%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT259-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 01:02:25 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 16 unt; 3 def)
% Number of atoms : 56 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 22 ~; 21 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
v_a != v_b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_r,T_a,V_V,V_U] :
( V_U = V_V
| ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Oantisym(V_r,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_P,T_a] :
( c_Relation_Oantisym(c_Tarski_Opotype_Oorder(V_P,T_a,tc_Product__Type_Ounit),T_a)
| ~ c_in(V_P,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,plain,
c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
c_in(c_Pair(v_b,v_a,t_a,t_a),v_r,tc_prod(t_a,t_a)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
v_a != v_b,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [V_V,V_U] :
( V_U = V_V
| ! [V_r,T_a] :
( ~ c_in(c_Pair(V_U,V_V,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_V,V_U,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_Relation_Oantisym(V_r,T_a) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( X3 = X2
| ~ c_in(c_Pair(X3,X2,X1,X1),X0,tc_prod(X1,X1))
| ~ c_in(c_Pair(X2,X3,X1,X1),X0,tc_prod(X1,X1))
| ~ c_Relation_Oantisym(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( c_Relation_Oantisym(c_Tarski_Opotype_Oorder(X0,X1,tc_Product__Type_Ounit),X1)
| ~ c_in(X0,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X1,tc_Product__Type_Ounit)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
c_in(v_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f16,plain,
c_Relation_Oantisym(c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),t_a),
inference(resolution,[status(thm)],[f13,f14]) ).
fof(f17,plain,
c_Relation_Oantisym(v_r,t_a),
inference(forward_demodulation,[status(thm)],[f15,f16]) ).
fof(f18,plain,
( v_b = v_a
| ~ c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Relation_Oantisym(v_r,t_a) ),
inference(resolution,[status(thm)],[f12,f9]) ).
fof(f20,definition,
( sQ0_spl
<=> c_Relation_Oantisym(v_r,t_a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( sQ0_spl
| ~ c_Relation_Oantisym(v_r,t_a) ),
inference(component_clause,[status(thm)],[f20]) ).
fof(f23,definition,
( sQ1_spl
<=> c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f25,plain,
( sQ1_spl
| ~ c_in(c_Pair(v_a,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f26,definition,
( sQ2_spl
<=> v_b = v_a ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( ~ sQ2_spl
| v_b = v_a ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f29,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f18,f20,f23,f26]) ).
fof(f34,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f10]) ).
fof(f35,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f34]) ).
fof(f36,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22,f17]) ).
fof(f37,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f36]) ).
fof(f38,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f8]) ).
fof(f39,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f38]) ).
fof(f40,plain,
$false,
inference(sat_refutation,[status(thm)],[f29,f35,f37,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT259-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 23:24:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.056085 seconds
% 0.14/0.43 % CPU time: 0.139367 seconds
% 0.14/0.43 % Total memory used: 33.221 MB
% 0.14/0.43 % Net memory used: 32.981 MB
%------------------------------------------------------------------------------