%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 4.32s 0.97s
% Output : CNFRefutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 84 ( 48 unt; 0 def)
% Number of atoms : 158 ( 29 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 150 ( 76 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 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 : 168 ( 168 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : sum(X,additive_identity,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_inverse(X),X,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : sum(X,additive_inverse(X),additive_identity),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
product(additive_inverse(a),additive_inverse(b),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
c != d,
file('/export/starexec/sandbox/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(f31,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f36,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(f37,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)],[f36]) ).
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(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(f48,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f49,plain,
product(additive_inverse(a),additive_inverse(b),d),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f50,plain,
c != d,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f31,f24]) ).
fof(f57,plain,
! [X0,X1] :
( additive_identity = X1
| ~ sum(additive_inverse(X0),X0,X1) ),
inference(resolution,[status(thm)],[f45,f25]) ).
fof(f58,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f45,f21]) ).
fof(f60,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f45,f22]) ).
fof(f61,plain,
! [X0,X1,X2] :
( add(X1,X0) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f45,f55]) ).
fof(f62,plain,
! [X0,X1,X2] :
( add(X0,X1) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f45,f24]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( sum(additive_inverse(X0),X2,X3)
| ~ sum(additive_identity,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f28,f25]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( sum(X0,X2,X3)
| ~ sum(additive_identity,X1,X3)
| ~ sum(additive_inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( sum(c,X1,X3)
| ~ product(a,X2,X3)
| ~ sum(b,X0,X2)
| ~ product(a,X0,X1) ),
inference(resolution,[status(thm)],[f37,f48]) ).
fof(f100,plain,
! [X0,X1,X2] :
( sum(c,multiply(a,X0),X2)
| ~ product(a,X1,X2)
| ~ sum(b,X0,X1) ),
inference(resolution,[status(thm)],[f82,f23]) ).
fof(f106,plain,
! [X0] : X0 = add(X0,additive_identity),
inference(resolution,[status(thm)],[f58,f55]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( sum(d,X1,X3)
| ~ product(X2,additive_inverse(b),X3)
| ~ sum(additive_inverse(a),X0,X2)
| ~ product(X0,additive_inverse(b),X1) ),
inference(resolution,[status(thm)],[f41,f49]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(multiply(X3,X1),X2,X5)
| ~ product(X4,X1,X5)
| ~ sum(X3,X0,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f41,f23]) ).
fof(f126,plain,
! [X0] : additive_identity = add(X0,additive_inverse(X0)),
inference(resolution,[status(thm)],[f57,f55]) ).
fof(f127,plain,
! [X0] : additive_identity = add(additive_inverse(X0),X0),
inference(resolution,[status(thm)],[f57,f24]) ).
fof(f145,plain,
! [X0,X1,X2] :
( sum(d,multiply(X0,additive_inverse(b)),X2)
| ~ product(X1,additive_inverse(b),X2)
| ~ sum(additive_inverse(a),X0,X1) ),
inference(resolution,[status(thm)],[f112,f23]) ).
fof(f171,plain,
! [X0,X1] :
( sum(additive_inverse(additive_inverse(X0)),additive_identity,X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f63,f25]) ).
fof(f175,plain,
! [X0,X1,X2] :
( sum(additive_inverse(X2),add(X0,X2),X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f63,f55]) ).
fof(f186,plain,
! [X0,X1,X2] :
( sum(X2,add(X0,additive_inverse(X2)),X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[status(thm)],[f65,f55]) ).
fof(f228,plain,
! [X0] :
( sum(c,multiply(a,additive_inverse(b)),X0)
| ~ product(a,additive_identity,X0) ),
inference(resolution,[status(thm)],[f100,f26]) ).
fof(f229,plain,
! [X0] :
( sum(c,multiply(a,additive_identity),X0)
| ~ product(a,b,X0) ),
inference(resolution,[status(thm)],[f100,f22]) ).
fof(f292,plain,
! [X0] :
( sum(d,multiply(additive_identity,additive_inverse(b)),X0)
| ~ product(additive_inverse(a),additive_inverse(b),X0) ),
inference(resolution,[status(thm)],[f145,f22]) ).
fof(f337,plain,
! [X0,X1,X2] :
( sum(multiply(X0,additive_inverse(b)),d,X2)
| ~ product(X1,additive_inverse(b),X2)
| ~ sum(X0,additive_inverse(a),X1) ),
inference(resolution,[status(thm)],[f115,f49]) ).
fof(f430,plain,
! [X0] : sum(additive_inverse(additive_inverse(X0)),additive_identity,X0),
inference(resolution,[status(thm)],[f171,f21]) ).
fof(f442,plain,
! [X0,X1] : sum(additive_inverse(X0),add(X1,X0),X1),
inference(resolution,[status(thm)],[f175,f21]) ).
fof(f513,plain,
! [X0] : additive_inverse(additive_inverse(X0)) = X0,
inference(resolution,[status(thm)],[f430,f60]) ).
fof(f565,plain,
! [X0,X1] : sum(X0,add(X1,additive_inverse(X0)),X1),
inference(resolution,[status(thm)],[f186,f21]) ).
fof(f599,plain,
! [X0] :
( sum(multiply(additive_inverse(additive_inverse(a)),additive_inverse(b)),d,X0)
| ~ product(additive_identity,additive_inverse(b),X0) ),
inference(resolution,[status(thm)],[f337,f25]) ).
fof(f604,plain,
! [X0] :
( sum(multiply(a,additive_inverse(b)),d,X0)
| ~ product(additive_identity,additive_inverse(b),X0) ),
inference(forward_demodulation,[status(thm)],[f513,f599]) ).
fof(f755,plain,
! [X0,X1] : add(add(X0,X1),additive_inverse(X1)) = X0,
inference(resolution,[status(thm)],[f442,f61]) ).
fof(f762,plain,
! [X0,X1] : add(additive_inverse(X0),add(X1,X0)) = X1,
inference(resolution,[status(thm)],[f442,f62]) ).
fof(f843,plain,
sum(c,multiply(a,additive_identity),c),
inference(resolution,[status(thm)],[f229,f48]) ).
fof(f850,plain,
add(multiply(a,additive_identity),c) = c,
inference(resolution,[status(thm)],[f843,f61]) ).
fof(f1064,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(resolution,[status(thm)],[f565,f62]) ).
fof(f1334,plain,
sum(d,multiply(additive_identity,additive_inverse(b)),d),
inference(resolution,[status(thm)],[f292,f49]) ).
fof(f1403,plain,
add(c,additive_inverse(c)) = multiply(a,additive_identity),
inference(paramodulation,[status(thm)],[f850,f755]) ).
fof(f1432,plain,
additive_identity = multiply(a,additive_identity),
inference(forward_demodulation,[status(thm)],[f126,f1403]) ).
fof(f1464,plain,
product(a,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f1432,f23]) ).
fof(f1472,plain,
sum(c,multiply(a,additive_inverse(b)),additive_identity),
inference(resolution,[status(thm)],[f1464,f228]) ).
fof(f2681,plain,
add(multiply(additive_identity,additive_inverse(b)),d) = d,
inference(resolution,[status(thm)],[f1334,f61]) ).
fof(f3529,plain,
add(multiply(a,additive_inverse(b)),c) = additive_identity,
inference(resolution,[status(thm)],[f1472,f61]) ).
fof(f5629,plain,
add(additive_inverse(d),d) = multiply(additive_identity,additive_inverse(b)),
inference(paramodulation,[status(thm)],[f2681,f762]) ).
fof(f5648,plain,
additive_identity = multiply(additive_identity,additive_inverse(b)),
inference(forward_demodulation,[status(thm)],[f127,f5629]) ).
fof(f5687,plain,
product(additive_identity,additive_inverse(b),additive_identity),
inference(paramodulation,[status(thm)],[f5648,f23]) ).
fof(f5807,plain,
add(additive_inverse(c),additive_identity) = multiply(a,additive_inverse(b)),
inference(paramodulation,[status(thm)],[f3529,f762]) ).
fof(f5841,plain,
additive_inverse(c) = multiply(a,additive_inverse(b)),
inference(forward_demodulation,[status(thm)],[f106,f5807]) ).
fof(f6095,plain,
! [X0] :
( sum(additive_inverse(c),d,X0)
| ~ product(additive_identity,additive_inverse(b),X0) ),
inference(backward_demodulation,[status(thm)],[f5841,f604]) ).
fof(f6160,plain,
sum(additive_inverse(c),d,additive_identity),
inference(resolution,[status(thm)],[f6095,f5687]) ).
fof(f6198,plain,
add(d,additive_inverse(c)) = additive_identity,
inference(resolution,[status(thm)],[f6160,f61]) ).
fof(f6551,plain,
add(c,additive_identity) = d,
inference(paramodulation,[status(thm)],[f6198,f1064]) ).
fof(f6615,plain,
c = d,
inference(forward_demodulation,[status(thm)],[f106,f6551]) ).
fof(f6616,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6615,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : RNG004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Mon Sep 21 04:09:39 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 % Drodi V4.1.1
% 4.32/0.97 % Refutation found
% 4.32/0.97 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.32/0.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.32/0.98 % Elapsed time: 0.669524 seconds
% 4.32/0.98 % CPU time: 5.066810 seconds
% 4.32/0.98 % Total memory used: 79.100 MB
% 4.32/0.98 % Net memory used: 71.482 MB
%------------------------------------------------------------------------------