%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN415+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 03:16:01 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of formulae : 61 ( 1 unt; 12 def)
% Number of atoms : 214 ( 34 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 259 ( 106 ~; 109 |; 24 &)
% ( 14 <=>; 4 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 13 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 57 ( 44 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ! [Y,Z] :
( ( f(Z)
& f(Y) )
=> Y = Z )
& ? [X] : f(X) )
<=> ? [U] :
( ! [V] :
( f(V)
=> U = V )
& f(U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ! [Y,Z] :
( ( f(Z)
& f(Y) )
=> Y = Z )
& ? [X] : f(X) )
<=> ? [U] :
( ! [V] :
( f(V)
=> U = V )
& f(U) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ! [Y,Z] :
( Y = Z
| ~ f(Z)
| ~ f(Y) )
& ? [X] : f(X) )
<~> ? [U] :
( ! [V] :
( U = V
| ~ f(V) )
& f(U) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( ! [Y,Z] :
( Y = Z
| ~ f(Z)
| ~ f(Y) )
& ? [X] : f(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( sP0_prd
<~> ? [U] :
( ! [V] :
( U = V
| ~ f(V) )
& f(U) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ! [U] :
( ? [V] :
( U != V
& f(V) )
| ~ f(U) )
| ~ sP0_prd )
& ( ? [U] :
( ! [V] :
( U = V
| ~ f(V) )
& f(U) )
| sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ! [U] :
( ( U != sK1_skl(U)
& f(sK1_skl(U)) )
| ~ f(U) )
| ~ sP0_prd )
& ( ( ! [V] :
( sK0_skl = V
| ~ f(V) )
& f(sK0_skl) )
| sP0_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl(U))],[f6]) ).
fof(f8,plain,
( f(sK0_skl)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0] :
( sK0_skl = X0
| ~ f(X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0] :
( f(sK1_skl(X0))
| ~ f(X0)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X0] :
( X0 != sK1_skl(X0)
| ~ f(X0)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f12,plain,
( ( ? [Y,Z] :
( Y != Z
& f(Z)
& f(Y) )
| ! [X] : ~ f(X)
| sP0_prd )
& ( ( ! [Y,Z] :
( Y = Z
| ~ f(Z)
| ~ f(Y) )
& ? [X] : f(X) )
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
( ( ( sK3_skl != sK4_skl
& f(sK4_skl)
& f(sK3_skl) )
| ! [X] : ~ f(X)
| sP0_prd )
& ( ( ! [Y,Z] :
( Y = Z
| ~ f(Z)
| ~ f(Y) )
& f(sK2_skl) )
| ~ sP0_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl),skolemize(Z,sK4_skl)],[f12]) ).
fof(f14,plain,
( f(sK2_skl)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( X0 = X1
| ~ f(X1)
| ~ f(X0)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X0] :
( f(sK3_skl)
| ~ f(X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
! [X0] :
( f(sK4_skl)
| ~ f(X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f18,plain,
! [X0] :
( sK3_skl != sK4_skl
| ~ f(X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f19,definition,
( sQ0_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f22,definition,
( sQ1_spl
<=> f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f23,plain,
( ~ sQ1_spl
| f(sK0_skl) ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f19,f22]) ).
fof(f26,definition,
! [X0] :
( sQ2_spl
<=> ( sK0_skl = X0
| ~ f(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f27,plain,
! [X0] :
( ~ sQ2_spl
| sK0_skl = X0
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f29,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f19,f26]) ).
fof(f30,definition,
! [X0] :
( sQ3_spl
<=> ( f(sK1_skl(X0))
| ~ f(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f31,plain,
! [X0] :
( ~ sQ3_spl
| f(sK1_skl(X0))
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f19,f30]) ).
fof(f34,definition,
! [X0] :
( sQ4_spl
<=> ( X0 != sK1_skl(X0)
| ~ f(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f35,plain,
! [X0] :
( ~ sQ4_spl
| X0 != sK1_skl(X0)
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f34]) ).
fof(f37,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f19,f34]) ).
fof(f38,definition,
( sQ5_spl
<=> f(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ5_spl
| f(sK2_skl) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f14,f19,f38]) ).
fof(f42,definition,
! [X0,X1] :
( sQ6_spl
<=> ( X0 = X1
| ~ f(X1)
| ~ f(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f43,plain,
! [X0,X1] :
( ~ sQ6_spl
| X0 = X1
| ~ f(X1)
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f15,f19,f42]) ).
fof(f46,definition,
! [X0] :
( sQ7_spl
<=> ~ f(X0) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f47,plain,
! [X0] :
( ~ sQ7_spl
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,definition,
( sQ8_spl
<=> f(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ8_spl
| f(sK3_skl) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( sQ8_spl
| sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f19,f46,f49]) ).
fof(f53,definition,
( sQ9_spl
<=> f(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( ~ sQ9_spl
| f(sK4_skl) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( sQ9_spl
| sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f17,f19,f46,f53]) ).
fof(f57,definition,
( sQ10_spl
<=> sK3_skl = sK4_skl ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ10_spl
| sK3_skl != sK4_skl ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( ~ sQ10_spl
| sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f18,f19,f46,f57]) ).
fof(f61,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23,f47]) ).
fof(f62,plain,
( ~ sQ1_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f61]) ).
fof(f64,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| X0 = sK2_skl
| ~ f(X0) ),
inference(resolution,[status(thm)],[f43,f39]) ).
fof(f65,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ f(X0)
| sK1_skl(X0) = sK2_skl ),
inference(resolution,[status(thm)],[f64,f31]) ).
fof(f67,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ f(sK2_skl)
| ~ f(sK2_skl) ),
inference(resolution,[status(thm)],[f65,f35]) ).
fof(f68,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f67,f38,f42,f30,f34]) ).
fof(f70,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| sK0_skl = sK4_skl ),
inference(resolution,[status(thm)],[f27,f54]) ).
fof(f71,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| sK0_skl = sK3_skl ),
inference(resolution,[status(thm)],[f27,f50]) ).
fof(f73,plain,
( sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| sK3_skl != sK0_skl ),
inference(backward_demodulation,[status(thm)],[f70,f59]) ).
fof(f76,plain,
( sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ8_spl
| sK0_skl != sK0_skl ),
inference(forward_demodulation,[status(thm)],[f71,f73]) ).
fof(f77,plain,
( sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f76]) ).
fof(f78,plain,
( sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f77]) ).
fof(f79,plain,
$false,
inference(sat_refutation,[status(thm)],[f25,f29,f33,f37,f41,f45,f52,f56,f60,f62,f68,f78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN415+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n019.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.42 % CPULimit : 300
% 0.18/0.42 % WCLimit : 300
% 0.18/0.42 % DateTime : Mon Sep 21 10:53:49 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Drodi V4.1.1
% 0.18/0.47 % Refutation found
% 0.18/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.51 % Elapsed time: 0.078816 seconds
% 0.24/0.51 % CPU time: 0.191372 seconds
% 0.24/0.51 % Total memory used: 79.830 MB
% 0.24/0.51 % Net memory used: 79.324 MB
%------------------------------------------------------------------------------