TSTP Solution File: SYN352+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN352+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:24:20 EDT 2022
% Result : Theorem 1.61s 1.81s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 11 ( 3 unt; 3 nHn; 7 RR)
% Number of literals : 23 ( 0 equ; 10 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ big_f(dollar_c1,dollar_f1(A,B))
| ~ big_f(A,dollar_f1(A,B))
| big_f(dollar_f1(A,B),dollar_f1(A,B)) ),
file('SYN352+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ big_f(A,B)
| big_f(A,dollar_f1(A,B))
| big_f(B,dollar_f1(A,B)) ),
file('SYN352+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ big_f(A,B)
| ~ big_f(A,dollar_f1(A,B))
| ~ big_f(B,dollar_f1(A,B)) ),
file('SYN352+1.p',unknown),
[] ).
cnf(6,plain,
( ~ big_f(dollar_c1,dollar_f1(dollar_c1,A))
| big_f(dollar_f1(dollar_c1,A),dollar_f1(dollar_c1,A)) ),
inference(factor,[status(thm)],[2]),
[iquote('factor,2.1.2')] ).
cnf(7,plain,
( ~ big_f(A,A)
| big_f(A,dollar_f1(A,A)) ),
inference(factor,[status(thm)],[3]),
[iquote('factor,3.2.3')] ).
cnf(8,plain,
( ~ big_f(A,A)
| ~ big_f(A,dollar_f1(A,A)) ),
inference(factor,[status(thm)],[4]),
[iquote('factor,4.2.3')] ).
cnf(11,axiom,
( big_f(dollar_c1,dollar_f1(A,B))
| big_f(A,dollar_f1(A,B))
| big_f(dollar_f1(A,B),dollar_f1(A,B)) ),
file('SYN352+1.p',unknown),
[] ).
cnf(12,plain,
( big_f(dollar_c1,dollar_f1(dollar_c1,A))
| big_f(dollar_f1(dollar_c1,A),dollar_f1(dollar_c1,A)) ),
inference(factor,[status(thm)],[11]),
[iquote('factor,11.1.2')] ).
cnf(32,plain,
big_f(dollar_f1(dollar_c1,A),dollar_f1(dollar_c1,A)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[12,6])]),
[iquote('hyper,12,6,factor_simp')] ).
cnf(48,plain,
big_f(dollar_f1(dollar_c1,A),dollar_f1(dollar_f1(dollar_c1,A),dollar_f1(dollar_c1,A))),
inference(hyper,[status(thm)],[32,7]),
[iquote('hyper,32,7')] ).
cnf(49,plain,
$false,
inference(hyper,[status(thm)],[48,8,32]),
[iquote('hyper,48,8,32')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN352+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 11:07:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.61/1.81 ----- Otter 3.3f, August 2004 -----
% 1.61/1.81 The process was started by sandbox2 on n018.cluster.edu,
% 1.61/1.81 Wed Jul 27 11:07:46 2022
% 1.61/1.81 The command was "./otter". The process ID is 10629.
% 1.61/1.81
% 1.61/1.81 set(prolog_style_variables).
% 1.61/1.81 set(auto).
% 1.61/1.81 dependent: set(auto1).
% 1.61/1.81 dependent: set(process_input).
% 1.61/1.81 dependent: clear(print_kept).
% 1.61/1.81 dependent: clear(print_new_demod).
% 1.61/1.81 dependent: clear(print_back_demod).
% 1.61/1.81 dependent: clear(print_back_sub).
% 1.61/1.81 dependent: set(control_memory).
% 1.61/1.81 dependent: assign(max_mem, 12000).
% 1.61/1.81 dependent: assign(pick_given_ratio, 4).
% 1.61/1.81 dependent: assign(stats_level, 1).
% 1.61/1.81 dependent: assign(max_seconds, 10800).
% 1.61/1.81 clear(print_given).
% 1.61/1.81
% 1.61/1.81 formula_list(usable).
% 1.61/1.81 -(all X1 X2 exists Y1 Y2 all Z (big_f(X1,X2)-> ((big_f(Y1,Y2)->big_f(X2,Z)|big_f(Y2,Z))-> (((big_f(Y1,Y2)-> (big_f(X2,Z)<->big_f(Y1,Z)))->big_f(Z,Z))->big_f(Y1,Y2)& (big_f(Y1,Z)<->big_f(Y2,Z)))))).
% 1.61/1.81 end_of_list.
% 1.61/1.81
% 1.61/1.81 -------> usable clausifies to:
% 1.61/1.81
% 1.61/1.81 list(usable).
% 1.61/1.81 0 [] big_f($c2,$c1).
% 1.61/1.81 0 [] -big_f(Y1,Y2)|big_f($c1,$f1(Y1,Y2))|big_f(Y2,$f1(Y1,Y2)).
% 1.61/1.81 0 [] big_f(Y1,Y2)|big_f($f1(Y1,Y2),$f1(Y1,Y2)).
% 1.61/1.81 0 [] big_f($c1,$f1(Y1,Y2))|big_f(Y1,$f1(Y1,Y2))|big_f($f1(Y1,Y2),$f1(Y1,Y2)).
% 1.61/1.81 0 [] -big_f($c1,$f1(Y1,Y2))| -big_f(Y1,$f1(Y1,Y2))|big_f($f1(Y1,Y2),$f1(Y1,Y2)).
% 1.61/1.81 0 [] -big_f(Y1,Y2)|big_f(Y1,$f1(Y1,Y2))|big_f(Y2,$f1(Y1,Y2)).
% 1.61/1.81 0 [] -big_f(Y1,Y2)| -big_f(Y1,$f1(Y1,Y2))| -big_f(Y2,$f1(Y1,Y2)).
% 1.61/1.81 end_of_list.
% 1.61/1.81
% 1.61/1.81 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=3.
% 1.61/1.81
% 1.61/1.81 This is a non-Horn set without equality. The strategy will
% 1.61/1.81 be ordered hyper_res, unit deletion, and factoring, with
% 1.61/1.81 satellites in sos and with nuclei in usable.
% 1.61/1.81
% 1.61/1.81 dependent: set(hyper_res).
% 1.61/1.81 dependent: set(factor).
% 1.61/1.81 dependent: set(unit_deletion).
% 1.61/1.81
% 1.61/1.81 ------------> process usable:
% 1.61/1.81 ** KEPT (pick-wt=13): 1 [] -big_f(A,B)|big_f($c1,$f1(A,B))|big_f(B,$f1(A,B)).
% 1.61/1.81 ** KEPT (pick-wt=17): 2 [] -big_f($c1,$f1(A,B))| -big_f(A,$f1(A,B))|big_f($f1(A,B),$f1(A,B)).
% 1.61/1.81 ** KEPT (pick-wt=13): 3 [] -big_f(A,B)|big_f(A,$f1(A,B))|big_f(B,$f1(A,B)).
% 1.61/1.81 ** KEPT (pick-wt=13): 4 [] -big_f(A,B)| -big_f(A,$f1(A,B))| -big_f(B,$f1(A,B)).
% 1.61/1.81
% 1.61/1.81 ------------> process sos:
% 1.61/1.81 ** KEPT (pick-wt=3): 9 [] big_f($c2,$c1).
% 1.61/1.81 ** KEPT (pick-wt=10): 10 [] big_f(A,B)|big_f($f1(A,B),$f1(A,B)).
% 1.61/1.81 ** KEPT (pick-wt=17): 11 [] big_f($c1,$f1(A,B))|big_f(A,$f1(A,B))|big_f($f1(A,B),$f1(A,B)).
% 1.61/1.81
% 1.61/1.81 ======= end of input processing =======
% 1.61/1.81
% 1.61/1.81 =========== start of search ===========
% 1.61/1.81
% 1.61/1.81 -------- PROOF --------
% 1.61/1.81
% 1.61/1.81 -----> EMPTY CLAUSE at 0.00 sec ----> 49 [hyper,48,8,32] $F.
% 1.61/1.81
% 1.61/1.81 Length of proof is 6. Level of proof is 3.
% 1.61/1.81
% 1.61/1.81 ---------------- PROOF ----------------
% 1.61/1.81 % SZS status Theorem
% 1.61/1.81 % SZS output start Refutation
% See solution above
% 1.61/1.81 ------------ end of proof -------------
% 1.61/1.81
% 1.61/1.81
% 1.61/1.81 Search stopped by max_proofs option.
% 1.61/1.81
% 1.61/1.81
% 1.61/1.81 Search stopped by max_proofs option.
% 1.61/1.81
% 1.61/1.81 ============ end of search ============
% 1.61/1.81
% 1.61/1.81 -------------- statistics -------------
% 1.61/1.81 clauses given 8
% 1.61/1.81 clauses generated 154
% 1.61/1.81 clauses kept 48
% 1.61/1.81 clauses forward subsumed 112
% 1.61/1.81 clauses back subsumed 14
% 1.61/1.81 Kbytes malloced 976
% 1.61/1.81
% 1.61/1.81 ----------- times (seconds) -----------
% 1.61/1.81 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.61/1.81 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.61/1.81 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.61/1.81
% 1.61/1.81 That finishes the proof of the theorem.
% 1.61/1.81
% 1.61/1.81 Process 10629 finished Wed Jul 27 11:07:48 2022
% 1.61/1.81 Otter interrupted
% 1.61/1.81 PROOF FOUND
%------------------------------------------------------------------------------