%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN014-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.09s 0.57s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 47
% Syntax : Number of formulae : 173 ( 4 unt; 31 def)
% Number of atoms : 541 ( 181 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 569 ( 201 ~; 337 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 32 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 53 ( 53 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
m != n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
( m = k
| n = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [Y] :
( element(Y,j)
| Y != k
| Y = j ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [Y] :
( ~ element(Y,j)
| Y = k
| Y = j ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [Y] :
( f(Y) != m
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [Y] :
( f(Y) != Y
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [Y] :
( element(Y,f(Y))
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
! [Y] :
( element(f(Y),Y)
| ~ element(Y,m)
| Y = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [Y,V1] :
( ~ element(V1,Y)
| ~ element(Y,V1)
| V1 = Y
| V1 = m
| element(Y,m)
| Y = m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
! [Y] :
( g(Y) != Y
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
! [Y] :
( element(Y,g(Y))
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
! [Y] :
( element(g(Y),Y)
| element(Y,n)
| Y = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
! [Y,V] :
( ~ element(V,Y)
| ~ element(Y,V)
| V = Y
| V = n
| ~ element(Y,n)
| Y = n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
! [Y] :
( element(Y,k)
| Y != m
| Y = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
! [Y] :
( element(Y,k)
| Y != n
| Y = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
! [Y] :
( ~ element(Y,k)
| Y = n
| Y = m
| Y = k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
m != n,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
( m = k
| n = k ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0] :
( element(X0,j)
| X0 != k
| X0 = j ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0] :
( ~ element(X0,j)
| X0 = k
| X0 = j ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [X0] :
( f(X0) != m
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
! [X0] :
( f(X0) != X0
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0] :
( element(X0,f(X0))
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0] :
( element(f(X0),X0)
| ~ element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = m
| element(X0,m)
| X0 = m ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0] :
( g(X0) != X0
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0] :
( element(X0,g(X0))
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0] :
( element(g(X0),X0)
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
! [X0,X1] :
( ~ element(X1,X0)
| ~ element(X0,X1)
| X1 = X0
| X1 = n
| ~ element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0] :
( element(X0,k)
| X0 != m
| X0 = k ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f33,plain,
! [X0] :
( element(X0,k)
| X0 != n
| X0 = k ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
! [X0] :
( ~ element(X0,k)
| X0 = n
| X0 = m
| X0 = k ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f35,definition,
( sQ0_spl
<=> n = k ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( ~ sQ0_spl
| n = k ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
( sQ1_spl
<=> m = k ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f39,plain,
( ~ sQ1_spl
| m = k ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f35,f38]) ).
fof(f42,plain,
( element(k,j)
| k = j ),
inference(destructive_equality_resolution,[status(thm)],[f20]) ).
fof(f43,plain,
( element(m,k)
| m = k ),
inference(destructive_equality_resolution,[status(thm)],[f32]) ).
fof(f44,plain,
( element(n,k)
| n = k ),
inference(destructive_equality_resolution,[status(thm)],[f33]) ).
fof(f45,plain,
( ~ sQ0_spl
| element(k,j)
| n = j ),
inference(forward_demodulation,[status(thm)],[f36,f42]) ).
fof(f46,plain,
( ~ sQ0_spl
| element(n,j)
| n = j ),
inference(forward_demodulation,[status(thm)],[f36,f45]) ).
fof(f47,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(X0,j)
| X0 = n
| X0 = j ),
inference(forward_demodulation,[status(thm)],[f36,f21]) ).
fof(f48,plain,
( ~ sQ0_spl
| n = j
| n = n
| n = j ),
inference(resolution,[status(thm)],[f47,f46]) ).
fof(f49,definition,
( sQ2_spl
<=> n = j ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ2_spl
| n = j ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,definition,
( sQ3_spl
<=> n = n ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( ~ sQ0_spl
| sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f48,f49,f52,f35]) ).
fof(f56,definition,
( sQ4_spl
<=> k = j ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ4_spl
| k = j ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,definition,
( sQ5_spl
<=> element(k,j) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ5_spl
| element(k,j) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f42,f56,f59]) ).
fof(f66,plain,
( ~ sQ1_spl
| element(n,k)
| n = m ),
inference(forward_demodulation,[status(thm)],[f39,f44]) ).
fof(f67,plain,
( ~ sQ1_spl
| element(n,m)
| n = m ),
inference(forward_demodulation,[status(thm)],[f39,f66]) ).
fof(f68,plain,
( ~ sQ1_spl
| element(n,m) ),
inference(forward_subsumption_resolution,[status(thm)],[f67,f18]) ).
fof(f77,definition,
( sQ6_spl
<=> element(n,j) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ0_spl
| sQ6_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f46,f49,f77,f35]) ).
fof(f81,definition,
( sQ7_spl
<=> element(n,k) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ7_spl
| element(n,k) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f35,f81]) ).
fof(f85,definition,
( sQ8_spl
<=> element(m,k) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ8_spl
| element(m,k) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ8_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f43,f38,f85]) ).
fof(f93,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| element(n,m) ),
inference(forward_demodulation,[status(thm)],[f39,f82]) ).
fof(f95,definition,
( sQ9_spl
<=> n = m ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ9_spl
| n = m ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,definition,
( sQ10_spl
<=> f(n) = n ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f102,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ2_spl
| ~ element(X0,j)
| X0 = n
| X0 = n ),
inference(forward_demodulation,[status(thm)],[f50,f47]) ).
fof(f103,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ2_spl
| ~ element(X0,n)
| X0 = n
| X0 = n ),
inference(forward_demodulation,[status(thm)],[f50,f102]) ).
fof(f104,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ2_spl
| ~ element(X0,n)
| X0 = n ),
inference(duplicate_literals_removal,[status(thm)],[f103]) ).
fof(f109,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| n = j ),
inference(forward_demodulation,[status(thm)],[f36,f57]) ).
fof(f111,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| element(m,n) ),
inference(forward_demodulation,[status(thm)],[f36,f86]) ).
fof(f112,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ2_spl
| m = n ),
inference(resolution,[status(thm)],[f104,f111]) ).
fof(f113,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f18]) ).
fof(f114,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f113]) ).
fof(f115,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f109,f49,f35,f56]) ).
fof(f121,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f18]) ).
fof(f122,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0] :
( ~ element(X0,m)
| X0 = m
| ~ element(f(X0),X0)
| X0 = f(X0)
| X0 = m
| element(f(X0),m)
| f(X0) = m ),
inference(resolution,[status(thm)],[f26,f24]) ).
fof(f124,plain,
! [X0] :
( ~ element(X0,m)
| ~ element(f(X0),X0)
| X0 = f(X0)
| X0 = m
| element(f(X0),m)
| f(X0) = m ),
inference(duplicate_literals_removal,[status(thm)],[f123]) ).
fof(f125,plain,
! [X0] :
( ~ element(X0,m)
| ~ element(f(X0),X0)
| X0 = m
| element(f(X0),m)
| f(X0) = m ),
inference(forward_subsumption_resolution,[status(thm)],[f124,f23]) ).
fof(f128,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| element(n,j) ),
inference(forward_demodulation,[status(thm)],[f36,f60]) ).
fof(f130,definition,
( sQ11_spl
<=> j = m ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ11_spl
| j = m ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ12_spl
<=> element(j,m) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ12_spl
| element(j,m) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
( sQ13_spl
<=> element(j,n) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ13_spl
| element(j,n) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f138,plain,
( sQ13_spl
| ~ element(j,n) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f140,plain,
! [X0] :
( ~ element(n,X0)
| X0 = n
| X0 = m
| element(n,m)
| n = m
| g(X0) != X0
| X0 = n ),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f141,definition,
! [X0] :
( sQ14_spl
<=> ( ~ element(n,X0)
| X0 = n
| X0 = m
| g(X0) != X0
| X0 = n ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f144,definition,
( sQ15_spl
<=> element(n,m) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ15_spl
| element(n,m) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( sQ15_spl
| sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f140,f141,f95,f144]) ).
fof(f152,definition,
( sQ16_spl
<=> m = m ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( sQ13_spl
| g(j) != j
| j = n ),
inference(resolution,[status(thm)],[f138,f28]) ).
fof(f158,definition,
( sQ17_spl
<=> g(j) = j ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( sQ13_spl
| ~ sQ17_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f157,f49,f158,f136]) ).
fof(f162,plain,
( ~ sQ15_spl
| element(f(n),n)
| n = m ),
inference(resolution,[status(thm)],[f145,f25]) ).
fof(f163,plain,
( ~ sQ15_spl
| f(n) != n
| n = m ),
inference(resolution,[status(thm)],[f145,f23]) ).
fof(f165,definition,
( sQ18_spl
<=> element(f(n),n) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ18_spl
| element(f(n),n) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( ~ sQ15_spl
| sQ18_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f162,f95,f165,f144]) ).
fof(f169,plain,
( ~ sQ15_spl
| ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f163,f95,f98,f144]) ).
fof(f173,definition,
( sQ20_spl
<=> element(m,n) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( sQ20_spl
| ~ element(m,n) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f177,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f111]) ).
fof(f178,plain,
( sQ20_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f179,plain,
( ~ sQ12_spl
| element(f(j),j)
| j = m ),
inference(resolution,[status(thm)],[f134,f25]) ).
fof(f180,plain,
( ~ sQ12_spl
| f(j) != j
| j = m ),
inference(resolution,[status(thm)],[f134,f23]) ).
fof(f182,definition,
( sQ21_spl
<=> element(f(j),j) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( ~ sQ21_spl
| element(f(j),j) ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( ~ sQ12_spl
| sQ21_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f179,f130,f182,f133]) ).
fof(f186,definition,
( sQ22_spl
<=> f(j) = j ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( ~ sQ12_spl
| ~ sQ22_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f180,f130,f186,f133]) ).
fof(f195,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ11_spl
| element(n,m) ),
inference(backward_demodulation,[status(thm)],[f131,f128]) ).
fof(f198,plain,
! [X0] :
( ~ element(n,X0)
| X0 = n
| X0 = m
| element(n,m)
| n = m
| element(g(X0),X0)
| X0 = n ),
inference(resolution,[status(thm)],[f30,f26]) ).
fof(f199,definition,
! [X0] :
( sQ24_spl
<=> ( ~ element(n,X0)
| X0 = n
| X0 = m
| element(g(X0),X0)
| X0 = n ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( sQ15_spl
| sQ9_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f198,f199,f95,f144]) ).
fof(f204,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ element(X0,m)
| ~ element(m,X0)
| X0 = m
| X0 = n
| m = n ),
inference(resolution,[status(thm)],[f31,f111]) ).
fof(f207,definition,
! [X0] :
( sQ25_spl
<=> ( ~ element(X0,m)
| ~ element(m,X0)
| X0 = m
| X0 = n ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| sQ25_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f204,f95,f207,f35,f85]) ).
fof(f213,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(X0,k)
| X0 = n
| X0 = m
| X0 = n ),
inference(forward_demodulation,[status(thm)],[f36,f34]) ).
fof(f214,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(X0,n)
| X0 = n
| X0 = m
| X0 = n ),
inference(forward_demodulation,[status(thm)],[f36,f213]) ).
fof(f215,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(X0,n)
| X0 = m
| X0 = n ),
inference(duplicate_literals_removal,[status(thm)],[f214]) ).
fof(f216,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| m = m
| m = n ),
inference(resolution,[status(thm)],[f215,f111]) ).
fof(f219,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| sQ16_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f216,f95,f152,f35,f85]) ).
fof(f251,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| f(n) = m
| f(n) = n ),
inference(resolution,[status(thm)],[f166,f215]) ).
fof(f254,definition,
( sQ28_spl
<=> f(n) = m ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ28_spl
| f(n) = m ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| sQ28_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f251,f98,f254,f165,f35]) ).
fof(f276,plain,
( ~ sQ28_spl
| ~ element(n,m)
| n = m ),
inference(resolution,[status(thm)],[f255,f22]) ).
fof(f279,plain,
( ~ sQ28_spl
| ~ sQ15_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f276,f95,f144,f254]) ).
fof(f287,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(X0,j)
| X0 = n
| X0 = j ),
inference(forward_demodulation,[status(thm)],[f36,f21]) ).
fof(f310,plain,
( ~ sQ0_spl
| ~ sQ21_spl
| f(j) = n
| f(j) = j ),
inference(resolution,[status(thm)],[f183,f287]) ).
fof(f312,definition,
( sQ31_spl
<=> f(j) = n ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( ~ sQ31_spl
| f(j) = n ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,plain,
( ~ sQ0_spl
| ~ sQ21_spl
| sQ31_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f310,f186,f312,f182,f35]) ).
fof(f323,plain,
( sQ13_spl
| element(g(j),j)
| j = n ),
inference(resolution,[status(thm)],[f138,f30]) ).
fof(f325,definition,
( sQ34_spl
<=> element(g(j),j) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( ~ sQ34_spl
| element(g(j),j) ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,plain,
( sQ13_spl
| sQ34_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f323,f49,f325,f136]) ).
fof(f331,plain,
( ~ sQ31_spl
| element(j,n)
| ~ element(j,m)
| j = m ),
inference(paramodulation,[status(thm)],[f313,f24]) ).
fof(f333,plain,
( ~ sQ31_spl
| sQ13_spl
| ~ sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f331,f130,f133,f136,f312]) ).
fof(f342,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| j = m
| j = n ),
inference(resolution,[status(thm)],[f137,f215]) ).
fof(f345,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f342,f49,f130,f136,f35]) ).
fof(f352,plain,
( ~ sQ5_spl
| k = k
| k = j ),
inference(resolution,[status(thm)],[f60,f21]) ).
fof(f354,definition,
( sQ36_spl
<=> k = k ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( ~ sQ5_spl
| sQ36_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f352,f56,f354,f59]) ).
fof(f444,plain,
! [X0] :
( ~ element(X0,m)
| ~ element(f(X0),X0)
| X0 = m
| element(f(X0),m) ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f22]) ).
fof(f490,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ element(f(n),n)
| n = m
| element(f(n),m) ),
inference(resolution,[status(thm)],[f93,f444]) ).
fof(f494,definition,
( sQ46_spl
<=> element(f(n),m) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( ~ sQ46_spl
| element(f(n),m) ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ18_spl
| sQ9_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f490,f494,f95,f165,f38,f81]) ).
fof(f501,plain,
! [X0] :
( ~ sQ1_spl
| ~ element(X0,k)
| X0 = n
| X0 = m
| X0 = m ),
inference(forward_demodulation,[status(thm)],[f39,f34]) ).
fof(f502,plain,
! [X0] :
( ~ sQ1_spl
| ~ element(X0,m)
| X0 = n
| X0 = m
| X0 = m ),
inference(forward_demodulation,[status(thm)],[f39,f501]) ).
fof(f503,plain,
! [X0] :
( ~ sQ1_spl
| ~ element(X0,m)
| X0 = n
| X0 = m ),
inference(duplicate_literals_removal,[status(thm)],[f502]) ).
fof(f511,plain,
( ~ sQ34_spl
| ~ element(j,g(j))
| g(j) = j
| g(j) = m
| element(j,m)
| j = m ),
inference(resolution,[status(thm)],[f326,f26]) ).
fof(f512,definition,
( sQ47_spl
<=> g(j) = m ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( ~ sQ47_spl
| g(j) = m ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f516,definition,
( sQ48_spl
<=> element(j,g(j)) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( sQ48_spl
| ~ element(j,g(j)) ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f519,plain,
( ~ sQ34_spl
| ~ sQ48_spl
| sQ17_spl
| sQ47_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f511,f130,f133,f512,f158,f516,f325]) ).
fof(f520,plain,
( ~ sQ47_spl
| element(j,m)
| element(j,n)
| j = n ),
inference(paramodulation,[status(thm)],[f513,f29]) ).
fof(f522,plain,
( ~ sQ47_spl
| sQ12_spl
| sQ13_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f520,f49,f136,f133,f512]) ).
fof(f542,plain,
( ~ sQ1_spl
| ~ sQ46_spl
| f(n) = n
| f(n) = m ),
inference(resolution,[status(thm)],[f495,f503]) ).
fof(f547,plain,
( ~ sQ1_spl
| ~ sQ46_spl
| sQ10_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f542,f254,f98,f494,f38]) ).
fof(f635,plain,
( sQ48_spl
| element(j,n)
| j = n ),
inference(resolution,[status(thm)],[f518,f29]) ).
fof(f636,plain,
( sQ48_spl
| sQ13_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f635,f49,f136,f516]) ).
fof(f640,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f195,f144,f130,f35,f59]) ).
fof(f646,plain,
( ~ sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f68,f144,f38]) ).
fof(f648,plain,
$false,
inference(sat_refutation,[status(thm)],[f41,f55,f62,f80,f84,f88,f114,f115,f122,f147,f161,f168,f169,f178,f185,f189,f202,f210,f219,f257,f279,f315,f328,f333,f345,f357,f497,f519,f522,f547,f636,f640,f646]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.54 % Computer : n014.cluster.edu
% 0.09/0.54 % Model : x86_64 x86_64
% 0.09/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.54 % Memory : 8046.5625MB
% 0.09/0.54 % OS : Linux 6.8.0-71-generic
% 0.09/0.54 % CPULimit : 300
% 0.09/0.54 % WCLimit : 300
% 0.09/0.54 % DateTime : Mon Sep 21 10:39:05 UTC 2026
% 0.09/0.54 % CPUTime :
% 0.09/0.55 % Drodi V4.1.1
% 0.09/0.57 % Refutation found
% 0.09/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.58 % Elapsed time: 0.040870 seconds
% 0.14/0.58 % CPU time: 0.139941 seconds
% 0.14/0.58 % Total memory used: 31.531 MB
% 0.14/0.58 % Net memory used: 31.359 MB
%------------------------------------------------------------------------------