%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT273-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 0.09s 0.59s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 33 ( 10 unt; 2 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 87 ( 41 ~; 44 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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/sandbox/benchmark/theBenchmark.p') ).
fof(f2,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/sandbox/benchmark/theBenchmark.p') ).
fof(f3,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/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
c_in(v_b,v_A,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,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/sandbox/benchmark/theBenchmark.p') ).
fof(f8,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)],[f1]) ).
fof(f9,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)],[f8]) ).
fof(f10,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)],[f2]) ).
fof(f11,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)],[f10]) ).
fof(f12,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)],[f3]) ).
fof(f13,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)],[f12]) ).
fof(f14,plain,
c_in(v_b,v_A,t_a),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f15,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)],[f5]) ).
fof(f16,plain,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,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)],[f7]) ).
fof(f19,plain,
! [X0,X1] :
( c_in(v_sko__4mi(X0,v_r,v_b),X0,t_a)
| c_in(c_Pair(X1,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a) ),
inference(resolution,[status(thm)],[f11,f14]) ).
fof(f20,plain,
( c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a)
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f19,f16]) ).
fof(f21,definition,
( sQ0_spl
<=> c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( ~ sQ0_spl
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,definition,
( sQ1_spl
<=> c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f25,plain,
( ~ sQ1_spl
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f21,f24]) ).
fof(f28,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22,f17]) ).
fof(f29,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_lessequals(X3,c_Tarski_Ointerval(v_r,X4,X2,t_a),tc_set(t_a))
| ~ c_in(v_sko__4mi(X0,v_r,X2),X3,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(resolution,[status(thm)],[f13,f9]) ).
fof(f31,plain,
! [X0,X1,X2,X3] :
( ~ c_lessequals(X2,c_Tarski_Ointerval(v_r,X3,v_b,t_a),tc_set(t_a))
| ~ c_in(v_sko__4mi(X0,v_r,v_b),X2,t_a)
| c_in(c_Pair(X1,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a) ),
inference(resolution,[status(thm)],[f30,f14]) ).
fof(f32,plain,
! [X0,X1] :
( ~ c_in(v_sko__4mi(X0,v_r,v_b),v_S,t_a)
| c_in(c_Pair(X1,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a) ),
inference(resolution,[status(thm)],[f31,f15]) ).
fof(f33,plain,
! [X0] :
( ~ sQ1_spl
| c_in(c_Pair(X0,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(v_S,v_cl,X0,t_a) ),
inference(resolution,[status(thm)],[f32,f25]) ).
fof(f34,plain,
( ~ sQ1_spl
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f33,f16]) ).
fof(f35,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f21,f24]) ).
fof(f36,plain,
$false,
inference(sat_refutation,[status(thm)],[f27,f29,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT273-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n006.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Sun Sep 20 23:24:27 UTC 2026
% 0.09/0.56 % CPUTime :
% 0.09/0.57 % Drodi V4.1.1
% 0.09/0.59 % Refutation found
% 0.09/0.59 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.61 % Elapsed time: 0.037134 seconds
% 0.09/0.61 % CPU time: 0.097415 seconds
% 0.09/0.61 % Total memory used: 13.180 MB
% 0.09/0.61 % Net memory used: 12.823 MB
%------------------------------------------------------------------------------