSet0(W0)| -isFinite0(W0)|$T.
% 1.98/2.16 0 [] W0!=slcrc0|aSet0(W0).
% 1.98/2.16 0 [] W0!=slcrc0| -aElementOf0(W1,W0).
% 1.98/2.16 0 [] W0=slcrc0| -aSet0(W0)|aElementOf0($f1(W0),W0).
% 1.98/2.16 0 [] isFinite0(slcrc0).
% 1.98/2.16 0 [] -aSet0(W0)| -isCountable0(W0)|$T.
% 1.98/2.16 0 [] -aSet0(W0)| -isCountable0(W0)| -isFinite0(W0).
% 1.98/2.16 0 [] -aSet0(W0)| -isCountable0(W0)|W0!=slcrc0.
% 1.98/2.16 0 [] -aSet0(W0)| -aSubsetOf0(W1,W0)|aSet0(W1).
% 1.98/2.16 0 [] -aSet0(W0)| -aSubsetOf0(W1,W0)| -aElementOf0(W2,W1)|aElementOf0(W2,W0).
% 1.98/2.16 0 [] -aSet0(W0)|aSubsetOf0(W1,W0)| -aSet0(W1)|aElementOf0($f2(W0,W1),W1).
% 1.98/2.16 0 [] -aSet0(W0)|aSubsetOf0(W1,W0)| -aSet0(W1)| -aElementOf0($f2(W0,W1),W0).
% 1.98/2.16 0 [] -aSet0(W0)| -isFinite0(W0)| -aSubsetOf0(W1,W0)|isFinite0(W1).
% 1.98/2.16 0 [] -aSet0(W0)|aSubsetOf0(W0,W0).
% 1.98/2.16 0 [] -aSet0(W0)| -aSet0(W1)| -aSubsetOf0(W0,W1)| -aSubsetOf0(W1,W0)|W0=W1.
% 1.98/2.16 0 [] aSet0(xA).
% 1.98/2.16 0 [] aSet0(xB).
% 1.98/2.16 0 [] aSet0(xC).
% 1.98/2.16 0 [] aSubsetOf0(xA,xB).
% 1.98/2.16 0 [] aSubsetOf0(xB,xC).
% 1.98/2.16 0 [] -aSubsetOf0(xA,xC).
% 1.98/2.16 end_of_list.
% 1.98/2.16
% 1.98/2.16 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.98/2.16
% 1.98/2.16 This ia a non-Horn set with equality. The strategy will be
% 1.98/2.16 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.98/2.16 deletion, with positive clauses in sos and nonpositive
% 1.98/2.16 clauses in usable.
% 1.98/2.16
% 1.98/2.16 dependent: set(knuth_bendix).
% 1.98/2.16 dependent: set(anl_eq).
% 1.98/2.16 dependent: set(para_from).
% 1.98/2.16 dependent: set(para_into).
% 1.98/2.16 dependent: clear(para_from_right).
% 1.98/2.16 dependent: clear(para_into_right).
% 1.98/2.16 dependent: set(para_from_vars).
% 1.98/2.16 dependent: set(eq_units_both_ways).
% 1.98/2.16 dependent: set(dynamic_demod_all).
% 1.98/2.16 dependent: set(dynamic_demod).
% 1.98/2.16 dependent: set(order_eq).
% 1.98/2.16 dependent: set(back_demod).
% 1.98/2.16 dependent: set(lrpo).
% 1.98/2.16 dependent: set(hyper_res).
% 1.98/2.16 dependent: set(unit_deletion).
% 1.98/2.16 dependent: set(factor).
% 1.98/2.16
% 1.98/2.16 ------------> process usable:
% 1.98/2.16 ** KEPT (pick-wt=7): 1 [] -aSet0(A)| -aElementOf0(B,A)|aElement0(B).
% 1.98/2.16 ** KEPT (pick-wt=5): 2 [] A!=slcrc0|aSet0(A).
% 1.98/2.16 ** KEPT (pick-wt=6): 3 [] A!=slcrc0| -aElementOf0(B,A).
% 1.98/2.16 ** KEPT (pick-wt=9): 4 [] A=slcrc0| -aSet0(A)|aElementOf0($f1(A),A).
% 1.98/2.16 ** KEPT (pick-wt=6): 5 [] -aSet0(A)| -isCountable0(A)| -isFinite0(A).
% 1.98/2.16 ** KEPT (pick-wt=7): 6 [] -aSet0(A)| -isCountable0(A)|A!=slcrc0.
% 1.98/2.16 ** KEPT (pick-wt=7): 7 [] -aSet0(A)| -aSubsetOf0(B,A)|aSet0(B).
% 1.98/2.16 ** KEPT (pick-wt=11): 8 [] -aSet0(A)| -aSubsetOf0(B,A)| -aElementOf0(C,B)|aElementOf0(C,A).
% 1.98/2.16 ** KEPT (pick-wt=12): 9 [] -aSet0(A)|aSubsetOf0(B,A)| -aSet0(B)|aElementOf0($f2(A,B),B).
% 1.98/2.16 ** KEPT (pick-wt=12): 10 [] -aSet0(A)|aSubsetOf0(B,A)| -aSet0(B)| -aElementOf0($f2(A,B),A).
% 1.98/2.16 ** KEPT (pick-wt=9): 11 [] -aSet0(A)| -isFinite0(A)| -aSubsetOf0(B,A)|isFinite0(B).
% 1.98/2.16 ** KEPT (pick-wt=5): 12 [] -aSet0(A)|aSubsetOf0(A,A).
% 1.98/2.16 ** KEPT (pick-wt=13): 13 [] -aSet0(A)| -aSet0(B)| -aSubsetOf0(A,B)| -aSubsetOf0(B,A)|A=B.
% 1.98/2.16 ** KEPT (pick-wt=3): 14 [] -aSubsetOf0(xA,xC).
% 1.98/2.16
% 1.98/2.16 ------------> process sos:
% 1.98/2.16 ** KEPT (pick-wt=3): 16 [] A=A.
% 1.98/2.16 ** KEPT (pick-wt=2): 17 [] isFinite0(slcrc0).
% 1.98/2.16 ** KEPT (pick-wt=2): 18 [] aSet0(xA).
% 1.98/2.16 ** KEPT (pick-wt=2): 19 [] aSet0(xB).
% 1.98/2.16 ** KEPT (pick-wt=2): 20 [] aSet0(xC).
% 1.98/2.16 ** KEPT (pick-wt=3): 21 [] aSubsetOf0(xA,xB).
% 1.98/2.16 ** KEPT (pick-wt=3): 22 [] aSubsetOf0(xB,xC).
% 1.98/2.16 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 1.98/2.16 16 back subsumes 15.
% 1.98/2.16
% 1.98/2.16 ======= end of input processing =======
% 1.98/2.16
% 1.98/2.16 =========== start of search ===========
% 1.98/2.16
% 1.98/2.16 -------- PROOF --------
% 1.98/2.16
% 1.98/2.16 ----> UNIT CONFLICT at 0.01 sec ----> 92 [binary,91.1,14.1] $F.
% 1.98/2.16
% 1.98/2.16 Length of proof is 4. Level of proof is 4.
% 1.98/2.16
% 1.98/2.16 ---------------- PROOF ----------------
% 1.98/2.16 % SZS status Theorem
% 1.98/2.16 % SZS output start Refutation
% See solution above
% 1.98/2.16 ------------ end of proof -------------
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Search stopped by max_proofs option.
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Search stopped by max_proofs option.
% 1.98/2.16
% 1.98/2.16 ============ end of search ============
% 1.98/2.16
% 1.98/2.16 -------------- statistics -------------
% 1.98/2.16 clauses given 18
% 1.98/2.16 clauses generated 181
% 1.98/2.16 clauses kept 91
% 1.98/2.16 clauses forward subsumed 100
% 1.98/2.16 clauses back subsumed 1
% 1.98/2.16 Kbytes malloced 976
% 1.98/2.16
% 1.98/2.16 ----------- times (seconds) -----------
% 1.98/2.16 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.98/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.16 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.16
% 1.98/2.16 That finishes the proof of the theorem.
% 1.98/2.16
% 1.98/2.16 Process 12205 finished Wed Jul 27 09:43:17 2022
% 1.98/2.16 Otter interrupted
% 1.98/2.16 PROOF FOUND
%------------------------------------------------------------------------------