%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU194+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:19:37 PM UTC 2026
% Result : Theorem 0.49s 16.33s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 66 ( 8 unt; 8 def)
% Number of atoms : 202 ( 20 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 229 ( 93 ~; 92 |; 28 &)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 74 ( 67 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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(f14,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A,B] :
( relation(B)
=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> relation_dom(relation_dom_restriction(B,A)) = set_intersection2(relation_dom(B),A) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f36,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)],[f4]) ).
fof(f37,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)],[f36]) ).
fof(f38,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))],[f37]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ in(sK0_skl(X0,X2,X1),X2)
| ~ in(sK0_skl(X0,X2,X1),X1)
| ~ in(sK0_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f43,plain,
! [X0,X1,X2] :
( in(sK0_skl(X0,X2,X1),X1)
| in(sK0_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f44,plain,
! [X0,X1,X2] :
( in(sK0_skl(X0,X2,X1),X2)
| in(sK0_skl(X0,X2,X1),X0)
| X0 = set_intersection2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f55,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f56,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f67,plain,
( relation(sK4_skl)
& ~ empty(sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f19]) ).
fof(f68,plain,
~ empty(sK4_skl),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
relation(sK4_skl),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f87,plain,
! [A,B,C] :
( ( in(A,relation_dom(relation_dom_restriction(C,B)))
<=> ( in(A,relation_dom(C))
& in(A,B) ) )
| ~ relation(C) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f88,plain,
! [A,B,C] :
( ( ( ~ in(A,relation_dom(C))
| ~ in(A,B)
| in(A,relation_dom(relation_dom_restriction(C,B))) )
& ( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(NNF_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
! [C] :
( ( ! [A,B] :
( ~ in(A,relation_dom(C))
| ~ in(A,B)
| in(A,relation_dom(relation_dom_restriction(C,B))) )
& ! [A,B] :
( ( in(A,relation_dom(C))
& in(A,B) )
| ~ in(A,relation_dom(relation_dom_restriction(C,B))) ) )
| ~ relation(C) ),
inference(miniscoping,[status(thm)],[f88]) ).
fof(f90,plain,
! [X0,X1,X2] :
( in(X1,X2)
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [X0,X1,X2] :
( in(X1,relation_dom(X0))
| ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ~ in(X1,relation_dom(X0))
| ~ in(X1,X2)
| in(X1,relation_dom(relation_dom_restriction(X0,X2)))
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f96,plain,
? [A,B] :
( relation_dom(relation_dom_restriction(B,A)) != set_intersection2(relation_dom(B),A)
& relation(B) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f97,plain,
? [B] :
( ? [A] : relation_dom(relation_dom_restriction(B,A)) != set_intersection2(relation_dom(B),A)
& relation(B) ),
inference(miniscoping,[status(thm)],[f96]) ).
fof(f98,plain,
( relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)) != set_intersection2(relation_dom(sK7_skl),sK8_skl)
& relation(sK7_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(B,sK7_skl),skolemize(A,sK8_skl)],[f97]) ).
fof(f99,plain,
relation(sK7_skl),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)) != set_intersection2(relation_dom(sK7_skl),sK8_skl),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f568,plain,
( ~ empty(relation_dom(sK4_skl))
| ~ relation(sK4_skl) ),
inference(resolution,[status(thm)],[f68,f56]) ).
fof(f569,definition,
( sQ0_spl
<=> relation(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f571,plain,
( sQ0_spl
| ~ relation(sK4_skl) ),
inference(component_clause,[status(thm)],[f569]) ).
fof(f572,definition,
( sQ1_spl
<=> empty(relation_dom(sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f568,f569,f572]) ).
fof(f576,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f571,f69]) ).
fof(f577,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f578,plain,
( ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),sK8_skl)
| ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(sK7_skl))
| ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(relation_dom_restriction(sK7_skl,sK8_skl))) ),
inference(resolution,[status(thm)],[f42,f100]) ).
fof(f582,definition,
( sQ2_spl
<=> in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(relation_dom_restriction(sK7_skl,sK8_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f583,plain,
( ~ sQ2_spl
| in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(relation_dom_restriction(sK7_skl,sK8_skl))) ),
inference(component_clause,[status(thm)],[f582]) ).
fof(f584,plain,
( sQ2_spl
| ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(relation_dom_restriction(sK7_skl,sK8_skl))) ),
inference(component_clause,[status(thm)],[f582]) ).
fof(f585,definition,
( sQ3_spl
<=> in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(sK7_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f587,plain,
( sQ3_spl
| ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(sK7_skl)) ),
inference(component_clause,[status(thm)],[f585]) ).
fof(f588,definition,
( sQ4_spl
<=> in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f590,plain,
( sQ4_spl
| ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),sK8_skl) ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f591,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f578,f582,f585,f588]) ).
fof(f596,plain,
! [X0] :
( sQ4_spl
| ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(relation_dom_restriction(X0,sK8_skl)))
| ~ relation(X0) ),
inference(resolution,[status(thm)],[f590,f90]) ).
fof(f600,definition,
( sQ5_spl
<=> relation(sK7_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( sQ5_spl
| ~ relation(sK7_skl) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f606,definition,
( sQ7_spl
<=> relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)) = set_intersection2(relation_dom(sK7_skl),sK8_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( ~ sQ7_spl
| relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)) = set_intersection2(relation_dom(sK7_skl),sK8_skl) ),
inference(component_clause,[status(thm)],[f606]) ).
fof(f625,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f607,f100]) ).
fof(f626,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f641,plain,
( sQ2_spl
| in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(sK7_skl))
| relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)) = set_intersection2(relation_dom(sK7_skl),sK8_skl) ),
inference(resolution,[status(thm)],[f584,f43]) ).
fof(f642,plain,
( sQ2_spl
| ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(sK7_skl))
| ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),sK8_skl)
| ~ relation(sK7_skl) ),
inference(resolution,[status(thm)],[f584,f92]) ).
fof(f649,plain,
( sQ2_spl
| sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f641,f606,f585,f582]) ).
fof(f650,plain,
( sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f642,f600,f588,f585,f582]) ).
fof(f665,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f602,f99]) ).
fof(f666,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f665]) ).
fof(f676,plain,
! [X0] :
( sQ3_spl
| ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(relation_dom_restriction(sK7_skl,X0)))
| ~ relation(sK7_skl) ),
inference(resolution,[status(thm)],[f587,f91]) ).
fof(f684,definition,
! [X0] :
( sQ18_spl
<=> ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(relation_dom_restriction(sK7_skl,X0))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f685,plain,
! [X0] :
( ~ sQ18_spl
| ~ in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),relation_dom(relation_dom_restriction(sK7_skl,X0))) ),
inference(component_clause,[status(thm)],[f684]) ).
fof(f687,plain,
( sQ3_spl
| sQ18_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f676,f600,f684,f585]) ).
fof(f695,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f583,f685]) ).
fof(f696,plain,
( ~ sQ2_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f695]) ).
fof(f759,plain,
( sQ4_spl
| in(sK0_skl(relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)),sK8_skl,relation_dom(sK7_skl)),sK8_skl)
| relation_dom(relation_dom_restriction(sK7_skl,sK8_skl)) = set_intersection2(relation_dom(sK7_skl),sK8_skl)
| ~ relation(sK7_skl) ),
inference(resolution,[status(thm)],[f596,f44]) ).
fof(f768,plain,
( sQ4_spl
| sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f759,f600,f606,f588]) ).
fof(f775,plain,
$false,
inference(sat_refutation,[status(thm)],[f575,f577,f591,f626,f649,f650,f666,f687,f696,f768]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU194+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/15.59 % CPULimit : 300
% 0.08/15.59 % WCLimit : 300
% 0.08/15.59 % DateTime : Mon Sep 21 05:56:53 UTC 2026
% 0.49/15.60 % CPUTime :
% 0.49/15.61 % Drodi V4.1.1
% 0.49/16.33 % Refutation found
% 0.49/16.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.49/16.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.97/16.36 % Elapsed time: 0.744246 seconds
% 0.97/16.36 % CPU time: 5.526807 seconds
% 0.97/16.36 % Total memory used: 148.177 MB
% 0.97/16.36 % Net memory used: 140.555 MB
%------------------------------------------------------------------------------