%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 10.93s 1.95s
% Output : CNFRefutation 11.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 16
% Syntax : Number of formulae : 101 ( 56 unt; 0 def)
% Number of atoms : 199 ( 30 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 198 ( 100 ~; 98 |; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 276 ( 276 !; 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(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(f10,axiom,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
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(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,
! [X] : product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ sum(a,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f21,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [X0] : sum(additive_inverse(X0),X0,additive_identity),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f25,plain,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f28,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(f29,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)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
! [X,V,W] :
( product(X,V,W)
| ! [U,Z] :
( ~ product(U,Z,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [U,Z,W] :
( product(U,Z,W)
| ! [X,V] :
( ~ product(X,V,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f34,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,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(f36,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)],[f35]) ).
fof(f39,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(f40,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)],[f39]) ).
fof(f43,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f48,plain,
~ sum(a,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
! [X0,X1] :
( X0 = X1
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f44,f21]) ).
fof(f72,plain,
! [X0] : X0 = add(X0,additive_identity),
inference(resolution,[status(thm)],[f23,f54]) ).
fof(f74,plain,
! [X0,X1,X2,X3,X4] :
( sum(add(X3,X0),X1,X4)
| ~ sum(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f23,f29]) ).
fof(f76,plain,
! [X0,X1,X2] :
( add(X0,X1) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f23,f44]) ).
fof(f78,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f23,f30]) ).
fof(f108,plain,
! [X0,X1,X2] :
( add(X1,X0) = X2
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f78,f44]) ).
fof(f115,plain,
! [X0] : add(X0,additive_inverse(X0)) = additive_identity,
inference(resolution,[status(thm)],[f76,f25]) ).
fof(f117,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(resolution,[status(thm)],[f76,f78]) ).
fof(f146,plain,
! [X0,X1,X2,X3,X4] :
( product(X3,X2,X4)
| ~ product(multiply(X3,X0),X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f32,f22]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4] :
( product(multiply(X3,X0),X1,X4)
| ~ product(X3,X2,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f34,f22]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4,X5] :
( sum(multiply(X0,X3),X2,X5)
| ~ product(X0,X4,X5)
| ~ sum(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f36,f22]) ).
fof(f171,plain,
! [X0,X1,X2] :
( sum(add(X0,additive_inverse(X2)),X2,X1)
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f74,f24]) ).
fof(f306,plain,
! [X0,X1] :
( X0 = X1
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f46,f47]) ).
fof(f307,plain,
! [X0] : X0 = multiply(X0,X0),
inference(resolution,[status(thm)],[f306,f22]) ).
fof(f379,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)],[f40,f22]) ).
fof(f432,plain,
! [X0,X1] : sum(add(X0,additive_inverse(X1)),X1,X0),
inference(resolution,[status(thm)],[f171,f21]) ).
fof(f452,plain,
! [X0,X1] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(resolution,[status(thm)],[f432,f108]) ).
fof(f478,plain,
! [X0,X1] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f117,f452]) ).
fof(f601,plain,
! [X0] : add(X0,additive_identity) = additive_inverse(additive_inverse(X0)),
inference(paramodulation,[status(thm)],[f115,f478]) ).
fof(f622,plain,
! [X0] : X0 = additive_inverse(additive_inverse(X0)),
inference(forward_demodulation,[status(thm)],[f72,f601]) ).
fof(f703,plain,
! [X0,X1,X2,X3] :
( product(X0,multiply(X1,X2),X3)
| ~ product(multiply(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f146,f22]) ).
fof(f707,plain,
! [X0,X1,X2,X3] :
( product(multiply(X0,X1),X2,X3)
| ~ product(X0,multiply(X1,X2),X3) ),
inference(resolution,[status(thm)],[f148,f22]) ).
fof(f1060,plain,
! [X0,X1,X2,X3,X4] :
( sum(multiply(X3,X0),multiply(X3,X1),X4)
| ~ product(X3,X2,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f150,f22]) ).
fof(f1061,plain,
! [X0,X1,X2,X3] :
( sum(multiply(X1,X0),X1,X3)
| ~ product(X1,X2,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f150,f47]) ).
fof(f1823,plain,
! [X0,X1,X2,X3,X4] :
( sum(multiply(X0,X3),multiply(X1,X3),X4)
| ~ product(X2,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f379,f22]) ).
fof(f1824,plain,
! [X0,X1,X2,X3] :
( sum(multiply(X0,X1),X1,X3)
| ~ product(X2,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f379,f47]) ).
fof(f3654,plain,
! [X0,X1,X2] : product(X0,multiply(X1,X2),multiply(multiply(X0,X1),X2)),
inference(resolution,[status(thm)],[f703,f22]) ).
fof(f3655,plain,
! [X0,X1] : product(X0,multiply(X1,multiply(X0,X1)),multiply(X0,X1)),
inference(resolution,[status(thm)],[f703,f47]) ).
fof(f3662,plain,
! [X0,X1,X2] : product(multiply(X0,X1),X2,multiply(X0,multiply(X1,X2))),
inference(resolution,[status(thm)],[f707,f22]) ).
fof(f3685,plain,
! [X0,X1,X2] :
( sum(multiply(X0,additive_identity),multiply(X0,X1),X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1060,f20]) ).
fof(f4594,plain,
! [X0,X1] :
( sum(multiply(X0,additive_inverse(X0)),X0,X1)
| ~ product(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f1061,f24]) ).
fof(f6534,plain,
! [X0,X1,X2] :
( sum(multiply(additive_identity,X1),multiply(X0,X1),X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1823,f20]) ).
fof(f6576,plain,
! [X0,X1,X2] :
( sum(multiply(X1,X0),X0,X2)
| ~ product(add(X0,X1),X0,X2) ),
inference(resolution,[status(thm)],[f1824,f78]) ).
fof(f9046,plain,
! [X0] : sum(multiply(X0,additive_identity),multiply(X0,X0),X0),
inference(resolution,[status(thm)],[f3685,f47]) ).
fof(f9051,plain,
! [X0] : sum(multiply(X0,additive_identity),X0,X0),
inference(forward_demodulation,[status(thm)],[f307,f9046]) ).
fof(f9083,plain,
! [X0] : add(X0,multiply(X0,additive_identity)) = X0,
inference(resolution,[status(thm)],[f9051,f108]) ).
fof(f9126,plain,
! [X0] : add(X0,additive_inverse(X0)) = multiply(additive_inverse(X0),additive_identity),
inference(paramodulation,[status(thm)],[f9083,f478]) ).
fof(f9210,plain,
! [X0] : additive_identity = multiply(additive_inverse(X0),additive_identity),
inference(forward_demodulation,[status(thm)],[f115,f9126]) ).
fof(f9322,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(paramodulation,[status(thm)],[f622,f9210]) ).
fof(f9371,plain,
! [X0,X1] : product(X0,multiply(X1,additive_identity),additive_identity),
inference(paramodulation,[status(thm)],[f9322,f3654]) ).
fof(f9395,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(forward_demodulation,[status(thm)],[f9322,f9371]) ).
fof(f9641,plain,
! [X0] : sum(multiply(X0,additive_inverse(X0)),X0,additive_identity),
inference(resolution,[status(thm)],[f4594,f9395]) ).
fof(f9737,plain,
! [X0] : add(X0,multiply(X0,additive_inverse(X0))) = additive_identity,
inference(resolution,[status(thm)],[f9641,f108]) ).
fof(f9789,plain,
! [X0] : add(X0,additive_identity) = multiply(additive_inverse(X0),additive_inverse(additive_inverse(X0))),
inference(paramodulation,[status(thm)],[f9737,f478]) ).
fof(f9890,plain,
! [X0] : X0 = multiply(additive_inverse(X0),additive_inverse(additive_inverse(X0))),
inference(forward_demodulation,[status(thm)],[f72,f9789]) ).
fof(f9891,plain,
! [X0] : X0 = multiply(additive_inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f622,f9890]) ).
fof(f9980,plain,
! [X0,X1] : product(multiply(X0,additive_inverse(X1)),X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f9891,f3662]) ).
fof(f9982,plain,
! [X0] : product(additive_inverse(X0),multiply(X0,multiply(additive_inverse(X0),X0)),X0),
inference(paramodulation,[status(thm)],[f9891,f3655]) ).
fof(f10001,plain,
! [X0] : product(additive_inverse(X0),multiply(X0,X0),X0),
inference(forward_demodulation,[status(thm)],[f9891,f9982]) ).
fof(f10002,plain,
! [X0] : product(additive_inverse(X0),X0,X0),
inference(forward_demodulation,[status(thm)],[f307,f10001]) ).
fof(f12073,plain,
! [X0] : sum(multiply(additive_identity,X0),multiply(additive_inverse(X0),X0),X0),
inference(resolution,[status(thm)],[f6534,f10002]) ).
fof(f12090,plain,
! [X0] : sum(multiply(additive_identity,X0),X0,X0),
inference(forward_demodulation,[status(thm)],[f9891,f12073]) ).
fof(f12140,plain,
! [X0] : add(X0,multiply(additive_identity,X0)) = X0,
inference(resolution,[status(thm)],[f12090,f108]) ).
fof(f12206,plain,
! [X0] : add(X0,additive_inverse(X0)) = multiply(additive_identity,additive_inverse(X0)),
inference(paramodulation,[status(thm)],[f12140,f478]) ).
fof(f12297,plain,
! [X0] : additive_identity = multiply(additive_identity,additive_inverse(X0)),
inference(forward_demodulation,[status(thm)],[f115,f12206]) ).
fof(f12445,plain,
! [X0] : additive_identity = multiply(additive_identity,X0),
inference(paramodulation,[status(thm)],[f622,f12297]) ).
fof(f12543,plain,
! [X0] : product(additive_identity,X0,multiply(additive_identity,X0)),
inference(paramodulation,[status(thm)],[f12445,f9980]) ).
fof(f12592,plain,
! [X0] : product(additive_identity,X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f12445,f12543]) ).
fof(f12913,plain,
! [X0,X1] :
( sum(multiply(additive_inverse(X0),X0),X0,X1)
| ~ product(additive_identity,X0,X1) ),
inference(paramodulation,[status(thm)],[f115,f6576]) ).
fof(f12920,plain,
! [X0,X1] :
( sum(X0,X0,X1)
| ~ product(additive_identity,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f9891,f12913]) ).
fof(f12926,plain,
! [X0] : sum(X0,X0,additive_identity),
inference(resolution,[status(thm)],[f12920,f12592]) ).
fof(f12953,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f48,f12926]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:15:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 10.93/1.95 % Refutation found
% 10.93/1.95 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 10.93/1.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 11.40/2.00 % Elapsed time: 1.616739 seconds
% 11.40/2.00 % CPU time: 12.142870 seconds
% 11.40/2.00 % Total memory used: 76.215 MB
% 11.40/2.00 % Net memory used: 69.836 MB
%------------------------------------------------------------------------------