%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG008-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:04:39 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.52s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 49 unt; 1 def)
% Number of atoms : 49 ( 48 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : add(additive_identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : additive_inverse(additive_inverse(X)) = X,
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(f16,axiom,
! [X] : add(X,additive_inverse(X)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
! [X] : multiply(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0,X1,X2] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f30,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f31,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f32,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f35,plain,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f36,plain,
! [X0] : multiply(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f37,plain,
multiply(a,b) = c,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f38,plain,
multiply(b,a) != c,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f39,definition,
sF0_fnc = multiply(b,a),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f40,plain,
sF0_fnc != c,
inference(definition_folding,[],[f38,f39]) ).
fof(f41,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = multiply(X0,additive_inverse(X1)),
inference(forward_demodulation,[status(thm)],[f29,f30]) ).
fof(f82,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(X0,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f36,f22]) ).
fof(f87,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f36,f22]) ).
fof(f104,plain,
! [X0] : multiply(X0,additive_inverse(X0)) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f36,f29]) ).
fof(f118,plain,
! [X0] : multiply(additive_inverse(X0),X0) = additive_inverse(additive_inverse(X0)),
inference(paramodulation,[status(thm)],[f25,f104]) ).
fof(f126,plain,
! [X0] : multiply(X0,additive_inverse(X0)) = additive_inverse(additive_inverse(X0)),
inference(forward_demodulation,[status(thm)],[f41,f118]) ).
fof(f127,plain,
! [X0] : additive_inverse(X0) = additive_inverse(additive_inverse(X0)),
inference(forward_demodulation,[status(thm)],[f104,f126]) ).
fof(f132,plain,
! [X0] : add(X0,X0) = additive_identity,
inference(backward_demodulation,[status(thm)],[f139,f35]) ).
fof(f139,plain,
! [X0] : additive_inverse(X0) = X0,
inference(forward_demodulation,[status(thm)],[f25,f127]) ).
fof(f237,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = add(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f36,f23]) ).
fof(f350,plain,
! [X0,X1] : add(additive_identity,X0) = add(X1,add(X1,X0)),
inference(paramodulation,[status(thm)],[f132,f31]) ).
fof(f365,plain,
! [X0,X1] : X0 = add(X1,add(X1,X0)),
inference(forward_demodulation,[status(thm)],[f20,f350]) ).
fof(f379,plain,
! [X0,X1] : X0 = add(X1,add(X0,X1)),
inference(paramodulation,[status(thm)],[f32,f365]) ).
fof(f421,plain,
! [X0,X1] : multiply(X0,add(X0,X1)) = add(multiply(X1,add(X0,X1)),add(X0,X1)),
inference(paramodulation,[status(thm)],[f379,f237]) ).
fof(f435,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = add(multiply(X1,add(X0,X1)),add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f82,f421]) ).
fof(f436,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = add(add(multiply(X1,X0),X1),add(X0,X1)),
inference(forward_demodulation,[status(thm)],[f87,f435]) ).
fof(f437,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = add(multiply(X1,X0),add(X1,add(X0,X1))),
inference(forward_demodulation,[status(thm)],[f31,f436]) ).
fof(f441,plain,
! [X0,X1] : add(X0,multiply(X0,X1)) = add(multiply(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f379,f437]) ).
fof(f694,plain,
add(a,multiply(a,b)) = add(sF0_fnc,a),
inference(paramodulation,[status(thm)],[f39,f441]) ).
fof(f731,plain,
add(a,c) = add(sF0_fnc,a),
inference(forward_demodulation,[status(thm)],[f37,f694]) ).
fof(f857,plain,
sF0_fnc = add(a,add(a,c)),
inference(paramodulation,[status(thm)],[f731,f379]) ).
fof(f871,plain,
sF0_fnc = c,
inference(forward_demodulation,[status(thm)],[f365,f857]) ).
fof(f872,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f871,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG008-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 04:11:17 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.52 % Refutation found
% 0.13/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.54 % Elapsed time: 0.158758 seconds
% 0.13/0.54 % CPU time: 1.043713 seconds
% 0.13/0.54 % Total memory used: 26.802 MB
% 0.13/0.54 % Net memory used: 26.350 MB
%------------------------------------------------------------------------------