TPTP Problem File: SWX110_1.p
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%------------------------------------------------------------------------------
% File : SWX000_1 : TPTP v9.1.0. Released v9.1.0.
% Domain : Software Verification
% Problem : Anthem problem formula_5_left_0
% 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 : 37 ( 3 unt; 16 typ; 0 def)
% Number of atoms : 167 ( 109 equ)
% Maximal formula atoms : 52 ( 7 avg)
% Number of connectives : 150 ( 4 ~; 4 |; 122 &)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 100 ( 17 atm; 10 fun; 22 num; 51 var)
% Number of types : 4 ( 2 usr; 1 ari)
% Number of type conns : 16 ( 12 >; 4 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 0 prp; 1-2 aty)
% Number of functors : 9 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 125 ( 39 !; 86 ?; 125 :)
% SPC : TF0_THM_EQU_ARI
% Comments :From https://github.com/ZachJHansen/anthem-benchmarks/tree/tptp
%------------------------------------------------------------------------------
include('Axioms/SWV014_0.ax').
%------------------------------------------------------------------------------
tff(predicate_0,type,
hcomposite: general > $o ).
tff(predicate_1,type,
tcomposite: general > $o ).
tff(predicate_2,type,
hprime: general > $o ).
tff(predicate_3,type,
tprime: general > $o ).
tff(formula_0_transition_axiom_0,axiom,
! [X1_g: general] :
( hcomposite(X1_g)
=> tcomposite(X1_g) ) ).
tff(formula_1_transition_axiom_1,axiom,
! [X1_g: general] :
( hprime(X1_g)
=> tprime(X1_g) ) ).
tff(formula_2_right_0,axiom,
! [I_g: general,J_g: general,N_g: general,V1_g: general] :
( ( ( ? [I1_i: $int,J1_i: $int] :
( ( V1_g = f__integer__($product(I1_i,J1_i)) )
& ( f__integer__(I1_i) = I_g )
& ( f__integer__(J1_i) = J_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = I_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 2 )
& ( f__integer__(J_i) = N_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 )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 2 )
& ( f__integer__(J_i) = N_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 = N_g )
& ( Z1_g = f__integer__(2) )
& p__greater__(Z_g,Z1_g) )
& ? [Z_g: general,Z1_g: general] :
( ? [I_i: $int,J_i: $int] :
( ( Z_g = f__integer__($sum(I_i,J_i)) )
& ( f__integer__(I_i) = N_g )
& ( J_i = 0 ) )
& ( Z1_g = N_g )
& ( Z_g = Z1_g ) ) )
=> hcomposite(V1_g) )
& ( ( ? [I1_i: $int,J1_i: $int] :
( ( V1_g = f__integer__($product(I1_i,J1_i)) )
& ( f__integer__(I1_i) = I_g )
& ( f__integer__(J1_i) = J_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = I_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 2 )
& ( f__integer__(J_i) = N_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 )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 2 )
& ( f__integer__(J_i) = N_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 = N_g )
& ( Z1_g = f__integer__(2) )
& p__greater__(Z_g,Z1_g) )
& ? [Z_g: general,Z1_g: general] :
( ? [I_i: $int,J_i: $int] :
( ( Z_g = f__integer__($sum(I_i,J_i)) )
& ( f__integer__(I_i) = N_g )
& ( J_i = 0 ) )
& ( Z1_g = N_g )
& ( Z_g = Z1_g ) ) )
=> tcomposite(V1_g) ) ) ).
tff(formula_3_right_1,axiom,
! [V1_g: general] :
( ( ( ( V1_g = f__integer__(4) )
& ? [Z_g: general] :
( ( Z_g = f__integer__(4) )
& hcomposite(Z_g) ) )
=> hcomposite(V1_g) )
& ( ( ( V1_g = f__integer__(4) )
& ? [Z_g: general] :
( ( Z_g = f__integer__(4) )
& tcomposite(Z_g) ) )
=> tcomposite(V1_g) ) ) ).
tff(formula_4_right_2,axiom,
! [I_g: general,V1_g: general] :
( ( ( ( V1_g = I_g )
& ? [Z_g: general,Z1_g: general] :
( ? [I1_i: $int,J_i: $int] :
( ( Z_g = f__integer__($sum(I1_i,J_i)) )
& ( f__integer__(I1_i) = I_g )
& ( J_i = 0 ) )
& ( Z1_g = I_g )
& ( Z_g = Z1_g ) )
& ? [Z_g: general] :
( ( Z_g = I_g )
& ~ tcomposite(Z_g) ) )
=> hprime(V1_g) )
& ( ( ( V1_g = I_g )
& ? [Z_g: general,Z1_g: general] :
( ? [I1_i: $int,J_i: $int] :
( ( Z_g = f__integer__($sum(I1_i,J_i)) )
& ( f__integer__(I1_i) = I_g )
& ( J_i = 0 ) )
& ( Z1_g = I_g )
& ( Z_g = Z1_g ) )
& ? [Z_g: general] :
( ( Z_g = I_g )
& ~ tcomposite(Z_g) ) )
=> tprime(V1_g) ) ) ).
tff(formula_5_left_0,conjecture,
! [I_g: general,J_g: general,N_g: general,V1_g: general] :
( ( ( ? [I1_i: $int,J1_i: $int] :
( ( V1_g = f__integer__($product(I1_i,J1_i)) )
& ( f__integer__(I1_i) = I_g )
& ( f__integer__(J1_i) = J_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = I_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 2 )
& ( f__integer__(J_i) = N_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 )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 2 )
& ( f__integer__(J_i) = N_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 = N_g )
& ( Z1_g = f__integer__(2) )
& p__greater__(Z_g,Z1_g) )
& ? [Z_g: general,Z1_g: general] :
( ? [I_i: $int,J_i: $int] :
( ( Z_g = f__integer__($sum(I_i,J_i)) )
& ( f__integer__(I_i) = N_g )
& ( J_i = 0 ) )
& ( Z1_g = N_g )
& ( Z_g = Z1_g ) ) )
=> hcomposite(V1_g) )
& ( ( ? [I1_i: $int,J1_i: $int] :
( ( V1_g = f__integer__($product(I1_i,J1_i)) )
& ( f__integer__(I1_i) = I_g )
& ( f__integer__(J1_i) = J_g ) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = I_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 2 )
& ( f__integer__(J_i) = N_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 )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 2 )
& ( f__integer__(J_i) = N_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 = N_g )
& ( Z1_g = f__integer__(2) )
& p__greater__(Z_g,Z1_g) )
& ? [Z_g: general,Z1_g: general] :
( ? [I_i: $int,J_i: $int] :
( ( Z_g = f__integer__($sum(I_i,J_i)) )
& ( f__integer__(I_i) = N_g )
& ( J_i = 0 ) )
& ( Z1_g = N_g )
& ( Z_g = Z1_g ) ) )
=> tcomposite(V1_g) ) ) ).
%------------------------------------------------------------------------------