%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP658+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 : n017.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 3.12s 0.87s
% Output : CNFRefutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 34 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 11 ~; 4 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 7 ( 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 : 92 ( 87 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,A] : mult(A,ld(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,B)),C) = mult(mult(A,B),mult(B,C)),
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(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,X1)),X2) = mult(mult(X0,X1),mult(X1,X2)),
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(f29,plain,
! [X0,X1,X2] : X0 = mult(mult(X1,X2),mult(X2,ld(mult(X1,mult(X2,X2)),X0))),
inference(paramodulation,[status(thm)],[f8,f12]) ).
fof(f31,plain,
! [X0,X1,X2] : mult(X0,X1) = mult(mult(rd(X0,mult(X2,X2)),X2),mult(X2,X1)),
inference(paramodulation,[status(thm)],[f10,f12]) ).
fof(f34,plain,
! [X0,X1,X2] : rd(mult(mult(X0,X1),mult(X1,X2)),X2) = mult(X0,mult(X1,X1)),
inference(paramodulation,[status(thm)],[f12,f11]) ).
fof(f49,plain,
! [X0,X1,X2] : rd(X0,mult(X1,ld(mult(X2,mult(X1,X1)),X0))) = mult(X2,X1),
inference(paramodulation,[status(thm)],[f29,f11]) ).
fof(f63,plain,
! [X0,X1,X2] : mult(X0,ld(X1,X2)) = mult(mult(rd(X0,mult(X1,X1)),X1),X2),
inference(paramodulation,[status(thm)],[f8,f31]) ).
fof(f66,plain,
! [X0,X1,X2] : X0 = mult(mult(mult(rd(X1,mult(X2,X2)),X2),X2),mult(X2,ld(mult(X1,X2),X0))),
inference(paramodulation,[status(thm)],[f31,f29]) ).
fof(f81,plain,
! [X0,X1,X2] : rd(mult(X0,mult(X1,X2)),X2) = mult(rd(X0,X1),mult(X1,X1)),
inference(paramodulation,[status(thm)],[f10,f34]) ).
fof(f251,plain,
! [X0,X1,X2] : rd(X0,mult(X1,ld(X2,X0))) = mult(rd(X2,mult(X1,X1)),X1),
inference(paramodulation,[status(thm)],[f10,f49]) ).
fof(f802,plain,
! [X0,X1] : rd(X0,X0) = mult(rd(X1,mult(X1,X1)),X1),
inference(paramodulation,[status(thm)],[f8,f251]) ).
fof(f892,plain,
! [X0,X1,X2] : mult(X0,ld(X0,X1)) = mult(rd(X2,X2),X1),
inference(paramodulation,[status(thm)],[f802,f63]) ).
fof(f910,plain,
! [X0,X1] : rd(rd(X0,X0),X1) = rd(X1,mult(X1,X1)),
inference(paramodulation,[status(thm)],[f802,f11]) ).
fof(f927,plain,
! [X0,X1] : X0 = mult(rd(X1,X1),X0),
inference(forward_demodulation,[status(thm)],[f8,f892]) ).
fof(f1155,plain,
! [X0,X1,X2] : rd(mult(X0,X1),X1) = mult(rd(rd(X2,X2),X0),mult(X0,X0)),
inference(paramodulation,[status(thm)],[f927,f81]) ).
fof(f1203,plain,
! [X0,X1] : X0 = mult(rd(rd(X1,X1),X0),mult(X0,X0)),
inference(forward_demodulation,[status(thm)],[f11,f1155]) ).
fof(f1999,plain,
! [X0,X1,X2] : rd(rd(X0,X0),X1) = rd(rd(X2,X2),X1),
inference(paramodulation,[status(thm)],[f910,f910]) ).
fof(f3555,plain,
! [X0,X1,X2] : X0 = mult(rd(rd(X1,X1),rd(X2,X2)),X0),
inference(paramodulation,[status(thm)],[f1999,f927]) ).
fof(f4308,plain,
! [X0,X1,X2] : X0 = mult(mult(X1,ld(X2,X2)),mult(X2,ld(mult(X1,X2),X0))),
inference(forward_demodulation,[status(thm)],[f63,f66]) ).
fof(f4316,plain,
! [X0,X1,X2,X3] : X0 = mult(ld(X1,X1),mult(X1,ld(mult(rd(rd(X2,X2),rd(X3,X3)),X1),X0))),
inference(paramodulation,[status(thm)],[f3555,f4308]) ).
fof(f4397,plain,
! [X0,X1] : X0 = mult(ld(X1,X1),mult(X1,ld(X1,X0))),
inference(forward_demodulation,[status(thm)],[f3555,f4316]) ).
fof(f4398,plain,
! [X0,X1] : X0 = mult(ld(X1,X1),X0),
inference(forward_demodulation,[status(thm)],[f8,f4397]) ).
fof(f4501,plain,
! [X0,X1] : ld(X0,X0) = mult(rd(rd(X1,X1),ld(X0,X0)),ld(X0,X0)),
inference(paramodulation,[status(thm)],[f4398,f1203]) ).
fof(f4646,plain,
! [X0,X1] : ld(X0,X0) = rd(X1,X1),
inference(forward_demodulation,[status(thm)],[f10,f4501]) ).
fof(f5053,plain,
! [X0,X1] : mult(X0,rd(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f4646,f8]) ).
fof(f5251,plain,
! [X0] : mult(rd(X0,X0),sK1_skl(rd(X0,X0))) != sK1_skl(rd(X0,X0)),
inference(resolution,[status(thm)],[f5053,f16]) ).
fof(f5338,plain,
! [X0] : sK1_skl(rd(X0,X0)) != sK1_skl(rd(X0,X0)),
inference(forward_demodulation,[status(thm)],[f927,f5251]) ).
fof(f5339,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f5338]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP658+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:24:57 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 3.12/0.87 % Refutation found
% 3.12/0.87 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.12/0.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.12/0.91 % Elapsed time: 0.528166 seconds
% 3.12/0.91 % CPU time: 3.791841 seconds
% 3.12/0.91 % Total memory used: 176.275 MB
% 3.12/0.91 % Net memory used: 173.983 MB
%------------------------------------------------------------------------------