%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT273-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:02:29 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.69s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 16 unt; 5 def)
% Number of atoms : 104 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 118 ( 62 ~; 51 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [V_x,V_S,T_a,V_r,V_a,V_b] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [V_S,V_L,V_z] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [V_S,V_L,V_z] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1693,axiom,
! [V_A,T_a] : c_lessequals(c_emptyset,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2753,negated_conjecture,
c_in(v_b,v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2754,negated_conjecture,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2755,negated_conjecture,
v_S != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2756,negated_conjecture,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2758,negated_conjecture,
~ c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2769,plain,
! [V_x,T_a,V_r,V_b] :
( c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ! [V_S] :
( ! [V_a] : ~ c_lessequals(V_S,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),tc_set(T_a))
| ~ c_in(V_x,V_S,T_a) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f2770,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_in(c_Pair(X0,X5,X2,X2),X3,tc_prod(X2,X2))
| ~ c_lessequals(X1,c_Tarski_Ointerval(X3,X4,X5,X2),tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f2769]) ).
fof(f2776,plain,
! [V_S,V_z] :
( c_in(v_sko__4mi(V_S,v_r,V_z),V_S,t_a)
| ! [V_L] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f2777,plain,
! [X0,X1,X2] :
( c_in(v_sko__4mi(X0,v_r,X2),X0,t_a)
| c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X2,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a) ),
inference(cnf_transformation,[status(thm)],[f2776]) ).
fof(f2778,plain,
! [V_L,V_z] :
( c_in(c_Pair(V_L,V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ! [V_S] :
( ~ c_in(c_Pair(v_sko__4mi(V_S,v_r,V_z),V_z,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_z,v_A,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f2779,plain,
! [X0,X1,X2] :
( c_in(c_Pair(X1,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mi(X0,v_r,X2),X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X2,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a) ),
inference(cnf_transformation,[status(thm)],[f2778]) ).
fof(f5064,plain,
! [X0,X1] : c_lessequals(c_emptyset,X0,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f1693]) ).
fof(f6138,plain,
c_in(v_b,v_A,t_a),
inference(cnf_transformation,[status(thm)],[f2753]) ).
fof(f6139,plain,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
inference(cnf_transformation,[status(thm)],[f2754]) ).
fof(f6140,plain,
v_S != c_emptyset,
inference(cnf_transformation,[status(thm)],[f2755]) ).
fof(f6141,plain,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
inference(cnf_transformation,[status(thm)],[f2756]) ).
fof(f6143,plain,
~ c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(thm)],[f2758]) ).
fof(f6166,definition,
! [X0] :
( sQ3_spl
<=> ~ c_lessequals(c_emptyset,X0,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f6167,plain,
! [X0] :
( ~ sQ3_spl
| ~ c_lessequals(c_emptyset,X0,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f6166]) ).
fof(f6200,plain,
! [X0] :
( c_in(v_sko__4mi(X0,v_r,v_b),X0,t_a)
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ),
inference(resolution,[status(thm)],[f2777,f6143]) ).
fof(f6201,definition,
! [X0] :
( sQ7_spl
<=> ( c_in(v_sko__4mi(X0,v_r,v_b),X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f6202,plain,
! [X0] :
( ~ sQ7_spl
| c_in(v_sko__4mi(X0,v_r,v_b),X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ),
inference(component_clause,[status(thm)],[f6201]) ).
fof(f6204,definition,
( sQ8_spl
<=> c_in(v_b,v_A,t_a) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f6206,plain,
( sQ8_spl
| ~ c_in(v_b,v_A,t_a) ),
inference(component_clause,[status(thm)],[f6204]) ).
fof(f6207,plain,
( ~ sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f6200,f6201,f6204]) ).
fof(f6208,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6206,f6138]) ).
fof(f6209,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f6208]) ).
fof(f6245,plain,
! [X0] :
( ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ),
inference(resolution,[status(thm)],[f2779,f6143]) ).
fof(f6246,definition,
! [X0] :
( sQ10_spl
<=> ( ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f6247,plain,
! [X0] :
( ~ sQ10_spl
| ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ),
inference(component_clause,[status(thm)],[f6246]) ).
fof(f6249,plain,
( ~ sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f6245,f6246,f6204]) ).
fof(f6252,plain,
( ~ sQ7_spl
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolution,[status(thm)],[f6202,f6141]) ).
fof(f6282,plain,
( ~ sQ10_spl
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f6247,f6141]) ).
fof(f6317,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ c_lessequals(X0,c_Tarski_Ointerval(v_r,X1,v_b,t_a),tc_set(t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),X0,t_a) ),
inference(resolution,[status(thm)],[f6282,f2770]) ).
fof(f6337,definition,
( sQ22_spl
<=> v_S = c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f6338,plain,
( ~ sQ22_spl
| v_S = c_emptyset ),
inference(component_clause,[status(thm)],[f6337]) ).
fof(f6342,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6167,f5064]) ).
fof(f6343,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f6342]) ).
fof(f6344,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6338,f6140]) ).
fof(f6345,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f6344]) ).
fof(f6366,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ10_spl
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,X0,v_b,t_a),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f6317,f6252]) ).
fof(f6373,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6139,f6366]) ).
fof(f6374,plain,
( ~ sQ7_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f6373]) ).
fof(f6375,plain,
$false,
inference(sat_refutation,[status(thm)],[f6207,f6209,f6249,f6343,f6345,f6374]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT273-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.53 % Computer : n004.cluster.edu
% 0.09/0.53 % Model : x86_64 x86_64
% 0.09/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.53 % Memory : 8046.5625MB
% 0.09/0.53 % OS : Linux 6.8.0-71-generic
% 0.09/0.53 % CPULimit : 300
% 0.09/0.53 % WCLimit : 300
% 0.09/0.53 % DateTime : Sun Sep 20 23:24:35 UTC 2026
% 0.09/0.53 % CPUTime :
% 0.13/0.65 % Drodi V4.1.1
% 0.13/0.69 % Refutation found
% 0.13/0.69 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.74 % Elapsed time: 0.198462 seconds
% 0.13/0.74 % CPU time: 0.427894 seconds
% 0.13/0.74 % Total memory used: 117.000 MB
% 0.13/0.74 % Net memory used: 116.422 MB
%------------------------------------------------------------------------------