%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP538-1 : TPTP v9.3.1. Released v2.6.0.
% 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 12:34:37 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 30 unt; 3 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(divide(A,B),divide(divide(A,C),B)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : inverse(A) = divide(divide(B,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = divide(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(X0,X1),divide(divide(X0,X2),X1)) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = divide(X0,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF2_fnc = inverse(b2),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f12,definition,
sF1_fnc = multiply(sF2_fnc,b2),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f13,definition,
sF0_fnc = multiply(sF1_fnc,a2),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f14,plain,
sF0_fnc != a2,
inference(definition_folding,[],[f10,f13,f12,f11]) ).
fof(f19,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f8,f7]) ).
fof(f21,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f8,f19]) ).
fof(f22,plain,
! [X0] : multiply(X0,b2) = divide(X0,sF2_fnc),
inference(paramodulation,[status(thm)],[f11,f19]) ).
fof(f32,plain,
! [X0] : inverse(X0) = divide(multiply(sF2_fnc,b2),X0),
inference(paramodulation,[status(thm)],[f22,f8]) ).
fof(f34,plain,
! [X0] : inverse(X0) = divide(sF1_fnc,X0),
inference(forward_demodulation,[status(thm)],[f12,f32]) ).
fof(f36,plain,
! [X0] : inverse(inverse(X0)) = multiply(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f19,f34]) ).
fof(f48,plain,
sF0_fnc = inverse(inverse(a2)),
inference(backward_demodulation,[status(thm)],[f36,f13]) ).
fof(f95,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f9,f21]) ).
fof(f97,plain,
! [X0] : inverse(X0) = divide(identity,X0),
inference(backward_demodulation,[status(thm)],[f9,f8]) ).
fof(f159,plain,
! [X0,X1] : divide(divide(X0,X1),divide(identity,X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f167,plain,
! [X0,X1] : divide(divide(X0,X1),inverse(X1)) = X0,
inference(forward_demodulation,[status(thm)],[f97,f159]) ).
fof(f168,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f19,f167]) ).
fof(f200,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f9,f168]) ).
fof(f203,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f95,f200]) ).
fof(f205,plain,
sF0_fnc = a2,
inference(backward_demodulation,[status(thm)],[f203,f48]) ).
fof(f212,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f205,f14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP538-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n009.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:16:12 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.37 % Refutation found
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.024269 seconds
% 0.13/0.39 % CPU time: 0.023230 seconds
% 0.13/0.39 % Total memory used: 713.552 KB
% 0.13/0.39 % Net memory used: 683.328 KB
%------------------------------------------------------------------------------