%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG038-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 02:04:45 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.58s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 10 unt; 2 def)
% Number of atoms : 90 ( 14 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 102 ( 51 ~; 49 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 90 ( 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
! [X,Y] :
( product(X,h(X,Y),Y)
| X != additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
b != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
! [U,Z,W] :
( sum(U,Z,W)
| ! [X,V] :
( ~ sum(X,V,W)
| ! [Y] :
( ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f41,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(V3,X,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,plain,
! [X] :
( ! [Y] : product(X,h(X,Y),Y)
| X != additive_identity ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f50,plain,
! [X0,X1] :
( product(X0,h(X0,X1),X1)
| X0 != additive_identity ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f53,plain,
b != additive_identity,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f54,plain,
! [X0] : product(additive_identity,h(additive_identity,X0),X0),
inference(destructive_equality_resolution,[status(thm)],[f50]) ).
fof(f56,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f46,f22]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( ~ sum(X2,X4,X0)
| ~ sum(X3,X1,X4)
| ~ sum(X2,X3,additive_identity)
| X0 = X1 ),
inference(resolution,[status(thm)],[f56,f31]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( ~ sum(additive_inverse(X2),X3,X0)
| ~ sum(X2,X1,X3)
| X0 = X1 ),
inference(resolution,[status(thm)],[f69,f26]) ).
fof(f122,plain,
! [X0,X1,X2] :
( sum(X2,X1,X1)
| ~ sum(X0,additive_identity,additive_identity)
| ~ product(X0,h(additive_identity,X1),X2) ),
inference(resolution,[status(thm)],[f42,f54]) ).
fof(f222,definition,
( sQ2_spl
<=> sum(additive_identity,additive_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( sQ2_spl
| ~ sum(additive_identity,additive_identity,additive_identity) ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f238,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f224,f22]) ).
fof(f239,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f258,plain,
! [X0,X1] :
( ~ sum(X1,X0,X1)
| additive_identity = X0 ),
inference(resolution,[status(thm)],[f88,f26]) ).
fof(f298,plain,
! [X0,X1] :
( ~ sum(X0,X1,X1)
| additive_identity = X0 ),
inference(resolution,[status(thm)],[f258,f32]) ).
fof(f333,plain,
! [X0] :
( sum(X0,X0,X0)
| ~ sum(additive_identity,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f122,f54]) ).
fof(f339,definition,
! [X0] :
( sQ6_spl
<=> sum(X0,X0,X0) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f340,plain,
! [X0] :
( ~ sQ6_spl
| sum(X0,X0,X0) ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f342,plain,
( sQ6_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f333,f222,f339]) ).
fof(f429,plain,
! [X0] :
( ~ sQ6_spl
| additive_identity = X0 ),
inference(resolution,[status(thm)],[f340,f298]) ).
fof(f440,plain,
( ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f53,f429]) ).
fof(f466,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f440]) ).
fof(f467,plain,
$false,
inference(sat_refutation,[status(thm)],[f239,f342,f466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG038-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n005.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 04:14:53 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.13/5.58 % Refutation found
% 0.13/5.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.59 % Elapsed time: 0.219044 seconds
% 0.13/5.59 % CPU time: 1.539368 seconds
% 0.13/5.59 % Total memory used: 56.048 MB
% 0.13/5.59 % Net memory used: 53.380 MB
%------------------------------------------------------------------------------