%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV488+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 0.08s 0.41s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% 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 : 9 ( 9 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) = real_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,conjecture,
! [I,J] :
( ( int_leq(I,n)
& int_leq(J,I)
& int_leq(int_one,J) )
=> ( I = J
=> a(I,J) != real_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ ! [I,J] :
( ( int_leq(I,n)
& int_leq(J,I)
& int_leq(int_one,J) )
=> ( 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) = real_zero
| ~ 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(I,n)
& int_leq(J,I)
& int_leq(int_one,J) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f47,plain,
( a(sK1_skl,sK2_skl) = real_zero
& sK1_skl = sK2_skl
& int_leq(sK1_skl,n)
& int_leq(sK2_skl,sK1_skl)
& int_leq(int_one,sK2_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,sK2_skl),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f50,plain,
int_leq(sK1_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(f66,plain,
int_leq(int_one,sK1_skl),
inference(backward_demodulation,[status(thm)],[f51,f48]) ).
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,f66]) ).
fof(f147,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f139,f50]) ).
fof(f148,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f182,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(f183,definition,
! [X0] :
( sQ9_spl
<=> ( ~ int_leq(sK1_skl,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f184,plain,
! [X0] :
( ~ sQ9_spl
| ~ int_leq(sK1_skl,X0)
| ~ int_leq(X0,n)
| ~ int_leq(int_one,X0) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,definition,
( sQ10_spl
<=> int_leq(int_one,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( sQ10_spl
| ~ int_leq(int_one,sK1_skl) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ11_spl
<=> real_zero = real_one ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ11_spl
| real_zero = real_one ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( ~ sQ1_spl
| sQ11_spl
| ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f182,f183,f186,f189,f56]) ).
fof(f193,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f41]) ).
fof(f194,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f201,plain,
( ~ sQ9_spl
| ~ int_leq(sK1_skl,n)
| ~ int_leq(int_one,sK1_skl) ),
inference(resolution,[status(thm)],[f184,f60]) ).
fof(f219,definition,
( sQ17_spl
<=> int_leq(sK1_skl,n) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( sQ17_spl
| ~ int_leq(sK1_skl,n) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f227,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f201,f186,f219,f183]) ).
fof(f228,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f188,f66]) ).
fof(f229,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f228]) ).
fof(f230,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f221,f50]) ).
fof(f231,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f232,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f148,f192,f194,f227,f229,f231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV488+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 08:52:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 0.08/0.41 % Refutation found
% 0.08/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.43 % Elapsed time: 0.056562 seconds
% 0.08/0.43 % CPU time: 0.184858 seconds
% 0.08/0.43 % Total memory used: 102.611 MB
% 0.08/0.43 % Net memory used: 102.170 MB
%------------------------------------------------------------------------------