%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP659+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 : n008.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 : Theorem 3.56s 0.86s
% Output : CNFRefutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of formulae : 73 ( 67 unt; 0 def)
% Number of atoms : 79 ( 78 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 4 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 141 ( 136 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,A] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,A] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,A] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,A] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [C,B,A] : mult(mult(A,mult(B,C)),B) = mult(mult(A,B),mult(C,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ? [X0] :
! [X1] :
( mult(X0,X1) = X1
& mult(X1,X0) = X1 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0,X1,X2] : mult(mult(X0,mult(X1,X2)),X1) = mult(mult(X0,X1),mult(X2,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0] :
? [X1] :
( mult(X0,X1) != X1
| mult(X1,X0) != X1 ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f14,plain,
! [X0] :
( ? [X1] : mult(X0,X1) != X1
| ? [X1] : mult(X1,X0) != X1 ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0] :
( mult(X0,sK1_skl(X0)) != sK1_skl(X0)
| mult(sK0_skl(X0),X0) != sK0_skl(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X1,sK0_skl(X0)),skolemize(X1,sK1_skl(X0))],[f14]) ).
fof(f16,plain,
! [X0] :
( mult(X0,sK1_skl(X0)) != sK1_skl(X0)
| mult(sK0_skl(X0),X0) != sK0_skl(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f10,f9]) ).
fof(f21,plain,
! [X0,X1] : rd(X0,ld(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f30,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(mult(rd(X0,mult(X1,X2)),X1),mult(X2,X1)),
inference(paramodulation,[status(thm)],[f10,f12]) ).
fof(f33,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,X2),mult(ld(X2,X1),X2)),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f34,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),mult(X2,X1)),X1) = mult(X0,mult(X1,X2)),
inference(paramodulation,[status(thm)],[f12,f11]) ).
fof(f35,plain,
! [X0,X1,X2] : ld(mult(X0,mult(X1,X2)),mult(mult(X0,X1),mult(X2,X1))) = X1,
inference(paramodulation,[status(thm)],[f12,f9]) ).
fof(f47,plain,
! [X0,X1,X2] : rd(mult(X0,X1),mult(X2,X1)) = mult(rd(X0,mult(X1,X2)),X1),
inference(paramodulation,[status(thm)],[f30,f11]) ).
fof(f48,plain,
! [X0,X1,X2] : ld(mult(rd(X0,mult(X1,X2)),X1),mult(X0,X1)) = mult(X2,X1),
inference(paramodulation,[status(thm)],[f30,f9]) ).
fof(f53,plain,
! [X0,X1,X2] : mult(mult(rd(X0,X1),X2),X1) = mult(X0,mult(ld(X1,X2),X1)),
inference(paramodulation,[status(thm)],[f10,f33]) ).
fof(f63,plain,
! [X0,X1,X2] : ld(mult(X0,X1),mult(mult(X0,X2),X1)) = mult(ld(X1,X2),X1),
inference(paramodulation,[status(thm)],[f33,f9]) ).
fof(f72,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),X2) = mult(rd(X0,X2),mult(X2,X1)),
inference(paramodulation,[status(thm)],[f10,f34]) ).
fof(f98,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X1),mult(X1,X2)),mult(X0,mult(X2,X1))) = X1,
inference(paramodulation,[status(thm)],[f10,f35]) ).
fof(f261,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X1),X2),mult(X0,X2)) = mult(ld(X2,X1),X2),
inference(paramodulation,[status(thm)],[f8,f48]) ).
fof(f277,plain,
! [X0,X1] : mult(X0,X1) = mult(X0,mult(ld(X1,X1),X1)),
inference(paramodulation,[status(thm)],[f10,f53]) ).
fof(f309,plain,
! [X0,X1,X2] : ld(mult(rd(X0,X1),X2),mult(X0,mult(ld(X1,X2),X1))) = X1,
inference(paramodulation,[status(thm)],[f53,f9]) ).
fof(f343,plain,
! [X0,X1] : mult(mult(X0,X1),ld(X1,X1)) = mult(mult(X0,ld(X1,X1)),mult(X1,ld(X1,X1))),
inference(paramodulation,[status(thm)],[f277,f12]) ).
fof(f360,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = mult(ld(X1,X1),X1),
inference(paramodulation,[status(thm)],[f277,f9]) ).
fof(f394,plain,
! [X0,X1] : mult(mult(X0,X1),ld(X1,X1)) = mult(mult(X0,ld(X1,X1)),X1),
inference(forward_demodulation,[status(thm)],[f8,f343]) ).
fof(f421,plain,
! [X0] : X0 = mult(ld(X0,X0),X0),
inference(forward_demodulation,[status(thm)],[f9,f360]) ).
fof(f431,plain,
! [X0,X1] : rd(X0,mult(X1,X0)) = mult(rd(ld(X0,X0),mult(X0,X1)),X0),
inference(paramodulation,[status(thm)],[f421,f47]) ).
fof(f435,plain,
! [X0,X1] : ld(mult(ld(X0,X0),mult(X0,X1)),mult(X0,mult(X1,X0))) = X0,
inference(paramodulation,[status(thm)],[f421,f35]) ).
fof(f443,plain,
! [X0] : rd(X0,X0) = ld(X0,X0),
inference(paramodulation,[status(thm)],[f421,f11]) ).
fof(f444,plain,
! [X0] : ld(ld(X0,X0),X0) = X0,
inference(paramodulation,[status(thm)],[f421,f9]) ).
fof(f756,plain,
! [X0,X1,X2] : ld(mult(X0,X1),mult(X2,X1)) = mult(ld(X1,ld(X0,X2)),X1),
inference(paramodulation,[status(thm)],[f8,f63]) ).
fof(f1083,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = mult(rd(ld(mult(X0,X1),mult(X0,X1)),X1),mult(X1,X0)),
inference(paramodulation,[status(thm)],[f421,f72]) ).
fof(f1120,plain,
! [X0,X1] : X0 = mult(rd(ld(mult(X0,X1),mult(X0,X1)),X1),mult(X1,X0)),
inference(forward_demodulation,[status(thm)],[f11,f1083]) ).
fof(f2064,plain,
! [X0,X1] : ld(mult(rd(X0,ld(X1,X1)),X1),mult(X0,mult(X1,ld(X1,X1)))) = ld(X1,X1),
inference(paramodulation,[status(thm)],[f444,f309]) ).
fof(f2088,plain,
! [X0,X1] : ld(mult(rd(X0,ld(X1,X1)),X1),mult(X0,X1)) = ld(X1,X1),
inference(forward_demodulation,[status(thm)],[f8,f2064]) ).
fof(f2089,plain,
! [X0] : mult(ld(X0,ld(X0,X0)),X0) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f261,f2088]) ).
fof(f2523,plain,
! [X0] : mult(mult(X0,X0),ld(X0,X0)) = mult(X0,X0),
inference(paramodulation,[status(thm)],[f8,f394]) ).
fof(f2846,plain,
! [X0,X1] : ld(mult(rd(X0,mult(X1,X1)),mult(X1,X1)),mult(X0,mult(ld(X1,X1),mult(X1,X1)))) = mult(X1,X1),
inference(paramodulation,[status(thm)],[f2523,f98]) ).
fof(f2870,plain,
! [X0] : ld(mult(X0,X0),mult(X0,X0)) = ld(X0,X0),
inference(paramodulation,[status(thm)],[f2523,f9]) ).
fof(f2892,plain,
! [X0,X1] : ld(X0,mult(X0,mult(ld(X1,X1),mult(X1,X1)))) = mult(X1,X1),
inference(forward_demodulation,[status(thm)],[f10,f2846]) ).
fof(f2893,plain,
! [X0] : mult(ld(X0,X0),mult(X0,X0)) = mult(X0,X0),
inference(forward_demodulation,[status(thm)],[f9,f2892]) ).
fof(f5179,plain,
! [X0] : ld(mult(ld(X0,X0),mult(X0,ld(X0,ld(X0,X0)))),mult(X0,ld(X0,X0))) = X0,
inference(paramodulation,[status(thm)],[f2089,f435]) ).
fof(f5233,plain,
! [X0] : ld(mult(ld(X0,X0),ld(X0,X0)),mult(X0,ld(X0,X0))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f5179]) ).
fof(f5234,plain,
! [X0] : ld(mult(ld(X0,X0),ld(X0,X0)),X0) = X0,
inference(forward_demodulation,[status(thm)],[f8,f5233]) ).
fof(f5256,plain,
! [X0] : rd(X0,X0) = mult(ld(X0,X0),ld(X0,X0)),
inference(paramodulation,[status(thm)],[f5234,f21]) ).
fof(f5264,plain,
! [X0] : ld(X0,X0) = mult(ld(X0,X0),ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f443,f5256]) ).
fof(f5271,plain,
! [X0] : ld(mult(ld(ld(X0,X0),ld(X0,X0)),mult(ld(X0,X0),ld(X0,X0))),mult(ld(X0,X0),ld(X0,X0))) = ld(X0,X0),
inference(paramodulation,[status(thm)],[f5264,f435]) ).
fof(f5336,plain,
! [X0] : ld(mult(ld(X0,X0),ld(X0,X0)),mult(ld(X0,X0),ld(X0,X0))) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f2893,f5271]) ).
fof(f5337,plain,
! [X0] : ld(ld(X0,X0),ld(X0,X0)) = ld(X0,X0),
inference(forward_demodulation,[status(thm)],[f2870,f5336]) ).
fof(f7783,plain,
! [X0,X1] : X0 = mult(rd(mult(ld(X1,ld(X0,X0)),X1),X1),mult(X1,X0)),
inference(forward_demodulation,[status(thm)],[f756,f1120]) ).
fof(f7785,plain,
! [X0,X1] : X0 = mult(ld(X1,ld(X0,X0)),mult(X1,X0)),
inference(forward_demodulation,[status(thm)],[f11,f7783]) ).
fof(f7823,plain,
! [X0,X1] : X0 = mult(ld(rd(ld(X0,X0),mult(X0,X1)),ld(X0,X0)),rd(X0,mult(X1,X0))),
inference(paramodulation,[status(thm)],[f431,f7785]) ).
fof(f7893,plain,
! [X0,X1] : rd(X0,mult(X1,X0)) = ld(X1,ld(X0,X0)),
inference(paramodulation,[status(thm)],[f7785,f11]) ).
fof(f7940,plain,
! [X0,X1] : X0 = mult(mult(X0,X1),rd(X0,mult(X1,X0))),
inference(forward_demodulation,[status(thm)],[f19,f7823]) ).
fof(f8311,plain,
! [X0,X1] : rd(X0,rd(X0,mult(X1,X0))) = mult(X0,X1),
inference(paramodulation,[status(thm)],[f7940,f11]) ).
fof(f10379,plain,
! [X0,X1] : rd(X0,ld(X1,ld(X0,X0))) = mult(X0,X1),
inference(forward_demodulation,[status(thm)],[f7893,f8311]) ).
fof(f10386,plain,
! [X0,X1] : rd(ld(X0,X0),ld(X1,ld(X0,X0))) = mult(ld(X0,X0),X1),
inference(paramodulation,[status(thm)],[f5337,f10379]) ).
fof(f10411,plain,
! [X0,X1] : X0 = mult(ld(X1,X1),X0),
inference(forward_demodulation,[status(thm)],[f21,f10386]) ).
fof(f10427,plain,
! [X0,X1] : ld(ld(X0,X0),X1) = X1,
inference(paramodulation,[status(thm)],[f8,f10411]) ).
fof(f10657,plain,
! [X0,X1] : rd(X0,ld(X0,X0)) = mult(X0,ld(X1,X1)),
inference(paramodulation,[status(thm)],[f10427,f10379]) ).
fof(f10702,plain,
! [X0,X1] : X0 = mult(X0,ld(X1,X1)),
inference(forward_demodulation,[status(thm)],[f21,f10657]) ).
fof(f11419,plain,
! [X0] : mult(ld(X0,X0),sK1_skl(ld(X0,X0))) != sK1_skl(ld(X0,X0)),
inference(resolution,[status(thm)],[f10702,f16]) ).
fof(f11545,plain,
! [X0] : sK1_skl(ld(X0,X0)) != sK1_skl(ld(X0,X0)),
inference(forward_demodulation,[status(thm)],[f10411,f11419]) ).
fof(f11546,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f11545]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP659+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.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 20:30:25 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 3.56/0.86 % Refutation found
% 3.56/0.86 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.56/0.86 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.90 % Elapsed time: 0.531236 seconds
% 0.23/0.90 % CPU time: 3.957887 seconds
% 0.23/0.90 % Total memory used: 206.496 MB
% 0.23/0.90 % Net memory used: 205.378 MB
%------------------------------------------------------------------------------