%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU039+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 02:19:07 PM UTC 2026
% Result : Theorem 0.13s 5.63s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 61 ( 12 unt; 0 def)
% Number of atoms : 296 ( 71 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 387 ( 152 ~; 147 |; 68 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 155 ( 137 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B] :
( ( function(B)
& relation(B) )
=> ! [C] :
( ( function(C)
& relation(C) )
=> ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( in(D,relation_dom(B))
=> apply(B,D) = apply(C,D) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,A)
=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( in(B,A)
& in(B,relation_dom(C)) )
=> in(apply(C,B),relation_rng(relation_dom_restriction(C,A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( ( in(B,A)
& in(B,relation_dom(C)) )
=> in(apply(C,B),relation_rng(relation_dom_restriction(C,A))) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f57,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ( ! [D] :
( ( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f58,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( in(D,B)
& in(D,A) )
| in(D,C) )
& ( ~ in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(miniscoping,[status(thm)],[f57]) ).
fof(f59,plain,
( ! [A,B,C] :
( ( ( ( in(sK0_skl(C,B,A),B)
& in(sK0_skl(C,B,A),A) )
| in(sK0_skl(C,B,A),C) )
& ( ~ in(sK0_skl(C,B,A),B)
| ~ in(sK0_skl(C,B,A),A)
| ~ in(sK0_skl(C,B,A),C) ) )
| C = set_intersection2(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( ~ in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_intersection2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B,A))],[f58]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f66,plain,
! [A] :
( ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) ) ) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f67,plain,
! [A] :
( ! [B] :
( ( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ( ! [C] :
( ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(NNF_transformation,[status(thm)],[f66]) ).
fof(f68,plain,
! [A] :
( ( ! [B] :
( ? [C] :
( ( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| in(C,B) )
& ( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ? [D] :
( C = apply(A,D)
& in(D,relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f69,plain,
! [A] :
( ( ! [B] :
( ( ( ( sK2_skl(B,A) = apply(A,sK3_skl(B,A))
& in(sK3_skl(B,A),relation_dom(A)) )
| in(sK2_skl(B,A),B) )
& ( ! [D] :
( sK2_skl(B,A) != apply(A,D)
| ~ in(D,relation_dom(A)) )
| ~ in(sK2_skl(B,A),B) ) )
| B = relation_rng(A) )
& ! [B] :
( ( ! [C] :
( ! [D] :
( C != apply(A,D)
| ~ in(D,relation_dom(A)) )
| in(C,B) )
& ! [C] :
( ( C = apply(A,sK1_skl(C,B,A))
& in(sK1_skl(C,B,A),relation_dom(A)) )
| ~ in(C,B) ) )
| B != relation_rng(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl]),skolemize(D,sK1_skl(C,B,A)),skolemize(C,sK2_skl(B,A)),skolemize(D,sK3_skl(B,A))],[f68]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( X2 != apply(X0,X3)
| ~ in(X3,relation_dom(X0))
| in(X2,X1)
| X1 != relation_rng(X0)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f76,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f77,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f92,plain,
! [A,B] :
( ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f93,plain,
! [A] :
( ( ! [B] : function(relation_dom_restriction(A,B))
& ! [B] : relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f95,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f158,plain,
! [A,B] :
( ! [C] :
( ( B = relation_dom_restriction(C,A)
<=> ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f39]) ).
fof(f159,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(NNF_transformation,[status(thm)],[f158]) ).
fof(f160,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ? [D] :
( apply(B,D) != apply(C,D)
& in(D,relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(miniscoping,[status(thm)],[f159]) ).
fof(f161,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK15_skl(A,C,B)) != apply(C,sK15_skl(A,C,B))
& in(sK15_skl(A,C,B),relation_dom(B)) )
| relation_dom(B) != set_intersection2(relation_dom(C),A)
| B = relation_dom_restriction(C,A) )
& ! [A] :
( ( ! [D] :
( apply(B,D) = apply(C,D)
| ~ in(D,relation_dom(B)) )
& relation_dom(B) = set_intersection2(relation_dom(C),A) )
| B != relation_dom_restriction(C,A) ) )
| ~ function(C)
| ~ relation(C) )
| ~ function(B)
| ~ relation(B) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl]),skolemize(D,sK15_skl(A,C,B))],[f160]) ).
fof(f162,plain,
! [X0,X1,X2] :
( relation_dom(X0) = set_intersection2(relation_dom(X1),X2)
| X0 != relation_dom_restriction(X1,X2)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f168,plain,
! [A,B,C] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,A)
| ~ function(C)
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f169,plain,
! [C] :
( ! [A,B] :
( apply(relation_dom_restriction(C,A),B) = apply(C,B)
| ~ in(B,A) )
| ~ function(C)
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f168]) ).
fof(f170,plain,
! [X0,X1,X2] :
( apply(relation_dom_restriction(X0,X2),X1) = apply(X0,X1)
| ~ in(X1,X2)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f171,plain,
? [A,B,C] :
( ~ in(apply(C,B),relation_rng(relation_dom_restriction(C,A)))
& in(B,A)
& in(B,relation_dom(C))
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f172,plain,
? [C] :
( ? [A,B] :
( ~ in(apply(C,B),relation_rng(relation_dom_restriction(C,A)))
& in(B,A)
& in(B,relation_dom(C)) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f171]) ).
fof(f173,plain,
( ~ in(apply(sK16_skl,sK18_skl),relation_rng(relation_dom_restriction(sK16_skl,sK17_skl)))
& in(sK18_skl,sK17_skl)
& in(sK18_skl,relation_dom(sK16_skl))
& function(sK16_skl)
& relation(sK16_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl,sK17_skl,sK18_skl]),skolemize(C,sK16_skl),skolemize(A,sK17_skl),skolemize(B,sK18_skl)],[f172]) ).
fof(f174,plain,
relation(sK16_skl),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f175,plain,
function(sK16_skl),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f176,plain,
in(sK18_skl,relation_dom(sK16_skl)),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f177,plain,
in(sK18_skl,sK17_skl),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f178,plain,
~ in(apply(sK16_skl,sK18_skl),relation_rng(relation_dom_restriction(sK16_skl,sK17_skl))),
inference(cnf_transformation,[status(thm)],[f173]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f62]) ).
fof(f191,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| in(apply(X0,X1),relation_rng(X0))
| ~ function(X0)
| ~ relation(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f72]) ).
fof(f192,plain,
! [X1,X2] :
( relation_dom(relation_dom_restriction(X1,X2)) = set_intersection2(relation_dom(X1),X2)
| ~ function(X1)
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2))
| ~ relation(relation_dom_restriction(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f162]) ).
fof(f193,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_dom_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f78]) ).
fof(f202,plain,
! [X0,X1] :
( apply(relation_dom_restriction(sK16_skl,X1),X0) = apply(sK16_skl,X0)
| ~ in(X0,X1)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f170,f175]) ).
fof(f205,plain,
! [X0,X1] :
( apply(relation_dom_restriction(sK16_skl,X1),X0) = apply(sK16_skl,X0)
| ~ in(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f202,f174]) ).
fof(f207,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f193,f95]) ).
fof(f209,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X0,X1)) = set_intersection2(relation_dom(X0),X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f207]) ).
fof(f228,plain,
apply(relation_dom_restriction(sK16_skl,sK17_skl),sK18_skl) = apply(sK16_skl,sK18_skl),
inference(resolution,[status(thm)],[f205,f177]) ).
fof(f229,plain,
( ~ in(sK18_skl,relation_dom(relation_dom_restriction(sK16_skl,sK17_skl)))
| in(apply(sK16_skl,sK18_skl),relation_rng(relation_dom_restriction(sK16_skl,sK17_skl)))
| ~ function(relation_dom_restriction(sK16_skl,sK17_skl))
| ~ relation(relation_dom_restriction(sK16_skl,sK17_skl)) ),
inference(paramodulation,[status(thm)],[f228,f191]) ).
fof(f230,plain,
( ~ in(sK18_skl,relation_dom(relation_dom_restriction(sK16_skl,sK17_skl)))
| ~ function(relation_dom_restriction(sK16_skl,sK17_skl))
| ~ relation(relation_dom_restriction(sK16_skl,sK17_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f229,f178]) ).
fof(f265,plain,
! [X0] :
( relation_dom(relation_dom_restriction(sK16_skl,X0)) = set_intersection2(relation_dom(sK16_skl),X0)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f209,f175]) ).
fof(f271,plain,
! [X0] : relation_dom(relation_dom_restriction(sK16_skl,X0)) = set_intersection2(relation_dom(sK16_skl),X0),
inference(forward_subsumption_resolution,[status(thm)],[f265,f174]) ).
fof(f346,plain,
! [X0] :
( ~ in(sK18_skl,X0)
| in(sK18_skl,set_intersection2(X0,sK17_skl)) ),
inference(resolution,[status(thm)],[f188,f177]) ).
fof(f358,plain,
in(sK18_skl,set_intersection2(relation_dom(sK16_skl),sK17_skl)),
inference(resolution,[status(thm)],[f346,f176]) ).
fof(f360,plain,
( ~ function(relation_dom_restriction(sK16_skl,sK17_skl))
| ~ relation(relation_dom_restriction(sK16_skl,sK17_skl)) ),
inference(backward_subsumption_resolution,[status(thm)],[f230,f361]) ).
fof(f361,plain,
in(sK18_skl,relation_dom(relation_dom_restriction(sK16_skl,sK17_skl))),
inference(forward_demodulation,[status(thm)],[f271,f358]) ).
fof(f1004,plain,
( ~ relation(sK16_skl)
| ~ function(relation_dom_restriction(sK16_skl,sK17_skl)) ),
inference(resolution,[status(thm)],[f360,f78]) ).
fof(f1005,plain,
~ function(relation_dom_restriction(sK16_skl,sK17_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f1004,f174]) ).
fof(f1006,plain,
( ~ function(sK16_skl)
| ~ relation(sK16_skl) ),
inference(resolution,[status(thm)],[f1005,f95]) ).
fof(f1009,plain,
~ function(sK16_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1006,f174]) ).
fof(f1010,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f175,f1009]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU039+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n019.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 05:48:12 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.13/5.63 % Refutation found
% 0.13/5.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.65 % Elapsed time: 0.261340 seconds
% 0.13/5.65 % CPU time: 1.784091 seconds
% 0.13/5.65 % Total memory used: 136.823 MB
% 0.13/5.65 % Net memory used: 133.810 MB
%------------------------------------------------------------------------------