%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG012-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 02:04:40 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.55s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 53 ( 53 unt; 4 def)
% Number of atoms : 53 ( 52 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 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(f4,axiom,
! [X] : multiply(X,additive_identity) = 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(a),additive_inverse(b)) != multiply(a,b),
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(f20,plain,
! [X0] : multiply(X0,additive_identity) = additive_identity,
inference(cnf_transformation,[status(thm)],[f4]) ).
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(a),additive_inverse(b)) != multiply(a,b),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF1_fnc = additive_inverse(a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f34,definition,
sF2_fnc = additive_inverse(b),
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,
sF3_fnc = multiply(a,b),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f37,plain,
sF0_fnc != sF3_fnc,
inference(definition_folding,[],[f32,f36,f35,f34,f33]) ).
fof(f39,plain,
add(sF1_fnc,a) = additive_identity,
inference(paramodulation,[status(thm)],[f33,f21]) ).
fof(f41,plain,
additive_inverse(sF2_fnc) = b,
inference(paramodulation,[status(thm)],[f34,f23]) ).
fof(f45,plain,
add(b,sF2_fnc) = additive_identity,
inference(paramodulation,[status(thm)],[f41,f21]) ).
fof(f63,plain,
additive_identity = additive_inverse(additive_identity),
inference(paramodulation,[status(thm)],[f22,f17]) ).
fof(f125,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = add(additive_identity,X1),
inference(paramodulation,[status(thm)],[f21,f27]) ).
fof(f127,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(paramodulation,[status(thm)],[f22,f27]) ).
fof(f140,plain,
! [X0,X1] : add(additive_inverse(X0),add(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f17,f125]) ).
fof(f141,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f17,f127]) ).
fof(f165,plain,
! [X0] : multiply(a,add(b,X0)) = add(sF3_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f36,f24]) ).
fof(f200,plain,
! [X0] : multiply(add(sF1_fnc,X0),sF2_fnc) = add(sF0_fnc,multiply(X0,sF2_fnc)),
inference(paramodulation,[status(thm)],[f35,f25]) ).
fof(f373,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f26,f140]) ).
fof(f395,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(paramodulation,[status(thm)],[f26,f141]) ).
fof(f544,plain,
! [X0,X1] : add(additive_inverse(add(X0,X1)),X1) = additive_inverse(X0),
inference(paramodulation,[status(thm)],[f140,f373]) ).
fof(f1191,plain,
multiply(a,additive_identity) = add(sF3_fnc,multiply(a,sF2_fnc)),
inference(paramodulation,[status(thm)],[f45,f165]) ).
fof(f1208,plain,
additive_identity = add(sF3_fnc,multiply(a,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f20,f1191]) ).
fof(f2988,plain,
add(additive_inverse(additive_identity),multiply(a,sF2_fnc)) = additive_inverse(sF3_fnc),
inference(paramodulation,[status(thm)],[f1208,f544]) ).
fof(f2998,plain,
add(additive_identity,multiply(a,sF2_fnc)) = additive_inverse(sF3_fnc),
inference(forward_demodulation,[status(thm)],[f63,f2988]) ).
fof(f2999,plain,
multiply(a,sF2_fnc) = additive_inverse(sF3_fnc),
inference(forward_demodulation,[status(thm)],[f17,f2998]) ).
fof(f4242,plain,
multiply(additive_identity,sF2_fnc) = add(sF0_fnc,multiply(a,sF2_fnc)),
inference(paramodulation,[status(thm)],[f39,f200]) ).
fof(f4273,plain,
additive_identity = add(sF0_fnc,multiply(a,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f19,f4242]) ).
fof(f4274,plain,
additive_identity = add(sF0_fnc,additive_inverse(sF3_fnc)),
inference(forward_demodulation,[status(thm)],[f2999,f4273]) ).
fof(f4291,plain,
add(sF3_fnc,additive_identity) = sF0_fnc,
inference(paramodulation,[status(thm)],[f4274,f395]) ).
fof(f4303,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f18,f4291]) ).
fof(f4304,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4303,f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG012-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:10:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.55 % Refutation found
% 0.13/0.55 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.58 % Elapsed time: 0.200054 seconds
% 0.13/0.58 % CPU time: 1.295947 seconds
% 0.13/0.58 % Total memory used: 39.358 MB
% 0.13/0.58 % Net memory used: 38.812 MB
%------------------------------------------------------------------------------