%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GEO474+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:25:06 PM UTC 2026
% Result : Theorem 2.43s 3.14s
% Output : CNFRefutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 7 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 29 ( 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f200,axiom,
! [N0] : s(num,i(s(fun(num,num),numeral),s(num,N0))) = s(num,N0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3502,axiom,
! [M,N,A5] :
( s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(num,num),numeral),s(num,u_0)))
<=> s(cart(cart(real,M),N),A5) = s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3503,conjecture,
! [Q133117,Q133118] : s(num,i(s(fun(cart(cart(real,Q133117),Q133118),num),rank),s(cart(cart(real,Q133117),Q133118),i(s(fun(num,cart(cart(real,Q133117),Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3504,negated_conjecture,
~ ! [Q133117,Q133118] : s(num,i(s(fun(cart(cart(real,Q133117),Q133118),num),rank),s(cart(cart(real,Q133117),Q133118),i(s(fun(num,cart(cart(real,Q133117),Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))),
inference(negated_conjecture,[status(cth)],[f3503]) ).
fof(f4521,plain,
! [X0] : s(num,i(s(fun(num,num),numeral),s(num,X0))) = s(num,X0),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f15465,plain,
! [M,N,A5] :
( ( s(cart(cart(real,M),N),A5) != s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) )
& ( s(cart(cart(real,M),N),A5) = s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) ) ),
inference(NNF_transformation,[status(thm)],[f3502]) ).
fof(f15466,plain,
( ! [M,N,A5] :
( s(cart(cart(real,M),N),A5) != s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) )
& ! [M,N,A5] :
( s(cart(cart(real,M),N),A5) = s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) != s(num,i(s(fun(num,num),numeral),s(num,u_0))) ) ),
inference(miniscoping,[status(thm)],[f15465]) ).
fof(f15468,plain,
! [X0,X1,X2] :
( s(cart(cart(real,X0),X1),X2) != s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),X2))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) ),
inference(cnf_transformation,[status(thm)],[f15466]) ).
fof(f15469,plain,
? [Q133117,Q133118] : s(num,i(s(fun(cart(cart(real,Q133117),Q133118),num),rank),s(cart(cart(real,Q133117),Q133118),i(s(fun(num,cart(cart(real,Q133117),Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) != s(num,i(s(fun(num,num),numeral),s(num,u_0))),
inference(pre_NNF_transformation,[status(thm)],[f3504]) ).
fof(f15470,plain,
s(num,i(s(fun(cart(cart(real,sK3705_skl),sK3706_skl),num),rank),s(cart(cart(real,sK3705_skl),sK3706_skl),i(s(fun(num,cart(cart(real,sK3705_skl),sK3706_skl)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) != s(num,i(s(fun(num,num),numeral),s(num,u_0))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3705_skl,sK3706_skl]),skolemize(Q133117,sK3705_skl),skolemize(Q133118,sK3706_skl)],[f15469]) ).
fof(f15471,plain,
s(num,i(s(fun(cart(cart(real,sK3705_skl),sK3706_skl),num),rank),s(cart(cart(real,sK3705_skl),sK3706_skl),i(s(fun(num,cart(cart(real,sK3705_skl),sK3706_skl)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) != s(num,i(s(fun(num,num),numeral),s(num,u_0))),
inference(cnf_transformation,[status(thm)],[f15470]) ).
fof(f18042,plain,
s(num,i(s(fun(cart(cart(real,sK3705_skl),sK3706_skl),num),rank),s(cart(cart(real,sK3705_skl),sK3706_skl),i(s(fun(num,cart(cart(real,sK3705_skl),sK3706_skl)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) != s(num,u_0),
inference(backward_demodulation,[status(thm)],[f4521,f15471]) ).
fof(f18048,plain,
s(num,i(s(fun(cart(cart(real,sK3705_skl),sK3706_skl),num),rank),s(cart(cart(real,sK3705_skl),sK3706_skl),i(s(fun(num,cart(cart(real,sK3705_skl),sK3706_skl)),mat),s(num,u_0))))) != s(num,u_0),
inference(forward_demodulation,[status(thm)],[f4521,f18042]) ).
fof(f18113,plain,
! [X0,X1,X2] :
( s(cart(cart(real,X0),X1),X2) != s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),X2))) = s(num,u_0) ),
inference(forward_demodulation,[status(thm)],[f4521,f15468]) ).
fof(f18114,plain,
! [X0,X1,X2] :
( s(cart(cart(real,X0),X1),X2) != s(cart(cart(real,X0),X1),i(s(fun(num,cart(cart(real,X0),X1)),mat),s(num,u_0)))
| s(num,i(s(fun(cart(cart(real,X0),X1),num),rank),s(cart(cart(real,X0),X1),X2))) = s(num,u_0) ),
inference(forward_demodulation,[status(thm)],[f4521,f18113]) ).
fof(f18115,plain,
s(cart(cart(real,sK3705_skl),sK3706_skl),i(s(fun(num,cart(cart(real,sK3705_skl),sK3706_skl)),mat),s(num,u_0))) != s(cart(cart(real,sK3705_skl),sK3706_skl),i(s(fun(num,cart(cart(real,sK3705_skl),sK3706_skl)),mat),s(num,u_0))),
inference(resolution,[status(thm)],[f18114,f18048]) ).
fof(f18122,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f18115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO474+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 16:32:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 2.26/2.56 % Drodi V4.1.1
% 2.43/3.14 % Refutation found
% 2.43/3.14 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.43/3.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.98/3.37 % Elapsed time: 2.956131 seconds
% 2.98/3.37 % CPU time: 6.847395 seconds
% 2.98/3.37 % Total memory used: 1.580 GB
% 2.98/3.37 % Net memory used: 1.577 GB
%------------------------------------------------------------------------------