TSTP Solution File: SEU159+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:14:58 EDT 2022
% Result : Theorem 76.50s 76.71s
% Output : Refutation 76.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 26 ( 14 unt; 6 nHn; 21 RR)
% Number of literals : 45 ( 16 equ; 18 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != unordered_pair(B,C)
| ~ in(D,A)
| D = B
| D = C ),
file('SEU159+1.p',unknown),
[] ).
cnf(3,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != B ),
file('SEU159+1.p',unknown),
[] ).
cnf(4,axiom,
( A != unordered_pair(B,C)
| in(D,A)
| D != C ),
file('SEU159+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SEU159+1.p',unknown),
[] ).
cnf(8,axiom,
( subset(A,B)
| ~ in(dollar_f2(A,B),B) ),
file('SEU159+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ subset(unordered_pair(dollar_c3,dollar_c2),dollar_c1)
| ~ in(dollar_c3,dollar_c1)
| ~ in(dollar_c2,dollar_c1) ),
file('SEU159+1.p',unknown),
[] ).
cnf(12,axiom,
A = A,
file('SEU159+1.p',unknown),
[] ).
cnf(13,axiom,
unordered_pair(A,B) = unordered_pair(B,A),
file('SEU159+1.p',unknown),
[] ).
cnf(15,axiom,
( subset(A,B)
| in(dollar_f2(A,B),A) ),
file('SEU159+1.p',unknown),
[] ).
cnf(17,axiom,
( subset(unordered_pair(dollar_c3,dollar_c2),dollar_c1)
| in(dollar_c3,dollar_c1) ),
file('SEU159+1.p',unknown),
[] ).
cnf(18,axiom,
( subset(unordered_pair(dollar_c3,dollar_c2),dollar_c1)
| in(dollar_c2,dollar_c1) ),
file('SEU159+1.p',unknown),
[] ).
cnf(20,plain,
in(A,unordered_pair(B,A)),
inference(hyper,[status(thm)],[12,4,12]),
[iquote('hyper,12,4,12')] ).
cnf(21,plain,
in(A,unordered_pair(A,B)),
inference(hyper,[status(thm)],[12,3,12]),
[iquote('hyper,12,3,12')] ).
cnf(39,plain,
( ~ subset(unordered_pair(dollar_c2,dollar_c3),dollar_c1)
| ~ in(dollar_c3,dollar_c1)
| ~ in(dollar_c2,dollar_c1) ),
inference(para_from,[status(thm),theory(equality)],[13,9]),
[iquote('para_from,13.1.1,9.1.1')] ).
cnf(135,plain,
in(dollar_c3,dollar_c1),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[17,7,21])]),
[iquote('hyper,17,7,21,factor_simp')] ).
cnf(151,plain,
in(dollar_c2,dollar_c1),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[18,7,20])]),
[iquote('hyper,18,7,20,factor_simp')] ).
cnf(168,plain,
in(dollar_f2(unordered_pair(dollar_c3,dollar_c2),dollar_c1),unordered_pair(dollar_c3,dollar_c2)),
inference(hyper,[status(thm)],[151,9,15,135]),
[iquote('hyper,151,9,15,135')] ).
cnf(366,plain,
( dollar_f2(unordered_pair(dollar_c3,dollar_c2),dollar_c1) = dollar_c2
| dollar_f2(unordered_pair(dollar_c3,dollar_c2),dollar_c1) = dollar_c3 ),
inference(hyper,[status(thm)],[168,2,13]),
[iquote('hyper,168,2,13')] ).
cnf(1213,plain,
~ subset(unordered_pair(dollar_c3,dollar_c2),dollar_c1),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[39,13]),135,151]),
[iquote('para_into,39.1.1,13.1.1,unit_del,135,151')] ).
cnf(1366,plain,
~ subset(unordered_pair(dollar_c2,dollar_c3),dollar_c1),
inference(para_into,[status(thm),theory(equality)],[1213,13]),
[iquote('para_into,1213.1.1,13.1.1')] ).
cnf(3014,plain,
( dollar_f2(unordered_pair(dollar_c3,dollar_c2),dollar_c1) = dollar_c2
| dollar_f2(unordered_pair(dollar_c2,dollar_c3),dollar_c1) = dollar_c3 ),
inference(para_into,[status(thm),theory(equality)],[366,13]),
[iquote('para_into,366.2.1.1,13.1.1')] ).
cnf(3018,plain,
dollar_f2(unordered_pair(dollar_c3,dollar_c2),dollar_c1) = dollar_c3,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[366,8]),1213,151]),
[iquote('para_from,366.1.1,8.2.1,unit_del,1213,151')] ).
cnf(3022,plain,
dollar_c3 = dollar_c2,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[366,8]),3018]),1213,135]),
[iquote('para_from,366.2.1,8.2.1,demod,3018,unit_del,1213,135')] ).
cnf(3025,plain,
dollar_f2(unordered_pair(dollar_c2,dollar_c2),dollar_c1) = dollar_c2,
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3014]),3022,3022,3022])]),
[iquote('back_demod,3014,demod,3022,3022,3022,factor_simp')] ).
cnf(3049,plain,
~ subset(unordered_pair(dollar_c2,dollar_c2),dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1366]),3022]),
[iquote('back_demod,1366,demod,3022')] ).
cnf(3058,plain,
$false,
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[3025,8]),3049,151]),
[iquote('para_from,3025.1.1,8.2.1,unit_del,3049,151')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU159+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 07:43:11 EDT 2022
% 0.13/0.33 % CPUTime :
% 76.50/76.71 ----- Otter 3.3f, August 2004 -----
% 76.50/76.71 The process was started by sandbox2 on n015.cluster.edu,
% 76.50/76.71 Wed Jul 27 07:43:12 2022
% 76.50/76.71 The command was "./otter". The process ID is 6565.
% 76.50/76.71
% 76.50/76.71 set(prolog_style_variables).
% 76.50/76.71 set(auto).
% 76.50/76.71 dependent: set(auto1).
% 76.50/76.71 dependent: set(process_input).
% 76.50/76.71 dependent: clear(print_kept).
% 76.50/76.71 dependent: clear(print_new_demod).
% 76.50/76.71 dependent: clear(print_back_demod).
% 76.50/76.71 dependent: clear(print_back_sub).
% 76.50/76.71 dependent: set(control_memory).
% 76.50/76.71 dependent: assign(max_mem, 12000).
% 76.50/76.71 dependent: assign(pick_given_ratio, 4).
% 76.50/76.71 dependent: assign(stats_level, 1).
% 76.50/76.71 dependent: assign(max_seconds, 10800).
% 76.50/76.71 clear(print_given).
% 76.50/76.71
% 76.50/76.71 formula_list(usable).
% 76.50/76.71 all A (A=A).
% 76.50/76.71 all A B (in(A,B)-> -in(B,A)).
% 76.50/76.71 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 76.50/76.71 all A B C (C=unordered_pair(A,B)<-> (all D (in(D,C)<->D=A|D=B))).
% 76.50/76.71 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 76.50/76.71 $T.
% 76.50/76.71 all A B subset(A,A).
% 76.50/76.71 -(all A B C (subset(unordered_pair(A,B),C)<->in(A,C)&in(B,C))).
% 76.50/76.71 end_of_list.
% 76.50/76.71
% 76.50/76.71 -------> usable clausifies to:
% 76.50/76.71
% 76.50/76.71 list(usable).
% 76.50/76.71 0 [] A=A.
% 76.50/76.71 0 [] -in(A,B)| -in(B,A).
% 76.50/76.71 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 76.50/76.71 0 [] C!=unordered_pair(A,B)| -in(D,C)|D=A|D=B.
% 76.50/76.71 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=A.
% 76.50/76.71 0 [] C!=unordered_pair(A,B)|in(D,C)|D!=B.
% 76.50/76.71 0 [] C=unordered_pair(A,B)|in($f1(A,B,C),C)|$f1(A,B,C)=A|$f1(A,B,C)=B.
% 76.50/76.71 0 [] C=unordered_pair(A,B)| -in($f1(A,B,C),C)|$f1(A,B,C)!=A.
% 76.50/76.71 0 [] C=unordered_pair(A,B)| -in($f1(A,B,C),C)|$f1(A,B,C)!=B.
% 76.50/76.71 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 76.50/76.71 0 [] subset(A,B)|in($f2(A,B),A).
% 76.50/76.71 0 [] subset(A,B)| -in($f2(A,B),B).
% 76.50/76.71 0 [] $T.
% 76.50/76.71 0 [] subset(A,A).
% 76.50/76.71 0 [] subset(unordered_pair($c3,$c2),$c1)|in($c3,$c1).
% 76.50/76.71 0 [] subset(unordered_pair($c3,$c2),$c1)|in($c2,$c1).
% 76.50/76.71 0 [] -subset(unordered_pair($c3,$c2),$c1)| -in($c3,$c1)| -in($c2,$c1).
% 76.50/76.71 end_of_list.
% 76.50/76.71
% 76.50/76.71 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 76.50/76.71
% 76.50/76.71 This ia a non-Horn set with equality. The strategy will be
% 76.50/76.71 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 76.50/76.71 deletion, with positive clauses in sos and nonpositive
% 76.50/76.71 clauses in usable.
% 76.50/76.71
% 76.50/76.71 dependent: set(knuth_bendix).
% 76.50/76.71 dependent: set(anl_eq).
% 76.50/76.71 dependent: set(para_from).
% 76.50/76.71 dependent: set(para_into).
% 76.50/76.71 dependent: clear(para_from_right).
% 76.50/76.71 dependent: clear(para_into_right).
% 76.50/76.71 dependent: set(para_from_vars).
% 76.50/76.71 dependent: set(eq_units_both_ways).
% 76.50/76.71 dependent: set(dynamic_demod_all).
% 76.50/76.71 dependent: set(dynamic_demod).
% 76.50/76.71 dependent: set(order_eq).
% 76.50/76.71 dependent: set(back_demod).
% 76.50/76.71 dependent: set(lrpo).
% 76.50/76.71 dependent: set(hyper_res).
% 76.50/76.71 dependent: set(unit_deletion).
% 76.50/76.71 dependent: set(factor).
% 76.50/76.71
% 76.50/76.71 ------------> process usable:
% 76.50/76.71 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 76.50/76.71 ** KEPT (pick-wt=14): 2 [] A!=unordered_pair(B,C)| -in(D,A)|D=B|D=C.
% 76.50/76.71 ** KEPT (pick-wt=11): 3 [] A!=unordered_pair(B,C)|in(D,A)|D!=B.
% 76.50/76.71 ** KEPT (pick-wt=11): 4 [] A!=unordered_pair(B,C)|in(D,A)|D!=C.
% 76.50/76.71 ** KEPT (pick-wt=17): 5 [] A=unordered_pair(B,C)| -in($f1(B,C,A),A)|$f1(B,C,A)!=B.
% 76.50/76.71 ** KEPT (pick-wt=17): 6 [] A=unordered_pair(B,C)| -in($f1(B,C,A),A)|$f1(B,C,A)!=C.
% 76.50/76.71 ** KEPT (pick-wt=9): 7 [] -subset(A,B)| -in(C,A)|in(C,B).
% 76.50/76.71 ** KEPT (pick-wt=8): 8 [] subset(A,B)| -in($f2(A,B),B).
% 76.50/76.71 ** KEPT (pick-wt=11): 9 [] -subset(unordered_pair($c3,$c2),$c1)| -in($c3,$c1)| -in($c2,$c1).
% 76.50/76.71
% 76.50/76.71 ------------> process sos:
% 76.50/76.71 ** KEPT (pick-wt=3): 12 [] A=A.
% 76.50/76.71 ** KEPT (pick-wt=7): 13 [] unordered_pair(A,B)=unordered_pair(B,A).
% 76.50/76.71 ** KEPT (pick-wt=23): 14 [] A=unordered_pair(B,C)|in($f1(B,C,A),A)|$f1(B,C,A)=B|$f1(B,C,A)=C.
% 76.50/76.71 ** KEPT (pick-wt=8): 15 [] subset(A,B)|in($f2(A,B),A).
% 76.50/76.71 ** KEPT (pick-wt=3): 16 [] subset(A,A).
% 76.50/76.71 ** KEPT (pick-wt=8): 17 [] subset(unordered_pair($c3,$c2),$c1)|in($c3,$c1).
% 76.50/76.71 ** KEPT (pick-wt=8): 18 [] subset(unordered_pair($c3,$c2),$c1)|in($c2,$c1).
% 76.50/76.71 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 76.50/76.71 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 76.50/76.71
% 76.50/76.71 ======= end of input processing =======
% 76.50/76.71
% 76.50/76.71 =========== start of search ===========
% 76.50/76.71
% 76.50/76.71
% 76.50/76.71 Resetting weight limit to 15.
% 76.50/76.71
% 76.50/76.71
% 76.50/76.71 Resetting weight limit to 15.
% 76.50/76.71
% 76.50/76.71 sos_size=2272
% 76.50/76.71
% 76.50/76.71
% 76.50/76.71 Resetting weight limit to 14.
% 76.50/76.71
% 76.50/76.71
% 76.50/76.71 Resetting weight limit to 14.
% 76.50/76.71
% 76.50/76.71 sos_size=2359
% 76.50/76.71
% 76.50/76.71 -- HEY sandbox2, WE HAVE A PROOF!! --
% 76.50/76.71
% 76.50/76.71 -----> EMPTY CLAUSE at 74.58 sec ----> 3058 [para_from,3025.1.1,8.2.1,unit_del,3049,151] $F.
% 76.50/76.71
% 76.50/76.71 Length of proof is 14. Level of proof is 7.
% 76.50/76.71
% 76.50/76.71 ---------------- PROOF ----------------
% 76.50/76.71 % SZS status Theorem
% 76.50/76.71 % SZS output start Refutation
% See solution above
% 76.50/76.71 ------------ end of proof -------------
% 76.50/76.71
% 76.50/76.71
% 76.50/76.71 Search stopped by max_proofs option.
% 76.50/76.71
% 76.50/76.71
% 76.50/76.71 Search stopped by max_proofs option.
% 76.50/76.71
% 76.50/76.71 ============ end of search ============
% 76.50/76.71
% 76.50/76.71 -------------- statistics -------------
% 76.50/76.71 clauses given 423
% 76.50/76.71 clauses generated 558047
% 76.50/76.71 clauses kept 3013
% 76.50/76.71 clauses forward subsumed 17324
% 76.50/76.71 clauses back subsumed 69
% 76.50/76.71 Kbytes malloced 5859
% 76.50/76.71
% 76.50/76.71 ----------- times (seconds) -----------
% 76.50/76.71 user CPU time 74.58 (0 hr, 1 min, 14 sec)
% 76.50/76.71 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 76.50/76.71 wall-clock time 76 (0 hr, 1 min, 16 sec)
% 76.50/76.71
% 76.50/76.71 That finishes the proof of the theorem.
% 76.50/76.71
% 76.50/76.71 Process 6565 finished Wed Jul 27 07:44:28 2022
% 76.50/76.71 Otter interrupted
% 76.50/76.71 PROOF FOUND
%------------------------------------------------------------------------------