%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:33:37 PM UTC 2026
% Result : Unsatisfiable 4.80s 1.13s
% Output : CNFRefutation 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] :
( A = C
| multiply(A,B) != multiply(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] :
( B = C
| multiply(A,B) != multiply(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : multiply(A,B) = multiply(B,multiply(A,commutator(A,B))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiply(commutator(A,B),C) = multiply(C,commutator(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [A,C] :
( A = C
| ! [B] : multiply(A,B) != multiply(C,B) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] :
( X0 = X2
| multiply(X0,X1) != multiply(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [B,C] :
( B = C
| ! [A] : multiply(A,B) != multiply(A,C) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1,X2] :
( X1 = X2
| multiply(X0,X1) != multiply(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f12,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,multiply(X0,commutator(X0,X1))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0,X1,X2] : multiply(commutator(X0,X1),X2) = multiply(X2,commutator(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
commutator(commutator(a,b),c) != commutator(a,commutator(b,c)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( commutator(X1,X2) = X3
| multiply(X0,commutator(X1,X2)) != multiply(X3,X0) ),
inference(paramodulation,[status(thm)],[f13,f9]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| multiply(commutator(X0,X1),X2) != multiply(X3,commutator(X0,X1)) ),
inference(paramodulation,[status(thm)],[f13,f9]) ).
fof(f38,plain,
! [X0,X1,X2] : multiply(X0,commutator(X0,commutator(X1,X2))) = X0,
inference(resolution,[status(thm)],[f22,f12]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( commutator(X0,commutator(X2,X3)) = X1
| X0 != multiply(X1,X0) ),
inference(paramodulation,[status(thm)],[f38,f21]) ).
fof(f94,plain,
! [X0] : X0 = multiply(X0,commutator(X0,X0)),
inference(resolution,[status(thm)],[f11,f12]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( commutator(X0,X1) = X3
| multiply(commutator(X0,X1),X2) != multiply(X2,X3) ),
inference(paramodulation,[status(thm)],[f13,f11]) ).
fof(f201,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X0,multiply(commutator(X0,X0),X1)),
inference(paramodulation,[status(thm)],[f94,f7]) ).
fof(f293,plain,
! [X0,X1,X2] : commutator(X0,X1) = multiply(commutator(X0,X1),commutator(commutator(X0,X1),X2)),
inference(resolution,[status(thm)],[f99,f12]) ).
fof(f403,plain,
! [X0,X1] : X0 = multiply(commutator(X1,X1),X0),
inference(resolution,[status(thm)],[f201,f11]) ).
fof(f493,plain,
! [X0,X1,X2,X3] : commutator(X0,commutator(X1,X2)) = commutator(X3,X3),
inference(resolution,[status(thm)],[f403,f51]) ).
fof(f507,plain,
! [X0,X1,X2] :
( commutator(X2,X2) = X1
| X0 != multiply(X0,X1) ),
inference(paramodulation,[status(thm)],[f403,f99]) ).
fof(f3767,plain,
! [X0,X1,X2,X3] : commutator(X0,X0) = commutator(commutator(X1,X2),X3),
inference(resolution,[status(thm)],[f293,f507]) ).
fof(f3981,plain,
! [X0] : commutator(X0,X0) != commutator(a,commutator(b,c)),
inference(paramodulation,[status(thm)],[f3767,f14]) ).
fof(f4051,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3981,f493]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP402-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:15:52 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 4.80/1.13 % Refutation found
% 4.80/1.13 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.80/1.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.80/1.15 % Elapsed time: 0.777610 seconds
% 4.80/1.15 % CPU time: 5.808421 seconds
% 4.80/1.15 % Total memory used: 112.112 MB
% 4.80/1.15 % Net memory used: 110.664 MB
%------------------------------------------------------------------------------