%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG005-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 02:04:38 PM UTC 2026
% Result : Unsatisfiable 3.02s 0.84s
% Output : CNFRefutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 72 ( 33 unt; 0 def)
% Number of atoms : 155 ( 21 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 168 ( 85 ~; 83 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 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 : 181 ( 181 !; 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(f8,axiom,
! [X,Y,U,Z,V,W] :
( sum(U,Z,W)
| ~ sum(X,V,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(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(f15,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V3,X,V4)
| ~ sum(V1,V2,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(f17,axiom,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
product(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
product(additive_inverse(a),b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,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(f28,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)],[f27]) ).
fof(f29,plain,
! [U,Z,W] :
( sum(U,Z,W)
| ! [X,V] :
( ~ sum(X,V,W)
| ! [Y] :
( ~ sum(Y,Z,V)
| ~ sum(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f30,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f40,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(f41,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)],[f40]) ).
fof(f42,plain,
! [X,V3,V4] :
( product(V3,X,V4)
| ! [V1,V2] :
( ~ sum(V1,V2,V4)
| ! [Y,Z] :
( ~ sum(Y,Z,V3)
| ~ product(Z,X,V2)
| ~ product(Y,X,V1) ) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f43,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
product(a,b,d),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f49,plain,
product(additive_inverse(a),b,c),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f50,plain,
~ sum(c,d,additive_identity),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f53,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f45,f21]) ).
fof(f67,plain,
! [X0,X1,X2] :
( add(X0,X1) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f24,f45]) ).
fof(f68,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f24,f31]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( sum(additive_identity,X1,X3)
| ~ sum(additive_inverse(X0),X2,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f30]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( sum(X0,X2,X3)
| ~ sum(additive_identity,X1,X3)
| ~ sum(additive_inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[f26,f28]) ).
fof(f130,plain,
! [X0,X1] :
( sum(additive_identity,X0,X1)
| ~ sum(additive_inverse(additive_inverse(X0)),additive_identity,X1) ),
inference(resolution,[status(thm)],[f90,f25]) ).
fof(f135,plain,
! [X0] : sum(additive_identity,X0,additive_inverse(additive_inverse(X0))),
inference(resolution,[status(thm)],[f130,f22]) ).
fof(f165,plain,
! [X0,X1,X2] :
( sum(X2,add(additive_inverse(X2),X0),X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f98,f24]) ).
fof(f190,plain,
! [X0,X1,X2,X3] :
( sum(d,X1,X3)
| ~ product(X2,b,X3)
| ~ sum(a,X0,X2)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[f41,f48]) ).
fof(f216,plain,
! [X0,X1,X2] :
( add(X1,X0) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f68,f45]) ).
fof(f285,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f67,f68]) ).
fof(f366,plain,
! [X0,X1,X2,X3] :
( product(X2,b,X3)
| ~ sum(c,X1,X3)
| ~ sum(additive_inverse(a),X0,X2)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[f43,f49]) ).
fof(f370,plain,
! [X0] :
( d = X0
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f47,f48]) ).
fof(f371,plain,
! [X0,X1,X2] :
( multiply(X0,X1) = X2
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f23]) ).
fof(f379,plain,
d = multiply(a,b),
inference(resolution,[status(thm)],[f370,f23]) ).
fof(f447,plain,
! [X0] : X0 = additive_inverse(additive_inverse(X0)),
inference(resolution,[status(thm)],[f135,f53]) ).
fof(f653,plain,
! [X0,X1,X2] :
( sum(d,multiply(X0,b),X2)
| ~ product(X1,b,X2)
| ~ sum(a,X0,X1) ),
inference(resolution,[status(thm)],[f190,f23]) ).
fof(f656,plain,
! [X0,X1,X2] :
( product(X1,b,X2)
| ~ sum(c,multiply(X0,b),X2)
| ~ sum(additive_inverse(a),X0,X1) ),
inference(resolution,[status(thm)],[f366,f23]) ).
fof(f657,plain,
! [X0] :
( product(additive_identity,b,X0)
| ~ sum(c,multiply(a,b),X0) ),
inference(resolution,[status(thm)],[f656,f25]) ).
fof(f662,plain,
! [X0] :
( product(additive_identity,b,X0)
| ~ sum(c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f379,f657]) ).
fof(f665,plain,
product(additive_identity,b,add(d,c)),
inference(resolution,[status(thm)],[f662,f68]) ).
fof(f811,plain,
multiply(additive_identity,b) = add(d,c),
inference(resolution,[status(thm)],[f665,f371]) ).
fof(f821,plain,
! [X0,X1] : sum(X0,add(additive_inverse(X0),X1),X1),
inference(resolution,[status(thm)],[f165,f21]) ).
fof(f851,plain,
sum(c,d,multiply(additive_identity,b)),
inference(paramodulation,[status(thm)],[f811,f68]) ).
fof(f1179,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ sum(X0,add(additive_inverse(X0),X1),X2) ),
inference(resolution,[status(thm)],[f821,f45]) ).
fof(f1221,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ sum(additive_inverse(X0),add(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f447,f1179]) ).
fof(f1514,plain,
! [X0] :
( sum(d,multiply(additive_identity,b),X0)
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f653,f22]) ).
fof(f1809,plain,
sum(d,multiply(additive_identity,b),d),
inference(resolution,[status(thm)],[f1514,f48]) ).
fof(f1820,plain,
add(multiply(additive_identity,b),d) = d,
inference(resolution,[status(thm)],[f1809,f216]) ).
fof(f1836,plain,
add(d,multiply(additive_identity,b)) = d,
inference(forward_demodulation,[status(thm)],[f285,f1820]) ).
fof(f1871,plain,
! [X0] :
( multiply(additive_identity,b) = X0
| ~ sum(additive_inverse(d),d,X0) ),
inference(paramodulation,[status(thm)],[f1836,f1221]) ).
fof(f2288,plain,
multiply(additive_identity,b) = additive_identity,
inference(resolution,[status(thm)],[f1871,f25]) ).
fof(f2327,plain,
sum(c,d,additive_identity),
inference(backward_demodulation,[status(thm)],[f2288,f851]) ).
fof(f2343,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2327,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 04:09:48 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 3.02/0.84 % Refutation found
% 3.02/0.84 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.02/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.02/0.88 % Elapsed time: 0.495709 seconds
% 3.02/0.88 % CPU time: 3.589053 seconds
% 3.02/0.88 % Total memory used: 65.120 MB
% 3.02/0.88 % Net memory used: 60.688 MB
%------------------------------------------------------------------------------