%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD064-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 12:22:06 PM UTC 2026
% Result : Unsatisfiable 134.96s 32.24s
% Output : CNFRefutation 134.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 29
% Syntax : Number of formulae : 117 ( 36 unt; 15 def)
% Number of atoms : 230 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 197 ( 84 ~; 98 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 16 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Z,Y] :
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Z,Y] :
( ~ less_or_equal(X,Y)
| ~ defined(Z)
| less_or_equal(add(X,Z),add(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [Y,Z,X] :
( ~ equalish(X,Y)
| ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ less_or_equal(additive_inverse(a),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,plain,
! [X0] :
( equalish(add(additive_identity,X0),X0)
| ~ defined(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f34,plain,
! [X0] :
( equalish(add(X0,additive_inverse(X0)),additive_identity)
| ~ defined(X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f45,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| defined(add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f46,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| defined(add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f48,plain,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f51,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f54,plain,
! [Z,Y] :
( ~ less_or_equal(Y,Z)
| ! [X] :
( ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X0,X2)
| ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f57,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ defined(X1)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X,Y] :
( ~ less_or_equal(X,Y)
| ! [Z] :
( ~ defined(Z)
| less_or_equal(add(X,Z),add(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f59,plain,
! [X0,X1,X2] :
( less_or_equal(add(X0,X2),add(X1,X2))
| ~ defined(X2)
| ~ less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f63,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f70,plain,
! [Y,X] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f71,plain,
! [X0,X1,X2] :
( less_or_equal(X1,X2)
| ~ less_or_equal(X0,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f74,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
~ less_or_equal(additive_inverse(a),additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f80,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_identity,X0)
| less_or_equal(X0,additive_identity) ),
inference(resolution,[status(thm)],[f57,f47]) ).
fof(f90,definition,
( sQ2_spl
<=> less_or_equal(additive_identity,a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( sQ2_spl
| ~ less_or_equal(additive_identity,a) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f113,plain,
( less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f80,f47]) ).
fof(f114,definition,
( sQ3_spl
<=> less_or_equal(additive_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f117,plain,
sQ3_spl,
inference(split_clause,[status(thm)],[f113,f114]) ).
fof(f189,plain,
! [X0] :
( defined(add(X0,a))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f46,f73]) ).
fof(f190,plain,
! [X0] :
( defined(add(X0,additive_identity))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f46,f47]) ).
fof(f309,plain,
! [X0,X1] :
( ~ defined(X0)
| less_or_equal(X0,X1)
| ~ less_or_equal(add(additive_identity,X0),X1) ),
inference(resolution,[status(thm)],[f33,f71]) ).
fof(f331,plain,
defined(additive_inverse(a)),
inference(resolution,[status(thm)],[f48,f73]) ).
fof(f332,plain,
defined(additive_inverse(additive_identity)),
inference(resolution,[status(thm)],[f48,f47]) ).
fof(f333,plain,
defined(additive_inverse(additive_inverse(a))),
inference(resolution,[status(thm)],[f331,f48]) ).
fof(f339,definition,
( sQ4_spl
<=> less_or_equal(additive_inverse(a),additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( ~ sQ4_spl
| less_or_equal(additive_inverse(a),additive_identity) ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f353,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f340,f75]) ).
fof(f354,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f404,plain,
defined(add(additive_inverse(additive_identity),a)),
inference(resolution,[status(thm)],[f189,f332]) ).
fof(f405,plain,
defined(add(additive_inverse(a),a)),
inference(resolution,[status(thm)],[f189,f331]) ).
fof(f407,plain,
defined(add(additive_identity,a)),
inference(resolution,[status(thm)],[f189,f47]) ).
fof(f416,plain,
defined(additive_inverse(add(additive_identity,a))),
inference(resolution,[status(thm)],[f407,f48]) ).
fof(f437,plain,
defined(add(additive_inverse(additive_identity),additive_identity)),
inference(resolution,[status(thm)],[f190,f332]) ).
fof(f438,plain,
defined(add(additive_inverse(a),additive_identity)),
inference(resolution,[status(thm)],[f190,f331]) ).
fof(f521,definition,
( sQ28_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f523,plain,
( sQ28_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f598,plain,
defined(add(multiplicative_identity,additive_identity)),
inference(resolution,[status(thm)],[f51,f190]) ).
fof(f600,plain,
defined(additive_inverse(multiplicative_identity)),
inference(resolution,[status(thm)],[f51,f48]) ).
fof(f615,plain,
! [X0,X1] :
( ~ defined(X1)
| less_or_equal(X1,add(X0,X1))
| ~ defined(X1)
| ~ less_or_equal(additive_identity,X0) ),
inference(resolution,[status(thm)],[f59,f309]) ).
fof(f621,plain,
! [X0,X1] :
( less_or_equal(X0,add(X1,X0))
| ~ less_or_equal(additive_identity,X1)
| ~ defined(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f615]) ).
fof(f790,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f73]) ).
fof(f791,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f790]) ).
fof(f844,plain,
! [X0,X1,X2] :
( less_or_equal(X2,X1)
| ~ equalish(X2,X0)
| ~ less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f63,f71]) ).
fof(f1155,plain,
! [X0,X1] :
( less_or_equal(add(X0,additive_inverse(X0)),X1)
| ~ less_or_equal(additive_identity,X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f844,f34]) ).
fof(f1203,definition,
( sQ83_spl
<=> defined(additive_inverse(additive_identity)) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1205,plain,
( sQ83_spl
| ~ defined(additive_inverse(additive_identity)) ),
inference(component_clause,[status(thm)],[f1203]) ).
fof(f1319,definition,
( sQ101_spl
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1321,plain,
( sQ101_spl
| ~ defined(additive_inverse(a)) ),
inference(component_clause,[status(thm)],[f1319]) ).
fof(f2428,plain,
( sQ101_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1321,f331]) ).
fof(f2429,plain,
sQ101_spl,
inference(contradiction_clause,[status(thm)],[f2428]) ).
fof(f2744,definition,
( sQ236_spl
<=> less_or_equal(add(a,additive_inverse(a)),additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2745,plain,
( ~ sQ236_spl
| less_or_equal(add(a,additive_inverse(a)),additive_identity) ),
inference(component_clause,[status(thm)],[f2744]) ).
fof(f2746,plain,
( sQ236_spl
| ~ less_or_equal(add(a,additive_inverse(a)),additive_identity) ),
inference(component_clause,[status(thm)],[f2744]) ).
fof(f2787,plain,
( sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1205,f332]) ).
fof(f2788,plain,
sQ83_spl,
inference(contradiction_clause,[status(thm)],[f2787]) ).
fof(f3139,plain,
! [X0,X1,X2] :
( ~ less_or_equal(additive_identity,X2)
| ~ less_or_equal(add(X2,X0),X1)
| less_or_equal(X0,X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f621,f55]) ).
fof(f3990,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f92,f74]) ).
fof(f3991,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f3990]) ).
fof(f6441,definition,
( sQ554_spl
<=> defined(additive_inverse(multiplicative_identity)) ),
introduced(definition,[new_symbols(definition,[sQ554_spl])],[split_symbol_definition]) ).
fof(f6443,plain,
( sQ554_spl
| ~ defined(additive_inverse(multiplicative_identity)) ),
inference(component_clause,[status(thm)],[f6441]) ).
fof(f6482,plain,
( sQ554_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6443,f600]) ).
fof(f6483,plain,
sQ554_spl,
inference(contradiction_clause,[status(thm)],[f6482]) ).
fof(f14400,definition,
( sQ1283_spl
<=> defined(additive_inverse(additive_inverse(a))) ),
introduced(definition,[new_symbols(definition,[sQ1283_spl])],[split_symbol_definition]) ).
fof(f14402,plain,
( sQ1283_spl
| ~ defined(additive_inverse(additive_inverse(a))) ),
inference(component_clause,[status(thm)],[f14400]) ).
fof(f14918,plain,
( sQ1283_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14402,f333]) ).
fof(f14919,plain,
sQ1283_spl,
inference(contradiction_clause,[status(thm)],[f14918]) ).
fof(f15610,definition,
( sQ1450_spl
<=> defined(add(additive_inverse(a),a)) ),
introduced(definition,[new_symbols(definition,[sQ1450_spl])],[split_symbol_definition]) ).
fof(f15612,plain,
( sQ1450_spl
| ~ defined(add(additive_inverse(a),a)) ),
inference(component_clause,[status(thm)],[f15610]) ).
fof(f15628,plain,
( sQ1450_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f15612,f405]) ).
fof(f15629,plain,
sQ1450_spl,
inference(contradiction_clause,[status(thm)],[f15628]) ).
fof(f16014,definition,
( sQ1498_spl
<=> defined(add(additive_inverse(additive_identity),a)) ),
introduced(definition,[new_symbols(definition,[sQ1498_spl])],[split_symbol_definition]) ).
fof(f16016,plain,
( sQ1498_spl
| ~ defined(add(additive_inverse(additive_identity),a)) ),
inference(component_clause,[status(thm)],[f16014]) ).
fof(f18725,definition,
( sQ1767_spl
<=> defined(add(additive_inverse(additive_identity),additive_identity)) ),
introduced(definition,[new_symbols(definition,[sQ1767_spl])],[split_symbol_definition]) ).
fof(f18727,plain,
( sQ1767_spl
| ~ defined(add(additive_inverse(additive_identity),additive_identity)) ),
inference(component_clause,[status(thm)],[f18725]) ).
fof(f18837,plain,
( sQ1767_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18727,f437]) ).
fof(f18838,plain,
sQ1767_spl,
inference(contradiction_clause,[status(thm)],[f18837]) ).
fof(f21309,plain,
( sQ236_spl
| ~ less_or_equal(additive_identity,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[f2746,f1155]) ).
fof(f21310,plain,
( sQ236_spl
| ~ sQ3_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f21309,f521,f114,f2744]) ).
fof(f21766,plain,
( sQ1498_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f16016,f404]) ).
fof(f21767,plain,
sQ1498_spl,
inference(contradiction_clause,[status(thm)],[f21766]) ).
fof(f22015,definition,
( sQ2189_spl
<=> defined(add(additive_inverse(a),additive_identity)) ),
introduced(definition,[new_symbols(definition,[sQ2189_spl])],[split_symbol_definition]) ).
fof(f22017,plain,
( sQ2189_spl
| ~ defined(add(additive_inverse(a),additive_identity)) ),
inference(component_clause,[status(thm)],[f22015]) ).
fof(f23970,definition,
( sQ2336_spl
<=> defined(add(multiplicative_identity,additive_identity)) ),
introduced(definition,[new_symbols(definition,[sQ2336_spl])],[split_symbol_definition]) ).
fof(f23972,plain,
( sQ2336_spl
| ~ defined(add(multiplicative_identity,additive_identity)) ),
inference(component_clause,[status(thm)],[f23970]) ).
fof(f24006,plain,
( sQ2336_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23972,f598]) ).
fof(f24007,plain,
sQ2336_spl,
inference(contradiction_clause,[status(thm)],[f24006]) ).
fof(f25237,definition,
( sQ2429_spl
<=> defined(additive_inverse(add(additive_identity,a))) ),
introduced(definition,[new_symbols(definition,[sQ2429_spl])],[split_symbol_definition]) ).
fof(f25239,plain,
( sQ2429_spl
| ~ defined(additive_inverse(add(additive_identity,a))) ),
inference(component_clause,[status(thm)],[f25237]) ).
fof(f25247,plain,
( sQ2429_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f25239,f416]) ).
fof(f25248,plain,
sQ2429_spl,
inference(contradiction_clause,[status(thm)],[f25247]) ).
fof(f26589,plain,
( sQ2189_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22017,f438]) ).
fof(f26590,plain,
sQ2189_spl,
inference(contradiction_clause,[status(thm)],[f26589]) ).
fof(f26677,plain,
! [X0,X1] :
( ~ less_or_equal(add(a,X0),X1)
| less_or_equal(X0,X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f3139,f74]) ).
fof(f26713,plain,
( ~ sQ236_spl
| less_or_equal(additive_inverse(a),additive_identity)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[status(thm)],[f26677,f2745]) ).
fof(f26793,plain,
( ~ sQ236_spl
| sQ4_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f26713,f1319,f339,f2744]) ).
fof(f26824,plain,
$false,
inference(sat_refutation,[status(thm)],[f117,f354,f791,f2429,f2788,f3991,f6483,f14919,f15629,f18838,f21310,f21767,f24007,f25248,f26590,f26793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : FLD064-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.02/15.22 % CPULimit : 300
% 0.02/15.22 % WCLimit : 300
% 0.02/15.22 % DateTime : Mon Sep 21 15:44:07 UTC 2026
% 0.02/15.22 % CPUTime :
% 0.02/15.23 % Drodi V4.1.1
% 134.96/32.24 % Refutation found
% 134.96/32.24 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 134.96/32.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 56.63/33.50 % Elapsed time: 18.062381 seconds
% 56.63/33.50 % CPU time: 131.439643 seconds
% 56.63/33.50 % Total memory used: 741.981 MB
% 56.63/33.50 % Net memory used: 653.965 MB
%------------------------------------------------------------------------------