%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG004-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:04:37 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 75 ( 36 unt; 0 def)
% Number of atoms : 154 ( 28 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 160 ( 81 ~; 79 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 175 ( 175 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( sum(X,V,W)
| ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(X,V3,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( sum(V1,V2,V4)
| ~ product(V3,X,V4)
| ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,Z,W] :
( Y = W
| ~ sum(X,W,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y,Z,W] :
( X = W
| ~ sum(W,Y,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f24,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f26,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f28,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f29,plain,
! [X,V,W] :
( sum(X,V,W)
| ! [U,Z] :
( ~ sum(U,Z,W)
| ! [Y] :
( ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X0,X4,X5)
| ~ sum(X2,X3,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f33,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(X,V3,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f39,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X0,X5,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [V1,V2,V4] :
( sum(V1,V2,V4)
| ! [X,V3] :
( ~ product(V3,X,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( sum(X2,X4,X6)
| ~ product(X5,X1,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f50,plain,
! [Y,W] :
( Y = W
| ! [X,Z] :
( ~ sum(X,W,Z)
| ~ sum(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
! [X,W] :
( X = W
| ! [Y,Z] :
( ~ sum(W,Y,Z)
| ~ sum(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
c != d,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f61,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f33,f26]) ).
fof(f63,plain,
! [X0,X1] :
( additive_identity = X1
| ~ sum(additive_inverse(X0),X0,X1) ),
inference(resolution,[status(thm)],[f47,f27]) ).
fof(f67,plain,
! [X0,X1,X2] :
( add(X1,X0) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f61]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( sum(additive_inverse(X0),X2,X3)
| ~ sum(additive_identity,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f30,f27]) ).
fof(f101,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(resolution,[status(thm)],[f63,f61]) ).
fof(f124,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f67,f26]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( sum(d,X1,X3)
| ~ product(additive_inverse(a),X2,X3)
| ~ sum(additive_inverse(b),X0,X2)
| ~ product(additive_inverse(a),X0,X1) ),
inference(resolution,[status(thm)],[f39,f55]) ).
fof(f184,plain,
! [X0,X1,X2] :
( sum(d,multiply(additive_inverse(a),X0),X2)
| ~ product(additive_inverse(a),X1,X2)
| ~ sum(additive_inverse(b),X0,X1) ),
inference(resolution,[status(thm)],[f158,f25]) ).
fof(f191,plain,
! [X0,X1] :
( additive_inverse(X0) = X1
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f51,f28]) ).
fof(f192,plain,
! [X0,X1] :
( additive_identity = X1
| ~ sum(X0,X1,X0) ),
inference(resolution,[status(thm)],[f51,f24]) ).
fof(f193,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ sum(X0,X1,add(X2,X0)) ),
inference(resolution,[status(thm)],[f51,f61]) ).
fof(f194,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ sum(X0,X1,add(X0,X2)) ),
inference(resolution,[status(thm)],[f51,f26]) ).
fof(f232,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(X0,additive_inverse(X1),additive_identity) ),
inference(resolution,[status(thm)],[f53,f28]) ).
fof(f242,plain,
! [X0,X1,X2,X3] :
( sum(c,X1,X3)
| ~ product(X2,b,X3)
| ~ sum(a,X0,X2)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[f43,f54]) ).
fof(f403,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X2),add(X0,X2),X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f74,f61]) ).
fof(f468,plain,
! [X0,X1,X2] :
( sum(c,multiply(X0,b),X2)
| ~ product(X1,b,X2)
| ~ sum(a,X0,X1) ),
inference(resolution,[status(thm)],[f242,f25]) ).
fof(f655,plain,
! [X0] :
( sum(d,multiply(additive_inverse(a),b),X0)
| ~ product(additive_inverse(a),additive_identity,X0) ),
inference(resolution,[status(thm)],[f184,f27]) ).
fof(f657,plain,
! [X0] :
( sum(d,multiply(additive_inverse(a),additive_identity),X0)
| ~ product(additive_inverse(a),additive_inverse(b),X0) ),
inference(resolution,[status(thm)],[f184,f24]) ).
fof(f760,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f403,f23]) ).
fof(f905,plain,
! [X0,X1] : X0 = add(add(X0,additive_inverse(X1)),X1),
inference(resolution,[status(thm)],[f760,f193]) ).
fof(f933,plain,
! [X0,X1] : X0 = add(X1,add(X0,additive_inverse(X1))),
inference(forward_demodulation,[status(thm)],[f124,f905]) ).
fof(f1033,plain,
! [X0,X1,X2] :
( add(X2,additive_inverse(X0)) = X1
| ~ sum(X0,X1,X2) ),
inference(paramodulation,[status(thm)],[f933,f194]) ).
fof(f1756,plain,
! [X0] :
( sum(c,multiply(additive_inverse(a),b),X0)
| ~ product(additive_identity,b,X0) ),
inference(resolution,[status(thm)],[f468,f28]) ).
fof(f1757,plain,
! [X0] :
( sum(c,multiply(additive_identity,b),X0)
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f468,f24]) ).
fof(f1782,plain,
sum(c,multiply(additive_identity,b),c),
inference(resolution,[status(thm)],[f1757,f54]) ).
fof(f1861,plain,
additive_identity = multiply(additive_identity,b),
inference(resolution,[status(thm)],[f1782,f192]) ).
fof(f1878,plain,
product(additive_identity,b,additive_identity),
inference(paramodulation,[status(thm)],[f1861,f25]) ).
fof(f4560,plain,
sum(d,multiply(additive_inverse(a),additive_identity),d),
inference(resolution,[status(thm)],[f657,f55]) ).
fof(f4640,plain,
add(d,additive_inverse(d)) = multiply(additive_inverse(a),additive_identity),
inference(resolution,[status(thm)],[f4560,f1033]) ).
fof(f4663,plain,
additive_identity = multiply(additive_inverse(a),additive_identity),
inference(forward_demodulation,[status(thm)],[f101,f4640]) ).
fof(f4680,plain,
product(additive_inverse(a),additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f4663,f25]) ).
fof(f4687,plain,
sum(d,multiply(additive_inverse(a),b),additive_identity),
inference(resolution,[status(thm)],[f4680,f655]) ).
fof(f4737,plain,
additive_inverse(d) = multiply(additive_inverse(a),b),
inference(resolution,[status(thm)],[f4687,f191]) ).
fof(f5058,plain,
! [X0] :
( sum(c,additive_inverse(d),X0)
| ~ product(additive_identity,b,X0) ),
inference(forward_demodulation,[status(thm)],[f4737,f1756]) ).
fof(f5059,plain,
sum(c,additive_inverse(d),additive_identity),
inference(resolution,[status(thm)],[f5058,f1878]) ).
fof(f5084,plain,
d = c,
inference(resolution,[status(thm)],[f5059,f232]) ).
fof(f5116,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5084,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG004-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Mon Sep 21 04:09:51 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 0.15/0.42 % Refutation found
% 0.15/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.44 % Elapsed time: 0.133240 seconds
% 0.15/0.44 % CPU time: 0.882264 seconds
% 0.15/0.44 % Total memory used: 55.598 MB
% 0.15/0.44 % Net memory used: 53.372 MB
%------------------------------------------------------------------------------