%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 01:02:27 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 50 ( 50 unt; 4 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 14 con; 0-4 aty)
% Number of variables : 51 ( 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
c_in(v_x,v_S,t_a) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_S,V_cl,T_a,V_x] : ifeq(c_lessequals(V_S,c_Tarski_Opotype_Opset(V_cl,T_a,tc_Product__Type_Ounit),tc_set(T_a)),true,ifeq(c_in(V_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_cl,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(T_a,tc_Product__Type_Ounit)),true,ifeq(c_in(V_x,V_S,T_a),true,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)),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_x,V_y,T_a,V_cl] : ifeq(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)),true,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)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
c_lessequals(v_S,v_A,tc_set(t_a)) = true,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
c_in(v_x,v_S,t_a) = true,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,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)) != true,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [X0,X1,X2,X3] : ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(X1,X2,tc_Product__Type_Ounit),tc_set(X2)),true,ifeq(c_in(X1,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),true,ifeq(c_in(X1,c_Tarski_OPartialOrder,tc_Tarski_Opotype_Opotype__ext__type(X2,tc_Product__Type_Ounit)),true,ifeq(c_in(X3,X0,X2),true,c_in(c_Pair(X3,c_Tarski_Olub(X0,X1,X2),X2,X2),c_Tarski_Opotype_Oorder(X1,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),true),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f19,plain,
! [X0,X1,X2,X3] : ifeq(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)),true,c_in(c_Pair(X1,X0,X2,X2),c_Tarski_Opotype_Oorder(X3,X2,tc_Product__Type_Ounit),tc_prod(X2,X2)),true) = true,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f20,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)) = true,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f21,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)) = true,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,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)],[f10]) ).
fof(f23,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)],[f11]) ).
fof(f24,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f25,definition,
sF2_fnc = c_Tarski_Oglb(v_S,v_cl,t_a),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f26,definition,
sF1_fnc = c_Pair(sF2_fnc,v_x,t_a,t_a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f27,definition,
sF3_fnc = tc_prod(t_a,t_a),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f28,definition,
sF0_fnc = c_in(sF1_fnc,v_r,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f29,plain,
sF0_fnc != true,
inference(definition_folding,[],[f16,f28,f27,f26,f25]) ).
fof(f32,plain,
! [X0] : ifeq(c_in(c_Pair(v_x,sF2_fnc,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X0,t_a),t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true,c_in(sF1_fnc,c_Tarski_Opotype_Oorder(X0,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = true,
inference(paramodulation,[status(thm)],[f26,f19]) ).
fof(f38,plain,
! [X0] : ifeq(c_in(c_Pair(v_x,sF2_fnc,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X0,t_a),t_a,tc_Product__Type_Ounit),sF3_fnc),true,c_in(sF1_fnc,c_Tarski_Opotype_Oorder(X0,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)),true) = true,
inference(forward_demodulation,[status(thm)],[f27,f32]) ).
fof(f39,plain,
! [X0] : ifeq(c_in(c_Pair(v_x,sF2_fnc,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(X0,t_a),t_a,tc_Product__Type_Ounit),sF3_fnc),true,c_in(sF1_fnc,c_Tarski_Opotype_Oorder(X0,t_a,tc_Product__Type_Ounit),sF3_fnc),true) = true,
inference(forward_demodulation,[status(thm)],[f27,f38]) ).
fof(f44,plain,
ifeq(c_in(c_Pair(v_x,sF2_fnc,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sF3_fnc),true,c_in(sF1_fnc,v_r,sF3_fnc),true) = true,
inference(paramodulation,[status(thm)],[f24,f39]) ).
fof(f45,plain,
ifeq(c_in(c_Pair(v_x,sF2_fnc,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sF3_fnc),true,sF0_fnc,true) = true,
inference(forward_demodulation,[status(thm)],[f28,f44]) ).
fof(f79,plain,
! [X0,X1] : ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,ifeq(c_in(X1,X0,t_a),true,c_in(c_Pair(X1,c_Tarski_Olub(X0,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),true) = true,
inference(paramodulation,[status(thm)],[f21,f18]) ).
fof(f81,plain,
! [X0,X1] : ifeq(c_lessequals(X0,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),tc_set(t_a)),true,ifeq(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,ifeq(true,true,ifeq(c_in(X1,X0,t_a),true,c_in(c_Pair(X1,c_Tarski_Olub(X0,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),true) = true,
inference(forward_demodulation,[status(thm)],[f23,f79]) ).
fof(f82,plain,
! [X0,X1] : ifeq(c_lessequals(X0,v_A,tc_set(t_a)),true,ifeq(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,ifeq(true,true,ifeq(c_in(X1,X0,t_a),true,c_in(c_Pair(X1,c_Tarski_Olub(X0,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),true) = true,
inference(forward_demodulation,[status(thm)],[f17,f81]) ).
fof(f83,plain,
! [X0,X1] : ifeq(c_lessequals(X0,v_A,tc_set(t_a)),true,ifeq(true,true,ifeq(true,true,ifeq(c_in(X1,X0,t_a),true,c_in(c_Pair(X1,c_Tarski_Olub(X0,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),true) = true,
inference(forward_demodulation,[status(thm)],[f20,f82]) ).
fof(f84,plain,
! [X0,X1] : ifeq(c_lessequals(X0,v_A,tc_set(t_a)),true,ifeq(true,true,ifeq(c_in(X1,X0,t_a),true,c_in(c_Pair(X1,c_Tarski_Olub(X0,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) = true,
inference(forward_demodulation,[status(thm)],[f13,f83]) ).
fof(f85,plain,
! [X0,X1] : ifeq(c_lessequals(X0,v_A,tc_set(t_a)),true,ifeq(c_in(X1,X0,t_a),true,c_in(c_Pair(X1,c_Tarski_Olub(X0,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(forward_demodulation,[status(thm)],[f13,f84]) ).
fof(f86,plain,
! [X0,X1] : ifeq(c_lessequals(X0,v_A,tc_set(t_a)),true,ifeq(c_in(X1,X0,t_a),true,c_in(c_Pair(X1,c_Tarski_Oglb(X0,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)),true),true) = true,
inference(forward_demodulation,[status(thm)],[f22,f85]) ).
fof(f87,plain,
! [X0,X1] : ifeq(c_lessequals(X0,v_A,tc_set(t_a)),true,ifeq(c_in(X1,X0,t_a),true,c_in(c_Pair(X1,c_Tarski_Oglb(X0,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),sF3_fnc),true),true) = true,
inference(forward_demodulation,[status(thm)],[f27,f86]) ).
fof(f90,plain,
ifeq(c_lessequals(v_S,v_A,tc_set(t_a)),true,ifeq(true,true,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),sF3_fnc),true),true) = true,
inference(paramodulation,[status(thm)],[f15,f87]) ).
fof(f94,plain,
ifeq(true,true,ifeq(true,true,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),sF3_fnc),true),true) = true,
inference(forward_demodulation,[status(thm)],[f14,f90]) ).
fof(f95,plain,
ifeq(true,true,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),sF3_fnc),true) = true,
inference(forward_demodulation,[status(thm)],[f13,f94]) ).
fof(f96,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),sF3_fnc) = true,
inference(forward_demodulation,[status(thm)],[f13,f95]) ).
fof(f97,plain,
c_in(c_Pair(v_x,sF2_fnc,t_a,t_a),c_Tarski_Opotype_Oorder(c_Tarski_Odual(v_cl,t_a),t_a,tc_Product__Type_Ounit),sF3_fnc) = true,
inference(forward_demodulation,[status(thm)],[f25,f96]) ).
fof(f100,plain,
ifeq(true,true,sF0_fnc,true) = true,
inference(backward_demodulation,[status(thm)],[f97,f45]) ).
fof(f107,plain,
sF0_fnc = true,
inference(forward_demodulation,[status(thm)],[f13,f100]) ).
fof(f108,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f107,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT268-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 23:28:54 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.025876 seconds
% 0.13/0.40 % CPU time: 0.039117 seconds
% 0.13/0.40 % Total memory used: 2.105 MB
% 0.13/0.40 % Net memory used: 1.988 MB
%------------------------------------------------------------------------------