%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU150+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 13:14:56 EDT 2022
% Result : Theorem 1.63s 1.85s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 9 ( 7 unt; 0 nHn; 8 RR)
% Number of literals : 11 ( 10 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( singleton(A) != unordered_pair(B,C)
| A = B ),
file('SEU150+3.p',unknown),
[] ).
cnf(3,axiom,
dollar_c4 != dollar_c3,
file('SEU150+3.p',unknown),
[] ).
cnf(5,axiom,
unordered_pair(A,B) = unordered_pair(B,A),
file('SEU150+3.p',unknown),
[] ).
cnf(7,axiom,
singleton(dollar_c5) = unordered_pair(dollar_c4,dollar_c3),
file('SEU150+3.p',unknown),
[] ).
cnf(11,plain,
dollar_c5 = dollar_c4,
inference(hyper,[status(thm)],[7,2]),
[iquote('hyper,7,2')] ).
cnf(13,plain,
singleton(dollar_c4) = unordered_pair(dollar_c4,dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[7]),11]),
[iquote('back_demod,7,demod,11')] ).
cnf(14,plain,
( A = dollar_c4
| unordered_pair(dollar_c4,dollar_c3) != unordered_pair(A,B) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,2]),11,13]),
[iquote('para_into,10.1.1,2.2.1,demod,11,13')] ).
cnf(21,plain,
dollar_c4 = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[14,5])]),
[iquote('hyper,14,5,flip.1')] ).
cnf(23,plain,
$false,
inference(binary,[status(thm)],[21,3]),
[iquote('binary,21.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU150+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Jul 27 07:39:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.63/1.85 ----- Otter 3.3f, August 2004 -----
% 1.63/1.85 The process was started by sandbox on n010.cluster.edu,
% 1.63/1.85 Wed Jul 27 07:39:54 2022
% 1.63/1.85 The command was "./otter". The process ID is 16068.
% 1.63/1.85
% 1.63/1.85 set(prolog_style_variables).
% 1.63/1.85 set(auto).
% 1.63/1.85 dependent: set(auto1).
% 1.63/1.85 dependent: set(process_input).
% 1.63/1.85 dependent: clear(print_kept).
% 1.63/1.85 dependent: clear(print_new_demod).
% 1.63/1.85 dependent: clear(print_back_demod).
% 1.63/1.85 dependent: clear(print_back_sub).
% 1.63/1.85 dependent: set(control_memory).
% 1.63/1.85 dependent: assign(max_mem, 12000).
% 1.63/1.85 dependent: assign(pick_given_ratio, 4).
% 1.63/1.85 dependent: assign(stats_level, 1).
% 1.63/1.85 dependent: assign(max_seconds, 10800).
% 1.63/1.85 clear(print_given).
% 1.63/1.85
% 1.63/1.85 formula_list(usable).
% 1.63/1.85 all A (A=A).
% 1.63/1.85 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.63/1.85 exists A empty(A).
% 1.63/1.85 exists A (-empty(A)).
% 1.63/1.85 all A B C (singleton(A)=unordered_pair(B,C)->A=B).
% 1.63/1.85 -(all A B C (singleton(A)=unordered_pair(B,C)->B=C)).
% 1.63/1.85 end_of_list.
% 1.63/1.85
% 1.63/1.85 -------> usable clausifies to:
% 1.63/1.85
% 1.63/1.85 list(usable).
% 1.63/1.85 0 [] A=A.
% 1.63/1.85 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.63/1.85 0 [] empty($c1).
% 1.63/1.85 0 [] -empty($c2).
% 1.63/1.85 0 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 1.63/1.85 0 [] singleton($c5)=unordered_pair($c4,$c3).
% 1.63/1.85 0 [] $c4!=$c3.
% 1.63/1.85 end_of_list.
% 1.63/1.85
% 1.63/1.85 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.63/1.85
% 1.63/1.85 This is a Horn set with equality. The strategy will be
% 1.63/1.85 Knuth-Bendix and hyper_res, with positive clauses in
% 1.63/1.85 sos and nonpositive clauses in usable.
% 1.63/1.85
% 1.63/1.85 dependent: set(knuth_bendix).
% 1.63/1.85 dependent: set(anl_eq).
% 1.63/1.85 dependent: set(para_from).
% 1.63/1.85 dependent: set(para_into).
% 1.63/1.85 dependent: clear(para_from_right).
% 1.63/1.85 dependent: clear(para_into_right).
% 1.63/1.85 dependent: set(para_from_vars).
% 1.63/1.85 dependent: set(eq_units_both_ways).
% 1.63/1.85 dependent: set(dynamic_demod_all).
% 1.63/1.85 dependent: set(dynamic_demod).
% 1.63/1.85 dependent: set(order_eq).
% 1.63/1.85 dependent: set(back_demod).
% 1.63/1.85 dependent: set(lrpo).
% 1.63/1.85 dependent: set(hyper_res).
% 1.63/1.85 dependent: clear(order_hyper).
% 1.63/1.85
% 1.63/1.85 ------------> process usable:
% 1.63/1.85 ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.63/1.85 ** KEPT (pick-wt=9): 2 [] singleton(A)!=unordered_pair(B,C)|A=B.
% 1.63/1.85 ** KEPT (pick-wt=3): 3 [] $c4!=$c3.
% 1.63/1.85
% 1.63/1.85 ------------> process sos:
% 1.63/1.85 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.63/1.85 ** KEPT (pick-wt=7): 5 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.63/1.85 ** KEPT (pick-wt=2): 6 [] empty($c1).
% 1.63/1.85 ** KEPT (pick-wt=6): 7 [] singleton($c5)=unordered_pair($c4,$c3).
% 1.63/1.85 ---> New Demodulator: 8 [new_demod,7] singleton($c5)=unordered_pair($c4,$c3).
% 1.63/1.85 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.63/1.85 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.63/1.85 >>>> Starting back demodulation with 8.
% 1.63/1.85
% 1.63/1.85 ======= end of input processing =======
% 1.63/1.85
% 1.63/1.85 =========== start of search ===========
% 1.63/1.85
% 1.63/1.85 -------- PROOF --------
% 1.63/1.85
% 1.63/1.85 ----> UNIT CONFLICT at 0.00 sec ----> 23 [binary,21.1,3.1] $F.
% 1.63/1.85
% 1.63/1.85 Length of proof is 4. Level of proof is 4.
% 1.63/1.85
% 1.63/1.85 ---------------- PROOF ----------------
% 1.63/1.85 % SZS status Theorem
% 1.63/1.85 % SZS output start Refutation
% See solution above
% 1.63/1.85 ------------ end of proof -------------
% 1.63/1.85
% 1.63/1.85
% 1.63/1.85 Search stopped by max_proofs option.
% 1.63/1.85
% 1.63/1.85
% 1.63/1.85 Search stopped by max_proofs option.
% 1.63/1.85
% 1.63/1.85 ============ end of search ============
% 1.63/1.85
% 1.63/1.85 -------------- statistics -------------
% 1.63/1.85 clauses given 8
% 1.63/1.85 clauses generated 17
% 1.63/1.85 clauses kept 18
% 1.63/1.85 clauses forward subsumed 9
% 1.63/1.85 clauses back subsumed 0
% 1.63/1.85 Kbytes malloced 976
% 1.63/1.85
% 1.63/1.85 ----------- times (seconds) -----------
% 1.63/1.85 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.63/1.85 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.63/1.85 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.63/1.85
% 1.63/1.85 That finishes the proof of the theorem.
% 1.63/1.85
% 1.63/1.85 Process 16068 finished Wed Jul 27 07:39:56 2022
% 1.63/1.85 Otter interrupted
% 1.63/1.85 PROOF FOUND
%------------------------------------------------------------------------------