TSTP Solution File: SET820-2 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET820-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:14:19 EDT 2022
% Result : Unsatisfiable 1.69s 1.87s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 11 ( 6 unt; 2 nHn; 7 RR)
% Number of literals : 18 ( 2 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_in(A,c_emptyset,B),
file('SET820-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(A,c_insert(B,C,D),D)
| c_in(A,C,D)
| A = B ),
file('SET820-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(A,B,tc_IntDef_Oint)
| c_in(v_x(B),B,tc_IntDef_Oint) ),
file('SET820-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ c_in(A,B,tc_IntDef_Oint)
| ~ v_P(v_x(B)) ),
file('SET820-2.p',unknown),
[] ).
cnf(6,axiom,
c_in(A,c_insert(A,B,C),C),
file('SET820-2.p',unknown),
[] ).
cnf(7,axiom,
v_P(v_a),
file('SET820-2.p',unknown),
[] ).
cnf(9,plain,
c_in(v_x(c_insert(A,B,tc_IntDef_Oint)),c_insert(A,B,tc_IntDef_Oint),tc_IntDef_Oint),
inference(hyper,[status(thm)],[6,3]),
[iquote('hyper,6,3')] ).
cnf(11,plain,
( c_in(v_x(c_insert(A,B,tc_IntDef_Oint)),B,tc_IntDef_Oint)
| v_x(c_insert(A,B,tc_IntDef_Oint)) = A ),
inference(hyper,[status(thm)],[9,2]),
[iquote('hyper,9,2')] ).
cnf(37,plain,
( ~ c_in(A,c_insert(B,C,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ v_P(B)
| c_in(v_x(c_insert(B,C,tc_IntDef_Oint)),C,tc_IntDef_Oint) ),
inference(para_from,[status(thm),theory(equality)],[11,4]),
[iquote('para_from,11.2.1,4.2.1')] ).
cnf(38,plain,
c_in(v_x(c_insert(v_a,A,tc_IntDef_Oint)),A,tc_IntDef_Oint),
inference(hyper,[status(thm)],[37,9,7]),
[iquote('hyper,37,9,7')] ).
cnf(39,plain,
$false,
inference(binary,[status(thm)],[38,1]),
[iquote('binary,38.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET820-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n008.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 10:31:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.69/1.87 ----- Otter 3.3f, August 2004 -----
% 1.69/1.87 The process was started by sandbox on n008.cluster.edu,
% 1.69/1.87 Wed Jul 27 10:31:08 2022
% 1.69/1.87 The command was "./otter". The process ID is 32520.
% 1.69/1.87
% 1.69/1.87 set(prolog_style_variables).
% 1.69/1.87 set(auto).
% 1.69/1.87 dependent: set(auto1).
% 1.69/1.87 dependent: set(process_input).
% 1.69/1.87 dependent: clear(print_kept).
% 1.69/1.87 dependent: clear(print_new_demod).
% 1.69/1.87 dependent: clear(print_back_demod).
% 1.69/1.87 dependent: clear(print_back_sub).
% 1.69/1.87 dependent: set(control_memory).
% 1.69/1.87 dependent: assign(max_mem, 12000).
% 1.69/1.87 dependent: assign(pick_given_ratio, 4).
% 1.69/1.87 dependent: assign(stats_level, 1).
% 1.69/1.87 dependent: assign(max_seconds, 10800).
% 1.69/1.87 clear(print_given).
% 1.69/1.87
% 1.69/1.87 list(usable).
% 1.69/1.87 0 [] A=A.
% 1.69/1.87 0 [] -c_in(V_a,c_emptyset,T_a).
% 1.69/1.87 0 [] c_in(V_x,c_insert(V_x,V_B,T_a),T_a).
% 1.69/1.87 0 [] -c_in(V_a,c_insert(V_b,V_A,T_a),T_a)|c_in(V_a,V_A,T_a)|V_a=V_b.
% 1.69/1.87 0 [] v_P(v_a).
% 1.69/1.87 0 [] -c_in(V_V,V_U,tc_IntDef_Oint)|c_in(v_x(V_U),V_U,tc_IntDef_Oint).
% 1.69/1.87 0 [] -c_in(V_W,V_U,tc_IntDef_Oint)| -v_P(v_x(V_U)).
% 1.69/1.87 end_of_list.
% 1.69/1.87
% 1.69/1.87 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.69/1.87
% 1.69/1.87 This ia a non-Horn set with equality. The strategy will be
% 1.69/1.87 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.69/1.87 deletion, with positive clauses in sos and nonpositive
% 1.69/1.87 clauses in usable.
% 1.69/1.87
% 1.69/1.87 dependent: set(knuth_bendix).
% 1.69/1.87 dependent: set(anl_eq).
% 1.69/1.87 dependent: set(para_from).
% 1.69/1.87 dependent: set(para_into).
% 1.69/1.87 dependent: clear(para_from_right).
% 1.69/1.87 dependent: clear(para_into_right).
% 1.69/1.87 dependent: set(para_from_vars).
% 1.69/1.87 dependent: set(eq_units_both_ways).
% 1.69/1.87 dependent: set(dynamic_demod_all).
% 1.69/1.87 dependent: set(dynamic_demod).
% 1.69/1.87 dependent: set(order_eq).
% 1.69/1.87 dependent: set(back_demod).
% 1.69/1.87 dependent: set(lrpo).
% 1.69/1.87 dependent: set(hyper_res).
% 1.69/1.87 dependent: set(unit_deletion).
% 1.69/1.87 dependent: set(factor).
% 1.69/1.87
% 1.69/1.87 ------------> process usable:
% 1.69/1.87 ** KEPT (pick-wt=4): 1 [] -c_in(A,c_emptyset,B).
% 1.69/1.87 ** KEPT (pick-wt=14): 2 [] -c_in(A,c_insert(B,C,D),D)|c_in(A,C,D)|A=B.
% 1.69/1.87 ** KEPT (pick-wt=9): 3 [] -c_in(A,B,tc_IntDef_Oint)|c_in(v_x(B),B,tc_IntDef_Oint).
% 1.69/1.87 ** KEPT (pick-wt=7): 4 [] -c_in(A,B,tc_IntDef_Oint)| -v_P(v_x(B)).
% 1.69/1.87
% 1.69/1.87 ------------> process sos:
% 1.69/1.87 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.69/1.87 ** KEPT (pick-wt=7): 6 [] c_in(A,c_insert(A,B,C),C).
% 1.69/1.87 ** KEPT (pick-wt=2): 7 [] v_P(v_a).
% 1.69/1.87 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.69/1.87
% 1.69/1.87 ======= end of input processing =======
% 1.69/1.87
% 1.69/1.87 =========== start of search ===========
% 1.69/1.87
% 1.69/1.87 -------- PROOF --------
% 1.69/1.87
% 1.69/1.87 ----> UNIT CONFLICT at 0.00 sec ----> 39 [binary,38.1,1.1] $F.
% 1.69/1.87
% 1.69/1.87 Length of proof is 4. Level of proof is 4.
% 1.69/1.87
% 1.69/1.87 ---------------- PROOF ----------------
% 1.69/1.87 % SZS status Unsatisfiable
% 1.69/1.87 % SZS output start Refutation
% See solution above
% 1.69/1.87 ------------ end of proof -------------
% 1.69/1.87
% 1.69/1.87
% 1.69/1.87 Search stopped by max_proofs option.
% 1.69/1.87
% 1.69/1.87
% 1.69/1.87 Search stopped by max_proofs option.
% 1.69/1.87
% 1.69/1.87 ============ end of search ============
% 1.69/1.87
% 1.69/1.87 -------------- statistics -------------
% 1.69/1.87 clauses given 8
% 1.69/1.87 clauses generated 52
% 1.69/1.87 clauses kept 38
% 1.69/1.87 clauses forward subsumed 22
% 1.69/1.87 clauses back subsumed 0
% 1.69/1.87 Kbytes malloced 976
% 1.69/1.87
% 1.69/1.87 ----------- times (seconds) -----------
% 1.69/1.87 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.87 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.69/1.87 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.69/1.87
% 1.69/1.87 That finishes the proof of the theorem.
% 1.69/1.87
% 1.69/1.87 Process 32520 finished Wed Jul 27 10:31:10 2022
% 1.69/1.87 Otter interrupted
% 1.69/1.87 PROOF FOUND
%------------------------------------------------------------------------------