%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG017-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 02:04:41 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.48s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 61 ( 61 unt; 8 def)
% Number of atoms : 61 ( 60 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 : 15 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : add(additive_identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : add(X,additive_identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : multiply(additive_identity,X) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : add(additive_inverse(X),X) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : add(X,additive_inverse(X)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : additive_inverse(additive_inverse(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] : multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] : add(X,add(Y,Z)) = add(add(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
multiply(additive_inverse(x),add(y,z)) != add(additive_inverse(multiply(x,y)),additive_inverse(multiply(x,z))),
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(X0,additive_identity) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] : multiply(additive_identity,X0) = additive_identity,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
! [X0,X1,X2] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f26,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(add(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f32,plain,
multiply(additive_inverse(x),add(y,z)) != add(additive_inverse(multiply(x,y)),additive_inverse(multiply(x,z))),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF1_fnc = additive_inverse(x),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f34,definition,
sF2_fnc = add(y,z),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f35,definition,
sF0_fnc = multiply(sF1_fnc,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f36,definition,
sF5_fnc = multiply(x,y),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f37,definition,
sF4_fnc = additive_inverse(sF5_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f38,definition,
sF7_fnc = multiply(x,z),
introduced(definition,[new_symbols(definition,[sF7_fnc])],[function_definition]) ).
fof(f39,definition,
sF6_fnc = additive_inverse(sF7_fnc),
introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition]) ).
fof(f40,definition,
sF3_fnc = add(sF4_fnc,sF6_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f41,plain,
sF0_fnc != sF3_fnc,
inference(definition_folding,[],[f32,f40,f39,f38,f37,f36,f35,f34,f33]) ).
fof(f44,plain,
additive_inverse(sF4_fnc) = sF5_fnc,
inference(paramodulation,[status(thm)],[f37,f23]) ).
fof(f53,plain,
! [X0,X1,X2] : add(X0,add(X1,X2)) = add(X2,add(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f27]) ).
fof(f57,plain,
! [X0] : add(y,add(z,X0)) = add(sF2_fnc,X0),
inference(paramodulation,[status(thm)],[f34,f27]) ).
fof(f73,plain,
! [X0] : multiply(x,add(z,X0)) = add(sF7_fnc,multiply(x,X0)),
inference(paramodulation,[status(thm)],[f38,f24]) ).
fof(f93,plain,
! [X0] : multiply(add(sF1_fnc,X0),sF2_fnc) = add(sF0_fnc,multiply(X0,sF2_fnc)),
inference(paramodulation,[status(thm)],[f35,f25]) ).
fof(f158,plain,
add(sF6_fnc,sF7_fnc) = additive_identity,
inference(paramodulation,[status(thm)],[f39,f21]) ).
fof(f160,plain,
add(sF1_fnc,x) = additive_identity,
inference(paramodulation,[status(thm)],[f33,f21]) ).
fof(f162,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = add(additive_identity,X1),
inference(paramodulation,[status(thm)],[f21,f27]) ).
fof(f165,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f17,f162]) ).
fof(f338,plain,
! [X0] : add(X0,additive_identity) = add(sF7_fnc,add(X0,sF6_fnc)),
inference(paramodulation,[status(thm)],[f158,f53]) ).
fof(f342,plain,
! [X0,X1] : add(X0,additive_identity) = add(X1,add(X0,additive_inverse(X1))),
inference(paramodulation,[status(thm)],[f21,f53]) ).
fof(f409,plain,
! [X0] : X0 = add(sF7_fnc,add(X0,sF6_fnc)),
inference(forward_demodulation,[status(thm)],[f18,f338]) ).
fof(f413,plain,
! [X0,X1] : X0 = add(X1,add(X0,additive_inverse(X1))),
inference(forward_demodulation,[status(thm)],[f18,f342]) ).
fof(f474,plain,
add(y,additive_identity) = add(sF2_fnc,additive_inverse(z)),
inference(paramodulation,[status(thm)],[f22,f57]) ).
fof(f483,plain,
y = add(sF2_fnc,additive_inverse(z)),
inference(forward_demodulation,[status(thm)],[f18,f474]) ).
fof(f675,plain,
add(additive_inverse(sF4_fnc),sF3_fnc) = sF6_fnc,
inference(paramodulation,[status(thm)],[f40,f165]) ).
fof(f706,plain,
add(sF5_fnc,sF3_fnc) = sF6_fnc,
inference(forward_demodulation,[status(thm)],[f44,f675]) ).
fof(f712,plain,
add(sF3_fnc,sF5_fnc) = sF6_fnc,
inference(paramodulation,[status(thm)],[f26,f706]) ).
fof(f723,plain,
add(additive_inverse(sF3_fnc),sF6_fnc) = sF5_fnc,
inference(paramodulation,[status(thm)],[f712,f165]) ).
fof(f1499,plain,
sF2_fnc = add(z,y),
inference(paramodulation,[status(thm)],[f483,f413]) ).
fof(f1510,plain,
multiply(x,sF2_fnc) = add(sF7_fnc,multiply(x,y)),
inference(paramodulation,[status(thm)],[f1499,f73]) ).
fof(f1521,plain,
multiply(x,sF2_fnc) = add(sF7_fnc,sF5_fnc),
inference(forward_demodulation,[status(thm)],[f36,f1510]) ).
fof(f2077,plain,
additive_inverse(sF3_fnc) = add(sF7_fnc,sF5_fnc),
inference(paramodulation,[status(thm)],[f723,f409]) ).
fof(f2830,plain,
multiply(additive_identity,sF2_fnc) = add(sF0_fnc,multiply(x,sF2_fnc)),
inference(paramodulation,[status(thm)],[f160,f93]) ).
fof(f2858,plain,
additive_identity = add(sF0_fnc,multiply(x,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f19,f2830]) ).
fof(f4527,plain,
multiply(x,sF2_fnc) = additive_inverse(sF3_fnc),
inference(forward_demodulation,[status(thm)],[f2077,f1521]) ).
fof(f5155,plain,
additive_identity = add(sF0_fnc,additive_inverse(sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f4527,f2858]) ).
fof(f5156,plain,
sF0_fnc = add(sF3_fnc,additive_identity),
inference(paramodulation,[status(thm)],[f5155,f413]) ).
fof(f5167,plain,
sF0_fnc = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f18,f5156]) ).
fof(f5168,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5167,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG017-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n002.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 04:13:16 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.48 % Refutation found
% 0.12/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.50 % Elapsed time: 0.135635 seconds
% 0.12/0.50 % CPU time: 0.949206 seconds
% 0.12/0.50 % Total memory used: 30.379 MB
% 0.12/0.50 % Net memory used: 29.859 MB
%------------------------------------------------------------------------------