TSTP Solution File: LAT268-10 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LAT268-10 : TPTP v8.1.0. Released v7.5.0.
% 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 1.72s 1.92s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 12 RR)
% Number of literals : 20 ( 19 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-4 aty)
% Number of variables : 23 ( 1 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)) != true,
file('LAT268-10.p',unknown),
[] ).
cnf(4,axiom,
ife_q(A,A,B,C) = B,
file('LAT268-10.p',unknown),
[] ).
cnf(6,axiom,
c_lesse_quals(v_S,v_A,tc_set(t_a)) = true,
file('LAT268-10.p',unknown),
[] ).
cnf(7,axiom,
c_in(v_x,v_S,t_a) = true,
file('LAT268-10.p',unknown),
[] ).
cnf(9,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('LAT268-10.p',unknown),
[] ).
cnf(11,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)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(12,axiom,
ife_q(c_lesse_quals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),true,ife_q(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ife_q(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ife_q(c_in(D,A,C),true,c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true) = true,
file('LAT268-10.p',unknown),
[] ).
cnf(14,axiom,
ife_q(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)),true,c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)),true) = true,
file('LAT268-10.p',unknown),
[] ).
cnf(16,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)) = true,
file('LAT268-10.p',unknown),
[] ).
cnf(19,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)) = true,
file('LAT268-10.p',unknown),
[] ).
cnf(20,axiom,
c_Tarski_Oglb(A,B,C) = c_Tarski_Olub(A,c_Tarski_Odual(B,C),C),
file('LAT268-10.p',unknown),
[] ).
cnf(22,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)],[20])]),
[iquote('copy,20,flip.1')] ).
cnf(24,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('LAT268-10.p',unknown),
[] ).
cnf(25,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('LAT268-10.p',unknown),
[] ).
cnf(26,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)],[25])]),
[iquote('copy,25,flip.1')] ).
cnf(32,plain,
ife_q(c_lesse_quals(A,v_A,tc_set(t_a)),true,ife_q(c_in(B,A,t_a),true,c_in(c_Pair(B,c_Tarski_Oglb(A,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)),true),true) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[12,16]),24,11,19,22,4,4]),
[iquote('para_into,12.1.1.3.1,16.1.1,demod,24,11,19,22,4,4')] ).
cnf(40,plain,
ife_q(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)),true,c_in(c_Pair(B,A,t_a,t_a),v_r,tc_prod(t_a,t_a)),true) = true,
inference(para_into,[status(thm),theory(equality)],[14,26]),
[iquote('para_into,14.1.1.3.2,26.1.1')] ).
cnf(44,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)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,7]),6,4,4]),
[iquote('para_into,32.1.1.3.1,7.1.1,demod,6,4,4')] ).
cnf(46,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)) = true,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[44,40]),4]),
[iquote('para_from,44.1.1,40.1.1.1,demod,4')] ).
cnf(48,plain,
$false,
inference(binary,[status(thm)],[46,1]),
[iquote('binary,46.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT268-10 : TPTP v8.1.0. Released v7.5.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 08:26:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.91 ----- Otter 3.3f, August 2004 -----
% 1.72/1.91 The process was started by sandbox on n012.cluster.edu,
% 1.72/1.91 Wed Jul 27 08:26:20 2022
% 1.72/1.91 The command was "./otter". The process ID is 17221.
% 1.72/1.91
% 1.72/1.91 set(prolog_style_variables).
% 1.72/1.91 set(auto).
% 1.72/1.91 dependent: set(auto1).
% 1.72/1.91 dependent: set(process_input).
% 1.72/1.91 dependent: clear(print_kept).
% 1.72/1.91 dependent: clear(print_new_demod).
% 1.72/1.91 dependent: clear(print_back_demod).
% 1.72/1.91 dependent: clear(print_back_sub).
% 1.72/1.91 dependent: set(control_memory).
% 1.72/1.91 dependent: assign(max_mem, 12000).
% 1.72/1.91 dependent: assign(pick_given_ratio, 4).
% 1.72/1.91 dependent: assign(stats_level, 1).
% 1.72/1.91 dependent: assign(max_seconds, 10800).
% 1.72/1.91 clear(print_given).
% 1.72/1.91
% 1.72/1.91 list(usable).
% 1.72/1.91 0 [] A=A.
% 1.72/1.91 0 [] ife_q(A,A,B,C)=B.
% 1.72/1.91 0 [] c_lesse_quals(v_S,v_A,tc_set(t_a))=true.
% 1.72/1.91 0 [] c_in(v_x,v_S,t_a)=true.
% 1.72/1.91 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))!=true.
% 1.72/1.91 0 [] v_A=c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit).
% 1.72/1.91 0 [] ife_q(c_lesse_quals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ife_q(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ife_q(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ife_q(c_in(V_x,V_S,T_a),true,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)),true),true),true),true)=true.
% 1.72/1.91 0 [] ife_q(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)),true,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)),true)=true.
% 1.72/1.91 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))=true.
% 1.72/1.91 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))=true.
% 1.72/1.91 0 [] c_Tarski_Oglb(V_S,V_cl,T_a)=c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a).
% 1.72/1.91 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).
% 1.72/1.91 0 [] v_r=c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit).
% 1.72/1.91 end_of_list.
% 1.72/1.91
% 1.72/1.91 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.72/1.91
% 1.72/1.91 All clauses are units, and equality is present; the
% 1.72/1.91 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.72/1.91
% 1.72/1.91 dependent: set(knuth_bendix).
% 1.72/1.91 dependent: set(anl_eq).
% 1.72/1.91 dependent: set(para_from).
% 1.72/1.91 dependent: set(para_into).
% 1.72/1.91 dependent: clear(para_from_right).
% 1.72/1.91 dependent: clear(para_into_right).
% 1.72/1.91 dependent: set(para_from_vars).
% 1.72/1.91 dependent: set(eq_units_both_ways).
% 1.72/1.91 dependent: set(dynamic_demod_all).
% 1.72/1.91 dependent: set(dynamic_demod).
% 1.72/1.91 dependent: set(order_eq).
% 1.72/1.91 dependent: set(back_demod).
% 1.72/1.91 dependent: set(lrpo).
% 1.72/1.91
% 1.72/1.91 ------------> process usable:
% 1.72/1.91 ** KEPT (pick-wt=15): 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))!=true.
% 1.72/1.91
% 1.72/1.91 ------------> process sos:
% 1.72/1.91 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.72/1.91 ** KEPT (pick-wt=7): 3 [] ife_q(A,A,B,C)=B.
% 1.72/1.91 ---> New Demodulator: 4 [new_demod,3] ife_q(A,A,B,C)=B.
% 1.72/1.91 ** KEPT (pick-wt=7): 5 [] c_lesse_quals(v_S,v_A,tc_set(t_a))=true.
% 1.72/1.91 ---> New Demodulator: 6 [new_demod,5] c_lesse_quals(v_S,v_A,tc_set(t_a))=true.
% 1.72/1.91 ** KEPT (pick-wt=6): 7 [] c_in(v_x,v_S,t_a)=true.
% 1.72/1.91 ---> New Demodulator: 8 [new_demod,7] c_in(v_x,v_S,t_a)=true.
% 1.72/1.91 ** KEPT (pick-wt=6): 10 [copy,9,flip.1] c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)=v_A.
% 1.72/1.91 ---> New Demodulator: 11 [new_demod,10] c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit)=v_A.
% 1.72/1.91 ** KEPT (pick-wt=54): 12 [] ife_q(c_lesse_quals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),true,ife_q(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ife_q(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ife_q(c_in(D,A,C),true,c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true)=true.
% 1.72/1.92 ---> New Demodulator: 13 [new_demod,12] ife_q(c_lesse_quals(A,c_Tarski_Opotype_Opset(B,C,tc_Product__Type_Ounit),tc_set(C)),true,ife_q(c_in(B,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ife_q(c_in(B,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(C,tc_Product__Type_Ounit)),true,ife_q(c_in(D,A,C),true,c_in(c_Pair(D,c_Tarski_Olub(A,B,C),C,C),c_Tarski_Opotype_Oorder(B,C,tc_Product__Type_Ounit),tc_prod(C,C)),true),true),true),true)=true.
% 1.72/1.92 ** KEPT (pick-wt=33): 14 [] ife_q(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)),true,c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)),true)=true.
% 1.72/1.92 ---> New Demodulator: 15 [new_demod,14] ife_q(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)),true,c_in(c_Pair(B,A,C,C),c_Tarski_Opotype_Oorder(D,C,tc_Product__Type_Ounit),tc_prod(C,C)),true)=true.
% 1.72/1.92 ** KEPT (pick-wt=10): 16 [] c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))=true.
% 1.72/1.92 ---> New Demodulator: 17 [new_demod,16] c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))=true.
% 1.72/1.92 ** KEPT (pick-wt=10): 18 [] c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))=true.
% 1.72/1.92 ---> New Demodulator: 19 [new_demod,18] c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))=true.
% 1.72/1.92 ** KEPT (pick-wt=11): 21 [copy,20,flip.1] c_Tarski_Olub(A,c_Tarski_Odual(B,C),C)=c_Tarski_Oglb(A,B,C).
% 1.72/1.92 ---> New Demodulator: 22 [new_demod,21] c_Tarski_Olub(A,c_Tarski_Odual(B,C),C)=c_Tarski_Oglb(A,B,C).
% 1.72/1.92 ** KEPT (pick-wt=11): 23 [] c_Tarski_Opotype_Opset(c_Tarski_Odual(A,B),B,tc_Product__Type_Ounit)=c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit).
% 1.72/1.92 ---> New Demodulator: 24 [new_demod,23] c_Tarski_Opotype_Opset(c_Tarski_Odual(A,B),B,tc_Product__Type_Ounit)=c_Tarski_Opotype_Opset(A,B,tc_Product__Type_Ounit).
% 1.72/1.92 ** KEPT (pick-wt=6): 26 [copy,25,flip.1] c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)=v_r.
% 1.72/1.92 ---> New Demodulator: 27 [new_demod,26] c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit)=v_r.
% 1.72/1.92 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.72/1.92 >>>> Starting back demodulation with 4.
% 1.72/1.92 >>>> Starting back demodulation with 6.
% 1.72/1.92 >>>> Starting back demodulation with 8.
% 1.72/1.92 >>>> Starting back demodulation with 11.
% 1.72/1.92 >>>> Starting back demodulation with 13.
% 1.72/1.92 >>>> Starting back demodulation with 15.
% 1.72/1.92 >>>> Starting back demodulation with 17.
% 1.72/1.92 >>>> Starting back demodulation with 19.
% 1.72/1.92 >>>> Starting back demodulation with 22.
% 1.72/1.92 >>>> Starting back demodulation with 24.
% 1.72/1.92 >>>> Starting back demodulation with 27.
% 1.72/1.92
% 1.72/1.92 ======= end of input processing =======
% 1.72/1.92
% 1.72/1.92 =========== start of search ===========
% 1.72/1.92
% 1.72/1.92 -------- PROOF --------
% 1.72/1.92
% 1.72/1.92 ----> UNIT CONFLICT at 0.00 sec ----> 48 [binary,46.1,1.1] $F.
% 1.72/1.92
% 1.72/1.92 Length of proof is 7. Level of proof is 4.
% 1.72/1.92
% 1.72/1.92 ---------------- PROOF ----------------
% 1.72/1.92 % SZS status Unsatisfiable
% 1.72/1.92 % SZS output start Refutation
% See solution above
% 1.72/1.92 ------------ end of proof -------------
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Search stopped by max_proofs option.
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Search stopped by max_proofs option.
% 1.72/1.92
% 1.72/1.92 ============ end of search ============
% 1.72/1.92
% 1.72/1.92 -------------- statistics -------------
% 1.72/1.92 clauses given 15
% 1.72/1.92 clauses generated 41
% 1.72/1.92 clauses kept 23
% 1.72/1.92 clauses forward subsumed 32
% 1.72/1.92 clauses back subsumed 0
% 1.72/1.92 Kbytes malloced 2929
% 1.72/1.92
% 1.72/1.92 ----------- times (seconds) -----------
% 1.72/1.92 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.92 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.72/1.92
% 1.72/1.92 That finishes the proof of the theorem.
% 1.72/1.92
% 1.72/1.92 Process 17221 finished Wed Jul 27 08:26:22 2022
% 1.72/1.92 Otter interrupted
% 1.72/1.92 PROOF FOUND
%------------------------------------------------------------------------------