TSTP Solution File: SET886+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:14:28 EDT 2022
% Result : Theorem 1.72s 1.92s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of clauses : 16 ( 14 unt; 0 nHn; 13 RR)
% Number of literals : 18 ( 12 equ; 7 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ subset(unordered_pair(A,B),singleton(C))
| A = C ),
file('SET886+1.p',unknown),
[] ).
cnf(3,axiom,
unordered_pair(dollar_c5,dollar_c4) != singleton(dollar_c3),
file('SET886+1.p',unknown),
[] ).
cnf(4,plain,
singleton(dollar_c3) != unordered_pair(dollar_c5,dollar_c4),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[3])]),
[iquote('copy,3,flip.1')] ).
cnf(6,axiom,
unordered_pair(A,B) = unordered_pair(B,A),
file('SET886+1.p',unknown),
[] ).
cnf(9,axiom,
subset(unordered_pair(dollar_c5,dollar_c4),singleton(dollar_c3)),
file('SET886+1.p',unknown),
[] ).
cnf(10,axiom,
unordered_pair(A,A) = singleton(A),
file('SET886+1.p',unknown),
[] ).
cnf(12,plain,
singleton(A) = unordered_pair(A,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(13,plain,
subset(unordered_pair(dollar_c5,dollar_c4),unordered_pair(dollar_c3,dollar_c3)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[9]),12]),
[iquote('back_demod,9,demod,12')] ).
cnf(14,plain,
unordered_pair(dollar_c5,dollar_c4) != unordered_pair(dollar_c3,dollar_c3),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),12])]),
[iquote('back_demod,4,demod,12,flip.1')] ).
cnf(15,plain,
( ~ subset(unordered_pair(A,B),unordered_pair(C,C))
| A = C ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),12]),
[iquote('back_demod,2,demod,12')] ).
cnf(16,plain,
subset(unordered_pair(dollar_c4,dollar_c5),unordered_pair(dollar_c3,dollar_c3)),
inference(para_into,[status(thm),theory(equality)],[13,6]),
[iquote('para_into,13.1.1,6.1.1')] ).
cnf(17,plain,
unordered_pair(dollar_c4,dollar_c5) != unordered_pair(dollar_c3,dollar_c3),
inference(para_into,[status(thm),theory(equality)],[14,6]),
[iquote('para_into,14.1.1,6.1.1')] ).
cnf(19,plain,
dollar_c4 = dollar_c3,
inference(hyper,[status(thm)],[15,16]),
[iquote('hyper,15,16')] ).
cnf(21,plain,
dollar_c5 = dollar_c3,
inference(hyper,[status(thm)],[15,13]),
[iquote('hyper,15,13')] ).
cnf(22,plain,
unordered_pair(dollar_c3,dollar_c3) != unordered_pair(dollar_c3,dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),19,21]),
[iquote('back_demod,17,demod,19,21')] ).
cnf(23,plain,
$false,
inference(binary,[status(thm)],[22,6]),
[iquote('binary,22.1,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET886+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 10:55:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.92 ----- Otter 3.3f, August 2004 -----
% 1.72/1.92 The process was started by sandbox on n014.cluster.edu,
% 1.72/1.92 Wed Jul 27 10:55:39 2022
% 1.72/1.92 The command was "./otter". The process ID is 29020.
% 1.72/1.92
% 1.72/1.92 set(prolog_style_variables).
% 1.72/1.92 set(auto).
% 1.72/1.92 dependent: set(auto1).
% 1.72/1.92 dependent: set(process_input).
% 1.72/1.92 dependent: clear(print_kept).
% 1.72/1.92 dependent: clear(print_new_demod).
% 1.72/1.92 dependent: clear(print_back_demod).
% 1.72/1.92 dependent: clear(print_back_sub).
% 1.72/1.92 dependent: set(control_memory).
% 1.72/1.92 dependent: assign(max_mem, 12000).
% 1.72/1.92 dependent: assign(pick_given_ratio, 4).
% 1.72/1.92 dependent: assign(stats_level, 1).
% 1.72/1.92 dependent: assign(max_seconds, 10800).
% 1.72/1.92 clear(print_given).
% 1.72/1.92
% 1.72/1.92 formula_list(usable).
% 1.72/1.92 all A (A=A).
% 1.72/1.92 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.72/1.92 exists A empty(A).
% 1.72/1.92 exists A (-empty(A)).
% 1.72/1.92 all A B subset(A,A).
% 1.72/1.92 all A B C (subset(unordered_pair(A,B),singleton(C))->A=C).
% 1.72/1.92 -(all A B C (subset(unordered_pair(A,B),singleton(C))->unordered_pair(A,B)=singleton(C))).
% 1.72/1.92 all A (unordered_pair(A,A)=singleton(A)).
% 1.72/1.92 end_of_list.
% 1.72/1.92
% 1.72/1.92 -------> usable clausifies to:
% 1.72/1.92
% 1.72/1.92 list(usable).
% 1.72/1.92 0 [] A=A.
% 1.72/1.92 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.72/1.92 0 [] empty($c1).
% 1.72/1.92 0 [] -empty($c2).
% 1.72/1.92 0 [] subset(A,A).
% 1.72/1.92 0 [] -subset(unordered_pair(A,B),singleton(C))|A=C.
% 1.72/1.92 0 [] subset(unordered_pair($c5,$c4),singleton($c3)).
% 1.72/1.92 0 [] unordered_pair($c5,$c4)!=singleton($c3).
% 1.72/1.92 0 [] unordered_pair(A,A)=singleton(A).
% 1.72/1.92 end_of_list.
% 1.72/1.92
% 1.72/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.72/1.92
% 1.72/1.92 This is a Horn set with equality. The strategy will be
% 1.72/1.92 Knuth-Bendix and hyper_res, with positive clauses in
% 1.72/1.92 sos and nonpositive clauses in usable.
% 1.72/1.92
% 1.72/1.92 dependent: set(knuth_bendix).
% 1.72/1.92 dependent: set(anl_eq).
% 1.72/1.92 dependent: set(para_from).
% 1.72/1.92 dependent: set(para_into).
% 1.72/1.92 dependent: clear(para_from_right).
% 1.72/1.92 dependent: clear(para_into_right).
% 1.72/1.92 dependent: set(para_from_vars).
% 1.72/1.92 dependent: set(eq_units_both_ways).
% 1.72/1.92 dependent: set(dynamic_demod_all).
% 1.72/1.92 dependent: set(dynamic_demod).
% 1.72/1.92 dependent: set(order_eq).
% 1.72/1.92 dependent: set(back_demod).
% 1.72/1.92 dependent: set(lrpo).
% 1.72/1.92 dependent: set(hyper_res).
% 1.72/1.92 dependent: clear(order_hyper).
% 1.72/1.92
% 1.72/1.92 ------------> process usable:
% 1.72/1.92 ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.72/1.92 ** KEPT (pick-wt=9): 2 [] -subset(unordered_pair(A,B),singleton(C))|A=C.
% 1.72/1.92 ** KEPT (pick-wt=6): 4 [copy,3,flip.1] singleton($c3)!=unordered_pair($c5,$c4).
% 1.72/1.92
% 1.72/1.92 ------------> process sos:
% 1.72/1.92 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.72/1.92 ** KEPT (pick-wt=7): 6 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.72/1.92 ** KEPT (pick-wt=2): 7 [] empty($c1).
% 1.72/1.92 ** KEPT (pick-wt=3): 8 [] subset(A,A).
% 1.72/1.92 ** KEPT (pick-wt=6): 9 [] subset(unordered_pair($c5,$c4),singleton($c3)).
% 1.72/1.92 ** KEPT (pick-wt=6): 11 [copy,10,flip.1] singleton(A)=unordered_pair(A,A).
% 1.72/1.92 ---> New Demodulator: 12 [new_demod,11] singleton(A)=unordered_pair(A,A).
% 1.72/1.92 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.72/1.92 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.72/1.92 >>>> Starting back demodulation with 12.
% 1.72/1.92 >> back demodulating 9 with 12.
% 1.72/1.92 >> back demodulating 4 with 12.
% 1.72/1.92 >> back demodulating 2 with 12.
% 1.72/1.92
% 1.72/1.92 ======= end of input processing =======
% 1.72/1.92
% 1.72/1.92 =========== start of search ===========
% 1.72/1.92
% 1.72/1.92 -------- PROOF --------
% 1.72/1.92
% 1.72/1.92 ----> UNIT CONFLICT at 0.00 sec ----> 23 [binary,22.1,6.1] $F.
% 1.72/1.92
% 1.72/1.92 Length of proof is 10. Level of proof is 5.
% 1.72/1.92
% 1.72/1.92 ---------------- PROOF ----------------
% 1.72/1.92 % SZS status Theorem
% 1.72/1.92 % SZS output start Refutation
% See solution above
% 1.72/1.92 ------------ end of proof -------------
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Search stopped by max_proofs option.
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Search stopped by max_proofs option.
% 1.72/1.92
% 1.72/1.92 ============ end of search ============
% 1.72/1.92
% 1.72/1.92 -------------- statistics -------------
% 1.72/1.92 clauses given 10
% 1.72/1.92 clauses generated 13
% 1.72/1.92 clauses kept 17
% 1.72/1.92 clauses forward subsumed 11
% 1.72/1.92 clauses back subsumed 0
% 1.72/1.92 Kbytes malloced 976
% 1.72/1.92
% 1.72/1.92 ----------- times (seconds) -----------
% 1.72/1.92 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.72/1.92
% 1.72/1.92 That finishes the proof of the theorem.
% 1.72/1.92
% 1.72/1.92 Process 29020 finished Wed Jul 27 10:55:40 2022
% 1.72/1.92 Otter interrupted
% 1.72/1.92 PROOF FOUND
%------------------------------------------------------------------------------