%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG349-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 11:49:15 AM UTC 2026
% Result : Unsatisfiable 31.52s 4.66s
% Output : CNFRefutation 33.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 17
% Syntax : Number of formulae : 117 ( 50 unt; 0 def)
% Number of atoms : 210 ( 125 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 149 ( 56 ~; 93 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-3 aty)
% Number of variables : 250 ( 250 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f109,axiom,
! [V_a,T_a] : ~ hBOOL(c_in(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f123,axiom,
! [T_a,V_x] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f158,axiom,
! [T_a,V_P] : hAPP(c_COMBI(T_a),V_P) = V_P,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f159,axiom,
! [V_P,T_a,T_b,V_Q] : hAPP(c_COMBK(V_P,T_a,T_b),V_Q) = V_P,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f241,axiom,
! [V_x,V_S,T_a] :
( ~ hBOOL(hAPP(V_S,V_x))
| hBOOL(c_in(V_x,V_S,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f242,axiom,
! [V_S,V_x,T_a] :
( ~ hBOOL(c_in(V_x,V_S,T_a))
| hBOOL(hAPP(V_S,V_x)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f296,axiom,
! [V_x,T_a,V_A,V_P] :
( ~ hBOOL(c_in(V_x,V_A,T_a))
| ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(c_in(V_x,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Collect(V_P,T_a)),T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f305,axiom,
hBOOL(hAPP(v_P,v_sko__local__Xex__1(v_P))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f307,axiom,
! [T_a,V_x] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)),V_x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f318,axiom,
! [V_P,T_a] : c_Collect(V_P,T_a) = V_P,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f322,axiom,
! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) = c_Collect(c_COMBK(c_True,tc_bool,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f323,axiom,
! [V_P,T_a,V_Q] :
( hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(V_P,V_Q,T_a)))
| hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(V_P,V_Q,T_a)))
| c_Collect(V_P,T_a) = c_Collect(V_Q,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f324,axiom,
! [V_P,T_a,V_Q] :
( ~ hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(V_P,V_Q,T_a)))
| ~ hBOOL(hAPP(V_Q,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(V_P,V_Q,T_a)))
| c_Collect(V_P,T_a) = c_Collect(V_Q,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f329,axiom,
hBOOL(c_in(v_sko__local__Xthx__1(v_P),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f337,axiom,
! [T_a,V_A] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool))) = V_A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f338,axiom,
! [T_a] : c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f354,negated_conjecture,
! [V_x] : ~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal),V_x)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f582,plain,
! [X0,X1] : ~ hBOOL(c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X1)),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f601,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f657,plain,
! [X0,X1] : hAPP(c_COMBI(X0),X1) = X1,
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f658,plain,
! [X0,X1,X2,X3] : hAPP(c_COMBK(X0,X1,X2),X3) = X0,
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f801,plain,
! [V_x,V_S] :
( ~ hBOOL(hAPP(V_S,V_x))
| ! [T_a] : hBOOL(c_in(V_x,V_S,T_a)) ),
inference(miniscoping,[status(thm)],[f241]) ).
fof(f802,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(c_in(X0,X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f801]) ).
fof(f803,plain,
! [V_S,V_x] :
( ! [T_a] : ~ hBOOL(c_in(V_x,V_S,T_a))
| hBOOL(hAPP(V_S,V_x)) ),
inference(miniscoping,[status(thm)],[f242]) ).
fof(f804,plain,
! [X0,X1,X2] :
( ~ hBOOL(c_in(X1,X0,X2))
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f803]) ).
fof(f892,plain,
! [V_x,T_a,V_A] :
( ~ hBOOL(c_in(V_x,V_A,T_a))
| ! [V_P] :
( ~ hBOOL(hAPP(V_P,V_x))
| hBOOL(c_in(V_x,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(T_a,tc_bool)),V_A),c_Collect(V_P,T_a)),T_a)) ) ),
inference(miniscoping,[status(thm)],[f296]) ).
fof(f893,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(c_in(X0,X2,X1))
| ~ hBOOL(hAPP(X3,X0))
| hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),c_Collect(X3,X1)),X1)) ),
inference(cnf_transformation,[status(thm)],[f892]) ).
fof(f908,plain,
hBOOL(hAPP(v_P,v_sko__local__Xex__1(v_P))),
inference(cnf_transformation,[status(thm)],[f305]) ).
fof(f911,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1)),
inference(cnf_transformation,[status(thm)],[f307]) ).
fof(f926,plain,
! [X0,X1] : c_Collect(X0,X1) = X0,
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f931,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Collect(c_COMBK(c_True,tc_bool,X0),X0),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f932,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X2,X1)))
| hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X2,X1)))
| c_Collect(X0,X1) = c_Collect(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f323]) ).
fof(f933,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X2,X1)))
| ~ hBOOL(hAPP(X2,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X2,X1)))
| c_Collect(X0,X1) = c_Collect(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f324]) ).
fof(f938,plain,
hBOOL(c_in(v_sko__local__Xthx__1(v_P),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(cnf_transformation,[status(thm)],[f329]) ).
fof(f949,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))) = X1,
inference(cnf_transformation,[status(thm)],[f337]) ).
fof(f950,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
inference(cnf_transformation,[status(thm)],[f338]) ).
fof(f975,plain,
! [X0] : ~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),c_Collect(v_P,tc_RealDef_Oreal),tc_RealDef_Oreal),X0)),
inference(cnf_transformation,[status(thm)],[f354]) ).
fof(f1034,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(c_in(X0,X2,X1))
| ~ hBOOL(hAPP(X3,X0))
| hBOOL(c_in(X0,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X1,tc_bool)),X2),X3),X1)) ),
inference(backward_demodulation,[status(thm)],[f926,f893]) ).
fof(f1044,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_COMBK(c_True,tc_bool,X0),
inference(forward_demodulation,[status(thm)],[f926,f931]) ).
fof(f1045,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X1,X2)))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X1,X2)))
| X0 = c_Collect(X1,X2) ),
inference(forward_demodulation,[status(thm)],[f926,f932]) ).
fof(f1046,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X1,X2)))
| hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X1,X2)))
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f926,f1045]) ).
fof(f1047,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X1,X2)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X1,X2)))
| X0 = c_Collect(X1,X2) ),
inference(forward_demodulation,[status(thm)],[f926,f933]) ).
fof(f1048,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X1,X2)))
| ~ hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,X1,X2)))
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f926,f1047]) ).
fof(f1049,plain,
hBOOL(c_in(v_sko__local__Xthx__1(v_P),v_P,tc_RealDef_Oreal)),
inference(forward_demodulation,[status(thm)],[f926,f938]) ).
fof(f1053,plain,
! [X0] : ~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(tc_RealDef_Oreal,tc_bool)),v_P,tc_RealDef_Oreal),X0)),
inference(forward_demodulation,[status(thm)],[f926,f975]) ).
fof(f1075,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),X2)))
| X0 = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) ),
inference(resolution,[status(thm)],[f1048,f911]) ).
fof(f1081,plain,
! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),
inference(resolution,[status(thm)],[f1075,f911]) ).
fof(f1092,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),v_P,tc_RealDef_Oreal),X1)),
inference(paramodulation,[status(thm)],[f1081,f1053]) ).
fof(f1093,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(X0,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(X0,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),X3)))
| X0 = c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)) ),
inference(paramodulation,[status(thm)],[f1081,f1075]) ).
fof(f1094,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(X0,tc_bool)),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool))) = X1,
inference(paramodulation,[status(thm)],[f1081,f949]) ).
fof(f1097,plain,
! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(paramodulation,[status(thm)],[f1081,f950]) ).
fof(f1122,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),v_P,tc_RealDef_Oreal),X1,X2)))
| c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),v_P,tc_RealDef_Oreal) = X1 ),
inference(resolution,[status(thm)],[f1092,f1046]) ).
fof(f1131,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X1,c_ATP__Linkup_Osko__Set__XCollect__cong__1__1(c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),v_P,tc_RealDef_Oreal),X1,X3)))
| c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),v_P,tc_RealDef_Oreal) = X1 ),
inference(paramodulation,[status(thm)],[f1081,f1122]) ).
fof(f1216,plain,
! [X0] :
( ~ hBOOL(hAPP(X0,v_sko__local__Xthx__1(v_P)))
| hBOOL(c_in(v_sko__local__Xthx__1(v_P),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_RealDef_Oreal,tc_bool)),v_P),X0),tc_RealDef_Oreal)) ),
inference(resolution,[status(thm)],[f1034,f1049]) ).
fof(f1239,plain,
! [X0,X1] : hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1) = c_True,
inference(paramodulation,[status(thm)],[f1044,f658]) ).
fof(f1240,plain,
! [X0,X1,X2,X3] :
( hBOOL(X1)
| c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),v_P,tc_RealDef_Oreal) = c_COMBK(X1,X2,X3) ),
inference(paramodulation,[status(thm)],[f658,f1131]) ).
fof(f1241,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(X0)
| c_COMBK(X0,X1,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) ),
inference(paramodulation,[status(thm)],[f658,f1093]) ).
fof(f1246,plain,
hBOOL(c_True),
inference(backward_demodulation,[status(thm)],[f1239,f911]) ).
fof(f1340,plain,
! [X0,X1,X2] : c_COMBK(c_True,X0,X1) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(resolution,[status(thm)],[f1241,f1246]) ).
fof(f1353,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_bool)),v_P,tc_RealDef_Oreal) = c_COMBK(X0,X5,X6)
| c_COMBK(X0,X1,X2) = c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)) ),
inference(resolution,[status(thm)],[f1241,f1240]) ).
fof(f1371,plain,
! [X0,X1,X2] : c_COMBK(c_True,X0,X1) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool)),
inference(paramodulation,[status(thm)],[f1340,f1097]) ).
fof(f1594,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X3,tc_bool)),v_P,tc_RealDef_Oreal) = c_COMBK(X2,X4,X5)
| hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1) = X2 ),
inference(paramodulation,[status(thm)],[f1353,f658]) ).
fof(f1619,plain,
! [X0,X1,X2,X3] :
( c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_bool)),v_P,tc_RealDef_Oreal) = c_COMBK(X0,X2,X3)
| c_True = X0 ),
inference(forward_demodulation,[status(thm)],[f1239,f1594]) ).
fof(f1621,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_True = X1
| c_COMBK(X1,X2,X3) = c_COMBK(X0,X4,X5)
| c_True = X0 ),
inference(paramodulation,[status(thm)],[f1619,f1619]) ).
fof(f1647,plain,
! [X0,X1,X2,X3] :
( c_True = X0
| ~ hBOOL(hAPP(c_COMBK(X0,X1,X2),X3)) ),
inference(paramodulation,[status(thm)],[f1619,f1092]) ).
fof(f1667,plain,
! [X0] :
( c_True = X0
| ~ hBOOL(X0) ),
inference(forward_demodulation,[status(thm)],[f658,f1647]) ).
fof(f1751,plain,
! [X0,X1,X2,X3,X4] :
( c_True = X4
| c_True = X0
| hAPP(c_COMBK(X0,X1,X2),X3) = X4 ),
inference(paramodulation,[status(thm)],[f1621,f658]) ).
fof(f1773,plain,
! [X0,X1] :
( c_True = X1
| c_True = X0
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f658,f1751]) ).
fof(f1776,plain,
! [X0,X1,X2] :
( c_True = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| c_True = c_COMBK(c_True,X0,X1) ),
inference(resolution,[status(thm)],[f1773,f1371]) ).
fof(f1803,plain,
! [X0,X1] :
( c_True = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| c_True != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
inference(paramodulation,[status(thm)],[f1776,f1371]) ).
fof(f1811,plain,
! [X0,X1] :
( c_True = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(c_True,X0) = c_True ),
inference(paramodulation,[status(thm)],[f1776,f658]) ).
fof(f1960,plain,
! [X0] :
( c_True = X0
| c_True = v_P
| hBOOL(hAPP(X0,v_sko__local__Xex__1(v_P))) ),
inference(paramodulation,[status(thm)],[f1773,f908]) ).
fof(f2057,plain,
! [X0,X1] : c_Lubs_OisUb(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),v_P,tc_RealDef_Oreal) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(resolution,[status(thm)],[f601,f1131]) ).
fof(f2180,plain,
! [X0] :
( c_True = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool))
| c_True = v_P ),
inference(resolution,[status(thm)],[f1960,f601]) ).
fof(f2214,plain,
! [X0] :
( c_True = v_P
| ~ hBOOL(hAPP(c_True,X0)) ),
inference(paramodulation,[status(thm)],[f2180,f601]) ).
fof(f2217,plain,
! [X0,X1] :
( c_True = v_P
| c_COMBK(c_True,X0,X1) != c_True ),
inference(paramodulation,[status(thm)],[f2180,f1371]) ).
fof(f2248,plain,
! [X0,X1,X2] :
( c_True = X0
| X0 = c_COMBK(c_True,X1,X2)
| c_True = v_P ),
inference(resolution,[status(thm)],[f2217,f1773]) ).
fof(f2333,plain,
! [X0,X1] :
( c_True = X0
| c_True = v_P
| hAPP(X0,X1) = c_True ),
inference(paramodulation,[status(thm)],[f2248,f658]) ).
fof(f2350,plain,
! [X0,X1] :
( c_True = c_COMBI(X1)
| c_True = v_P
| X0 = c_True ),
inference(paramodulation,[status(thm)],[f657,f2333]) ).
fof(f2406,plain,
! [X0] :
( c_True = v_P
| c_True = c_COMBI(X0)
| c_True = v_P ),
inference(resolution,[status(thm)],[f2350,f2217]) ).
fof(f2434,plain,
! [X0] :
( c_True = c_COMBI(X0)
| c_True = v_P ),
inference(duplicate_literals_removal,[status(thm)],[f2406]) ).
fof(f2453,plain,
! [X0] :
( c_True = v_P
| hAPP(c_True,X0) = X0 ),
inference(paramodulation,[status(thm)],[f2434,f657]) ).
fof(f2476,plain,
! [X0] :
( c_True = v_P
| c_True = v_P
| ~ hBOOL(X0) ),
inference(paramodulation,[status(thm)],[f2453,f2214]) ).
fof(f2488,plain,
! [X0] :
( c_True = X0
| c_True = v_P ),
inference(backward_subsumption_resolution,[status(thm)],[f1960,f2507]) ).
fof(f2507,plain,
! [X0] :
( c_True = v_P
| ~ hBOOL(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2476]) ).
fof(f2508,plain,
c_True = v_P,
inference(backward_subsumption_resolution,[status(thm)],[f2217,f2488]) ).
fof(f2523,plain,
! [X0,X1] :
( v_P = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| c_True != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
inference(backward_demodulation,[status(thm)],[f2508,f1803]) ).
fof(f2526,plain,
! [X0,X1] :
( v_P = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(c_True,X0) = c_True ),
inference(backward_demodulation,[status(thm)],[f2508,f1811]) ).
fof(f2528,plain,
! [X0,X1] :
( v_P = X1
| c_True = X0
| X0 = X1 ),
inference(backward_demodulation,[status(thm)],[f2508,f1773]) ).
fof(f2533,plain,
! [X0] :
( v_P = X0
| ~ hBOOL(X0) ),
inference(backward_demodulation,[status(thm)],[f2508,f1667]) ).
fof(f2542,plain,
! [X0,X1,X2] : c_COMBK(v_P,X0,X1) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_bool)),
inference(backward_demodulation,[status(thm)],[f2508,f1340]) ).
fof(f2544,plain,
hBOOL(v_P),
inference(backward_demodulation,[status(thm)],[f2508,f1246]) ).
fof(f2691,plain,
! [X0,X1] :
( v_P = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| v_P != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) ),
inference(forward_demodulation,[status(thm)],[f2508,f2523]) ).
fof(f2695,plain,
! [X0,X1] :
( v_P = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(v_P,X0) = c_True ),
inference(forward_demodulation,[status(thm)],[f2508,f2526]) ).
fof(f2696,plain,
! [X0,X1] :
( v_P = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(v_P,X0) = v_P ),
inference(forward_demodulation,[status(thm)],[f2508,f2695]) ).
fof(f2699,plain,
! [X0,X1] :
( v_P = X1
| v_P = X0
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f2508,f2528]) ).
fof(f3026,plain,
! [X0,X1] : hAPP(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool)),X1) = v_P,
inference(paramodulation,[status(thm)],[f2542,f658]) ).
fof(f3303,plain,
! [X0,X1,X2] :
( v_P = c_in(X1,X0,X2)
| ~ hBOOL(hAPP(X0,X1)) ),
inference(resolution,[status(thm)],[f802,f2533]) ).
fof(f3400,plain,
! [X0,X1,X2] :
( v_P = c_in(X0,c_COMBI(X1),X2)
| ~ hBOOL(X0) ),
inference(paramodulation,[status(thm)],[f657,f3303]) ).
fof(f3408,plain,
! [X0,X1] : v_P = c_in(v_P,c_COMBI(X0),X1),
inference(resolution,[status(thm)],[f3400,f2544]) ).
fof(f3425,plain,
! [X0,X1,X2] :
( v_P = X0
| v_P = c_COMBI(X2)
| v_P = c_in(v_P,X0,X1) ),
inference(paramodulation,[status(thm)],[f2699,f3408]) ).
fof(f3881,plain,
! [X0] :
( ~ hBOOL(v_P)
| hBOOL(c_in(v_sko__local__Xthx__1(v_P),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(tc_RealDef_Oreal,tc_bool)),v_P),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_bool))),tc_RealDef_Oreal)) ),
inference(paramodulation,[status(thm)],[f3026,f1216]) ).
fof(f3902,plain,
( ~ hBOOL(v_P)
| hBOOL(c_in(v_sko__local__Xthx__1(v_P),v_P,tc_RealDef_Oreal)) ),
inference(forward_demodulation,[status(thm)],[f1094,f3881]) ).
fof(f3903,plain,
hBOOL(c_in(v_sko__local__Xthx__1(v_P),v_P,tc_RealDef_Oreal)),
inference(forward_subsumption_resolution,[status(thm)],[f3902,f2544]) ).
fof(f3915,plain,
hBOOL(hAPP(v_P,v_sko__local__Xthx__1(v_P))),
inference(resolution,[status(thm)],[f3903,f804]) ).
fof(f3945,plain,
v_P = hAPP(v_P,v_sko__local__Xthx__1(v_P)),
inference(resolution,[status(thm)],[f3915,f2533]) ).
fof(f4417,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),
inference(paramodulation,[status(thm)],[f2057,f2057]) ).
fof(f4511,plain,
! [X0,X1,X2] : ~ hBOOL(c_in(X0,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2)),
inference(paramodulation,[status(thm)],[f4417,f582]) ).
fof(f5918,plain,
! [X0,X1] :
( v_P = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| v_P = c_COMBI(X0)
| ~ hBOOL(v_P) ),
inference(paramodulation,[status(thm)],[f3425,f4511]) ).
fof(f5930,plain,
! [X0,X1] :
( v_P = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| v_P = c_COMBI(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f5918,f2544]) ).
fof(f5952,plain,
! [X0,X1] :
( v_P = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| hAPP(v_P,X0) = X0 ),
inference(paramodulation,[status(thm)],[f5930,f657]) ).
fof(f6013,plain,
! [X0,X1,X2] :
( v_P = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_bool))
| v_P = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| v_P = X0 ),
inference(paramodulation,[status(thm)],[f2696,f5952]) ).
fof(f6039,plain,
! [X0] : v_P = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_bool)),
inference(backward_subsumption_resolution,[status(thm)],[f2691,f6042]) ).
fof(f6042,plain,
! [X0,X1] :
( v_P = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool))
| v_P = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f6013,f2691]) ).
fof(f6058,plain,
! [X0] : ~ hBOOL(hAPP(v_P,X0)),
inference(backward_demodulation,[status(thm)],[f6039,f601]) ).
fof(f6829,plain,
~ hBOOL(v_P),
inference(paramodulation,[status(thm)],[f3945,f6058]) ).
fof(f6836,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6829,f2544]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG349-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 13:14:50 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.14/0.41 % Drodi V4.1.1
% 31.52/4.66 % Refutation found
% 31.52/4.66 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 31.52/4.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.37/4.83 % Elapsed time: 4.437786 seconds
% 2.37/4.83 % CPU time: 34.023781 seconds
% 2.37/4.83 % Total memory used: 488.074 MB
% 2.37/4.83 % Net memory used: 447.224 MB
%------------------------------------------------------------------------------