TSTP Solution File: SEU142+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 13:14:53 EDT 2022
% Result : Theorem 1.91s 2.07s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 14 ( 7 unt; 4 nHn; 8 RR)
% Number of literals : 28 ( 21 equ; 10 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 23 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( A = singleton(B)
| ~ in(dollar_f1(B,A),A)
| dollar_f1(B,A) != B ),
file('SEU142+1.p',unknown),
[] ).
cnf(5,axiom,
( A != unordered_pair(B,C)
| ~ in(D,A)
| D = B
| D = C ),
file('SEU142+1.p',unknown),
[] ).
cnf(6,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != B ),
file('SEU142+1.p',unknown),
[] ).
cnf(11,axiom,
unordered_pair(dollar_c1,dollar_c1) != singleton(dollar_c1),
file('SEU142+1.p',unknown),
[] ).
cnf(12,plain,
singleton(dollar_c1) != unordered_pair(dollar_c1,dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.1')] ).
cnf(14,plain,
( A != unordered_pair(B,B)
| ~ in(C,A)
| C = B ),
inference(factor,[status(thm)],[5]),
[iquote('factor,5.3.4')] ).
cnf(16,axiom,
A = A,
file('SEU142+1.p',unknown),
[] ).
cnf(17,axiom,
unordered_pair(A,B) = unordered_pair(B,A),
file('SEU142+1.p',unknown),
[] ).
cnf(18,axiom,
( A = singleton(B)
| in(dollar_f1(B,A),A)
| dollar_f1(B,A) = B ),
file('SEU142+1.p',unknown),
[] ).
cnf(23,plain,
in(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[16,6,16]),
[iquote('hyper,16,6,16')] ).
cnf(60,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)],[18,14,17]),
[iquote('hyper,18,14,17')] ).
cnf(63,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)],[60])]),
[iquote('factor,60.2.3,flip.1')] ).
cnf(468,plain,
dollar_f1(dollar_c1,unordered_pair(dollar_c1,dollar_c1)) = dollar_c1,
inference(hyper,[status(thm)],[63,12]),
[iquote('hyper,63,12')] ).
cnf(616,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[468,4]),468]),12,23,16]),
[iquote('para_from,467.1.1,4.3.1,demod,468,unit_del,12,23,16')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 08:23:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.90/2.07 ----- Otter 3.3f, August 2004 -----
% 1.90/2.07 The process was started by sandbox on n016.cluster.edu,
% 1.90/2.07 Wed Jul 27 08:23:22 2022
% 1.90/2.07 The command was "./otter". The process ID is 5813.
% 1.90/2.07
% 1.90/2.07 set(prolog_style_variables).
% 1.90/2.07 set(auto).
% 1.90/2.07 dependent: set(auto1).
% 1.90/2.07 dependent: set(process_input).
% 1.90/2.07 dependent: clear(print_kept).
% 1.90/2.07 dependent: clear(print_new_demod).
% 1.90/2.07 dependent: clear(print_back_demod).
% 1.90/2.07 dependent: clear(print_back_sub).
% 1.90/2.07 dependent: set(control_memory).
% 1.90/2.07 dependent: assign(max_mem, 12000).
% 1.90/2.07 dependent: assign(pick_given_ratio, 4).
% 1.90/2.07 dependent: assign(stats_level, 1).
% 1.90/2.07 dependent: assign(max_seconds, 10800).
% 1.90/2.07 clear(print_given).
% 1.90/2.07
% 1.90/2.07 formula_list(usable).
% 1.90/2.07 all A (A=A).
% 1.90/2.07 all A B (in(A,B)-> -in(B,A)).
% 1.90/2.07 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.90/2.07 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.90/2.07 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 1.90/2.07 $T.
% 1.90/2.07 $T.
% 1.90/2.07 all A B ((all C (in(C,A)<->in(C,B)))->A=B).
% 1.90/2.07 -(all A (unordered_pair(A,A)=singleton(A))).
% 1.90/2.07 end_of_list.
% 1.90/2.07
% 1.90/2.07 -------> usable clausifies to:
% 1.90/2.07
% 1.90/2.07 list(usable).
% 1.90/2.07 0 [] A=A.
% 1.90/2.07 0 [] -in(A,B)| -in(B,A).
% 1.90/2.07 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.90/2.07 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.90/2.07 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.90/2.07 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.90/2.07 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.90/2.07 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 1.90/2.07 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 1.90/2.07 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 1.90/2.07 0 [] C=unordered_pair(A,B)|in($f2(A,B,C),C)|$f2(A,B,C)=A|$f2(A,B,C)=B.
% 1.90/2.07 0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=A.
% 1.90/2.07 0 [] C=unordered_pair(A,B)| -in($f2(A,B,C),C)|$f2(A,B,C)!=B.
% 1.90/2.07 0 [] $T.
% 1.90/2.07 0 [] $T.
% 1.90/2.07 0 [] in($f3(A,B),A)|in($f3(A,B),B)|A=B.
% 1.90/2.07 0 [] -in($f3(A,B),A)| -in($f3(A,B),B)|A=B.
% 1.90/2.07 0 [] unordered_pair($c1,$c1)!=singleton($c1).
% 1.90/2.07 end_of_list.
% 1.90/2.07
% 1.90/2.07 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.90/2.07
% 1.90/2.07 This ia a non-Horn set with equality. The strategy will be
% 1.90/2.07 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.90/2.07 deletion, with positive clauses in sos and nonpositive
% 1.90/2.07 clauses in usable.
% 1.90/2.07
% 1.90/2.07 dependent: set(knuth_bendix).
% 1.90/2.07 dependent: set(anl_eq).
% 1.91/2.07 dependent: set(para_from).
% 1.91/2.07 dependent: set(para_into).
% 1.91/2.07 dependent: clear(para_from_right).
% 1.91/2.07 dependent: clear(para_into_right).
% 1.91/2.07 dependent: set(para_from_vars).
% 1.91/2.07 dependent: set(eq_units_both_ways).
% 1.91/2.07 dependent: set(dynamic_demod_all).
% 1.91/2.07 dependent: set(dynamic_demod).
% 1.91/2.07 dependent: set(order_eq).
% 1.91/2.07 dependent: set(back_demod).
% 1.91/2.07 dependent: set(lrpo).
% 1.91/2.07 dependent: set(hyper_res).
% 1.91/2.07 dependent: set(unit_deletion).
% 1.91/2.07 dependent: set(factor).
% 1.91/2.07
% 1.91/2.07 ------------> process usable:
% 1.91/2.07 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.91/2.07 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.91/2.07 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.91/2.07 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.91/2.07 ** KEPT (pick-wt=14): 5 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 1.91/2.07 ** KEPT (pick-wt=11): 6 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 1.91/2.07 ** KEPT (pick-wt=11): 7 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 1.91/2.07 ** KEPT (pick-wt=17): 8 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=B.
% 1.91/2.07 ** KEPT (pick-wt=17): 9 [] A=unordered_pair(B,C)| -in($f2(B,C,A),A)|$f2(B,C,A)!=C.
% 1.91/2.07 ** KEPT (pick-wt=13): 10 [] -in($f3(A,B),A)| -in($f3(A,B),B)|A=B.
% 1.91/2.07 ** KEPT (pick-wt=6): 12 [copy,11,flip.1] singleton($c1)!=unordered_pair($c1,$c1).
% 1.91/2.07
% 1.91/2.07 ------------> process sos:
% 1.91/2.07 ** KEPT (pick-wt=3): 16 [] A=A.
% 1.91/2.07 ** KEPT (pick-wt=7): 17 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.91/2.07 ** KEPT (pick-wt=14): 18 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.91/2.07 ** KEPT (pick-wt=23): 19 [] A=unordered_pair(B,C)|in($f2(B,C,A),A)|$f2(B,C,A)=B|$f2(B,C,A)=C.
% 1.91/2.07 ** KEPT (pick-wt=13): 20 [] in($f3(A,B),A)|in($f3(A,B),B)|A=B.
% 1.91/2.07 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 1.91/2.07 16 back subsumes 15.
% 1.91/2.07 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.91/2.07
% 1.91/2.07 ======= end of input processing =======
% 1.91/2.07
% 1.91/2.07 =========== start of search ===========
% 1.91/2.07
% 1.91/2.07 -------- PROOF --------
% 1.91/2.07
% 1.91/2.07 -----> EMPTY CLAUSE at 0.06 sec ----> 616 [para_from,467.1.1,4.3.1,demod,468,unit_del,12,23,16] $F.
% 1.91/2.07
% 1.91/2.07 Length of proof is 6. Level of proof is 4.
% 1.91/2.07
% 1.91/2.07 ---------------- PROOF ----------------
% 1.91/2.07 % SZS status Theorem
% 1.91/2.07 % SZS output start Refutation
% See solution above
% 1.91/2.07 ------------ end of proof -------------
% 1.91/2.07
% 1.91/2.07
% 1.91/2.07 Search stopped by max_proofs option.
% 1.91/2.07
% 1.91/2.07
% 1.91/2.07 Search stopped by max_proofs option.
% 1.91/2.07
% 1.91/2.07 ============ end of search ============
% 1.91/2.07
% 1.91/2.07 -------------- statistics -------------
% 1.91/2.07 clauses given 20
% 1.91/2.07 clauses generated 1090
% 1.91/2.07 clauses kept 613
% 1.91/2.07 clauses forward subsumed 485
% 1.91/2.07 clauses back subsumed 2
% 1.91/2.07 Kbytes malloced 2929
% 1.91/2.07
% 1.91/2.07 ----------- times (seconds) -----------
% 1.91/2.07 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.91/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.07 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.91/2.07
% 1.91/2.07 That finishes the proof of the theorem.
% 1.91/2.07
% 1.91/2.07 Process 5813 finished Wed Jul 27 08:23:24 2022
% 1.91/2.07 Otter interrupted
% 1.91/2.07 PROOF FOUND
%------------------------------------------------------------------------------