%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT274-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12.55s 2.05s
% Output : CNFRefutation 12.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 52
% Syntax : Number of formulae : 179 ( 34 unt; 29 def)
% Number of atoms : 469 ( 39 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 512 ( 222 ~; 261 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 35 ( 33 usr; 30 prp; 0-4 aty)
% Number of functors : 21 ( 21 usr; 13 con; 0-4 aty)
% Number of variables : 215 ( 215 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_S,V_A,V_a,V_L] :
( V_S = c_emptyset
| c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_L,V_S,V_A,V_a] :
( V_S = c_emptyset
| c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_a,V_S,V_A,V_L] :
( V_S = c_emptyset
| c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_a,V_S,V_L,V_A] :
( V_S = c_emptyset
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_x,V_S,T_a,V_r,V_a,V_b] :
( c_in(c_Pair(V_a,V_x,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_x,V_b,T_a,V_r,V_a] :
( c_in(V_x,c_Tarski_Ointerval(V_r,V_a,V_b,T_a),T_a)
| ~ c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ~ c_in(c_Pair(V_x,V_b,T_a,T_a),V_r,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [V_S,V_L,V_y] :
( c_in(c_Pair(V_y,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_y,V_S,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f142,axiom,
! [T_a] :
( c_Finite__Set_Ocard(c_emptyset,T_a) = c_0
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f143,axiom,
! [T_a] : c_Finite__Set_Ocard(c_emptyset,T_a) = c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1260,axiom,
! [T_a] :
( c_0 != c_1
| ~ class_Ring__and__Field_Oaxclass__0__neq__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1537,axiom,
! [V_c,T_a] : ~ c_in(V_c,c_emptyset,T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1620,axiom,
! [T_a] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1693,axiom,
! [V_A,T_a] : c_lessequals(c_emptyset,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1704,axiom,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f1795,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2753,negated_conjecture,
c_in(v_b,v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2754,negated_conjecture,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2755,negated_conjecture,
v_S != c_emptyset,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2756,negated_conjecture,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2758,negated_conjecture,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2759,plain,
! [V_S] :
( V_S = c_emptyset
| ! [V_L] :
( c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| ! [V_a] :
( c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ! [V_A] : ~ c_lessequals(V_S,V_A,tc_set(t_a)) ) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f2760,plain,
! [X0,X1,X2,X3] :
( X0 = c_emptyset
| c_in(v_sko__4mk(X3,X0,v_r),X0,t_a)
| c_in(v_sko__4mj(X0,X2,v_r),X0,t_a)
| c_in(c_Pair(X2,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X0,X1,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f2759]) ).
fof(f2761,plain,
! [V_S] :
( V_S = c_emptyset
| ! [V_a] :
( c_in(v_sko__4mj(V_S,V_a,v_r),V_S,t_a)
| ! [V_L] :
( c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ! [V_A] : ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f2762,plain,
! [X0,X1,X2,X3] :
( X1 = c_emptyset
| c_in(v_sko__4mj(X1,X3,v_r),X1,t_a)
| c_in(c_Pair(X3,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X2,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(X0,X1,v_r),X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f2761]) ).
fof(f2763,plain,
! [V_S] :
( V_S = c_emptyset
| ! [V_L] :
( c_in(v_sko__4mk(V_L,V_S,v_r),V_S,t_a)
| ! [V_a] :
( c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ! [V_A] : ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f2764,plain,
! [X0,X1,X2,X3] :
( X1 = c_emptyset
| c_in(v_sko__4mk(X3,X1,v_r),X1,t_a)
| c_in(c_Pair(X0,X3,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X2,tc_set(t_a))
| ~ c_in(c_Pair(X0,v_sko__4mj(X1,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f2763]) ).
fof(f2765,plain,
! [V_S] :
( V_S = c_emptyset
| ! [V_a,V_L] :
( c_in(c_Pair(V_a,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ! [V_A] : ~ c_lessequals(V_S,V_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(V_a,v_sko__4mj(V_S,V_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f2766,plain,
! [X0,X1,X2,X3] :
( X1 = c_emptyset
| c_in(c_Pair(X0,X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,X3,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(X2,X1,v_r),X2,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,v_sko__4mj(X1,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f2765]) ).
fof(f2767,plain,
! [V_x,T_a,V_r,V_a] :
( c_in(c_Pair(V_a,V_x,T_a,T_a),V_r,tc_prod(T_a,T_a))
| ! [V_S] :
( ! [V_b] : ~ 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)],[f5]) ).
fof(f2768,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_in(c_Pair(X4,X0,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)],[f2767]) ).
fof(f2769,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)],[f6]) ).
fof(f2770,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)],[f2769]) ).
fof(f2771,plain,
! [X0,X1,X2,X3,X4] :
( c_in(X0,c_Tarski_Ointerval(X3,X4,X1,X2),X2)
| ~ c_in(c_Pair(X4,X0,X2,X2),X3,tc_prod(X2,X2))
| ~ c_in(c_Pair(X0,X1,X2,X2),X3,tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f2774,plain,
! [V_L,V_y] :
( c_in(c_Pair(V_y,V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ! [V_S] :
( ~ c_in(V_y,V_S,t_a)
| ~ c_Tarski_OisLub(V_S,v_cl,V_L,t_a) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f2775,plain,
! [X0,X1,X2] :
( c_in(c_Pair(X2,X1,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X2,X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,X1,t_a) ),
inference(cnf_transformation,[status(thm)],[f2774]) ).
fof(f2776,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)],[f10]) ).
fof(f2777,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)],[f2776]) ).
fof(f2778,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)],[f11]) ).
fof(f2779,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)],[f2778]) ).
fof(f2953,plain,
! [X0] :
( c_Finite__Set_Ocard(c_emptyset,X0) = c_0
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f2954,plain,
! [X0] : c_Finite__Set_Ocard(c_emptyset,X0) = c_0,
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f4468,plain,
( c_0 != c_1
| ! [T_a] : ~ class_Ring__and__Field_Oaxclass__0__neq__1(T_a) ),
inference(miniscoping,[status(thm)],[f1260]) ).
fof(f4469,plain,
! [X0] :
( c_0 != c_1
| ~ class_Ring__and__Field_Oaxclass__0__neq__1(X0) ),
inference(cnf_transformation,[status(thm)],[f4468]) ).
fof(f4861,plain,
! [X0,X1] : ~ c_in(X0,c_emptyset,X1),
inference(cnf_transformation,[status(thm)],[f1537]) ).
fof(f4977,plain,
! [X0] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)),
inference(cnf_transformation,[status(thm)],[f1620]) ).
fof(f5064,plain,
! [X0,X1] : c_lessequals(c_emptyset,X0,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f1693]) ).
fof(f5080,plain,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[status(thm)],[f1704]) ).
fof(f5178,plain,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
inference(cnf_transformation,[status(thm)],[f1795]) ).
fof(f6138,plain,
c_in(v_b,v_A,t_a),
inference(cnf_transformation,[status(thm)],[f2753]) ).
fof(f6139,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)],[f2754]) ).
fof(f6140,plain,
v_S != c_emptyset,
inference(cnf_transformation,[status(thm)],[f2755]) ).
fof(f6141,plain,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
inference(cnf_transformation,[status(thm)],[f2756]) ).
fof(f6143,plain,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
inference(cnf_transformation,[status(thm)],[f2758]) ).
fof(f6144,definition,
! [X0] :
( sQ0_spl
<=> ~ class_Ring__and__Field_Oaxclass__0__neq__1(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f6145,plain,
! [X0] :
( ~ sQ0_spl
| ~ class_Ring__and__Field_Oaxclass__0__neq__1(X0) ),
inference(component_clause,[status(thm)],[f6144]) ).
fof(f6147,definition,
( sQ1_spl
<=> c_0 = c_1 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f6150,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f4469,f6144,f6147]) ).
fof(f6153,plain,
! [X0] :
( c_0 = c_0
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)) ),
inference(backward_demodulation,[status(thm)],[f2954,f2953]) ).
fof(f6267,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f5178,f6145]) ).
fof(f6282,definition,
! [X0] :
( sQ2_spl
<=> ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f6283,plain,
! [X0] :
( ~ sQ2_spl
| ~ c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)) ),
inference(component_clause,[status(thm)],[f6282]) ).
fof(f6285,definition,
( sQ3_spl
<=> c_0 = c_0 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f6288,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f6153,f6282,f6285]) ).
fof(f6303,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f6267]) ).
fof(f6304,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6283,f4977]) ).
fof(f6305,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f6304]) ).
fof(f6312,plain,
! [X0,X1,X2,X3,X4] :
( ~ c_lessequals(X1,c_Tarski_Ointerval(c_emptyset,X3,X4,X2),tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(resolution,[status(thm)],[f2768,f4861]) ).
fof(f6331,plain,
! [X0,X1,X2,X3] : ~ c_in(X0,c_Tarski_Ointerval(c_emptyset,X1,X2,X3),X3),
inference(resolution,[status(thm)],[f6312,f5080]) ).
fof(f6340,plain,
( ~ c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,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)],[f2771,f6143]) ).
fof(f6345,definition,
( sQ6_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,[sQ6_spl])],[split_symbol_definition]) ).
fof(f6347,plain,
( sQ6_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)],[f6345]) ).
fof(f6348,definition,
( sQ7_spl
<=> c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f6350,plain,
( sQ7_spl
| ~ c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f6348]) ).
fof(f6351,plain,
( ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f6340,f6345,f6348]) ).
fof(f6373,plain,
! [X0] :
( sQ6_spl
| c_in(v_sko__4mi(X0,v_r,v_b),X0,t_a)
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ),
inference(resolution,[status(thm)],[f2777,f6347]) ).
fof(f6374,definition,
! [X0] :
( sQ10_spl
<=> ( c_in(v_sko__4mi(X0,v_r,v_b),X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f6375,plain,
! [X0] :
( ~ sQ10_spl
| c_in(v_sko__4mi(X0,v_r,v_b),X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ),
inference(component_clause,[status(thm)],[f6374]) ).
fof(f6377,definition,
( sQ11_spl
<=> c_in(v_b,v_A,t_a) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f6379,plain,
( sQ11_spl
| ~ c_in(v_b,v_A,t_a) ),
inference(component_clause,[status(thm)],[f6377]) ).
fof(f6380,plain,
( sQ6_spl
| ~ sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f6373,f6374,f6377,f6345]) ).
fof(f6381,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6379,f6138]) ).
fof(f6382,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f6381]) ).
fof(f6383,plain,
! [X0] :
( sQ7_spl
| ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_L),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_L,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_a,t_a) ),
inference(resolution,[status(thm)],[f6350,f2779]) ).
fof(f6384,plain,
! [X0] :
( sQ7_spl
| c_in(v_sko__4mi(X0,v_r,v_L),X0,t_a)
| ~ c_in(v_L,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_a,t_a) ),
inference(resolution,[status(thm)],[f6350,f2777]) ).
fof(f6385,plain,
! [X0,X1] :
( sQ7_spl
| X0 = c_emptyset
| ~ c_lessequals(X0,X1,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(v_L,X0,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_a,v_sko__4mj(X0,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f6350,f2766]) ).
fof(f6387,plain,
! [X0,X1] :
( sQ7_spl
| X0 = c_emptyset
| c_in(v_sko__4mk(v_L,X0,v_r),X0,t_a)
| ~ c_lessequals(X0,X1,tc_set(t_a))
| ~ c_in(c_Pair(v_a,v_sko__4mj(X0,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f6350,f2764]) ).
fof(f6388,plain,
! [X0,X1] :
( sQ7_spl
| X0 = c_emptyset
| c_in(v_sko__4mj(X0,v_a,v_r),X0,t_a)
| ~ c_lessequals(X0,X1,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(v_L,X0,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f6350,f2762]) ).
fof(f6389,plain,
! [X0,X1] :
( sQ7_spl
| X0 = c_emptyset
| c_in(v_sko__4mk(v_L,X0,v_r),X0,t_a)
| c_in(v_sko__4mj(X0,v_a,v_r),X0,t_a)
| ~ c_lessequals(X0,X1,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f6350,f2760]) ).
fof(f6393,definition,
! [X0] :
( sQ12_spl
<=> ( ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_L),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X0,v_cl,v_a,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f6396,definition,
( sQ13_spl
<=> c_in(v_L,v_A,t_a) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f6399,plain,
( sQ7_spl
| ~ sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f6383,f6393,f6396,f6348]) ).
fof(f6400,definition,
! [X0] :
( sQ14_spl
<=> ( c_in(v_sko__4mi(X0,v_r,v_L),X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_a,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f6403,plain,
( sQ7_spl
| ~ sQ13_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f6384,f6400,f6396,f6348]) ).
fof(f6413,plain,
( ~ sQ10_spl
| c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolution,[status(thm)],[f6375,f6141]) ).
fof(f6431,plain,
( sQ7_spl
| v_S = c_emptyset
| ~ c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f6385,f6139]) ).
fof(f6437,definition,
( sQ17_spl
<=> c_in(c_Pair(v_sko__4mk(v_L,c_emptyset,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f6439,plain,
( sQ17_spl
| ~ c_in(c_Pair(v_sko__4mk(v_L,c_emptyset,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f6437]) ).
fof(f6440,definition,
( sQ18_spl
<=> c_emptyset = c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f6444,definition,
( sQ19_spl
<=> c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f6446,plain,
( sQ19_spl
| ~ c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f6444]) ).
fof(f6447,definition,
( sQ20_spl
<=> c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f6449,plain,
( sQ20_spl
| ~ c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f6447]) ).
fof(f6450,definition,
( sQ21_spl
<=> v_S = c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f6451,plain,
( ~ sQ21_spl
| v_S = c_emptyset ),
inference(component_clause,[status(thm)],[f6450]) ).
fof(f6453,plain,
( sQ7_spl
| sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f6431,f6444,f6447,f6450,f6348]) ).
fof(f6454,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6451,f6140]) ).
fof(f6455,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f6454]) ).
fof(f6459,definition,
! [X0] :
( sQ22_spl
<=> ~ c_lessequals(c_emptyset,X0,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f6460,plain,
! [X0] :
( ~ sQ22_spl
| ~ c_lessequals(c_emptyset,X0,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f6459]) ).
fof(f6471,plain,
! [X0,X1] :
( sQ19_spl
| ~ c_lessequals(X0,c_Tarski_Ointerval(v_r,v_a,X1,t_a),tc_set(t_a))
| ~ c_in(v_sko__4mj(v_S,v_a,v_r),X0,t_a) ),
inference(resolution,[status(thm)],[f6446,f2768]) ).
fof(f6493,definition,
! [X0] :
( sQ26_spl
<=> ~ c_lessequals(v_S,X0,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f6494,plain,
! [X0] :
( ~ sQ26_spl
| ~ c_lessequals(v_S,X0,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f6493]) ).
fof(f6501,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6460,f5064]) ).
fof(f6502,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f6501]) ).
fof(f6503,plain,
( ~ sQ26_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6139,f6494]) ).
fof(f6504,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f6503]) ).
fof(f6508,plain,
! [X0] :
( sQ20_spl
| ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_L),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_L,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_sko__4mk(v_L,v_S,v_r),t_a) ),
inference(resolution,[status(thm)],[f6449,f2779]) ).
fof(f6509,plain,
! [X0] :
( sQ20_spl
| c_in(v_sko__4mi(X0,v_r,v_L),X0,t_a)
| ~ c_in(v_L,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_sko__4mk(v_L,v_S,v_r),t_a) ),
inference(resolution,[status(thm)],[f6449,f2777]) ).
fof(f6511,plain,
! [X0] :
( sQ20_spl
| ~ c_in(v_sko__4mk(v_L,v_S,v_r),X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ),
inference(resolution,[status(thm)],[f6449,f2775]) ).
fof(f6518,definition,
! [X0] :
( sQ28_spl
<=> ( ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_L),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X0,v_cl,v_sko__4mk(v_L,v_S,v_r),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f6521,plain,
( sQ20_spl
| ~ sQ13_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f6508,f6518,f6396,f6447]) ).
fof(f6522,definition,
! [X0] :
( sQ29_spl
<=> ( c_in(v_sko__4mi(X0,v_r,v_L),X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_sko__4mk(v_L,v_S,v_r),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f6525,plain,
( sQ20_spl
| ~ sQ13_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f6509,f6522,f6396,f6447]) ).
fof(f6529,plain,
! [X0] :
( sQ17_spl
| ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_L),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_L,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_sko__4mk(v_L,c_emptyset,v_r),t_a) ),
inference(resolution,[status(thm)],[f6439,f2779]) ).
fof(f6530,plain,
! [X0] :
( sQ17_spl
| c_in(v_sko__4mi(X0,v_r,v_L),X0,t_a)
| ~ c_in(v_L,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_sko__4mk(v_L,c_emptyset,v_r),t_a) ),
inference(resolution,[status(thm)],[f6439,f2777]) ).
fof(f6539,definition,
! [X0] :
( sQ30_spl
<=> ( ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_L),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X0,v_cl,v_sko__4mk(v_L,c_emptyset,v_r),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f6542,plain,
( sQ17_spl
| ~ sQ13_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f6529,f6539,f6396,f6437]) ).
fof(f6543,definition,
! [X0] :
( sQ31_spl
<=> ( c_in(v_sko__4mi(X0,v_r,v_L),X0,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_sko__4mk(v_L,c_emptyset,v_r),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f6546,plain,
( sQ17_spl
| ~ sQ13_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f6530,f6543,f6396,f6437]) ).
fof(f6572,definition,
( sQ35_spl
<=> c_lessequals(c_emptyset,v_A,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f6574,plain,
( sQ35_spl
| ~ c_lessequals(c_emptyset,v_A,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f6572]) ).
fof(f6576,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6574,f5064]) ).
fof(f6577,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f6576]) ).
fof(f6591,plain,
! [X0,X1,X2] :
( sQ7_spl
| c_Tarski_Ointerval(c_emptyset,X0,X1,t_a) = c_emptyset
| c_in(v_sko__4mj(c_Tarski_Ointerval(c_emptyset,X0,X1,t_a),v_a,v_r),c_Tarski_Ointerval(c_emptyset,X0,X1,t_a),t_a)
| ~ c_lessequals(c_Tarski_Ointerval(c_emptyset,X0,X1,t_a),X2,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f6389,f6331]) ).
fof(f6592,plain,
! [X0] :
( sQ7_spl
| c_emptyset = c_emptyset
| c_in(v_sko__4mj(c_emptyset,v_a,v_r),c_emptyset,t_a)
| ~ c_lessequals(c_emptyset,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f6389,f4861]) ).
fof(f6594,plain,
! [X0,X1,X2] :
( sQ7_spl
| c_Tarski_Ointerval(c_emptyset,X0,X1,t_a) = c_emptyset
| ~ c_lessequals(c_Tarski_Ointerval(c_emptyset,X0,X1,t_a),X2,tc_set(t_a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f6591,f6331]) ).
fof(f6595,definition,
( sQ36_spl
<=> c_in(v_sko__4mj(c_emptyset,v_a,v_r),c_emptyset,t_a) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f6596,plain,
( ~ sQ36_spl
| c_in(v_sko__4mj(c_emptyset,v_a,v_r),c_emptyset,t_a) ),
inference(component_clause,[status(thm)],[f6595]) ).
fof(f6598,plain,
( sQ7_spl
| sQ18_spl
| sQ36_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f6592,f6459,f6595,f6440,f6348]) ).
fof(f6599,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6596,f4861]) ).
fof(f6600,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f6599]) ).
fof(f6603,plain,
! [X0] :
( sQ6_spl
| ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_b,v_A,t_a)
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ),
inference(resolution,[status(thm)],[f6347,f2779]) ).
fof(f6613,definition,
! [X0] :
( sQ37_spl
<=> ( ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f6614,plain,
! [X0] :
( ~ sQ37_spl
| ~ c_in(c_Pair(v_sko__4mi(X0,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(X0,v_cl,v_L,t_a) ),
inference(component_clause,[status(thm)],[f6613]) ).
fof(f6616,plain,
( sQ6_spl
| ~ sQ11_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f6603,f6613,f6377,f6345]) ).
fof(f6660,plain,
( ~ sQ37_spl
| ~ c_in(c_Pair(v_sko__4mi(v_S,v_r,v_b),v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f6614,f6141]) ).
fof(f6671,plain,
! [X0,X1] :
( sQ7_spl
| c_Tarski_Ointerval(c_emptyset,X0,X1,t_a) = c_emptyset ),
inference(resolution,[status(thm)],[f6594,f5080]) ).
fof(f6673,definition,
! [X0,X1,X2] :
( sQ40_spl
<=> ~ c_lessequals(c_Tarski_Ointerval(c_emptyset,X0,X1,t_a),X2,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f6674,plain,
! [X0,X1,X2] :
( ~ sQ40_spl
| ~ c_lessequals(c_Tarski_Ointerval(c_emptyset,X0,X1,t_a),X2,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f6673]) ).
fof(f6677,plain,
! [X0] :
( ~ sQ40_spl
| sQ7_spl
| ~ c_lessequals(c_emptyset,X0,tc_set(t_a)) ),
inference(forward_demodulation,[status(thm)],[f6671,f6674]) ).
fof(f6678,plain,
( ~ sQ40_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6677,f5064]) ).
fof(f6679,plain,
( ~ sQ40_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f6678]) ).
fof(f6728,plain,
! [X0,X1] :
( ~ sQ37_spl
| ~ c_lessequals(X0,c_Tarski_Ointerval(v_r,X1,v_b,t_a),tc_set(t_a))
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),X0,t_a) ),
inference(resolution,[status(thm)],[f6660,f2770]) ).
fof(f6748,plain,
! [X0,X1] :
( sQ19_spl
| sQ7_spl
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,X1,t_a),tc_set(t_a))
| v_S = c_emptyset
| ~ c_lessequals(v_S,X0,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(v_L,v_S,v_r),v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f6388,f6471]) ).
fof(f6752,definition,
! [X1] :
( sQ46_spl
<=> ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,X1,t_a),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f6753,plain,
! [X0] :
( ~ sQ46_spl
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,X0,t_a),tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f6752]) ).
fof(f6755,plain,
( sQ19_spl
| sQ7_spl
| sQ46_spl
| sQ21_spl
| sQ26_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f6748,f6447,f6493,f6450,f6752,f6348,f6444]) ).
fof(f6759,plain,
( ~ sQ46_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6139,f6753]) ).
fof(f6760,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f6759]) ).
fof(f6763,plain,
( sQ20_spl
| ~ c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[f6511,f6141]) ).
fof(f6764,plain,
! [X0] :
( sQ7_spl
| sQ20_spl
| v_S = c_emptyset
| ~ c_lessequals(v_S,X0,tc_set(t_a))
| ~ c_in(c_Pair(v_a,v_sko__4mj(v_S,v_a,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f6763,f6387]) ).
fof(f6766,plain,
( sQ7_spl
| sQ20_spl
| sQ21_spl
| sQ26_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f6764,f6444,f6493,f6450,f6447,f6348]) ).
fof(f6781,plain,
! [X0] :
( sQ20_spl
| sQ7_spl
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a)
| ~ c_lessequals(v_S,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f6389,f6763]) ).
fof(f6785,definition,
( sQ47_spl
<=> c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f6786,plain,
( ~ sQ47_spl
| c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(component_clause,[status(thm)],[f6785]) ).
fof(f6788,plain,
( sQ20_spl
| sQ7_spl
| sQ21_spl
| sQ47_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f6781,f6493,f6785,f6450,f6348,f6447]) ).
fof(f6793,plain,
! [X0] :
( sQ19_spl
| ~ sQ47_spl
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,X0,t_a),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f6786,f6471]) ).
fof(f6794,plain,
( sQ19_spl
| ~ sQ47_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f6793,f6752,f6785,f6444]) ).
fof(f6866,definition,
( sQ51_spl
<=> c_in(v_sko__4mj(c_emptyset,v_L,v_r),c_emptyset,t_a) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f6867,plain,
( ~ sQ51_spl
| c_in(v_sko__4mj(c_emptyset,v_L,v_r),c_emptyset,t_a) ),
inference(component_clause,[status(thm)],[f6866]) ).
fof(f6870,plain,
( ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6867,f4861]) ).
fof(f6871,plain,
~ sQ51_spl,
inference(contradiction_clause,[status(thm)],[f6870]) ).
fof(f6879,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ37_spl
| ~ c_lessequals(v_S,c_Tarski_Ointerval(v_r,X0,v_b,t_a),tc_set(t_a)) ),
inference(resolution,[status(thm)],[f6728,f6413]) ).
fof(f6882,plain,
( ~ sQ10_spl
| ~ sQ37_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f6139,f6879]) ).
fof(f6883,plain,
( ~ sQ10_spl
| ~ sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f6882]) ).
fof(f6884,plain,
$false,
inference(sat_refutation,[status(thm)],[f6150,f6288,f6303,f6305,f6351,f6380,f6382,f6399,f6403,f6453,f6455,f6502,f6504,f6521,f6525,f6542,f6546,f6577,f6598,f6600,f6616,f6679,f6755,f6760,f6766,f6788,f6794,f6871,f6883]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT274-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 23:24:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.41 % Drodi V4.1.1
% 12.55/2.05 % Refutation found
% 12.55/2.05 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 12.55/2.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.55/2.11 % Elapsed time: 1.741578 seconds
% 12.55/2.11 % CPU time: 13.032572 seconds
% 12.55/2.11 % Total memory used: 308.317 MB
% 12.55/2.11 % Net memory used: 295.007 MB
%------------------------------------------------------------------------------