%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP541-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:34:38 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.37s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 23 ( 23 unt; 4 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 12 ( 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : multiply(A,B) = divide(A,divide(identity,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = divide(identity,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(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = divide(identity,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(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF1_fnc = inverse(a1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f12,definition,
sF0_fnc = multiply(sF1_fnc,a1),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f13,definition,
sF3_fnc = inverse(b1),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f14,definition,
sF2_fnc = multiply(sF3_fnc,b1),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f15,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f10,f14,f13,f12,f11]) ).
fof(f16,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f8,f7]) ).
fof(f18,plain,
! [X0] : multiply(X0,b1) = divide(X0,sF3_fnc),
inference(paramodulation,[status(thm)],[f13,f16]) ).
fof(f19,plain,
! [X0] : multiply(X0,a1) = divide(X0,sF1_fnc),
inference(paramodulation,[status(thm)],[f11,f16]) ).
fof(f81,plain,
identity = multiply(sF1_fnc,a1),
inference(paramodulation,[status(thm)],[f19,f9]) ).
fof(f82,plain,
identity = multiply(sF3_fnc,b1),
inference(paramodulation,[status(thm)],[f18,f9]) ).
fof(f91,plain,
identity = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f12,f81]) ).
fof(f92,plain,
identity = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f14,f82]) ).
fof(f99,plain,
identity != sF2_fnc,
inference(backward_demodulation,[status(thm)],[f91,f15]) ).
fof(f101,plain,
identity != identity,
inference(forward_demodulation,[status(thm)],[f92,f99]) ).
fof(f102,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP541-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n005.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:15:49 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.37 % Refutation found
% 0.11/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.39 % Elapsed time: 0.026923 seconds
% 0.13/0.39 % CPU time: 0.026298 seconds
% 0.13/0.39 % Total memory used: 911.504 KB
% 0.13/0.39 % Net memory used: 882.800 KB
%------------------------------------------------------------------------------