%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO474+1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:26:49 EDT 2022
% Result : Theorem 238.31s 238.55s
% Output : CNFRefutation 238.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 24
% Syntax : Number of formulae : 67 ( 31 unt; 0 def)
% Number of atoms : 119 ( 118 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 109 ( 57 ~; 48 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 24 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aNUMERAL,axiom,
! [N0] : s(num,i(s(fun(num,num),numeral),s(num,N0))) = s(num,N0) ).
fof(aRANKu_EQu_0,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))))) ) ).
fof(aRANKu_0,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))) ).
fof(subgoal_0,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(strip,[],[aRANKu_0]) ).
fof(negate_0_0,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(negate,[],[subgoal_0]) ).
fof(normalize_0_0,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(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_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(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A5,M,N] :
( 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(canonicalize,[],[aRANKu_EQu_0]) ).
fof(normalize_0_3,plain,
! [A5,M,N] :
( 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(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A5,M,N] :
( ( 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(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))))) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A5,M,N] :
( 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(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [N0] : s(num,i(s(fun(num,num),numeral),s(num,N0))) = s(num,N0),
inference(canonicalize,[],[aNUMERAL]) ).
fof(normalize_0_7,plain,
! [N0] : s(num,i(s(fun(num,num),numeral),s(num,N0))) = s(num,N0),
inference(specialize,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_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(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( 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(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
s(num,i(s(fun(num,num),numeral),s(num,N0))) = s(num,N0),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
s(num,i(s(fun(num,num),numeral),s(num,u_0))) = s(num,u_0),
inference(subst,[],[refute_0_2:[bind(N0,$fot(u_0))]]) ).
cnf(refute_0_4,plain,
i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) = i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))),
introduced(tautology,[refl,[$fot(i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))]]) ).
cnf(refute_0_5,plain,
( i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) != 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(num,num),numeral),s(num,u_0))) != s(num,u_0)
| i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) = i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0)) ),
introduced(tautology,[equality,[$cnf( $equal(i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ),[1,1],$fot(s(num,u_0))]]) ).
cnf(refute_0_6,plain,
( s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,u_0)
| i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) = i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0)) ),
inference(resolve,[$cnf( $equal(i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) = i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0)),
inference(resolve,[$cnf( $equal(s(num,i(s(fun(num,num),numeral),s(num,u_0))),s(num,u_0)) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
introduced(tautology,[refl,[$fot(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))))))]]) ).
cnf(refute_0_9,plain,
( i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) != i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))
| 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(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(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(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))) ),
introduced(tautology,[equality,[$cnf( $equal(s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) ),[1,1],$fot(i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0)))]]) ).
cnf(refute_0_10,plain,
( i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) != i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))
| 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(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))) ),
inference(resolve,[$cnf( $equal(s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))),
inference(resolve,[$cnf( $equal(i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( s(cart(cart(real,M),N),A5) != s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0)))
| s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0)))
| s(cart(cart(real,M),N),A5) = s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(s(cart(cart(real,M),N),A5),s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) ),[1],$fot(s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))))]]) ).
cnf(refute_0_13,plain,
( 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,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))))) ),
inference(resolve,[$cnf( $equal(s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0)))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( s(cart(cart(real,M),N),A5) != s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0)))
| s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) ),
inference(resolve,[$cnf( $equal(s(cart(cart(real,M),N),A5),s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) )],[refute_0_13,refute_0_1]) ).
cnf(refute_0_15,plain,
( s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) != s(num,i(s(fun(num,num),numeral),s(num,u_0)))
| s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,u_0)
| s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,u_0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))),s(num,u_0)) ),[0],$fot(s(num,i(s(fun(num,num),numeral),s(num,u_0))))]]) ).
cnf(refute_0_16,plain,
( 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(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,u_0) ),
inference(resolve,[$cnf( $equal(s(num,i(s(fun(num,num),numeral),s(num,u_0))),s(num,u_0)) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( s(cart(cart(real,M),N),A5) != s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0)))
| s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))) = s(num,u_0) ),
inference(resolve,[$cnf( $equal(s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),A5))),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))) != s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0)))
| s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))))) = s(num,u_0) ),
inference(subst,[],[refute_0_17:[bind(A5,$fot(i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))))]]) ).
cnf(refute_0_19,plain,
s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))) = s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))),
introduced(tautology,[refl,[$fot(s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))))]]) ).
cnf(refute_0_20,plain,
s(num,i(s(fun(cart(cart(real,M),N),num),rank),s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))))) = s(num,u_0),
inference(resolve,[$cnf( $equal(s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0))),s(cart(cart(real,M),N),i(s(fun(num,cart(cart(real,M),N)),mat),s(num,u_0)))) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))) = s(num,u_0),
inference(subst,[],[refute_0_20:[bind(M,$fot(skolemFOFtoCNF_Q133117)),bind(N,$fot(skolemFOFtoCNF_Q133118))]]) ).
cnf(refute_0_22,plain,
i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) = i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))),
introduced(tautology,[refl,[$fot(i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))]]) ).
cnf(refute_0_23,plain,
( i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) != i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_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))) != s(num,u_0)
| i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) = i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)) ),
introduced(tautology,[equality,[$cnf( $equal(i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) ),[1,1],$fot(s(num,u_0))]]) ).
cnf(refute_0_24,plain,
( s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,u_0)
| i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) = i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)) ),
inference(resolve,[$cnf( $equal(i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) = i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)),
inference(resolve,[$cnf( $equal(s(num,i(s(fun(num,num),numeral),s(num,u_0))),s(num,u_0)) )],[refute_0_3,refute_0_24]) ).
cnf(refute_0_26,plain,
s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),
introduced(tautology,[refl,[$fot(s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))]]) ).
cnf(refute_0_27,plain,
( i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) != i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))
| s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))
| s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))) ),
introduced(tautology,[equality,[$cnf( $equal(s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) ),[1,1],$fot(i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)))]]) ).
cnf(refute_0_28,plain,
( i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) != i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))
| s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))) ),
inference(resolve,[$cnf( $equal(s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) = s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))),
inference(resolve,[$cnf( $equal(i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) = i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))),
introduced(tautology,[refl,[$fot(i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))]]) ).
cnf(refute_0_31,plain,
( i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) != i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))
| s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)))
| i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) = i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)))) ),
introduced(tautology,[equality,[$cnf( $equal(i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))),i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) ),[1,1],$fot(s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))]]) ).
cnf(refute_0_32,plain,
( s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))) != s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)))
| i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) = i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)))) ),
inference(resolve,[$cnf( $equal(i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))),i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) = i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)))),
inference(resolve,[$cnf( $equal(s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),
introduced(tautology,[refl,[$fot(s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))]]) ).
cnf(refute_0_35,plain,
( i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) != i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))
| s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) != s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))
| s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))) ),
introduced(tautology,[equality,[$cnf( $equal(s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) ),[1,1],$fot(i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)))))]]) ).
cnf(refute_0_36,plain,
( i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))) != i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))
| s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))) ),
inference(resolve,[$cnf( $equal(s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))),
inference(resolve,[$cnf( $equal(i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0)))))),i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_39,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_40,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_42,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) != s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)))))
| s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))) != s(num,u_0)
| s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,u_0) ),
inference(subst,[],[refute_0_42:[bind(X,$fot(s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))))),bind(Y,$fot(s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))))),bind(Z,$fot(s(num,u_0)))]]) ).
cnf(refute_0_44,plain,
( s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))) != s(num,u_0)
| s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,u_0) ),
inference(resolve,[$cnf( $equal(s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0)))))) )],[refute_0_37,refute_0_43]) ).
cnf(refute_0_45,plain,
s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,u_0),
inference(resolve,[$cnf( $equal(s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,u_0))))),s(num,u_0)) )],[refute_0_21,refute_0_44]) ).
cnf(refute_0_46,plain,
( s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) != s(num,u_0)
| s(num,u_0) != s(num,i(s(fun(num,num),numeral),s(num,u_0)))
| s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) ),[0],$fot(s(num,u_0))]]) ).
cnf(refute_0_47,plain,
( s(num,u_0) != s(num,i(s(fun(num,num),numeral),s(num,u_0)))
| s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_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(resolve,[$cnf( $equal(s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(num,u_0)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( s(num,i(s(fun(num,num),numeral),s(num,u_0))) != s(num,u_0)
| s(num,u_0) != s(num,u_0)
| s(num,u_0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(s(num,u_0),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) ),[1],$fot(s(num,u_0))]]) ).
cnf(refute_0_49,plain,
( s(num,u_0) != s(num,u_0)
| s(num,u_0) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) ),
inference(resolve,[$cnf( $equal(s(num,i(s(fun(num,num),numeral),s(num,u_0))),s(num,u_0)) )],[refute_0_3,refute_0_48]) ).
cnf(refute_0_50,plain,
( s(num,u_0) != s(num,u_0)
| s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))) = s(num,i(s(fun(num,num),numeral),s(num,u_0))) ),
inference(resolve,[$cnf( $equal(s(num,u_0),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) )],[refute_0_49,refute_0_47]) ).
cnf(refute_0_51,plain,
s(num,u_0) != s(num,u_0),
inference(resolve,[$cnf( $equal(s(num,i(s(fun(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),num),rank),s(cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118),i(s(fun(num,cart(cart(real,skolemFOFtoCNF_Q133117),skolemFOFtoCNF_Q133118)),mat),s(num,i(s(fun(num,num),numeral),s(num,u_0))))))),s(num,i(s(fun(num,num),numeral),s(num,u_0)))) )],[refute_0_50,refute_0_0]) ).
cnf(refute_0_52,plain,
s(num,u_0) = s(num,u_0),
introduced(tautology,[refl,[$fot(s(num,u_0))]]) ).
cnf(refute_0_53,plain,
$false,
inference(resolve,[$cnf( $equal(s(num,u_0),s(num,u_0)) )],[refute_0_52,refute_0_51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO474+1 : TPTP v8.1.0. Released v7.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 10:09:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 238.31/238.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 238.31/238.55
% 238.31/238.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 238.31/238.57
%------------------------------------------------------------------------------