%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT274-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 0.13s 5.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 31
% Syntax : Number of formulae : 115 ( 14 unt; 16 def)
% Number of atoms : 346 ( 21 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 407 ( 176 ~; 215 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 17 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-4 aty)
% Number of variables : 156 ( 156 !; 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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f8,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/sandbox/benchmark/theBenchmark.p') ).
fof(f9,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/sandbox/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
c_in(v_b,v_A,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
c_lessequals(v_S,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
v_S != c_emptyset,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,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(f17,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)],[f16]) ).
fof(f18,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(f19,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)],[f18]) ).
fof(f20,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(f21,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)],[f20]) ).
fof(f22,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(f23,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)],[f22]) ).
fof(f24,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(f25,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)],[f24]) ).
fof(f26,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(f27,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)],[f26]) ).
fof(f28,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(f29,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)],[f8]) ).
fof(f30,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)],[f29]) ).
fof(f31,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)],[f9]) ).
fof(f32,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)],[f31]) ).
fof(f33,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)],[f10]) ).
fof(f34,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)],[f33]) ).
fof(f35,plain,
c_in(v_b,v_A,t_a),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f36,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)],[f12]) ).
fof(f37,plain,
v_S != c_emptyset,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f38,plain,
c_Tarski_OisLub(v_S,v_cl,v_L,t_a),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f39,plain,
~ c_in(v_L,c_Tarski_Ointerval(v_r,v_a,v_b,t_a),t_a),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f40,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)],[f28,f39]) ).
fof(f41,definition,
( sQ0_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,[sQ0_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( sQ0_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)],[f41]) ).
fof(f44,definition,
( sQ1_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,[sQ1_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ1_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)],[f44]) ).
fof(f47,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f41,f44]) ).
fof(f52,plain,
! [X0] :
( sQ0_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)],[f34,f43]) ).
fof(f53,definition,
! [X0] :
( sQ2_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,[sQ2_spl])],[split_symbol_definition]) ).
fof(f54,plain,
! [X0] :
( ~ sQ2_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)],[f53]) ).
fof(f56,definition,
( sQ3_spl
<=> c_in(v_b,v_A,t_a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( sQ3_spl
| ~ c_in(v_b,v_A,t_a) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( sQ0_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f52,f53,f56,f41]) ).
fof(f60,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f58,f35]) ).
fof(f61,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0] :
( sQ1_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)],[f46,f34]) ).
fof(f66,definition,
! [X0] :
( sQ4_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,[sQ4_spl])],[split_symbol_definition]) ).
fof(f69,definition,
( sQ5_spl
<=> c_in(v_L,v_A,t_a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( sQ1_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f62,f66,f69,f44]) ).
fof(f80,plain,
( ~ sQ2_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)],[f54,f38]) ).
fof(f82,plain,
! [X0] :
( ~ sQ2_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_sko__4mi(v_S,v_r,v_b),t_a) ),
inference(resolution,[status(thm)],[f80,f34]) ).
fof(f84,plain,
! [X0,X1] :
( ~ sQ2_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)],[f80,f27]) ).
fof(f86,definition,
! [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_Tarski_OisLub(X0,v_cl,v_sko__4mi(v_S,v_r,v_b),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f82,f86,f56,f53]) ).
fof(f90,plain,
( ~ sQ2_spl
| ~ c_in(v_sko__4mi(v_S,v_r,v_b),v_S,t_a) ),
inference(resolution,[status(thm)],[f84,f36]) ).
fof(f91,plain,
! [X0] :
( ~ sQ2_spl
| c_in(c_Pair(X0,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(v_S,v_cl,X0,t_a) ),
inference(resolution,[status(thm)],[f90,f32]) ).
fof(f92,definition,
! [X0] :
( sQ7_spl
<=> ( c_in(c_Pair(X0,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(v_S,v_cl,X0,t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f93,plain,
! [X0] :
( ~ sQ7_spl
| c_in(c_Pair(X0,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_Tarski_OisLub(v_S,v_cl,X0,t_a) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f91,f92,f56,f53]) ).
fof(f96,plain,
( ~ sQ7_spl
| c_in(c_Pair(v_L,v_b,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f93,f38]) ).
fof(f97,plain,
( ~ sQ7_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f43]) ).
fof(f98,plain,
( ~ sQ7_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f97]) ).
fof(f100,plain,
! [X0,X1] :
( sQ1_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)],[f46,f23]) ).
fof(f107,plain,
( sQ1_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)],[f100,f36]) ).
fof(f108,definition,
( sQ8_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,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( sQ8_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)],[f108]) ).
fof(f111,definition,
( sQ9_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,[sQ9_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( sQ9_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)],[f111]) ).
fof(f114,definition,
( sQ10_spl
<=> v_S = c_emptyset ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( ~ sQ10_spl
| v_S = c_emptyset ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,plain,
( sQ1_spl
| sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f107,f108,f111,f114,f44]) ).
fof(f118,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f37]) ).
fof(f119,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f118]) ).
fof(f124,plain,
! [X0,X1] :
( sQ8_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)],[f110,f25]) ).
fof(f133,plain,
! [X0] :
( sQ9_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)],[f113,f34]) ).
fof(f134,plain,
! [X0] :
( sQ9_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)],[f113,f30]) ).
fof(f137,definition,
! [X0] :
( sQ13_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,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ9_spl
| ~ sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f133,f137,f69,f111]) ).
fof(f147,plain,
( sQ8_spl
| ~ c_in(v_sko__4mj(v_S,v_a,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[f124,f36]) ).
fof(f148,plain,
! [X0,X1] :
( sQ8_spl
| v_S = c_emptyset
| c_in(c_Pair(v_a,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X1,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mk(X0,v_S,v_r),X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f147,f19]) ).
fof(f149,definition,
! [X0] :
( sQ14_spl
<=> ( c_in(c_Pair(v_a,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(X0,v_S,v_r),X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f150,plain,
! [X0] :
( ~ sQ14_spl
| c_in(c_Pair(v_a,X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_sko__4mk(X0,v_S,v_r),X0,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,definition,
! [X1] :
( sQ15_spl
<=> ~ c_lessequals(v_S,X1,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f153,plain,
! [X0] :
( ~ sQ15_spl
| ~ c_lessequals(v_S,X0,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( sQ8_spl
| sQ10_spl
| sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f148,f149,f152,f114,f108]) ).
fof(f197,plain,
( sQ1_spl
| ~ sQ14_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(resolution,[status(thm)],[f150,f46]) ).
fof(f199,plain,
! [X0] :
( sQ1_spl
| ~ sQ14_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)],[f197,f34]) ).
fof(f200,plain,
! [X0] :
( sQ1_spl
| ~ sQ14_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)],[f197,f30]) ).
fof(f203,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f199,f137,f69,f149,f44]) ).
fof(f204,plain,
( ~ sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f36,f153]) ).
fof(f205,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f214,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[f200,f38]) ).
fof(f216,plain,
! [X0,X1] :
( sQ1_spl
| ~ sQ14_spl
| v_S = c_emptyset
| c_in(v_sko__4mj(v_S,X1,v_r),v_S,t_a)
| c_in(c_Pair(X1,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X0,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f214,f17]) ).
fof(f217,definition,
! [X0] :
( sQ22_spl
<=> ( c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,v_sko__4mj(v_S,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f218,plain,
! [X0] :
( ~ sQ22_spl
| c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(X0,v_sko__4mj(v_S,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f221,definition,
! [X1] :
( sQ23_spl
<=> ( c_in(v_sko__4mj(v_S,X1,v_r),v_S,t_a)
| c_in(c_Pair(X1,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f222,plain,
! [X0] :
( ~ sQ23_spl
| c_in(v_sko__4mj(v_S,X0,v_r),v_S,t_a)
| c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( sQ1_spl
| ~ sQ14_spl
| sQ10_spl
| sQ23_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f216,f152,f221,f114,f149,f44]) ).
fof(f236,plain,
( sQ8_spl
| ~ sQ23_spl
| c_in(c_Pair(v_a,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f222,f147]) ).
fof(f237,plain,
( sQ8_spl
| ~ sQ23_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f236,f46]) ).
fof(f238,plain,
( sQ8_spl
| ~ sQ23_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f237]) ).
fof(f239,plain,
( sQ9_spl
| ~ c_in(v_sko__4mk(v_L,v_S,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[f134,f38]) ).
fof(f240,plain,
! [X0,X1] :
( sQ9_spl
| v_S = c_emptyset
| c_in(c_Pair(X0,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(v_S,X1,tc_set(t_a))
| ~ c_in(c_Pair(X0,v_sko__4mj(v_S,X0,v_r),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(resolution,[status(thm)],[f239,f21]) ).
fof(f242,plain,
( sQ9_spl
| sQ10_spl
| sQ15_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f240,f217,f152,f114,f111]) ).
fof(f256,plain,
( sQ1_spl
| ~ sQ22_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(resolution,[status(thm)],[f218,f46]) ).
fof(f257,plain,
( sQ1_spl
| ~ sQ22_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f256,f108,f217,f44]) ).
fof(f258,plain,
$false,
inference(sat_refutation,[status(thm)],[f47,f59,f61,f72,f89,f95,f98,f117,f119,f140,f155,f203,f205,f224,f238,f242,f257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT274-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n003.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sun Sep 20 23:26:20 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.13/5.41 % Refutation found
% 0.13/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.44 % Elapsed time: 0.058920 seconds
% 0.13/5.44 % CPU time: 0.188517 seconds
% 0.13/5.44 % Total memory used: 82.670 MB
% 0.13/5.44 % Net memory used: 82.048 MB
%------------------------------------------------------------------------------