TPTP Problem File: SWX095_1.p
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%------------------------------------------------------------------------------
% File : SWX000_1 : TPTP v9.1.0. Released v9.1.0.
% Domain : Software Verification
% Problem : Anthem problem formula_7_base_case
% Version : Especial.
% English :
% Refs : [FL+20] Fandinno et al. (2020), Verifying Tight Logic Programs
% : [FH+23] Fandinno et al. (2023), External Behavior of a Logic P
% : [Han25] Hansen (2025), Email to Geoff Sutcliffe
% Source : [Han25]
% Names :
% Status : Theorem
% Rating : 0.75 v9.1.0
% Syntax : Number of formulae : 41 ( 5 unt; 18 typ; 0 def)
% Number of atoms : 164 ( 105 equ)
% Maximal formula atoms : 45 ( 7 avg)
% Number of connectives : 144 ( 3 ~; 4 |; 121 &)
% ( 13 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 138 ( 26 atm; 24 fun; 18 num; 70 var)
% Number of types : 4 ( 2 usr; 1 ari)
% Number of type conns : 18 ( 13 >; 5 *; 0 +; 0 <<)
% Number of predicates : 15 ( 11 usr; 0 prp; 1-2 aty)
% Number of functors : 9 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 136 ( 34 !; 102 ?; 136 :)
% SPC : TF0_THM_EQU_ARI
% Comments :From https://github.com/ZachJHansen/anthem-benchmarks/tree/tptp
%------------------------------------------------------------------------------
include('Axioms/SWV014_0.ax').
%------------------------------------------------------------------------------
tff(predicate_0,type,
three: general > $o ).
tff(predicate_1,type,
sqrt: general > $o ).
tff(predicate_2,type,
three_p: general > $o ).
tff(predicate_3,type,
more_than_three: general > $o ).
tff(predicate_4,type,
sqrt: ( general * general ) > $o ).
tff(type_function_constant_0,type,
n_i: $int ).
tff(formula_0_unnamed_formula,axiom,
$greatereq(n_i,1) ).
tff(formula_1_completed_definition_of_three_1,axiom,
! [V1_g: general] :
( three(V1_g)
<=> ? [N_g: general,I_g: general,J_g: general,K_g: general] :
( ( V1_g = N_g )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = N_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 1 )
& ( J_i = n_i )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I_i,K_i)
& $lesseq(K_i,J_i) )
& ( Z_g = Z1_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = I_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 0 )
& ( J_i = n_i )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I_i,K_i)
& $lesseq(K_i,J_i) )
& ( Z_g = Z1_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = J_g )
& ? [I1_i: $int,J_i: $int,K_i: $int] :
( ( f__integer__(I1_i) = I_g )
& ( J_i = n_i )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I1_i,K_i)
& $lesseq(K_i,J_i) )
& ( Z_g = Z1_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = K_g )
& ? [I_i: $int,J1_i: $int,K_i: $int] :
( ( f__integer__(I_i) = J_g )
& ( J1_i = n_i )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I_i,K_i)
& $lesseq(K_i,J1_i) )
& ( Z_g = Z1_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = N_g )
& ? [I1_i: $int,J1_i: $int] :
( ( Z1_g = f__integer__($sum(I1_i,J1_i)) )
& ? [I2_i: $int,J1_i: $int] :
( ( I1_i = $sum(I2_i,J1_i) )
& ? [I1_i: $int,J_i: $int] :
( ( I2_i = $product(I1_i,J_i) )
& ( f__integer__(I1_i) = I_g )
& ( f__integer__(J_i) = I_g ) )
& ? [I_i: $int,J2_i: $int] :
( ( J1_i = $product(I_i,J2_i) )
& ( f__integer__(I_i) = J_g )
& ( f__integer__(J2_i) = J_g ) ) )
& ? [I_i: $int,J_i: $int] :
( ( J1_i = $product(I_i,J_i) )
& ( f__integer__(I_i) = K_g )
& ( f__integer__(J_i) = K_g ) ) )
& ( Z_g = Z1_g ) ) ) ) ).
tff(formula_2_completed_definition_of_sqrt_1,axiom,
! [V1_g: general] :
( sqrt(V1_g)
<=> ? [S_g: general] :
( ( V1_g = S_g )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = S_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 1 )
& ( J_i = n_i )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I_i,K_i)
& $lesseq(K_i,J_i) )
& ( Z_g = Z1_g ) )
& ? [Z_g: general,Z1_g: general] :
( ? [I_i: $int,J_i: $int] :
( ( Z_g = f__integer__($product(I_i,J_i)) )
& ( f__integer__(I_i) = S_g )
& ( f__integer__(J_i) = S_g ) )
& ( Z1_g = f__integer__(n_i) )
& p__less_equal__(Z_g,Z1_g) )
& ? [Z_g: general,Z1_g: general] :
( ? [I_i: $int,J_i: $int] :
( ( Z_g = f__integer__($product(I_i,J_i)) )
& ? [I1_i: $int,J_i: $int] :
( ( I_i = $sum(I1_i,J_i) )
& ( f__integer__(I1_i) = S_g )
& ( J_i = 1 ) )
& ? [I_i: $int,J1_i: $int] :
( ( J_i = $sum(I_i,J1_i) )
& ( f__integer__(I_i) = S_g )
& ( J1_i = 1 ) ) )
& ( Z1_g = f__integer__(n_i) )
& p__greater__(Z_g,Z1_g) ) ) ) ).
tff(formula_3_completed_definition_of_three_1,axiom,
! [V1_g: general] :
( three_p(V1_g)
<=> ? [N_g: general,S_g: general,I_g: general,J_g: general,K_g: general] :
( ( V1_g = N_g )
& ? [Z_g: general] :
( ( Z_g = S_g )
& sqrt(Z_g) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = N_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 1 )
& ( J_i = n_i )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I_i,K_i)
& $lesseq(K_i,J_i) )
& ( Z_g = Z1_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = I_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 0 )
& ( f__integer__(J_i) = S_g )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I_i,K_i)
& $lesseq(K_i,J_i) )
& ( Z_g = Z1_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = J_g )
& ? [I1_i: $int,J_i: $int,K_i: $int] :
( ( f__integer__(I1_i) = I_g )
& ( f__integer__(J_i) = S_g )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I1_i,K_i)
& $lesseq(K_i,J_i) )
& ( Z_g = Z1_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = K_g )
& ? [I_i: $int,J1_i: $int,K_i: $int] :
( ( f__integer__(I_i) = J_g )
& ( f__integer__(J1_i) = S_g )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I_i,K_i)
& $lesseq(K_i,J1_i) )
& ( Z_g = Z1_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = N_g )
& ? [I1_i: $int,J1_i: $int] :
( ( Z1_g = f__integer__($sum(I1_i,J1_i)) )
& ? [I2_i: $int,J1_i: $int] :
( ( I1_i = $sum(I2_i,J1_i) )
& ? [I1_i: $int,J_i: $int] :
( ( I2_i = $product(I1_i,J_i) )
& ( f__integer__(I1_i) = I_g )
& ( f__integer__(J_i) = I_g ) )
& ? [I_i: $int,J2_i: $int] :
( ( J1_i = $product(I_i,J2_i) )
& ( f__integer__(I_i) = J_g )
& ( f__integer__(J2_i) = J_g ) ) )
& ? [I_i: $int,J_i: $int] :
( ( J1_i = $product(I_i,J_i) )
& ( f__integer__(I_i) = K_g )
& ( f__integer__(J_i) = K_g ) ) )
& ( Z_g = Z1_g ) ) ) ) ).
tff(formula_4_completed_definition_of_more_than_three_1,axiom,
! [V1_g: general] :
( more_than_three(V1_g)
<=> ? [N_g: general] :
( ( V1_g = N_g )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = N_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 1 )
& ( J_i = n_i )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I_i,K_i)
& $lesseq(K_i,J_i) )
& ( Z_g = Z1_g ) )
& ? [Z_g: general] :
( ( Z_g = N_g )
& ~ three_p(Z_g) ) ) ) ).
tff(formula_5_unnamed_formula,axiom,
! [I_i: $int,N_i: $int] :
( sqrt(f__integer__(I_i),f__integer__(N_i))
<=> ( $greatereq(I_i,0)
& $lesseq($product(I_i,I_i),N_i)
& $less(N_i,$product($sum(I_i,1),$sum(I_i,1))) ) ) ).
tff(formula_6_unnamed_formula,axiom,
! [I_i: $int,N_i: $int] :
( ( sqrt(f__integer__(I_i),f__integer__(N_i))
& $lesseq($product($sum(I_i,1),$sum(I_i,1)),$sum(N_i,1)) )
=> sqrt(f__integer__($sum(I_i,1)),f__integer__($sum(N_i,1))) ) ).
tff(formula_7_base_case,conjecture,
? [I_i: $int] : sqrt(f__integer__(I_i),f__integer__(0)) ).
%------------------------------------------------------------------------------