%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP658-10 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:35:02 PM UTC 2026
% Result : Unsatisfiable 5.75s 1.27s
% Output : CNFRefutation 5.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 45 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 0 con; 1-2 aty)
% Number of variables : 127 ( 127 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : mult(mult(A,mult(B,B)),C) = mult(mult(A,B),mult(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [X0] : tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f10,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
! [X0,X1,X2] : mult(mult(X0,mult(X1,X1)),X2) = mult(mult(X0,X1),mult(X1,X2)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0] : tuple(mult(X0,x1(X0)),mult(x1_2(X0),X0)) != tuple(x1(X0),x1_2(X0)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0,X1] : X0 = ld(rd(X1,X0),X1),
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f21,plain,
! [X0,X1,X2] : mult(mult(X0,X1),mult(X1,ld(mult(X0,mult(X1,X1)),X2))) = X2,
inference(paramodulation,[status(thm)],[f7,f11]) ).
fof(f23,plain,
! [X0,X1,X2] : mult(mult(rd(X0,mult(X1,X1)),X1),mult(X1,X2)) = mult(X0,X2),
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f39,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(mult(rd(X0,mult(rd(X2,X1),rd(X2,X1))),rd(X2,X1)),X2),
inference(paramodulation,[status(thm)],[f9,f23]) ).
fof(f40,plain,
! [X0,X1,X2] : mult(X0,ld(X1,X2)) = mult(mult(rd(X0,mult(X1,X1)),X1),X2),
inference(paramodulation,[status(thm)],[f7,f23]) ).
fof(f43,plain,
! [X0,X1,X2] : mult(rd(X0,mult(X1,X1)),X1) = rd(mult(X0,X2),mult(X1,X2)),
inference(paramodulation,[status(thm)],[f23,f10]) ).
fof(f47,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(X0,ld(rd(X2,X1),X2)),
inference(backward_demodulation,[status(thm)],[f40,f39]) ).
fof(f50,plain,
! [X0,X1,X2] : mult(rd(X0,ld(rd(X1,X2),X1)),X2) = X0,
inference(paramodulation,[status(thm)],[f9,f47]) ).
fof(f69,plain,
! [X0,X1,X2,X3] : mult(mult(rd(X0,ld(rd(X1,mult(X2,X2)),X1)),X2),mult(X2,X3)) = mult(X0,X3),
inference(paramodulation,[status(thm)],[f50,f11]) ).
fof(f74,plain,
! [X0,X1,X2] : mult(mult(rd(X0,mult(X1,X1)),X1),mult(X1,X2)) = mult(X0,X2),
inference(forward_demodulation,[status(thm)],[f18,f69]) ).
fof(f107,plain,
! [X0,X1,X2,X3] : X0 = mult(mult(rd(X1,ld(rd(X2,mult(X3,X3)),X2)),X3),mult(X3,ld(X1,X0))),
inference(paramodulation,[status(thm)],[f50,f21]) ).
fof(f119,plain,
! [X0,X1,X2] : X0 = mult(mult(rd(X1,mult(X2,X2)),X2),mult(X2,ld(X1,X0))),
inference(forward_demodulation,[status(thm)],[f18,f107]) ).
fof(f145,plain,
! [X0,X1,X2] : mult(X0,X1) = ld(mult(rd(X2,mult(X0,X0)),X0),mult(X2,X1)),
inference(paramodulation,[status(thm)],[f74,f8]) ).
fof(f216,plain,
! [X0,X1] : X0 = mult(mult(rd(X1,mult(X1,X1)),X1),X0),
inference(paramodulation,[status(thm)],[f7,f119]) ).
fof(f251,plain,
! [X0] : tuple(x1(mult(rd(X0,mult(X0,X0)),X0)),x1_2(mult(rd(X0,mult(X0,X0)),X0))) != tuple(x1(mult(rd(X0,mult(X0,X0)),X0)),mult(x1_2(mult(rd(X0,mult(X0,X0)),X0)),mult(rd(X0,mult(X0,X0)),X0))),
inference(paramodulation,[status(thm)],[f216,f12]) ).
fof(f1473,plain,
! [X0,X1,X2,X3] : mult(X0,X1) = ld(rd(mult(X2,X3),mult(X0,X3)),mult(X2,X1)),
inference(paramodulation,[status(thm)],[f43,f145]) ).
fof(f1484,plain,
! [X0,X1,X2] : X0 = ld(rd(X1,mult(X0,X0)),rd(mult(X1,X2),mult(X0,X2))),
inference(paramodulation,[status(thm)],[f43,f8]) ).
fof(f1555,plain,
! [X0,X1,X2] : X0 = ld(rd(X1,mult(X0,X0)),rd(X2,mult(X0,ld(X1,X2)))),
inference(paramodulation,[status(thm)],[f7,f1484]) ).
fof(f1591,plain,
! [X0,X1] : X0 = ld(rd(X0,mult(X0,X0)),rd(X1,X1)),
inference(paramodulation,[status(thm)],[f7,f1555]) ).
fof(f1782,plain,
! [X0,X1,X2,X3,X4] : mult(X0,X1) = ld(rd(mult(X2,ld(X3,X4)),mult(X0,X4)),mult(mult(rd(X2,mult(X3,X3)),X3),X1)),
inference(paramodulation,[status(thm)],[f40,f1473]) ).
fof(f1790,plain,
! [X0,X1,X2,X3] : mult(X0,X1) = ld(rd(X2,mult(X0,ld(X3,X2))),mult(X3,X1)),
inference(paramodulation,[status(thm)],[f7,f1473]) ).
fof(f1795,plain,
! [X0,X1,X2,X3,X4] : mult(rd(X0,ld(rd(X1,X2),X1)),X3) = ld(rd(mult(X4,X2),X0),mult(X4,X3)),
inference(paramodulation,[status(thm)],[f50,f1473]) ).
fof(f1816,plain,
! [X0,X1,X2,X3,X4] : mult(X0,X1) = ld(rd(mult(X2,ld(X3,X4)),mult(X0,X4)),mult(X2,ld(X3,X1))),
inference(forward_demodulation,[status(thm)],[f40,f1782]) ).
fof(f1825,plain,
! [X0,X1,X2,X3] : mult(X0,X1) = mult(rd(mult(X0,X2),ld(X3,X2)),ld(X3,X1)),
inference(backward_demodulation,[status(thm)],[f1831,f1816]) ).
fof(f1831,plain,
! [X0,X1,X2,X3] : mult(rd(X0,X1),X2) = ld(rd(mult(X3,X1),X0),mult(X3,X2)),
inference(forward_demodulation,[status(thm)],[f18,f1795]) ).
fof(f3192,plain,
! [X0,X1,X2,X3,X4] : mult(rd(X0,ld(rd(X1,ld(X2,X3)),X1)),X4) = ld(rd(X3,X0),mult(X2,X4)),
inference(paramodulation,[status(thm)],[f50,f1790]) ).
fof(f3222,plain,
! [X0,X1,X2,X3] : mult(X0,X1) = ld(rd(X2,mult(X0,X2)),mult(X3,ld(X3,X1))),
inference(backward_demodulation,[status(thm)],[f3224,f1825]) ).
fof(f3224,plain,
! [X0,X1,X2,X3] : mult(rd(X0,ld(X1,X2)),X3) = ld(rd(X2,X0),mult(X1,X3)),
inference(forward_demodulation,[status(thm)],[f18,f3192]) ).
fof(f3235,plain,
! [X0,X1] : X0 = mult(X0,rd(X1,X1)),
inference(backward_demodulation,[status(thm)],[f3236,f1591]) ).
fof(f3236,plain,
! [X0,X1,X2] : mult(X0,X1) = ld(rd(X2,mult(X0,X2)),X1),
inference(forward_demodulation,[status(thm)],[f7,f3222]) ).
fof(f3900,plain,
! [X0,X1] : X0 = mult(X0,mult(rd(X1,mult(X1,X1)),X1)),
inference(paramodulation,[status(thm)],[f43,f3235]) ).
fof(f3941,plain,
! [X0] : tuple(x1(mult(rd(X0,mult(X0,X0)),X0)),x1_2(mult(rd(X0,mult(X0,X0)),X0))) != tuple(x1(mult(rd(X0,mult(X0,X0)),X0)),x1_2(mult(rd(X0,mult(X0,X0)),X0))),
inference(backward_demodulation,[status(thm)],[f3900,f251]) ).
fof(f4258,plain,
$false,
inference(equality_resolution,[status(thm)],[f3941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP658-10 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.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 : Sun Sep 20 20:31:59 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 5.75/1.27 % Refutation found
% 5.75/1.27 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.75/1.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.61/1.30 % Elapsed time: 0.938197 seconds
% 0.61/1.30 % CPU time: 7.252018 seconds
% 0.61/1.30 % Total memory used: 183.952 MB
% 0.61/1.30 % Net memory used: 181.873 MB
%------------------------------------------------------------------------------