%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU107+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 02:19:14 PM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 61 ( 18 unt; 4 def)
% Number of atoms : 150 ( 21 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 153 ( 64 ~; 64 |; 14 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 64 ( 61 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> element(prebool_difference(A,B,C),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A,B,C] :
( ( element(C,A)
& element(B,A)
& preboolean(A)
& ~ empty(A) )
=> prebool_difference(A,B,C) = set_difference(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
! [A] :
( ( preboolean(A)
& ~ empty(A) )
=> in(empty_set,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ ! [A] :
( ( preboolean(A)
& ~ empty(A) )
=> in(empty_set,A) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f25,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,plain,
! [A,B,C] :
( element(prebool_difference(A,B,C),A)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f47,plain,
! [X0,X1,X2] :
( element(prebool_difference(X0,X1,X2),X0)
| ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [A] : element(sK0_skl(A),A),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f7]) ).
fof(f49,plain,
! [X0] : element(sK0_skl(X0),X0),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f68,plain,
empty(sK4_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f14]) ).
fof(f69,plain,
empty(sK4_skl),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f96,plain,
! [A,B,C] :
( prebool_difference(A,B,C) = set_difference(B,C)
| ~ element(C,A)
| ~ element(B,A)
| ~ preboolean(A)
| empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f97,plain,
! [X0,X1,X2] :
( prebool_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f99,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
? [A] :
( ~ in(empty_set,A)
& preboolean(A)
& ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f101,plain,
( ~ in(empty_set,sK10_skl)
& preboolean(sK10_skl)
& ~ empty(sK10_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(A,sK10_skl)],[f100]) ).
fof(f102,plain,
~ empty(sK10_skl),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
preboolean(sK10_skl),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f104,plain,
~ in(empty_set,sK10_skl),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f107,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f108,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f110,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f109]) ).
fof(f112,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f125,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f126,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f137,plain,
! [X0,X1] :
( element(prebool_difference(X0,X1,sK0_skl(X0)),X0)
| ~ element(X1,X0)
| ~ preboolean(X0)
| empty(X0) ),
inference(resolution,[status(thm)],[f49,f47]) ).
fof(f146,plain,
sK4_skl = empty_set,
inference(resolution,[status(thm)],[f69,f126]) ).
fof(f154,plain,
~ in(sK4_skl,sK10_skl),
inference(backward_demodulation,[status(thm)],[f146,f104]) ).
fof(f243,plain,
! [X0,X1] :
( prebool_difference(sK10_skl,X0,X1) = set_difference(X0,X1)
| ~ element(X1,sK10_skl)
| ~ element(X0,sK10_skl)
| empty(sK10_skl) ),
inference(resolution,[status(thm)],[f97,f103]) ).
fof(f252,definition,
( sQ5_spl
<=> empty(sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( ~ sQ5_spl
| empty(sK10_skl) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
! [X0,X1] :
( sQ6_spl
<=> ( prebool_difference(sK10_skl,X0,X1) = set_difference(X0,X1)
| ~ element(X1,sK10_skl)
| ~ element(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f256,plain,
! [X0,X1] :
( ~ sQ6_spl
| prebool_difference(sK10_skl,X0,X1) = set_difference(X0,X1)
| ~ element(X1,sK10_skl)
| ~ element(X0,sK10_skl) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f243,f252,f255]) ).
fof(f259,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f102]) ).
fof(f260,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f264,plain,
! [X0] :
( ~ sQ6_spl
| prebool_difference(sK10_skl,X0,sK0_skl(sK10_skl)) = set_difference(X0,sK0_skl(sK10_skl))
| ~ element(X0,sK10_skl) ),
inference(resolution,[status(thm)],[f256,f49]) ).
fof(f265,plain,
( ~ sQ6_spl
| prebool_difference(sK10_skl,sK0_skl(sK10_skl),sK0_skl(sK10_skl)) = set_difference(sK0_skl(sK10_skl),sK0_skl(sK10_skl)) ),
inference(resolution,[status(thm)],[f264,f49]) ).
fof(f294,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f146,f112]) ).
fof(f296,plain,
! [X0] : set_difference(X0,X0) = sK4_skl,
inference(resolution,[status(thm)],[f294,f99]) ).
fof(f311,plain,
! [X0] :
( element(prebool_difference(sK10_skl,X0,sK0_skl(sK10_skl)),sK10_skl)
| ~ element(X0,sK10_skl)
| empty(sK10_skl) ),
inference(resolution,[status(thm)],[f137,f103]) ).
fof(f317,definition,
! [X0] :
( sQ12_spl
<=> ( element(prebool_difference(sK10_skl,X0,sK0_skl(sK10_skl)),sK10_skl)
| ~ element(X0,sK10_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f318,plain,
! [X0] :
( ~ sQ12_spl
| element(prebool_difference(sK10_skl,X0,sK0_skl(sK10_skl)),sK10_skl)
| ~ element(X0,sK10_skl) ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,plain,
( sQ12_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f311,f252,f317]) ).
fof(f321,plain,
( ~ sQ12_spl
| element(prebool_difference(sK10_skl,sK0_skl(sK10_skl),sK0_skl(sK10_skl)),sK10_skl) ),
inference(resolution,[status(thm)],[f318,f49]) ).
fof(f322,plain,
( ~ sQ6_spl
| prebool_difference(sK10_skl,sK0_skl(sK10_skl),sK0_skl(sK10_skl)) = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f296,f265]) ).
fof(f342,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| element(sK4_skl,sK10_skl) ),
inference(forward_demodulation,[status(thm)],[f322,f321]) ).
fof(f347,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| in(sK4_skl,sK10_skl)
| empty(sK10_skl) ),
inference(resolution,[status(thm)],[f342,f108]) ).
fof(f357,definition,
( sQ15_spl
<=> in(sK4_skl,sK10_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f358,plain,
( ~ sQ15_spl
| in(sK4_skl,sK10_skl) ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f360,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| sQ15_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f347,f252,f357,f255,f317]) ).
fof(f361,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f358,f154]) ).
fof(f362,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f361]) ).
fof(f363,plain,
$false,
inference(sat_refutation,[status(thm)],[f258,f260,f320,f360,f362]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU107+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35 % Computer : n019.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8046.5625MB
% 0.12/0.35 % OS : Linux 6.8.0-71-generic
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Mon Sep 21 05:51:04 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.047454 seconds
% 0.14/0.40 % CPU time: 0.156234 seconds
% 0.14/0.40 % Total memory used: 50.032 MB
% 0.14/0.40 % Net memory used: 49.847 MB
%------------------------------------------------------------------------------