TPTP Problem File: PRV015+1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : PRV015+1.s : ProoVer 2026
% Proof : Problems/PRV015+1.p
%------------------------------------------------------------------------------
% SZS output start Proof
fof(s0,axiom,
! [X0,X2] :
? [X1] :
~ ( X2 != X1 ),
file('Problems/PRV015+1.p',s0) ).
fof(s1,axiom,
! [X3] :
( ? [X4] : r(g(X4,b),g(X4,c))
=> ! [X5] :
? [X6] : b = a ),
file('Problems/PRV015+1.p',s1) ).
fof(s2,axiom,
! [X7,X9] :
? [X8] :
! [X10] :
? [X11,X12] : t,
file('Problems/PRV015+1.p',s2) ).
fof(s3,axiom,
p(a),
file('Problems/PRV015+1.p',s3) ).
fof(s4,axiom,
( ! [X13] : p(f(f(X13)))
| t ),
file('Problems/PRV015+1.p',s4) ).
fof(c,conjecture,
( ( ! [X31] :
? [X32] : t
=> ( t
& p(g(b,b)) ) )
| ~ ( ! [X31] :
? [X32] : t
=> ( t
& p(g(b,b)) ) )
| q(c) ),
file('Problems/PRV015+1.p',c) ).
fof(s5,plain,
( p(a)
& ! [X3] :
( ? [X4] : r(g(X4,b),g(X4,c))
=> ! [X5] :
? [X6] : b = a ) ),
inference(conjunction,[status(thm)],[s3,s1]) ).
fof(s6,plain,
! [X0,X2] :
~ ( X2 != sK0(X2,X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X2,X0))],[s0]) ).
fof(s7,plain,
( t
| ~ t ),
inference(excluded_middle,[status(thm)],[s2]) ).
fof(s8,plain,
( ! [X0,X2] :
? [X1] :
~ ( X2 != X1 )
| ! [X14] : r(X14,X14)
| ! [X15] :
? [X16] : r(X15,b) ),
inference(weaken,[status(thm)],[s0]) ).
fof(s9,plain,
( ! [X13] : p(f(f(X13)))
| t
| ( ! [X17] : p(X17)
& t
& g(a,b) = f(a) ) ),
inference(weaken,[status(thm)],[s4]) ).
fof(s10,plain,
b = b,
inference(reflexivity,[status(thm)],[s2]) ).
fof(s11,plain,
! [X7,X9,X10] :
? [X11,X12] : t,
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X8,sK1(X7,X9))],[s2]) ).
fof(s12,plain,
~ ~ ! [X7,X9,X10] :
? [X11,X12] : t,
inference(double_negation,[status(thm)],[s11]) ).
fof(s13,plain,
! [X18,X2] :
? [X1] :
~ ( X2 != X1 ),
inference(rename_variable,[status(thm)],[s0]) ).
fof(s14,plain,
? [X19] :
! [X3] :
( ? [X4] : r(g(X4,b),g(X4,c))
=> ! [X5] :
? [X6] : b = X19 ),
inference(existential_gen,[status(thm)],[s1]) ).
fof(s15,plain,
( ! [X20] :
? [X21] : q(b)
| ~ ! [X20] :
? [X21] : q(b) ),
inference(excluded_middle,[status(thm)],[s11]) ).
fof(s16,plain,
( ! [X7,X9] :
? [X8] :
! [X10] :
? [X11,X12] : t
& p(a) ),
inference(conjunction,[status(thm)],[s2,s3]) ).
fof(s17,plain,
( ? [X22] :
! [X23] :
? [X24] : q(X22)
=> ( ! [X0,X2] :
? [X1] :
~ ( X2 != X1 )
| ! [X14] : r(X14,X14)
| ! [X15] :
? [X16] : r(X15,b) ) ),
inference(add_hypothesis,[status(thm)],[s8]) ).
fof(s18,plain,
p(a),
inference(split_conjunct,[status(thm)],[s5]) ).
fof(s19,plain,
! [X25,X9] :
? [X8] :
! [X10] :
? [X11,X12] : t,
inference(rename_variable,[status(thm)],[s2]) ).
fof(s20,plain,
! [X7,X9,X10] :
? [X11,X12] : t,
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X8,sK2(X7,X9))],[s2]) ).
fof(s21,plain,
! [X25,X9,X10] :
? [X11,X12] : t,
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X8,sK3(X9,X25))],[s19]) ).
fof(s22,plain,
? [X26] : p(X26),
inference(existential_gen,[status(thm)],[s18]) ).
fof(s23,plain,
! [X7,X9,X10] :
? [X12] : t,
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X11,sK4(X9,X7,X10))],[s20]) ).
fof(s24,plain,
! [X27,X2] :
? [X1] :
~ ( X2 != X1 ),
inference(rename_variable,[status(thm)],[s13]) ).
fof(s25,plain,
( ! [X7,X9,X10] :
? [X12] : t
& ! [X7,X9,X10] :
? [X11,X12] : t ),
inference(conjunction,[status(thm)],[s23,s20]) ).
fof(s26,plain,
( ! [X28] : ~ r(X28,b)
| ~ ! [X28] : ~ r(X28,b) ),
inference(excluded_middle,[status(thm)],[s15]) ).
fof(s27,plain,
! [X29,X9,X10] :
? [X11,X12] : t,
inference(rename_variable,[status(thm)],[s20]) ).
fof(s28,plain,
! [X30,X2] :
? [X1] :
~ ( X2 != X1 ),
inference(rename_variable,[status(thm)],[s24]) ).
fof(s29,plain,
( ( ! [X31] :
? [X32] : t
=> ( t
& p(g(b,b)) ) )
| ~ ( ! [X31] :
? [X32] : t
=> ( t
& p(g(b,b)) ) ) ),
inference(excluded_middle,[status(thm)],[s24]) ).
fof(s30,plain,
? [X33] : X33 = X33,
inference(existential_gen,[status(thm)],[s10]) ).
fof(s31,plain,
? [X34,X19] :
! [X3] :
( ? [X4] : r(g(X4,b),g(X4,X34))
=> ! [X5] :
? [X6] : b = X19 ),
inference(existential_gen,[status(thm)],[s14]) ).
fof(s32,plain,
? [X35] : p(X35),
inference(existential_gen,[status(thm)],[s18]) ).
fof(s33,plain,
! [X7,X9,X10] :
? [X12] : t,
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X11,sK5(X10,X7,X9))],[s20]) ).
fof(s34,plain,
! [X7,X9,X10] :
? [X12] : t,
inference(split_conjunct,[status(thm)],[s25]) ).
fof(s35,plain,
! [X7,X9,X10] :
? [X11,X12] : t,
inference(remove_double_negation,[status(thm)],[s12]) ).
fof(s36,plain,
? [X36] :
( ! [X13] : p(f(f(X13)))
| t
| ( ! [X17] : p(X17)
& t
& X36 = f(a) ) ),
inference(existential_gen,[status(thm)],[s9]) ).
fof(s37,plain,
! [X27,X2] :
~ ( X2 != sK6(X27,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X1,sK6(X27,X2))],[s24]) ).
fof(s38,plain,
( ! [X3] :
( ? [X4] : r(g(X4,b),g(X4,c))
=> ! [X5] :
? [X6] : b = a )
& p(a) ),
inference(commute,[status(thm)],[s5]) ).
fof(s39,plain,
( ! [X37] :
? [X38] :
! [X39] :
? [X40] : r(X39,X37)
=> ( ! [X7,X9] :
? [X8] :
! [X10] :
? [X11,X12] : t
& p(a) ) ),
inference(add_hypothesis,[status(thm)],[s16]) ).
fof(s40,plain,
( ( ! [X31] :
? [X32] : t
=> ( t
& p(g(b,b)) ) )
| ~ ( ! [X31] :
? [X32] : t
=> ( t
& p(g(b,b)) ) )
| q(c) ),
inference(weaken,[status(thm)],[s29]) ).
fof(negc,negated_conjecture,
~ ( ( ! [X31] :
? [X32] : t
=> ( t
& p(g(b,b)) ) )
| ~ ( ! [X31] :
? [X32] : t
=> ( t
& p(g(b,b)) ) )
| q(c) ),
inference(negated_conjecture,[status(cth)],[c]) ).
fof(bot,plain,
$false,
inference(consequence,[status(thm)],[negc,s40]) ).
% SZS output end Proof