TSTP Solution File: LAT263-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT263-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 13:02:14 EDT 2022
% Result : Unsatisfiable 1.95s 2.11s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 14 ( 11 unt; 0 nHn; 11 RR)
% Number of literals : 23 ( 5 equ; 10 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-3 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a),
file('LAT263-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(A,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit))
| ~ c_in(A,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit))
| ~ c_lesse_quals(C,c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),tc_set(B))
| c_in(c_Tarski_Olub(C,A,B),c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),B) ),
file('LAT263-2.p',unknown),
[] ).
cnf(4,axiom,
c_lesse_quals(v_S,v_A,tc_set(t_a)),
file('LAT263-2.p',unknown),
[] ).
cnf(5,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('LAT263-2.p',unknown),
[] ).
cnf(7,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(8,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('LAT263-2.p',unknown),
[] ).
cnf(9,axiom,
c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('LAT263-2.p',unknown),
[] ).
cnf(10,axiom,
c_Tarski_Oglb(A,B,C) = c_Tarski_Olub(A,c_Tarski_Odual(B,C),C),
file('LAT263-2.p',unknown),
[] ).
cnf(11,plain,
c_Tarski_Olub(A,c_Tarski_Odual(B,C),C) = c_Tarski_Oglb(A,B,C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(14,axiom,
c_Tarski_Opotype_Opset(c_Tarski_Odual(A,B),B,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),
file('LAT263-2.p',unknown),
[] ).
cnf(16,plain,
( ~ c_in(c_Tarski_Odual(A,B),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(A,B),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit))
| ~ c_lesse_quals(C,c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),tc_set(B))
| c_in(c_Tarski_Oglb(C,A,B),c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),B) ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[11,2]),14,14]),
[iquote('para_from,11.1.1,2.4.1,demod,14,14')] ).
cnf(18,plain,
( ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_lesse_quals(A,v_A,tc_set(t_a))
| c_in(c_Tarski_Oglb(A,v_cl,t_a),v_A,t_a) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,7]),7]),
[iquote('para_into,16.3.2,6.1.1,demod,7')] ).
cnf(19,plain,
c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a),
inference(hyper,[status(thm)],[18,8,9,4]),
[iquote('hyper,18,8,9,4')] ).
cnf(20,plain,
$false,
inference(binary,[status(thm)],[19,1]),
[iquote('binary,19.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT263-2 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n026.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 08:29:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.11 ----- Otter 3.3f, August 2004 -----
% 1.95/2.11 The process was started by sandbox2 on n026.cluster.edu,
% 1.95/2.11 Wed Jul 27 08:29:24 2022
% 1.95/2.11 The command was "./otter". The process ID is 6554.
% 1.95/2.11
% 1.95/2.11 set(prolog_style_variables).
% 1.95/2.11 set(auto).
% 1.95/2.11 dependent: set(auto1).
% 1.95/2.11 dependent: set(process_input).
% 1.95/2.11 dependent: clear(print_kept).
% 1.95/2.11 dependent: clear(print_new_demod).
% 1.95/2.11 dependent: clear(print_back_demod).
% 1.95/2.11 dependent: clear(print_back_sub).
% 1.95/2.11 dependent: set(control_memory).
% 1.95/2.11 dependent: assign(max_mem, 12000).
% 1.95/2.11 dependent: assign(pick_given_ratio, 4).
% 1.95/2.11 dependent: assign(stats_level, 1).
% 1.95/2.11 dependent: assign(max_seconds, 10800).
% 1.95/2.11 clear(print_given).
% 1.95/2.11
% 1.95/2.11 list(usable).
% 1.95/2.11 0 [] A=A.
% 1.95/2.11 0 [] c_lesse_quals(v_S,v_A,tc_set(t_a)).
% 1.95/2.11 0 [] -c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a).
% 1.95/2.11 0 [] v_A=c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit).
% 1.95/2.11 0 [] -c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))| -c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))| -c_lesse_quals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))|c_in(c_Tarski_Olub(V_S,V_cl,T_a),c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),T_a).
% 1.95/2.11 0 [] c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)).
% 1.95/2.11 0 [] c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)).
% 1.95/2.11 0 [] c_Tarski_Oglb(V_S,V_cl,T_a)=c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a).
% 1.95/2.11 0 [] c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit)=c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit).
% 1.95/2.11 end_of_list.
% 1.95/2.11
% 1.95/2.11 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.95/2.11
% 1.95/2.11 This is a Horn set with equality. The strategy will be
% 1.95/2.11 Knuth-Bendix and hyper_res, with positive clauses in
% 1.95/2.11 sos and nonpositive clauses in usable.
% 1.95/2.11
% 1.95/2.11 dependent: set(knuth_bendix).
% 1.95/2.11 dependent: set(anl_eq).
% 1.95/2.11 dependent: set(para_from).
% 1.95/2.11 dependent: set(para_into).
% 1.95/2.11 dependent: clear(para_from_right).
% 1.95/2.11 dependent: clear(para_into_right).
% 1.95/2.11 dependent: set(para_from_vars).
% 1.95/2.11 dependent: set(eq_units_both_ways).
% 1.95/2.11 dependent: set(dynamic_demod_all).
% 1.95/2.11 dependent: set(dynamic_demod).
% 1.95/2.11 dependent: set(order_eq).
% 1.95/2.11 dependent: set(back_demod).
% 1.95/2.11 dependent: set(lrpo).
% 1.95/2.11 dependent: set(hyper_res).
% 1.95/2.11 dependent: clear(order_hyper).
% 1.95/2.11
% 1.95/2.11 ------------> process usable:
% 1.95/2.11 ** KEPT (pick-wt=7): 1 [] -c_in(c_Tarski_Oglb(v_S,v_cl,t_a),v_A,t_a).
% 1.95/2.11 ** KEPT (pick-wt=30): 2 [] -c_in(A,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit))| -c_in(A,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(B,tc_Product__Type_Ounit))| -c_lesse_quals(C,c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),tc_set(B))|c_in(c_Tarski_Olub(C,A,B),c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit),B).
% 1.95/2.11
% 1.95/2.11 ------------> process sos:
% 1.95/2.11 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.95/2.11 ** KEPT (pick-wt=5): 4 [] c_lesse_quals(v_S,v_A,tc_set(t_a)).
% 1.95/2.11 ** KEPT (pick-wt=6): 6 [copy,5,flip.1] c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)=v_A.
% 1.95/2.11 ---> New Demodulator: 7 [new_demod,6] c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)=v_A.
% 1.95/2.11 ** KEPT (pick-wt=8): 8 [] c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)).
% 1.95/2.11 ** KEPT (pick-wt=8): 9 [] c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)).
% 1.95/2.11 ** KEPT (pick-wt=11): 11 [copy,10,flip.1] c_Tarski_Olub(A,c_Tarski_Odual(B,C),C)=c_Tarski_Oglb(A,B,C).
% 1.95/2.11 ---> New Demodulator: 12 [new_demod,11] c_Tarski_Olub(A,c_Tarski_Odual(B,C),C)=c_Tarski_Oglb(A,B,C).
% 1.95/2.11 ** KEPT (pick-wt=11): 13 [] c_Tarski_Opotype_Opset(c_Tarski_Odual(A,B),B,tc_Product__Type_Ounit)=c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit).
% 1.95/2.11 ---> New Demodulator: 14 [new_demod,13] c_Tarski_Opotype_Opset(c_Tarski_Odual(A,B),B,tc_Product__Type_Ounit)=c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit).
% 1.95/2.11 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.95/2.11 >>>> Starting back demodulation with 7.
% 1.95/2.11 >>>> Starting back demodulation with 12.
% 1.95/2.11 >>>> Starting back demodulation with 14.
% 1.95/2.11
% 1.95/2.11 ======= end of input processing =======
% 1.95/2.11
% 1.95/2.11 =========== start of search ===========
% 1.95/2.11
% 1.95/2.11 -------- PROOF --------
% 1.95/2.11
% 1.95/2.11 ----> UNIT CONFLICT at 0.00 sec ----> 20 [binary,19.1,1.1] $F.
% 1.95/2.11
% 1.95/2.11 Length of proof is 5. Level of proof is 4.
% 1.95/2.11
% 1.95/2.11 ---------------- PROOF ----------------
% 1.95/2.11 % SZS status Unsatisfiable
% 1.95/2.11 % SZS output start Refutation
% See solution above
% 1.95/2.11 ------------ end of proof -------------
% 1.95/2.11
% 1.95/2.11
% 1.95/2.11 Search stopped by max_proofs option.
% 1.95/2.11
% 1.95/2.11
% 1.95/2.11 Search stopped by max_proofs option.
% 1.95/2.11
% 1.95/2.11 ============ end of search ============
% 1.95/2.11
% 1.95/2.11 -------------- statistics -------------
% 1.95/2.11 clauses given 10
% 1.95/2.11 clauses generated 16
% 1.95/2.11 clauses kept 14
% 1.95/2.11 clauses forward subsumed 12
% 1.95/2.11 clauses back subsumed 0
% 1.95/2.11 Kbytes malloced 976
% 1.95/2.11
% 1.95/2.11 ----------- times (seconds) -----------
% 1.95/2.11 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.11 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.11 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.95/2.11
% 1.95/2.11 That finishes the proof of the theorem.
% 1.95/2.11
% 1.95/2.11 Process 6554 finished Wed Jul 27 08:29:26 2022
% 1.99/2.11 Otter interrupted
% 1.99/2.11 PROOF FOUND
%------------------------------------------------------------------------------