%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN015-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 03:14:56 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.51s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 51
% Syntax : Number of formulae : 222 ( 5 unt; 35 def)
% Number of atoms : 711 ( 228 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 775 ( 286 ~; 454 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 36 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
m != n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [Y] :
( element(Y,j)
| Y != k
| Y = j ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [Y] :
( ~ element(Y,j)
| Y = k
| Y = j ),
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,V1] :
( ~ element(V1,Y)
| ~ element(Y,V1)
| V1 = Y
| V1 = m
| element(Y,m)
| Y = m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [Y] :
( g(Y) != n
| element(Y,n)
| Y = n ),
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,
! [X0] :
( element(X0,j)
| X0 != k
| X0 = j ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] :
( ~ element(X0,j)
| X0 = k
| X0 = j ),
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(f25,plain,
! [X0] :
( g(X0) != n
| element(X0,n)
| X0 = n ),
inference(cnf_transformation,[status(thm)],[f9]) ).
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(k,j)
| k = j ),
inference(destructive_equality_resolution,[status(thm)],[f18]) ).
fof(f34,plain,
( element(m,k)
| m = k ),
inference(destructive_equality_resolution,[status(thm)],[f30]) ).
fof(f35,plain,
( element(n,k)
| n = k ),
inference(destructive_equality_resolution,[status(thm)],[f31]) ).
fof(f36,plain,
( k = j
| k = k
| k = j ),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f37,definition,
( sQ0_spl
<=> k = j ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( ~ sQ0_spl
| k = j ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f39,plain,
( sQ0_spl
| k != j ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f40,definition,
( sQ1_spl
<=> k = k ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f37,f40]) ).
fof(f44,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(X0,k)
| X0 = k
| X0 = j ),
inference(backward_demodulation,[status(thm)],[f38,f19]) ).
fof(f46,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(X0,k)
| X0 = k
| X0 = k ),
inference(forward_demodulation,[status(thm)],[f38,f44]) ).
fof(f47,plain,
! [X0] :
( ~ sQ0_spl
| ~ element(X0,k)
| X0 = k ),
inference(duplicate_literals_removal,[status(thm)],[f46]) ).
fof(f52,plain,
( ~ sQ0_spl
| n = k ),
inference(backward_subsumption_resolution,[status(thm)],[f35,f47]) ).
fof(f53,plain,
( ~ sQ0_spl
| m = k ),
inference(backward_subsumption_resolution,[status(thm)],[f34,f47]) ).
fof(f57,plain,
( ~ sQ0_spl
| n = m ),
inference(backward_demodulation,[status(thm)],[f53,f52]) ).
fof(f58,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f57,f17]) ).
fof(f59,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f58]) ).
fof(f60,definition,
( sQ3_spl
<=> n = k ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f61,plain,
( ~ sQ3_spl
| n = k ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ4_spl
<=> element(n,k) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ4_spl
| element(n,k) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f35,f60,f63]) ).
fof(f67,definition,
( sQ5_spl
<=> m = k ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ5_spl
| m = k ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,definition,
( sQ6_spl
<=> element(m,k) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ6_spl
| element(m,k) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f34,f67,f70]) ).
fof(f74,definition,
( sQ7_spl
<=> element(k,j) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ7_spl
| element(k,j) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f37,f74]) ).
fof(f79,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| n = m ),
inference(forward_demodulation,[status(thm)],[f68,f61]) ).
fof(f80,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f17]) ).
fof(f81,plain,
( ~ sQ3_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f80]) ).
fof(f84,plain,
( f(j) = k
| f(j) = j
| ~ element(j,m)
| j = m ),
inference(resolution,[status(thm)],[f23,f19]) ).
fof(f85,definition,
( sQ8_spl
<=> j = m ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ8_spl
| j = m ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ9_spl
<=> element(j,m) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f91,definition,
( sQ10_spl
<=> f(j) = j ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ10_spl
| f(j) = j ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,definition,
( sQ11_spl
<=> f(j) = k ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ11_spl
| f(j) = k ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,plain,
( sQ11_spl
| sQ10_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f84,f85,f88,f91,f94]) ).
fof(f99,plain,
( ~ sQ11_spl
| element(j,k)
| ~ element(j,m)
| j = m ),
inference(paramodulation,[status(thm)],[f95,f22]) ).
fof(f103,definition,
( sQ12_spl
<=> element(j,k) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( sQ12_spl
| ~ element(j,k) ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( ~ sQ11_spl
| sQ12_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f99,f85,f88,f103,f94]) ).
fof(f116,definition,
( sQ13_spl
<=> m = m ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ4_spl
| ~ element(k,n)
| n = k
| n = m
| element(k,m)
| k = m ),
inference(resolution,[status(thm)],[f24,f64]) ).
fof(f129,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)],[f24,f22]) ).
fof(f130,definition,
( sQ15_spl
<=> element(k,m) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ15_spl
| element(k,m) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ16_spl
<=> n = m ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ16_spl
| n = m ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
( sQ17_spl
<=> element(k,n) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ17_spl
| element(k,n) ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| sQ3_spl
| sQ16_spl
| sQ15_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f126,f67,f130,f133,f60,f136,f63]) ).
fof(f141,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)],[f129]) ).
fof(f142,plain,
! [X0] :
( ~ element(X0,m)
| ~ element(f(X0),X0)
| X0 = f(X0)
| X0 = m
| element(f(X0),m) ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f20]) ).
fof(f147,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| element(m,n) ),
inference(backward_demodulation,[status(thm)],[f61,f71]) ).
fof(f149,plain,
( sQ0_spl
| ~ sQ3_spl
| n != j ),
inference(backward_demodulation,[status(thm)],[f61,f39]) ).
fof(f150,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| element(n,j) ),
inference(forward_demodulation,[status(thm)],[f61,f75]) ).
fof(f151,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ element(j,n)
| n = j
| n = m
| element(j,m)
| j = m ),
inference(resolution,[status(thm)],[f150,f24]) ).
fof(f152,definition,
( sQ18_spl
<=> n = j ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ18_spl
| n = j ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,definition,
( sQ19_spl
<=> element(j,n) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ19_spl
| element(j,n) ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ19_spl
| sQ18_spl
| sQ16_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f151,f85,f88,f133,f152,f155,f60,f74]) ).
fof(f159,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f134,f17]) ).
fof(f160,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f159]) ).
fof(f161,plain,
( ~ sQ18_spl
| sQ0_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f149]) ).
fof(f162,plain,
( ~ sQ18_spl
| sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f171,definition,
( sQ22_spl
<=> n = n ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f178,definition,
( sQ24_spl
<=> f(n) = n ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( ~ sQ24_spl
| f(n) = n ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f184,definition,
( sQ26_spl
<=> element(n,m) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ26_spl
| element(n,m) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f186,plain,
( sQ26_spl
| ~ element(n,m) ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f188,plain,
( ~ sQ10_spl
| ~ element(j,m)
| j = m ),
inference(resolution,[status(thm)],[f92,f21]) ).
fof(f193,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f188,f85,f88,f91]) ).
fof(f214,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| element(n,m) ),
inference(forward_demodulation,[status(thm)],[f68,f64]) ).
fof(f220,plain,
( sQ26_spl
| ~ sQ4_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f214]) ).
fof(f221,plain,
( sQ26_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f222,plain,
( ~ sQ24_spl
| ~ element(n,m)
| n = m ),
inference(resolution,[status(thm)],[f179,f21]) ).
fof(f227,plain,
( ~ sQ24_spl
| ~ sQ26_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f222,f133,f184,f178]) ).
fof(f239,plain,
( element(k,n)
| k = n
| g(k) = n
| g(k) = m
| g(k) = k ),
inference(resolution,[status(thm)],[f32,f28]) ).
fof(f240,plain,
( ~ element(k,m)
| k = m
| f(k) = n
| f(k) = m
| f(k) = k ),
inference(resolution,[status(thm)],[f32,f23]) ).
fof(f241,definition,
( sQ32_spl
<=> g(k) = k ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( ~ sQ32_spl
| g(k) = k ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
( sQ33_spl
<=> g(k) = m ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ33_spl
| g(k) = m ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,definition,
( sQ34_spl
<=> g(k) = n ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( ~ sQ34_spl
| g(k) = n ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( sQ17_spl
| sQ3_spl
| sQ34_spl
| sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f239,f241,f244,f247,f60,f136]) ).
fof(f251,definition,
( sQ35_spl
<=> f(k) = k ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( ~ sQ35_spl
| f(k) = k ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,definition,
( sQ36_spl
<=> f(k) = m ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ36_spl
| f(k) = m ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,definition,
( sQ37_spl
<=> f(k) = n ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ37_spl
| f(k) = n ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( ~ sQ15_spl
| sQ5_spl
| sQ37_spl
| sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f240,f251,f254,f257,f67,f130]) ).
fof(f261,plain,
( element(j,n)
| j = n
| g(j) = k
| g(j) = j ),
inference(resolution,[status(thm)],[f19,f28]) ).
fof(f263,definition,
( sQ38_spl
<=> g(j) = j ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ38_spl
| g(j) = j ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,definition,
( sQ39_spl
<=> g(j) = k ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ39_spl
| g(j) = k ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,plain,
( sQ19_spl
| sQ18_spl
| sQ39_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f261,f263,f266,f152,f155]) ).
fof(f272,plain,
! [X0] :
( ~ sQ3_spl
| ~ element(X0,j)
| X0 = n
| X0 = j ),
inference(backward_demodulation,[status(thm)],[f61,f19]) ).
fof(f273,plain,
! [X0] :
( ~ sQ3_spl
| ~ element(X0,n)
| X0 = n
| X0 = m
| X0 = k ),
inference(backward_demodulation,[status(thm)],[f61,f32]) ).
fof(f276,plain,
! [X0] :
( ~ sQ3_spl
| ~ element(X0,n)
| X0 = n
| X0 = m
| X0 = n ),
inference(forward_demodulation,[status(thm)],[f61,f273]) ).
fof(f277,plain,
! [X0] :
( ~ sQ3_spl
| ~ element(X0,n)
| X0 = m
| X0 = n ),
inference(duplicate_literals_removal,[status(thm)],[f276]) ).
fof(f338,plain,
( ~ sQ38_spl
| element(j,n)
| j = n ),
inference(resolution,[status(thm)],[f264,f26]) ).
fof(f343,plain,
( ~ sQ38_spl
| sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f338,f152,f155,f263]) ).
fof(f381,plain,
( ~ sQ18_spl
| ~ sQ8_spl
| n = m ),
inference(forward_demodulation,[status(thm)],[f86,f153]) ).
fof(f382,plain,
( ~ sQ18_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f381,f17]) ).
fof(f383,plain,
( ~ sQ18_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f382]) ).
fof(f388,plain,
! [X0] :
( ~ sQ19_spl
| ~ element(X0,j)
| ~ element(j,X0)
| X0 = j
| X0 = n
| j = n ),
inference(resolution,[status(thm)],[f156,f29]) ).
fof(f390,definition,
! [X0] :
( sQ41_spl
<=> ( ~ element(X0,j)
| ~ element(j,X0)
| X0 = j
| X0 = n ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( ~ sQ19_spl
| sQ41_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f388,f152,f390,f155]) ).
fof(f394,definition,
( sQ42_spl
<=> element(n,j) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( sQ42_spl
| ~ element(n,j) ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f439,plain,
( ~ sQ4_spl
| n = n
| n = m
| n = k ),
inference(resolution,[status(thm)],[f64,f32]) ).
fof(f441,plain,
( ~ sQ4_spl
| sQ22_spl
| sQ16_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f439,f60,f133,f171,f63]) ).
fof(f444,plain,
( ~ sQ32_spl
| element(k,n)
| k = n ),
inference(resolution,[status(thm)],[f242,f26]) ).
fof(f449,plain,
( ~ sQ32_spl
| sQ17_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f444,f60,f136,f241]) ).
fof(f455,plain,
( ~ sQ33_spl
| element(k,m)
| element(k,n)
| k = n ),
inference(paramodulation,[status(thm)],[f245,f27]) ).
fof(f457,plain,
( ~ sQ33_spl
| m != k
| element(k,n)
| k = n ),
inference(paramodulation,[status(thm)],[f245,f26]) ).
fof(f459,plain,
( ~ sQ33_spl
| sQ15_spl
| sQ17_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f455,f60,f136,f130,f244]) ).
fof(f461,plain,
( ~ sQ33_spl
| ~ sQ5_spl
| sQ17_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f457,f60,f136,f67,f244]) ).
fof(f465,plain,
( ~ sQ6_spl
| m = n
| m = m
| m = k ),
inference(resolution,[status(thm)],[f71,f32]) ).
fof(f467,plain,
( ~ sQ6_spl
| sQ16_spl
| sQ13_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f465,f67,f116,f133,f70]) ).
fof(f471,plain,
( ~ sQ7_spl
| ~ sQ18_spl
| element(k,n) ),
inference(backward_demodulation,[status(thm)],[f153,f75]) ).
fof(f472,plain,
( ~ sQ7_spl
| ~ sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f471,f136,f152,f74]) ).
fof(f473,plain,
( ~ sQ35_spl
| ~ element(k,m)
| k = m ),
inference(resolution,[status(thm)],[f252,f21]) ).
fof(f478,plain,
( ~ sQ35_spl
| ~ sQ15_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f473,f67,f130,f251]) ).
fof(f487,definition,
! [X0] :
( sQ43_spl
<=> ( ~ element(X0,m)
| ~ element(m,X0)
| X0 = m
| X0 = n ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( sQ12_spl
| ~ sQ18_spl
| ~ element(n,k) ),
inference(forward_demodulation,[status(thm)],[f153,f105]) ).
fof(f497,plain,
( sQ12_spl
| ~ sQ18_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f496,f64]) ).
fof(f498,plain,
( sQ12_spl
| ~ sQ18_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f499,plain,
! [X0] :
( ~ sQ17_spl
| ~ element(X0,k)
| ~ element(k,X0)
| X0 = k
| X0 = n
| k = n ),
inference(resolution,[status(thm)],[f137,f29]) ).
fof(f501,definition,
! [X0] :
( sQ44_spl
<=> ( ~ element(X0,k)
| ~ element(k,X0)
| X0 = k
| X0 = n ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f502,plain,
! [X0] :
( ~ sQ44_spl
| ~ element(X0,k)
| ~ element(k,X0)
| X0 = k
| X0 = n ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,plain,
( ~ sQ17_spl
| sQ44_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f499,f60,f501,f136]) ).
fof(f514,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ3_spl
| ~ element(X0,m)
| ~ element(m,X0)
| X0 = m
| X0 = n
| m = n ),
inference(resolution,[status(thm)],[f147,f29]) ).
fof(f516,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| sQ43_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f514,f133,f487,f60,f70]) ).
fof(f518,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| element(n,j) ),
inference(backward_demodulation,[status(thm)],[f61,f75]) ).
fof(f544,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ8_spl
| element(n,m) ),
inference(forward_demodulation,[status(thm)],[f86,f150]) ).
fof(f545,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ8_spl
| sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f544,f186]) ).
fof(f546,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ8_spl
| sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f545]) ).
fof(f576,plain,
( sQ42_spl
| ~ sQ7_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f518]) ).
fof(f577,plain,
( sQ42_spl
| ~ sQ7_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f578,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| n = n
| n = j ),
inference(resolution,[status(thm)],[f272,f518]) ).
fof(f580,plain,
( ~ sQ3_spl
| ~ element(j,m)
| j = m
| f(j) = n
| f(j) = j ),
inference(resolution,[status(thm)],[f272,f23]) ).
fof(f581,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| sQ22_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f578,f152,f171,f60,f74]) ).
fof(f586,definition,
( sQ46_spl
<=> f(j) = n ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f587,plain,
( ~ sQ46_spl
| f(j) = n ),
inference(component_clause,[status(thm)],[f586]) ).
fof(f589,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| sQ8_spl
| sQ46_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f580,f91,f586,f85,f88,f60]) ).
fof(f593,plain,
( ~ sQ3_spl
| ~ element(n,m)
| n = m
| f(n) = m
| f(n) = n ),
inference(resolution,[status(thm)],[f277,f23]) ).
fof(f600,definition,
( sQ48_spl
<=> f(n) = m ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( ~ sQ48_spl
| f(n) = m ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f603,plain,
( ~ sQ3_spl
| ~ sQ26_spl
| sQ16_spl
| sQ48_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f593,f178,f600,f133,f184,f60]) ).
fof(f605,plain,
( ~ sQ37_spl
| element(k,n)
| ~ element(k,m)
| k = m ),
inference(paramodulation,[status(thm)],[f258,f22]) ).
fof(f609,plain,
( ~ sQ37_spl
| sQ17_spl
| ~ sQ15_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f605,f67,f130,f136,f257]) ).
fof(f615,plain,
( ~ sQ39_spl
| ~ sQ3_spl
| g(j) = n ),
inference(forward_demodulation,[status(thm)],[f61,f267]) ).
fof(f616,plain,
( ~ sQ39_spl
| ~ sQ3_spl
| element(j,n)
| j = n ),
inference(resolution,[status(thm)],[f615,f25]) ).
fof(f621,plain,
( ~ sQ39_spl
| ~ sQ3_spl
| sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f616,f152,f155,f60,f266]) ).
fof(f660,plain,
! [X0] :
( ~ element(X0,m)
| ~ element(f(X0),X0)
| X0 = m
| element(f(X0),m) ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f21]) ).
fof(f661,plain,
! [X0] :
( ~ element(X0,m)
| X0 = m
| ~ element(X0,m)
| X0 = m
| element(f(X0),m) ),
inference(resolution,[status(thm)],[f660,f23]) ).
fof(f663,plain,
! [X0] :
( ~ element(X0,m)
| X0 = m
| element(f(X0),m) ),
inference(duplicate_literals_removal,[status(thm)],[f661]) ).
fof(f701,plain,
( ~ sQ46_spl
| ~ element(j,m)
| j = m
| element(n,m) ),
inference(paramodulation,[status(thm)],[f587,f663]) ).
fof(f706,plain,
( ~ sQ46_spl
| ~ sQ9_spl
| sQ8_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f701,f184,f85,f88,f586]) ).
fof(f717,plain,
( ~ sQ15_spl
| ~ sQ44_spl
| ~ element(m,k)
| m = k
| m = n ),
inference(resolution,[status(thm)],[f502,f131]) ).
fof(f719,plain,
( ~ sQ7_spl
| ~ sQ44_spl
| ~ element(j,k)
| j = k
| j = n ),
inference(resolution,[status(thm)],[f502,f75]) ).
fof(f722,plain,
( ~ sQ15_spl
| ~ sQ44_spl
| ~ sQ6_spl
| sQ5_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f717,f133,f67,f70,f501,f130]) ).
fof(f724,plain,
( ~ sQ7_spl
| ~ sQ44_spl
| ~ sQ12_spl
| sQ0_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f719,f152,f37,f103,f501,f74]) ).
fof(f736,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| element(k,m) ),
inference(backward_demodulation,[status(thm)],[f86,f75]) ).
fof(f742,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f736,f130,f85,f74]) ).
fof(f750,plain,
( ~ sQ48_spl
| ~ element(n,m)
| n = m ),
inference(resolution,[status(thm)],[f601,f20]) ).
fof(f756,plain,
( ~ sQ48_spl
| ~ sQ26_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f750,f133,f184,f600]) ).
fof(f792,plain,
( ~ sQ36_spl
| ~ element(k,m)
| k = m ),
inference(resolution,[status(thm)],[f255,f20]) ).
fof(f798,plain,
( ~ sQ36_spl
| ~ sQ15_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f792,f67,f130,f254]) ).
fof(f829,plain,
( ~ sQ34_spl
| element(k,n)
| k = n ),
inference(resolution,[status(thm)],[f248,f25]) ).
fof(f835,plain,
( ~ sQ34_spl
| sQ17_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f829,f60,f136,f247]) ).
fof(f845,plain,
! [X0] :
( ~ sQ5_spl
| ~ element(X0,m)
| X0 = n
| X0 = m
| X0 = k ),
inference(backward_demodulation,[status(thm)],[f68,f32]) ).
fof(f848,plain,
! [X0] :
( ~ sQ5_spl
| ~ element(X0,m)
| X0 = n
| X0 = m
| X0 = m ),
inference(forward_demodulation,[status(thm)],[f68,f845]) ).
fof(f849,plain,
! [X0] :
( ~ sQ5_spl
| ~ element(X0,m)
| X0 = n
| X0 = m ),
inference(duplicate_literals_removal,[status(thm)],[f848]) ).
fof(f864,plain,
! [X0] :
( ~ sQ5_spl
| ~ element(X0,m)
| X0 = m
| f(X0) = n
| f(X0) = m ),
inference(resolution,[status(thm)],[f849,f663]) ).
fof(f876,plain,
! [X0] :
( ~ sQ5_spl
| ~ element(X0,m)
| X0 = m
| f(X0) = n ),
inference(forward_subsumption_resolution,[status(thm)],[f864,f20]) ).
fof(f887,plain,
( ~ sQ26_spl
| ~ sQ5_spl
| n = m
| f(n) = n ),
inference(resolution,[status(thm)],[f876,f185]) ).
fof(f892,plain,
( ~ sQ26_spl
| ~ sQ5_spl
| sQ16_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f887,f178,f133,f67,f184]) ).
fof(f903,plain,
$false,
inference(sat_refutation,[status(thm)],[f43,f59,f66,f73,f77,f81,f97,f106,f139,f158,f160,f162,f193,f221,f227,f250,f260,f269,f343,f383,f393,f441,f449,f459,f461,f467,f472,f478,f498,f504,f516,f546,f577,f581,f589,f603,f609,f621,f706,f722,f724,f742,f756,f798,f835,f892]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN015-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n015.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 10:42:21 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.51 % Refutation found
% 0.16/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.53 % Elapsed time: 0.089793 seconds
% 0.16/0.53 % CPU time: 0.431896 seconds
% 0.16/0.53 % Total memory used: 84.964 MB
% 0.16/0.53 % Net memory used: 84.314 MB
%------------------------------------------------------------------------------