TSTP Solution File: LAT268-10 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT268-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n006.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 : Thu Aug 31 06:00:21 EDT 2023
% Result : Unsatisfiable 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 34
% Syntax : Number of formulae : 50 ( 28 unt; 22 typ; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 8 ( 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 : 34 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(decl_23,type,
v_S: $i ).
tff(decl_24,type,
v_A: $i ).
tff(decl_25,type,
t_a: $i ).
tff(decl_26,type,
tc_set: $i > $i ).
tff(decl_27,type,
c_lessequals: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
true: $i ).
tff(decl_29,type,
v_x: $i ).
tff(decl_30,type,
c_in: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
v_cl: $i ).
tff(decl_32,type,
c_Tarski_Oglb: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(decl_34,type,
v_r: $i ).
tff(decl_35,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_36,type,
tc_Product__Type_Ounit: $i ).
tff(decl_37,type,
c_Tarski_Opotype_Opset: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
c_Tarski_OCompleteLattice: $i ).
tff(decl_39,type,
tc_Tarski_Opotype_Opotype__ext__type: ( $i * $i ) > $i ).
tff(decl_40,type,
c_Tarski_OPartialOrder: $i ).
tff(decl_41,type,
c_Tarski_Olub: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_Tarski_Opotype_Oorder: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
c_Tarski_Odual: ( $i * $i ) > $i ).
cnf(cls_Tarski_OCL_Olub__upper_0,axiom,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),true,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_in(X4,X1,X3),true,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OCL_Olub__upper_0) ).
cnf(cls_Tarski_Odual_Acl_A_58_APartialOrder_0,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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_APartialOrder_0) ).
cnf(cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0,axiom,
c_Tarski_Opotype_Opset(c_Tarski_Odual(X1,X2),X2,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0) ).
cnf(cls_Tarski_OA_A_61_61_Apset_Acl_0,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
cnf(cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0,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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_x,v_S,t_a) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_2,negated_conjecture,
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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_Tarski_Oglb__dual__lub_0,axiom,
c_Tarski_Oglb(X1,X2,X3) = c_Tarski_Olub(X1,c_Tarski_Odual(X2,X3),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Oglb__dual__lub_0) ).
cnf(cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0,axiom,
ifeq(c_in(c_Pair(X1,X2,X3,X3),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X4,X3),X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true,c_in(c_Pair(X2,X1,X3,X3),c_Tarski_Opotype_Oorder(X4,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0) ).
cnf(cls_Tarski_Or_A_61_61_Aorder_Acl_0,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
cnf(c_0_12,axiom,
ifeq(c_lessequals(X1,c_Tarski_Opotype_Opset(X2,X3,tc_Product__Type_Ounit),tc_set(X3)),true,ifeq(c_in(X2,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_in(X2,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit)),true,ifeq(c_in(X4,X1,X3),true,c_in(c_Pair(X4,c_Tarski_Olub(X1,X2,X3),X3,X3),c_Tarski_Opotype_Oorder(X2,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true),true),true),true) = true,
cls_Tarski_OCL_Olub__upper_0 ).
cnf(c_0_13,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,
cls_Tarski_Odual_Acl_A_58_APartialOrder_0 ).
cnf(c_0_14,axiom,
c_Tarski_Opotype_Opset(c_Tarski_Odual(X1,X2),X2,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),
cls_Tarski_Opset_A_Idual_Acl_J_A_61_61_Apset_Acl_0 ).
cnf(c_0_15,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
cls_Tarski_OA_A_61_61_Apset_Acl_0 ).
cnf(c_0_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,
cls_Tarski_Odual_Acl_A_58_ACompleteLattice_0 ).
cnf(c_0_17,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_18,plain,
ifeq(c_lessequals(X1,v_A,tc_set(t_a)),true,ifeq(c_in(X2,X1,t_a),true,c_in(c_Pair(X2,c_Tarski_Olub(X1,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,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_15]),c_0_16]),c_0_17]),c_0_17]) ).
cnf(c_0_19,negated_conjecture,
c_in(v_x,v_S,t_a) = true,
cls_conjecture_1 ).
cnf(c_0_20,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
cls_conjecture_0 ).
cnf(c_0_21,negated_conjecture,
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,
cls_conjecture_2 ).
cnf(c_0_22,axiom,
c_Tarski_Oglb(X1,X2,X3) = c_Tarski_Olub(X1,c_Tarski_Odual(X2,X3),X3),
cls_Tarski_Oglb__dual__lub_0 ).
cnf(c_0_23,axiom,
ifeq(c_in(c_Pair(X1,X2,X3,X3),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X4,X3),X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true,c_in(c_Pair(X2,X1,X3,X3),c_Tarski_Opotype_Oorder(X4,X3,tc_Product__Type_Ounit),tc_prod(X3,X3)),true) = true,
cls_Tarski_O_Ix1_M_Ay1_J_A_58_Aorder_A_Idual_Acl_J_A_61_61_A_Iy1_M_Ax1_J_A_58_Aorder_Acl_0 ).
cnf(c_0_24,negated_conjecture,
c_in(c_Pair(v_x,c_Tarski_Olub(v_S,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,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_17]),c_0_17]) ).
cnf(c_0_25,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
cls_Tarski_Or_A_61_61_Aorder_Acl_0 ).
cnf(c_0_26,negated_conjecture,
c_in(c_Pair(c_Tarski_Olub(v_S,c_Tarski_Odual(v_cl,t_a),t_a),v_x,t_a,t_a),v_r,tc_prod(t_a,t_a)) != true,
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_17]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT268-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n006.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 : Thu Aug 24 07:32:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.58 % Total time : 0.005000 s
% 0.19/0.58 % SZS output end Proof
% 0.19/0.58 % Total time : 0.008000 s
%------------------------------------------------------------------------------