%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP669-1 : TPTP v9.3.1. Released v4.0.0.
% 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 12:35:05 PM UTC 2026
% Result : Unsatisfiable 0.24s 1.32s
% Output : CNFRefutation 5.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 42 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 108 ( 108 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C] : mult(A,mult(B,mult(A,C))) = mult(mult(mult(A,B),A),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : mult(A,mult(B,mult(C,B))) = mult(mult(mult(A,B),C),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C] : mult(mult(A,B),mult(C,A)) = mult(A,mult(mult(B,C),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,mult(b,c)),a),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X0,X2))) = mult(mult(mult(X0,X1),X0),X2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X2,X1))) = mult(mult(mult(X0,X1),X2),X1),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f21,plain,
! [X0,X1,X2] : mult(mult(X0,X1),mult(X2,X0)) = mult(X0,mult(mult(X1,X2),X0)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f22,plain,
mult(mult(a,b),mult(c,mult(a,b))) != mult(mult(mult(a,mult(b,c)),a),b),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f32,plain,
mult(mult(a,b),mult(c,mult(a,b))) != mult(a,mult(mult(b,c),mult(a,b))),
inference(forward_demodulation,[status(thm)],[f18,f22]) ).
fof(f33,plain,
mult(mult(a,b),mult(c,mult(a,b))) != mult(a,mult(b,mult(mult(c,a),b))),
inference(forward_demodulation,[status(thm)],[f21,f32]) ).
fof(f36,plain,
! [X0,X1,X2,X3] : mult(mult(mult(X0,X1),X0),mult(X2,mult(mult(mult(X0,X1),X0),X3))) = mult(mult(mult(X0,mult(X1,mult(X0,X2))),mult(mult(X0,X1),X0)),X3),
inference(paramodulation,[status(thm)],[f18,f18]) ).
fof(f37,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X1,mult(X0,mult(X2,mult(mult(mult(X0,X1),X0),X3))))) = mult(mult(mult(X0,mult(X1,mult(X0,X2))),mult(mult(X0,X1),X0)),X3),
inference(forward_demodulation,[status(thm)],[f18,f36]) ).
fof(f38,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X1,mult(X0,mult(X2,mult(X0,mult(X1,mult(X0,X3))))))) = mult(mult(mult(X0,mult(X1,mult(X0,X2))),mult(mult(X0,X1),X0)),X3),
inference(forward_demodulation,[status(thm)],[f18,f37]) ).
fof(f39,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X1,mult(X0,mult(X2,mult(X0,mult(X1,mult(X0,X3))))))) = mult(mult(X0,mult(mult(mult(X1,mult(X0,X2)),mult(X0,X1)),X0)),X3),
inference(forward_demodulation,[status(thm)],[f21,f38]) ).
fof(f40,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X1,mult(X0,mult(X2,mult(X0,mult(X1,mult(X0,X3))))))) = mult(mult(X0,mult(mult(X1,mult(mult(mult(X0,X2),X0),X1)),X0)),X3),
inference(forward_demodulation,[status(thm)],[f21,f39]) ).
fof(f41,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X1,mult(X0,mult(X2,mult(X0,mult(X1,mult(X0,X3))))))) = mult(mult(X0,mult(mult(X1,mult(X0,mult(X2,mult(X0,X1)))),X0)),X3),
inference(forward_demodulation,[status(thm)],[f18,f40]) ).
fof(f53,plain,
! [X0,X1,X2,X3] : mult(mult(X0,mult(mult(X1,X2),X0)),mult(X3,mult(X0,X1))) = mult(mult(X0,X1),mult(mult(mult(X2,X0),X3),mult(X0,X1))),
inference(paramodulation,[status(thm)],[f21,f21]) ).
fof(f55,plain,
! [X0,X1,X2,X3] : mult(mult(X0,X1),mult(X2,mult(X3,mult(X2,X0)))) = mult(X0,mult(mult(X1,mult(mult(X2,X3),X2)),X0)),
inference(paramodulation,[status(thm)],[f18,f21]) ).
fof(f260,plain,
! [X0,X1,X2] : mult(unit,mult(X0,mult(unit,mult(X1,mult(unit,mult(X0,mult(unit,X2))))))) = mult(mult(mult(X0,mult(unit,mult(X1,mult(unit,X0)))),unit),X2),
inference(paramodulation,[status(thm)],[f17,f41]) ).
fof(f269,plain,
! [X0,X1] : mult(mult(X0,X1),X0) = mult(X0,mult(mult(X1,unit),X0)),
inference(paramodulation,[status(thm)],[f17,f21]) ).
fof(f273,plain,
! [X0,X1,X2] : mult(X0,mult(unit,mult(X1,mult(unit,mult(X0,mult(unit,X2)))))) = mult(mult(mult(X0,mult(unit,mult(X1,mult(unit,X0)))),unit),X2),
inference(forward_demodulation,[status(thm)],[f17,f260]) ).
fof(f274,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(unit,mult(X0,mult(unit,X2))))) = mult(mult(mult(X0,mult(unit,mult(X1,mult(unit,X0)))),unit),X2),
inference(forward_demodulation,[status(thm)],[f17,f273]) ).
fof(f275,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X0,mult(unit,X2)))) = mult(mult(mult(X0,mult(unit,mult(X1,mult(unit,X0)))),unit),X2),
inference(forward_demodulation,[status(thm)],[f17,f274]) ).
fof(f276,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X0,X2))) = mult(mult(mult(X0,mult(unit,mult(X1,mult(unit,X0)))),unit),X2),
inference(forward_demodulation,[status(thm)],[f17,f275]) ).
fof(f277,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X0,X2))) = mult(mult(X0,mult(unit,mult(X1,mult(unit,X0)))),X2),
inference(forward_demodulation,[status(thm)],[f16,f276]) ).
fof(f278,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X0,X2))) = mult(mult(X0,mult(X1,mult(unit,X0))),X2),
inference(forward_demodulation,[status(thm)],[f17,f277]) ).
fof(f291,plain,
! [X0,X1,X2,X3] : mult(X0,mult(mult(X1,X2),mult(X0,mult(X3,mult(X0,X1))))) = mult(mult(X0,X1),mult(mult(mult(X2,X0),X3),mult(X0,X1))),
inference(backward_demodulation,[status(thm)],[f295,f53]) ).
fof(f295,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(X0,X2))) = mult(mult(X0,mult(X1,X0)),X2),
inference(forward_demodulation,[status(thm)],[f17,f278]) ).
fof(f344,plain,
! [X0,X1] : mult(mult(X0,X1),X0) = mult(X0,mult(X1,X0)),
inference(forward_demodulation,[status(thm)],[f16,f269]) ).
fof(f355,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X1,mult(mult(X2,mult(mult(X0,X3),X0)),X1))) = mult(mult(X0,X1),mult(mult(mult(X2,X0),X3),mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f55,f291]) ).
fof(f356,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X1,mult(mult(X2,mult(X0,mult(X3,X0))),X1))) = mult(mult(X0,X1),mult(mult(mult(X2,X0),X3),mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f344,f355]) ).
fof(f407,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(ld(mult(X0,X1),X2),X1))) = mult(X2,X1),
inference(paramodulation,[status(thm)],[f12,f19]) ).
fof(f2389,plain,
! [X0,X1,X2,X3] : mult(X0,mult(X1,mult(mult(X2,mult(X0,mult(ld(mult(X2,X0),X3),X0))),X1))) = mult(mult(X0,X1),mult(X3,mult(X0,X1))),
inference(paramodulation,[status(thm)],[f12,f356]) ).
fof(f2557,plain,
mult(a,mult(b,mult(mult(c,a),b))) != mult(a,mult(b,mult(mult(c,a),b))),
inference(backward_demodulation,[status(thm)],[f2681,f33]) ).
fof(f2681,plain,
! [X0,X1,X2] : mult(X0,mult(X1,mult(mult(X2,X0),X1))) = mult(mult(X0,X1),mult(X2,mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f407,f2389]) ).
fof(f2965,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2557]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP669-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n016.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sun Sep 20 20:36:23 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.49 % Drodi V4.1.1
% 0.24/1.32 % Refutation found
% 0.24/1.32 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/1.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.84/2.58 % Elapsed time: 1.879158 seconds
% 9.84/2.58 % CPU time: 5.263411 seconds
% 9.84/2.58 % Total memory used: 102.241 MB
% 9.84/2.58 % Net memory used: 101.142 MB
%------------------------------------------------------------------------------