TSTP Solution File: SET628+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:13:54 EDT 2022
% Result : Theorem 1.75s 1.96s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 23 ( 7 unt; 11 nHn; 14 RR)
% Number of literals : 44 ( 7 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),B) ),
file('SET628+3.p',unknown),
[] ).
cnf(3,axiom,
( intersect(A,B)
| ~ member(C,A)
| ~ member(C,B) ),
file('SET628+3.p',unknown),
[] ).
cnf(4,axiom,
~ member(A,empty_set),
file('SET628+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ not_e_qual(A,B)
| A != B ),
file('SET628+3.p',unknown),
[] ).
cnf(11,axiom,
( ~ intersect(dollar_c1,dollar_c1)
| ~ not_e_qual(dollar_c1,empty_set) ),
file('SET628+3.p',unknown),
[] ).
cnf(12,plain,
( intersect(A,A)
| ~ member(B,A) ),
inference(factor,[status(thm)],[3]),
[iquote('factor,3.2.3')] ).
cnf(14,axiom,
A = A,
file('SET628+3.p',unknown),
[] ).
cnf(15,axiom,
( A = B
| member(dollar_f2(A,B),A)
| member(dollar_f2(A,B),B) ),
file('SET628+3.p',unknown),
[] ).
cnf(16,axiom,
( not_e_qual(A,B)
| A = B ),
file('SET628+3.p',unknown),
[] ).
cnf(18,axiom,
( intersect(dollar_c1,dollar_c1)
| not_e_qual(dollar_c1,empty_set) ),
file('SET628+3.p',unknown),
[] ).
cnf(30,plain,
( intersect(A,dollar_c1)
| not_e_qual(dollar_c1,empty_set)
| not_e_qual(dollar_c1,A) ),
inference(para_into,[status(thm),theory(equality)],[18,16]),
[iquote('para_into,18.1.1,16.2.1')] ).
cnf(34,plain,
( intersect(empty_set,dollar_c1)
| not_e_qual(dollar_c1,empty_set) ),
inference(factor,[status(thm)],[30]),
[iquote('factor,30.2.3')] ).
cnf(40,plain,
( empty_set = A
| member(dollar_f2(empty_set,A),A) ),
inference(hyper,[status(thm)],[15,4]),
[iquote('hyper,15,4')] ).
cnf(68,plain,
( intersect(empty_set,A)
| not_e_qual(dollar_c1,empty_set)
| not_e_qual(dollar_c1,A) ),
inference(para_into,[status(thm),theory(equality)],[34,16]),
[iquote('para_into,34.1.2,16.2.1')] ).
cnf(76,plain,
( intersect(empty_set,empty_set)
| not_e_qual(dollar_c1,empty_set) ),
inference(factor,[status(thm)],[68]),
[iquote('factor,68.2.3')] ).
cnf(94,plain,
( intersect(empty_set,empty_set)
| not_e_qual(dollar_c1,A)
| not_e_qual(empty_set,A) ),
inference(para_into,[status(thm),theory(equality)],[76,16]),
[iquote('para_into,76.2.2,16.2.1')] ).
cnf(96,plain,
( empty_set = A
| intersect(A,A) ),
inference(hyper,[status(thm)],[40,12]),
[iquote('hyper,40,12')] ).
cnf(126,plain,
empty_set = dollar_c1,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[96,11,16])]),
[iquote('hyper,96,11,16,factor_simp')] ).
cnf(151,plain,
( intersect(dollar_c1,dollar_c1)
| not_e_qual(dollar_c1,A) ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[94]),126,126,126])]),
[iquote('back_demod,94,demod,126,126,126,factor_simp')] ).
cnf(173,plain,
~ member(A,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),126]),
[iquote('back_demod,4,demod,126')] ).
cnf(208,plain,
intersect(dollar_c1,dollar_c1),
inference(hyper,[status(thm)],[151,8,14]),
[iquote('hyper,151,8,14')] ).
cnf(209,plain,
member(dollar_f1(dollar_c1,dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[208,2]),
[iquote('hyper,208,2')] ).
cnf(210,plain,
$false,
inference(binary,[status(thm)],[209,173]),
[iquote('binary,209.1,173.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET628+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Jul 27 10:54:08 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.75/1.96 ----- Otter 3.3f, August 2004 -----
% 1.75/1.96 The process was started by sandbox2 on n008.cluster.edu,
% 1.75/1.96 Wed Jul 27 10:54:08 2022
% 1.75/1.96 The command was "./otter". The process ID is 9548.
% 1.75/1.96
% 1.75/1.96 set(prolog_style_variables).
% 1.75/1.96 set(auto).
% 1.75/1.96 dependent: set(auto1).
% 1.75/1.96 dependent: set(process_input).
% 1.75/1.96 dependent: clear(print_kept).
% 1.75/1.96 dependent: clear(print_new_demod).
% 1.75/1.96 dependent: clear(print_back_demod).
% 1.75/1.96 dependent: clear(print_back_sub).
% 1.75/1.96 dependent: set(control_memory).
% 1.75/1.96 dependent: assign(max_mem, 12000).
% 1.75/1.96 dependent: assign(pick_given_ratio, 4).
% 1.75/1.96 dependent: assign(stats_level, 1).
% 1.75/1.96 dependent: assign(max_seconds, 10800).
% 1.75/1.96 clear(print_given).
% 1.75/1.96
% 1.75/1.96 formula_list(usable).
% 1.75/1.96 all A (A=A).
% 1.75/1.96 all B C (intersect(B,C)<-> (exists D (member(D,B)&member(D,C)))).
% 1.75/1.96 all B (-member(B,empty_set)).
% 1.75/1.96 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.75/1.96 all B C (not_e_qual(B,C)<->B!=C).
% 1.75/1.96 all B C (intersect(B,C)->intersect(C,B)).
% 1.75/1.96 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.75/1.96 -(all B (intersect(B,B)<->not_e_qual(B,empty_set))).
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 -------> usable clausifies to:
% 1.75/1.96
% 1.75/1.96 list(usable).
% 1.75/1.96 0 [] A=A.
% 1.75/1.96 0 [] -intersect(B,C)|member($f1(B,C),B).
% 1.75/1.96 0 [] -intersect(B,C)|member($f1(B,C),C).
% 1.75/1.96 0 [] intersect(B,C)| -member(D,B)| -member(D,C).
% 1.75/1.96 0 [] -member(B,empty_set).
% 1.75/1.96 0 [] B!=C| -member(D,B)|member(D,C).
% 1.75/1.96 0 [] B!=C|member(D,B)| -member(D,C).
% 1.75/1.96 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.75/1.96 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.75/1.96 0 [] -not_e_qual(B,C)|B!=C.
% 1.75/1.96 0 [] not_e_qual(B,C)|B=C.
% 1.75/1.96 0 [] -intersect(B,C)|intersect(C,B).
% 1.75/1.96 0 [] -empty(B)| -member(C,B).
% 1.75/1.96 0 [] empty(B)|member($f3(B),B).
% 1.75/1.96 0 [] intersect($c1,$c1)|not_e_qual($c1,empty_set).
% 1.75/1.96 0 [] -intersect($c1,$c1)| -not_e_qual($c1,empty_set).
% 1.75/1.96 end_of_list.
% 1.75/1.96
% 1.75/1.96 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.75/1.96
% 1.75/1.96 This ia a non-Horn set with equality. The strategy will be
% 1.75/1.96 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.75/1.96 deletion, with positive clauses in sos and nonpositive
% 1.75/1.96 clauses in usable.
% 1.75/1.96
% 1.75/1.96 dependent: set(knuth_bendix).
% 1.75/1.96 dependent: set(anl_eq).
% 1.75/1.96 dependent: set(para_from).
% 1.75/1.96 dependent: set(para_into).
% 1.75/1.96 dependent: clear(para_from_right).
% 1.75/1.96 dependent: clear(para_into_right).
% 1.75/1.96 dependent: set(para_from_vars).
% 1.75/1.96 dependent: set(eq_units_both_ways).
% 1.75/1.96 dependent: set(dynamic_demod_all).
% 1.75/1.96 dependent: set(dynamic_demod).
% 1.75/1.96 dependent: set(order_eq).
% 1.75/1.96 dependent: set(back_demod).
% 1.75/1.96 dependent: set(lrpo).
% 1.75/1.96 dependent: set(hyper_res).
% 1.75/1.96 dependent: set(unit_deletion).
% 1.75/1.96 dependent: set(factor).
% 1.75/1.96
% 1.75/1.96 ------------> process usable:
% 1.75/1.96 ** KEPT (pick-wt=8): 1 [] -intersect(A,B)|member($f1(A,B),A).
% 1.75/1.96 ** KEPT (pick-wt=8): 2 [] -intersect(A,B)|member($f1(A,B),B).
% 1.75/1.96 ** KEPT (pick-wt=9): 3 [] intersect(A,B)| -member(C,A)| -member(C,B).
% 1.75/1.96 ** KEPT (pick-wt=3): 4 [] -member(A,empty_set).
% 1.75/1.96 ** KEPT (pick-wt=9): 5 [] A!=B| -member(C,A)|member(C,B).
% 1.75/1.96 ** KEPT (pick-wt=9): 6 [] A!=B|member(C,A)| -member(C,B).
% 1.75/1.96 ** KEPT (pick-wt=13): 7 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.75/1.96 ** KEPT (pick-wt=6): 8 [] -not_e_qual(A,B)|A!=B.
% 1.75/1.96 ** KEPT (pick-wt=6): 9 [] -intersect(A,B)|intersect(B,A).
% 1.75/1.96 ** KEPT (pick-wt=5): 10 [] -empty(A)| -member(B,A).
% 1.75/1.96 ** KEPT (pick-wt=6): 11 [] -intersect($c1,$c1)| -not_e_qual($c1,empty_set).
% 1.75/1.96
% 1.75/1.96 ------------> process sos:
% 1.75/1.96 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.75/1.96 ** KEPT (pick-wt=13): 15 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.75/1.96 ** KEPT (pick-wt=6): 16 [] not_e_qual(A,B)|A=B.
% 1.75/1.96 ** KEPT (pick-wt=6): 17 [] empty(A)|member($f3(A),A).
% 1.75/1.96 ** KEPT (pick-wt=6): 18 [] intersect($c1,$c1)|not_e_qual($c1,empty_set).
% 1.75/1.96 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.75/1.96 14 back subsumes 13.
% 1.75/1.96
% 1.75/1.96 ======= end of input processing =======
% 1.75/1.96
% 1.75/1.96 =========== start of search ===========
% 1.75/1.96
% 1.75/1.96 -------- PROOF --------
% 1.75/1.96
% 1.75/1.96 ----> UNIT CONFLICT at 0.01 sec ----> 210 [binary,209.1,173.1] $F.
% 1.75/1.96
% 1.75/1.96 Length of proof is 13. Level of proof is 8.
% 1.75/1.96
% 1.75/1.96 ---------------- PROOF ----------------
% 1.75/1.96 % SZS status Theorem
% 1.75/1.96 % SZS output start Refutation
% See solution above
% 1.75/1.96 ------------ end of proof -------------
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Search stopped by max_proofs option.
% 1.75/1.96
% 1.75/1.96
% 1.75/1.96 Search stopped by max_proofs option.
% 1.75/1.96
% 1.75/1.96 ============ end of search ============
% 1.75/1.96
% 1.75/1.96 -------------- statistics -------------
% 1.75/1.96 clauses given 18
% 1.75/1.96 clauses generated 353
% 1.75/1.96 clauses kept 208
% 1.75/1.96 clauses forward subsumed 245
% 1.75/1.96 clauses back subsumed 10
% 1.75/1.96 Kbytes malloced 976
% 1.75/1.96
% 1.75/1.96 ----------- times (seconds) -----------
% 1.75/1.96 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.75/1.96 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.96 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.75/1.96
% 1.75/1.96 That finishes the proof of the theorem.
% 1.75/1.96
% 1.75/1.96 Process 9548 finished Wed Jul 27 10:54:10 2022
% 1.75/1.96 Otter interrupted
% 1.75/1.96 PROOF FOUND
%------------------------------------------------------------------------------