%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 03:14:55 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 27
% Syntax : Number of formulae : 91 ( 13 unt; 12 def)
% Number of atoms : 271 ( 110 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 265 ( 85 ~; 168 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
m != n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
n != k,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
k != m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [Y] :
( f(Y) != m
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [Y] :
( f(Y) != Y
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [Y] :
( element(Y,f(Y))
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [Y] :
( element(f(Y),Y)
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
! [Y,V] :
( ~ element(V,Y)
| ~ element(Y,V)
| V = Y
| V = m
| element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
! [Y] :
( g(Y) != Y
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
! [Y] :
( element(Y,g(Y))
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [Y] :
( element(g(Y),Y)
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
! [Y,V] :
( ~ element(V,Y)
| ~ element(Y,V)
| V = Y
| V = n
| ~ element(Y,n)
| Y = n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [Y] :
( element(Y,k)
| Y != m
| Y = k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
! [Y] :
( element(Y,k)
| Y != n
| Y = k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
! [Y] :
( ~ element(Y,k)
| Y = n
| Y = m
| Y = k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
m != n,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
n != k,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
k != m,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0] :
( f(X0) != m
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0] :
( f(X0) != X0
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0] :
( element(X0,f(X0))
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0] :
( element(f(X0),X0)
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = m
| element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
! [X0] :
( g(X0) != X0
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
! [X0] :
( element(X0,g(X0))
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0] :
( element(g(X0),X0)
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = n
| ~ element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
! [X0] :
( element(X0,k)
| X0 != m
| X0 = k ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
! [X0] :
( element(X0,k)
| X0 != n
| X0 = k ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f32,plain,
! [X0] :
( ~ element(X0,k)
| X0 = n
| X0 = m
| X0 = k ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,plain,
( element(m,k)
| m = k ),
inference(destructive_equality_resolution,[status(thm)],[f30]) ).
fof(f34,plain,
( element(n,k)
| n = k ),
inference(destructive_equality_resolution,[status(thm)],[f31]) ).
fof(f35,plain,
element(m,k),
inference(forward_subsumption_resolution,[status(thm)],[f33,f19]) ).
fof(f36,plain,
element(n,k),
inference(forward_subsumption_resolution,[status(thm)],[f34,f18]) ).
fof(f38,plain,
( ~ element(k,m)
| k = m
| f(k) = n
| f(k) = m
| f(k) = k ),
inference(resolution,[status(thm)],[f32,f23]) ).
fof(f39,plain,
( n = n
| n = m
| n = k ),
inference(resolution,[status(thm)],[f32,f36]) ).
fof(f40,plain,
( m = n
| m = m
| m = k ),
inference(resolution,[status(thm)],[f32,f35]) ).
fof(f50,definition,
( sQ3_spl
<=> k = n ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ3_spl
| k = n ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,definition,
( sQ4_spl
<=> element(k,n) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ4_spl
| element(k,n) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f55,plain,
( sQ4_spl
| ~ element(k,n) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f57,definition,
( sQ5_spl
<=> f(k) = k ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( ~ sQ5_spl
| f(k) = k ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,definition,
( sQ6_spl
<=> f(k) = m ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ6_spl
| f(k) = m ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ7_spl
<=> f(k) = n ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ7_spl
| f(k) = n ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,definition,
( sQ8_spl
<=> k = m ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( ~ sQ8_spl
| k = m ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,definition,
( sQ9_spl
<=> element(k,m) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ9_spl
| element(k,m) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( ~ sQ9_spl
| sQ8_spl
| sQ7_spl
| sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f38,f57,f60,f63,f66,f69]) ).
fof(f73,definition,
( sQ10_spl
<=> n = m ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ10_spl
| n = m ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,definition,
( sQ11_spl
<=> n = n ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( sQ11_spl
| sQ10_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f39,f50,f73,f76]) ).
fof(f80,definition,
( sQ12_spl
<=> m = m ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( sQ10_spl
| sQ12_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f40,f66,f80,f73]) ).
fof(f84,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f17]) ).
fof(f85,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f84]) ).
fof(f86,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f67,f19]) ).
fof(f87,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f86]) ).
fof(f88,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f51,f18]) ).
fof(f89,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( ~ sQ7_spl
| element(k,n)
| ~ element(k,m)
| k = m ),
inference(paramodulation,[status(thm)],[f64,f22]) ).
fof(f98,plain,
( ~ sQ7_spl
| sQ4_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f91,f66,f69,f53,f63]) ).
fof(f102,plain,
! [X0] :
( element(X0,n)
| X0 = n
| ~ element(X0,g(X0))
| g(X0) = X0
| g(X0) = m
| element(X0,m)
| X0 = m ),
inference(resolution,[status(thm)],[f24,f28]) ).
fof(f104,plain,
( ~ element(k,n)
| n = k
| n = m
| element(k,m)
| k = m ),
inference(resolution,[status(thm)],[f24,f36]) ).
fof(f112,plain,
! [X0] :
( element(X0,n)
| X0 = n
| ~ element(X0,g(X0))
| g(X0) = m
| element(X0,m)
| X0 = m ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f26]) ).
fof(f113,plain,
( ~ sQ4_spl
| sQ3_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f104,f66,f69,f73,f50,f53]) ).
fof(f118,plain,
( ~ sQ5_spl
| ~ element(k,m)
| k = m ),
inference(resolution,[status(thm)],[f58,f21]) ).
fof(f123,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f118,f66,f69,f57]) ).
fof(f153,plain,
! [X0] :
( element(X0,n)
| X0 = n
| g(X0) = m
| element(X0,m)
| X0 = m ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f27]) ).
fof(f156,plain,
! [X0] :
( element(X0,n)
| X0 = n
| element(X0,m)
| X0 = m
| element(X0,m)
| element(X0,n)
| X0 = n ),
inference(paramodulation,[status(thm)],[f153,f27]) ).
fof(f167,plain,
! [X0] :
( X0 = m
| element(X0,m)
| element(X0,n)
| X0 = n ),
inference(duplicate_literals_removal,[status(thm)],[f156]) ).
fof(f175,definition,
( sQ25_spl
<=> element(m,k) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( sQ25_spl
| ~ element(m,k) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f188,plain,
! [X0] :
( ~ sQ4_spl
| ~ element(X0,k)
| ~ element(k,X0)
| X0 = k
| X0 = n
| k = n ),
inference(resolution,[status(thm)],[f54,f29]) ).
fof(f190,definition,
! [X0] :
( sQ26_spl
<=> ( ~ element(X0,k)
| ~ element(k,X0)
| X0 = k
| X0 = n ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f191,plain,
! [X0] :
( ~ sQ26_spl
| ~ element(X0,k)
| ~ element(k,X0)
| X0 = k
| X0 = n ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,plain,
( ~ sQ4_spl
| sQ26_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f188,f50,f190,f53]) ).
fof(f213,plain,
( ~ sQ9_spl
| ~ sQ26_spl
| ~ element(m,k)
| m = k
| m = n ),
inference(resolution,[status(thm)],[f191,f70]) ).
fof(f218,plain,
( ~ sQ9_spl
| ~ sQ26_spl
| ~ sQ25_spl
| sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f213,f73,f66,f175,f190,f69]) ).
fof(f228,plain,
( sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f35]) ).
fof(f229,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f243,plain,
( ~ sQ6_spl
| ~ element(k,m)
| k = m ),
inference(resolution,[status(thm)],[f61,f20]) ).
fof(f248,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f243,f66,f69,f60]) ).
fof(f253,plain,
( sQ4_spl
| k = m
| element(k,m)
| k = n ),
inference(resolution,[status(thm)],[f55,f167]) ).
fof(f254,plain,
( sQ4_spl
| sQ8_spl
| sQ9_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f253,f50,f69,f66,f53]) ).
fof(f255,plain,
$false,
inference(sat_refutation,[status(thm)],[f72,f79,f83,f85,f87,f89,f98,f113,f123,f193,f218,f229,f248,f254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n017.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Mon Sep 21 10:34:27 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.055172 seconds
% 0.14/0.41 % CPU time: 0.157238 seconds
% 0.14/0.41 % Total memory used: 80.622 MB
% 0.14/0.41 % Net memory used: 80.192 MB
%------------------------------------------------------------------------------