%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:35:07 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 6 ( 2 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 : 55 ( 55 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] : rd(mult(A,A),A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : mult(rd(A,B),B) = rd(mult(A,B),B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C,D] : rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0] : rd(mult(X0,X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = rd(mult(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = mult(X0,rd(mult(X1,X3),X3)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),X2),rd(mult(X2,X2),X2)) = mult(X0,rd(mult(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f10,f14]) ).
fof(f38,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),rd(X2,X3)),rd(X2,X3)) = rd(mult(mult(X0,X1),X3),X3),
inference(backward_demodulation,[status(thm)],[f42,f14]) ).
fof(f42,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),X2),X2) = mult(X0,rd(mult(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f10,f29]) ).
fof(f65,plain,
! [X0,X1] : rd(mult(mult(X0,X1),X1),X1) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f10,f42]) ).
fof(f111,plain,
! [X0,X1,X2] : rd(mult(mult(X0,mult(X1,X2)),X2),X2) = mult(X0,mult(X1,X2)),
inference(paramodulation,[status(thm)],[f65,f42]) ).
fof(f112,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),rd(mult(mult(X2,X3),X3),X3)),mult(X2,X3)) = rd(mult(mult(X0,X1),X3),X3),
inference(paramodulation,[status(thm)],[f65,f38]) ).
fof(f125,plain,
! [X0,X1,X2,X3] : rd(rd(mult(mult(mult(X0,X1),mult(X2,X3)),X3),X3),mult(X2,X3)) = rd(mult(mult(X0,X1),X3),X3),
inference(forward_demodulation,[status(thm)],[f42,f112]) ).
fof(f127,plain,
! [X0,X1,X2,X3] : rd(mult(mult(X0,X1),mult(X2,X3)),mult(X2,X3)) = rd(mult(mult(X0,X1),X3),X3),
inference(forward_demodulation,[status(thm)],[f111,f125]) ).
fof(f131,plain,
! [X0,X1,X2,X3] : rd(mult(rd(mult(X0,X1),X1),mult(X2,X3)),mult(X2,X3)) = rd(mult(mult(rd(X0,X1),X1),X3),X3),
inference(paramodulation,[status(thm)],[f12,f127]) ).
fof(f143,plain,
! [X0,X1,X2,X3] : rd(mult(rd(mult(X0,X1),X1),mult(X2,X3)),mult(X2,X3)) = rd(mult(rd(mult(X0,X1),X1),X3),X3),
inference(forward_demodulation,[status(thm)],[f12,f131]) ).
fof(f264,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),mult(X1,X2)) = rd(mult(rd(mult(X0,X0),X0),X2),X2),
inference(paramodulation,[status(thm)],[f10,f143]) ).
fof(f292,plain,
rd(mult(a,c),c) != rd(mult(a,c),c),
inference(backward_demodulation,[status(thm)],[f294,f16]) ).
fof(f294,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),mult(X1,X2)) = rd(mult(X0,X2),X2),
inference(forward_demodulation,[status(thm)],[f10,f264]) ).
fof(f336,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n013.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:32:36 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.64/1.69 % Elapsed time: 1.112516 seconds
% 2.64/1.69 % CPU time: 0.368600 seconds
% 2.64/1.69 % Total memory used: 12.025 MB
% 2.64/1.69 % Net memory used: 11.911 MB
%------------------------------------------------------------------------------