%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET860-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:10:51 PM UTC 2026
% Result : Unsatisfiable 2.91s 1.02s
% Output : CNFRefutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 72 ( 10 unt; 4 def)
% Number of atoms : 188 ( 5 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 206 ( 90 ~; 112 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 149 ( 149 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
~ c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [V_U] :
( ~ c_in(V_U,v_C,tc_set(t_a))
| c_lessequals(V_U,v_A,tc_set(t_a))
| c_lessequals(v_B,V_U,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [V_A,V_C,T_a] :
( c_in(c_Main_OUnionE__1(V_A,V_C,T_a),V_C,tc_set(T_a))
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [V_A,V_C,T_a] :
( c_in(V_A,c_Main_OUnionE__1(V_A,V_C,T_a),T_a)
| ~ c_in(V_A,c_Union(V_C,T_a),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [V_A,V_X,T_a,V_C] :
( c_in(V_A,c_Union(V_C,T_a),T_a)
| ~ c_in(V_X,V_C,tc_set(T_a))
| ~ c_in(V_A,V_X,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,plain,
~ c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
~ c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f27,plain,
! [X0] :
( ~ c_in(X0,v_C,tc_set(t_a))
| c_lessequals(X0,v_A,tc_set(t_a))
| c_lessequals(v_B,X0,tc_set(t_a)) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f32,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)],[f8]) ).
fof(f33,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X2,X3)
| ~ c_in(X0,c_inter(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,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)],[f10]) ).
fof(f42,plain,
! [X0,X1,X2] :
( c_in(c_Main_OUnionE__1(X0,X1,X2),X1,tc_set(X2))
| ~ c_in(X0,c_Union(X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f43,plain,
! [X0,X1,X2] :
( c_in(X0,c_Main_OUnionE__1(X0,X1,X2),X2)
| ~ c_in(X0,c_Union(X1,X2),X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f44,plain,
! [V_A,T_a,V_C] :
( c_in(V_A,c_Union(V_C,T_a),T_a)
| ! [V_X] :
( ~ c_in(V_X,V_C,tc_set(T_a))
| ~ c_in(V_A,V_X,T_a) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_Union(X3,X2),X2)
| ~ c_in(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f52,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)],[f21]) ).
fof(f53,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)],[f52]) ).
fof(f54,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)],[f22]) ).
fof(f55,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)],[f23]) ).
fof(f56,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)],[f24]) ).
fof(f57,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)],[f56]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( c_in(c_Main_OsubsetI__1(c_inter(X0,X1,X2),X3,X2),X1,X2)
| c_lessequals(c_inter(X0,X1,X2),X3,tc_set(X2)) ),
inference(resolution,[status(thm)],[f54,f33]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( ~ c_in(X3,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,c_Union(X1,X2),X2),X3,X2)
| c_lessequals(X0,c_Union(X1,X2),tc_set(X2)) ),
inference(resolution,[status(thm)],[f55,f45]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( c_lessequals(X0,c_inter(X1,X2,X3),tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X2,X3),X3),X1,X3)
| ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X2,X3),X3),X2,X3) ),
inference(resolution,[status(thm)],[f36,f55]) ).
fof(f100,plain,
! [X0] :
( c_lessequals(c_Main_OUnionE__1(X0,v_C,t_a),v_A,tc_set(t_a))
| c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(resolution,[status(thm)],[f42,f27]) ).
fof(f138,plain,
! [X0,X1,X2] :
( c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2))
| c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2)) ),
inference(resolution,[status(thm)],[f63,f55]) ).
fof(f147,plain,
! [X0,X1,X2] : c_lessequals(c_inter(X0,X1,X2),X1,tc_set(X2)),
inference(duplicate_literals_removal,[status(thm)],[f138]) ).
fof(f154,plain,
! [X0,X1] :
( c_in(X1,v_A,t_a)
| ~ c_in(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a)
| c_lessequals(v_B,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(resolution,[status(thm)],[f100,f53]) ).
fof(f156,plain,
! [X0,X1,X2] :
( c_in(X2,c_Main_OUnionE__1(X0,v_C,t_a),t_a)
| ~ c_in(X2,v_B,t_a)
| c_in(X1,v_A,t_a)
| ~ c_in(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(resolution,[status(thm)],[f154,f53]) ).
fof(f162,plain,
! [X0,X1] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_in(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a)
| ~ c_in(X1,v_B,t_a)
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(resolution,[status(thm)],[f156,f43]) ).
fof(f163,plain,
! [X0,X1] :
( c_in(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a)
| ~ c_in(X1,v_B,t_a)
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(duplicate_literals_removal,[status(thm)],[f162]) ).
fof(f165,plain,
! [X0,X1] :
( c_lessequals(X1,c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a),v_B,t_a)
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(resolution,[status(thm)],[f163,f55]) ).
fof(f176,plain,
! [X0,X1] :
( c_lessequals(c_inter(X1,v_B,t_a),c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| c_lessequals(c_inter(X1,v_B,t_a),c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(resolution,[status(thm)],[f165,f63]) ).
fof(f180,plain,
! [X0,X1] :
( c_lessequals(c_inter(X1,v_B,t_a),c_Main_OUnionE__1(X0,v_C,t_a),tc_set(t_a))
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(duplicate_literals_removal,[status(thm)],[f176]) ).
fof(f269,plain,
! [X0,X1,X2] :
( c_inter(X1,X0,X2) = X0
| ~ c_lessequals(X0,c_inter(X1,X0,X2),tc_set(X2)) ),
inference(resolution,[status(thm)],[f147,f57]) ).
fof(f404,plain,
! [X0,X1,X2] :
( c_in(X1,c_Main_OUnionE__1(X0,v_C,t_a),t_a)
| ~ c_in(X1,c_inter(X2,v_B,t_a),t_a)
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(resolution,[status(thm)],[f180,f53]) ).
fof(f414,plain,
! [X0,X1,X2] :
( c_lessequals(c_inter(X1,v_B,t_a),X2,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_inter(X1,v_B,t_a),X2,t_a),c_Main_OUnionE__1(X0,v_C,t_a),t_a)
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(resolution,[status(thm)],[f404,f54]) ).
fof(f612,plain,
! [X0,X1,X2] :
( c_lessequals(X0,c_inter(X1,X0,X2),tc_set(X2))
| c_lessequals(X0,c_inter(X1,X0,X2),tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X0,X2),X2),X1,X2) ),
inference(resolution,[status(thm)],[f89,f54]) ).
fof(f628,plain,
! [X0,X1,X2] :
( c_lessequals(X0,c_inter(X1,X0,X2),tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,c_inter(X1,X0,X2),X2),X1,X2) ),
inference(duplicate_literals_removal,[status(thm)],[f612]) ).
fof(f997,plain,
! [X0,X1,X2] :
( ~ c_in(c_Main_OUnionE__1(X0,v_C,t_a),X2,tc_set(t_a))
| c_lessequals(c_inter(X1,v_B,t_a),c_Union(X2,t_a),tc_set(t_a))
| c_lessequals(c_inter(X1,v_B,t_a),c_Union(X2,t_a),tc_set(t_a))
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(resolution,[status(thm)],[f414,f80]) ).
fof(f1004,plain,
! [X0,X1,X2] :
( ~ c_in(c_Main_OUnionE__1(X0,v_C,t_a),X2,tc_set(t_a))
| c_lessequals(c_inter(X1,v_B,t_a),c_Union(X2,t_a),tc_set(t_a))
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(duplicate_literals_removal,[status(thm)],[f997]) ).
fof(f2085,plain,
! [X0,X1] :
( c_lessequals(X0,c_inter(X0,X0,X1),tc_set(X1))
| c_lessequals(X0,c_inter(X0,X0,X1),tc_set(X1)) ),
inference(resolution,[status(thm)],[f628,f54]) ).
fof(f2117,plain,
! [X0,X1] : c_lessequals(X0,c_inter(X0,X0,X1),tc_set(X1)),
inference(duplicate_literals_removal,[status(thm)],[f2085]) ).
fof(f2130,plain,
! [X0,X1] : c_inter(X0,X0,X1) = X0,
inference(resolution,[status(thm)],[f2117,f269]) ).
fof(f2162,plain,
! [X0,X1] :
( ~ c_in(c_Main_OUnionE__1(X0,v_C,t_a),X1,tc_set(t_a))
| c_lessequals(v_B,c_Union(X1,t_a),tc_set(t_a))
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(paramodulation,[status(thm)],[f2130,f1004]) ).
fof(f3432,plain,
! [X0] :
( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a))
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(resolution,[status(thm)],[f2162,f42]) ).
fof(f3449,definition,
! [X0] :
( sQ19_spl
<=> ( ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f3450,plain,
! [X0] :
( ~ sQ19_spl
| ~ c_in(X0,c_Union(v_C,t_a),t_a)
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(component_clause,[status(thm)],[f3449]) ).
fof(f3452,definition,
( sQ20_spl
<=> c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f3453,plain,
( ~ sQ20_spl
| c_lessequals(v_B,c_Union(v_C,t_a),tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f3452]) ).
fof(f3455,plain,
( sQ20_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f3432,f3449,f3452]) ).
fof(f3456,definition,
! [X0] :
( sQ21_spl
<=> ( c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f3457,plain,
! [X0] :
( ~ sQ21_spl
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(component_clause,[status(thm)],[f3456]) ).
fof(f3491,plain,
! [X0] :
( ~ sQ19_spl
| c_in(X0,v_A,t_a)
| ~ c_in(X0,c_Union(v_C,t_a),t_a) ),
inference(duplicate_literals_removal,[status(thm)],[f3450]) ).
fof(f3521,plain,
! [X0] :
( ~ sQ21_spl
| c_lessequals(c_Union(v_C,t_a),X0,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Union(v_C,t_a),X0,t_a),v_A,t_a) ),
inference(resolution,[status(thm)],[f3457,f54]) ).
fof(f3575,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3453,f26]) ).
fof(f3576,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f3575]) ).
fof(f3906,plain,
( ~ sQ21_spl
| c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a))
| c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f3521,f55]) ).
fof(f3916,definition,
( sQ33_spl
<=> c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f3917,plain,
( ~ sQ33_spl
| c_lessequals(c_Union(v_C,t_a),v_A,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f3916]) ).
fof(f3919,plain,
( ~ sQ21_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f3906,f3916,f3456]) ).
fof(f3920,plain,
( ~ sQ19_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f3491,f3456,f3449]) ).
fof(f3921,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3917,f25]) ).
fof(f3922,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f3921]) ).
fof(f3923,plain,
$false,
inference(sat_refutation,[status(thm)],[f3455,f3576,f3919,f3920,f3922]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET860-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:46:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 2.91/1.02 % Refutation found
% 2.91/1.02 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.91/1.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.91/1.06 % Elapsed time: 0.681728 seconds
% 2.91/1.06 % CPU time: 5.108064 seconds
% 2.91/1.06 % Total memory used: 127.600 MB
% 2.91/1.06 % Net memory used: 119.899 MB
%------------------------------------------------------------------------------