TSTP Solution File: SET838-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET838-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n007.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 13:14:21 EDT 2022
% Result : Unsatisfiable 1.71s 1.91s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 8 unt; 0 nHn; 13 RR)
% Number of literals : 20 ( 19 equ; 9 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( A = v_x
| v_f(v_g(A)) != A ),
file('SET838-2.p',unknown),
[] ).
cnf(2,axiom,
( v_g(v_f(v_xa(A))) = v_xa(A)
| v_g(v_f(A)) != A ),
file('SET838-2.p',unknown),
[] ).
cnf(3,axiom,
( v_xa(A) != A
| v_g(v_f(A)) != A ),
file('SET838-2.p',unknown),
[] ).
cnf(4,axiom,
A = A,
file('SET838-2.p',unknown),
[] ).
cnf(5,axiom,
v_f(v_g(v_x)) = v_x,
file('SET838-2.p',unknown),
[] ).
cnf(9,plain,
( v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x))
| v_g(v_x) != v_g(v_x) ),
inference(para_from,[status(thm),theory(equality)],[5,2]),
[iquote('para_from,5.1.1,2.2.1.1')] ).
cnf(17,plain,
v_g(v_f(v_xa(v_g(v_x)))) = v_xa(v_g(v_x)),
inference(hyper,[status(thm)],[9,4]),
[iquote('hyper,9,4')] ).
cnf(22,plain,
v_g(v_f(v_xa(v_xa(v_g(v_x))))) = v_xa(v_xa(v_g(v_x))),
inference(hyper,[status(thm)],[17,2]),
[iquote('hyper,16,2')] ).
cnf(26,plain,
( v_xa(v_g(v_x)) = v_g(v_x)
| v_f(v_xa(v_g(v_x))) != v_f(v_xa(v_g(v_x))) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,1]),17])]),
[iquote('para_into,16.1.1.1,1.1.1,demod,17,flip.1')] ).
cnf(29,plain,
v_g(v_f(v_xa(v_xa(v_xa(v_g(v_x)))))) = v_xa(v_xa(v_xa(v_g(v_x)))),
inference(hyper,[status(thm)],[22,2]),
[iquote('hyper,22,2')] ).
cnf(44,plain,
( v_xa(v_xa(v_xa(v_xa(v_g(v_x))))) != v_xa(v_xa(v_xa(v_g(v_x))))
| v_xa(v_xa(v_xa(v_g(v_x)))) != v_xa(v_xa(v_xa(v_g(v_x)))) ),
inference(para_from,[status(thm),theory(equality)],[29,3]),
[iquote('para_from,29.1.1,3.2.1')] ).
cnf(71,plain,
v_xa(v_g(v_x)) = v_g(v_x),
inference(hyper,[status(thm)],[26,4]),
[iquote('hyper,26,4')] ).
cnf(78,plain,
v_g(v_x) != v_g(v_x),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),71,71,71,71,71,71,71,71,71,71,71,71,71]),
[iquote('back_demod,44,demod,71,71,71,71,71,71,71,71,71,71,71,71,71')] ).
cnf(79,plain,
$false,
inference(binary,[status(thm)],[78,4]),
[iquote('binary,78.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET838-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 10:39:46 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.71/1.91 ----- Otter 3.3f, August 2004 -----
% 1.71/1.91 The process was started by sandbox2 on n007.cluster.edu,
% 1.71/1.91 Wed Jul 27 10:39:46 2022
% 1.71/1.91 The command was "./otter". The process ID is 13428.
% 1.71/1.91
% 1.71/1.91 set(prolog_style_variables).
% 1.71/1.91 set(auto).
% 1.71/1.91 dependent: set(auto1).
% 1.71/1.91 dependent: set(process_input).
% 1.71/1.91 dependent: clear(print_kept).
% 1.71/1.91 dependent: clear(print_new_demod).
% 1.71/1.91 dependent: clear(print_back_demod).
% 1.71/1.91 dependent: clear(print_back_sub).
% 1.71/1.91 dependent: set(control_memory).
% 1.71/1.91 dependent: assign(max_mem, 12000).
% 1.71/1.91 dependent: assign(pick_given_ratio, 4).
% 1.71/1.91 dependent: assign(stats_level, 1).
% 1.71/1.91 dependent: assign(max_seconds, 10800).
% 1.71/1.91 clear(print_given).
% 1.71/1.91
% 1.71/1.91 list(usable).
% 1.71/1.91 0 [] A=A.
% 1.71/1.91 0 [] v_f(v_g(v_x))=v_x.
% 1.71/1.91 0 [] V_U=v_x|v_f(v_g(V_U))!=V_U.
% 1.71/1.91 0 [] v_g(v_f(v_xa(V_U)))=v_xa(V_U)|v_g(v_f(V_U))!=V_U.
% 1.71/1.91 0 [] v_xa(V_U)!=V_U|v_g(v_f(V_U))!=V_U.
% 1.71/1.91 end_of_list.
% 1.71/1.91
% 1.71/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=2.
% 1.71/1.91
% 1.71/1.91 This is a Horn set with equality. The strategy will be
% 1.71/1.91 Knuth-Bendix and hyper_res, with positive clauses in
% 1.71/1.91 sos and nonpositive clauses in usable.
% 1.71/1.91
% 1.71/1.91 dependent: set(knuth_bendix).
% 1.71/1.91 dependent: set(anl_eq).
% 1.71/1.91 dependent: set(para_from).
% 1.71/1.91 dependent: set(para_into).
% 1.71/1.91 dependent: clear(para_from_right).
% 1.71/1.91 dependent: clear(para_into_right).
% 1.71/1.91 dependent: set(para_from_vars).
% 1.71/1.91 dependent: set(eq_units_both_ways).
% 1.71/1.91 dependent: set(dynamic_demod_all).
% 1.71/1.91 dependent: set(dynamic_demod).
% 1.71/1.91 dependent: set(order_eq).
% 1.71/1.91 dependent: set(back_demod).
% 1.71/1.91 dependent: set(lrpo).
% 1.71/1.91 dependent: set(hyper_res).
% 1.71/1.91 dependent: clear(order_hyper).
% 1.71/1.91
% 1.71/1.91 ------------> process usable:
% 1.71/1.91 ** KEPT (pick-wt=8): 1 [] A=v_x|v_f(v_g(A))!=A.
% 1.71/1.91 ** KEPT (pick-wt=12): 2 [] v_g(v_f(v_xa(A)))=v_xa(A)|v_g(v_f(A))!=A.
% 1.71/1.91 ** KEPT (pick-wt=9): 3 [] v_xa(A)!=A|v_g(v_f(A))!=A.
% 1.71/1.91
% 1.71/1.91 ------------> process sos:
% 1.71/1.91 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.71/1.91 ** KEPT (pick-wt=5): 5 [] v_f(v_g(v_x))=v_x.
% 1.71/1.91 ---> New Demodulator: 6 [new_demod,5] v_f(v_g(v_x))=v_x.
% 1.71/1.91 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.71/1.91 >>>> Starting back demodulation with 6.
% 1.71/1.91
% 1.71/1.91 ======= end of input processing =======
% 1.71/1.91
% 1.71/1.91 =========== start of search ===========
% 1.71/1.91
% 1.71/1.91 -------- PROOF --------
% 1.71/1.91
% 1.71/1.91 ----> UNIT CONFLICT at 0.00 sec ----> 79 [binary,78.1,4.1] $F.
% 1.71/1.91
% 1.71/1.91 Length of proof is 8. Level of proof is 6.
% 1.71/1.91
% 1.71/1.91 ---------------- PROOF ----------------
% 1.71/1.91 % SZS status Unsatisfiable
% 1.71/1.91 % SZS output start Refutation
% See solution above
% 1.71/1.91 ------------ end of proof -------------
% 1.71/1.91
% 1.71/1.91
% 1.71/1.91 Search stopped by max_proofs option.
% 1.71/1.91
% 1.71/1.91
% 1.71/1.91 Search stopped by max_proofs option.
% 1.71/1.91
% 1.71/1.91 ============ end of search ============
% 1.71/1.91
% 1.71/1.91 -------------- statistics -------------
% 1.71/1.91 clauses given 15
% 1.71/1.91 clauses generated 143
% 1.71/1.91 clauses kept 72
% 1.71/1.91 clauses forward subsumed 81
% 1.71/1.91 clauses back subsumed 3
% 1.71/1.91 Kbytes malloced 1953
% 1.71/1.91
% 1.71/1.91 ----------- times (seconds) -----------
% 1.71/1.91 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.91 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.71/1.91
% 1.71/1.91 That finishes the proof of the theorem.
% 1.71/1.91
% 1.71/1.91 Process 13428 finished Wed Jul 27 10:39:47 2022
% 1.71/1.91 Otter interrupted
% 1.71/1.91 PROOF FOUND
%------------------------------------------------------------------------------