TSTP Solution File: SET787-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET787-1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:14:15 EDT 2022
% Result : Unsatisfiable 1.70s 1.94s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 7 unt; 6 nHn; 13 RR)
% Number of literals : 29 ( 1 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,union(B))
| member(A,unionE_sk1(A,B)) ),
file('SET787-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(A,union(B))
| member(unionE_sk1(A,B),B) ),
file('SET787-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ member(A,cons(B,C))
| A = B
| member(A,C) ),
file('SET787-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(A,B)
| member(A,un(B,C)) ),
file('SET787-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(A,B)
| member(A,un(C,B)) ),
file('SET787-1.p',unknown),
[] ).
cnf(7,axiom,
~ member(A,eptset),
file('SET787-1.p',unknown),
[] ).
cnf(13,axiom,
~ member(sk2,un(a,b)),
file('SET787-1.p',unknown),
[] ).
cnf(16,axiom,
member(sk2,union(cons(a,cons(b,eptset)))),
file('SET787-1.p',unknown),
[] ).
cnf(20,plain,
member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))),
inference(hyper,[status(thm)],[16,2]),
[iquote('hyper,16,2')] ).
cnf(21,plain,
member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))),
inference(hyper,[status(thm)],[16,1]),
[iquote('hyper,16,1')] ).
cnf(38,plain,
( member(sk2,A)
| ~ member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(A,B))
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),B) ),
inference(para_into,[status(thm),theory(equality)],[21,4]),
[iquote('para_into,21.1.2,4.2.1')] ).
cnf(396,plain,
( member(sk2,a)
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
inference(hyper,[status(thm)],[38,20]),
[iquote('hyper,38,20')] ).
cnf(399,plain,
( member(sk2,a)
| member(sk2,b) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[396,38]),7]),
[iquote('hyper,396,38,unit_del,7')] ).
cnf(404,plain,
( member(sk2,b)
| member(sk2,un(a,A)) ),
inference(hyper,[status(thm)],[399,5]),
[iquote('hyper,399,5')] ).
cnf(443,plain,
( member(sk2,un(a,A))
| member(sk2,un(B,b)) ),
inference(hyper,[status(thm)],[404,6]),
[iquote('hyper,404,6')] ).
cnf(446,plain,
member(sk2,un(a,b)),
inference(factor,[status(thm)],[443]),
[iquote('factor,443.1.2')] ).
cnf(447,plain,
$false,
inference(binary,[status(thm)],[446,13]),
[iquote('binary,446.1,13.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET787-1 : TPTP v8.1.0. Released v2.7.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 10:32:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.94 ----- Otter 3.3f, August 2004 -----
% 1.70/1.94 The process was started by sandbox on n003.cluster.edu,
% 1.70/1.94 Wed Jul 27 10:32:41 2022
% 1.70/1.94 The command was "./otter". The process ID is 6857.
% 1.70/1.94
% 1.70/1.94 set(prolog_style_variables).
% 1.70/1.94 set(auto).
% 1.70/1.94 dependent: set(auto1).
% 1.70/1.94 dependent: set(process_input).
% 1.70/1.94 dependent: clear(print_kept).
% 1.70/1.94 dependent: clear(print_new_demod).
% 1.70/1.94 dependent: clear(print_back_demod).
% 1.70/1.94 dependent: clear(print_back_sub).
% 1.70/1.94 dependent: set(control_memory).
% 1.70/1.94 dependent: assign(max_mem, 12000).
% 1.70/1.94 dependent: assign(pick_given_ratio, 4).
% 1.70/1.94 dependent: assign(stats_level, 1).
% 1.70/1.94 dependent: assign(max_seconds, 10800).
% 1.70/1.94 clear(print_given).
% 1.70/1.94
% 1.70/1.94 list(usable).
% 1.70/1.94 0 [] A=A.
% 1.70/1.94 0 [] -member(U,union(V))|member(U,unionE_sk1(U,V)).
% 1.70/1.94 0 [] -member(U,union(V))|member(unionE_sk1(U,V),V).
% 1.70/1.94 0 [] member(subsetI_sk1(A,B),A)|subset(A,B).
% 1.70/1.94 0 [] -member(subsetI_sk1(A,B),B)|subset(A,B).
% 1.70/1.94 0 [] -member(U,cons(V,W))|U=V|member(U,W).
% 1.70/1.94 0 [] -member(C,A)|member(C,un(A,B)).
% 1.70/1.94 0 [] -member(C,B)|member(C,un(A,B)).
% 1.70/1.94 0 [] -member(X,eptset).
% 1.70/1.94 0 [] -member(pair(U,V),W)|member(pair(V,U),converse(W)).
% 1.70/1.94 0 [] -member(pair(A,B),converse(R))|member(pair(B,A),R).
% 1.70/1.94 0 [] -member(YX,converse(R))|YX=pair(converseE_sk2(YX),converseE_sk1(YX)).
% 1.70/1.94 0 [] -member(YX,converse(R))|member(pair(converse_sk1(YX),converse_sk2(YX)),R).
% 1.70/1.94 0 [] member(sk2,union(cons(a,cons(b,eptset)))).
% 1.70/1.94 0 [] -member(sk2,un(a,b)).
% 1.70/1.94 end_of_list.
% 1.70/1.94
% 1.70/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.70/1.94
% 1.70/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.70/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.94 deletion, with positive clauses in sos and nonpositive
% 1.70/1.94 clauses in usable.
% 1.70/1.94
% 1.70/1.94 dependent: set(knuth_bendix).
% 1.70/1.94 dependent: set(anl_eq).
% 1.70/1.94 dependent: set(para_from).
% 1.70/1.94 dependent: set(para_into).
% 1.70/1.94 dependent: clear(para_from_right).
% 1.70/1.94 dependent: clear(para_into_right).
% 1.70/1.94 dependent: set(para_from_vars).
% 1.70/1.94 dependent: set(eq_units_both_ways).
% 1.70/1.94 dependent: set(dynamic_demod_all).
% 1.70/1.94 dependent: set(dynamic_demod).
% 1.70/1.94 dependent: set(order_eq).
% 1.70/1.94 dependent: set(back_demod).
% 1.70/1.94 dependent: set(lrpo).
% 1.70/1.94 dependent: set(hyper_res).
% 1.70/1.94 dependent: set(unit_deletion).
% 1.70/1.94 dependent: set(factor).
% 1.70/1.94
% 1.70/1.94 ------------> process usable:
% 1.70/1.94 ** KEPT (pick-wt=9): 1 [] -member(A,union(B))|member(A,unionE_sk1(A,B)).
% 1.70/1.94 ** KEPT (pick-wt=9): 2 [] -member(A,union(B))|member(unionE_sk1(A,B),B).
% 1.70/1.94 ** KEPT (pick-wt=8): 3 [] -member(subsetI_sk1(A,B),B)|subset(A,B).
% 1.70/1.94 ** KEPT (pick-wt=11): 4 [] -member(A,cons(B,C))|A=B|member(A,C).
% 1.70/1.94 ** KEPT (pick-wt=8): 5 [] -member(A,B)|member(A,un(B,C)).
% 1.70/1.94 ** KEPT (pick-wt=8): 6 [] -member(A,B)|member(A,un(C,B)).
% 1.70/1.94 ** KEPT (pick-wt=3): 7 [] -member(A,eptset).
% 1.70/1.94 ** KEPT (pick-wt=11): 8 [] -member(pair(A,B),C)|member(pair(B,A),converse(C)).
% 1.70/1.94 ** KEPT (pick-wt=11): 9 [] -member(pair(A,B),converse(C))|member(pair(B,A),C).
% 1.70/1.94 ** KEPT (pick-wt=11): 11 [copy,10,flip.2] -member(A,converse(B))|pair(converseE_sk2(A),converseE_sk1(A))=A.
% 1.70/1.94 ** KEPT (pick-wt=11): 12 [] -member(A,converse(B))|member(pair(converse_sk1(A),converse_sk2(A)),B).
% 1.70/1.94 ** KEPT (pick-wt=5): 13 [] -member(sk2,un(a,b)).
% 1.70/1.94
% 1.70/1.94 ------------> process sos:
% 1.70/1.94 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.70/1.94 ** KEPT (pick-wt=8): 15 [] member(subsetI_sk1(A,B),A)|subset(A,B).
% 1.70/1.94 ** KEPT (pick-wt=8): 16 [] member(sk2,union(cons(a,cons(b,eptset)))).
% 1.70/1.94 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.70/1.94
% 1.70/1.94 ======= end of input processing =======
% 1.70/1.94
% 1.70/1.94 =========== start of search ===========
% 1.70/1.94
% 1.70/1.94
% 1.70/1.94 Resetting weight limit to 16.
% 1.70/1.94
% 1.70/1.94
% 1.70/1.94 Resetting weight limit to 16.
% 1.70/1.94
% 1.70/1.94 sos_size=347
% 1.70/1.94
% 1.70/1.94 -------- PROOF --------
% 1.70/1.94
% 1.70/1.94 ----> UNIT CONFLICT at 0.03 sec ----> 447 [binary,446.1,13.1] $F.
% 1.70/1.94
% 1.70/1.94 Length of proof is 8. Level of proof is 7.
% 1.70/1.94
% 1.70/1.94 ---------------- PROOF ----------------
% 1.70/1.94 % SZS status Unsatisfiable
% 1.70/1.94 % SZS output start Refutation
% See solution above
% 1.70/1.94 ------------ end of proof -------------
% 1.70/1.94
% 1.70/1.94
% 1.70/1.94 Search stopped by max_proofs option.
% 1.70/1.94
% 1.70/1.94
% 1.70/1.94 Search stopped by max_proofs option.
% 1.70/1.94
% 1.70/1.94 ============ end of search ============
% 1.70/1.94
% 1.70/1.94 -------------- statistics -------------
% 1.70/1.94 clauses given 84
% 1.70/1.94 clauses generated 1092
% 1.70/1.94 clauses kept 445
% 1.70/1.94 clauses forward subsumed 85
% 1.70/1.94 clauses back subsumed 0
% 1.70/1.94 Kbytes malloced 5859
% 1.70/1.94
% 1.70/1.94 ----------- times (seconds) -----------
% 1.70/1.94 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.70/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.70/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.70/1.94
% 1.70/1.94 That finishes the proof of the theorem.
% 1.70/1.94
% 1.70/1.94 Process 6857 finished Wed Jul 27 10:32:43 2022
% 1.70/1.94 Otter interrupted
% 1.70/1.94 PROOF FOUND
%------------------------------------------------------------------------------