%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM532+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 2.02s 2.19s
% Output : Refutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 5 unt; 2 nHn; 9 RR)
% Number of literals : 19 ( 0 equ; 9 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
( ~ aSet0(A)
| aSubsetOf0(B,A)
| ~ aSet0(B)
| aElementOf0(dollar_f2(A,B),B) ),
file('NUM532+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ aSet0(A)
| aSubsetOf0(B,A)
| ~ aSet0(B)
| ~ aElementOf0(dollar_f2(A,B),A) ),
file('NUM532+1.p',unknown),
[] ).
cnf(12,axiom,
~ aSubsetOf0(xA,xA),
file('NUM532+1.p',unknown),
[] ).
cnf(13,plain,
( ~ aSet0(A)
| aSubsetOf0(A,A)
| aElementOf0(dollar_f2(A,A),A) ),
inference(factor,[status(thm)],[9]),
[iquote('factor,9.1.3')] ).
cnf(14,plain,
( ~ aSet0(A)
| aSubsetOf0(A,A)
| ~ aElementOf0(dollar_f2(A,A),A) ),
inference(factor,[status(thm)],[10]),
[iquote('factor,10.1.3')] ).
cnf(17,axiom,
aSet0(xA),
file('NUM532+1.p',unknown),
[] ).
cnf(19,plain,
aElementOf0(dollar_f2(xA,xA),xA),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[17,13]),12]),
[iquote('hyper,17,13,unit_del,12')] ).
cnf(24,plain,
aSubsetOf0(xA,xA),
inference(hyper,[status(thm)],[19,14,17]),
[iquote('hyper,19,14,17')] ).
cnf(25,plain,
$false,
inference(binary,[status(thm)],[24,12]),
[iquote('binary,24.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM532+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:36:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.02/2.19 ----- Otter 3.3f, August 2004 -----
% 2.02/2.19 The process was started by sandbox2 on n020.cluster.edu,
% 2.02/2.19 Wed Jul 27 09:36:08 2022
% 2.02/2.19 The command was "./otter". The process ID is 24490.
% 2.02/2.19
% 2.02/2.19 set(prolog_style_variables).
% 2.02/2.19 set(auto).
% 2.02/2.19 dependent: set(auto1).
% 2.02/2.19 dependent: set(process_input).
% 2.02/2.19 dependent: clear(print_kept).
% 2.02/2.19 dependent: clear(print_new_demod).
% 2.02/2.19 dependent: clear(print_back_demod).
% 2.02/2.19 dependent: clear(print_back_sub).
% 2.02/2.19 dependent: set(control_memory).
% 2.02/2.19 dependent: assign(max_mem, 12000).
% 2.02/2.19 dependent: assign(pick_given_ratio, 4).
% 2.02/2.19 dependent: assign(stats_level, 1).
% 2.02/2.19 dependent: assign(max_seconds, 10800).
% 2.02/2.19 clear(print_given).
% 2.02/2.19
% 2.02/2.19 formula_list(usable).
% 2.02/2.19 all A (A=A).
% 2.02/2.19 all W0 (aSet0(W0)->$T).
% 2.02/2.19 all W0 (aElement0(W0)->$T).
% 2.02/2.19 all W0 (aSet0(W0)-> (all W1 (aElementOf0(W1,W0)->aElement0(W1)))).
% 2.02/2.19 all W0 (aSet0(W0)-> (isFinite0(W0)->$T)).
% 2.02/2.19 all W0 (W0=slcrc0<->aSet0(W0)& -(exists W1 aElementOf0(W1,W0))).
% 2.02/2.19 isFinite0(slcrc0).
% 2.02/2.19 all W0 (aSet0(W0)-> (isCountable0(W0)->$T)).
% 2.02/2.19 all W0 (aSet0(W0)&isCountable0(W0)-> -isFinite0(W0)).
% 2.02/2.19 all W0 (aSet0(W0)&isCountable0(W0)->W0!=slcrc0).
% 2.02/2.19 all W0 (aSet0(W0)-> (all W1 (aSubsetOf0(W1,W0)<->aSet0(W1)& (all W2 (aElementOf0(W2,W1)->aElementOf0(W2,W0)))))).
% 2.02/2.19 all W0 (aSet0(W0)&isFinite0(W0)-> (all W1 (aSubsetOf0(W1,W0)->isFinite0(W1)))).
% 2.02/2.19 aSet0(xA).
% 2.02/2.19 -aSubsetOf0(xA,xA).
% 2.02/2.19 end_of_list.
% 2.02/2.19
% 2.02/2.19 -------> usable clausifies to:
% 2.02/2.19
% 2.02/2.19 list(usable).
% 2.02/2.19 0 [] A=A.
% 2.02/2.19 0 [] -aSet0(W0)|$T.
% 2.02/2.19 0 [] -aElement0(W0)|$T.
% 2.02/2.19 0 [] -aSet0(W0)| -aElementOf0(W1,W0)|aElement0(W1).
% 2.02/2.19 0 [] -aSet0(W0)| -isFinite0(W0)|$T.
% 2.02/2.19 0 [] W0!=slcrc0|aSet0(W0).
% 2.02/2.19 0 [] W0!=slcrc0| -aElementOf0(W1,W0).
% 2.02/2.19 0 [] W0=slcrc0| -aSet0(W0)|aElementOf0($f1(W0),W0).
% 2.02/2.19 0 [] isFinite0(slcrc0).
% 2.02/2.19 0 [] -aSet0(W0)| -isCountable0(W0)|$T.
% 2.02/2.19 0 [] -aSet0(W0)| -isCountable0(W0)| -isFinite0(W0).
% 2.02/2.19 0 [] -aSet0(W0)| -isCountable0(W0)|W0!=slcrc0.
% 2.02/2.19 0 [] -aSet0(W0)| -aSubsetOf0(W1,W0)|aSet0(W1).
% 2.02/2.19 0 [] -aSet0(W0)| -aSubsetOf0(W1,W0)| -aElementOf0(W2,W1)|aElementOf0(W2,W0).
% 2.02/2.19 0 [] -aSet0(W0)|aSubsetOf0(W1,W0)| -aSet0(W1)|aElementOf0($f2(W0,W1),W1).
% 2.02/2.19 0 [] -aSet0(W0)|aSubsetOf0(W1,W0)| -aSet0(W1)| -aElementOf0($f2(W0,W1),W0).
% 2.02/2.19 0 [] -aSet0(W0)| -isFinite0(W0)| -aSubsetOf0(W1,W0)|isFinite0(W1).
% 2.02/2.19 0 [] aSet0(xA).
% 2.02/2.19 0 [] -aSubsetOf0(xA,xA).
% 2.02/2.19 end_of_list.
% 2.02/2.19
% 2.02/2.19 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.02/2.19
% 2.02/2.19 This ia a non-Horn set with equality. The strategy will be
% 2.02/2.19 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.02/2.19 deletion, with positive clauses in sos and nonpositive
% 2.02/2.19 clauses in usable.
% 2.02/2.19
% 2.02/2.19 dependent: set(knuth_bendix).
% 2.02/2.19 dependent: set(anl_eq).
% 2.02/2.19 dependent: set(para_from).
% 2.02/2.19 dependent: set(para_into).
% 2.02/2.19 dependent: clear(para_from_right).
% 2.02/2.19 dependent: clear(para_into_right).
% 2.02/2.19 dependent: set(para_from_vars).
% 2.02/2.19 dependent: set(eq_units_both_ways).
% 2.02/2.19 dependent: set(dynamic_demod_all).
% 2.02/2.19 dependent: set(dynamic_demod).
% 2.02/2.19 dependent: set(order_eq).
% 2.02/2.19 dependent: set(back_demod).
% 2.02/2.19 dependent: set(lrpo).
% 2.02/2.19 dependent: set(hyper_res).
% 2.02/2.19 dependent: set(unit_deletion).
% 2.02/2.19 dependent: set(factor).
% 2.02/2.19
% 2.02/2.19 ------------> process usable:
% 2.02/2.19 ** KEPT (pick-wt=7): 1 [] -aSet0(A)| -aElementOf0(B,A)|aElement0(B).
% 2.02/2.19 ** KEPT (pick-wt=5): 2 [] A!=slcrc0|aSet0(A).
% 2.02/2.19 ** KEPT (pick-wt=6): 3 [] A!=slcrc0| -aElementOf0(B,A).
% 2.02/2.19 ** KEPT (pick-wt=9): 4 [] A=slcrc0| -aSet0(A)|aElementOf0($f1(A),A).
% 2.02/2.19 ** KEPT (pick-wt=6): 5 [] -aSet0(A)| -isCountable0(A)| -isFinite0(A).
% 2.02/2.19 ** KEPT (pick-wt=7): 6 [] -aSet0(A)| -isCountable0(A)|A!=slcrc0.
% 2.02/2.19 ** KEPT (pick-wt=7): 7 [] -aSet0(A)| -aSubsetOf0(B,A)|aSet0(B).
% 2.02/2.19 ** KEPT (pick-wt=11): 8 [] -aSet0(A)| -aSubsetOf0(B,A)| -aElementOf0(C,B)|aElementOf0(C,A).
% 2.02/2.19 ** KEPT (pick-wt=12): 9 [] -aSet0(A)|aSubsetOf0(B,A)| -aSet0(B)|aElementOf0($f2(A,B),B).
% 2.02/2.19 ** KEPT (pick-wt=12): 10 [] -aSet0(A)|aSubsetOf0(B,A)| -aSet0(B)| -aElementOf0($f2(A,B),A).
% 2.02/2.19 ** KEPT (pick-wt=9): 11 [] -aSet0(A)| -isFinite0(A)| -aSubsetOf0(B,A)|isFinite0(B).
% 2.02/2.19 ** KEPT (pick-wt=3): 12 [] -aSubsetOf0(xA,xA).
% 2.02/2.19
% 2.02/2.19 ------------> process sos:
% 2.02/2.19 ** KEPT (pick-wt=3): 15 [] A=A.
% 2.02/2.19 ** KEPT (pick-wt=2): 16 [] isFinite0(slcrc0).
% 2.02/2.19 ** KEPT (pick-wt=2): 17 [] aSet0(xA).
% 2.02/2.19 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 2.02/2.19
% 2.02/2.19 ======= end of input processing =======
% 2.02/2.19
% 2.02/2.19 =========== start of search ===========
% 2.02/2.19
% 2.02/2.19 -------- PROOF --------
% 2.02/2.19
% 2.02/2.19 ----> UNIT CONFLICT at 0.00 sec ----> 25 [binary,24.1,12.1] $F.
% 2.02/2.19
% 2.02/2.19 Length of proof is 4. Level of proof is 3.
% 2.02/2.19
% 2.02/2.19 ---------------- PROOF ----------------
% 2.02/2.19 % SZS status Theorem
% 2.02/2.19 % SZS output start Refutation
% See solution above
% 2.02/2.19 ------------ end of proof -------------
% 2.02/2.19
% 2.02/2.19
% 2.02/2.19 Search stopped by max_proofs option.
% 2.02/2.19
% 2.02/2.19
% 2.02/2.19 Search stopped by max_proofs option.
% 2.02/2.19
% 2.02/2.19 ============ end of search ============
% 2.02/2.19
% 2.02/2.19 -------------- statistics -------------
% 2.02/2.19 clauses given 5
% 2.02/2.19 clauses generated 17
% 2.02/2.19 clauses kept 24
% 2.02/2.20 clauses forward subsumed 9
% 2.02/2.20 clauses back subsumed 0
% 2.02/2.20 Kbytes malloced 976
% 2.02/2.20
% 2.02/2.20 ----------- times (seconds) -----------
% 2.02/2.20 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.20 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.02/2.20 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.02/2.20
% 2.02/2.20 That finishes the proof of the theorem.
% 2.02/2.20
% 2.02/2.20 Process 24490 finished Wed Jul 27 09:36:10 2022
% 2.02/2.20 Otter interrupted
% 2.02/2.20 PROOF FOUND
%------------------------------------------------------------------------------