TSTP Solution File: LAT268-10 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LAT268-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n029.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 : Tue Aug 22 10:46:34 EDT 2023
% Result : Unsatisfiable 2.89s 1.77s
% Output : CNFRefutation 3.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 34
% Syntax : Number of formulae : 53 ( 31 unt; 22 typ; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 33 ( 12 >; 21 *; 0 +; 0 <<)
% 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 : 36 (; 36 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ ifeq > c_Pair > c_lessequals > c_in > c_Tarski_Opotype_Opset > c_Tarski_Opotype_Oorder > c_Tarski_Olub > c_Tarski_Oglb > tc_prod > tc_Tarski_Opotype_Opotype__ext__type > c_Tarski_Odual > #nlpp > tc_set > v_x > v_r > v_cl > v_S > v_A > true > tc_Product__Type_Ounit > t_a > c_Tarski_OPartialOrder > c_Tarski_OCompleteLattice
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(v_x,type,
v_x: $i ).
tff(v_S,type,
v_S: $i ).
tff(tc_set,type,
tc_set: $i > $i ).
tff(c_Tarski_Opotype_Opset,type,
c_Tarski_Opotype_Opset: ( $i * $i * $i ) > $i ).
tff(c_Tarski_Odual,type,
c_Tarski_Odual: ( $i * $i ) > $i ).
tff(t_a,type,
t_a: $i ).
tff(v_cl,type,
v_cl: $i ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $i ).
tff(tc_prod,type,
tc_prod: ( $i * $i ) > $i ).
tff(c_Tarski_Oglb,type,
c_Tarski_Oglb: ( $i * $i * $i ) > $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $i ).
tff(tc_Product__Type_Ounit,type,
tc_Product__Type_Ounit: $i ).
tff(c_Tarski_Opotype_Oorder,type,
c_Tarski_Opotype_Oorder: ( $i * $i * $i ) > $i ).
tff(c_Tarski_Olub,type,
c_Tarski_Olub: ( $i * $i * $i ) > $i ).
tff(v_r,type,
v_r: $i ).
tff(c_Pair,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(true,type,
true: $i ).
tff(c_Tarski_OPartialOrder,type,
c_Tarski_OPartialOrder: $i ).
tff(v_A,type,
v_A: $i ).
tff(tc_Tarski_Opotype_Opotype__ext__type,type,
tc_Tarski_Opotype_Opotype__ext__type: ( $i * $i ) > $i ).
tff(ifeq,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(c_Tarski_OCompleteLattice,type,
c_Tarski_OCompleteLattice: $i ).
tff(f_28,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(unknown,unknown) ).
tff(f_24,axiom,
! [A,B,C] : ( ifeq(A,A,B,C) = B ),
file(unknown,unknown) ).
tff(f_40,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file(unknown,unknown) ).
tff(f_25,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
file(unknown,unknown) ).
tff(f_26,axiom,
c_in(v_x,v_S,t_a) = true,
file(unknown,unknown) ).
tff(f_29,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file(unknown,unknown) ).
tff(f_39,axiom,
! [V_cl,T_a] : ( 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) ),
file(unknown,unknown) ).
tff(f_37,axiom,
! [V_S,V_cl,T_a] : ( c_Tarski_Oglb(V_S,V_cl,T_a) = c_Tarski_Olub(V_S,c_Tarski_Odual(V_cl,T_a),T_a) ),
file(unknown,unknown) ).
tff(f_35,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(unknown,unknown) ).
tff(f_34,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(unknown,unknown) ).
tff(f_31,axiom,
! [V_S,V_cl,T_a,V_x] : ( ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(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 ),
file(unknown,unknown) ).
tff(f_33,axiom,
! [V_x,V_y,T_a,V_cl] : ( ifeq(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 ),
file(unknown,unknown) ).
tff(c_8,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(cnfTransformation,[status(thm)],[f_28]) ).
tff(c_2,plain,
! [A_1,B_2,C_3] : ( ifeq(A_1,A_1,B_2,C_3) = B_2 ),
inference(cnfTransformation,[status(thm)],[f_24]) ).
tff(c_24,plain,
c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) = v_r,
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_4,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
inference(cnfTransformation,[status(thm)],[f_25]) ).
tff(c_6,plain,
c_in(v_x,v_S,t_a) = true,
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_10,plain,
c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) = v_A,
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_22,plain,
! [V_cl_15,T_a_16] : ( c_Tarski_Opotype_Opset(c_Tarski_Odual(V_cl_15,T_a_16),T_a_16,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(V_cl_15,T_a_16,tc_Product__Type_Ounit) ),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_20,plain,
! [V_S_12,V_cl_13,T_a_14] : ( c_Tarski_Olub(V_S_12,c_Tarski_Odual(V_cl_13,T_a_14),T_a_14) = c_Tarski_Oglb(V_S_12,V_cl_13,T_a_14) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_18,plain,
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,
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_16,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)) = true,
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_93,plain,
! [V_S_31,V_cl_32,T_a_33,V_x_34] : ( ifeq(c_lessequals(V_S_31,c_Tarski_Opotype_Opset(V_cl_32,T_a_33,tc_Product__Type_Ounit),tc_set(T_a_33)),true,ifeq(c_in(V_cl_32,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a_33,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl_32,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a_33,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x_34,V_S_31,T_a_33),true,c_in(c_Pair(V_x_34,c_Tarski_Olub(V_S_31,V_cl_32,T_a_33),T_a_33,T_a_33),c_Tarski_Opotype_Oorder(V_cl_32,T_a_33,tc_Product__Type_Ounit),tc_prod(T_a_33,T_a_33)),true),true),true),true) = true ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_106,plain,
! [V_S_31,V_x_34] : ( ifeq(c_lessequals(V_S_31,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(true,true,ifeq(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,ifeq(c_in(V_x_34,V_S_31,t_a),true,c_in(c_Pair(V_x_34,c_Tarski_Olub(V_S_31,c_Tarski_Odual(v_cl,t_a),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),true) = true ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_93]) ).
tff(c_136,plain,
! [V_S_35,V_x_36] : ( ifeq(c_lessequals(V_S_35,v_A,tc_set(t_a)),true,ifeq(c_in(V_x_36,V_S_35,t_a),true,c_in(c_Pair(V_x_36,c_Tarski_Oglb(V_S_35,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(demodulation,[status(thm),theory(equality)],[c_10,c_22,c_20,c_2,c_18,c_2,c_106]) ).
tff(c_146,plain,
ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),true,ifeq(true,true,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),true) = true,
inference(superposition,[status(thm),theory(equality)],[c_6,c_136]) ).
tff(c_149,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(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_4,c_146]) ).
tff(c_14,plain,
! [V_x_8,V_y_9,T_a_10,V_cl_11] : ( ifeq(c_in(c_Pair(V_x_8,V_y_9,T_a_10,T_a_10),c_Tarski_Opotype_Oorder(c_Tarski_Odual(V_cl_11,T_a_10),T_a_10,tc_Product__Type_Ounit),tc_prod(T_a_10,T_a_10)),true,c_in(c_Pair(V_y_9,V_x_8,T_a_10,T_a_10),c_Tarski_Opotype_Oorder(V_cl_11,T_a_10,tc_Product__Type_Ounit),tc_prod(T_a_10,T_a_10)),true) = true ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_162,plain,
ifeq(true,true,c_in(c_Pair(c_Tarski_Oglb(v_S,v_cl,t_a),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,
inference(superposition,[status(thm),theory(equality)],[c_149,c_14]) ).
tff(c_170,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(demodulation,[status(thm),theory(equality)],[c_2,c_24,c_162]) ).
tff(c_172,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_8,c_170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LAT268-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 12:56:37 EDT 2023
% 0.13/0.35 % CPUTime :
% 2.89/1.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.89/1.78
% 2.89/1.78 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.16/1.81
% 3.16/1.81 Inference rules
% 3.16/1.81 ----------------------
% 3.16/1.81 #Ref : 0
% 3.16/1.81 #Sup : 45
% 3.16/1.81 #Fact : 0
% 3.16/1.81 #Define : 0
% 3.16/1.81 #Split : 0
% 3.16/1.81 #Chain : 0
% 3.16/1.81 #Close : 0
% 3.16/1.81
% 3.16/1.81 Ordering : KBO
% 3.16/1.81
% 3.16/1.81 Simplification rules
% 3.16/1.81 ----------------------
% 3.16/1.81 #Subsume : 0
% 3.16/1.82 #Demod : 29
% 3.16/1.82 #Tautology : 28
% 3.16/1.82 #SimpNegUnit : 1
% 3.16/1.82 #BackRed : 0
% 3.16/1.82
% 3.16/1.82 #Partial instantiations: 0
% 3.16/1.82 #Strategies tried : 1
% 3.16/1.82
% 3.16/1.82 Timing (in seconds)
% 3.16/1.82 ----------------------
% 3.16/1.82 Preprocessing : 0.48
% 3.16/1.82 Parsing : 0.25
% 3.16/1.82 CNF conversion : 0.03
% 3.16/1.82 Main loop : 0.26
% 3.16/1.82 Inferencing : 0.10
% 3.16/1.82 Reduction : 0.09
% 3.16/1.82 Demodulation : 0.07
% 3.16/1.82 BG Simplification : 0.02
% 3.16/1.82 Subsumption : 0.04
% 3.16/1.82 Abstraction : 0.01
% 3.16/1.82 MUC search : 0.00
% 3.16/1.82 Cooper : 0.00
% 3.16/1.82 Total : 0.80
% 3.16/1.82 Index Insertion : 0.00
% 3.16/1.82 Index Deletion : 0.00
% 3.16/1.82 Index Matching : 0.00
% 3.16/1.82 BG Taut test : 0.00
%------------------------------------------------------------------------------