%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM386+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 : n001.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 01:40:25 PM UTC 2026
% Result : Theorem 0.13s 5.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of formulae : 108 ( 19 unt; 12 def)
% Number of atoms : 300 ( 49 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 300 ( 108 ~; 128 |; 42 &)
% ( 18 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 13 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 106 ( 95 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [A,B] :
( in(A,succ(B))
<=> ( A = B
| in(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [A,B] :
( in(A,succ(B))
<=> ( A = B
| in(A,B) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f38,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f39,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f41,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f47,plain,
! [X0] : succ(X0) = set_union2(X0,singleton(X0)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f48,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f49,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f50,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f49]) ).
fof(f51,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,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_union2(A,B) )
& ( ! [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| in(D,C) )
& ( in(D,B)
| in(D,A)
| ~ in(D,C) ) )
| C != set_union2(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f56,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_union2(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_union2(A,B) ) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
( ! [A,B,C] :
( ( ( in(sK1_skl(C,B,A),B)
| in(sK1_skl(C,B,A),A)
| in(sK1_skl(C,B,A),C) )
& ( ( ~ in(sK1_skl(C,B,A),B)
& ~ in(sK1_skl(C,B,A),A) )
| ~ in(sK1_skl(C,B,A),C) ) )
| C = set_union2(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_union2(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B,A))],[f56]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X1)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ~ in(X3,X2)
| in(X3,X0)
| X0 != set_union2(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f66,plain,
empty(empty_set),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f86,plain,
( relation(sK4_skl)
& empty(sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(A,sK4_skl)],[f19]) ).
fof(f87,plain,
empty(sK4_skl),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f89,plain,
empty(sK5_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(A,sK5_skl)],[f20]) ).
fof(f90,plain,
empty(sK5_skl),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
( function(sK6_skl)
& empty(sK6_skl)
& relation(sK6_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(A,sK6_skl)],[f21]) ).
fof(f93,plain,
empty(sK6_skl),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
function(sK6_skl),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f115,plain,
? [A,B] :
( in(A,succ(B))
<~> ( A = B
| in(A,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f116,plain,
? [A,B] :
( ( ( A != B
& ~ in(A,B) )
| ~ in(A,succ(B)) )
& ( A = B
| in(A,B)
| in(A,succ(B)) ) ),
inference(NNF_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
( ( ( sK13_skl != sK14_skl
& ~ in(sK13_skl,sK14_skl) )
| ~ in(sK13_skl,succ(sK14_skl)) )
& ( sK13_skl = sK14_skl
| in(sK13_skl,sK14_skl)
| in(sK13_skl,succ(sK14_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(A,sK13_skl),skolemize(B,sK14_skl)],[f116]) ).
fof(f118,plain,
( sK13_skl = sK14_skl
| in(sK13_skl,sK14_skl)
| in(sK13_skl,succ(sK14_skl)) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f119,plain,
( ~ in(sK13_skl,sK14_skl)
| ~ in(sK13_skl,succ(sK14_skl)) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f120,plain,
( sK13_skl != sK14_skl
| ~ in(sK13_skl,succ(sK14_skl)) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f134,definition,
( sQ0_spl
<=> in(sK13_skl,succ(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( ~ sQ0_spl
| in(sK13_skl,succ(sK14_skl)) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f136,plain,
( sQ0_spl
| ~ in(sK13_skl,succ(sK14_skl)) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,definition,
( sQ1_spl
<=> in(sK13_skl,sK14_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ1_spl
| in(sK13_skl,sK14_skl) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,definition,
( sQ2_spl
<=> sK13_skl = sK14_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( ~ sQ2_spl
| sK13_skl = sK14_skl ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f118,f134,f137,f140]) ).
fof(f144,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f119,f134,f137]) ).
fof(f145,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f120,f134,f140]) ).
fof(f146,plain,
! [X0,X1] :
( X0 = X1
| ~ in(X0,singleton(X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f51]) ).
fof(f147,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f52]) ).
fof(f148,plain,
! [X0,X1,X2] :
( in(X0,X2)
| in(X0,X1)
| ~ in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f58]) ).
fof(f149,plain,
! [X0,X1,X2] :
( ~ in(X0,X1)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f59]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ~ in(X0,X2)
| in(X0,set_union2(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f60]) ).
fof(f152,plain,
function(sK4_skl),
inference(resolution,[status(thm)],[f39,f87]) ).
fof(f153,plain,
function(empty_set),
inference(resolution,[status(thm)],[f39,f66]) ).
fof(f157,plain,
function(sK5_skl),
inference(resolution,[status(thm)],[f90,f39]) ).
fof(f160,plain,
! [X0] :
( one_to_one(X0)
| ~ function(X0)
| ~ empty(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f41]) ).
fof(f161,plain,
( one_to_one(sK6_skl)
| ~ function(sK6_skl) ),
inference(resolution,[status(thm)],[f160,f93]) ).
fof(f162,plain,
( one_to_one(sK5_skl)
| ~ function(sK5_skl) ),
inference(resolution,[status(thm)],[f160,f90]) ).
fof(f163,plain,
( one_to_one(sK4_skl)
| ~ function(sK4_skl) ),
inference(resolution,[status(thm)],[f160,f87]) ).
fof(f164,plain,
( one_to_one(empty_set)
| ~ function(empty_set) ),
inference(resolution,[status(thm)],[f160,f66]) ).
fof(f165,definition,
( sQ3_spl
<=> function(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( sQ3_spl
| ~ function(sK6_skl) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,definition,
( sQ4_spl
<=> one_to_one(sK6_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f161,f165,f168]) ).
fof(f172,definition,
( sQ5_spl
<=> function(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( sQ5_spl
| ~ function(sK5_skl) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
( sQ6_spl
<=> one_to_one(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f162,f172,f175]) ).
fof(f179,definition,
( sQ7_spl
<=> function(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ7_spl
| ~ function(sK4_skl) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,definition,
( sQ8_spl
<=> one_to_one(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f163,f179,f182]) ).
fof(f186,definition,
( sQ9_spl
<=> function(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( sQ9_spl
| ~ function(empty_set) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ10_spl
<=> one_to_one(empty_set) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f164,f186,f189]) ).
fof(f193,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f94]) ).
fof(f194,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f201,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f153]) ).
fof(f202,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f201]) ).
fof(f203,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f152]) ).
fof(f204,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f203]) ).
fof(f205,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f174,f157]) ).
fof(f206,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f260,plain,
! [X0,X1] :
( in(X0,singleton(X1))
| in(X0,X1)
| ~ in(X0,succ(X1)) ),
inference(paramodulation,[status(thm)],[f47,f148]) ).
fof(f269,plain,
! [X0,X1] :
( ~ in(X0,X1)
| in(X0,succ(X1)) ),
inference(paramodulation,[status(thm)],[f47,f149]) ).
fof(f278,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| in(X0,succ(X1)) ),
inference(paramodulation,[status(thm)],[f47,f150]) ).
fof(f306,plain,
( sQ0_spl
| ~ in(sK13_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f269,f136]) ).
fof(f309,plain,
( sQ0_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f138]) ).
fof(f310,plain,
( sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f313,plain,
( ~ sQ0_spl
| in(sK13_skl,singleton(sK14_skl))
| in(sK13_skl,sK14_skl) ),
inference(resolution,[status(thm)],[f260,f135]) ).
fof(f317,definition,
( sQ11_spl
<=> in(sK13_skl,singleton(sK14_skl)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( ~ sQ11_spl
| in(sK13_skl,singleton(sK14_skl)) ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,plain,
( ~ sQ0_spl
| sQ11_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f313,f137,f317,f134]) ).
fof(f322,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ in(sK14_skl,succ(sK14_skl)) ),
inference(backward_demodulation,[status(thm)],[f141,f136]) ).
fof(f480,plain,
! [X0] : in(X0,succ(X0)),
inference(resolution,[status(thm)],[f278,f147]) ).
fof(f483,plain,
( sQ0_spl
| ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f322,f480]) ).
fof(f492,plain,
( sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f483]) ).
fof(f503,plain,
( ~ sQ11_spl
| sK13_skl = sK14_skl ),
inference(resolution,[status(thm)],[f318,f146]) ).
fof(f507,plain,
( ~ sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f503,f140,f317]) ).
fof(f508,plain,
$false,
inference(sat_refutation,[status(thm)],[f143,f144,f145,f171,f178,f185,f192,f194,f202,f204,f206,f310,f320,f492,f507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM386+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/5.41 % Computer : n001.cluster.edu
% 0.13/5.41 % Model : x86_64 x86_64
% 0.13/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.41 % Memory : 8046.5625MB
% 0.13/5.41 % OS : Linux 6.8.0-71-generic
% 0.13/5.41 % CPULimit : 300
% 0.13/5.41 % WCLimit : 300
% 0.13/5.41 % DateTime : Mon Sep 21 02:32:03 UTC 2026
% 0.13/5.42 % CPUTime :
% 0.13/5.43 % Drodi V4.1.1
% 0.13/5.45 % Refutation found
% 0.13/5.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/5.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.49 % Elapsed time: 0.062983 seconds
% 0.13/5.49 % CPU time: 0.108107 seconds
% 0.13/5.49 % Total memory used: 10.161 MB
% 0.13/5.49 % Net memory used: 10.090 MB
%------------------------------------------------------------------------------