%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG007-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 02:04:38 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.30s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 32 unt; 1 def)
% Number of atoms : 32 ( 31 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : add(additive_identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : add(additive_inverse(X),X) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] : add(add(X,Y),Z) = add(X,add(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
! [X] : multiply(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
add(a,a) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
! [X0] : multiply(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f32,plain,
add(a,a) != additive_identity,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF0_fnc = add(a,a),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f34,plain,
sF0_fnc != additive_identity,
inference(definition_folding,[],[f32,f33]) ).
fof(f38,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(paramodulation,[status(thm)],[f18,f29]) ).
fof(f39,plain,
! [X0] : X0 = add(X0,additive_identity),
inference(paramodulation,[status(thm)],[f17,f29]) ).
fof(f66,plain,
! [X0,X1] : add(additive_identity,X0) = add(additive_inverse(X1),add(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f79,plain,
! [X0,X1] : X0 = add(additive_inverse(X1),add(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f66]) ).
fof(f86,plain,
! [X0] : X0 = add(additive_inverse(additive_inverse(X0)),additive_identity),
inference(paramodulation,[status(thm)],[f18,f79]) ).
fof(f95,plain,
! [X0] : X0 = additive_inverse(additive_inverse(X0)),
inference(forward_demodulation,[status(thm)],[f39,f86]) ).
fof(f241,plain,
! [X0] : additive_inverse(X0) = additive_inverse(multiply(additive_inverse(X0),X0)),
inference(paramodulation,[status(thm)],[f31,f26]) ).
fof(f268,plain,
! [X0] : multiply(additive_inverse(X0),X0) = additive_inverse(additive_inverse(X0)),
inference(paramodulation,[status(thm)],[f241,f95]) ).
fof(f282,plain,
! [X0] : multiply(additive_inverse(X0),X0) = X0,
inference(forward_demodulation,[status(thm)],[f95,f268]) ).
fof(f326,plain,
! [X0] : additive_inverse(multiply(X0,X0)) = X0,
inference(backward_demodulation,[status(thm)],[f27,f282]) ).
fof(f339,plain,
! [X0] : additive_inverse(X0) = X0,
inference(forward_demodulation,[status(thm)],[f31,f326]) ).
fof(f451,plain,
! [X0] : additive_identity = add(X0,X0),
inference(backward_demodulation,[status(thm)],[f339,f38]) ).
fof(f456,plain,
sF0_fnc = additive_identity,
inference(backward_demodulation,[status(thm)],[f451,f33]) ).
fof(f469,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f456,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG007-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Mon Sep 21 04:10:06 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Drodi V4.1.1
% 0.03/0.30 % Refutation found
% 0.03/0.30 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.32 % Elapsed time: 0.016410 seconds
% 0.03/0.32 % CPU time: 0.038741 seconds
% 0.03/0.32 % Total memory used: 2.675 MB
% 0.03/0.32 % Net memory used: 2.585 MB
%------------------------------------------------------------------------------