TSTP Solution File: SEU149+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU149+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:14:55 EDT 2022
% Result : Theorem 2.28s 2.49s
% Output : Refutation 2.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 22 ( 12 unt; 4 nHn; 14 RR)
% Number of literals : 41 ( 31 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 31 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( A != singleton(B)
| in(C,A)
| C != B ),
file('SEU149+1.p',unknown),
[] ).
cnf(4,axiom,
( A = singleton(B)
| ~ in(dollar_f1(B,A),A)
| dollar_f1(B,A) != B ),
file('SEU149+1.p',unknown),
[] ).
cnf(5,axiom,
( A != unordered_pair(B,C)
| ~ in(D,A)
| D = B
| D = C ),
file('SEU149+1.p',unknown),
[] ).
cnf(6,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != B ),
file('SEU149+1.p',unknown),
[] ).
cnf(10,axiom,
dollar_c3 != dollar_c2,
file('SEU149+1.p',unknown),
[] ).
cnf(12,plain,
( A != unordered_pair(B,B)
| ~ in(C,A)
| C = B ),
inference(factor,[status(thm)],[5]),
[iquote('factor,5.3.4')] ).
cnf(13,axiom,
A = A,
file('SEU149+1.p',unknown),
[] ).
cnf(14,axiom,
unordered_pair(A,B) = unordered_pair(B,A),
file('SEU149+1.p',unknown),
[] ).
cnf(15,axiom,
( A = singleton(B)
| in(dollar_f1(B,A),A)
| dollar_f1(B,A) = B ),
file('SEU149+1.p',unknown),
[] ).
cnf(17,axiom,
singleton(dollar_c3) = unordered_pair(dollar_c2,dollar_c1),
file('SEU149+1.p',unknown),
[] ).
cnf(21,plain,
in(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[13,6,13]),
[iquote('hyper,13,6,13')] ).
cnf(22,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[13,3,13]),
[iquote('hyper,13,3,13')] ).
cnf(45,plain,
dollar_c3 = dollar_c1,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[17,5,22]),10]),
[iquote('hyper,17,5,22,unit_del,10')] ).
cnf(47,plain,
singleton(dollar_c1) = unordered_pair(dollar_c2,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[17]),45]),
[iquote('back_demod,17,demod,45')] ).
cnf(49,plain,
dollar_c2 != dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[10]),45])]),
[iquote('back_demod,10,demod,45,flip.1')] ).
cnf(67,plain,
( A != dollar_c1
| B != unordered_pair(A,A)
| ~ in(dollar_c2,B) ),
inference(para_into,[status(thm),theory(equality)],[49,12]),
[iquote('para_into,49.1.1,12.3.1')] ).
cnf(109,plain,
( unordered_pair(A,A) = singleton(B)
| dollar_f1(B,unordered_pair(A,A)) = B
| dollar_f1(B,unordered_pair(A,A)) = A ),
inference(hyper,[status(thm)],[15,12,14]),
[iquote('hyper,15,12,14')] ).
cnf(113,plain,
( singleton(A) = unordered_pair(A,A)
| dollar_f1(A,unordered_pair(A,A)) = A ),
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[109])]),
[iquote('factor,109.2.3,flip.1')] ).
cnf(1560,plain,
( singleton(A) = unordered_pair(A,A)
| dollar_f1(A,unordered_pair(A,A)) != A ),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[113,4]),21])]),
[iquote('para_from,113.2.1,4.2.1,unit_del,21,factor_simp')] ).
cnf(1682,plain,
singleton(A) = unordered_pair(A,A),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[1560,113])]),
[iquote('hyper,1560,113,factor_simp')] ).
cnf(1700,plain,
unordered_pair(dollar_c2,dollar_c1) = unordered_pair(dollar_c1,dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),1682])]),
[iquote('back_demod,47,demod,1682,flip.1')] ).
cnf(1708,plain,
$false,
inference(hyper,[status(thm)],[1700,67,13,21]),
[iquote('hyper,1700,67,13,21')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU149+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 08:09:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.28/2.49 ----- Otter 3.3f, August 2004 -----
% 2.28/2.49 The process was started by sandbox2 on n027.cluster.edu,
% 2.28/2.49 Wed Jul 27 08:09:22 2022
% 2.28/2.49 The command was "./otter". The process ID is 11222.
% 2.28/2.49
% 2.28/2.49 set(prolog_style_variables).
% 2.28/2.49 set(auto).
% 2.28/2.49 dependent: set(auto1).
% 2.28/2.49 dependent: set(process_input).
% 2.28/2.49 dependent: clear(print_kept).
% 2.28/2.49 dependent: clear(print_new_demod).
% 2.28/2.49 dependent: clear(print_back_demod).
% 2.28/2.49 dependent: clear(print_back_sub).
% 2.28/2.49 dependent: set(control_memory).
% 2.28/2.49 dependent: assign(max_mem, 12000).
% 2.28/2.49 dependent: assign(pick_given_ratio, 4).
% 2.28/2.49 dependent: assign(stats_level, 1).
% 2.28/2.49 dependent: assign(max_seconds, 10800).
% 2.28/2.49 clear(print_given).
% 2.28/2.49
% 2.28/2.49 formula_list(usable).
% 2.28/2.49 all A (A=A).
% 2.28/2.49 all A B (in(A,B)-> -in(B,A)).
% 2.28/2.49 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 2.28/2.49 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 2.28/2.49 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 2.28/2.49 $T.
% 2.28/2.49 $T.
% 2.28/2.49 -(all A B C (singleton(A)=unordered_pair(B,C)->A=B)).
% 2.28/2.49 end_of_list.
% 2.28/2.49
% 2.28/2.49 -------> usable clausifies to:
% 2.28/2.49
% 2.28/2.49 list(usable).
% 2.28/2.49 0 [] A=A.
% 2.28/2.49 0 [] -in(A,B)| -in(B,A).
% 2.28/2.49 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.28/2.49 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 2.28/2.49 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 2.28/2.49 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 2.28/2.49 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 2.28/2.49 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 2.28/2.49 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 2.28/2.49 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 2.28/2.49 0 [] C=unordered_pair(A,B)|in($f2(A,B,C),C)|$f2(A,B,C)=A|$f2(A,B,C)=B.
% 2.28/2.49 0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=A.
% 2.28/2.49 0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=B.
% 2.28/2.49 0 [] $T.
% 2.28/2.49 0 [] $T.
% 2.28/2.49 0 [] singleton($c3)=unordered_pair($c2,$c1).
% 2.28/2.49 0 [] $c3!=$c2.
% 2.28/2.49 end_of_list.
% 2.28/2.49
% 2.28/2.49 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.28/2.49
% 2.28/2.49 This ia a non-Horn set with equality. The strategy will be
% 2.28/2.49 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.28/2.49 deletion, with positive clauses in sos and nonpositive
% 2.28/2.49 clauses in usable.
% 2.28/2.49
% 2.28/2.49 dependent: set(knuth_bendix).
% 2.28/2.49 dependent: set(anl_eq).
% 2.28/2.49 dependent: set(para_from).
% 2.28/2.49 dependent: set(para_into).
% 2.28/2.49 dependent: clear(para_from_right).
% 2.28/2.49 dependent: clear(para_into_right).
% 2.28/2.49 dependent: set(para_from_vars).
% 2.28/2.49 dependent: set(eq_units_both_ways).
% 2.28/2.49 dependent: set(dynamic_demod_all).
% 2.28/2.49 dependent: set(dynamic_demod).
% 2.28/2.49 dependent: set(order_eq).
% 2.28/2.49 dependent: set(back_demod).
% 2.28/2.49 dependent: set(lrpo).
% 2.28/2.49 dependent: set(hyper_res).
% 2.28/2.49 dependent: set(unit_deletion).
% 2.28/2.49 dependent: set(factor).
% 2.28/2.49
% 2.28/2.49 ------------> process usable:
% 2.28/2.49 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.28/2.49 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 2.28/2.49 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 2.28/2.49 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 2.28/2.49 ** KEPT (pick-wt=14): 5 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 2.28/2.49 ** KEPT (pick-wt=11): 6 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 2.28/2.49 ** KEPT (pick-wt=11): 7 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 2.28/2.49 ** KEPT (pick-wt=17): 8 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=B.
% 2.28/2.49 ** KEPT (pick-wt=17): 9 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=C.
% 2.28/2.49 ** KEPT (pick-wt=3): 10 [] $c3!=$c2.
% 2.28/2.49
% 2.28/2.49 ------------> process sos:
% 2.28/2.49 ** KEPT (pick-wt=3): 13 [] A=A.
% 2.28/2.49 ** KEPT (pick-wt=7): 14 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.28/2.49 ** KEPT (pick-wt=14): 15 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 2.28/2.49 ** KEPT (pick-wt=23): 16 [] A=unordered_pair(B,C)|in($f2(B,C,A),A)|$f2(B,C,A)=B|$f2(B,C,A)=C.
% 2.28/2.49 ** KEPT (pick-wt=6): 17 [] singleton($c3)=unordered_pair($c2,$c1).
% 2.28/2.49 ---> New Demodulator: 18 [new_demod,17] singleton($c3)=unordered_pair($c2,$c1).
% 2.28/2.49 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 2.28/2.49 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 2.28/2.49 >>>> Starting back demodulation with 18.
% 2.28/2.49
% 2.28/2.49 ======= end of input processing =======
% 2.28/2.49
% 2.28/2.49 =========== start of search ===========
% 2.28/2.49
% 2.28/2.49
% 2.28/2.49 Resetting weight limit to 16.
% 2.28/2.49
% 2.28/2.49
% 2.28/2.49 Resetting weight limit to 16.
% 2.28/2.49
% 2.28/2.49 sos_size=1585
% 2.28/2.49
% 2.28/2.49 -------- PROOF --------
% 2.28/2.49
% 2.28/2.49 -----> EMPTY CLAUSE at 0.58 sec ----> 1708 [hyper,1700,67,13,21] $F.
% 2.28/2.49
% 2.28/2.49 Length of proof is 12. Level of proof is 6.
% 2.28/2.49
% 2.28/2.49 ---------------- PROOF ----------------
% 2.28/2.49 % SZS status Theorem
% 2.28/2.49 % SZS output start Refutation
% See solution above
% 2.28/2.49 ------------ end of proof -------------
% 2.28/2.49
% 2.28/2.49
% 2.28/2.49 Search stopped by max_proofs option.
% 2.28/2.49
% 2.28/2.49
% 2.28/2.49 Search stopped by max_proofs option.
% 2.28/2.49
% 2.28/2.49 ============ end of search ============
% 2.28/2.49
% 2.28/2.49 -------------- statistics -------------
% 2.28/2.49 clauses given 53
% 2.28/2.49 clauses generated 2930
% 2.28/2.49 clauses kept 1702
% 2.28/2.49 clauses forward subsumed 1080
% 2.28/2.49 clauses back subsumed 33
% 2.28/2.49 Kbytes malloced 4882
% 2.28/2.49
% 2.28/2.49 ----------- times (seconds) -----------
% 2.28/2.49 user CPU time 0.58 (0 hr, 0 min, 0 sec)
% 2.28/2.49 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.28/2.49 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.28/2.49
% 2.28/2.49 That finishes the proof of the theorem.
% 2.28/2.49
% 2.28/2.49 Process 11222 finished Wed Jul 27 08:09:24 2022
% 2.28/2.49 Otter interrupted
% 2.28/2.49 PROOF FOUND
%------------------------------------------------------------------------------