TSTP Solution File: LAT268-2 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT268-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:02:15 EDT 2022
% Result : Unsatisfiable 1.82s 1.98s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of clauses : 20 ( 15 unt; 0 nHn; 17 RR)
% Number of literals : 34 ( 7 equ; 15 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
~ c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('LAT268-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_in(A,B,C)
| ~ c_in(D,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit))
| ~ c_in(D,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit))
| ~ c_lesse_quals(B,c_Tarski_Opotype_Opset(D,C,tc_Product__Type_Ounit),tc_set(C))
| c_in(c_Pair(A,c_Tarski_Olub(B,D,C),C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)) ),
file('LAT268-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ c_in(c_Pair(A,B,C,C),c_Tarski_Opotype_Oorder(c_Tarski_Odual(D,C),C,tc_Product__Type_Ounit),tc_prod(C,C))
| c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)) ),
file('LAT268-2.p',unknown),
[] ).
cnf(5,axiom,
c_lesse_quals(v_S,v_A,tc_set(t_a)),
file('LAT268-2.p',unknown),
[] ).
cnf(6,axiom,
c_in(v_x,v_S,t_a),
file('LAT268-2.p',unknown),
[] ).
cnf(7,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('LAT268-2.p',unknown),
[] ).
cnf(8,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)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(10,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('LAT268-2.p',unknown),
[] ).
cnf(11,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('LAT268-2.p',unknown),
[] ).
cnf(12,axiom,
c_Tarski_Oglb(A,B,C) = c_Tarski_Olub(A,c_Tarski_Odual(B,C),C),
file('LAT268-2.p',unknown),
[] ).
cnf(13,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)],[12])]),
[iquote('copy,12,flip.1')] ).
cnf(16,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('LAT268-2.p',unknown),
[] ).
cnf(17,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('LAT268-2.p',unknown),
[] ).
cnf(18,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[17])]),
[iquote('copy,17,flip.1')] ).
cnf(21,plain,
( ~ c_in(c_Pair(A,B,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| c_in(c_Pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(para_from,[status(thm),theory(equality)],[18,3]),
[iquote('para_from,18.1.1,3.2.2')] ).
cnf(22,plain,
( ~ c_in(A,B,C)
| ~ c_in(c_Tarski_Odual(D,C),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(D,C),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit))
| ~ c_lesse_quals(B,c_Tarski_Opotype_Opset(D,C,tc_Product__Type_Ounit),tc_set(C))
| c_in(c_Pair(A,c_Tarski_Oglb(B,D,C),C,C),c_Tarski_Opotype_Oorder(c_Tarski_Odual(D,C),C,tc_Product__Type_Ounit),tc_prod(C,C)) ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[13,2]),16]),
[iquote('para_from,13.1.1,2.5.1.2,demod,16')] ).
cnf(24,plain,
( ~ c_in(A,B,t_a)
| ~ 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(B,v_A,tc_set(t_a))
| c_in(c_Pair(A,c_Tarski_Oglb(B,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(para_into,[status(thm),theory(equality)],[22,8]),
[iquote('para_into,22.4.2,8.1.1')] ).
cnf(25,plain,
c_in(c_Pair(v_x,c_Tarski_Oglb(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[24,6,10,11,5]),
[iquote('hyper,24,6,10,11,5')] ).
cnf(26,plain,
c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(hyper,[status(thm)],[25,21]),
[iquote('hyper,25,21')] ).
cnf(27,plain,
$false,
inference(binary,[status(thm)],[26,1]),
[iquote('binary,26.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT268-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n012.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 08:10:05 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.78/1.98 ----- Otter 3.3f, August 2004 -----
% 1.78/1.98 The process was started by sandbox2 on n012.cluster.edu,
% 1.78/1.98 Wed Jul 27 08:10:05 2022
% 1.78/1.98 The command was "./otter". The process ID is 23441.
% 1.78/1.98
% 1.78/1.98 set(prolog_style_variables).
% 1.78/1.98 set(auto).
% 1.78/1.98 dependent: set(auto1).
% 1.78/1.98 dependent: set(process_input).
% 1.78/1.98 dependent: clear(print_kept).
% 1.78/1.98 dependent: clear(print_new_demod).
% 1.78/1.98 dependent: clear(print_back_demod).
% 1.78/1.98 dependent: clear(print_back_sub).
% 1.78/1.98 dependent: set(control_memory).
% 1.78/1.98 dependent: assign(max_mem, 12000).
% 1.78/1.98 dependent: assign(pick_given_ratio, 4).
% 1.78/1.98 dependent: assign(stats_level, 1).
% 1.78/1.98 dependent: assign(max_seconds, 10800).
% 1.78/1.98 clear(print_given).
% 1.78/1.98
% 1.78/1.98 list(usable).
% 1.78/1.98 0 [] A=A.
% 1.78/1.98 0 [] c_lesse_quals(v_S,v_A,tc_set(t_a)).
% 1.78/1.98 0 [] c_in(v_x,v_S,t_a).
% 1.78/1.98 0 [] -c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.78/1.98 0 [] v_A=c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit).
% 1.78/1.98 0 [] -c_in(V_x,V_S,T_a)| -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_Pair(V_x,c_Tarski_Olub(V_S,V_cl,T_a),T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)).
% 1.78/1.98 0 [] -c_in(c_Pair(V_x,V_y,T_a,T_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl,T_a),T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a))|c_in(c_Pair(V_y,V_x,T_a,T_a),c_Tarski_Opotype_Oorder(V_cl,T_a,tc_Product__Type_Ounit),tc_prod(T_a,T_a)).
% 1.78/1.98 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)).
% 1.78/1.98 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)).
% 1.78/1.98 0 [] c_Tarski_Oglb(V_S,V_cl,T_a)=c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a).
% 1.78/1.98 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).
% 1.78/1.98 0 [] v_r=c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit).
% 1.78/1.98 end_of_list.
% 1.78/1.98
% 1.78/1.98 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=5.
% 1.78/1.98
% 1.78/1.98 This is a Horn set with equality. The strategy will be
% 1.78/1.98 Knuth-Bendix and hyper_res, with positive clauses in
% 1.78/1.98 sos and nonpositive clauses in usable.
% 1.78/1.98
% 1.78/1.98 dependent: set(knuth_bendix).
% 1.78/1.98 dependent: set(anl_eq).
% 1.78/1.98 dependent: set(para_from).
% 1.78/1.98 dependent: set(para_into).
% 1.78/1.98 dependent: clear(para_from_right).
% 1.78/1.98 dependent: clear(para_into_right).
% 1.78/1.98 dependent: set(para_from_vars).
% 1.78/1.98 dependent: set(eq_units_both_ways).
% 1.78/1.98 dependent: set(dynamic_demod_all).
% 1.78/1.98 dependent: set(dynamic_demod).
% 1.78/1.98 dependent: set(order_eq).
% 1.78/1.98 dependent: set(back_demod).
% 1.78/1.98 dependent: set(lrpo).
% 1.78/1.98 dependent: set(hyper_res).
% 1.78/1.98 dependent: clear(order_hyper).
% 1.78/1.98
% 1.78/1.98 ------------> process usable:
% 1.78/1.98 ** KEPT (pick-wt=13): 1 [] -c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)).
% 1.78/1.98 ** KEPT (pick-wt=40): 2 [] -c_in(A,B,C)| -c_in(D,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit))| -c_in(D,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit))| -c_lesse_quals(B,c_Tarski_Opotype_Opset(D,C,tc_Product__Type_Ounit),tc_set(C))|c_in(c_Pair(A,c_Tarski_Olub(B,D,C),C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)).
% 1.78/1.98 ** KEPT (pick-wt=28): 3 [] -c_in(c_Pair(A,B,C,C),c_Tarski_Opotype_Oorder(c_Tarski_Odual(D,C),C,tc_Product__Type_Ounit),tc_prod(C,C))|c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)).
% 1.78/1.98
% 1.78/1.98 ------------> process sos:
% 1.78/1.98 ** KEPT (pick-wt=3): 4 [] A=A.
% 1.78/1.98 ** KEPT (pick-wt=5): 5 [] c_lesse_quals(v_S,v_A,tc_set(t_a)).
% 1.78/1.98 ** KEPT (pick-wt=4): 6 [] c_in(v_x,v_S,t_a).
% 1.78/1.98 ** KEPT (pick-wt=6): 8 [copy,7,flip.1] c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)=v_A.
% 1.78/1.98 ---> New Demodulator: 9 [new_demod,8] c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)=v_A.
% 1.78/1.98 ** KEPT (pick-wt=8): 10 [] c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)).
% 1.82/1.98 ** KEPT (pick-wt=8): 11 [] c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)).
% 1.82/1.98 ** KEPT (pick-wt=11): 13 [copy,12,flip.1] c_Tarski_Olub(A,c_Tarski_Odual(B,C),C)=c_Tarski_Oglb(A,B,C).
% 1.82/1.98 ---> New Demodulator: 14 [new_demod,13] c_Tarski_Olub(A,c_Tarski_Odual(B,C),C)=c_Tarski_Oglb(A,B,C).
% 1.82/1.98 ** KEPT (pick-wt=11): 15 [] c_Tarski_Opotype_Opset(c_Tarski_Odual(A,B),B,tc_Product__Type_Ounit)=c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit).
% 1.82/1.98 ---> New Demodulator: 16 [new_demod,15] c_Tarski_Opotype_Opset(c_Tarski_Odual(A,B),B,tc_Product__Type_Ounit)=c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit).
% 1.82/1.98 ** KEPT (pick-wt=6): 18 [copy,17,flip.1] c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)=v_r.
% 1.82/1.98 ---> New Demodulator: 19 [new_demod,18] c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)=v_r.
% 1.82/1.98 Following clause subsumed by 4 during input processing: 0 [copy,4,flip.1] A=A.
% 1.82/1.98 >>>> Starting back demodulation with 9.
% 1.82/1.98 >>>> Starting back demodulation with 14.
% 1.82/1.98 >>>> Starting back demodulation with 16.
% 1.82/1.98 >>>> Starting back demodulation with 19.
% 1.82/1.98
% 1.82/1.98 ======= end of input processing =======
% 1.82/1.98
% 1.82/1.98 =========== start of search ===========
% 1.82/1.98
% 1.82/1.98 -------- PROOF --------
% 1.82/1.98
% 1.82/1.98 ----> UNIT CONFLICT at 0.00 sec ----> 27 [binary,26.1,1.1] $F.
% 1.82/1.98
% 1.82/1.98 Length of proof is 8. Level of proof is 5.
% 1.82/1.98
% 1.82/1.98 ---------------- PROOF ----------------
% 1.82/1.98 % SZS status Unsatisfiable
% 1.82/1.98 % SZS output start Refutation
% See solution above
% 1.82/1.98 ------------ end of proof -------------
% 1.82/1.98
% 1.82/1.98
% 1.82/1.98 Search stopped by max_proofs option.
% 1.82/1.98
% 1.82/1.98
% 1.82/1.98 Search stopped by max_proofs option.
% 1.82/1.98
% 1.82/1.98 ============ end of search ============
% 1.82/1.98
% 1.82/1.98 -------------- statistics -------------
% 1.82/1.98 clauses given 14
% 1.82/1.98 clauses generated 17
% 1.82/1.98 clauses kept 19
% 1.82/1.98 clauses forward subsumed 11
% 1.82/1.98 clauses back subsumed 0
% 1.82/1.98 Kbytes malloced 1953
% 1.82/1.98
% 1.82/1.98 ----------- times (seconds) -----------
% 1.82/1.98 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/1.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/1.98 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.82/1.98
% 1.82/1.98 That finishes the proof of the theorem.
% 1.82/1.98
% 1.82/1.98 Process 23441 finished Wed Jul 27 08:10:07 2022
% 1.82/1.98 Otter interrupted
% 1.82/1.98 PROOF FOUND
%------------------------------------------------------------------------------