%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 02:19:46 PM UTC 2026
% Result : Theorem 0.21s 5.50s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 9 unt; 0 def)
% Number of atoms : 234 ( 44 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 291 ( 111 ~; 114 |; 52 &)
% ( 6 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 120 ( 107 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( ( function(A)
& relation(A) )
=> ( function(relation_dom_restriction(A,B))
& relation(relation_dom_restriction(A,B)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ! [A,B,C] :
( ( function(C)
& relation(C) )
=> ( in(B,relation_dom(relation_dom_restriction(C,A)))
<=> ( in(B,A)
& in(B,relation_dom(C)) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f36,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f51,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(f52,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)],[f51]) ).
fof(f53,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))],[f52]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f60,plain,
! [A,B] :
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f61,plain,
! [A] :
( ! [B] : relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f75,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)],[f18]) ).
fof(f76,plain,
! [A] :
( ( ! [B] : function(relation_dom_restriction(A,B))
& ! [B] : relation(relation_dom_restriction(A,B)) )
| ~ function(A)
| ~ relation(A) ),
inference(miniscoping,[status(thm)],[f75]) ).
fof(f78,plain,
! [X0,X1] :
( function(relation_dom_restriction(X0,X1))
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f88,plain,
? [A,B,C] :
( ( in(B,relation_dom(relation_dom_restriction(C,A)))
<~> ( in(B,A)
& in(B,relation_dom(C)) ) )
& function(C)
& relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f89,plain,
? [A,B,C] :
( ( ~ in(B,A)
| ~ in(B,relation_dom(C))
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| in(B,relation_dom(relation_dom_restriction(C,A))) )
& function(C)
& relation(C) ),
inference(NNF_transformation,[status(thm)],[f88]) ).
fof(f90,plain,
? [C] :
( ? [A,B] :
( ( ~ in(B,A)
| ~ in(B,relation_dom(C))
| ~ in(B,relation_dom(relation_dom_restriction(C,A))) )
& ( ( in(B,A)
& in(B,relation_dom(C)) )
| in(B,relation_dom(relation_dom_restriction(C,A))) ) )
& function(C)
& relation(C) ),
inference(miniscoping,[status(thm)],[f89]) ).
fof(f91,plain,
( ( ~ in(sK4_skl,sK3_skl)
| ~ in(sK4_skl,relation_dom(sK2_skl))
| ~ in(sK4_skl,relation_dom(relation_dom_restriction(sK2_skl,sK3_skl))) )
& ( ( in(sK4_skl,sK3_skl)
& in(sK4_skl,relation_dom(sK2_skl)) )
| in(sK4_skl,relation_dom(relation_dom_restriction(sK2_skl,sK3_skl))) )
& function(sK2_skl)
& relation(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(C,sK2_skl),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f90]) ).
fof(f92,plain,
relation(sK2_skl),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
function(sK2_skl),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
( in(sK4_skl,relation_dom(sK2_skl))
| in(sK4_skl,relation_dom(relation_dom_restriction(sK2_skl,sK3_skl))) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f95,plain,
( in(sK4_skl,sK3_skl)
| in(sK4_skl,relation_dom(relation_dom_restriction(sK2_skl,sK3_skl))) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f96,plain,
( ~ in(sK4_skl,sK3_skl)
| ~ in(sK4_skl,relation_dom(sK2_skl))
| ~ in(sK4_skl,relation_dom(relation_dom_restriction(sK2_skl,sK3_skl))) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f126,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)],[f36]) ).
fof(f127,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)],[f126]) ).
fof(f128,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)],[f127]) ).
fof(f129,plain,
! [B] :
( ! [C] :
( ( ! [A] :
( ( apply(B,sK13_skl(A,C,B)) != apply(C,sK13_skl(A,C,B))
& in(sK13_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,[sK13_skl]),skolemize(D,sK13_skl(A,C,B))],[f128]) ).
fof(f130,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)],[f129]) ).
fof(f142,plain,
! [X0,X1,X2] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f54]) ).
fof(f143,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f55]) ).
fof(f144,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_intersection2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f56]) ).
fof(f145,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))
| ~ relation(relation_dom_restriction(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f183,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)],[f145,f62]) ).
fof(f184,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)],[f183,f78]) ).
fof(f185,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)],[f184]) ).
fof(f192,plain,
! [X0] :
( relation_dom(relation_dom_restriction(sK2_skl,X0)) = set_intersection2(relation_dom(sK2_skl),X0)
| ~ relation(sK2_skl) ),
inference(resolution,[status(thm)],[f185,f93]) ).
fof(f197,plain,
! [X0] : relation_dom(relation_dom_restriction(sK2_skl,X0)) = set_intersection2(relation_dom(sK2_skl),X0),
inference(forward_subsumption_resolution,[status(thm)],[f192,f92]) ).
fof(f221,plain,
( ~ in(sK4_skl,sK3_skl)
| ~ in(sK4_skl,relation_dom(sK2_skl))
| ~ in(sK4_skl,set_intersection2(relation_dom(sK2_skl),sK3_skl)) ),
inference(backward_demodulation,[status(thm)],[f197,f96]) ).
fof(f223,plain,
( in(sK4_skl,sK3_skl)
| in(sK4_skl,set_intersection2(relation_dom(sK2_skl),sK3_skl)) ),
inference(backward_demodulation,[status(thm)],[f197,f95]) ).
fof(f224,plain,
( in(sK4_skl,relation_dom(sK2_skl))
| in(sK4_skl,set_intersection2(relation_dom(sK2_skl),sK3_skl)) ),
inference(backward_demodulation,[status(thm)],[f197,f94]) ).
fof(f230,plain,
( ~ in(sK4_skl,sK3_skl)
| ~ in(sK4_skl,relation_dom(sK2_skl))
| ~ in(sK4_skl,set_intersection2(sK3_skl,relation_dom(sK2_skl))) ),
inference(forward_demodulation,[status(thm)],[f50,f221]) ).
fof(f231,plain,
( ~ in(sK4_skl,sK3_skl)
| ~ in(sK4_skl,relation_dom(sK2_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f230,f144]) ).
fof(f233,plain,
( in(sK4_skl,sK3_skl)
| in(sK4_skl,set_intersection2(sK3_skl,relation_dom(sK2_skl))) ),
inference(forward_demodulation,[status(thm)],[f50,f223]) ).
fof(f234,plain,
in(sK4_skl,sK3_skl),
inference(forward_subsumption_resolution,[status(thm)],[f233,f142]) ).
fof(f235,plain,
( in(sK4_skl,relation_dom(sK2_skl))
| in(sK4_skl,set_intersection2(sK3_skl,relation_dom(sK2_skl))) ),
inference(forward_demodulation,[status(thm)],[f50,f224]) ).
fof(f236,plain,
in(sK4_skl,relation_dom(sK2_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f235,f143]) ).
fof(f239,plain,
~ in(sK4_skl,relation_dom(sK2_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f231,f234]) ).
fof(f245,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f236,f239]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU224+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/5.43 % Computer : n008.cluster.edu
% 0.17/5.43 % Model : x86_64 x86_64
% 0.17/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.43 % Memory : 8046.5625MB
% 0.17/5.43 % OS : Linux 6.8.0-71-generic
% 0.17/5.43 % CPULimit : 300
% 0.17/5.43 % WCLimit : 300
% 0.17/5.43 % DateTime : Mon Sep 21 06:00:46 UTC 2026
% 0.17/5.43 % CPUTime :
% 0.17/5.45 % Drodi V4.1.1
% 0.21/5.50 % Refutation found
% 0.21/5.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/5.57 % Elapsed time: 0.125458 seconds
% 0.21/5.57 % CPU time: 0.151875 seconds
% 0.21/5.57 % Total memory used: 20.146 MB
% 0.21/5.57 % Net memory used: 20.069 MB
%------------------------------------------------------------------------------