%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 11:47:43 AM UTC 2026
% Result : Unsatisfiable 0.13s 5.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 63 ( 14 unt; 6 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 136 ( 64 ~; 66 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(X,multiplicative_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( product(additive_inverse(X),additive_inverse(Y),Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] :
( product(X,additive_inverse(Y),additive_inverse(Z))
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( product(X,X,additive_identity)
| product(X,multiplicative_inverse(X),multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( ~ product(X,X,additive_identity)
| ~ greater_than_0(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( product(Y,X,Z)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] :
( greater_than_0(additive_inverse(X))
| product(X,X,additive_identity)
| greater_than_0(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Y,Z,X] :
( product(X,X,additive_identity)
| ~ product(Y,Y,additive_identity)
| ~ product(Y,Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Y,Z,X] :
( greater_than_0(X)
| ~ greater_than_0(Z)
| ~ greater_than_0(Y)
| ~ product(Y,Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
greater_than_0(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ greater_than_0(multiplicative_inverse(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
~ product(multiplicative_identity,multiplicative_identity,additive_identity),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] :
( product(additive_inverse(X0),additive_inverse(X1),X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f19,plain,
! [X0,X1,X2] :
( product(X0,additive_inverse(X1),additive_inverse(X2))
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f20,plain,
! [X0] :
( product(X0,X0,additive_identity)
| product(X0,multiplicative_inverse(X0),multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0] :
( ~ product(X0,X0,additive_identity)
| ~ greater_than_0(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0,X1,X2] :
( product(X1,X0,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0] :
( greater_than_0(additive_inverse(X0))
| product(X0,X0,additive_identity)
| greater_than_0(X0) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f25,plain,
! [X] :
( product(X,X,additive_identity)
| ! [Y] :
( ~ product(Y,Y,additive_identity)
| ! [Z] : ~ product(Y,Z,X) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f26,plain,
! [X0,X1,X2] :
( product(X2,X2,additive_identity)
| ~ product(X0,X0,additive_identity)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [X] :
( greater_than_0(X)
| ! [Z] :
( ~ greater_than_0(Z)
| ! [Y] :
( ~ greater_than_0(Y)
| ~ product(Y,Z,X) ) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f28,plain,
! [X0,X1,X2] :
( greater_than_0(X2)
| ~ greater_than_0(X1)
| ~ greater_than_0(X0)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
greater_than_0(a),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
~ greater_than_0(multiplicative_inverse(a)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f33,plain,
! [X0,X1] :
( ~ greater_than_0(X1)
| ~ greater_than_0(X0)
| ~ product(X0,X1,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f28,f30]) ).
fof(f55,definition,
( sQ4_spl
<=> greater_than_0(multiplicative_inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ4_spl
| greater_than_0(multiplicative_inverse(a)) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f66,plain,
! [X0] : product(multiplicative_identity,X0,X0),
inference(resolution,[status(thm)],[f23,f15]) ).
fof(f67,plain,
! [X0] :
( product(X0,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f23,f20]) ).
fof(f82,plain,
! [X0] : product(additive_inverse(multiplicative_identity),additive_inverse(X0),X0),
inference(resolution,[status(thm)],[f17,f66]) ).
fof(f86,plain,
( ~ greater_than_0(additive_inverse(multiplicative_inverse(a)))
| ~ greater_than_0(additive_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[f82,f33]) ).
fof(f93,definition,
( sQ8_spl
<=> greater_than_0(additive_inverse(multiplicative_identity)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( sQ8_spl
| ~ greater_than_0(additive_inverse(multiplicative_identity)) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f97,definition,
( sQ9_spl
<=> greater_than_0(additive_inverse(multiplicative_inverse(a))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f99,plain,
( sQ9_spl
| ~ greater_than_0(additive_inverse(multiplicative_inverse(a))) ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f86,f93,f97]) ).
fof(f105,plain,
! [X0,X1] :
( sQ8_spl
| ~ greater_than_0(X1)
| ~ greater_than_0(X0)
| ~ product(X0,X1,additive_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[f95,f28]) ).
fof(f106,plain,
! [X0] :
( sQ8_spl
| ~ greater_than_0(X0)
| ~ product(X0,a,additive_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[f105,f29]) ).
fof(f121,plain,
! [X0,X1,X2] :
( product(additive_inverse(X1),X0,additive_inverse(X2))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f19,f23]) ).
fof(f128,definition,
( sQ11_spl
<=> product(multiplicative_identity,multiplicative_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ11_spl
| product(multiplicative_identity,multiplicative_identity,additive_identity) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f144,definition,
( sQ13_spl
<=> product(a,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ13_spl
| product(a,a,additive_identity) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f149,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f129,f16]) ).
fof(f150,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ9_spl
| product(multiplicative_inverse(a),multiplicative_inverse(a),additive_identity)
| greater_than_0(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f99,f24]) ).
fof(f154,definition,
( sQ14_spl
<=> product(multiplicative_inverse(a),multiplicative_inverse(a),additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ14_spl
| product(multiplicative_inverse(a),multiplicative_inverse(a),additive_identity) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( sQ9_spl
| sQ14_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f152,f55,f154,f97]) ).
fof(f158,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f30]) ).
fof(f159,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f218,plain,
! [X0,X1] :
( ~ sQ14_spl
| product(X1,X1,additive_identity)
| ~ product(multiplicative_inverse(a),X0,X1) ),
inference(resolution,[status(thm)],[f155,f26]) ).
fof(f265,plain,
! [X0] :
( sQ8_spl
| ~ greater_than_0(additive_inverse(X0))
| ~ product(a,X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f121,f106]) ).
fof(f272,plain,
( ~ sQ14_spl
| product(a,a,additive_identity)
| product(multiplicative_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[f218,f67]) ).
fof(f276,plain,
( ~ sQ14_spl
| sQ13_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f272,f128,f144,f154]) ).
fof(f305,plain,
( ~ sQ13_spl
| ~ greater_than_0(a) ),
inference(resolution,[status(thm)],[f145,f22]) ).
fof(f310,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f305,f29]) ).
fof(f311,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f310]) ).
fof(f312,plain,
( sQ8_spl
| product(a,a,additive_identity)
| ~ greater_than_0(additive_inverse(multiplicative_inverse(a))) ),
inference(resolution,[status(thm)],[f265,f20]) ).
fof(f313,plain,
( sQ8_spl
| sQ13_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f312,f97,f144,f93]) ).
fof(f314,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f150,f157,f159,f276,f311,f313]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n015.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 12:55:27 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.38 % Drodi V4.1.1
% 0.13/5.42 % Refutation found
% 0.13/5.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.44 % Elapsed time: 0.062060 seconds
% 0.13/5.44 % CPU time: 0.255347 seconds
% 0.13/5.44 % Total memory used: 19.194 MB
% 0.13/5.44 % Net memory used: 18.454 MB
%------------------------------------------------------------------------------