TSTP Solution File: SET185+3 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:13:14 EDT 2022
% Result : Theorem 25.94s 26.16s
% Output : Refutation 25.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 24 ( 11 unt; 7 nHn; 15 RR)
% Number of literals : 49 ( 14 equ; 15 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,union(B,C))
| member(A,B)
| member(A,C) ),
file('SET185+3.p',unknown),
[] ).
cnf(3,axiom,
( member(A,union(B,C))
| ~ member(A,C) ),
file('SET185+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET185+3.p',unknown),
[] ).
cnf(10,axiom,
( A != B
| member(C,A)
| ~ member(C,B) ),
file('SET185+3.p',unknown),
[] ).
cnf(11,axiom,
( A = B
| ~ member(dollar_f2(A,B),A)
| ~ member(dollar_f2(A,B),B) ),
file('SET185+3.p',unknown),
[] ).
cnf(12,axiom,
union(dollar_c2,dollar_c1) != dollar_c1,
file('SET185+3.p',unknown),
[] ).
cnf(16,axiom,
A = A,
file('SET185+3.p',unknown),
[] ).
cnf(18,axiom,
union(A,B) = union(B,A),
file('SET185+3.p',unknown),
[] ).
cnf(20,axiom,
( A = B
| member(dollar_f2(A,B),A)
| member(dollar_f2(A,B),B) ),
file('SET185+3.p',unknown),
[] ).
cnf(21,axiom,
subset(dollar_c2,dollar_c1),
file('SET185+3.p',unknown),
[] ).
cnf(27,plain,
( A = union(B,C)
| ~ member(dollar_f2(union(C,B),A),union(C,B))
| ~ member(dollar_f2(union(C,B),A),A) ),
inference(para_into,[status(thm),theory(equality)],[18,11]),
[iquote('para_into,18.1.1,11.1.1')] ).
cnf(29,plain,
union(dollar_c1,dollar_c2) != dollar_c1,
inference(para_from,[status(thm),theory(equality)],[18,12]),
[iquote('para_from,18.1.1,12.1.1')] ).
cnf(34,plain,
( A != dollar_c1
| ~ member(dollar_f2(union(dollar_c1,dollar_c2),A),union(dollar_c1,dollar_c2))
| ~ member(dollar_f2(union(dollar_c1,dollar_c2),A),A) ),
inference(para_into,[status(thm),theory(equality)],[29,11]),
[iquote('para_into,29.1.1,11.1.1')] ).
cnf(73,plain,
( union(A,B) = C
| member(dollar_f2(union(A,B),C),C)
| member(dollar_f2(union(A,B),C),union(B,A)) ),
inference(hyper,[status(thm)],[20,10,18]),
[iquote('hyper,20,10,18')] ).
cnf(78,plain,
( union(A,B) = C
| member(dollar_f2(union(A,B),C),C)
| member(dollar_f2(union(A,B),C),A)
| member(dollar_f2(union(A,B),C),B) ),
inference(hyper,[status(thm)],[20,1]),
[iquote('hyper,20,1')] ).
cnf(83,plain,
( A = B
| member(dollar_f2(A,B),A)
| member(dollar_f2(A,B),union(C,B)) ),
inference(hyper,[status(thm)],[20,3]),
[iquote('hyper,20,3')] ).
cnf(91,plain,
( union(A,B) = A
| member(dollar_f2(union(A,B),A),A)
| member(dollar_f2(union(A,B),A),B) ),
inference(factor,[status(thm)],[78]),
[iquote('factor,78.2.3')] ).
cnf(96,plain,
( union(A,B) = B
| member(dollar_f2(union(A,B),B),union(A,B)) ),
inference(factor,[status(thm)],[83]),
[iquote('factor,83.2.3')] ).
cnf(4668,plain,
member(dollar_f2(union(dollar_c1,dollar_c2),dollar_c1),union(dollar_c2,dollar_c1)),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[83,34,16,73]),29,29])]),
[iquote('hyper,83,34,16,73,unit_del,29,29,factor_simp')] ).
cnf(4669,plain,
member(dollar_f2(union(dollar_c1,dollar_c2),dollar_c1),union(dollar_c1,dollar_c2)),
inference(hyper,[status(thm)],[4668,10,18]),
[iquote('hyper,4668,10,18')] ).
cnf(4879,plain,
member(dollar_f2(union(dollar_c1,dollar_c2),dollar_c1),dollar_c2),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[91,34,16,4669]),29]),
[iquote('hyper,91,34,16,4669,unit_del,29')] ).
cnf(4881,plain,
member(dollar_f2(union(dollar_c1,dollar_c2),dollar_c1),dollar_c1),
inference(hyper,[status(thm)],[4879,4,21]),
[iquote('hyper,4879,4,21')] ).
cnf(4896,plain,
member(dollar_f2(union(dollar_c2,dollar_c1),dollar_c1),dollar_c1),
inference(para_into,[status(thm),theory(equality)],[4881,18]),
[iquote('para_into,4881.1.1.1,18.1.1')] ).
cnf(4955,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[96,27,4896]),12,29]),
[iquote('hyper,96,27,4896,unit_del,12,29')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET185+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:37:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 25.94/26.16 ----- Otter 3.3f, August 2004 -----
% 25.94/26.16 The process was started by sandbox on n012.cluster.edu,
% 25.94/26.16 Wed Jul 27 10:37:50 2022
% 25.94/26.16 The command was "./otter". The process ID is 15900.
% 25.94/26.16
% 25.94/26.16 set(prolog_style_variables).
% 25.94/26.16 set(auto).
% 25.94/26.16 dependent: set(auto1).
% 25.94/26.16 dependent: set(process_input).
% 25.94/26.16 dependent: clear(print_kept).
% 25.94/26.16 dependent: clear(print_new_demod).
% 25.94/26.16 dependent: clear(print_back_demod).
% 25.94/26.16 dependent: clear(print_back_sub).
% 25.94/26.16 dependent: set(control_memory).
% 25.94/26.16 dependent: assign(max_mem, 12000).
% 25.94/26.16 dependent: assign(pick_given_ratio, 4).
% 25.94/26.16 dependent: assign(stats_level, 1).
% 25.94/26.16 dependent: assign(max_seconds, 10800).
% 25.94/26.16 clear(print_given).
% 25.94/26.16
% 25.94/26.16 formula_list(usable).
% 25.94/26.16 all A (A=A).
% 25.94/26.16 all B C D (member(D,union(B,C))<->member(D,B)|member(D,C)).
% 25.94/26.16 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 25.94/26.16 all B C (B=C<->subset(B,C)&subset(C,B)).
% 25.94/26.16 all B C (union(B,C)=union(C,B)).
% 25.94/26.16 all B subset(B,B).
% 25.94/26.16 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 25.94/26.16 -(all B C (subset(B,C)->union(B,C)=C)).
% 25.94/26.16 end_of_list.
% 25.94/26.16
% 25.94/26.16 -------> usable clausifies to:
% 25.94/26.16
% 25.94/26.16 list(usable).
% 25.94/26.16 0 [] A=A.
% 25.94/26.16 0 [] -member(D,union(B,C))|member(D,B)|member(D,C).
% 25.94/26.16 0 [] member(D,union(B,C))| -member(D,B).
% 25.94/26.16 0 [] member(D,union(B,C))| -member(D,C).
% 25.94/26.16 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 25.94/26.16 0 [] subset(B,C)|member($f1(B,C),B).
% 25.94/26.16 0 [] subset(B,C)| -member($f1(B,C),C).
% 25.94/26.16 0 [] B!=C|subset(B,C).
% 25.94/26.16 0 [] B!=C|subset(C,B).
% 25.94/26.16 0 [] B=C| -subset(B,C)| -subset(C,B).
% 25.94/26.16 0 [] union(B,C)=union(C,B).
% 25.94/26.16 0 [] subset(B,B).
% 25.94/26.16 0 [] B!=C| -member(D,B)|member(D,C).
% 25.94/26.16 0 [] B!=C|member(D,B)| -member(D,C).
% 25.94/26.16 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 25.94/26.16 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 25.94/26.16 0 [] subset($c2,$c1).
% 25.94/26.16 0 [] union($c2,$c1)!=$c1.
% 25.94/26.16 end_of_list.
% 25.94/26.16
% 25.94/26.16 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 25.94/26.16
% 25.94/26.16 This ia a non-Horn set with equality. The strategy will be
% 25.94/26.16 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 25.94/26.16 deletion, with positive clauses in sos and nonpositive
% 25.94/26.16 clauses in usable.
% 25.94/26.16
% 25.94/26.16 dependent: set(knuth_bendix).
% 25.94/26.16 dependent: set(anl_eq).
% 25.94/26.16 dependent: set(para_from).
% 25.94/26.16 dependent: set(para_into).
% 25.94/26.16 dependent: clear(para_from_right).
% 25.94/26.16 dependent: clear(para_into_right).
% 25.94/26.16 dependent: set(para_from_vars).
% 25.94/26.16 dependent: set(eq_units_both_ways).
% 25.94/26.16 dependent: set(dynamic_demod_all).
% 25.94/26.16 dependent: set(dynamic_demod).
% 25.94/26.16 dependent: set(order_eq).
% 25.94/26.16 dependent: set(back_demod).
% 25.94/26.16 dependent: set(lrpo).
% 25.94/26.16 dependent: set(hyper_res).
% 25.94/26.16 dependent: set(unit_deletion).
% 25.94/26.16 dependent: set(factor).
% 25.94/26.16
% 25.94/26.16 ------------> process usable:
% 25.94/26.16 ** KEPT (pick-wt=11): 1 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 25.94/26.16 ** KEPT (pick-wt=8): 2 [] member(A,union(B,C))| -member(A,B).
% 25.94/26.16 ** KEPT (pick-wt=8): 3 [] member(A,union(B,C))| -member(A,C).
% 25.94/26.16 ** KEPT (pick-wt=9): 4 [] -subset(A,B)| -member(C,A)|member(C,B).
% 25.94/26.16 ** KEPT (pick-wt=8): 5 [] subset(A,B)| -member($f1(A,B),B).
% 25.94/26.16 ** KEPT (pick-wt=6): 6 [] A!=B|subset(A,B).
% 25.94/26.16 ** KEPT (pick-wt=6): 7 [] A!=B|subset(B,A).
% 25.94/26.16 ** KEPT (pick-wt=9): 8 [] A=B| -subset(A,B)| -subset(B,A).
% 25.94/26.16 ** KEPT (pick-wt=9): 9 [] A!=B| -member(C,A)|member(C,B).
% 25.94/26.16 ** KEPT (pick-wt=9): 10 [] A!=B|member(C,A)| -member(C,B).
% 25.94/26.16 ** KEPT (pick-wt=13): 11 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 25.94/26.16 ** KEPT (pick-wt=5): 12 [] union($c2,$c1)!=$c1.
% 25.94/26.16
% 25.94/26.16 ------------> process sos:
% 25.94/26.16 ** KEPT (pick-wt=3): 16 [] A=A.
% 25.94/26.16 ** KEPT (pick-wt=8): 17 [] subset(A,B)|member($f1(A,B),A).
% 25.94/26.16 ** KEPT (pick-wt=7): 18 [] union(A,B)=union(B,A).
% 25.94/26.16 ** KEPT (pick-wt=3): 19 [] subset(A,A).
% 25.94/26.16 ** KEPT (pick-wt=13): 20 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 25.94/26.16 ** KEPT (pick-wt=3): 21 [] subset($c2,$c1).
% 25.94/26.16 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 25.94/26.16 16 back subsumes 15.
% 25.94/26.16 16 back subsumes 14.
% 25.94/26.16 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] union(A,B)=union(B,A).
% 25.94/26.16
% 25.94/26.16 ======= end of input processing =======
% 25.94/26.16
% 25.94/26.16 =========== start of search ===========
% 25.94/26.16
% 25.94/26.16
% 25.94/26.16 Resetting weight limit to 14.
% 25.94/26.16
% 25.94/26.16
% 25.94/26.16 Resetting weight limit to 14.
% 25.94/26.16
% 25.94/26.16 sos_size=4177
% 25.94/26.16
% 25.94/26.16
% 25.94/26.16 Resetting weight limit to 13.
% 25.94/26.16
% 25.94/26.16
% 25.94/26.16 Resetting weight limit to 13.
% 25.94/26.16
% 25.94/26.16 sos_size=1383
% 25.94/26.16
% 25.94/26.16
% 25.94/26.16 Resetting weight limit to 12.
% 25.94/26.16
% 25.94/26.16
% 25.94/26.16 Resetting weight limit to 12.
% 25.94/26.16
% 25.94/26.16 sos_size=1408
% 25.94/26.16
% 25.94/26.16 -- HEY sandbox, WE HAVE A PROOF!! --
% 25.94/26.16
% 25.94/26.16 -----> EMPTY CLAUSE at 24.18 sec ----> 4955 [hyper,96,27,4896,unit_del,12,29] $F.
% 25.94/26.16
% 25.94/26.16 Length of proof is 13. Level of proof is 7.
% 25.94/26.16
% 25.94/26.16 ---------------- PROOF ----------------
% 25.94/26.16 % SZS status Theorem
% 25.94/26.16 % SZS output start Refutation
% See solution above
% 25.94/26.16 ------------ end of proof -------------
% 25.94/26.16
% 25.94/26.16
% 25.94/26.16 Search stopped by max_proofs option.
% 25.94/26.16
% 25.94/26.16
% 25.94/26.16 Search stopped by max_proofs option.
% 25.94/26.16
% 25.94/26.16 ============ end of search ============
% 25.94/26.16
% 25.94/26.16 -------------- statistics -------------
% 25.94/26.16 clauses given 306
% 25.94/26.16 clauses generated 252163
% 25.94/26.16 clauses kept 4953
% 25.94/26.16 clauses forward subsumed 9343
% 25.94/26.16 clauses back subsumed 2578
% 25.94/26.16 Kbytes malloced 4882
% 25.94/26.16
% 25.94/26.16 ----------- times (seconds) -----------
% 25.94/26.16 user CPU time 24.18 (0 hr, 0 min, 24 sec)
% 25.94/26.16 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 25.94/26.16 wall-clock time 26 (0 hr, 0 min, 26 sec)
% 25.94/26.16
% 25.94/26.16 That finishes the proof of the theorem.
% 25.94/26.16
% 25.94/26.16 Process 15900 finished Wed Jul 27 10:38:16 2022
% 25.94/26.16 Otter interrupted
% 25.94/26.16 PROOF FOUND
%------------------------------------------------------------------------------