%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV486+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:48:02 PM UTC 2026
% Result : Theorem 1.35s 0.76s
% Output : CNFRefutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 23
% Syntax : Number of formulae : 124 ( 18 unt; 15 def)
% Number of atoms : 333 ( 53 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 348 ( 139 ~; 149 |; 33 &)
% ( 18 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 16 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 100 ( 95 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [I,J] :
( int_leq(I,J)
<=> ( I = J
| int_less(I,J) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [I,J,K] :
( ( int_less(J,K)
& int_less(I,J) )
=> int_less(I,K) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [I,J] :
( int_less(I,J)
=> I != J ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [I,J] :
( int_leq(J,I)
| int_less(I,J) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [I,J] :
( int_less(I,J)
<=> ? [K] :
( int_less(int_zero,K)
& plus(I,K) = J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [I] :
( int_less(int_zero,I)
<=> int_leq(int_one,I) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
! [I,J] :
( ( int_leq(J,n)
& int_leq(int_one,J)
& int_leq(I,n)
& int_leq(int_one,I) )
=> ( ! [C] :
( ( J = plus(I,C)
& int_less(int_zero,C) )
=> ! [K] :
( ( int_leq(K,I)
& int_leq(int_one,K) )
=> a(K,plus(K,C)) = real_zero ) )
& ! [C] :
( ( I = plus(J,C)
& int_less(int_zero,C) )
=> ! [K] :
( ( int_leq(K,J)
& int_leq(int_one,K) )
=> a(plus(K,C),K) = qr(plus(K,C),K) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [I,J] :
( ( int_leq(J,n)
& int_less(I,J)
& int_leq(int_one,I) )
=> a(I,J) = real_zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [I,J] :
( ( int_leq(J,n)
& int_less(I,J)
& int_leq(int_one,I) )
=> a(I,J) = real_zero ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
! [I,J] :
( ( ( I != J
& ~ int_less(I,J) )
| int_leq(I,J) )
& ( I = J
| int_less(I,J)
| ~ int_leq(I,J) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
( ! [I,J] :
( ( I != J
& ~ int_less(I,J) )
| int_leq(I,J) )
& ! [I,J] :
( I = J
| int_less(I,J)
| ~ int_leq(I,J) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( X0 = X1
| int_less(X0,X1)
| ~ int_leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ~ int_less(X0,X1)
| int_leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0,X1] :
( X0 != X1
| int_leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
! [I,J,K] :
( int_less(I,K)
| ~ int_less(J,K)
| ~ int_less(I,J) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [I,K] :
( int_less(I,K)
| ! [J] :
( ~ int_less(J,K)
| ~ int_less(I,J) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( int_less(X0,X2)
| ~ int_less(X1,X2)
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [I,J] :
( I != J
| ~ int_less(I,J) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0,X1] :
( X0 != X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( int_leq(X1,X0)
| int_less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f31,plain,
! [I,J] :
( ( ! [K] :
( ~ int_less(int_zero,K)
| plus(I,K) != J )
| int_less(I,J) )
& ( ? [K] :
( int_less(int_zero,K)
& plus(I,K) = J )
| ~ int_less(I,J) ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f32,plain,
( ! [I,J] :
( ! [K] :
( ~ int_less(int_zero,K)
| plus(I,K) != J )
| int_less(I,J) )
& ! [I,J] :
( ? [K] :
( int_less(int_zero,K)
& plus(I,K) = J )
| ~ int_less(I,J) ) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f33,plain,
( ! [I,J] :
( ! [K] :
( ~ int_less(int_zero,K)
| plus(I,K) != J )
| int_less(I,J) )
& ! [I,J] :
( ( int_less(int_zero,sK0_skl(J,I))
& plus(I,sK0_skl(J,I)) = J )
| ~ int_less(I,J) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(K,sK0_skl(J,I))],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( plus(X0,sK0_skl(X1,X0)) = X1
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( int_less(int_zero,sK0_skl(X1,X0))
| ~ int_less(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f37,plain,
! [I] :
( ( ~ int_leq(int_one,I)
| int_less(int_zero,I) )
& ( int_leq(int_one,I)
| ~ int_less(int_zero,I) ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f38,plain,
( ! [I] :
( ~ int_leq(int_one,I)
| int_less(int_zero,I) )
& ! [I] :
( int_leq(int_one,I)
| ~ int_less(int_zero,I) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f39,plain,
! [X0] :
( int_leq(int_one,X0)
| ~ int_less(int_zero,X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0] :
( ~ int_leq(int_one,X0)
| int_less(int_zero,X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [I,J] :
( ( ! [C] :
( ! [K] :
( a(K,plus(K,C)) = real_zero
| ~ int_leq(K,I)
| ~ int_leq(int_one,K) )
| J != plus(I,C)
| ~ int_less(int_zero,C) )
& ! [C] :
( ! [K] :
( a(plus(K,C),K) = qr(plus(K,C),K)
| ~ int_leq(K,J)
| ~ int_leq(int_one,K) )
| I != plus(J,C)
| ~ int_less(int_zero,C) ) )
| ~ int_leq(J,n)
| ~ int_leq(int_one,J)
| ~ int_leq(I,n)
| ~ int_leq(int_one,I) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( a(X3,plus(X3,X2)) = real_zero
| ~ int_leq(X3,X0)
| ~ int_leq(int_one,X3)
| X1 != plus(X0,X2)
| ~ int_less(int_zero,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
? [I,J] :
( a(I,J) != real_zero
& int_leq(J,n)
& int_less(I,J)
& int_leq(int_one,I) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f46,plain,
( a(sK1_skl,sK2_skl) != real_zero
& int_leq(sK2_skl,n)
& int_less(sK1_skl,sK2_skl)
& int_leq(int_one,sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(I,sK1_skl),skolemize(J,sK2_skl)],[f45]) ).
fof(f47,plain,
int_leq(int_one,sK1_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
int_less(sK1_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
int_leq(sK2_skl,n),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
a(sK1_skl,sK2_skl) != real_zero,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f51,plain,
! [X0] : int_leq(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f52,plain,
! [X0] : ~ int_less(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f24]) ).
fof(f55,plain,
! [X0,X1,X2] :
( a(X2,plus(X2,X1)) = real_zero
| ~ int_leq(X2,X0)
| ~ int_leq(int_one,X2)
| ~ int_less(int_zero,X1)
| ~ int_leq(plus(X0,X1),n)
| ~ int_leq(int_one,plus(X0,X1))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(destructive_equality_resolution,[status(thm)],[f44]) ).
fof(f57,plain,
! [X0,X1] :
( ~ int_less(X1,X0)
| ~ int_less(X0,X1) ),
inference(resolution,[status(thm)],[f22,f52]) ).
fof(f58,plain,
~ int_less(sK2_skl,sK1_skl),
inference(resolution,[status(thm)],[f57,f48]) ).
fof(f60,plain,
! [X0,X1] :
( X1 = X0
| ~ int_leq(X1,X0)
| ~ int_less(X0,X1) ),
inference(resolution,[status(thm)],[f57,f17]) ).
fof(f61,plain,
! [X0] :
( ~ int_less(X0,sK1_skl)
| ~ int_less(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f58,f22]) ).
fof(f62,plain,
( sK2_skl = sK1_skl
| ~ int_leq(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f58,f17]) ).
fof(f63,definition,
( sQ0_spl
<=> int_leq(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( sQ0_spl
| ~ int_leq(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,definition,
( sQ1_spl
<=> sK2_skl = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( ~ sQ1_spl
| sK2_skl = sK1_skl ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f63,f66]) ).
fof(f162,definition,
( sQ8_spl
<=> int_less(int_zero,sK0_skl(sK2_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f165,definition,
( sQ9_spl
<=> int_leq(int_one,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( sQ9_spl
| ~ int_leq(int_one,sK1_skl) ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f174,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f167,f47]) ).
fof(f175,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f174]) ).
fof(f182,plain,
( sK2_skl = n
| ~ int_less(n,sK2_skl) ),
inference(resolution,[status(thm)],[f60,f49]) ).
fof(f188,definition,
( sQ11_spl
<=> int_less(n,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( sQ11_spl
| ~ int_less(n,sK2_skl) ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,definition,
( sQ12_spl
<=> sK2_skl = n ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( ~ sQ12_spl
| sK2_skl = n ),
inference(component_clause,[status(thm)],[f191]) ).
fof(f194,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f182,f188,f191]) ).
fof(f218,plain,
( sQ11_spl
| n = sK2_skl
| ~ int_leq(n,sK2_skl) ),
inference(resolution,[status(thm)],[f190,f17]) ).
fof(f219,definition,
( sQ16_spl
<=> int_leq(n,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( sQ16_spl
| ~ int_leq(n,sK2_skl) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( sQ11_spl
| sQ12_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f218,f219,f191,f188]) ).
fof(f280,plain,
( sQ16_spl
| int_less(sK2_skl,n) ),
inference(resolution,[status(thm)],[f221,f25]) ).
fof(f301,plain,
( ~ sQ1_spl
| int_less(sK2_skl,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f67,f48]) ).
fof(f302,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f301,f52]) ).
fof(f303,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f302]) ).
fof(f1446,plain,
int_less(int_zero,sK1_skl),
inference(resolution,[status(thm)],[f40,f47]) ).
fof(f1451,plain,
! [X0,X1] :
( X1 = X0
| ~ int_leq(X1,X0)
| int_less(int_zero,sK0_skl(X0,X1)) ),
inference(resolution,[status(thm)],[f35,f17]) ).
fof(f1470,plain,
plus(sK1_skl,sK0_skl(sK2_skl,sK1_skl)) = sK2_skl,
inference(resolution,[status(thm)],[f48,f34]) ).
fof(f1474,plain,
~ int_less(sK2_skl,sK1_skl),
inference(resolution,[status(thm)],[f48,f57]) ).
fof(f1496,definition,
( sQ63_spl
<=> int_leq(sK1_skl,n) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1498,plain,
( sQ63_spl
| ~ int_leq(sK1_skl,n) ),
inference(component_clause,[status(thm)],[f1496]) ).
fof(f1504,plain,
! [X0,X1] :
( a(sK1_skl,plus(sK1_skl,X1)) = real_zero
| ~ int_leq(sK1_skl,X0)
| ~ int_less(int_zero,X1)
| ~ int_leq(plus(X0,X1),n)
| ~ int_leq(int_one,plus(X0,X1))
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(resolution,[status(thm)],[f47,f55]) ).
fof(f1683,plain,
( sQ63_spl
| int_less(n,sK1_skl) ),
inference(resolution,[status(thm)],[f1498,f25]) ).
fof(f1849,definition,
( sQ80_spl
<=> int_leq(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1850,plain,
( ~ sQ80_spl
| int_leq(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f1849]) ).
fof(f1851,plain,
( sQ80_spl
| ~ int_leq(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f1849]) ).
fof(f1857,plain,
( sQ80_spl
| int_less(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f1851,f25]) ).
fof(f1859,plain,
( sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1857,f1474]) ).
fof(f1860,plain,
sQ80_spl,
inference(contradiction_clause,[status(thm)],[f1859]) ).
fof(f2033,plain,
~ int_less(sK2_skl,int_zero),
inference(resolution,[status(thm)],[f61,f1446]) ).
fof(f2035,plain,
( sQ63_spl
| ~ int_less(sK2_skl,n) ),
inference(resolution,[status(thm)],[f61,f1683]) ).
fof(f2043,plain,
( sQ63_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2035,f280]) ).
fof(f2044,plain,
( sQ63_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f2043]) ).
fof(f2076,plain,
( sK2_skl = int_zero
| ~ int_leq(sK2_skl,int_zero) ),
inference(resolution,[status(thm)],[f2033,f17]) ).
fof(f2077,definition,
( sQ87_spl
<=> int_leq(sK2_skl,int_zero) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f2079,plain,
( sQ87_spl
| ~ int_leq(sK2_skl,int_zero) ),
inference(component_clause,[status(thm)],[f2077]) ).
fof(f2080,definition,
( sQ88_spl
<=> sK2_skl = int_zero ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f2081,plain,
( ~ sQ88_spl
| sK2_skl = int_zero ),
inference(component_clause,[status(thm)],[f2080]) ).
fof(f2083,plain,
( sQ88_spl
| ~ sQ87_spl ),
inference(split_clause,[status(thm)],[f2076,f2077,f2080]) ).
fof(f2108,plain,
( sQ87_spl
| int_less(int_zero,sK2_skl) ),
inference(resolution,[status(thm)],[f2079,f25]) ).
fof(f2197,plain,
( sQ0_spl
| ~ int_less(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f65,f18]) ).
fof(f2271,plain,
( sQ87_spl
| int_leq(int_one,sK2_skl) ),
inference(resolution,[status(thm)],[f2108,f39]) ).
fof(f2336,plain,
( ~ sQ80_spl
| ~ sQ12_spl
| int_leq(sK1_skl,n) ),
inference(backward_demodulation,[status(thm)],[f192,f1850]) ).
fof(f2345,plain,
( ~ sQ80_spl
| ~ sQ12_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f2336,f1496,f191,f1849]) ).
fof(f2363,definition,
( sQ104_spl
<=> int_leq(sK2_skl,n) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f2365,plain,
( sQ104_spl
| ~ int_leq(sK2_skl,n) ),
inference(component_clause,[status(thm)],[f2363]) ).
fof(f2384,plain,
( sQ0_spl
| ~ sQ88_spl
| ~ int_less(int_zero,sK1_skl) ),
inference(backward_demodulation,[status(thm)],[f2081,f2197]) ).
fof(f2521,plain,
( sQ104_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2365,f49]) ).
fof(f2522,plain,
sQ104_spl,
inference(contradiction_clause,[status(thm)],[f2521]) ).
fof(f2567,definition,
( sQ114_spl
<=> int_leq(int_one,plus(sK1_skl,sK0_skl(sK2_skl,sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f2569,plain,
( sQ114_spl
| ~ int_leq(int_one,plus(sK1_skl,sK0_skl(sK2_skl,sK1_skl))) ),
inference(component_clause,[status(thm)],[f2567]) ).
fof(f2585,plain,
( sQ114_spl
| ~ int_leq(int_one,sK2_skl) ),
inference(forward_demodulation,[status(thm)],[f1470,f2569]) ).
fof(f2586,plain,
( sQ114_spl
| sQ87_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2585,f2271]) ).
fof(f2587,plain,
( sQ114_spl
| sQ87_spl ),
inference(contradiction_clause,[status(thm)],[f2586]) ).
fof(f2711,plain,
( ~ sQ80_spl
| sK1_skl = sK2_skl
| int_less(int_zero,sK0_skl(sK2_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f1451,f1850]) ).
fof(f2724,plain,
( ~ sQ80_spl
| sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f2711,f162,f66,f1849]) ).
fof(f2753,plain,
( sQ0_spl
| ~ sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2384,f1446]) ).
fof(f2754,plain,
( sQ0_spl
| ~ sQ88_spl ),
inference(contradiction_clause,[status(thm)],[f2753]) ).
fof(f2966,plain,
( a(sK1_skl,plus(sK1_skl,sK0_skl(sK2_skl,sK1_skl))) = real_zero
| ~ int_leq(sK1_skl,sK1_skl)
| ~ int_less(int_zero,sK0_skl(sK2_skl,sK1_skl))
| ~ int_leq(sK2_skl,n)
| ~ int_leq(int_one,plus(sK1_skl,sK0_skl(sK2_skl,sK1_skl)))
| ~ int_leq(sK1_skl,n)
| ~ int_leq(int_one,sK1_skl) ),
inference(paramodulation,[status(thm)],[f1470,f1504]) ).
fof(f2971,definition,
( sQ137_spl
<=> int_leq(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f2973,plain,
( sQ137_spl
| ~ int_leq(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f2971]) ).
fof(f2974,definition,
( sQ138_spl
<=> a(sK1_skl,plus(sK1_skl,sK0_skl(sK2_skl,sK1_skl))) = real_zero ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f2975,plain,
( ~ sQ138_spl
| a(sK1_skl,plus(sK1_skl,sK0_skl(sK2_skl,sK1_skl))) = real_zero ),
inference(component_clause,[status(thm)],[f2974]) ).
fof(f2977,plain,
( sQ138_spl
| ~ sQ137_spl
| ~ sQ8_spl
| ~ sQ104_spl
| ~ sQ114_spl
| ~ sQ63_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2966,f165,f1496,f2567,f2363,f162,f2971,f2974]) ).
fof(f2989,plain,
( sQ137_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2973,f51]) ).
fof(f2990,plain,
sQ137_spl,
inference(contradiction_clause,[status(thm)],[f2989]) ).
fof(f2996,plain,
( ~ sQ138_spl
| a(sK1_skl,sK2_skl) = real_zero ),
inference(forward_demodulation,[status(thm)],[f1470,f2975]) ).
fof(f2997,plain,
( ~ sQ138_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2996,f50]) ).
fof(f2998,plain,
~ sQ138_spl,
inference(contradiction_clause,[status(thm)],[f2997]) ).
fof(f2999,plain,
$false,
inference(sat_refutation,[status(thm)],[f69,f175,f194,f222,f303,f1860,f2044,f2083,f2345,f2522,f2587,f2724,f2754,f2977,f2990,f2998]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV486+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:53:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 1.35/0.76 % Refutation found
% 1.35/0.76 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.35/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.67/0.78 % Elapsed time: 0.417234 seconds
% 2.67/0.78 % CPU time: 3.011557 seconds
% 2.67/0.78 % Total memory used: 130.532 MB
% 2.67/0.78 % Net memory used: 124.807 MB
%------------------------------------------------------------------------------