%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET831-2 : 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 02:10:43 PM UTC 2026
% Result : Unsatisfiable 0.16s 5.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 28
% Syntax : Number of formulae : 109 ( 3 unt; 15 def)
% Number of atoms : 283 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 312 ( 138 ~; 159 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 16 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 80 ( 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
( c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
( c_lessequals(v_X,v_Z,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Z,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [V_U] :
( ~ c_lessequals(V_U,v_Y,tc_set(t_a))
| ~ c_lessequals(V_U,v_Z,tc_set(t_a))
| c_lessequals(V_U,v_X,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_B,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [V_c,V_B,T_a,V_A] :
( c_in(V_c,c_inter(V_A,V_B,T_a),T_a)
| ~ c_in(V_c,V_A,T_a)
| ~ c_in(V_c,V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [V_B,V_A,T_a] :
( V_A = V_B
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,plain,
( c_lessequals(v_X,v_Y,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
( c_lessequals(v_X,v_Z,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Y,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| c_lessequals(v_x,v_Z,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
( v_X != c_inter(v_Y,v_Z,t_a)
| ~ c_lessequals(v_X,v_Y,tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a))
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
! [X0] :
( ~ c_lessequals(X0,v_Y,tc_set(t_a))
| ~ c_lessequals(X0,v_Z,tc_set(t_a))
| c_lessequals(X0,v_X,tc_set(t_a))
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f20,plain,
! [V_c,V_B,T_a] :
( c_in(V_c,V_B,T_a)
| ! [V_A] : ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X2,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [V_c,V_A,T_a] :
( c_in(V_c,V_A,T_a)
| ! [V_B] : ~ c_in(V_c,c_inter(V_A,V_B,T_a),T_a) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X1,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_inter(X3,X1,X2),X2)
| ~ c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [V_c,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ! [V_A] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
! [V_B,V_A] :
( V_A = V_B
| ! [T_a] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f30,plain,
! [X0,X1,X2] :
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,definition,
( sQ0_spl
<=> v_X = c_inter(v_Y,v_Z,t_a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f32,plain,
( ~ sQ0_spl
| v_X = c_inter(v_Y,v_Z,t_a) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f33,plain,
( sQ0_spl
| v_X != c_inter(v_Y,v_Z,t_a) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,definition,
( sQ1_spl
<=> c_lessequals(v_X,v_Y,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( sQ1_spl
| ~ c_lessequals(v_X,v_Y,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f14,f31,f34]) ).
fof(f38,definition,
( sQ2_spl
<=> c_lessequals(v_X,v_Z,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( sQ2_spl
| ~ c_lessequals(v_X,v_Z,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f15,f31,f38]) ).
fof(f42,definition,
( sQ3_spl
<=> c_lessequals(v_x,v_Y,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f45,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f16,f42,f38,f34,f31]) ).
fof(f46,definition,
( sQ4_spl
<=> c_lessequals(v_x,v_Z,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f17,f46,f38,f34,f31]) ).
fof(f50,definition,
( sQ5_spl
<=> c_lessequals(v_x,v_X,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( sQ5_spl
| ~ c_lessequals(v_x,v_X,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f18,f50,f38,f34,f31]) ).
fof(f54,definition,
! [X0] :
( sQ6_spl
<=> ( ~ c_lessequals(X0,v_Y,tc_set(t_a))
| ~ c_lessequals(X0,v_Z,tc_set(t_a))
| c_lessequals(X0,v_X,tc_set(t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f55,plain,
! [X0] :
( ~ sQ6_spl
| ~ c_lessequals(X0,v_Y,tc_set(t_a))
| ~ c_lessequals(X0,v_Z,tc_set(t_a))
| c_lessequals(X0,v_X,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f31,f54]) ).
fof(f60,plain,
! [X0] :
( ~ sQ0_spl
| c_in(X0,v_X,t_a)
| ~ c_in(X0,v_Y,t_a)
| ~ c_in(X0,v_Z,t_a) ),
inference(paramodulation,[status(thm)],[f32,f24]) ).
fof(f61,plain,
( sQ1_spl
| ~ c_in(c_Main_OsubsetI__1(v_X,v_Y,t_a),v_Y,t_a) ),
inference(resolution,[status(thm)],[f28,f36]) ).
fof(f62,plain,
( sQ2_spl
| ~ c_in(c_Main_OsubsetI__1(v_X,v_Z,t_a),v_Z,t_a) ),
inference(resolution,[status(thm)],[f28,f40]) ).
fof(f63,plain,
! [X0] :
( sQ1_spl
| ~ c_in(c_Main_OsubsetI__1(v_X,v_Y,t_a),c_inter(v_Y,X0,t_a),t_a) ),
inference(resolution,[status(thm)],[f61,f23]) ).
fof(f66,plain,
! [X0] :
( sQ2_spl
| ~ c_in(c_Main_OsubsetI__1(v_X,v_Z,t_a),c_inter(X0,v_Z,t_a),t_a) ),
inference(resolution,[status(thm)],[f62,f21]) ).
fof(f73,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ c_in(c_Main_OsubsetI__1(v_X,v_Y,t_a),v_X,t_a) ),
inference(paramodulation,[status(thm)],[f32,f63]) ).
fof(f81,plain,
( sQ5_spl
| ~ c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_X,t_a) ),
inference(resolution,[status(thm)],[f52,f28]) ).
fof(f82,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_Y,t_a)
| ~ c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_Z,t_a) ),
inference(resolution,[status(thm)],[f81,f60]) ).
fof(f86,definition,
( sQ9_spl
<=> c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_Z,t_a) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( sQ9_spl
| ~ c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_Z,t_a) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,definition,
( sQ10_spl
<=> c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_Y,t_a) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( sQ10_spl
| ~ c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),v_Y,t_a) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f82,f86,f89,f50,f31]) ).
fof(f108,plain,
! [X0] :
( sQ10_spl
| ~ c_lessequals(X0,v_Y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),X0,t_a) ),
inference(resolution,[status(thm)],[f91,f26]) ).
fof(f111,plain,
! [X0] :
( sQ9_spl
| ~ c_lessequals(X0,v_Z,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_x,v_X,t_a),X0,t_a) ),
inference(resolution,[status(thm)],[f88,f26]) ).
fof(f135,plain,
( ~ sQ0_spl
| sQ2_spl
| ~ c_in(c_Main_OsubsetI__1(v_X,v_Z,t_a),v_X,t_a) ),
inference(paramodulation,[status(thm)],[f32,f66]) ).
fof(f153,plain,
( ~ sQ0_spl
| sQ1_spl
| c_lessequals(v_X,v_Y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f73,f27]) ).
fof(f158,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f153,f34,f31]) ).
fof(f160,plain,
! [X0] :
( sQ0_spl
| ~ c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(X0))
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(X0)) ),
inference(resolution,[status(thm)],[f33,f30]) ).
fof(f175,plain,
( ~ sQ0_spl
| sQ2_spl
| c_lessequals(v_X,v_Z,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f135,f27]) ).
fof(f179,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f175,f38,f31]) ).
fof(f279,plain,
! [X0] :
( sQ0_spl
| ~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),X0),c_inter(v_Y,v_Z,t_a),X0)
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(X0)) ),
inference(resolution,[status(thm)],[f160,f28]) ).
fof(f280,plain,
( sQ0_spl
| ~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Y,t_a)
| ~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Z,t_a)
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f279,f24]) ).
fof(f284,definition,
( sQ18_spl
<=> c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( sQ18_spl
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f287,definition,
( sQ19_spl
<=> c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Z,t_a) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( sQ19_spl
| ~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Z,t_a) ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f290,definition,
( sQ20_spl
<=> c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Y,t_a) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ20_spl
| ~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),v_Y,t_a) ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,plain,
( sQ0_spl
| ~ sQ20_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f280,f284,f287,f290,f31]) ).
fof(f332,plain,
( sQ10_spl
| c_lessequals(v_x,v_X,tc_set(t_a))
| ~ c_lessequals(v_x,v_Y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f108,f27]) ).
fof(f337,plain,
( sQ10_spl
| sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f332,f42,f50,f89]) ).
fof(f368,plain,
( sQ9_spl
| c_lessequals(v_x,v_X,tc_set(t_a))
| ~ c_lessequals(v_x,v_Z,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f111,f27]) ).
fof(f373,plain,
( sQ9_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f368,f46,f50,f86]) ).
fof(f374,plain,
! [X0] :
( sQ20_spl
| ~ c_lessequals(X0,v_Y,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),X0,t_a) ),
inference(resolution,[status(thm)],[f292,f26]) ).
fof(f431,plain,
! [X0] :
( sQ19_spl
| ~ c_lessequals(X0,v_Z,tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(v_X,c_inter(v_Y,v_Z,t_a),t_a),X0,t_a) ),
inference(resolution,[status(thm)],[f289,f26]) ).
fof(f434,plain,
( ~ sQ6_spl
| sQ18_spl
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_Y,tc_set(t_a))
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_Z,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f286,f55]) ).
fof(f436,definition,
( sQ22_spl
<=> c_lessequals(c_inter(v_Y,v_Z,t_a),v_Z,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( sQ22_spl
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_Z,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,definition,
( sQ23_spl
<=> c_lessequals(c_inter(v_Y,v_Z,t_a),v_Y,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( sQ23_spl
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_Y,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( ~ sQ6_spl
| sQ18_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f434,f436,f439,f284,f54]) ).
fof(f446,plain,
( sQ23_spl
| ~ c_in(c_Main_OsubsetI__1(c_inter(v_Y,v_Z,t_a),v_Y,t_a),v_Y,t_a) ),
inference(resolution,[status(thm)],[f441,f28]) ).
fof(f447,plain,
( sQ22_spl
| ~ c_in(c_Main_OsubsetI__1(c_inter(v_Y,v_Z,t_a),v_Z,t_a),v_Z,t_a) ),
inference(resolution,[status(thm)],[f438,f28]) ).
fof(f473,definition,
( sQ24_spl
<=> c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( ~ sQ24_spl
| c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f521,plain,
! [X0] :
( sQ23_spl
| ~ c_in(c_Main_OsubsetI__1(c_inter(v_Y,v_Z,t_a),v_Y,t_a),c_inter(v_Y,X0,t_a),t_a) ),
inference(resolution,[status(thm)],[f446,f23]) ).
fof(f530,plain,
! [X0] :
( sQ22_spl
| ~ c_in(c_Main_OsubsetI__1(c_inter(v_Y,v_Z,t_a),v_Z,t_a),c_inter(X0,v_Z,t_a),t_a) ),
inference(resolution,[status(thm)],[f447,f21]) ).
fof(f537,plain,
( sQ0_spl
| ~ sQ24_spl
| ~ c_lessequals(c_inter(v_Y,v_Z,t_a),v_X,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f474,f160]) ).
fof(f603,plain,
( sQ20_spl
| c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a))
| ~ c_lessequals(v_X,v_Y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f374,f27]) ).
fof(f608,plain,
( sQ20_spl
| sQ24_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f603,f34,f473,f290]) ).
fof(f609,plain,
( sQ19_spl
| c_lessequals(v_X,c_inter(v_Y,v_Z,t_a),tc_set(t_a))
| ~ c_lessequals(v_X,v_Z,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f431,f27]) ).
fof(f614,plain,
( sQ19_spl
| sQ24_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f609,f38,f473,f287]) ).
fof(f671,plain,
( sQ23_spl
| c_lessequals(c_inter(v_Y,v_Z,t_a),v_Y,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f521,f27]) ).
fof(f676,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f671,f441]) ).
fof(f677,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f676]) ).
fof(f701,plain,
( sQ0_spl
| ~ sQ24_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f537,f284,f473,f31]) ).
fof(f900,plain,
( sQ22_spl
| c_lessequals(c_inter(v_Y,v_Z,t_a),v_Z,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f530,f27]) ).
fof(f905,plain,
sQ22_spl,
inference(split_clause,[status(thm)],[f900,f436]) ).
fof(f907,plain,
$false,
inference(sat_refutation,[status(thm)],[f37,f41,f45,f49,f53,f57,f92,f158,f179,f293,f337,f373,f442,f608,f614,f677,f701,f905]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET831-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.38 % Computer : n003.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Mon Sep 21 05:42:06 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.39 % Drodi V4.1.1
% 0.16/5.45 % Refutation found
% 0.16/5.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/5.48 % Elapsed time: 0.081399 seconds
% 0.16/5.48 % CPU time: 0.446449 seconds
% 0.16/5.48 % Total memory used: 83.807 MB
% 0.16/5.48 % Net memory used: 83.043 MB
%------------------------------------------------------------------------------