%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SYN079+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 13:23:31 EDT 2022
% Result : Theorem 1.89s 2.07s
% Output : Refutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 6 ( 5 unt; 0 nHn; 6 RR)
% Number of literals : 8 ( 0 equ; 3 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 3 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ big_f(A,B)
| ~ big_f(B,C)
| big_f(A,C) ),
file('SYN079+1.p',unknown),
[] ).
cnf(2,axiom,
~ big_f(f(a,b),f(a,c)),
file('SYN079+1.p',unknown),
[] ).
cnf(3,axiom,
big_f(f(a,b),f(b,c)),
file('SYN079+1.p',unknown),
[] ).
cnf(4,axiom,
big_f(f(b,c),f(a,c)),
file('SYN079+1.p',unknown),
[] ).
cnf(5,plain,
big_f(f(a,b),f(a,c)),
inference(hyper,[status(thm)],[4,1,3]),
[iquote('hyper,4,1,3')] ).
cnf(6,plain,
$false,
inference(binary,[status(thm)],[5,2]),
[iquote('binary,5.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN079+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n006.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 10:58:46 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.89/2.07 ----- Otter 3.3f, August 2004 -----
% 1.89/2.07 The process was started by sandbox on n006.cluster.edu,
% 1.89/2.07 Wed Jul 27 10:58:47 2022
% 1.89/2.07 The command was "./otter". The process ID is 23345.
% 1.89/2.07
% 1.89/2.07 set(prolog_style_variables).
% 1.89/2.07 set(auto).
% 1.89/2.07 dependent: set(auto1).
% 1.89/2.07 dependent: set(process_input).
% 1.89/2.07 dependent: clear(print_kept).
% 1.89/2.07 dependent: clear(print_new_demod).
% 1.89/2.07 dependent: clear(print_back_demod).
% 1.89/2.07 dependent: clear(print_back_sub).
% 1.89/2.07 dependent: set(control_memory).
% 1.89/2.07 dependent: assign(max_mem, 12000).
% 1.89/2.07 dependent: assign(pick_given_ratio, 4).
% 1.89/2.07 dependent: assign(stats_level, 1).
% 1.89/2.07 dependent: assign(max_seconds, 10800).
% 1.89/2.07 clear(print_given).
% 1.89/2.07
% 1.89/2.07 formula_list(usable).
% 1.89/2.07 big_f(f(a,b),f(b,c)).
% 1.89/2.07 big_f(f(b,c),f(a,c)).
% 1.89/2.07 all X Y Z (big_f(X,Y)&big_f(Y,Z)->big_f(X,Z)).
% 1.89/2.07 -big_f(f(a,b),f(a,c)).
% 1.89/2.07 end_of_list.
% 1.89/2.07
% 1.89/2.07 -------> usable clausifies to:
% 1.89/2.07
% 1.89/2.07 list(usable).
% 1.89/2.07 0 [] big_f(f(a,b),f(b,c)).
% 1.89/2.07 0 [] big_f(f(b,c),f(a,c)).
% 1.89/2.07 0 [] -big_f(X,Y)| -big_f(Y,Z)|big_f(X,Z).
% 1.89/2.07 0 [] -big_f(f(a,b),f(a,c)).
% 1.89/2.07 end_of_list.
% 1.89/2.07
% 1.89/2.07 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=3.
% 1.89/2.07
% 1.89/2.07 This is a Horn set without equality. The strategy will
% 1.89/2.07 be hyperresolution, with satellites in sos and nuclei
% 1.89/2.07 in usable.
% 1.89/2.07
% 1.89/2.07 dependent: set(hyper_res).
% 1.89/2.07 dependent: clear(order_hyper).
% 1.89/2.07
% 1.89/2.07 ------------> process usable:
% 1.89/2.07 ** KEPT (pick-wt=9): 1 [] -big_f(A,B)| -big_f(B,C)|big_f(A,C).
% 1.89/2.07 ** KEPT (pick-wt=7): 2 [] -big_f(f(a,b),f(a,c)).
% 1.89/2.07
% 1.89/2.07 ------------> process sos:
% 1.89/2.07 ** KEPT (pick-wt=7): 3 [] big_f(f(a,b),f(b,c)).
% 1.89/2.07 ** KEPT (pick-wt=7): 4 [] big_f(f(b,c),f(a,c)).
% 1.89/2.07
% 1.89/2.07 ======= end of input processing =======
% 1.89/2.07
% 1.89/2.07 =========== start of search ===========
% 1.89/2.07
% 1.89/2.07 -------- PROOF --------
% 1.89/2.07
% 1.89/2.07 ----> UNIT CONFLICT at 0.00 sec ----> 6 [binary,5.1,2.1] $F.
% 1.89/2.07
% 1.89/2.07 Length of proof is 1. Level of proof is 1.
% 1.89/2.07
% 1.89/2.07 ---------------- PROOF ----------------
% 1.89/2.07 % SZS status Theorem
% 1.89/2.07 % SZS output start Refutation
% See solution above
% 1.89/2.07 ------------ end of proof -------------
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Search stopped by max_proofs option.
% 1.89/2.07
% 1.89/2.07
% 1.89/2.07 Search stopped by max_proofs option.
% 1.89/2.07
% 1.89/2.07 ============ end of search ============
% 1.89/2.07
% 1.89/2.07 -------------- statistics -------------
% 1.89/2.07 clauses given 2
% 1.89/2.07 clauses generated 1
% 1.89/2.07 clauses kept 5
% 1.89/2.07 clauses forward subsumed 0
% 1.89/2.07 clauses back subsumed 0
% 1.89/2.07 Kbytes malloced 976
% 1.89/2.07
% 1.89/2.07 ----------- times (seconds) -----------
% 1.89/2.07 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.89/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.89/2.07 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.89/2.07
% 1.89/2.07 That finishes the proof of the theorem.
% 1.89/2.07
% 1.89/2.07 Process 23345 finished Wed Jul 27 10:58:48 2022
% 1.89/2.07 Otter interrupted
% 1.89/2.07 PROOF FOUND
%------------------------------------------------------------------------------