%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG015-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 0.08s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 45 ( 45 unt; 7 def)
% Number of atoms : 45 ( 44 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 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : add(additive_identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : add(additive_inverse(X),X) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : additive_inverse(additive_inverse(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] : add(X,add(Y,Z)) = add(add(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
multiply(x,add(y,additive_inverse(z))) != add(multiply(x,y),additive_inverse(multiply(x,z))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
inference(cnf_transformation,[status(thm)],[f5]) ).
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(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(x,add(y,additive_inverse(z))) != add(multiply(x,y),additive_inverse(multiply(x,z))),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF2_fnc = additive_inverse(z),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f34,definition,
sF1_fnc = add(y,sF2_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f35,definition,
sF0_fnc = multiply(x,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f36,definition,
sF4_fnc = multiply(x,y),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f37,definition,
sF6_fnc = multiply(x,z),
introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition]) ).
fof(f38,definition,
sF5_fnc = additive_inverse(sF6_fnc),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f39,definition,
sF3_fnc = add(sF4_fnc,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f40,plain,
sF0_fnc != sF3_fnc,
inference(definition_folding,[],[f32,f39,f38,f37,f36,f35,f34,f33]) ).
fof(f42,plain,
additive_inverse(sF5_fnc) = sF6_fnc,
inference(paramodulation,[status(thm)],[f38,f23]) ).
fof(f43,plain,
additive_inverse(sF2_fnc) = z,
inference(paramodulation,[status(thm)],[f33,f23]) ).
fof(f46,plain,
add(z,sF2_fnc) = additive_identity,
inference(paramodulation,[status(thm)],[f43,f21]) ).
fof(f47,plain,
add(sF6_fnc,sF5_fnc) = additive_identity,
inference(paramodulation,[status(thm)],[f42,f21]) ).
fof(f49,plain,
add(sF5_fnc,sF6_fnc) = additive_identity,
inference(paramodulation,[status(thm)],[f38,f21]) ).
fof(f74,plain,
! [X0] : multiply(x,add(z,X0)) = add(sF6_fnc,multiply(x,X0)),
inference(paramodulation,[status(thm)],[f37,f24]) ).
fof(f150,plain,
! [X0] : add(sF5_fnc,add(sF6_fnc,X0)) = add(additive_identity,X0),
inference(paramodulation,[status(thm)],[f49,f27]) ).
fof(f151,plain,
! [X0] : add(sF6_fnc,add(sF5_fnc,X0)) = add(additive_identity,X0),
inference(paramodulation,[status(thm)],[f47,f27]) ).
fof(f152,plain,
! [X0] : add(z,add(sF2_fnc,X0)) = add(additive_identity,X0),
inference(paramodulation,[status(thm)],[f46,f27]) ).
fof(f167,plain,
! [X0] : add(sF5_fnc,add(sF6_fnc,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f17,f150]) ).
fof(f168,plain,
! [X0] : add(sF6_fnc,add(sF5_fnc,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f17,f151]) ).
fof(f169,plain,
! [X0] : add(z,add(sF2_fnc,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f17,f152]) ).
fof(f236,plain,
! [X0] : add(sF6_fnc,add(X0,sF5_fnc)) = X0,
inference(paramodulation,[status(thm)],[f26,f168]) ).
fof(f246,plain,
! [X0] : add(z,add(X0,sF2_fnc)) = X0,
inference(paramodulation,[status(thm)],[f26,f169]) ).
fof(f374,plain,
add(sF6_fnc,sF3_fnc) = sF4_fnc,
inference(paramodulation,[status(thm)],[f39,f236]) ).
fof(f388,plain,
add(sF5_fnc,sF4_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f374,f167]) ).
fof(f489,plain,
add(z,sF1_fnc) = y,
inference(paramodulation,[status(thm)],[f34,f246]) ).
fof(f501,plain,
multiply(x,y) = add(sF6_fnc,multiply(x,sF1_fnc)),
inference(paramodulation,[status(thm)],[f489,f74]) ).
fof(f505,plain,
sF4_fnc = add(sF6_fnc,multiply(x,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f36,f501]) ).
fof(f506,plain,
sF4_fnc = add(sF6_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f35,f505]) ).
fof(f510,plain,
add(sF5_fnc,sF4_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f506,f167]) ).
fof(f517,plain,
sF3_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f388,f510]) ).
fof(f518,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f517,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG015-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n003.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 04:12:15 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.08/0.36 % Refutation found
% 0.08/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.30/1.59 % Elapsed time: 1.019449 seconds
% 1.30/1.59 % CPU time: 0.055633 seconds
% 1.30/1.59 % Total memory used: 2.354 MB
% 1.30/1.59 % Net memory used: 2.301 MB
%------------------------------------------------------------------------------