%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG008-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 50 ( 50 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : add(additive_identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : add(additive_inverse(X),X) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : additive_inverse(additive_inverse(X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] : add(add(X,Y),Z) = add(X,add(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
! [X] : multiply(X,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
multiply(b,a) != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0] : add(additive_inverse(X0),X0) = additive_identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1,X2] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0,X1] : multiply(X0,additive_inverse(X1)) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
! [X0,X1] : multiply(additive_inverse(X0),X1) = additive_inverse(multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
! [X0,X1,X2] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
! [X0] : multiply(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f33,plain,
multiply(a,b) = c,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
multiply(b,a) != c,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f37,plain,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
inference(backward_demodulation,[status(thm)],[f30,f19]) ).
fof(f595,plain,
! [X0] : additive_inverse(X0) = additive_inverse(multiply(additive_inverse(X0),X0)),
inference(paramodulation,[status(thm)],[f32,f27]) ).
fof(f612,plain,
! [X0] : additive_inverse(X0) = additive_inverse(additive_inverse(multiply(X0,X0))),
inference(forward_demodulation,[status(thm)],[f28,f595]) ).
fof(f613,plain,
! [X0] : additive_inverse(X0) = multiply(X0,X0),
inference(forward_demodulation,[status(thm)],[f23,f612]) ).
fof(f616,plain,
! [X0] : add(X0,X0) = additive_identity,
inference(backward_demodulation,[status(thm)],[f620,f37]) ).
fof(f620,plain,
! [X0] : additive_inverse(X0) = X0,
inference(forward_demodulation,[status(thm)],[f32,f613]) ).
fof(f727,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f32,f20]) ).
fof(f761,plain,
! [X0,X1] : multiply(X0,add(X1,X0)) = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f30,f727]) ).
fof(f988,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = add(X0,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f32,f21]) ).
fof(f1006,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = add(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f32,f21]) ).
fof(f1054,plain,
! [X0,X1] : multiply(add(X0,X1),X1) = add(X1,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f30,f1006]) ).
fof(f1123,plain,
! [X0,X1] : add(additive_identity,X0) = add(X1,add(X1,X0)),
inference(paramodulation,[status(thm)],[f616,f29]) ).
fof(f1136,plain,
! [X0,X1] : X0 = add(X1,add(X1,X0)),
inference(forward_demodulation,[status(thm)],[f18,f1123]) ).
fof(f1381,plain,
! [X0,X1] : X0 = add(X1,add(X0,X1)),
inference(paramodulation,[status(thm)],[f30,f1136]) ).
fof(f1432,plain,
! [X0,X1] : multiply(add(X0,X1),X0) = add(add(X0,X1),multiply(add(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f1381,f761]) ).
fof(f1447,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = add(add(X0,X1),multiply(add(X0,X1),X1)),
inference(forward_demodulation,[status(thm)],[f988,f1432]) ).
fof(f1448,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = add(X0,add(X1,multiply(add(X0,X1),X1))),
inference(forward_demodulation,[status(thm)],[f29,f1447]) ).
fof(f1449,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = add(X0,add(X1,add(X1,multiply(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f1054,f1448]) ).
fof(f1450,plain,
! [X0,X1] : add(X0,multiply(X1,X0)) = add(X0,multiply(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1136,f1449]) ).
fof(f1457,plain,
! [X0,X1] : multiply(X0,X1) = add(X1,multiply(add(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f1381,f988]) ).
fof(f1488,plain,
! [X0,X1] : multiply(X0,X1) = add(X1,multiply(X1,add(X0,X1))),
inference(forward_demodulation,[status(thm)],[f1450,f1457]) ).
fof(f1489,plain,
! [X0,X1] : multiply(X0,X1) = add(X1,add(X1,multiply(X1,X0))),
inference(forward_demodulation,[status(thm)],[f761,f1488]) ).
fof(f1494,plain,
multiply(a,b) != c,
inference(backward_demodulation,[status(thm)],[f1508,f34]) ).
fof(f1508,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f1136,f1489]) ).
fof(f1550,plain,
c != c,
inference(forward_demodulation,[status(thm)],[f33,f1494]) ).
fof(f1551,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1550]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:10:25 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.048387 seconds
% 0.14/0.41 % CPU time: 0.198225 seconds
% 0.14/0.41 % Total memory used: 7.232 MB
% 0.14/0.41 % Net memory used: 7.056 MB
%------------------------------------------------------------------------------