%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO010-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:06:20 PM UTC 2026
% Result : Unsatisfiable 1.33s 0.60s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 11
% Syntax : Number of formulae : 54 ( 29 unt; 0 def)
% Number of atoms : 105 ( 18 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 104 ( 53 ~; 51 |; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 140 ( 140 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : sum(X,Y,add(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] :
( sum(Y,X,Z)
| ~ sum(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : sum(additive_identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : product(X,multiplicative_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,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(f15,axiom,
! [Y,X,V1,Z,V2,V3,V4] :
( product(V1,V2,V4)
| ~ sum(V3,X,V4)
| ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X] : product(X,inverse(X),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y,U,V] :
( U = V
| ~ product(X,Y,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ sum(x,multiply(x,y),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0,X1] : sum(X0,X1,add(X0,X1)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0,X1,X2] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f28,plain,
! [X0] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
! [X0] : product(X0,multiplicative_identity,X0),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f32,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)],[f9]) ).
fof(f33,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)],[f32]) ).
fof(f44,plain,
! [V1,V2,V4] :
( product(V1,V2,V4)
| ! [X,V3] :
( ~ sum(V3,X,V4)
| ! [Y,Z] :
( ~ product(Y,Z,V3)
| ~ sum(Z,X,V2)
| ~ sum(Y,X,V1) ) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( product(X2,X4,X6)
| ~ sum(X5,X1,X6)
| ~ product(X0,X3,X5)
| ~ sum(X3,X1,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f51,plain,
! [X0] : product(X0,inverse(X0),additive_identity),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f52,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ sum(X,Y,V)
| ~ sum(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f54,plain,
! [U,V] :
( U = V
| ! [X,Y] :
( ~ product(X,Y,V)
| ~ product(X,Y,U) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
~ sum(x,multiply(x,y),x),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
! [X0] : sum(X0,additive_identity,X0),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f59,plain,
! [X0,X1] :
( X1 = X0
| ~ sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f58,f53]) ).
fof(f66,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(resolution,[status(thm)],[f24,f59]) ).
fof(f67,plain,
! [X0,X1,X2] :
( X2 = add(X0,X1)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f24,f53]) ).
fof(f68,plain,
! [X0,X1] : sum(X0,X1,add(X1,X0)),
inference(resolution,[status(thm)],[f24,f26]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( sum(X2,multiply(X0,X3),multiply(X0,X3))
| ~ sum(X1,X3,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f33,f25]) ).
fof(f175,plain,
! [X0,X1,X2] :
( sum(X1,multiply(X0,X2),multiply(X0,X2))
| ~ product(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f153,f28]) ).
fof(f179,plain,
! [X0,X1] : sum(multiply(X0,additive_identity),multiply(X0,X1),multiply(X0,X1)),
inference(resolution,[status(thm)],[f175,f25]) ).
fof(f187,plain,
! [X0,X1] : multiply(X0,X1) = add(multiply(X0,additive_identity),multiply(X0,X1)),
inference(resolution,[status(thm)],[f179,f67]) ).
fof(f274,plain,
! [X0,X1] :
( X1 = X0
| ~ product(X0,multiplicative_identity,X1) ),
inference(resolution,[status(thm)],[f55,f31]) ).
fof(f275,plain,
! [X0,X1,X2] :
( X2 = multiply(X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f55,f25]) ).
fof(f338,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(resolution,[status(thm)],[f274,f25]) ).
fof(f555,plain,
! [X0] : additive_identity = multiply(X0,inverse(X0)),
inference(resolution,[status(thm)],[f275,f51]) ).
fof(f644,plain,
! [X0] : multiply(X0,inverse(X0)) = add(multiply(X0,additive_identity),additive_identity),
inference(paramodulation,[status(thm)],[f555,f187]) ).
fof(f682,plain,
! [X0] : additive_identity = add(multiply(X0,additive_identity),additive_identity),
inference(forward_demodulation,[status(thm)],[f555,f644]) ).
fof(f683,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f66,f682]) ).
fof(f749,plain,
! [X0] : product(X0,additive_identity,additive_identity),
inference(paramodulation,[status(thm)],[f683,f25]) ).
fof(f830,plain,
! [X0,X1,X2] :
( product(X2,X1,X1)
| ~ product(X0,additive_identity,additive_identity)
| ~ sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f45,f28]) ).
fof(f847,plain,
! [X0,X1,X2] :
( product(X2,X1,X1)
| ~ sum(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f830,f749]) ).
fof(f947,plain,
! [X0,X1] : product(add(X0,X1),X0,X0),
inference(resolution,[status(thm)],[f847,f68]) ).
fof(f991,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(resolution,[status(thm)],[f947,f274]) ).
fof(f1023,plain,
! [X0] : sum(X0,multiplicative_identity,multiplicative_identity),
inference(paramodulation,[status(thm)],[f991,f68]) ).
fof(f1077,plain,
! [X0,X1,X2] :
( sum(X2,multiply(X0,multiplicative_identity),multiply(X0,multiplicative_identity))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1023,f153]) ).
fof(f1087,plain,
! [X0,X1,X2] :
( sum(X2,X0,multiply(X0,multiplicative_identity))
| ~ product(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f338,f1077]) ).
fof(f1088,plain,
! [X0,X1,X2] :
( sum(X2,X0,X0)
| ~ product(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f338,f1087]) ).
fof(f1418,plain,
! [X0,X1] : sum(multiply(X0,X1),X0,X0),
inference(resolution,[status(thm)],[f1088,f25]) ).
fof(f1530,plain,
! [X0,X1] : sum(X0,multiply(X0,X1),X0),
inference(resolution,[status(thm)],[f1418,f26]) ).
fof(f1734,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f56,f1530]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 13:47:25 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 1.33/0.60 % Refutation found
% 1.33/0.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.33/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.33/0.60 % Elapsed time: 0.234639 seconds
% 1.33/0.60 % CPU time: 1.646070 seconds
% 1.33/0.60 % Total memory used: 56.990 MB
% 1.33/0.60 % Net memory used: 54.213 MB
%------------------------------------------------------------------------------