%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU186+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 : n020.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 02:19:34 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 8 unt; 2 def)
% Number of atoms : 89 ( 27 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 37 ~; 31 |; 11 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 60 ( 50 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
( relation(A)
<=> ! [B] :
~ ( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( ! [B,C] : ~ in(ordered_pair(B,C),A)
=> A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,plain,
! [A] :
( relation(A)
<=> ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
! [A] :
( ( ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) )
| relation(A) )
& ( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(NNF_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
( ! [A] :
( ? [B] :
( ! [C,D] : B != ordered_pair(C,D)
& in(B,A) )
| relation(A) )
& ! [A] :
( ! [B] :
( ? [C,D] : B = ordered_pair(C,D)
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
( ! [A] :
( ( ! [C,D] : sK2_skl(A) != ordered_pair(C,D)
& in(sK2_skl(A),A) )
| relation(A) )
& ! [A] :
( ! [B] :
( B = ordered_pair(sK0_skl(B,A),sK1_skl(B,A))
| ~ in(B,A) )
| ~ relation(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(C,sK0_skl(B,A)),skolemize(D,sK1_skl(B,A)),skolemize(B,sK2_skl(A))],[f35]) ).
fof(f37,plain,
! [X0,X1] :
( X1 = ordered_pair(sK0_skl(X1,X0),sK1_skl(X1,X0))
| ~ in(X1,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f41,plain,
! [A] : element(sK3_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(B,sK3_skl(A))],[f11]) ).
fof(f42,plain,
! [X0] : element(sK3_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f61,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f62,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
? [A] :
( A != empty_set
& ! [B,C] : ~ in(ordered_pair(B,C),A)
& relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f64,plain,
( sK8_skl != empty_set
& ! [B,C] : ~ in(ordered_pair(B,C),sK8_skl)
& relation(sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(A,sK8_skl)],[f63]) ).
fof(f65,plain,
relation(sK8_skl),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,plain,
! [X0,X1] : ~ in(ordered_pair(X0,X1),sK8_skl),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f67,plain,
sK8_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f68,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f69,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f83,plain,
! [X0] :
( X0 = ordered_pair(sK0_skl(X0,sK8_skl),sK1_skl(X0,sK8_skl))
| ~ in(X0,sK8_skl) ),
inference(resolution,[status(thm)],[f37,f65]) ).
fof(f133,plain,
! [X0,X1] :
( X1 = empty_set
| in(X0,X1)
| ~ element(X0,X1) ),
inference(resolution,[status(thm)],[f62,f69]) ).
fof(f138,plain,
! [X0] :
( X0 = empty_set
| in(sK3_skl(X0),X0) ),
inference(resolution,[status(thm)],[f133,f42]) ).
fof(f141,plain,
( sK3_skl(sK8_skl) = ordered_pair(sK0_skl(sK3_skl(sK8_skl),sK8_skl),sK1_skl(sK3_skl(sK8_skl),sK8_skl))
| sK8_skl = empty_set ),
inference(resolution,[status(thm)],[f138,f83]) ).
fof(f143,definition,
( sQ4_spl
<=> sK8_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ4_spl
| sK8_skl = empty_set ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,definition,
( sQ5_spl
<=> sK3_skl(sK8_skl) = ordered_pair(sK0_skl(sK3_skl(sK8_skl),sK8_skl),sK1_skl(sK3_skl(sK8_skl),sK8_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f147,plain,
( ~ sQ5_spl
| sK3_skl(sK8_skl) = ordered_pair(sK0_skl(sK3_skl(sK8_skl),sK8_skl),sK1_skl(sK3_skl(sK8_skl),sK8_skl)) ),
inference(component_clause,[status(thm)],[f146]) ).
fof(f149,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f141,f143,f146]) ).
fof(f150,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f67]) ).
fof(f151,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f150]) ).
fof(f194,plain,
( ~ sQ5_spl
| ~ in(sK3_skl(sK8_skl),sK8_skl) ),
inference(paramodulation,[status(thm)],[f147,f66]) ).
fof(f197,plain,
( ~ sQ5_spl
| sK8_skl = empty_set ),
inference(resolution,[status(thm)],[f194,f138]) ).
fof(f198,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f197,f143,f146]) ).
fof(f199,plain,
$false,
inference(sat_refutation,[status(thm)],[f149,f151,f198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU186+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n020.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 05:56:17 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.48 % Refutation found
% 0.17/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.50 % Elapsed time: 0.063178 seconds
% 0.17/0.50 % CPU time: 0.201831 seconds
% 0.17/0.50 % Total memory used: 77.461 MB
% 0.17/0.50 % Net memory used: 77.305 MB
%------------------------------------------------------------------------------