TPTP Problem File: SWX086_1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : SWX000_1 : TPTP v9.1.0. Released v9.1.0.
% Domain : Software Verification
% Problem : Anthem problem formula_9_constraint_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 : 0.62 v9.1.0
% Syntax : Number of formulae : 45 ( 4 unt; 20 typ; 0 def)
% Number of atoms : 133 ( 82 equ)
% Maximal formula atoms : 37 ( 5 avg)
% Number of connectives : 114 ( 6 ~; 6 |; 83 &)
% ( 12 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 35 ( 6 atm; 3 fun; 7 num; 19 var)
% Number of types : 4 ( 2 usr; 1 ari)
% Number of type conns : 27 ( 15 >; 12 *; 0 +; 0 <<)
% Number of predicates : 17 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 123 ( 50 !; 73 ?; 123 :)
% SPC : TF0_THM_EQU_ARI
% Comments :From https://github.com/ZachJHansen/anthem-benchmarks/tree/tptp
%------------------------------------------------------------------------------
include('Axioms/SWV014_0.ax').
%------------------------------------------------------------------------------
tff(predicate_0,type,
in0: ( general * general ) > $o ).
tff(predicate_1,type,
person: general > $o ).
tff(predicate_2,type,
goto: ( general * general * general ) > $o ).
tff(predicate_3,type,
go: ( general * general ) > $o ).
tff(predicate_4,type,
in_building: ( general * general ) > $o ).
tff(predicate_5,type,
in: ( general * general * general ) > $o ).
tff(predicate_6,type,
in_building_p: ( general * general ) > $o ).
tff(type_function_constant_0,type,
h_i: $int ).
tff(formula_0_unnamed_formula,axiom,
$greatereq(h_i,0) ).
tff(formula_1_unnamed_formula,axiom,
! [X_g: general,Y_g: general] :
( in0(X_g,Y_g)
=> person(X_g) ) ).
tff(formula_2_unnamed_formula,axiom,
! [X_g: general,Y_g: general,Z_g: general] :
( goto(X_g,Y_g,Z_g)
=> person(X_g) ) ).
tff(formula_3_completed_definition_of_go_2,axiom,
! [V1_g: general,V2_g: general] :
( go(V1_g,V2_g)
<=> ? [P_g: general,T_g: general,R_g: general] :
( ( V1_g = P_g )
& ( V2_g = T_g )
& ? [Z_g: general,Z1_g: general,Z2_g: general] :
( ( Z_g = P_g )
& ( Z1_g = R_g )
& ( Z2_g = T_g )
& goto(Z_g,Z1_g,Z2_g) ) ) ) ).
tff(formula_4_completed_definition_of_in_building_2,axiom,
! [V1_g: general,V2_g: general] :
( in_building(V1_g,V2_g)
<=> ? [P_g: general,T_g: general,R_g: general] :
( ( V1_g = P_g )
& ( V2_g = T_g )
& ? [Z_g: general,Z1_g: general,Z2_g: general] :
( ( Z_g = P_g )
& ( Z1_g = R_g )
& ( Z2_g = T_g )
& in(Z_g,Z1_g,Z2_g) ) ) ) ).
tff(formula_5_completed_definition_of_in_building_2,axiom,
! [V1_g: general,V2_g: general] :
( in_building_p(V1_g,V2_g)
<=> ? [P_g: general,T_g: general,R_g: general] :
( ( V1_g = P_g )
& ( V2_g = T_g )
& ? [Z_g: general,Z1_g: general,Z2_g: general] :
( ( Z_g = P_g )
& ( Z1_g = R_g )
& ( Z2_g = T_g )
& in(Z_g,Z1_g,Z2_g) ) ) ) ).
tff(formula_6_constraint_0,axiom,
! [P_g: general,R1_g: general,T_g: general,R2_g: general] :
( ( ? [Z_g: general,Z1_g: general,Z2_g: general] :
( ( Z_g = P_g )
& ( Z1_g = R1_g )
& ( Z2_g = T_g )
& in(Z_g,Z1_g,Z2_g) )
& ? [Z_g: general,Z1_g: general,Z2_g: general] :
( ( Z_g = P_g )
& ( Z1_g = R2_g )
& ( Z2_g = T_g )
& in(Z_g,Z1_g,Z2_g) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = R1_g )
& ( Z1_g = R2_g )
& ( Z_g != Z1_g ) ) )
=> $false ) ).
tff(formula_7_constraint_1,axiom,
! [P_g: general,T_g: general] :
( ( ? [Z_g: general,Z1_g: general] :
( ( Z_g = P_g )
& ( Z1_g = T_g )
& ~ in_building(Z_g,Z1_g) )
& ? [Z_g: general] :
( ( Z_g = P_g )
& person(Z_g) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = T_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 0 )
& ( J_i = h_i )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I_i,K_i)
& $lesseq(K_i,J_i) )
& ( Z_g = Z1_g ) ) )
=> $false ) ).
tff(formula_8_completed_definition_of_in_3,axiom,
! [V1_g: general,V2_g: general,V3_g: general] :
( in(V1_g,V2_g,V3_g)
<=> ( ? [P_g: general,R_g: general] :
( ( V1_g = P_g )
& ( V2_g = R_g )
& ( V3_g = f__integer__(0) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = P_g )
& ( Z1_g = R_g )
& in0(Z_g,Z1_g) ) )
| ? [P_g: general,R_g: general,T_g: general] :
( ( V1_g = P_g )
& ( V2_g = R_g )
& ? [I_i: $int,J_i: $int] :
( ( V3_g = f__integer__($sum(I_i,J_i)) )
& ( f__integer__(I_i) = T_g )
& ( J_i = 1 ) )
& ? [Z_g: general,Z1_g: general,Z2_g: general] :
( ( Z_g = P_g )
& ( Z1_g = R_g )
& ( Z2_g = T_g )
& goto(Z_g,Z1_g,Z2_g) ) )
| ? [P_g: general,R_g: general,T_g: general] :
( ( V1_g = P_g )
& ( V2_g = R_g )
& ? [I_i: $int,J_i: $int] :
( ( V3_g = f__integer__($sum(I_i,J_i)) )
& ( f__integer__(I_i) = T_g )
& ( J_i = 1 ) )
& ? [Z_g: general,Z1_g: general,Z2_g: general] :
( ( Z_g = P_g )
& ( Z1_g = R_g )
& ( Z2_g = T_g )
& in(Z_g,Z1_g,Z2_g) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = P_g )
& ( Z1_g = T_g )
& ~ go(Z_g,Z1_g) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = T_g )
& ? [I_i: $int,J_i: $int,K_i: $int] :
( ( I_i = 0 )
& ? [I_i: $int,J1_i: $int] :
( ( J_i = $difference(I_i,J1_i) )
& ( I_i = h_i )
& ( J1_i = 1 ) )
& ( Z1_g = f__integer__(K_i) )
& $lesseq(I_i,K_i)
& $lesseq(K_i,J_i) )
& ( Z_g = Z1_g ) ) ) ) ) ).
tff(formula_9_constraint_0,conjecture,
! [P_g: general,R1_g: general,T_g: general,R2_g: general] :
( ( ? [Z_g: general,Z1_g: general,Z2_g: general] :
( ( Z_g = P_g )
& ( Z1_g = R1_g )
& ( Z2_g = T_g )
& in(Z_g,Z1_g,Z2_g) )
& ? [Z_g: general,Z1_g: general,Z2_g: general] :
( ( Z_g = P_g )
& ( Z1_g = R2_g )
& ( Z2_g = T_g )
& in(Z_g,Z1_g,Z2_g) )
& ? [Z_g: general,Z1_g: general] :
( ( Z_g = R1_g )
& ( Z1_g = R2_g )
& ( Z_g != Z1_g ) ) )
=> $false ) ).
%------------------------------------------------------------------------------