TSTP Solution File: SYN345+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN345+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 13:24:18 EDT 2022
% Result : Theorem 1.87s 2.07s
% Output : Refutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 13 ( 5 unt; 5 nHn; 8 RR)
% Number of literals : 26 ( 0 equ; 9 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 13 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( big_f(dollar_c2,dollar_c1,A)
| ~ big_f(dollar_c2,dollar_c2,dollar_c1)
| big_f(dollar_c2,dollar_c1,dollar_c1) ),
file('SYN345+1.p',unknown),
[] ).
cnf(2,plain,
( big_f(dollar_c2,dollar_c1,dollar_c1)
| ~ big_f(dollar_c2,dollar_c2,dollar_c1) ),
inference(factor_simp,[status(thm)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,factor_simp')] ).
cnf(3,axiom,
( big_f(dollar_c1,A,B)
| ~ big_f(dollar_c2,dollar_c1,dollar_c1)
| big_f(dollar_c2,dollar_c2,dollar_c1) ),
file('SYN345+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ big_f(A,dollar_f1(A,B),dollar_f1(A,B))
| ~ big_f(dollar_c2,dollar_c1,dollar_c1)
| big_f(dollar_c2,dollar_c2,dollar_c1) ),
file('SYN345+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ big_f(dollar_c1,dollar_c1,A)
| big_f(dollar_c2,dollar_c2,dollar_c1)
| big_f(dollar_c2,dollar_c1,dollar_c1) ),
file('SYN345+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ big_f(dollar_c1,dollar_c1,A)
| ~ big_f(dollar_c2,dollar_c2,dollar_c1)
| ~ big_f(dollar_c2,dollar_c1,dollar_c1) ),
file('SYN345+1.p',unknown),
[] ).
cnf(7,axiom,
big_f(A,B,dollar_f1(A,B)),
file('SYN345+1.p',unknown),
[] ).
cnf(8,plain,
( big_f(dollar_c2,dollar_c2,dollar_c1)
| big_f(dollar_c2,dollar_c1,dollar_c1) ),
inference(hyper,[status(thm)],[7,5]),
[iquote('hyper,7,5')] ).
cnf(9,plain,
big_f(dollar_c2,dollar_c1,dollar_c1),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[8,2])]),
[iquote('hyper,8,2,factor_simp')] ).
cnf(10,plain,
( big_f(dollar_c2,dollar_c2,dollar_c1)
| big_f(dollar_c1,A,B) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[8,3])]),
[iquote('hyper,8,3,factor_simp')] ).
cnf(11,plain,
big_f(dollar_c1,A,B),
inference(hyper,[status(thm)],[10,6,7,9]),
[iquote('hyper,10,6,7,9')] ).
cnf(12,plain,
big_f(dollar_c2,dollar_c2,dollar_c1),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[10,4,9])]),
[iquote('hyper,10,4,9,factor_simp')] ).
cnf(13,plain,
$false,
inference(hyper,[status(thm)],[12,6,11,9]),
[iquote('hyper,12,6,11,9')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SYN345+1 : TPTP v8.1.0. Released v2.0.0.
% 0.02/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 11:15:45 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.87/2.07 ----- Otter 3.3f, August 2004 -----
% 1.87/2.07 The process was started by sandbox on n025.cluster.edu,
% 1.87/2.07 Wed Jul 27 11:15:45 2022
% 1.87/2.07 The command was "./otter". The process ID is 4841.
% 1.87/2.07
% 1.87/2.07 set(prolog_style_variables).
% 1.87/2.07 set(auto).
% 1.87/2.07 dependent: set(auto1).
% 1.87/2.07 dependent: set(process_input).
% 1.87/2.07 dependent: clear(print_kept).
% 1.87/2.07 dependent: clear(print_new_demod).
% 1.87/2.07 dependent: clear(print_back_demod).
% 1.87/2.07 dependent: clear(print_back_sub).
% 1.87/2.07 dependent: set(control_memory).
% 1.87/2.07 dependent: assign(max_mem, 12000).
% 1.87/2.07 dependent: assign(pick_given_ratio, 4).
% 1.87/2.07 dependent: assign(stats_level, 1).
% 1.87/2.07 dependent: assign(max_seconds, 10800).
% 1.87/2.07 clear(print_given).
% 1.87/2.07
% 1.87/2.07 formula_list(usable).
% 1.87/2.07 -(all X1 X2 exists Y1 Y2 all Z (((big_f(X1,X2,Y1)->big_f(Y2,Y1,Z))-> (big_f(X1,X1,X2)->big_f(X1,X2,X2)))-> (((big_f(X2,Y1,Y2)->big_f(Y1,Z,Z))-> (big_f(X1,X2,X2)->big_f(X1,X1,X2)))-> (big_f(Y1,Y2,Z)->big_f(X2,X2,Y1)& (big_f(X1,X1,X2)<->big_f(X1,X2,X2)))))).
% 1.87/2.07 end_of_list.
% 1.87/2.07
% 1.87/2.07 -------> usable clausifies to:
% 1.87/2.07
% 1.87/2.07 list(usable).
% 1.87/2.07 0 [] big_f($c2,$c1,Y1)| -big_f($c2,$c2,$c1)|big_f($c2,$c1,$c1).
% 1.87/2.07 0 [] -big_f(Y2,Y1,$f1(Y1,Y2))| -big_f($c2,$c2,$c1)|big_f($c2,$c1,$c1).
% 1.87/2.07 0 [] big_f($c1,Y1,Y2)| -big_f($c2,$c1,$c1)|big_f($c2,$c2,$c1).
% 1.87/2.07 0 [] -big_f(Y1,$f1(Y1,Y2),$f1(Y1,Y2))| -big_f($c2,$c1,$c1)|big_f($c2,$c2,$c1).
% 1.87/2.07 0 [] big_f(Y1,Y2,$f1(Y1,Y2)).
% 1.87/2.07 0 [] -big_f($c1,$c1,Y1)|big_f($c2,$c2,$c1)|big_f($c2,$c1,$c1).
% 1.87/2.07 0 [] -big_f($c1,$c1,Y1)| -big_f($c2,$c2,$c1)| -big_f($c2,$c1,$c1).
% 1.87/2.07 end_of_list.
% 1.87/2.07
% 1.87/2.07 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.87/2.07
% 1.87/2.07 This is a non-Horn set without equality. The strategy will
% 1.87/2.07 be ordered hyper_res, unit deletion, and factoring, with
% 1.87/2.07 satellites in sos and with nuclei in usable.
% 1.87/2.07
% 1.87/2.07 dependent: set(hyper_res).
% 1.87/2.07 dependent: set(factor).
% 1.87/2.07 dependent: set(unit_deletion).
% 1.87/2.07
% 1.87/2.07 ------------> process usable:
% 1.87/2.07 ** KEPT (pick-wt=8): 2 [copy,1,factor_simp] big_f($c2,$c1,$c1)| -big_f($c2,$c2,$c1).
% 1.87/2.07 Following clause subsumed by 2 during input processing: 0 [] -big_f(A,B,$f1(B,A))| -big_f($c2,$c2,$c1)|big_f($c2,$c1,$c1).
% 1.87/2.07 ** KEPT (pick-wt=12): 3 [] big_f($c1,A,B)| -big_f($c2,$c1,$c1)|big_f($c2,$c2,$c1).
% 1.87/2.07 ** KEPT (pick-wt=16): 4 [] -big_f(A,$f1(A,B),$f1(A,B))| -big_f($c2,$c1,$c1)|big_f($c2,$c2,$c1).
% 1.87/2.07 ** KEPT (pick-wt=12): 5 [] -big_f($c1,$c1,A)|big_f($c2,$c2,$c1)|big_f($c2,$c1,$c1).
% 1.87/2.07 ** KEPT (pick-wt=12): 6 [] -big_f($c1,$c1,A)| -big_f($c2,$c2,$c1)| -big_f($c2,$c1,$c1).
% 1.87/2.07
% 1.87/2.07 ------------> process sos:
% 1.87/2.07 ** KEPT (pick-wt=6): 7 [] big_f(A,B,$f1(A,B)).
% 1.87/2.07
% 1.87/2.07 ======= end of input processing =======
% 1.87/2.07
% 1.87/2.07 =========== start of search ===========
% 1.87/2.07
% 1.87/2.07 -------- PROOF --------
% 1.87/2.07
% 1.87/2.07 -----> EMPTY CLAUSE at 0.00 sec ----> 13 [hyper,12,6,11,9] $F.
% 1.87/2.07
% 1.87/2.07 Length of proof is 6. Level of proof is 3.
% 1.87/2.07
% 1.87/2.07 ---------------- PROOF ----------------
% 1.87/2.07 % SZS status Theorem
% 1.87/2.07 % SZS output start Refutation
% See solution above
% 1.87/2.07 ------------ end of proof -------------
% 1.87/2.07
% 1.87/2.07
% 1.87/2.07 Search stopped by max_proofs option.
% 1.87/2.07
% 1.87/2.07
% 1.87/2.07 Search stopped by max_proofs option.
% 1.87/2.07
% 1.87/2.07 ============ end of search ============
% 1.87/2.07
% 1.87/2.07 -------------- statistics -------------
% 1.87/2.07 clauses given 6
% 1.87/2.07 clauses generated 10
% 1.87/2.07 clauses kept 11
% 1.87/2.07 clauses forward subsumed 5
% 1.87/2.07 clauses back subsumed 6
% 1.87/2.07 Kbytes malloced 976
% 1.87/2.07
% 1.87/2.07 ----------- times (seconds) -----------
% 1.87/2.07 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.87/2.07 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.87/2.07
% 1.87/2.07 That finishes the proof of the theorem.
% 1.87/2.07
% 1.87/2.07 Process 4841 finished Wed Jul 27 11:15:47 2022
% 1.87/2.07 Otter interrupted
% 1.87/2.07 PROOF FOUND
%------------------------------------------------------------------------------