TSTP Solution File: SET956+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET956+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 1.79s 2.01s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 12 ( 7 unt; 1 nHn; 11 RR)
% Number of literals : 19 ( 3 equ; 7 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 : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( subset(A,B)
| ~ in(dollar_f1(A,B),B) ),
file('SET956+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ subset(A,cartesian_product2(B,C))
| ~ in(D,A)
| D = ordered_pair(dollar_f3(A,B,C,D),dollar_f2(A,B,C,D)) ),
file('SET956+1.p',unknown),
[] ).
cnf(9,plain,
( ~ subset(A,cartesian_product2(B,C))
| ~ in(D,A)
| ordered_pair(dollar_f3(A,B,C,D),dollar_f2(A,B,C,D)) = D ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.3')] ).
cnf(10,axiom,
( ~ in(ordered_pair(A,B),dollar_c6)
| in(ordered_pair(A,B),dollar_c3) ),
file('SET956+1.p',unknown),
[] ).
cnf(11,axiom,
~ subset(dollar_c6,dollar_c3),
file('SET956+1.p',unknown),
[] ).
cnf(15,axiom,
( subset(A,B)
| in(dollar_f1(A,B),A) ),
file('SET956+1.p',unknown),
[] ).
cnf(21,axiom,
subset(dollar_c6,cartesian_product2(dollar_c5,dollar_c4)),
file('SET956+1.p',unknown),
[] ).
cnf(22,plain,
in(dollar_f1(dollar_c6,dollar_c3),dollar_c6),
inference(hyper,[status(thm)],[15,11]),
[iquote('hyper,15,11')] ).
cnf(24,plain,
ordered_pair(dollar_f3(dollar_c6,dollar_c5,dollar_c4,dollar_f1(dollar_c6,dollar_c3)),dollar_f2(dollar_c6,dollar_c5,dollar_c4,dollar_f1(dollar_c6,dollar_c3))) = dollar_f1(dollar_c6,dollar_c3),
inference(hyper,[status(thm)],[22,9,21]),
[iquote('hyper,22,9,21')] ).
cnf(95,plain,
in(dollar_f1(dollar_c6,dollar_c3),dollar_c3),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[24,10]),24]),22]),
[iquote('para_from,23.1.1,10.2.1,demod,24,unit_del,22')] ).
cnf(100,plain,
subset(dollar_c6,dollar_c3),
inference(hyper,[status(thm)],[95,3]),
[iquote('hyper,95,3')] ).
cnf(101,plain,
$false,
inference(binary,[status(thm)],[100,11]),
[iquote('binary,100.1,11.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET956+1 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n024.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 10:51:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.79/2.00 ----- Otter 3.3f, August 2004 -----
% 1.79/2.00 The process was started by sandbox2 on n024.cluster.edu,
% 1.79/2.00 Wed Jul 27 10:51:40 2022
% 1.79/2.00 The command was "./otter". The process ID is 13443.
% 1.79/2.00
% 1.79/2.00 set(prolog_style_variables).
% 1.79/2.00 set(auto).
% 1.79/2.00 dependent: set(auto1).
% 1.79/2.00 dependent: set(process_input).
% 1.79/2.00 dependent: clear(print_kept).
% 1.79/2.00 dependent: clear(print_new_demod).
% 1.79/2.00 dependent: clear(print_back_demod).
% 1.79/2.00 dependent: clear(print_back_sub).
% 1.79/2.00 dependent: set(control_memory).
% 1.79/2.00 dependent: assign(max_mem, 12000).
% 1.79/2.00 dependent: assign(pick_given_ratio, 4).
% 1.79/2.00 dependent: assign(stats_level, 1).
% 1.79/2.00 dependent: assign(max_seconds, 10800).
% 1.79/2.00 clear(print_given).
% 1.79/2.00
% 1.79/2.00 formula_list(usable).
% 1.79/2.00 all A (A=A).
% 1.79/2.00 all A B (in(A,B)-> -in(B,A)).
% 1.79/2.00 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.79/2.00 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.79/2.00 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.79/2.00 all A B (-empty(ordered_pair(A,B))).
% 1.79/2.00 exists A empty(A).
% 1.79/2.00 exists A (-empty(A)).
% 1.79/2.00 all A B subset(A,A).
% 1.79/2.00 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)))))).
% 1.79/2.00 -(all A B C D (subset(A,cartesian_product2(B,C))& (all E F (in(ordered_pair(E,F),A)->in(ordered_pair(E,F),D)))->subset(A,D))).
% 1.79/2.00 end_of_list.
% 1.79/2.00
% 1.79/2.00 -------> usable clausifies to:
% 1.79/2.00
% 1.79/2.00 list(usable).
% 1.79/2.00 0 [] A=A.
% 1.79/2.00 0 [] -in(A,B)| -in(B,A).
% 1.79/2.00 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.79/2.00 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.79/2.00 0 [] subset(A,B)|in($f1(A,B),A).
% 1.79/2.00 0 [] subset(A,B)| -in($f1(A,B),B).
% 1.79/2.00 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.79/2.00 0 [] -empty(ordered_pair(A,B)).
% 1.79/2.00 0 [] empty($c1).
% 1.79/2.00 0 [] -empty($c2).
% 1.79/2.00 0 [] subset(A,A).
% 1.79/2.00 0 [] -subset(A,cartesian_product2(B,C))| -in(D,A)|in($f3(A,B,C,D),B).
% 1.79/2.00 0 [] -subset(A,cartesian_product2(B,C))| -in(D,A)|in($f2(A,B,C,D),C).
% 1.79/2.00 0 [] -subset(A,cartesian_product2(B,C))| -in(D,A)|D=ordered_pair($f3(A,B,C,D),$f2(A,B,C,D)).
% 1.79/2.00 0 [] subset($c6,cartesian_product2($c5,$c4)).
% 1.79/2.00 0 [] -in(ordered_pair(E,F),$c6)|in(ordered_pair(E,F),$c3).
% 1.79/2.00 0 [] -subset($c6,$c3).
% 1.79/2.00 end_of_list.
% 1.79/2.00
% 1.79/2.00 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.79/2.00
% 1.79/2.00 This ia a non-Horn set with equality. The strategy will be
% 1.79/2.00 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.79/2.00 deletion, with positive clauses in sos and nonpositive
% 1.79/2.00 clauses in usable.
% 1.79/2.00
% 1.79/2.00 dependent: set(knuth_bendix).
% 1.79/2.00 dependent: set(anl_eq).
% 1.79/2.00 dependent: set(para_from).
% 1.79/2.00 dependent: set(para_into).
% 1.79/2.00 dependent: clear(para_from_right).
% 1.79/2.00 dependent: clear(para_into_right).
% 1.79/2.00 dependent: set(para_from_vars).
% 1.79/2.00 dependent: set(eq_units_both_ways).
% 1.79/2.00 dependent: set(dynamic_demod_all).
% 1.79/2.00 dependent: set(dynamic_demod).
% 1.79/2.00 dependent: set(order_eq).
% 1.79/2.00 dependent: set(back_demod).
% 1.79/2.00 dependent: set(lrpo).
% 1.79/2.00 dependent: set(hyper_res).
% 1.79/2.00 dependent: set(unit_deletion).
% 1.79/2.00 dependent: set(factor).
% 1.79/2.00
% 1.79/2.00 ------------> process usable:
% 1.79/2.00 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.79/2.00 ** KEPT (pick-wt=9): 2 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.79/2.00 ** KEPT (pick-wt=8): 3 [] subset(A,B)| -in($f1(A,B),B).
% 1.79/2.00 ** KEPT (pick-wt=4): 4 [] -empty(ordered_pair(A,B)).
% 1.79/2.00 ** KEPT (pick-wt=2): 5 [] -empty($c2).
% 1.79/2.00 ** KEPT (pick-wt=15): 6 [] -subset(A,cartesian_product2(B,C))| -in(D,A)|in($f3(A,B,C,D),B).
% 1.79/2.00 ** KEPT (pick-wt=15): 7 [] -subset(A,cartesian_product2(B,C))| -in(D,A)|in($f2(A,B,C,D),C).
% 1.79/2.00 ** KEPT (pick-wt=21): 9 [copy,8,flip.3] -subset(A,cartesian_product2(B,C))| -in(D,A)|ordered_pair($f3(A,B,C,D),$f2(A,B,C,D))=D.
% 1.79/2.00 ** KEPT (pick-wt=10): 10 [] -in(ordered_pair(A,B),$c6)|in(ordered_pair(A,B),$c3).
% 1.79/2.00 ** KEPT (pick-wt=3): 11 [] -subset($c6,$c3).
% 1.79/2.00
% 1.79/2.00 ------------> process sos:
% 1.79/2.00 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.79/2.00 ** KEPT (pick-wt=7): 14 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.79/2.00 ** KEPT (pick-wt=8): 15 [] subset(A,B)|in($f1(A,B),A).
% 1.79/2.00 ** KEPT (pick-wt=10): 17 [copy,16,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.79/2.00 ---> New Demodulator: 18 [new_demod,17] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.79/2.00 ** KEPT (pick-wt=2): 19 [] empty($c1).
% 1.79/2.00 ** KEPT (pick-wt=3): 20 [] subset(A,A).
% 1.79/2.00 ** KEPT (pick-wt=5): 21 [] subset($c6,cartesian_product2($c5,$c4)).
% 1.79/2.00 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.79/2.01 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.79/2.01 >>>> Starting back demodulation with 18.
% 1.79/2.01
% 1.79/2.01 ======= end of input processing =======
% 1.79/2.01
% 1.79/2.01 =========== start of search ===========
% 1.79/2.01
% 1.79/2.01 -------- PROOF --------
% 1.79/2.01
% 1.79/2.01 ----> UNIT CONFLICT at 0.00 sec ----> 101 [binary,100.1,11.1] $F.
% 1.79/2.01
% 1.79/2.01 Length of proof is 5. Level of proof is 4.
% 1.79/2.01
% 1.79/2.01 ---------------- PROOF ----------------
% 1.79/2.01 % SZS status Theorem
% 1.79/2.01 % SZS output start Refutation
% See solution above
% 1.79/2.01 ------------ end of proof -------------
% 1.79/2.01
% 1.79/2.01
% 1.79/2.01 Search stopped by max_proofs option.
% 1.79/2.01
% 1.79/2.01
% 1.79/2.01 Search stopped by max_proofs option.
% 1.79/2.01
% 1.79/2.01 ============ end of search ============
% 1.79/2.01
% 1.79/2.01 -------------- statistics -------------
% 1.79/2.01 clauses given 18
% 1.79/2.01 clauses generated 108
% 1.79/2.01 clauses kept 87
% 1.79/2.01 clauses forward subsumed 42
% 1.79/2.01 clauses back subsumed 0
% 1.79/2.01 Kbytes malloced 1953
% 1.79/2.01
% 1.79/2.01 ----------- times (seconds) -----------
% 1.79/2.01 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/2.01 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/2.01 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.79/2.01
% 1.79/2.01 That finishes the proof of the theorem.
% 1.79/2.01
% 1.79/2.01 Process 13443 finished Wed Jul 27 10:51:41 2022
% 1.79/2.01 Otter interrupted
% 1.79/2.01 PROOF FOUND
%------------------------------------------------------------------------------