%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV488+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:48:03 PM UTC 2026
% Result : Theorem 0.20s 0.52s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 47 ( 14 unt; 6 def)
% Number of atoms : 158 ( 35 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 186 ( 75 ~; 66 |; 28 &)
% ( 7 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 43 ( 41 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [I,J] :
( int_leq(I,J)
<=> ( I = J
| int_less(I,J) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
real_zero != real_one,
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 ) )
& ! [K] :
( ( int_leq(K,J)
& int_leq(int_one,K) )
=> a(K,K) = real_one )
& ! [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) = lu(plus(K,C),K) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [I,J] :
( ( int_leq(J,n)
& int_leq(I,J)
& int_leq(int_one,I) )
=> ( I = J
=> a(I,J) != real_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [I,J] :
( ( int_leq(J,n)
& int_leq(I,J)
& int_leq(int_one,I) )
=> ( I = J
=> 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(f19,plain,
! [X0,X1] :
( X0 != X1
| int_leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f41,plain,
real_zero != real_one,
inference(cnf_transformation,[status(thm)],[f11]) ).
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) )
& ! [K] :
( a(K,K) = real_one
| ~ int_leq(K,J)
| ~ int_leq(int_one,K) )
& ! [C] :
( ! [K] :
( a(plus(K,C),K) = lu(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] :
( a(X2,X2) = real_one
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,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(f46,plain,
? [I,J] :
( a(I,J) = real_zero
& I = J
& int_leq(J,n)
& int_leq(I,J)
& int_leq(int_one,I) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f47,plain,
( a(sK1_skl,sK2_skl) = real_zero
& sK1_skl = sK2_skl
& int_leq(sK2_skl,n)
& int_leq(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)],[f46]) ).
fof(f48,plain,
int_leq(int_one,sK1_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
int_leq(sK2_skl,n),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f51,plain,
sK1_skl = sK2_skl,
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f52,plain,
a(sK1_skl,sK2_skl) = real_zero,
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f53,definition,
! [X0] :
( sQ0_spl
<=> ( ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f54,plain,
! [X0] :
( ~ sQ0_spl
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
! [X1,X2] :
( sQ1_spl
<=> ( a(X2,X2) = real_one
| ~ int_leq(X2,X1)
| ~ int_leq(int_one,X2)
| ~ int_leq(X1,n)
| ~ int_leq(int_one,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f57,plain,
! [X0,X1] :
( ~ sQ1_spl
| a(X1,X1) = real_one
| ~ int_leq(X1,X0)
| ~ int_leq(int_one,X1)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f53,f56]) ).
fof(f60,plain,
! [X0] : int_leq(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f65,plain,
int_leq(sK1_skl,n),
inference(backward_demodulation,[status(thm)],[f51,f50]) ).
fof(f67,plain,
a(sK1_skl,sK1_skl) = real_zero,
inference(forward_demodulation,[status(thm)],[f51,f52]) ).
fof(f139,plain,
( ~ sQ0_spl
| ~ int_leq(sK1_skl,n) ),
inference(resolution,[status(thm)],[f54,f48]) ).
fof(f147,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f65]) ).
fof(f148,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f167,plain,
! [X0] :
( ~ sQ1_spl
| real_zero = real_one
| ~ int_leq(sK1_skl,X0)
| ~ int_leq(int_one,sK1_skl)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(paramodulation,[status(thm)],[f67,f57]) ).
fof(f168,definition,
! [X0] :
( sQ8_spl
<=> ( ~ int_leq(sK1_skl,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f169,plain,
! [X0] :
( ~ sQ8_spl
| ~ int_leq(sK1_skl,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ9_spl
<=> int_leq(int_one,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( sQ9_spl
| ~ int_leq(int_one,sK1_skl) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,definition,
( sQ10_spl
<=> real_zero = real_one ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ10_spl
| real_zero = real_one ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( ~ sQ1_spl
| sQ10_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f167,f168,f171,f174,f56]) ).
fof(f178,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f175,f41]) ).
fof(f179,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f186,plain,
( ~ sQ8_spl
| ~ int_leq(sK1_skl,n)
| ~ int_leq(int_one,sK1_skl) ),
inference(resolution,[status(thm)],[f169,f60]) ).
fof(f204,definition,
( sQ16_spl
<=> int_leq(sK1_skl,n) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( sQ16_spl
| ~ int_leq(sK1_skl,n) ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f212,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f186,f171,f204,f168]) ).
fof(f213,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f48]) ).
fof(f214,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f213]) ).
fof(f215,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f206,f65]) ).
fof(f216,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f215]) ).
fof(f217,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f148,f177,f179,f212,f214,f216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV488+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.46 % Computer : n009.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 08:54:42 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.50 % Drodi V4.1.1
% 0.20/0.52 % Refutation found
% 0.20/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.58 % Elapsed time: 0.083709 seconds
% 0.25/0.58 % CPU time: 0.172043 seconds
% 0.25/0.58 % Total memory used: 26.153 MB
% 0.25/0.58 % Net memory used: 26.044 MB
%------------------------------------------------------------------------------