%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : NUM531+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 1.71s 1.90s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 7 unt; 0 nHn; 8 RR)
% Number of literals : 10 ( 2 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 1 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( ~ aSet0(A)
| ~ isCountable0(A)
| ~ isFinite0(A) ),
file('NUM531+1.p',unknown),
[] ).
cnf(7,axiom,
isFinite0(slcrc0),
file('NUM531+1.p',unknown),
[] ).
cnf(8,axiom,
aSet0(dollar_c1),
file('NUM531+1.p',unknown),
[] ).
cnf(9,axiom,
isCountable0(dollar_c1),
file('NUM531+1.p',unknown),
[] ).
cnf(10,axiom,
dollar_c1 = slcrc0,
file('NUM531+1.p',unknown),
[] ).
cnf(12,plain,
slcrc0 = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(13,plain,
isFinite0(dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[7]),12]),
[iquote('back_demod,7,demod,12')] ).
cnf(17,plain,
$false,
inference(hyper,[status(thm)],[13,5,8,9]),
[iquote('hyper,13,5,8,9')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM531+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 09:56:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.90 ----- Otter 3.3f, August 2004 -----
% 1.71/1.90 The process was started by sandbox2 on n018.cluster.edu,
% 1.71/1.90 Wed Jul 27 09:56:01 2022
% 1.71/1.90 The command was "./otter". The process ID is 22519.
% 1.71/1.90
% 1.71/1.90 set(prolog_style_variables).
% 1.71/1.90 set(auto).
% 1.71/1.90 dependent: set(auto1).
% 1.71/1.90 dependent: set(process_input).
% 1.71/1.90 dependent: clear(print_kept).
% 1.71/1.90 dependent: clear(print_new_demod).
% 1.71/1.90 dependent: clear(print_back_demod).
% 1.71/1.90 dependent: clear(print_back_sub).
% 1.71/1.90 dependent: set(control_memory).
% 1.71/1.90 dependent: assign(max_mem, 12000).
% 1.71/1.90 dependent: assign(pick_given_ratio, 4).
% 1.71/1.90 dependent: assign(stats_level, 1).
% 1.71/1.90 dependent: assign(max_seconds, 10800).
% 1.71/1.90 clear(print_given).
% 1.71/1.90
% 1.71/1.90 formula_list(usable).
% 1.71/1.90 all A (A=A).
% 1.71/1.90 all W0 (aSet0(W0)->$T).
% 1.71/1.90 all W0 (aElement0(W0)->$T).
% 1.71/1.90 all W0 (aSet0(W0)-> (all W1 (aElementOf0(W1,W0)->aElement0(W1)))).
% 1.71/1.90 all W0 (aSet0(W0)-> (isFinite0(W0)->$T)).
% 1.71/1.90 all W0 (W0=slcrc0<->aSet0(W0)& -(exists W1 aElementOf0(W1,W0))).
% 1.71/1.90 isFinite0(slcrc0).
% 1.71/1.90 all W0 (aSet0(W0)-> (isCountable0(W0)->$T)).
% 1.71/1.90 all W0 (aSet0(W0)&isCountable0(W0)-> -isFinite0(W0)).
% 1.71/1.90 -(all W0 (aSet0(W0)&isCountable0(W0)->W0!=slcrc0)).
% 1.71/1.90 end_of_list.
% 1.71/1.90
% 1.71/1.90 -------> usable clausifies to:
% 1.71/1.90
% 1.71/1.90 list(usable).
% 1.71/1.90 0 [] A=A.
% 1.71/1.90 0 [] -aSet0(W0)|$T.
% 1.71/1.90 0 [] -aElement0(W0)|$T.
% 1.71/1.90 0 [] -aSet0(W0)| -aElementOf0(W1,W0)|aElement0(W1).
% 1.71/1.90 0 [] -aSet0(W0)| -isFinite0(W0)|$T.
% 1.71/1.90 0 [] W0!=slcrc0|aSet0(W0).
% 1.71/1.90 0 [] W0!=slcrc0| -aElementOf0(W1,W0).
% 1.71/1.90 0 [] W0=slcrc0| -aSet0(W0)|aElementOf0($f1(W0),W0).
% 1.71/1.90 0 [] isFinite0(slcrc0).
% 1.71/1.90 0 [] -aSet0(W0)| -isCountable0(W0)|$T.
% 1.71/1.90 0 [] -aSet0(W0)| -isCountable0(W0)| -isFinite0(W0).
% 1.71/1.90 0 [] aSet0($c1).
% 1.71/1.90 0 [] isCountable0($c1).
% 1.71/1.90 0 [] $c1=slcrc0.
% 1.71/1.90 end_of_list.
% 1.71/1.90
% 1.71/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.71/1.90
% 1.71/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.71/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.90 deletion, with positive clauses in sos and nonpositive
% 1.71/1.90 clauses in usable.
% 1.71/1.90
% 1.71/1.90 dependent: set(knuth_bendix).
% 1.71/1.90 dependent: set(anl_eq).
% 1.71/1.90 dependent: set(para_from).
% 1.71/1.90 dependent: set(para_into).
% 1.71/1.90 dependent: clear(para_from_right).
% 1.71/1.90 dependent: clear(para_into_right).
% 1.71/1.90 dependent: set(para_from_vars).
% 1.71/1.90 dependent: set(eq_units_both_ways).
% 1.71/1.90 dependent: set(dynamic_demod_all).
% 1.71/1.90 dependent: set(dynamic_demod).
% 1.71/1.90 dependent: set(order_eq).
% 1.71/1.90 dependent: set(back_demod).
% 1.71/1.90 dependent: set(lrpo).
% 1.71/1.90 dependent: set(hyper_res).
% 1.71/1.90 dependent: set(unit_deletion).
% 1.71/1.90 dependent: set(factor).
% 1.71/1.90
% 1.71/1.90 ------------> process usable:
% 1.71/1.90 ** KEPT (pick-wt=7): 1 [] -aSet0(A)| -aElementOf0(B,A)|aElement0(B).
% 1.71/1.90 ** KEPT (pick-wt=5): 2 [] A!=slcrc0|aSet0(A).
% 1.71/1.90 ** KEPT (pick-wt=6): 3 [] A!=slcrc0| -aElementOf0(B,A).
% 1.71/1.90 ** KEPT (pick-wt=9): 4 [] A=slcrc0| -aSet0(A)|aElementOf0($f1(A),A).
% 1.71/1.90 ** KEPT (pick-wt=6): 5 [] -aSet0(A)| -isCountable0(A)| -isFinite0(A).
% 1.71/1.90
% 1.71/1.90 ------------> process sos:
% 1.71/1.90 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.71/1.90 ** KEPT (pick-wt=2): 7 [] isFinite0(slcrc0).
% 1.71/1.90 ** KEPT (pick-wt=2): 8 [] aSet0($c1).
% 1.71/1.90 ** KEPT (pick-wt=2): 9 [] isCountable0($c1).
% 1.71/1.90 ** KEPT (pick-wt=3): 11 [copy,10,flip.1] slcrc0=$c1.
% 1.71/1.90 ---> New Demodulator: 12 [new_demod,11] slcrc0=$c1.
% 1.71/1.90 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.71/1.90 >>>> Starting back demodulation with 12.
% 1.71/1.90 >> back demodulating 7 with 12.
% 1.71/1.90 >> back demodulating 4 with 12.
% 1.71/1.90 >> back demodulating 3 with 12.
% 1.71/1.90 >> back demodulating 2 with 12.
% 1.71/1.90
% 1.71/1.90 ======= end of input processing =======
% 1.71/1.90
% 1.71/1.90 =========== start of search ===========
% 1.71/1.90
% 1.71/1.90 -------- PROOF --------
% 1.71/1.90
% 1.71/1.90 -----> EMPTY CLAUSE at 0.00 sec ----> 17 [hyper,13,5,8,9] $F.
% 1.71/1.90
% 1.71/1.90 Length of proof is 2. Level of proof is 2.
% 1.71/1.90
% 1.71/1.90 ---------------- PROOF ----------------
% 1.71/1.90 % SZS status Theorem
% 1.71/1.90 % SZS output start Refutation
% See solution above
% 1.71/1.90 ------------ end of proof -------------
% 1.71/1.90
% 1.71/1.90
% 1.71/1.90 Search stopped by max_proofs option.
% 1.71/1.90
% 1.71/1.90
% 1.71/1.90 Search stopped by max_proofs option.
% 1.71/1.90
% 1.71/1.90 ============ end of search ============
% 1.71/1.90
% 1.71/1.90 -------------- statistics -------------
% 1.71/1.90 clauses given 4
% 1.71/1.90 clauses generated 1
% 1.71/1.90 clauses kept 14
% 1.71/1.90 clauses forward subsumed 1
% 1.71/1.90 clauses back subsumed 0
% 1.71/1.90 Kbytes malloced 976
% 1.71/1.90
% 1.71/1.90 ----------- times (seconds) -----------
% 1.71/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.90 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.71/1.90
% 1.71/1.90 That finishes the proof of the theorem.
% 1.71/1.90
% 1.71/1.90 Process 22519 finished Wed Jul 27 09:56:03 2022
% 1.71/1.90 Otter interrupted
% 1.71/1.90 PROOF FOUND
%------------------------------------------------------------------------------