%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT268-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 01:02:28 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.62s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 32 ( 21 unt; 0 def)
% Number of atoms : 60 ( 8 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 64 ( 36 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_x,V_S,T_a,V_cl] :
( 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))
| ~ c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a))
| ~ c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit))
| ~ c_in(V_x,V_S,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_x,V_y,T_a,V_cl] :
( 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))
| ~ 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)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,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)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,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)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,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('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2750,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2751,negated_conjecture,
c_in(v_x,v_S,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2752,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)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2753,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f2754,plain,
! [X0,X1,X2,X3] :
( c_in(c_Pair(X0,c_Tarski_Olub(X1,X3,X2),X2,X2),c_Tarski_Opotype_Oorder(X3,X2,tc_Product__Type_Ounit),tc_prod(X2,X2))
| ~ c_lessequals(X1,c_Tarski_Opotype_Opset(X3,X2,tc_Product__Type_Ounit),tc_set(X2))
| ~ c_in(X3,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit))
| ~ c_in(X3,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f2755,plain,
! [X0,X1,X2,X3] :
( c_in(c_Pair(X1,X0,X2,X2),c_Tarski_Opotype_Oorder(X3,X2,tc_Product__Type_Ounit),tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X3,X2),X2,tc_Product__Type_Ounit),tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f2761,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)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f2762,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)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f2763,plain,
! [X0,X1,X2] : c_Tarski_Oglb(X0,X1,X2) = c_Tarski_Olub(X0,c_Tarski_Odual(X1,X2),X2),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f2764,plain,
! [X0,X1] : c_Tarski_Opotype_Opset(c_Tarski_Odual(X0,X1),X1,tc_Product__Type_Ounit) = c_Tarski_Opotype_Opset(X0,X1,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f2765,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f6119,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(cnf_transformation,[status(thm)],[f2750]) ).
fof(f6120,plain,
c_in(v_x,v_S,t_a),
inference(cnf_transformation,[status(thm)],[f2751]) ).
fof(f6121,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)),
inference(cnf_transformation,[status(thm)],[f2752]) ).
fof(f6123,plain,
! [X0,X1] :
( c_in(c_Pair(X1,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,X1,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)) ),
inference(paramodulation,[status(thm)],[f2765,f2755]) ).
fof(f6128,plain,
! [X0,X1,X2,X3] :
( c_in(c_Pair(X0,c_Tarski_Oglb(X1,X3,X2),X2,X2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X3,X2),X2,tc_Product__Type_Ounit),tc_prod(X2,X2))
| ~ c_lessequals(X1,c_Tarski_Opotype_Opset(c_Tarski_Odual(X3,X2),X2,tc_Product__Type_Ounit),tc_set(X2))
| ~ c_in(c_Tarski_Odual(X3,X2),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(X3,X2),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit))
| ~ c_in(X0,X1,X2) ),
inference(paramodulation,[status(thm)],[f2763,f2754]) ).
fof(f6147,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)),
inference(resolution,[status(thm)],[f6123,f6121]) ).
fof(f6165,plain,
! [X0,X1,X2,X3] :
( c_in(c_Pair(X0,c_Tarski_Oglb(X1,X3,X2),X2,X2),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X3,X2),X2,tc_Product__Type_Ounit),tc_prod(X2,X2))
| ~ c_lessequals(X1,c_Tarski_Opotype_Opset(X3,X2,tc_Product__Type_Ounit),tc_set(X2))
| ~ c_in(c_Tarski_Odual(X3,X2),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(X3,X2),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit))
| ~ c_in(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f2764,f6128]) ).
fof(f6166,plain,
( ~ c_lessequals(v_S,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(v_x,v_S,t_a) ),
inference(resolution,[status(thm)],[f6165,f6147]) ).
fof(f6167,plain,
( ~ c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(v_x,v_S,t_a) ),
inference(forward_demodulation,[status(thm)],[f2753,f6166]) ).
fof(f6168,plain,
( ~ c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(forward_subsumption_resolution,[status(thm)],[f6167,f6120]) ).
fof(f6169,plain,
( ~ c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_in(c_Tarski_Odual(v_cl,t_a),c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
inference(forward_subsumption_resolution,[status(thm)],[f6168,f2761]) ).
fof(f6170,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)),
inference(resolution,[status(thm)],[f6169,f6119]) ).
fof(f6171,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6170,f2762]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT268-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.52 % Computer : n008.cluster.edu
% 0.12/0.52 % Model : x86_64 x86_64
% 0.12/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.52 % Memory : 8046.5625MB
% 0.12/0.52 % OS : Linux 6.8.0-71-generic
% 0.12/0.52 % CPULimit : 300
% 0.12/0.52 % WCLimit : 300
% 0.12/0.52 % DateTime : Sun Sep 20 23:24:55 UTC 2026
% 0.12/0.53 % CPUTime :
% 0.17/0.58 % Drodi V4.1.1
% 0.17/0.62 % Refutation found
% 0.17/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.67 % Elapsed time: 0.141808 seconds
% 0.21/0.67 % CPU time: 0.420502 seconds
% 0.21/0.67 % Total memory used: 217.232 MB
% 0.21/0.67 % Net memory used: 216.197 MB
%------------------------------------------------------------------------------